1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> 4<title>Special Function Error Rates Report</title> 5<link rel="stylesheet" href="http://www.boost.org/doc/libs/1_58_0/doc/src/boostbook.css" type="text/css"> 6<meta name="generator" content="DocBook XSL Stylesheets V1.77.1"> 7<link rel="home" href="index.html" title="Special Function Error Rates Report"> 8</head> 9<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> 10<table cellpadding="2" width="100%"><tr> 11<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td> 12<td align="center"><a href="../../../../../index.html">Home</a></td> 13<td align="center"><a href="../../../../../libs/libraries.htm">Libraries</a></td> 14<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> 15<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> 16<td align="center"><a href="../../../../../more/index.htm">More</a></td> 17</tr></table> 18<hr> 19<div class="spirit-nav"></div> 20<div class="article"> 21<div class="titlepage"> 22<div> 23<div><h2 class="title"> 24<a name="special_function_error_rates_rep"></a>Special Function Error Rates Report</h2></div> 25<div><div class="legalnotice"> 26<a name="special_function_error_rates_rep.legal"></a><p> 27 Distributed under the Boost Software License, Version 1.0. (See accompanying 28 file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) 29 </p> 30</div></div> 31</div> 32<hr> 33</div> 34<div class="toc"> 35<p><b>Table of Contents</b></p> 36<dl> 37<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_beta">beta</a></span></dt> 38<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_beta_incomplete_">beta 39 (incomplete)</a></span></dt> 40<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_betac">betac</a></span></dt> 41<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_binomial_coefficient">binomial_coefficient</a></span></dt> 42<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_boost_math_powm1">boost::math::powm1</a></span></dt> 43<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cbrt">cbrt</a></span></dt> 44<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cos_pi">cos_pi</a></span></dt> 45<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_i">cyl_bessel_i</a></span></dt> 46<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_i_integer_orders_">cyl_bessel_i 47 (integer orders)</a></span></dt> 48<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_i_prime">cyl_bessel_i_prime</a></span></dt> 49<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_i_prime_integer_orders_">cyl_bessel_i_prime 50 (integer orders)</a></span></dt> 51<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_j">cyl_bessel_j</a></span></dt> 52<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_j_integer_orders_">cyl_bessel_j 53 (integer orders)</a></span></dt> 54<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_j_prime">cyl_bessel_j_prime</a></span></dt> 55<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_j_prime_integer_orders_">cyl_bessel_j_prime 56 (integer orders)</a></span></dt> 57<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_k">cyl_bessel_k</a></span></dt> 58<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_k_integer_orders_">cyl_bessel_k 59 (integer orders)</a></span></dt> 60<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_k_prime">cyl_bessel_k_prime</a></span></dt> 61<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_k_prime_integer_orders_">cyl_bessel_k_prime 62 (integer orders)</a></span></dt> 63<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_neumann">cyl_neumann</a></span></dt> 64<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_neumann_integer_orders_">cyl_neumann 65 (integer orders)</a></span></dt> 66<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_neumann_prime">cyl_neumann_prime</a></span></dt> 67<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_neumann_prime_integer_orders_">cyl_neumann_prime 68 (integer orders)</a></span></dt> 69<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_digamma">digamma</a></span></dt> 70<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_1">ellint_1</a></span></dt> 71<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_1_complete_">ellint_1 72 (complete)</a></span></dt> 73<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_2">ellint_2</a></span></dt> 74<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_2_complete_">ellint_2 75 (complete)</a></span></dt> 76<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_3">ellint_3</a></span></dt> 77<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_3_complete_">ellint_3 78 (complete)</a></span></dt> 79<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_d">ellint_d</a></span></dt> 80<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_d_complete_">ellint_d 81 (complete)</a></span></dt> 82<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_rc">ellint_rc</a></span></dt> 83<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_rd">ellint_rd</a></span></dt> 84<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_rf">ellint_rf</a></span></dt> 85<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_rg">ellint_rg</a></span></dt> 86<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_rj">ellint_rj</a></span></dt> 87<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_erf">erf</a></span></dt> 88<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_erf_inv">erf_inv</a></span></dt> 89<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_erfc">erfc</a></span></dt> 90<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_erfc_inv">erfc_inv</a></span></dt> 91<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_expint_Ei_">expint 92 (Ei)</a></span></dt> 93<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_expint_En_">expint 94 (En)</a></span></dt> 95<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_expm1">expm1</a></span></dt> 96<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_gamma_p">gamma_p</a></span></dt> 97<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_gamma_p_inv">gamma_p_inv</a></span></dt> 98<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_gamma_p_inva">gamma_p_inva</a></span></dt> 99<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_gamma_q">gamma_q</a></span></dt> 100<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_gamma_q_inv">gamma_q_inv</a></span></dt> 101<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_gamma_q_inva">gamma_q_inva</a></span></dt> 102<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_hermite">hermite</a></span></dt> 103<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_heuman_lambda">heuman_lambda</a></span></dt> 104<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ibeta">ibeta</a></span></dt> 105<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ibeta_inv">ibeta_inv</a></span></dt> 106<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ibeta_inva">ibeta_inva</a></span></dt> 107<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ibeta_invb">ibeta_invb</a></span></dt> 108<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ibetac">ibetac</a></span></dt> 109<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ibetac_inv">ibetac_inv</a></span></dt> 110<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ibetac_inva">ibetac_inva</a></span></dt> 111<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ibetac_invb">ibetac_invb</a></span></dt> 112<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_jacobi_cn">jacobi_cn</a></span></dt> 113<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_jacobi_dn">jacobi_dn</a></span></dt> 114<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_jacobi_sn">jacobi_sn</a></span></dt> 115<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_jacobi_zeta">jacobi_zeta</a></span></dt> 116<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_laguerre_n_m_x_">laguerre(n, 117 m, x)</a></span></dt> 118<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_laguerre_n_x_">laguerre(n, 119 x)</a></span></dt> 120<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_legendre_p">legendre_p</a></span></dt> 121<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_legendre_p_associated_">legendre_p 122 (associated)</a></span></dt> 123<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_legendre_q">legendre_q</a></span></dt> 124<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_lgamma">lgamma</a></span></dt> 125<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_log1p">log1p</a></span></dt> 126<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_non_central_beta_CDF">non 127 central beta CDF</a></span></dt> 128<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_non_central_beta_CDF_complement">non 129 central beta CDF complement</a></span></dt> 130<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_non_central_chi_squared_CDF">non 131 central chi squared CDF</a></span></dt> 132<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_non_central_chi_squared_CDF_complement">non 133 central chi squared CDF complement</a></span></dt> 134<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_non_central_t_CDF">non 135 central t CDF</a></span></dt> 136<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_non_central_t_CDF_complement">non 137 central t CDF complement</a></span></dt> 138<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_owens_t">owens_t</a></span></dt> 139<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_polygamma">polygamma</a></span></dt> 140<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_powm1">powm1</a></span></dt> 141<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_sin_pi">sin_pi</a></span></dt> 142<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_sph_bessel">sph_bessel</a></span></dt> 143<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_sph_bessel_prime">sph_bessel_prime</a></span></dt> 144<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_sph_neumann">sph_neumann</a></span></dt> 145<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_sph_neumann_prime">sph_neumann_prime</a></span></dt> 146<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_spherical_harmonic_i">spherical_harmonic_i</a></span></dt> 147<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_spherical_harmonic_r">spherical_harmonic_r</a></span></dt> 148<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_sqrt1pm1">sqrt1pm1</a></span></dt> 149<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_tgamma">tgamma</a></span></dt> 150<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_tgamma1pm1">tgamma1pm1</a></span></dt> 151<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_tgamma_delta_ratio">tgamma_delta_ratio</a></span></dt> 152<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_tgamma_incomplete_">tgamma 153 (incomplete)</a></span></dt> 154<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_tgamma_lower">tgamma_lower</a></span></dt> 155<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_tgamma_ratio">tgamma_ratio</a></span></dt> 156<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_trigamma">trigamma</a></span></dt> 157<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_zeta">zeta</a></span></dt> 158<dt><span class="section"><a href="index.html#special_function_error_rates_rep.error_logs">Error Logs</a></span></dt> 159<dt><span class="section"><a href="index.html#special_function_error_rates_rep.all_the_tables">Tables</a></span></dt> 160</dl> 161</div> 162<div class="section"> 163<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 164<a name="special_function_error_rates_rep.section_beta"></a><a class="link" href="index.html#special_function_error_rates_rep.section_beta" title="beta">beta</a> 165</h2></div></div></div> 166<div class="table"> 167<a name="special_function_error_rates_rep.section_beta.table_beta"></a><p class="title"><b>Table 1. Error rates for beta</b></p> 168<div class="table-contents"><table class="table" summary="Error rates for beta"> 169<colgroup> 170<col> 171<col> 172<col> 173<col> 174<col> 175</colgroup> 176<thead><tr> 177<th> 178 </th> 179<th> 180 <p> 181 GNU C++ version 7.1.0<br> linux<br> double 182 </p> 183 </th> 184<th> 185 <p> 186 GNU C++ version 7.1.0<br> linux<br> long double 187 </p> 188 </th> 189<th> 190 <p> 191 Sun compiler version 0x5150<br> Sun Solaris<br> long double 192 </p> 193 </th> 194<th> 195 <p> 196 Microsoft Visual C++ version 14.1<br> Win32<br> double 197 </p> 198 </th> 199</tr></thead> 200<tbody> 201<tr> 202<td> 203 <p> 204 Beta Function: Small Values 205 </p> 206 </td> 207<td> 208 <p> 209 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 210 2.1:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_beta_GSL_2_1_Beta_Function_Small_Values">And 211 other failures.</a>)</span><br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 212 Max = 1.14ε (Mean = 0.574ε)) 213 </p> 214 </td> 215<td> 216 <p> 217 <span class="blue">Max = 2.86ε (Mean = 1.22ε)</span><br> <br> 218 (<span class="emphasis"><em><cmath>:</em></span> Max = 364ε (Mean = 76.2ε)) 219 </p> 220 </td> 221<td> 222 <p> 223 <span class="blue">Max = 2.86ε (Mean = 1.22ε)</span> 224 </p> 225 </td> 226<td> 227 <p> 228 <span class="blue">Max = 2.23ε (Mean = 1.14ε)</span> 229 </p> 230 </td> 231</tr> 232<tr> 233<td> 234 <p> 235 Beta Function: Medium Values 236 </p> 237 </td> 238<td> 239 <p> 240 <span class="blue">Max = 0.978ε (Mean = 0.0595ε)</span><br> <br> 241 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.18e+03ε (Mean = 238ε))<br> 242 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.09e+03ε (Mean = 265ε)) 243 </p> 244 </td> 245<td> 246 <p> 247 <span class="blue">Max = 61.4ε (Mean = 19.4ε)</span><br> <br> 248 (<span class="emphasis"><em><cmath>:</em></span> Max = 1.07e+03ε (Mean = 264ε)) 249 </p> 250 </td> 251<td> 252 <p> 253 <span class="blue">Max = 107ε (Mean = 24.5ε)</span> 254 </p> 255 </td> 256<td> 257 <p> 258 <span class="blue">Max = 96.5ε (Mean = 22.4ε)</span> 259 </p> 260 </td> 261</tr> 262<tr> 263<td> 264 <p> 265 Beta Function: Divergent Values 266 </p> 267 </td> 268<td> 269 <p> 270 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 271 2.1:</em></span> Max = 12.1ε (Mean = 1.99ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 272 Max = 176ε (Mean = 28ε)) 273 </p> 274 </td> 275<td> 276 <p> 277 <span class="blue">Max = 8.99ε (Mean = 2.44ε)</span><br> <br> 278 (<span class="emphasis"><em><cmath>:</em></span> Max = 128ε (Mean = 23.8ε)) 279 </p> 280 </td> 281<td> 282 <p> 283 <span class="blue">Max = 18.8ε (Mean = 2.71ε)</span> 284 </p> 285 </td> 286<td> 287 <p> 288 <span class="blue">Max = 11.4ε (Mean = 2.19ε)</span> 289 </p> 290 </td> 291</tr> 292</tbody> 293</table></div> 294</div> 295<br class="table-break"> 296</div> 297<div class="section"> 298<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 299<a name="special_function_error_rates_rep.section_beta_incomplete_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_beta_incomplete_" title="beta (incomplete)">beta 300 (incomplete)</a> 301</h2></div></div></div> 302<div class="table"> 303<a name="special_function_error_rates_rep.section_beta_incomplete_.table_beta_incomplete_"></a><p class="title"><b>Table 2. Error rates for beta (incomplete)</b></p> 304<div class="table-contents"><table class="table" summary="Error rates for beta (incomplete)"> 305<colgroup> 306<col> 307<col> 308<col> 309<col> 310<col> 311</colgroup> 312<thead><tr> 313<th> 314 </th> 315<th> 316 <p> 317 GNU C++ version 7.1.0<br> linux<br> double 318 </p> 319 </th> 320<th> 321 <p> 322 GNU C++ version 7.1.0<br> linux<br> long double 323 </p> 324 </th> 325<th> 326 <p> 327 Sun compiler version 0x5150<br> Sun Solaris<br> long double 328 </p> 329 </th> 330<th> 331 <p> 332 Microsoft Visual C++ version 14.1<br> Win32<br> double 333 </p> 334 </th> 335</tr></thead> 336<tbody> 337<tr> 338<td> 339 <p> 340 Incomplete Beta Function: Small Values 341 </p> 342 </td> 343<td> 344 <p> 345 <span class="blue">Max = 0ε (Mean = 0ε)</span> 346 </p> 347 </td> 348<td> 349 <p> 350 <span class="blue">Max = 11.1ε (Mean = 2.32ε)</span> 351 </p> 352 </td> 353<td> 354 <p> 355 <span class="blue">Max = 18.7ε (Mean = 3.19ε)</span> 356 </p> 357 </td> 358<td> 359 <p> 360 <span class="blue">Max = 9.94ε (Mean = 2.17ε)</span> 361 </p> 362 </td> 363</tr> 364<tr> 365<td> 366 <p> 367 Incomplete Beta Function: Medium Values 368 </p> 369 </td> 370<td> 371 <p> 372 <span class="blue">Max = 0.568ε (Mean = 0.0254ε)</span> 373 </p> 374 </td> 375<td> 376 <p> 377 <span class="blue">Max = 69.2ε (Mean = 13.4ε)</span> 378 </p> 379 </td> 380<td> 381 <p> 382 <span class="blue">Max = 174ε (Mean = 25ε)</span> 383 </p> 384 </td> 385<td> 386 <p> 387 <span class="blue">Max = 90ε (Mean = 12.7ε)</span> 388 </p> 389 </td> 390</tr> 391<tr> 392<td> 393 <p> 394 Incomplete Beta Function: Large and Diverse Values 395 </p> 396 </td> 397<td> 398 <p> 399 <span class="blue">Max = 0.999ε (Mean = 0.0325ε)</span> 400 </p> 401 </td> 402<td> 403 <p> 404 <span class="blue">Max = 6.84e+04ε (Mean = 2.76e+03ε)</span> 405 </p> 406 </td> 407<td> 408 <p> 409 <span class="blue">Max = 6.86e+04ε (Mean = 2.79e+03ε)</span> 410 </p> 411 </td> 412<td> 413 <p> 414 <span class="blue">Max = 633ε (Mean = 29.7ε)</span> 415 </p> 416 </td> 417</tr> 418<tr> 419<td> 420 <p> 421 Incomplete Beta Function: Small Integer Values 422 </p> 423 </td> 424<td> 425 <p> 426 <span class="blue">Max = 0.786ε (Mean = 0.0323ε)</span> 427 </p> 428 </td> 429<td> 430 <p> 431 <span class="blue">Max = 11.6ε (Mean = 3.6ε)</span> 432 </p> 433 </td> 434<td> 435 <p> 436 <span class="blue">Max = 51.8ε (Mean = 11ε)</span> 437 </p> 438 </td> 439<td> 440 <p> 441 <span class="blue">Max = 26ε (Mean = 6.28ε)</span> 442 </p> 443 </td> 444</tr> 445</tbody> 446</table></div> 447</div> 448<br class="table-break"> 449</div> 450<div class="section"> 451<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 452<a name="special_function_error_rates_rep.section_betac"></a><a class="link" href="index.html#special_function_error_rates_rep.section_betac" title="betac">betac</a> 453</h2></div></div></div> 454<div class="table"> 455<a name="special_function_error_rates_rep.section_betac.table_betac"></a><p class="title"><b>Table 3. Error rates for betac</b></p> 456<div class="table-contents"><table class="table" summary="Error rates for betac"> 457<colgroup> 458<col> 459<col> 460<col> 461<col> 462<col> 463</colgroup> 464<thead><tr> 465<th> 466 </th> 467<th> 468 <p> 469 GNU C++ version 7.1.0<br> linux<br> double 470 </p> 471 </th> 472<th> 473 <p> 474 GNU C++ version 7.1.0<br> linux<br> long double 475 </p> 476 </th> 477<th> 478 <p> 479 Sun compiler version 0x5150<br> Sun Solaris<br> long double 480 </p> 481 </th> 482<th> 483 <p> 484 Microsoft Visual C++ version 14.1<br> Win32<br> double 485 </p> 486 </th> 487</tr></thead> 488<tbody> 489<tr> 490<td> 491 <p> 492 Incomplete Beta Function: Small Values 493 </p> 494 </td> 495<td> 496 <p> 497 <span class="blue">Max = 0.676ε (Mean = 0.0302ε)</span> 498 </p> 499 </td> 500<td> 501 <p> 502 <span class="blue">Max = 9.92ε (Mean = 2.3ε)</span> 503 </p> 504 </td> 505<td> 506 <p> 507 <span class="blue">Max = 11.2ε (Mean = 2.94ε)</span> 508 </p> 509 </td> 510<td> 511 <p> 512 <span class="blue">Max = 8.94ε (Mean = 2.06ε)</span> 513 </p> 514 </td> 515</tr> 516<tr> 517<td> 518 <p> 519 Incomplete Beta Function: Medium Values 520 </p> 521 </td> 522<td> 523 <p> 524 <span class="blue">Max = 0.949ε (Mean = 0.098ε)</span> 525 </p> 526 </td> 527<td> 528 <p> 529 <span class="blue">Max = 63.5ε (Mean = 13.5ε)</span> 530 </p> 531 </td> 532<td> 533 <p> 534 <span class="blue">Max = 97.6ε (Mean = 24.3ε)</span> 535 </p> 536 </td> 537<td> 538 <p> 539 <span class="blue">Max = 90.6ε (Mean = 14.8ε)</span> 540 </p> 541 </td> 542</tr> 543<tr> 544<td> 545 <p> 546 Incomplete Beta Function: Large and Diverse Values 547 </p> 548 </td> 549<td> 550 <p> 551 <span class="blue">Max = 1.12ε (Mean = 0.0458ε)</span> 552 </p> 553 </td> 554<td> 555 <p> 556 <span class="blue">Max = 1.05e+05ε (Mean = 5.45e+03ε)</span> 557 </p> 558 </td> 559<td> 560 <p> 561 <span class="blue">Max = 1.04e+05ε (Mean = 5.46e+03ε)</span> 562 </p> 563 </td> 564<td> 565 <p> 566 <span class="blue">Max = 3.72e+03ε (Mean = 113ε)</span> 567 </p> 568 </td> 569</tr> 570<tr> 571<td> 572 <p> 573 Incomplete Beta Function: Small Integer Values 574 </p> 575 </td> 576<td> 577 <p> 578 <span class="blue">Max = 0.586ε (Mean = 0.0314ε)</span> 579 </p> 580 </td> 581<td> 582 <p> 583 <span class="blue">Max = 11.1ε (Mean = 3.65ε)</span> 584 </p> 585 </td> 586<td> 587 <p> 588 <span class="blue">Max = 103ε (Mean = 17.4ε)</span> 589 </p> 590 </td> 591<td> 592 <p> 593 <span class="blue">Max = 26.2ε (Mean = 6.36ε)</span> 594 </p> 595 </td> 596</tr> 597</tbody> 598</table></div> 599</div> 600<br class="table-break"> 601</div> 602<div class="section"> 603<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 604<a name="special_function_error_rates_rep.section_binomial_coefficient"></a><a class="link" href="index.html#special_function_error_rates_rep.section_binomial_coefficient" title="binomial_coefficient">binomial_coefficient</a> 605</h2></div></div></div> 606<div class="table"> 607<a name="special_function_error_rates_rep.section_binomial_coefficient.table_binomial_coefficient"></a><p class="title"><b>Table 4. Error rates for binomial_coefficient</b></p> 608<div class="table-contents"><table class="table" summary="Error rates for binomial_coefficient"> 609<colgroup> 610<col> 611<col> 612<col> 613<col> 614<col> 615</colgroup> 616<thead><tr> 617<th> 618 </th> 619<th> 620 <p> 621 GNU C++ version 7.1.0<br> linux<br> double 622 </p> 623 </th> 624<th> 625 <p> 626 GNU C++ version 7.1.0<br> linux<br> long double 627 </p> 628 </th> 629<th> 630 <p> 631 Sun compiler version 0x5150<br> Sun Solaris<br> long double 632 </p> 633 </th> 634<th> 635 <p> 636 Microsoft Visual C++ version 14.1<br> Win32<br> double 637 </p> 638 </th> 639</tr></thead> 640<tbody> 641<tr> 642<td> 643 <p> 644 Binomials: small arguments 645 </p> 646 </td> 647<td> 648 <p> 649 <span class="blue">Max = 1ε (Mean = 0.369ε)</span> 650 </p> 651 </td> 652<td> 653 <p> 654 <span class="blue">Max = 1.5ε (Mean = 0.339ε)</span> 655 </p> 656 </td> 657<td> 658 <p> 659 <span class="blue">Max = 1.5ε (Mean = 0.339ε)</span> 660 </p> 661 </td> 662<td> 663 <p> 664 <span class="blue">Max = 1ε (Mean = 0.369ε)</span> 665 </p> 666 </td> 667</tr> 668<tr> 669<td> 670 <p> 671 Binomials: large arguments 672 </p> 673 </td> 674<td> 675 <p> 676 <span class="blue">Max = 0.939ε (Mean = 0.314ε)</span> 677 </p> 678 </td> 679<td> 680 <p> 681 <span class="blue">Max = 26.6ε (Mean = 6.13ε)</span> 682 </p> 683 </td> 684<td> 685 <p> 686 <span class="blue">Max = 53.2ε (Mean = 10.8ε)</span> 687 </p> 688 </td> 689<td> 690 <p> 691 <span class="blue">Max = 37.2ε (Mean = 7.4ε)</span> 692 </p> 693 </td> 694</tr> 695</tbody> 696</table></div> 697</div> 698<br class="table-break"> 699</div> 700<div class="section"> 701<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 702<a name="special_function_error_rates_rep.section_boost_math_powm1"></a><a class="link" href="index.html#special_function_error_rates_rep.section_boost_math_powm1" title="boost::math::powm1">boost::math::powm1</a> 703</h2></div></div></div> 704<div class="table"> 705<a name="special_function_error_rates_rep.section_boost_math_powm1.table_boost_math_powm1"></a><p class="title"><b>Table 5. Error rates for boost::math::powm1</b></p> 706<div class="table-contents"><table class="table" summary="Error rates for boost::math::powm1"> 707<colgroup> 708<col> 709<col> 710<col> 711<col> 712<col> 713</colgroup> 714<thead><tr> 715<th> 716 </th> 717<th> 718 <p> 719 GNU C++ version 7.1.0<br> linux<br> long double 720 </p> 721 </th> 722<th> 723 <p> 724 GNU C++ version 7.1.0<br> linux<br> double 725 </p> 726 </th> 727<th> 728 <p> 729 Sun compiler version 0x5150<br> Sun Solaris<br> long double 730 </p> 731 </th> 732<th> 733 <p> 734 Microsoft Visual C++ version 14.1<br> Win32<br> double 735 </p> 736 </th> 737</tr></thead> 738<tbody><tr> 739<td> 740 <p> 741 powm1 742 </p> 743 </td> 744<td> 745 <p> 746 (<span class="emphasis"><em><math.h>:</em></span> Max = 2.04ε (Mean = 0.493ε))<br> 747 <br> <span class="blue">Max = 2.04ε (Mean = 0.493ε)</span><br> 748 <br> (<span class="emphasis"><em><cmath>:</em></span> Max = 2.04ε (Mean = 0.493ε)) 749 </p> 750 </td> 751<td> 752 <p> 753 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.06ε (Mean = 0.425ε))<br> 754 <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.06ε (Mean = 0.425ε))<br> 755 <br> <span class="blue">Max = 1.06ε (Mean = 0.425ε)</span> 756 </p> 757 </td> 758<td> 759 <p> 760 <span class="blue">Max = 1.88ε (Mean = 0.49ε)</span><br> <br> 761 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.88ε (Mean = 0.49ε)) 762 </p> 763 </td> 764<td> 765 <p> 766 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.84ε (Mean = 0.486ε))<br> 767 <br> <span class="blue">Max = 1.84ε (Mean = 0.486ε)</span> 768 </p> 769 </td> 770</tr></tbody> 771</table></div> 772</div> 773<br class="table-break"> 774</div> 775<div class="section"> 776<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 777<a name="special_function_error_rates_rep.section_cbrt"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cbrt" title="cbrt">cbrt</a> 778</h2></div></div></div> 779<div class="table"> 780<a name="special_function_error_rates_rep.section_cbrt.table_cbrt"></a><p class="title"><b>Table 6. Error rates for cbrt</b></p> 781<div class="table-contents"><table class="table" summary="Error rates for cbrt"> 782<colgroup> 783<col> 784<col> 785<col> 786<col> 787<col> 788</colgroup> 789<thead><tr> 790<th> 791 </th> 792<th> 793 <p> 794 GNU C++ version 7.1.0<br> linux<br> double 795 </p> 796 </th> 797<th> 798 <p> 799 GNU C++ version 7.1.0<br> linux<br> long double 800 </p> 801 </th> 802<th> 803 <p> 804 Sun compiler version 0x5150<br> Sun Solaris<br> long double 805 </p> 806 </th> 807<th> 808 <p> 809 Microsoft Visual C++ version 14.1<br> Win32<br> double 810 </p> 811 </th> 812</tr></thead> 813<tbody><tr> 814<td> 815 <p> 816 cbrt Function 817 </p> 818 </td> 819<td> 820 <p> 821 <span class="blue">Max = 0ε (Mean = 0ε)</span> 822 </p> 823 </td> 824<td> 825 <p> 826 <span class="blue">Max = 1.34ε (Mean = 0.471ε)</span><br> <br> 827 (<span class="emphasis"><em><cmath>:</em></span> Max = 1.34ε (Mean = 0.471ε))<br> 828 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.34ε (Mean = 0.471ε)) 829 </p> 830 </td> 831<td> 832 <p> 833 <span class="blue">Max = 1.34ε (Mean = 0.471ε)</span><br> <br> 834 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.34ε (Mean = 0.471ε)) 835 </p> 836 </td> 837<td> 838 <p> 839 <span class="blue">Max = 1.7ε (Mean = 0.565ε)</span><br> <br> 840 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.7ε (Mean = 0.565ε)) 841 </p> 842 </td> 843</tr></tbody> 844</table></div> 845</div> 846<br class="table-break"> 847</div> 848<div class="section"> 849<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 850<a name="special_function_error_rates_rep.section_cos_pi"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cos_pi" title="cos_pi">cos_pi</a> 851</h2></div></div></div> 852<div class="table"> 853<a name="special_function_error_rates_rep.section_cos_pi.table_cos_pi"></a><p class="title"><b>Table 7. Error rates for cos_pi</b></p> 854<div class="table-contents"><table class="table" summary="Error rates for cos_pi"> 855<colgroup> 856<col> 857<col> 858<col> 859<col> 860<col> 861</colgroup> 862<thead><tr> 863<th> 864 </th> 865<th> 866 <p> 867 GNU C++ version 7.1.0<br> linux<br> double 868 </p> 869 </th> 870<th> 871 <p> 872 GNU C++ version 7.1.0<br> linux<br> long double 873 </p> 874 </th> 875<th> 876 <p> 877 Sun compiler version 0x5150<br> Sun Solaris<br> long double 878 </p> 879 </th> 880<th> 881 <p> 882 Microsoft Visual C++ version 14.1<br> Win32<br> double 883 </p> 884 </th> 885</tr></thead> 886<tbody> 887<tr> 888<td> 889 <p> 890 sin_pi and cos_pi 891 </p> 892 </td> 893<td> 894 <p> 895 <span class="blue">Max = 0ε (Mean = 0ε)</span> 896 </p> 897 </td> 898<td> 899 <p> 900 <span class="blue">Max = 0.991ε (Mean = 0.302ε)</span> 901 </p> 902 </td> 903<td> 904 <p> 905 <span class="blue">Max = 0.991ε (Mean = 0.302ε)</span> 906 </p> 907 </td> 908<td> 909 <p> 910 <span class="blue">Max = 0.996ε (Mean = 0.284ε)</span> 911 </p> 912 </td> 913</tr> 914<tr> 915<td> 916 <p> 917 sin_pi and cos_pi near integers and half integers 918 </p> 919 </td> 920<td> 921 <p> 922 <span class="blue">Max = 0ε (Mean = 0ε)</span> 923 </p> 924 </td> 925<td> 926 <p> 927 <span class="blue">Max = 0.976ε (Mean = 0.28ε)</span> 928 </p> 929 </td> 930<td> 931 <p> 932 <span class="blue">Max = 0.976ε (Mean = 0.28ε)</span> 933 </p> 934 </td> 935<td> 936 <p> 937 <span class="blue">Max = 0.996ε (Mean = 0.298ε)</span> 938 </p> 939 </td> 940</tr> 941</tbody> 942</table></div> 943</div> 944<br class="table-break"> 945</div> 946<div class="section"> 947<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 948<a name="special_function_error_rates_rep.section_cyl_bessel_i"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_i" title="cyl_bessel_i">cyl_bessel_i</a> 949</h2></div></div></div> 950<div class="table"> 951<a name="special_function_error_rates_rep.section_cyl_bessel_i.table_cyl_bessel_i"></a><p class="title"><b>Table 8. Error rates for cyl_bessel_i</b></p> 952<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i"> 953<colgroup> 954<col> 955<col> 956<col> 957<col> 958<col> 959</colgroup> 960<thead><tr> 961<th> 962 </th> 963<th> 964 <p> 965 GNU C++ version 7.1.0<br> linux<br> double 966 </p> 967 </th> 968<th> 969 <p> 970 GNU C++ version 7.1.0<br> linux<br> long double 971 </p> 972 </th> 973<th> 974 <p> 975 Sun compiler version 0x5150<br> Sun Solaris<br> long double 976 </p> 977 </th> 978<th> 979 <p> 980 Microsoft Visual C++ version 14.1<br> Win32<br> double 981 </p> 982 </th> 983</tr></thead> 984<tbody> 985<tr> 986<td> 987 <p> 988 Bessel I0: Mathworld Data 989 </p> 990 </td> 991<td> 992 <p> 993 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 994 2.1:</em></span> Max = 270ε (Mean = 91.6ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_I0_Mathworld_Data">And 995 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 996 Max = 1.52ε (Mean = 0.622ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_I0_Mathworld_Data">And 997 other failures.</a>) 998 </p> 999 </td> 1000<td> 1001 <p> 1002 <span class="blue">Max = 1.95ε (Mean = 0.738ε)</span><br> <br> 1003 (<span class="emphasis"><em><cmath>:</em></span> Max = 8.49ε (Mean = 3.46ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_I0_Mathworld_Data">And 1004 other failures.</a>) 1005 </p> 1006 </td> 1007<td> 1008 <p> 1009 <span class="blue">Max = 1.95ε (Mean = 0.661ε)</span> 1010 </p> 1011 </td> 1012<td> 1013 <p> 1014 <span class="blue">Max = 0.762ε (Mean = 0.329ε)</span> 1015 </p> 1016 </td> 1017</tr> 1018<tr> 1019<td> 1020 <p> 1021 Bessel I1: Mathworld Data 1022 </p> 1023 </td> 1024<td> 1025 <p> 1026 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 1027 2.1:</em></span> Max = 128ε (Mean = 41ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_I1_Mathworld_Data">And 1028 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 1029 Max = 1.53ε (Mean = 0.483ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_I1_Mathworld_Data">And 1030 other failures.</a>) 1031 </p> 1032 </td> 1033<td> 1034 <p> 1035 <span class="blue">Max = 0.64ε (Mean = 0.202ε)</span><br> <br> 1036 (<span class="emphasis"><em><cmath>:</em></span> Max = 5ε (Mean = 2.15ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_I1_Mathworld_Data">And 1037 other failures.</a>) 1038 </p> 1039 </td> 1040<td> 1041 <p> 1042 <span class="blue">Max = 0.64ε (Mean = 0.202ε)</span> 1043 </p> 1044 </td> 1045<td> 1046 <p> 1047 <span class="blue">Max = 0.767ε (Mean = 0.398ε)</span> 1048 </p> 1049 </td> 1050</tr> 1051<tr> 1052<td> 1053 <p> 1054 Bessel In: Mathworld Data 1055 </p> 1056 </td> 1057<td> 1058 <p> 1059 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 1060 2.1:</em></span> Max = 2.31ε (Mean = 0.838ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_In_Mathworld_Data">And 1061 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 1062 Max = 1.73ε (Mean = 0.601ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_In_Mathworld_Data">And 1063 other failures.</a>) 1064 </p> 1065 </td> 1066<td> 1067 <p> 1068 <span class="blue">Max = 1.8ε (Mean = 1.33ε)</span><br> <br> 1069 (<span class="emphasis"><em><cmath>:</em></span> Max = 430ε (Mean = 163ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_In_Mathworld_Data">And 1070 other failures.</a>) 1071 </p> 1072 </td> 1073<td> 1074 <p> 1075 <span class="blue">Max = 463ε (Mean = 140ε)</span> 1076 </p> 1077 </td> 1078<td> 1079 <p> 1080 <span class="blue">Max = 3.46ε (Mean = 1.32ε)</span> 1081 </p> 1082 </td> 1083</tr> 1084<tr> 1085<td> 1086 <p> 1087 Bessel Iv: Mathworld Data 1088 </p> 1089 </td> 1090<td> 1091 <p> 1092 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 1093 2.1:</em></span> Max = 5.95ε (Mean = 2.08ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Mathworld_Data">And 1094 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 1095 Max = 3.53ε (Mean = 1.39ε)) 1096 </p> 1097 </td> 1098<td> 1099 <p> 1100 <span class="blue">Max = 4.12ε (Mean = 1.85ε)</span><br> <br> 1101 (<span class="emphasis"><em><cmath>:</em></span> Max = 616ε (Mean = 221ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Mathworld_Data">And 1102 other failures.</a>) 1103 </p> 1104 </td> 1105<td> 1106 <p> 1107 <span class="blue">Max = 4.12ε (Mean = 1.95ε)</span> 1108 </p> 1109 </td> 1110<td> 1111 <p> 1112 <span class="blue">Max = 2.97ε (Mean = 1.24ε)</span> 1113 </p> 1114 </td> 1115</tr> 1116<tr> 1117<td> 1118 <p> 1119 Bessel In: Random Data 1120 </p> 1121 </td> 1122<td> 1123 <p> 1124 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 1125 2.1:</em></span> Max = 261ε (Mean = 53.2ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_In_Random_Data">And 1126 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 1127 Max = 7.37ε (Mean = 2.4ε)) 1128 </p> 1129 </td> 1130<td> 1131 <p> 1132 <span class="blue">Max = 4.62ε (Mean = 1.06ε)</span><br> <br> 1133 (<span class="emphasis"><em><cmath>:</em></span> Max = 645ε (Mean = 132ε)) 1134 </p> 1135 </td> 1136<td> 1137 <p> 1138 <span class="blue">Max = 176ε (Mean = 39.1ε)</span> 1139 </p> 1140 </td> 1141<td> 1142 <p> 1143 <span class="blue">Max = 9.67ε (Mean = 1.88ε)</span> 1144 </p> 1145 </td> 1146</tr> 1147<tr> 1148<td> 1149 <p> 1150 Bessel Iv: Random Data 1151 </p> 1152 </td> 1153<td> 1154 <p> 1155 <span class="blue">Max = 0.661ε (Mean = 0.0441ε)</span><br> <br> 1156 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 6.18e+03ε (Mean = 1.55e+03ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Random_Data">And 1157 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 1158 <span class="red">Max = 4.28e+08ε (Mean = 2.85e+07ε))</span> 1159 </p> 1160 </td> 1161<td> 1162 <p> 1163 <span class="blue">Max = 8.35ε (Mean = 1.62ε)</span><br> <br> 1164 (<span class="emphasis"><em><cmath>:</em></span> Max = 1.05e+03ε (Mean = 224ε) 1165 <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Random_Data">And 1166 other failures.</a>) 1167 </p> 1168 </td> 1169<td> 1170 <p> 1171 <span class="blue">Max = 283ε (Mean = 88.4ε)</span> 1172 </p> 1173 </td> 1174<td> 1175 <p> 1176 <span class="blue">Max = 7.46ε (Mean = 1.71ε)</span> 1177 </p> 1178 </td> 1179</tr> 1180<tr> 1181<td> 1182 <p> 1183 Bessel Iv: Mathworld Data (large values) 1184 </p> 1185 </td> 1186<td> 1187 <p> 1188 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 1189 2.1:</em></span> Max = 37ε (Mean = 18ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Mathworld_Data_large_values_">And 1190 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 1191 <span class="red">Max = 3.77e+168ε (Mean = 2.39e+168ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_Iv_Mathworld_Data_large_values_">And 1192 other failures.</a>)</span> 1193 </p> 1194 </td> 1195<td> 1196 <p> 1197 <span class="blue">Max = 14.7ε (Mean = 6.66ε)</span><br> <br> 1198 (<span class="emphasis"><em><cmath>:</em></span> Max = 118ε (Mean = 57.2ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Mathworld_Data_large_values_">And 1199 other failures.</a>) 1200 </p> 1201 </td> 1202<td> 1203 <p> 1204 <span class="blue">Max = 14.7ε (Mean = 6.59ε)</span> 1205 </p> 1206 </td> 1207<td> 1208 <p> 1209 <span class="blue">Max = 3.67ε (Mean = 1.64ε)</span> 1210 </p> 1211 </td> 1212</tr> 1213</tbody> 1214</table></div> 1215</div> 1216<br class="table-break"> 1217</div> 1218<div class="section"> 1219<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 1220<a name="special_function_error_rates_rep.section_cyl_bessel_i_integer_orders_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_i_integer_orders_" title="cyl_bessel_i (integer orders)">cyl_bessel_i 1221 (integer orders)</a> 1222</h2></div></div></div> 1223<div class="table"> 1224<a name="special_function_error_rates_rep.section_cyl_bessel_i_integer_orders_.table_cyl_bessel_i_integer_orders_"></a><p class="title"><b>Table 9. Error rates for cyl_bessel_i (integer orders)</b></p> 1225<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i (integer orders)"> 1226<colgroup> 1227<col> 1228<col> 1229<col> 1230<col> 1231<col> 1232</colgroup> 1233<thead><tr> 1234<th> 1235 </th> 1236<th> 1237 <p> 1238 GNU C++ version 7.1.0<br> linux<br> double 1239 </p> 1240 </th> 1241<th> 1242 <p> 1243 GNU C++ version 7.1.0<br> linux<br> long double 1244 </p> 1245 </th> 1246<th> 1247 <p> 1248 Sun compiler version 0x5150<br> Sun Solaris<br> long double 1249 </p> 1250 </th> 1251<th> 1252 <p> 1253 Microsoft Visual C++ version 14.1<br> Win32<br> double 1254 </p> 1255 </th> 1256</tr></thead> 1257<tbody> 1258<tr> 1259<td> 1260 <p> 1261 Bessel I0: Mathworld Data (Integer Version) 1262 </p> 1263 </td> 1264<td> 1265 <p> 1266 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 1267 2.1:</em></span> Max = 0.79ε (Mean = 0.482ε))<br> (<span class="emphasis"><em>Rmath 1268 3.2.3:</em></span> Max = 1.52ε (Mean = 0.622ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_I0_Mathworld_Data_Integer_Version_">And 1269 other failures.</a>) 1270 </p> 1271 </td> 1272<td> 1273 <p> 1274 <span class="blue">Max = 1.95ε (Mean = 0.738ε)</span><br> <br> 1275 (<span class="emphasis"><em><cmath>:</em></span> Max = 8.49ε (Mean = 3.46ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_I0_Mathworld_Data_Integer_Version_">And 1276 other failures.</a>) 1277 </p> 1278 </td> 1279<td> 1280 <p> 1281 <span class="blue">Max = 1.95ε (Mean = 0.661ε)</span> 1282 </p> 1283 </td> 1284<td> 1285 <p> 1286 <span class="blue">Max = 0.762ε (Mean = 0.329ε)</span> 1287 </p> 1288 </td> 1289</tr> 1290<tr> 1291<td> 1292 <p> 1293 Bessel I1: Mathworld Data (Integer Version) 1294 </p> 1295 </td> 1296<td> 1297 <p> 1298 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 1299 2.1:</em></span> Max = 0.82ε (Mean = 0.456ε))<br> (<span class="emphasis"><em>Rmath 1300 3.2.3:</em></span> Max = 1.53ε (Mean = 0.483ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_I1_Mathworld_Data_Integer_Version_">And 1301 other failures.</a>) 1302 </p> 1303 </td> 1304<td> 1305 <p> 1306 <span class="blue">Max = 0.64ε (Mean = 0.202ε)</span><br> <br> 1307 (<span class="emphasis"><em><cmath>:</em></span> Max = 5ε (Mean = 2.15ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_I1_Mathworld_Data_Integer_Version_">And 1308 other failures.</a>) 1309 </p> 1310 </td> 1311<td> 1312 <p> 1313 <span class="blue">Max = 0.64ε (Mean = 0.202ε)</span> 1314 </p> 1315 </td> 1316<td> 1317 <p> 1318 <span class="blue">Max = 0.767ε (Mean = 0.398ε)</span> 1319 </p> 1320 </td> 1321</tr> 1322<tr> 1323<td> 1324 <p> 1325 Bessel In: Mathworld Data (Integer Version) 1326 </p> 1327 </td> 1328<td> 1329 <p> 1330 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 1331 2.1:</em></span> Max = 5.15ε (Mean = 2.13ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__GSL_2_1_Bessel_In_Mathworld_Data_Integer_Version_">And 1332 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 1333 Max = 1.73ε (Mean = 0.601ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_In_Mathworld_Data_Integer_Version_">And 1334 other failures.</a>) 1335 </p> 1336 </td> 1337<td> 1338 <p> 1339 <span class="blue">Max = 1.8ε (Mean = 1.33ε)</span><br> <br> 1340 (<span class="emphasis"><em><cmath>:</em></span> Max = 430ε (Mean = 163ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_In_Mathworld_Data_Integer_Version_">And 1341 other failures.</a>) 1342 </p> 1343 </td> 1344<td> 1345 <p> 1346 <span class="blue">Max = 463ε (Mean = 140ε)</span> 1347 </p> 1348 </td> 1349<td> 1350 <p> 1351 <span class="blue">Max = 3.46ε (Mean = 1.32ε)</span> 1352 </p> 1353 </td> 1354</tr> 1355</tbody> 1356</table></div> 1357</div> 1358<br class="table-break"> 1359</div> 1360<div class="section"> 1361<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 1362<a name="special_function_error_rates_rep.section_cyl_bessel_i_prime"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_i_prime" title="cyl_bessel_i_prime">cyl_bessel_i_prime</a> 1363</h2></div></div></div> 1364<div class="table"> 1365<a name="special_function_error_rates_rep.section_cyl_bessel_i_prime.table_cyl_bessel_i_prime"></a><p class="title"><b>Table 10. Error rates for cyl_bessel_i_prime</b></p> 1366<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i_prime"> 1367<colgroup> 1368<col> 1369<col> 1370<col> 1371<col> 1372<col> 1373</colgroup> 1374<thead><tr> 1375<th> 1376 </th> 1377<th> 1378 <p> 1379 GNU C++ version 7.1.0<br> linux<br> double 1380 </p> 1381 </th> 1382<th> 1383 <p> 1384 GNU C++ version 7.1.0<br> linux<br> long double 1385 </p> 1386 </th> 1387<th> 1388 <p> 1389 Sun compiler version 0x5150<br> Sun Solaris<br> long double 1390 </p> 1391 </th> 1392<th> 1393 <p> 1394 Microsoft Visual C++ version 14.1<br> Win32<br> double 1395 </p> 1396 </th> 1397</tr></thead> 1398<tbody> 1399<tr> 1400<td> 1401 <p> 1402 Bessel I'0: Mathworld Data 1403 </p> 1404 </td> 1405<td> 1406 <p> 1407 <span class="blue">Max = 0ε (Mean = 0ε)</span> 1408 </p> 1409 </td> 1410<td> 1411 <p> 1412 <span class="blue">Max = 0.82ε (Mean = 0.259ε)</span> 1413 </p> 1414 </td> 1415<td> 1416 <p> 1417 <span class="blue">Max = 0.82ε (Mean = 0.259ε)</span> 1418 </p> 1419 </td> 1420<td> 1421 <p> 1422 <span class="blue">Max = 0.82ε (Mean = 0.354ε)</span> 1423 </p> 1424 </td> 1425</tr> 1426<tr> 1427<td> 1428 <p> 1429 Bessel I'1: Mathworld Data 1430 </p> 1431 </td> 1432<td> 1433 <p> 1434 <span class="blue">Max = 0ε (Mean = 0ε)</span> 1435 </p> 1436 </td> 1437<td> 1438 <p> 1439 <span class="blue">Max = 1.97ε (Mean = 0.757ε)</span> 1440 </p> 1441 </td> 1442<td> 1443 <p> 1444 <span class="blue">Max = 1.97ε (Mean = 0.757ε)</span> 1445 </p> 1446 </td> 1447<td> 1448 <p> 1449 <span class="blue">Max = 1.36ε (Mean = 0.782ε)</span> 1450 </p> 1451 </td> 1452</tr> 1453<tr> 1454<td> 1455 <p> 1456 Bessel I'n: Mathworld Data 1457 </p> 1458 </td> 1459<td> 1460 <p> 1461 <span class="blue">Max = 0ε (Mean = 0ε)</span> 1462 </p> 1463 </td> 1464<td> 1465 <p> 1466 <span class="blue">Max = 2.31ε (Mean = 1.41ε)</span> 1467 </p> 1468 </td> 1469<td> 1470 <p> 1471 <span class="blue">Max = 701ε (Mean = 212ε)</span> 1472 </p> 1473 </td> 1474<td> 1475 <p> 1476 <span class="blue">Max = 3.61ε (Mean = 1.22ε)</span> 1477 </p> 1478 </td> 1479</tr> 1480<tr> 1481<td> 1482 <p> 1483 Bessel I'v: Mathworld Data 1484 </p> 1485 </td> 1486<td> 1487 <p> 1488 <span class="blue">Max = 1.62ε (Mean = 0.512ε)</span> 1489 </p> 1490 </td> 1491<td> 1492 <p> 1493 <span class="blue">Max = 2.89e+03ε (Mean = 914ε)</span> 1494 </p> 1495 </td> 1496<td> 1497 <p> 1498 <span class="blue">Max = 2.89e+03ε (Mean = 914ε)</span> 1499 </p> 1500 </td> 1501<td> 1502 <p> 1503 <span class="blue">Max = 3.76e+03ε (Mean = 1.19e+03ε)</span> 1504 </p> 1505 </td> 1506</tr> 1507<tr> 1508<td> 1509 <p> 1510 Bessel I'n: Random Data 1511 </p> 1512 </td> 1513<td> 1514 <p> 1515 <span class="blue">Max = 0ε (Mean = 0ε)</span> 1516 </p> 1517 </td> 1518<td> 1519 <p> 1520 <span class="blue">Max = 3.95ε (Mean = 1.06ε)</span> 1521 </p> 1522 </td> 1523<td> 1524 <p> 1525 <span class="blue">Max = 195ε (Mean = 37.1ε)</span> 1526 </p> 1527 </td> 1528<td> 1529 <p> 1530 <span class="blue">Max = 9.85ε (Mean = 1.82ε)</span> 1531 </p> 1532 </td> 1533</tr> 1534<tr> 1535<td> 1536 <p> 1537 Bessel I'v: Random Data 1538 </p> 1539 </td> 1540<td> 1541 <p> 1542 <span class="blue">Max = 0ε (Mean = 0ε)</span> 1543 </p> 1544 </td> 1545<td> 1546 <p> 1547 <span class="blue">Max = 14.1ε (Mean = 2.93ε)</span> 1548 </p> 1549 </td> 1550<td> 1551 <p> 1552 <span class="blue">Max = 336ε (Mean = 68.5ε)</span> 1553 </p> 1554 </td> 1555<td> 1556 <p> 1557 <span class="blue">Max = 14ε (Mean = 2.5ε)</span> 1558 </p> 1559 </td> 1560</tr> 1561<tr> 1562<td> 1563 <p> 1564 Bessel I'v: Mathworld Data (large values) 1565 </p> 1566 </td> 1567<td> 1568 <p> 1569 <span class="blue">Max = 0ε (Mean = 0ε)</span> 1570 </p> 1571 </td> 1572<td> 1573 <p> 1574 <span class="blue">Max = 42.6ε (Mean = 20.2ε)</span> 1575 </p> 1576 </td> 1577<td> 1578 <p> 1579 <span class="blue">Max = 42.6ε (Mean = 20.2ε)</span> 1580 </p> 1581 </td> 1582<td> 1583 <p> 1584 <span class="blue">Max = 59.5ε (Mean = 26.6ε)</span> 1585 </p> 1586 </td> 1587</tr> 1588</tbody> 1589</table></div> 1590</div> 1591<br class="table-break"> 1592</div> 1593<div class="section"> 1594<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 1595<a name="special_function_error_rates_rep.section_cyl_bessel_i_prime_integer_orders_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_i_prime_integer_orders_" title="cyl_bessel_i_prime (integer orders)">cyl_bessel_i_prime 1596 (integer orders)</a> 1597</h2></div></div></div> 1598<div class="table"> 1599<a name="special_function_error_rates_rep.section_cyl_bessel_i_prime_integer_orders_.table_cyl_bessel_i_prime_integer_orders_"></a><p class="title"><b>Table 11. Error rates for cyl_bessel_i_prime (integer orders)</b></p> 1600<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i_prime (integer orders)"> 1601<colgroup> 1602<col> 1603<col> 1604<col> 1605<col> 1606<col> 1607</colgroup> 1608<thead><tr> 1609<th> 1610 </th> 1611<th> 1612 <p> 1613 GNU C++ version 7.1.0<br> linux<br> double 1614 </p> 1615 </th> 1616<th> 1617 <p> 1618 GNU C++ version 7.1.0<br> linux<br> long double 1619 </p> 1620 </th> 1621<th> 1622 <p> 1623 Sun compiler version 0x5150<br> Sun Solaris<br> long double 1624 </p> 1625 </th> 1626<th> 1627 <p> 1628 Microsoft Visual C++ version 14.1<br> Win32<br> double 1629 </p> 1630 </th> 1631</tr></thead> 1632<tbody> 1633<tr> 1634<td> 1635 <p> 1636 Bessel I'0: Mathworld Data (Integer Version) 1637 </p> 1638 </td> 1639<td> 1640 <p> 1641 <span class="blue">Max = 0ε (Mean = 0ε)</span> 1642 </p> 1643 </td> 1644<td> 1645 <p> 1646 <span class="blue">Max = 0.82ε (Mean = 0.259ε)</span> 1647 </p> 1648 </td> 1649<td> 1650 <p> 1651 <span class="blue">Max = 0.82ε (Mean = 0.259ε)</span> 1652 </p> 1653 </td> 1654<td> 1655 <p> 1656 <span class="blue">Max = 0.82ε (Mean = 0.354ε)</span> 1657 </p> 1658 </td> 1659</tr> 1660<tr> 1661<td> 1662 <p> 1663 Bessel I'1: Mathworld Data (Integer Version) 1664 </p> 1665 </td> 1666<td> 1667 <p> 1668 <span class="blue">Max = 0ε (Mean = 0ε)</span> 1669 </p> 1670 </td> 1671<td> 1672 <p> 1673 <span class="blue">Max = 1.97ε (Mean = 0.757ε)</span> 1674 </p> 1675 </td> 1676<td> 1677 <p> 1678 <span class="blue">Max = 1.97ε (Mean = 0.757ε)</span> 1679 </p> 1680 </td> 1681<td> 1682 <p> 1683 <span class="blue">Max = 1.36ε (Mean = 0.782ε)</span> 1684 </p> 1685 </td> 1686</tr> 1687<tr> 1688<td> 1689 <p> 1690 Bessel I'n: Mathworld Data (Integer Version) 1691 </p> 1692 </td> 1693<td> 1694 <p> 1695 <span class="blue">Max = 0ε (Mean = 0ε)</span> 1696 </p> 1697 </td> 1698<td> 1699 <p> 1700 <span class="blue">Max = 2.31ε (Mean = 1.41ε)</span> 1701 </p> 1702 </td> 1703<td> 1704 <p> 1705 <span class="blue">Max = 701ε (Mean = 212ε)</span> 1706 </p> 1707 </td> 1708<td> 1709 <p> 1710 <span class="blue">Max = 3.61ε (Mean = 1.22ε)</span> 1711 </p> 1712 </td> 1713</tr> 1714</tbody> 1715</table></div> 1716</div> 1717<br class="table-break"> 1718</div> 1719<div class="section"> 1720<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 1721<a name="special_function_error_rates_rep.section_cyl_bessel_j"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_j" title="cyl_bessel_j">cyl_bessel_j</a> 1722</h2></div></div></div> 1723<div class="table"> 1724<a name="special_function_error_rates_rep.section_cyl_bessel_j.table_cyl_bessel_j"></a><p class="title"><b>Table 12. Error rates for cyl_bessel_j</b></p> 1725<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j"> 1726<colgroup> 1727<col> 1728<col> 1729<col> 1730<col> 1731<col> 1732</colgroup> 1733<thead><tr> 1734<th> 1735 </th> 1736<th> 1737 <p> 1738 GNU C++ version 7.1.0<br> linux<br> long double 1739 </p> 1740 </th> 1741<th> 1742 <p> 1743 GNU C++ version 7.1.0<br> linux<br> double 1744 </p> 1745 </th> 1746<th> 1747 <p> 1748 Sun compiler version 0x5150<br> Sun Solaris<br> long double 1749 </p> 1750 </th> 1751<th> 1752 <p> 1753 Microsoft Visual C++ version 14.1<br> Win32<br> double 1754 </p> 1755 </th> 1756</tr></thead> 1757<tbody> 1758<tr> 1759<td> 1760 <p> 1761 Bessel J0: Mathworld Data 1762 </p> 1763 </td> 1764<td> 1765 <p> 1766 <span class="blue">Max = 6.55ε (Mean = 2.86ε)</span><br> <br> 1767 (<span class="emphasis"><em><cmath>:</em></span> Max = 5.04ε (Mean = 1.78ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J0_Mathworld_Data">And 1768 other failures.</a>) 1769 </p> 1770 </td> 1771<td> 1772 <p> 1773 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 1774 2.1:</em></span> Max = 0.629ε (Mean = 0.223ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J0_Mathworld_Data">And 1775 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 1776 Max = 0.629ε (Mean = 0.223ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J0_Mathworld_Data">And 1777 other failures.</a>) 1778 </p> 1779 </td> 1780<td> 1781 <p> 1782 <span class="blue">Max = 6.55ε (Mean = 2.86ε)</span> 1783 </p> 1784 </td> 1785<td> 1786 <p> 1787 <span class="blue">Max = 2.52ε (Mean = 1.2ε)</span> 1788 </p> 1789 </td> 1790</tr> 1791<tr> 1792<td> 1793 <p> 1794 Bessel J0: Mathworld Data (Tricky cases) 1795 </p> 1796 </td> 1797<td> 1798 <p> 1799 <span class="blue">Max = 1.64e+08ε (Mean = 6.69e+07ε)</span><br> 1800 <br> (<span class="emphasis"><em><cmath>:</em></span> Max = 4.79e+08ε (Mean = 1801 1.96e+08ε)) 1802 </p> 1803 </td> 1804<td> 1805 <p> 1806 <span class="blue">Max = 8e+04ε (Mean = 3.27e+04ε)</span><br> 1807 <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 6.5e+07ε (Mean = 2.66e+07ε))<br> 1808 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.04e+07ε (Mean = 4.29e+06ε)) 1809 </p> 1810 </td> 1811<td> 1812 <p> 1813 <span class="blue">Max = 1.64e+08ε (Mean = 6.69e+07ε)</span> 1814 </p> 1815 </td> 1816<td> 1817 <p> 1818 <span class="blue">Max = 1e+07ε (Mean = 4.09e+06ε)</span> 1819 </p> 1820 </td> 1821</tr> 1822<tr> 1823<td> 1824 <p> 1825 Bessel J1: Mathworld Data 1826 </p> 1827 </td> 1828<td> 1829 <p> 1830 <span class="blue">Max = 3.59ε (Mean = 1.33ε)</span><br> <br> 1831 (<span class="emphasis"><em><cmath>:</em></span> Max = 6.1ε (Mean = 2.95ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J1_Mathworld_Data">And 1832 other failures.</a>) 1833 </p> 1834 </td> 1835<td> 1836 <p> 1837 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 1838 2.1:</em></span> Max = 6.62ε (Mean = 2.35ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J1_Mathworld_Data">And 1839 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 1840 Max = 0.946ε (Mean = 0.39ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J1_Mathworld_Data">And 1841 other failures.</a>) 1842 </p> 1843 </td> 1844<td> 1845 <p> 1846 <span class="blue">Max = 1.44ε (Mean = 0.637ε)</span> 1847 </p> 1848 </td> 1849<td> 1850 <p> 1851 <span class="blue">Max = 1.73ε (Mean = 0.976ε)</span> 1852 </p> 1853 </td> 1854</tr> 1855<tr> 1856<td> 1857 <p> 1858 Bessel J1: Mathworld Data (tricky cases) 1859 </p> 1860 </td> 1861<td> 1862 <p> 1863 <span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span><br> 1864 <br> (<span class="emphasis"><em><cmath>:</em></span> Max = 2.15e+06ε (Mean = 1865 1.58e+06ε)) 1866 </p> 1867 </td> 1868<td> 1869 <p> 1870 <span class="blue">Max = 106ε (Mean = 47.5ε)</span><br> <br> 1871 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.75e+05ε (Mean = 5.32e+05ε))<br> 1872 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.93e+06ε (Mean = 1.7e+06ε)) 1873 </p> 1874 </td> 1875<td> 1876 <p> 1877 <span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span> 1878 </p> 1879 </td> 1880<td> 1881 <p> 1882 <span class="blue">Max = 3.23e+04ε (Mean = 1.45e+04ε)</span> 1883 </p> 1884 </td> 1885</tr> 1886<tr> 1887<td> 1888 <p> 1889 Bessel JN: Mathworld Data 1890 </p> 1891 </td> 1892<td> 1893 <p> 1894 <span class="blue">Max = 6.85ε (Mean = 3.35ε)</span><br> <br> 1895 (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 2.13e+19ε (Mean 1896 = 5.16e+18ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_JN_Mathworld_Data">And 1897 other failures.</a>)</span> 1898 </p> 1899 </td> 1900<td> 1901 <p> 1902 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 1903 2.1:</em></span> Max = 6.9e+05ε (Mean = 2.15e+05ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_JN_Mathworld_Data">And 1904 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 1905 <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_JN_Mathworld_Data">And 1906 other failures.</a>)</span> 1907 </p> 1908 </td> 1909<td> 1910 <p> 1911 <span class="blue">Max = 463ε (Mean = 112ε)</span> 1912 </p> 1913 </td> 1914<td> 1915 <p> 1916 <span class="blue">Max = 14.7ε (Mean = 5.4ε)</span> 1917 </p> 1918 </td> 1919</tr> 1920<tr> 1921<td> 1922 <p> 1923 Bessel J: Mathworld Data 1924 </p> 1925 </td> 1926<td> 1927 <p> 1928 <span class="blue">Max = 14.7ε (Mean = 4.11ε)</span><br> <br> 1929 (<span class="emphasis"><em><cmath>:</em></span> Max = 3.49e+05ε (Mean = 8.09e+04ε) 1930 <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J_Mathworld_Data">And 1931 other failures.</a>) 1932 </p> 1933 </td> 1934<td> 1935 <p> 1936 <span class="blue">Max = 10ε (Mean = 2.24ε)</span><br> <br> (<span class="emphasis"><em>GSL 1937 2.1:</em></span> Max = 2.39e+05ε (Mean = 5.37e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Mathworld_Data">And 1938 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 1939 <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J_Mathworld_Data">And 1940 other failures.</a>)</span> 1941 </p> 1942 </td> 1943<td> 1944 <p> 1945 <span class="blue">Max = 14.7ε (Mean = 4.22ε)</span> 1946 </p> 1947 </td> 1948<td> 1949 <p> 1950 <span class="blue">Max = 14.9ε (Mean = 3.89ε)</span> 1951 </p> 1952 </td> 1953</tr> 1954<tr> 1955<td> 1956 <p> 1957 Bessel J: Mathworld Data (large values) 1958 </p> 1959 </td> 1960<td> 1961 <p> 1962 <span class="blue">Max = 607ε (Mean = 305ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span> 1963 Max = 34.9ε (Mean = 17.4ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J_Mathworld_Data_large_values_">And 1964 other failures.</a>) 1965 </p> 1966 </td> 1967<td> 1968 <p> 1969 <span class="blue">Max = 0.536ε (Mean = 0.268ε)</span><br> <br> 1970 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 4.91e+03ε (Mean = 2.46e+03ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Mathworld_Data_large_values_">And 1971 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 1972 Max = 5.9ε (Mean = 3.76ε)) 1973 </p> 1974 </td> 1975<td> 1976 <p> 1977 <span class="blue">Max = 607ε (Mean = 305ε)</span> 1978 </p> 1979 </td> 1980<td> 1981 <p> 1982 <span class="blue">Max = 9.31ε (Mean = 5.52ε)</span> 1983 </p> 1984 </td> 1985</tr> 1986<tr> 1987<td> 1988 <p> 1989 Bessel JN: Random Data 1990 </p> 1991 </td> 1992<td> 1993 <p> 1994 <span class="blue">Max = 50.8ε (Mean = 3.69ε)</span><br> <br> 1995 (<span class="emphasis"><em><cmath>:</em></span> Max = 1.12e+03ε (Mean = 88.7ε)) 1996 </p> 1997 </td> 1998<td> 1999 <p> 2000 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 2001 2.1:</em></span> Max = 75.7ε (Mean = 5.36ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 2002 Max = 3.93ε (Mean = 1.22ε)) 2003 </p> 2004 </td> 2005<td> 2006 <p> 2007 <span class="blue">Max = 99.6ε (Mean = 22ε)</span> 2008 </p> 2009 </td> 2010<td> 2011 <p> 2012 <span class="blue">Max = 17.5ε (Mean = 1.46ε)</span> 2013 </p> 2014 </td> 2015</tr> 2016<tr> 2017<td> 2018 <p> 2019 Bessel J: Random Data 2020 </p> 2021 </td> 2022<td> 2023 <p> 2024 <span class="blue">Max = 11.4ε (Mean = 1.68ε)</span><br> <br> 2025 (<span class="emphasis"><em><cmath>:</em></span> Max = 501ε (Mean = 52.3ε)) 2026 </p> 2027 </td> 2028<td> 2029 <p> 2030 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 2031 2.1:</em></span> Max = 15.5ε (Mean = 3.33ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Random_Data">And 2032 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 2033 Max = 6.74ε (Mean = 1.3ε)) 2034 </p> 2035 </td> 2036<td> 2037 <p> 2038 <span class="blue">Max = 260ε (Mean = 34ε)</span> 2039 </p> 2040 </td> 2041<td> 2042 <p> 2043 <span class="blue">Max = 9.24ε (Mean = 1.17ε)</span> 2044 </p> 2045 </td> 2046</tr> 2047<tr> 2048<td> 2049 <p> 2050 Bessel J: Random Data (Tricky large values) 2051 </p> 2052 </td> 2053<td> 2054 <p> 2055 <span class="blue">Max = 785ε (Mean = 94.2ε)</span><br> <br> 2056 (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 5.01e+17ε (Mean 2057 = 6.23e+16ε))</span> 2058 </p> 2059 </td> 2060<td> 2061 <p> 2062 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 2063 2.1:</em></span> Max = 2.48e+05ε (Mean = 5.11e+04ε))<br> (<span class="emphasis"><em>Rmath 2064 3.2.3:</em></span> Max = 71.6ε (Mean = 11.7ε)) 2065 </p> 2066 </td> 2067<td> 2068 <p> 2069 <span class="blue">Max = 785ε (Mean = 97.4ε)</span> 2070 </p> 2071 </td> 2072<td> 2073 <p> 2074 <span class="blue">Max = 59.2ε (Mean = 8.67ε)</span> 2075 </p> 2076 </td> 2077</tr> 2078</tbody> 2079</table></div> 2080</div> 2081<br class="table-break"> 2082</div> 2083<div class="section"> 2084<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 2085<a name="special_function_error_rates_rep.section_cyl_bessel_j_integer_orders_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_j_integer_orders_" title="cyl_bessel_j (integer orders)">cyl_bessel_j 2086 (integer orders)</a> 2087</h2></div></div></div> 2088<div class="table"> 2089<a name="special_function_error_rates_rep.section_cyl_bessel_j_integer_orders_.table_cyl_bessel_j_integer_orders_"></a><p class="title"><b>Table 13. Error rates for cyl_bessel_j (integer orders)</b></p> 2090<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j (integer orders)"> 2091<colgroup> 2092<col> 2093<col> 2094<col> 2095<col> 2096<col> 2097</colgroup> 2098<thead><tr> 2099<th> 2100 </th> 2101<th> 2102 <p> 2103 GNU C++ version 7.1.0<br> linux<br> long double 2104 </p> 2105 </th> 2106<th> 2107 <p> 2108 GNU C++ version 7.1.0<br> linux<br> double 2109 </p> 2110 </th> 2111<th> 2112 <p> 2113 Sun compiler version 0x5150<br> Sun Solaris<br> long double 2114 </p> 2115 </th> 2116<th> 2117 <p> 2118 Microsoft Visual C++ version 14.1<br> Win32<br> double 2119 </p> 2120 </th> 2121</tr></thead> 2122<tbody> 2123<tr> 2124<td> 2125 <p> 2126 Bessel J0: Mathworld Data (Integer Version) 2127 </p> 2128 </td> 2129<td> 2130 <p> 2131 <span class="blue">Max = 6.55ε (Mean = 2.86ε)</span><br> <br> 2132 (<span class="emphasis"><em><cmath>:</em></span> Max = 5.04ε (Mean = 1.78ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_J0_Mathworld_Data_Integer_Version_">And 2133 other failures.</a>) 2134 </p> 2135 </td> 2136<td> 2137 <p> 2138 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 2139 2.1:</em></span> Max = 1.12ε (Mean = 0.488ε))<br> (<span class="emphasis"><em>Rmath 2140 3.2.3:</em></span> Max = 0.629ε (Mean = 0.223ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_J0_Mathworld_Data_Integer_Version_">And 2141 other failures.</a>) 2142 </p> 2143 </td> 2144<td> 2145 <p> 2146 <span class="blue">Max = 6.55ε (Mean = 2.86ε)</span> 2147 </p> 2148 </td> 2149<td> 2150 <p> 2151 <span class="blue">Max = 2.52ε (Mean = 1.2ε)</span><br> <br> 2152 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.89ε (Mean = 0.988ε)) 2153 </p> 2154 </td> 2155</tr> 2156<tr> 2157<td> 2158 <p> 2159 Bessel J0: Mathworld Data (Tricky cases) (Integer Version) 2160 </p> 2161 </td> 2162<td> 2163 <p> 2164 <span class="blue">Max = 1.64e+08ε (Mean = 6.69e+07ε)</span><br> 2165 <br> (<span class="emphasis"><em><cmath>:</em></span> Max = 4.79e+08ε (Mean = 2166 1.96e+08ε)) 2167 </p> 2168 </td> 2169<td> 2170 <p> 2171 <span class="blue">Max = 8e+04ε (Mean = 3.27e+04ε)</span><br> 2172 <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1e+07ε (Mean = 4.11e+06ε))<br> 2173 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.04e+07ε (Mean = 4.29e+06ε)) 2174 </p> 2175 </td> 2176<td> 2177 <p> 2178 <span class="blue">Max = 1.64e+08ε (Mean = 6.69e+07ε)</span> 2179 </p> 2180 </td> 2181<td> 2182 <p> 2183 <span class="blue">Max = 1e+07ε (Mean = 4.09e+06ε)</span><br> 2184 <br> (<span class="emphasis"><em><math.h>:</em></span> <span class="red">Max 2185 = 2.54e+08ε (Mean = 1.04e+08ε))</span> 2186 </p> 2187 </td> 2188</tr> 2189<tr> 2190<td> 2191 <p> 2192 Bessel J1: Mathworld Data (Integer Version) 2193 </p> 2194 </td> 2195<td> 2196 <p> 2197 <span class="blue">Max = 3.59ε (Mean = 1.33ε)</span><br> <br> 2198 (<span class="emphasis"><em><cmath>:</em></span> Max = 6.1ε (Mean = 2.95ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_J1_Mathworld_Data_Integer_Version_">And 2199 other failures.</a>) 2200 </p> 2201 </td> 2202<td> 2203 <p> 2204 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 2205 2.1:</em></span> Max = 1.89ε (Mean = 0.721ε))<br> (<span class="emphasis"><em>Rmath 2206 3.2.3:</em></span> Max = 0.946ε (Mean = 0.39ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_J1_Mathworld_Data_Integer_Version_">And 2207 other failures.</a>) 2208 </p> 2209 </td> 2210<td> 2211 <p> 2212 <span class="blue">Max = 1.44ε (Mean = 0.637ε)</span> 2213 </p> 2214 </td> 2215<td> 2216 <p> 2217 <span class="blue">Max = 1.73ε (Mean = 0.976ε)</span><br> <br> 2218 (<span class="emphasis"><em><math.h>:</em></span> Max = 11.4ε (Mean = 4.15ε)) 2219 </p> 2220 </td> 2221</tr> 2222<tr> 2223<td> 2224 <p> 2225 Bessel J1: Mathworld Data (tricky cases) (Integer Version) 2226 </p> 2227 </td> 2228<td> 2229 <p> 2230 <span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span><br> 2231 <br> (<span class="emphasis"><em><cmath>:</em></span> Max = 2.15e+06ε (Mean = 2232 1.58e+06ε)) 2233 </p> 2234 </td> 2235<td> 2236 <p> 2237 <span class="blue">Max = 106ε (Mean = 47.5ε)</span><br> <br> 2238 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.26e+06ε (Mean = 6.28e+05ε))<br> 2239 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.93e+06ε (Mean = 1.7e+06ε)) 2240 </p> 2241 </td> 2242<td> 2243 <p> 2244 <span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span> 2245 </p> 2246 </td> 2247<td> 2248 <p> 2249 <span class="blue">Max = 3.23e+04ε (Mean = 1.45e+04ε)</span><br> 2250 <br> (<span class="emphasis"><em><math.h>:</em></span> Max = 1.44e+07ε (Mean 2251 = 6.5e+06ε)) 2252 </p> 2253 </td> 2254</tr> 2255<tr> 2256<td> 2257 <p> 2258 Bessel JN: Mathworld Data (Integer Version) 2259 </p> 2260 </td> 2261<td> 2262 <p> 2263 <span class="blue">Max = 6.85ε (Mean = 3.35ε)</span><br> <br> 2264 (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 2.13e+19ε (Mean 2265 = 5.16e+18ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_JN_Mathworld_Data_Integer_Version_">And 2266 other failures.</a>)</span> 2267 </p> 2268 </td> 2269<td> 2270 <p> 2271 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 2272 2.1:</em></span> Max = 6.9e+05ε (Mean = 2.53e+05ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__GSL_2_1_Bessel_JN_Mathworld_Data_Integer_Version_">And 2273 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 2274 <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_JN_Mathworld_Data_Integer_Version_">And 2275 other failures.</a>)</span> 2276 </p> 2277 </td> 2278<td> 2279 <p> 2280 <span class="blue">Max = 463ε (Mean = 112ε)</span> 2281 </p> 2282 </td> 2283<td> 2284 <p> 2285 <span class="blue">Max = 14.7ε (Mean = 5.4ε)</span><br> <br> 2286 (<span class="emphasis"><em><math.h>:</em></span> <span class="red">Max = +INFε (Mean 2287 = +INFε) <a class="link" href="index.html#errors_Microsoft_Visual_C_version_14_1_Win32_double_cyl_bessel_j_integer_orders___math_h__Bessel_JN_Mathworld_Data_Integer_Version_">And 2288 other failures.</a>)</span> 2289 </p> 2290 </td> 2291</tr> 2292</tbody> 2293</table></div> 2294</div> 2295<br class="table-break"> 2296</div> 2297<div class="section"> 2298<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 2299<a name="special_function_error_rates_rep.section_cyl_bessel_j_prime"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_j_prime" title="cyl_bessel_j_prime">cyl_bessel_j_prime</a> 2300</h2></div></div></div> 2301<div class="table"> 2302<a name="special_function_error_rates_rep.section_cyl_bessel_j_prime.table_cyl_bessel_j_prime"></a><p class="title"><b>Table 14. Error rates for cyl_bessel_j_prime</b></p> 2303<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j_prime"> 2304<colgroup> 2305<col> 2306<col> 2307<col> 2308<col> 2309<col> 2310</colgroup> 2311<thead><tr> 2312<th> 2313 </th> 2314<th> 2315 <p> 2316 GNU C++ version 7.1.0<br> linux<br> double 2317 </p> 2318 </th> 2319<th> 2320 <p> 2321 GNU C++ version 7.1.0<br> linux<br> long double 2322 </p> 2323 </th> 2324<th> 2325 <p> 2326 Sun compiler version 0x5150<br> Sun Solaris<br> long double 2327 </p> 2328 </th> 2329<th> 2330 <p> 2331 Microsoft Visual C++ version 14.1<br> Win32<br> double 2332 </p> 2333 </th> 2334</tr></thead> 2335<tbody> 2336<tr> 2337<td> 2338 <p> 2339 Bessel J0': Mathworld Data 2340 </p> 2341 </td> 2342<td> 2343 <p> 2344 <span class="blue">Max = 0ε (Mean = 0ε)</span> 2345 </p> 2346 </td> 2347<td> 2348 <p> 2349 <span class="blue">Max = 18.9ε (Mean = 6.82ε)</span> 2350 </p> 2351 </td> 2352<td> 2353 <p> 2354 <span class="blue">Max = 18.9ε (Mean = 6.72ε)</span> 2355 </p> 2356 </td> 2357<td> 2358 <p> 2359 <span class="blue">Max = 6.62ε (Mean = 2.55ε)</span> 2360 </p> 2361 </td> 2362</tr> 2363<tr> 2364<td> 2365 <p> 2366 Bessel J0': Mathworld Data (Tricky cases) 2367 </p> 2368 </td> 2369<td> 2370 <p> 2371 <span class="blue">Max = 0ε (Mean = 0ε)</span> 2372 </p> 2373 </td> 2374<td> 2375 <p> 2376 <span class="blue">Max = 7.44ε (Mean = 3.34ε)</span> 2377 </p> 2378 </td> 2379<td> 2380 <p> 2381 <span class="blue">Max = 7.44ε (Mean = 3.31ε)</span> 2382 </p> 2383 </td> 2384<td> 2385 <p> 2386 <span class="blue">Max = 3.67ε (Mean = 1.74ε)</span> 2387 </p> 2388 </td> 2389</tr> 2390<tr> 2391<td> 2392 <p> 2393 Bessel J1': Mathworld Data 2394 </p> 2395 </td> 2396<td> 2397 <p> 2398 <span class="blue">Max = 0ε (Mean = 0ε)</span> 2399 </p> 2400 </td> 2401<td> 2402 <p> 2403 <span class="blue">Max = 7.9ε (Mean = 3.37ε)</span> 2404 </p> 2405 </td> 2406<td> 2407 <p> 2408 <span class="blue">Max = 7.9ε (Mean = 3.37ε)</span> 2409 </p> 2410 </td> 2411<td> 2412 <p> 2413 <span class="blue">Max = 0.999ε (Mean = 0.627ε)</span> 2414 </p> 2415 </td> 2416</tr> 2417<tr> 2418<td> 2419 <p> 2420 Bessel J1': Mathworld Data (tricky cases) 2421 </p> 2422 </td> 2423<td> 2424 <p> 2425 <span class="blue">Max = 287ε (Mean = 129ε)</span> 2426 </p> 2427 </td> 2428<td> 2429 <p> 2430 <span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span> 2431 </p> 2432 </td> 2433<td> 2434 <p> 2435 <span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span> 2436 </p> 2437 </td> 2438<td> 2439 <p> 2440 <span class="blue">Max = 288ε (Mean = 129ε)</span> 2441 </p> 2442 </td> 2443</tr> 2444<tr> 2445<td> 2446 <p> 2447 Bessel JN': Mathworld Data 2448 </p> 2449 </td> 2450<td> 2451 <p> 2452 <span class="blue">Max = 0.527ε (Mean = 0.128ε)</span> 2453 </p> 2454 </td> 2455<td> 2456 <p> 2457 <span class="blue">Max = 1.29e+03ε (Mean = 312ε)</span> 2458 </p> 2459 </td> 2460<td> 2461 <p> 2462 <span class="blue">Max = 1.29e+03ε (Mean = 355ε)</span> 2463 </p> 2464 </td> 2465<td> 2466 <p> 2467 <span class="blue">Max = 14ε (Mean = 6.13ε)</span> 2468 </p> 2469 </td> 2470</tr> 2471<tr> 2472<td> 2473 <p> 2474 Bessel J': Mathworld Data 2475 </p> 2476 </td> 2477<td> 2478 <p> 2479 <span class="blue">Max = 21.5ε (Mean = 4.7ε)</span> 2480 </p> 2481 </td> 2482<td> 2483 <p> 2484 <span class="blue">Max = 42.5ε (Mean = 9.31ε)</span> 2485 </p> 2486 </td> 2487<td> 2488 <p> 2489 <span class="blue">Max = 42.5ε (Mean = 9.32ε)</span> 2490 </p> 2491 </td> 2492<td> 2493 <p> 2494 <span class="blue">Max = 23.7ε (Mean = 8ε)</span> 2495 </p> 2496 </td> 2497</tr> 2498<tr> 2499<td> 2500 <p> 2501 Bessel J': Mathworld Data (large values) 2502 </p> 2503 </td> 2504<td> 2505 <p> 2506 <span class="blue">Max = 0ε (Mean = 0ε)</span> 2507 </p> 2508 </td> 2509<td> 2510 <p> 2511 <span class="blue">Max = 989ε (Mean = 495ε)</span> 2512 </p> 2513 </td> 2514<td> 2515 <p> 2516 <span class="blue">Max = 989ε (Mean = 495ε)</span> 2517 </p> 2518 </td> 2519<td> 2520 <p> 2521 <span class="blue">Max = 2.9ε (Mean = 1.61ε)</span> 2522 </p> 2523 </td> 2524</tr> 2525<tr> 2526<td> 2527 <p> 2528 Bessel JN': Random Data 2529 </p> 2530 </td> 2531<td> 2532 <p> 2533 <span class="blue">Max = 0.593ε (Mean = 0.0396ε)</span> 2534 </p> 2535 </td> 2536<td> 2537 <p> 2538 <span class="blue">Max = 11.3ε (Mean = 1.85ε)</span> 2539 </p> 2540 </td> 2541<td> 2542 <p> 2543 <span class="blue">Max = 79.4ε (Mean = 16.2ε)</span> 2544 </p> 2545 </td> 2546<td> 2547 <p> 2548 <span class="blue">Max = 6.34ε (Mean = 0.999ε)</span> 2549 </p> 2550 </td> 2551</tr> 2552<tr> 2553<td> 2554 <p> 2555 Bessel J': Random Data 2556 </p> 2557 </td> 2558<td> 2559 <p> 2560 <span class="blue">Max = 0.885ε (Mean = 0.033ε)</span> 2561 </p> 2562 </td> 2563<td> 2564 <p> 2565 <span class="blue">Max = 139ε (Mean = 6.47ε)</span> 2566 </p> 2567 </td> 2568<td> 2569 <p> 2570 <span class="blue">Max = 279ε (Mean = 27.2ε)</span> 2571 </p> 2572 </td> 2573<td> 2574 <p> 2575 <span class="blue">Max = 176ε (Mean = 9.75ε)</span> 2576 </p> 2577 </td> 2578</tr> 2579<tr> 2580<td> 2581 <p> 2582 Bessel J': Random Data (Tricky large values) 2583 </p> 2584 </td> 2585<td> 2586 <p> 2587 <span class="blue">Max = 0ε (Mean = 0ε)</span> 2588 </p> 2589 </td> 2590<td> 2591 <p> 2592 <span class="blue">Max = 474ε (Mean = 62.2ε)</span> 2593 </p> 2594 </td> 2595<td> 2596 <p> 2597 <span class="blue">Max = 474ε (Mean = 64.5ε)</span> 2598 </p> 2599 </td> 2600<td> 2601 <p> 2602 <span class="blue">Max = 379ε (Mean = 45.4ε)</span> 2603 </p> 2604 </td> 2605</tr> 2606</tbody> 2607</table></div> 2608</div> 2609<br class="table-break"> 2610</div> 2611<div class="section"> 2612<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 2613<a name="special_function_error_rates_rep.section_cyl_bessel_j_prime_integer_orders_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_j_prime_integer_orders_" title="cyl_bessel_j_prime (integer orders)">cyl_bessel_j_prime 2614 (integer orders)</a> 2615</h2></div></div></div> 2616<div class="table"> 2617<a name="special_function_error_rates_rep.section_cyl_bessel_j_prime_integer_orders_.table_cyl_bessel_j_prime_integer_orders_"></a><p class="title"><b>Table 15. Error rates for cyl_bessel_j_prime (integer orders)</b></p> 2618<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j_prime (integer orders)"> 2619<colgroup> 2620<col> 2621<col> 2622<col> 2623<col> 2624<col> 2625</colgroup> 2626<thead><tr> 2627<th> 2628 </th> 2629<th> 2630 <p> 2631 GNU C++ version 7.1.0<br> linux<br> double 2632 </p> 2633 </th> 2634<th> 2635 <p> 2636 GNU C++ version 7.1.0<br> linux<br> long double 2637 </p> 2638 </th> 2639<th> 2640 <p> 2641 Sun compiler version 0x5150<br> Sun Solaris<br> long double 2642 </p> 2643 </th> 2644<th> 2645 <p> 2646 Microsoft Visual C++ version 14.1<br> Win32<br> double 2647 </p> 2648 </th> 2649</tr></thead> 2650<tbody> 2651<tr> 2652<td> 2653 <p> 2654 Bessel J0': Mathworld Data (Integer Version) 2655 </p> 2656 </td> 2657<td> 2658 <p> 2659 <span class="blue">Max = 0ε (Mean = 0ε)</span> 2660 </p> 2661 </td> 2662<td> 2663 <p> 2664 <span class="blue">Max = 18.9ε (Mean = 6.82ε)</span> 2665 </p> 2666 </td> 2667<td> 2668 <p> 2669 <span class="blue">Max = 18.9ε (Mean = 6.72ε)</span> 2670 </p> 2671 </td> 2672<td> 2673 <p> 2674 <span class="blue">Max = 6.62ε (Mean = 2.55ε)</span> 2675 </p> 2676 </td> 2677</tr> 2678<tr> 2679<td> 2680 <p> 2681 Bessel J0': Mathworld Data (Tricky cases) (Integer Version) 2682 </p> 2683 </td> 2684<td> 2685 <p> 2686 <span class="blue">Max = 0ε (Mean = 0ε)</span> 2687 </p> 2688 </td> 2689<td> 2690 <p> 2691 <span class="blue">Max = 7.44ε (Mean = 3.34ε)</span> 2692 </p> 2693 </td> 2694<td> 2695 <p> 2696 <span class="blue">Max = 7.44ε (Mean = 3.31ε)</span> 2697 </p> 2698 </td> 2699<td> 2700 <p> 2701 <span class="blue">Max = 3.67ε (Mean = 1.74ε)</span> 2702 </p> 2703 </td> 2704</tr> 2705<tr> 2706<td> 2707 <p> 2708 Bessel J1': Mathworld Data (Integer Version) 2709 </p> 2710 </td> 2711<td> 2712 <p> 2713 <span class="blue">Max = 0ε (Mean = 0ε)</span> 2714 </p> 2715 </td> 2716<td> 2717 <p> 2718 <span class="blue">Max = 7.9ε (Mean = 3.37ε)</span> 2719 </p> 2720 </td> 2721<td> 2722 <p> 2723 <span class="blue">Max = 7.9ε (Mean = 3.37ε)</span> 2724 </p> 2725 </td> 2726<td> 2727 <p> 2728 <span class="blue">Max = 0.999ε (Mean = 0.627ε)</span> 2729 </p> 2730 </td> 2731</tr> 2732<tr> 2733<td> 2734 <p> 2735 Bessel J1': Mathworld Data (tricky cases) (Integer Version) 2736 </p> 2737 </td> 2738<td> 2739 <p> 2740 <span class="blue">Max = 287ε (Mean = 129ε)</span> 2741 </p> 2742 </td> 2743<td> 2744 <p> 2745 <span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span> 2746 </p> 2747 </td> 2748<td> 2749 <p> 2750 <span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span> 2751 </p> 2752 </td> 2753<td> 2754 <p> 2755 <span class="blue">Max = 288ε (Mean = 129ε)</span> 2756 </p> 2757 </td> 2758</tr> 2759<tr> 2760<td> 2761 <p> 2762 Bessel JN': Mathworld Data (Integer Version) 2763 </p> 2764 </td> 2765<td> 2766 <p> 2767 <span class="blue">Max = 0.527ε (Mean = 0.128ε)</span> 2768 </p> 2769 </td> 2770<td> 2771 <p> 2772 <span class="blue">Max = 1.29e+03ε (Mean = 312ε)</span> 2773 </p> 2774 </td> 2775<td> 2776 <p> 2777 <span class="blue">Max = 1.29e+03ε (Mean = 355ε)</span> 2778 </p> 2779 </td> 2780<td> 2781 <p> 2782 <span class="blue">Max = 14ε (Mean = 6.13ε)</span> 2783 </p> 2784 </td> 2785</tr> 2786</tbody> 2787</table></div> 2788</div> 2789<br class="table-break"> 2790</div> 2791<div class="section"> 2792<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 2793<a name="special_function_error_rates_rep.section_cyl_bessel_k"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_k" title="cyl_bessel_k">cyl_bessel_k</a> 2794</h2></div></div></div> 2795<div class="table"> 2796<a name="special_function_error_rates_rep.section_cyl_bessel_k.table_cyl_bessel_k"></a><p class="title"><b>Table 16. Error rates for cyl_bessel_k</b></p> 2797<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k"> 2798<colgroup> 2799<col> 2800<col> 2801<col> 2802<col> 2803<col> 2804</colgroup> 2805<thead><tr> 2806<th> 2807 </th> 2808<th> 2809 <p> 2810 GNU C++ version 7.1.0<br> linux<br> long double 2811 </p> 2812 </th> 2813<th> 2814 <p> 2815 GNU C++ version 7.1.0<br> linux<br> double 2816 </p> 2817 </th> 2818<th> 2819 <p> 2820 Sun compiler version 0x5150<br> Sun Solaris<br> long double 2821 </p> 2822 </th> 2823<th> 2824 <p> 2825 Microsoft Visual C++ version 14.1<br> Win32<br> double 2826 </p> 2827 </th> 2828</tr></thead> 2829<tbody> 2830<tr> 2831<td> 2832 <p> 2833 Bessel K0: Mathworld Data 2834 </p> 2835 </td> 2836<td> 2837 <p> 2838 <span class="blue">Max = 0.833ε (Mean = 0.436ε)</span><br> <br> 2839 (<span class="emphasis"><em><cmath>:</em></span> Max = 9.33ε (Mean = 3.25ε)) 2840 </p> 2841 </td> 2842<td> 2843 <p> 2844 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 2845 2.1:</em></span> Max = 6.04ε (Mean = 2.16ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 2846 Max = 0.833ε (Mean = 0.601ε)) 2847 </p> 2848 </td> 2849<td> 2850 <p> 2851 <span class="blue">Max = 0.833ε (Mean = 0.436ε)</span> 2852 </p> 2853 </td> 2854<td> 2855 <p> 2856 <span class="blue">Max = 0.833ε (Mean = 0.552ε)</span> 2857 </p> 2858 </td> 2859</tr> 2860<tr> 2861<td> 2862 <p> 2863 Bessel K1: Mathworld Data 2864 </p> 2865 </td> 2866<td> 2867 <p> 2868 <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span><br> <br> 2869 (<span class="emphasis"><em><cmath>:</em></span> Max = 8.94ε (Mean = 3.19ε)) 2870 </p> 2871 </td> 2872<td> 2873 <p> 2874 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 2875 2.1:</em></span> Max = 6.26ε (Mean = 2.21ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 2876 Max = 0.894ε (Mean = 0.516ε)) 2877 </p> 2878 </td> 2879<td> 2880 <p> 2881 <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span> 2882 </p> 2883 </td> 2884<td> 2885 <p> 2886 <span class="blue">Max = 0.786ε (Mean = 0.39ε)</span> 2887 </p> 2888 </td> 2889</tr> 2890<tr> 2891<td> 2892 <p> 2893 Bessel Kn: Mathworld Data 2894 </p> 2895 </td> 2896<td> 2897 <p> 2898 <span class="blue">Max = 2.6ε (Mean = 1.21ε)</span><br> <br> 2899 (<span class="emphasis"><em><cmath>:</em></span> Max = 12.9ε (Mean = 4.91ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kn_Mathworld_Data">And 2900 other failures.</a>) 2901 </p> 2902 </td> 2903<td> 2904 <p> 2905 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 2906 2.1:</em></span> Max = 3.36ε (Mean = 1.43ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kn_Mathworld_Data">And 2907 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 2908 Max = 8.48ε (Mean = 2.98ε)) 2909 </p> 2910 </td> 2911<td> 2912 <p> 2913 <span class="blue">Max = 2.6ε (Mean = 1.21ε)</span> 2914 </p> 2915 </td> 2916<td> 2917 <p> 2918 <span class="blue">Max = 3.63ε (Mean = 1.46ε)</span> 2919 </p> 2920 </td> 2921</tr> 2922<tr> 2923<td> 2924 <p> 2925 Bessel Kv: Mathworld Data 2926 </p> 2927 </td> 2928<td> 2929 <p> 2930 <span class="blue">Max = 3.58ε (Mean = 2.39ε)</span><br> <br> 2931 (<span class="emphasis"><em><cmath>:</em></span> Max = 13ε (Mean = 4.81ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Mathworld_Data">And 2932 other failures.</a>) 2933 </p> 2934 </td> 2935<td> 2936 <p> 2937 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 2938 2.1:</em></span> Max = 5.47ε (Mean = 2.04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Mathworld_Data">And 2939 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 2940 Max = 3.15ε (Mean = 1.35ε)) 2941 </p> 2942 </td> 2943<td> 2944 <p> 2945 <span class="blue">Max = 5.21ε (Mean = 2.53ε)</span> 2946 </p> 2947 </td> 2948<td> 2949 <p> 2950 <span class="blue">Max = 4.78ε (Mean = 2.19ε)</span> 2951 </p> 2952 </td> 2953</tr> 2954<tr> 2955<td> 2956 <p> 2957 Bessel Kv: Mathworld Data (large values) 2958 </p> 2959 </td> 2960<td> 2961 <p> 2962 <span class="blue">Max = 42.3ε (Mean = 21ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span> 2963 Max = 42.3ε (Mean = 19.8ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Mathworld_Data_large_values_">And 2964 other failures.</a>) 2965 </p> 2966 </td> 2967<td> 2968 <p> 2969 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 2970 2.1:</em></span> Max = 308ε (Mean = 142ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Mathworld_Data_large_values_">And 2971 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 2972 Max = 84.6ε (Mean = 37.8ε)) 2973 </p> 2974 </td> 2975<td> 2976 <p> 2977 <span class="blue">Max = 42.3ε (Mean = 21ε)</span> 2978 </p> 2979 </td> 2980<td> 2981 <p> 2982 <span class="blue">Max = 59.8ε (Mean = 26.9ε)</span> 2983 </p> 2984 </td> 2985</tr> 2986<tr> 2987<td> 2988 <p> 2989 Bessel Kn: Random Data 2990 </p> 2991 </td> 2992<td> 2993 <p> 2994 <span class="blue">Max = 4.55ε (Mean = 1.12ε)</span><br> <br> 2995 (<span class="emphasis"><em><cmath>:</em></span> Max = 13.9ε (Mean = 2.91ε)) 2996 </p> 2997 </td> 2998<td> 2999 <p> 3000 <span class="blue">Max = 0.764ε (Mean = 0.0348ε)</span><br> <br> 3001 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.71ε (Mean = 1.76ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kn_Random_Data">And 3002 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 3003 Max = 7.47ε (Mean = 1.34ε)) 3004 </p> 3005 </td> 3006<td> 3007 <p> 3008 <span class="blue">Max = 4.55ε (Mean = 1.12ε)</span> 3009 </p> 3010 </td> 3011<td> 3012 <p> 3013 <span class="blue">Max = 9.34ε (Mean = 1.7ε)</span> 3014 </p> 3015 </td> 3016</tr> 3017<tr> 3018<td> 3019 <p> 3020 Bessel Kv: Random Data 3021 </p> 3022 </td> 3023<td> 3024 <p> 3025 <span class="blue">Max = 7.88ε (Mean = 1.48ε)</span><br> <br> 3026 (<span class="emphasis"><em><cmath>:</em></span> Max = 13.6ε (Mean = 2.68ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Random_Data">And 3027 other failures.</a>) 3028 </p> 3029 </td> 3030<td> 3031 <p> 3032 <span class="blue">Max = 0.507ε (Mean = 0.0313ε)</span><br> <br> 3033 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 9.71ε (Mean = 1.47ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Random_Data">And 3034 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 3035 Max = 7.37ε (Mean = 1.49ε)) 3036 </p> 3037 </td> 3038<td> 3039 <p> 3040 <span class="blue">Max = 7.88ε (Mean = 1.47ε)</span> 3041 </p> 3042 </td> 3043<td> 3044 <p> 3045 <span class="blue">Max = 8.33ε (Mean = 1.62ε)</span> 3046 </p> 3047 </td> 3048</tr> 3049</tbody> 3050</table></div> 3051</div> 3052<br class="table-break"> 3053</div> 3054<div class="section"> 3055<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 3056<a name="special_function_error_rates_rep.section_cyl_bessel_k_integer_orders_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_k_integer_orders_" title="cyl_bessel_k (integer orders)">cyl_bessel_k 3057 (integer orders)</a> 3058</h2></div></div></div> 3059<div class="table"> 3060<a name="special_function_error_rates_rep.section_cyl_bessel_k_integer_orders_.table_cyl_bessel_k_integer_orders_"></a><p class="title"><b>Table 17. Error rates for cyl_bessel_k (integer orders)</b></p> 3061<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k (integer orders)"> 3062<colgroup> 3063<col> 3064<col> 3065<col> 3066<col> 3067<col> 3068</colgroup> 3069<thead><tr> 3070<th> 3071 </th> 3072<th> 3073 <p> 3074 GNU C++ version 7.1.0<br> linux<br> long double 3075 </p> 3076 </th> 3077<th> 3078 <p> 3079 GNU C++ version 7.1.0<br> linux<br> double 3080 </p> 3081 </th> 3082<th> 3083 <p> 3084 Sun compiler version 0x5150<br> Sun Solaris<br> long double 3085 </p> 3086 </th> 3087<th> 3088 <p> 3089 Microsoft Visual C++ version 14.1<br> Win32<br> double 3090 </p> 3091 </th> 3092</tr></thead> 3093<tbody> 3094<tr> 3095<td> 3096 <p> 3097 Bessel K0: Mathworld Data (Integer Version) 3098 </p> 3099 </td> 3100<td> 3101 <p> 3102 <span class="blue">Max = 0.833ε (Mean = 0.436ε)</span><br> <br> 3103 (<span class="emphasis"><em><cmath>:</em></span> Max = 9.33ε (Mean = 3.25ε)) 3104 </p> 3105 </td> 3106<td> 3107 <p> 3108 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 3109 2.1:</em></span> Max = 1.2ε (Mean = 0.733ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 3110 Max = 0.833ε (Mean = 0.601ε)) 3111 </p> 3112 </td> 3113<td> 3114 <p> 3115 <span class="blue">Max = 0.833ε (Mean = 0.436ε)</span> 3116 </p> 3117 </td> 3118<td> 3119 <p> 3120 <span class="blue">Max = 0.833ε (Mean = 0.552ε)</span> 3121 </p> 3122 </td> 3123</tr> 3124<tr> 3125<td> 3126 <p> 3127 Bessel K1: Mathworld Data (Integer Version) 3128 </p> 3129 </td> 3130<td> 3131 <p> 3132 <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span><br> <br> 3133 (<span class="emphasis"><em><cmath>:</em></span> Max = 8.94ε (Mean = 3.19ε)) 3134 </p> 3135 </td> 3136<td> 3137 <p> 3138 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 3139 2.1:</em></span> Max = 0.626ε (Mean = 0.333ε))<br> (<span class="emphasis"><em>Rmath 3140 3.2.3:</em></span> Max = 0.894ε (Mean = 0.516ε)) 3141 </p> 3142 </td> 3143<td> 3144 <p> 3145 <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span> 3146 </p> 3147 </td> 3148<td> 3149 <p> 3150 <span class="blue">Max = 0.786ε (Mean = 0.39ε)</span> 3151 </p> 3152 </td> 3153</tr> 3154<tr> 3155<td> 3156 <p> 3157 Bessel Kn: Mathworld Data (Integer Version) 3158 </p> 3159 </td> 3160<td> 3161 <p> 3162 <span class="blue">Max = 2.6ε (Mean = 1.21ε)</span><br> <br> 3163 (<span class="emphasis"><em><cmath>:</em></span> Max = 12.9ε (Mean = 4.91ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k_integer_orders___cmath__Bessel_Kn_Mathworld_Data_Integer_Version_">And 3164 other failures.</a>) 3165 </p> 3166 </td> 3167<td> 3168 <p> 3169 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 3170 2.1:</em></span> Max = 168ε (Mean = 59.5ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 3171 Max = 8.48ε (Mean = 2.98ε)) 3172 </p> 3173 </td> 3174<td> 3175 <p> 3176 <span class="blue">Max = 2.6ε (Mean = 1.21ε)</span> 3177 </p> 3178 </td> 3179<td> 3180 <p> 3181 <span class="blue">Max = 3.63ε (Mean = 1.46ε)</span> 3182 </p> 3183 </td> 3184</tr> 3185</tbody> 3186</table></div> 3187</div> 3188<br class="table-break"> 3189</div> 3190<div class="section"> 3191<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 3192<a name="special_function_error_rates_rep.section_cyl_bessel_k_prime"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_k_prime" title="cyl_bessel_k_prime">cyl_bessel_k_prime</a> 3193</h2></div></div></div> 3194<div class="table"> 3195<a name="special_function_error_rates_rep.section_cyl_bessel_k_prime.table_cyl_bessel_k_prime"></a><p class="title"><b>Table 18. Error rates for cyl_bessel_k_prime</b></p> 3196<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k_prime"> 3197<colgroup> 3198<col> 3199<col> 3200<col> 3201<col> 3202<col> 3203</colgroup> 3204<thead><tr> 3205<th> 3206 </th> 3207<th> 3208 <p> 3209 GNU C++ version 7.1.0<br> linux<br> double 3210 </p> 3211 </th> 3212<th> 3213 <p> 3214 GNU C++ version 7.1.0<br> linux<br> long double 3215 </p> 3216 </th> 3217<th> 3218 <p> 3219 Sun compiler version 0x5150<br> Sun Solaris<br> long double 3220 </p> 3221 </th> 3222<th> 3223 <p> 3224 Microsoft Visual C++ version 14.1<br> Win32<br> double 3225 </p> 3226 </th> 3227</tr></thead> 3228<tbody> 3229<tr> 3230<td> 3231 <p> 3232 Bessel K'0: Mathworld Data 3233 </p> 3234 </td> 3235<td> 3236 <p> 3237 <span class="blue">Max = 0ε (Mean = 0ε)</span> 3238 </p> 3239 </td> 3240<td> 3241 <p> 3242 <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span> 3243 </p> 3244 </td> 3245<td> 3246 <p> 3247 <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span> 3248 </p> 3249 </td> 3250<td> 3251 <p> 3252 <span class="blue">Max = 0.786ε (Mean = 0.39ε)</span> 3253 </p> 3254 </td> 3255</tr> 3256<tr> 3257<td> 3258 <p> 3259 Bessel K'1: Mathworld Data 3260 </p> 3261 </td> 3262<td> 3263 <p> 3264 <span class="blue">Max = 0ε (Mean = 0ε)</span> 3265 </p> 3266 </td> 3267<td> 3268 <p> 3269 <span class="blue">Max = 0.736ε (Mean = 0.389ε)</span> 3270 </p> 3271 </td> 3272<td> 3273 <p> 3274 <span class="blue">Max = 0.736ε (Mean = 0.389ε)</span> 3275 </p> 3276 </td> 3277<td> 3278 <p> 3279 <span class="blue">Max = 0.761ε (Mean = 0.444ε)</span> 3280 </p> 3281 </td> 3282</tr> 3283<tr> 3284<td> 3285 <p> 3286 Bessel K'n: Mathworld Data 3287 </p> 3288 </td> 3289<td> 3290 <p> 3291 <span class="blue">Max = 0ε (Mean = 0ε)</span> 3292 </p> 3293 </td> 3294<td> 3295 <p> 3296 <span class="blue">Max = 2.16ε (Mean = 1.08ε)</span> 3297 </p> 3298 </td> 3299<td> 3300 <p> 3301 <span class="blue">Max = 2.16ε (Mean = 1.08ε)</span> 3302 </p> 3303 </td> 3304<td> 3305 <p> 3306 <span class="blue">Max = 4.17ε (Mean = 1.75ε)</span> 3307 </p> 3308 </td> 3309</tr> 3310<tr> 3311<td> 3312 <p> 3313 Bessel K'v: Mathworld Data 3314 </p> 3315 </td> 3316<td> 3317 <p> 3318 <span class="blue">Max = 0ε (Mean = 0ε)</span> 3319 </p> 3320 </td> 3321<td> 3322 <p> 3323 <span class="blue">Max = 3.94ε (Mean = 2.44ε)</span> 3324 </p> 3325 </td> 3326<td> 3327 <p> 3328 <span class="blue">Max = 3.94ε (Mean = 2.34ε)</span> 3329 </p> 3330 </td> 3331<td> 3332 <p> 3333 <span class="blue">Max = 3.94ε (Mean = 1.47ε)</span> 3334 </p> 3335 </td> 3336</tr> 3337<tr> 3338<td> 3339 <p> 3340 Bessel K'v: Mathworld Data (large values) 3341 </p> 3342 </td> 3343<td> 3344 <p> 3345 <span class="blue">Max = 0ε (Mean = 0ε)</span> 3346 </p> 3347 </td> 3348<td> 3349 <p> 3350 <span class="blue">Max = 59.2ε (Mean = 42.9ε)</span> 3351 </p> 3352 </td> 3353<td> 3354 <p> 3355 <span class="blue">Max = 58.7ε (Mean = 42.6ε)</span> 3356 </p> 3357 </td> 3358<td> 3359 <p> 3360 <span class="blue">Max = 18.6ε (Mean = 11.8ε)</span> 3361 </p> 3362 </td> 3363</tr> 3364<tr> 3365<td> 3366 <p> 3367 Bessel K'n: Random Data 3368 </p> 3369 </td> 3370<td> 3371 <p> 3372 <span class="blue">Max = 0ε (Mean = 0ε)</span> 3373 </p> 3374 </td> 3375<td> 3376 <p> 3377 <span class="blue">Max = 4.45ε (Mean = 1.19ε)</span> 3378 </p> 3379 </td> 3380<td> 3381 <p> 3382 <span class="blue">Max = 4.45ε (Mean = 1.19ε)</span> 3383 </p> 3384 </td> 3385<td> 3386 <p> 3387 <span class="blue">Max = 9.67ε (Mean = 1.73ε)</span> 3388 </p> 3389 </td> 3390</tr> 3391<tr> 3392<td> 3393 <p> 3394 Bessel K'v: Random Data 3395 </p> 3396 </td> 3397<td> 3398 <p> 3399 <span class="blue">Max = 0ε (Mean = 0ε)</span> 3400 </p> 3401 </td> 3402<td> 3403 <p> 3404 <span class="blue">Max = 7.95ε (Mean = 1.53ε)</span> 3405 </p> 3406 </td> 3407<td> 3408 <p> 3409 <span class="blue">Max = 7.95ε (Mean = 1.52ε)</span> 3410 </p> 3411 </td> 3412<td> 3413 <p> 3414 <span class="blue">Max = 8.32ε (Mean = 1.65ε)</span> 3415 </p> 3416 </td> 3417</tr> 3418</tbody> 3419</table></div> 3420</div> 3421<br class="table-break"> 3422</div> 3423<div class="section"> 3424<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 3425<a name="special_function_error_rates_rep.section_cyl_bessel_k_prime_integer_orders_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_k_prime_integer_orders_" title="cyl_bessel_k_prime (integer orders)">cyl_bessel_k_prime 3426 (integer orders)</a> 3427</h2></div></div></div> 3428<div class="table"> 3429<a name="special_function_error_rates_rep.section_cyl_bessel_k_prime_integer_orders_.table_cyl_bessel_k_prime_integer_orders_"></a><p class="title"><b>Table 19. Error rates for cyl_bessel_k_prime (integer orders)</b></p> 3430<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k_prime (integer orders)"> 3431<colgroup> 3432<col> 3433<col> 3434<col> 3435<col> 3436<col> 3437</colgroup> 3438<thead><tr> 3439<th> 3440 </th> 3441<th> 3442 <p> 3443 GNU C++ version 7.1.0<br> linux<br> double 3444 </p> 3445 </th> 3446<th> 3447 <p> 3448 GNU C++ version 7.1.0<br> linux<br> long double 3449 </p> 3450 </th> 3451<th> 3452 <p> 3453 Sun compiler version 0x5150<br> Sun Solaris<br> long double 3454 </p> 3455 </th> 3456<th> 3457 <p> 3458 Microsoft Visual C++ version 14.1<br> Win32<br> double 3459 </p> 3460 </th> 3461</tr></thead> 3462<tbody> 3463<tr> 3464<td> 3465 <p> 3466 Bessel K'0: Mathworld Data (Integer Version) 3467 </p> 3468 </td> 3469<td> 3470 <p> 3471 <span class="blue">Max = 0ε (Mean = 0ε)</span> 3472 </p> 3473 </td> 3474<td> 3475 <p> 3476 <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span> 3477 </p> 3478 </td> 3479<td> 3480 <p> 3481 <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span> 3482 </p> 3483 </td> 3484<td> 3485 <p> 3486 <span class="blue">Max = 0.786ε (Mean = 0.39ε)</span> 3487 </p> 3488 </td> 3489</tr> 3490<tr> 3491<td> 3492 <p> 3493 Bessel K'1: Mathworld Data (Integer Version) 3494 </p> 3495 </td> 3496<td> 3497 <p> 3498 <span class="blue">Max = 0ε (Mean = 0ε)</span> 3499 </p> 3500 </td> 3501<td> 3502 <p> 3503 <span class="blue">Max = 0.736ε (Mean = 0.389ε)</span> 3504 </p> 3505 </td> 3506<td> 3507 <p> 3508 <span class="blue">Max = 0.736ε (Mean = 0.389ε)</span> 3509 </p> 3510 </td> 3511<td> 3512 <p> 3513 <span class="blue">Max = 0.761ε (Mean = 0.444ε)</span> 3514 </p> 3515 </td> 3516</tr> 3517<tr> 3518<td> 3519 <p> 3520 Bessel K'n: Mathworld Data (Integer Version) 3521 </p> 3522 </td> 3523<td> 3524 <p> 3525 <span class="blue">Max = 0ε (Mean = 0ε)</span> 3526 </p> 3527 </td> 3528<td> 3529 <p> 3530 <span class="blue">Max = 2.16ε (Mean = 1.08ε)</span> 3531 </p> 3532 </td> 3533<td> 3534 <p> 3535 <span class="blue">Max = 2.16ε (Mean = 1.08ε)</span> 3536 </p> 3537 </td> 3538<td> 3539 <p> 3540 <span class="blue">Max = 4.17ε (Mean = 1.75ε)</span> 3541 </p> 3542 </td> 3543</tr> 3544</tbody> 3545</table></div> 3546</div> 3547<br class="table-break"> 3548</div> 3549<div class="section"> 3550<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 3551<a name="special_function_error_rates_rep.section_cyl_neumann"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_neumann" title="cyl_neumann">cyl_neumann</a> 3552</h2></div></div></div> 3553<div class="table"> 3554<a name="special_function_error_rates_rep.section_cyl_neumann.table_cyl_neumann"></a><p class="title"><b>Table 20. Error rates for cyl_neumann</b></p> 3555<div class="table-contents"><table class="table" summary="Error rates for cyl_neumann"> 3556<colgroup> 3557<col> 3558<col> 3559<col> 3560<col> 3561<col> 3562</colgroup> 3563<thead><tr> 3564<th> 3565 </th> 3566<th> 3567 <p> 3568 GNU C++ version 7.1.0<br> linux<br> long double 3569 </p> 3570 </th> 3571<th> 3572 <p> 3573 GNU C++ version 7.1.0<br> linux<br> double 3574 </p> 3575 </th> 3576<th> 3577 <p> 3578 Sun compiler version 0x5150<br> Sun Solaris<br> long double 3579 </p> 3580 </th> 3581<th> 3582 <p> 3583 Microsoft Visual C++ version 14.1<br> Win32<br> double 3584 </p> 3585 </th> 3586</tr></thead> 3587<tbody> 3588<tr> 3589<td> 3590 <p> 3591 Y0: Mathworld Data 3592 </p> 3593 </td> 3594<td> 3595 <p> 3596 <span class="blue">Max = 5.53ε (Mean = 2.4ε)</span><br> <br> 3597 (<span class="emphasis"><em><cmath>:</em></span> Max = 2.05e+05ε (Mean = 6.87e+04ε)) 3598 </p> 3599 </td> 3600<td> 3601 <p> 3602 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 3603 2.1:</em></span> Max = 60.9ε (Mean = 20.4ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 3604 Max = 167ε (Mean = 56.5ε)) 3605 </p> 3606 </td> 3607<td> 3608 <p> 3609 <span class="blue">Max = 5.53ε (Mean = 2.4ε)</span> 3610 </p> 3611 </td> 3612<td> 3613 <p> 3614 <span class="blue">Max = 4.61ε (Mean = 2.29ε)</span> 3615 </p> 3616 </td> 3617</tr> 3618<tr> 3619<td> 3620 <p> 3621 Y1: Mathworld Data 3622 </p> 3623 </td> 3624<td> 3625 <p> 3626 <span class="blue">Max = 6.33ε (Mean = 2.25ε)</span><br> <br> 3627 (<span class="emphasis"><em><cmath>:</em></span> Max = 9.71e+03ε (Mean = 4.08e+03ε)) 3628 </p> 3629 </td> 3630<td> 3631 <p> 3632 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 3633 2.1:</em></span> Max = 23.4ε (Mean = 8.1ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 3634 Max = 193ε (Mean = 64.4ε)) 3635 </p> 3636 </td> 3637<td> 3638 <p> 3639 <span class="blue">Max = 6.33ε (Mean = 2.29ε)</span> 3640 </p> 3641 </td> 3642<td> 3643 <p> 3644 <span class="blue">Max = 4.75ε (Mean = 1.72ε)</span> 3645 </p> 3646 </td> 3647</tr> 3648<tr> 3649<td> 3650 <p> 3651 Yn: Mathworld Data 3652 </p> 3653 </td> 3654<td> 3655 <p> 3656 <span class="blue">Max = 55.2ε (Mean = 17.8ε)</span><br> <br> 3657 (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 2.2e+20ε (Mean 3658 = 6.97e+19ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yn_Mathworld_Data">And 3659 other failures.</a>)</span> 3660 </p> 3661 </td> 3662<td> 3663 <p> 3664 <span class="blue">Max = 0.993ε (Mean = 0.314ε)</span><br> <br> 3665 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.41e+05ε (Mean = 7.62e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yn_Mathworld_Data">And 3666 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 3667 Max = 1.24e+04ε (Mean = 4e+03ε)) 3668 </p> 3669 </td> 3670<td> 3671 <p> 3672 <span class="blue">Max = 55.2ε (Mean = 17.8ε)</span> 3673 </p> 3674 </td> 3675<td> 3676 <p> 3677 <span class="blue">Max = 35ε (Mean = 11.9ε)</span> 3678 </p> 3679 </td> 3680</tr> 3681<tr> 3682<td> 3683 <p> 3684 Yv: Mathworld Data 3685 </p> 3686 </td> 3687<td> 3688 <p> 3689 <span class="blue">Max = 10.7ε (Mean = 4.93ε)</span><br> <br> 3690 (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 3.49e+15ε (Mean 3691 = 1.05e+15ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Mathworld_Data">And 3692 other failures.</a>)</span> 3693 </p> 3694 </td> 3695<td> 3696 <p> 3697 <span class="blue">Max = 10ε (Mean = 3.02ε)</span><br> <br> (<span class="emphasis"><em>GSL 3698 2.1:</em></span> Max = 1.07e+05ε (Mean = 3.22e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yv_Mathworld_Data">And 3699 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 3700 Max = 243ε (Mean = 73.9ε)) 3701 </p> 3702 </td> 3703<td> 3704 <p> 3705 <span class="blue">Max = 10.7ε (Mean = 5.1ε)</span> 3706 </p> 3707 </td> 3708<td> 3709 <p> 3710 <span class="blue">Max = 7.89ε (Mean = 3.27ε)</span> 3711 </p> 3712 </td> 3713</tr> 3714<tr> 3715<td> 3716 <p> 3717 Yv: Mathworld Data (large values) 3718 </p> 3719 </td> 3720<td> 3721 <p> 3722 <span class="blue">Max = 1.7ε (Mean = 1.33ε)</span><br> <br> 3723 (<span class="emphasis"><em><cmath>:</em></span> Max = 43.2ε (Mean = 16.3ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Mathworld_Data_large_values_">And 3724 other failures.</a>) 3725 </p> 3726 </td> 3727<td> 3728 <p> 3729 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 3730 2.1:</em></span> Max = 60.8ε (Mean = 23ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yv_Mathworld_Data_large_values_">And 3731 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 3732 Max = 0.682ε (Mean = 0.335ε)) 3733 </p> 3734 </td> 3735<td> 3736 <p> 3737 <span class="blue">Max = 1.7ε (Mean = 1.33ε)</span> 3738 </p> 3739 </td> 3740<td> 3741 <p> 3742 <span class="blue">Max = 0.682ε (Mean = 0.423ε)</span> 3743 </p> 3744 </td> 3745</tr> 3746<tr> 3747<td> 3748 <p> 3749 Y0 and Y1: Random Data 3750 </p> 3751 </td> 3752<td> 3753 <p> 3754 <span class="blue">Max = 10.8ε (Mean = 3.04ε)</span><br> <br> 3755 (<span class="emphasis"><em><cmath>:</em></span> Max = 2.59e+03ε (Mean = 500ε)) 3756 </p> 3757 </td> 3758<td> 3759 <p> 3760 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 3761 2.1:</em></span> Max = 34.4ε (Mean = 8.9ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 3762 Max = 83ε (Mean = 14.2ε)) 3763 </p> 3764 </td> 3765<td> 3766 <p> 3767 <span class="blue">Max = 10.8ε (Mean = 3.04ε)</span> 3768 </p> 3769 </td> 3770<td> 3771 <p> 3772 <span class="blue">Max = 4.17ε (Mean = 1.24ε)</span> 3773 </p> 3774 </td> 3775</tr> 3776<tr> 3777<td> 3778 <p> 3779 Yn: Random Data 3780 </p> 3781 </td> 3782<td> 3783 <p> 3784 <span class="blue">Max = 338ε (Mean = 27.5ε)</span><br> <br> 3785 (<span class="emphasis"><em><cmath>:</em></span> Max = 4.01e+03ε (Mean = 348ε)) 3786 </p> 3787 </td> 3788<td> 3789 <p> 3790 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 3791 2.1:</em></span> Max = 500ε (Mean = 47.8ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 3792 Max = 691ε (Mean = 67.9ε)) 3793 </p> 3794 </td> 3795<td> 3796 <p> 3797 <span class="blue">Max = 338ε (Mean = 27.5ε)</span> 3798 </p> 3799 </td> 3800<td> 3801 <p> 3802 <span class="blue">Max = 117ε (Mean = 10.2ε)</span> 3803 </p> 3804 </td> 3805</tr> 3806<tr> 3807<td> 3808 <p> 3809 Yv: Random Data 3810 </p> 3811 </td> 3812<td> 3813 <p> 3814 <span class="blue">Max = 2.08e+03ε (Mean = 149ε)</span><br> <br> 3815 (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = +INFε (Mean 3816 = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Random_Data">And 3817 other failures.</a>)</span> 3818 </p> 3819 </td> 3820<td> 3821 <p> 3822 <span class="blue">Max = 1.53ε (Mean = 0.102ε)</span><br> <br> 3823 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.41e+06ε (Mean = 7.67e+04ε))<br> 3824 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.79e+05ε (Mean = 9.64e+03ε)) 3825 </p> 3826 </td> 3827<td> 3828 <p> 3829 <span class="blue">Max = 2.08e+03ε (Mean = 149ε)</span> 3830 </p> 3831 </td> 3832<td> 3833 <p> 3834 <span class="blue">Max = 1.23e+03ε (Mean = 69.9ε)</span> 3835 </p> 3836 </td> 3837</tr> 3838</tbody> 3839</table></div> 3840</div> 3841<br class="table-break"> 3842</div> 3843<div class="section"> 3844<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 3845<a name="special_function_error_rates_rep.section_cyl_neumann_integer_orders_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_neumann_integer_orders_" title="cyl_neumann (integer orders)">cyl_neumann 3846 (integer orders)</a> 3847</h2></div></div></div> 3848<div class="table"> 3849<a name="special_function_error_rates_rep.section_cyl_neumann_integer_orders_.table_cyl_neumann_integer_orders_"></a><p class="title"><b>Table 21. Error rates for cyl_neumann (integer orders)</b></p> 3850<div class="table-contents"><table class="table" summary="Error rates for cyl_neumann (integer orders)"> 3851<colgroup> 3852<col> 3853<col> 3854<col> 3855<col> 3856<col> 3857</colgroup> 3858<thead><tr> 3859<th> 3860 </th> 3861<th> 3862 <p> 3863 GNU C++ version 7.1.0<br> linux<br> long double 3864 </p> 3865 </th> 3866<th> 3867 <p> 3868 GNU C++ version 7.1.0<br> linux<br> double 3869 </p> 3870 </th> 3871<th> 3872 <p> 3873 Sun compiler version 0x5150<br> Sun Solaris<br> long double 3874 </p> 3875 </th> 3876<th> 3877 <p> 3878 Microsoft Visual C++ version 14.1<br> Win32<br> double 3879 </p> 3880 </th> 3881</tr></thead> 3882<tbody> 3883<tr> 3884<td> 3885 <p> 3886 Y0: Mathworld Data (Integer Version) 3887 </p> 3888 </td> 3889<td> 3890 <p> 3891 <span class="blue">Max = 5.53ε (Mean = 2.4ε)</span><br> <br> 3892 (<span class="emphasis"><em><cmath>:</em></span> Max = 2.05e+05ε (Mean = 6.87e+04ε)) 3893 </p> 3894 </td> 3895<td> 3896 <p> 3897 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 3898 2.1:</em></span> Max = 6.46ε (Mean = 2.38ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 3899 Max = 167ε (Mean = 56.5ε)) 3900 </p> 3901 </td> 3902<td> 3903 <p> 3904 <span class="blue">Max = 5.53ε (Mean = 2.4ε)</span> 3905 </p> 3906 </td> 3907<td> 3908 <p> 3909 <span class="blue">Max = 4.61ε (Mean = 2.29ε)</span><br> <br> 3910 (<span class="emphasis"><em><math.h>:</em></span> Max = 5.37e+03ε (Mean = 1.81e+03ε)) 3911 </p> 3912 </td> 3913</tr> 3914<tr> 3915<td> 3916 <p> 3917 Y1: Mathworld Data (Integer Version) 3918 </p> 3919 </td> 3920<td> 3921 <p> 3922 <span class="blue">Max = 6.33ε (Mean = 2.25ε)</span><br> <br> 3923 (<span class="emphasis"><em><cmath>:</em></span> Max = 9.71e+03ε (Mean = 4.08e+03ε)) 3924 </p> 3925 </td> 3926<td> 3927 <p> 3928 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 3929 2.1:</em></span> Max = 1.51ε (Mean = 0.839ε))<br> (<span class="emphasis"><em>Rmath 3930 3.2.3:</em></span> Max = 193ε (Mean = 64.4ε)) 3931 </p> 3932 </td> 3933<td> 3934 <p> 3935 <span class="blue">Max = 6.33ε (Mean = 2.29ε)</span> 3936 </p> 3937 </td> 3938<td> 3939 <p> 3940 <span class="blue">Max = 4.75ε (Mean = 1.72ε)</span><br> <br> 3941 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.86e+04ε (Mean = 6.2e+03ε)) 3942 </p> 3943 </td> 3944</tr> 3945<tr> 3946<td> 3947 <p> 3948 Yn: Mathworld Data (Integer Version) 3949 </p> 3950 </td> 3951<td> 3952 <p> 3953 <span class="blue">Max = 55.2ε (Mean = 17.8ε)</span><br> <br> 3954 (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 2.2e+20ε (Mean 3955 = 6.97e+19ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann_integer_orders___cmath__Yn_Mathworld_Data_Integer_Version_">And 3956 other failures.</a>)</span> 3957 </p> 3958 </td> 3959<td> 3960 <p> 3961 <span class="blue">Max = 0.993ε (Mean = 0.314ε)</span><br> <br> 3962 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.41e+05ε (Mean = 7.62e+04ε))<br> 3963 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.24e+04ε (Mean = 4e+03ε)) 3964 </p> 3965 </td> 3966<td> 3967 <p> 3968 <span class="blue">Max = 55.2ε (Mean = 17.8ε)</span> 3969 </p> 3970 </td> 3971<td> 3972 <p> 3973 <span class="blue">Max = 35ε (Mean = 11.9ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span> 3974 Max = 2.49e+05ε (Mean = 8.14e+04ε)) 3975 </p> 3976 </td> 3977</tr> 3978</tbody> 3979</table></div> 3980</div> 3981<br class="table-break"> 3982</div> 3983<div class="section"> 3984<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 3985<a name="special_function_error_rates_rep.section_cyl_neumann_prime"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_neumann_prime" title="cyl_neumann_prime">cyl_neumann_prime</a> 3986</h2></div></div></div> 3987<div class="table"> 3988<a name="special_function_error_rates_rep.section_cyl_neumann_prime.table_cyl_neumann_prime"></a><p class="title"><b>Table 22. Error rates for cyl_neumann_prime</b></p> 3989<div class="table-contents"><table class="table" summary="Error rates for cyl_neumann_prime"> 3990<colgroup> 3991<col> 3992<col> 3993<col> 3994<col> 3995<col> 3996</colgroup> 3997<thead><tr> 3998<th> 3999 </th> 4000<th> 4001 <p> 4002 GNU C++ version 7.1.0<br> linux<br> double 4003 </p> 4004 </th> 4005<th> 4006 <p> 4007 GNU C++ version 7.1.0<br> linux<br> long double 4008 </p> 4009 </th> 4010<th> 4011 <p> 4012 Sun compiler version 0x5150<br> Sun Solaris<br> long double 4013 </p> 4014 </th> 4015<th> 4016 <p> 4017 Microsoft Visual C++ version 14.1<br> Win32<br> double 4018 </p> 4019 </th> 4020</tr></thead> 4021<tbody> 4022<tr> 4023<td> 4024 <p> 4025 Y'0: Mathworld Data 4026 </p> 4027 </td> 4028<td> 4029 <p> 4030 <span class="blue">Max = 0ε (Mean = 0ε)</span> 4031 </p> 4032 </td> 4033<td> 4034 <p> 4035 <span class="blue">Max = 6.33ε (Mean = 3.12ε)</span> 4036 </p> 4037 </td> 4038<td> 4039 <p> 4040 <span class="blue">Max = 6.33ε (Mean = 3.14ε)</span> 4041 </p> 4042 </td> 4043<td> 4044 <p> 4045 <span class="blue">Max = 4.75ε (Mean = 1.75ε)</span> 4046 </p> 4047 </td> 4048</tr> 4049<tr> 4050<td> 4051 <p> 4052 Y'1: Mathworld Data 4053 </p> 4054 </td> 4055<td> 4056 <p> 4057 <span class="blue">Max = 0.58ε (Mean = 0.193ε)</span> 4058 </p> 4059 </td> 4060<td> 4061 <p> 4062 <span class="blue">Max = 37.1ε (Mean = 12.8ε)</span> 4063 </p> 4064 </td> 4065<td> 4066 <p> 4067 <span class="blue">Max = 34ε (Mean = 11.8ε)</span> 4068 </p> 4069 </td> 4070<td> 4071 <p> 4072 <span class="blue">Max = 3.08ε (Mean = 1.2ε)</span> 4073 </p> 4074 </td> 4075</tr> 4076<tr> 4077<td> 4078 <p> 4079 Y'n: Mathworld Data 4080 </p> 4081 </td> 4082<td> 4083 <p> 4084 <span class="blue">Max = 2.05ε (Mean = 0.677ε)</span> 4085 </p> 4086 </td> 4087<td> 4088 <p> 4089 <span class="blue">Max = 56ε (Mean = 18.2ε)</span> 4090 </p> 4091 </td> 4092<td> 4093 <p> 4094 <span class="blue">Max = 56ε (Mean = 21.3ε)</span> 4095 </p> 4096 </td> 4097<td> 4098 <p> 4099 <span class="blue">Max = 563ε (Mean = 178ε)</span> 4100 </p> 4101 </td> 4102</tr> 4103<tr> 4104<td> 4105 <p> 4106 Y'v: Mathworld Data 4107 </p> 4108 </td> 4109<td> 4110 <p> 4111 <span class="blue">Max = 21.5ε (Mean = 6.49ε)</span> 4112 </p> 4113 </td> 4114<td> 4115 <p> 4116 <span class="blue">Max = 42.5ε (Mean = 13.4ε)</span> 4117 </p> 4118 </td> 4119<td> 4120 <p> 4121 <span class="blue">Max = 42.5ε (Mean = 13.6ε)</span> 4122 </p> 4123 </td> 4124<td> 4125 <p> 4126 <span class="blue">Max = 23.7ε (Mean = 10.1ε)</span> 4127 </p> 4128 </td> 4129</tr> 4130<tr> 4131<td> 4132 <p> 4133 Y'v: Mathworld Data (large values) 4134 </p> 4135 </td> 4136<td> 4137 <p> 4138 <span class="blue">Max = 0ε (Mean = 0ε)</span> 4139 </p> 4140 </td> 4141<td> 4142 <p> 4143 <span class="blue">Max = 1.57ε (Mean = 1.24ε)</span> 4144 </p> 4145 </td> 4146<td> 4147 <p> 4148 <span class="blue">Max = 1.57ε (Mean = 1.24ε)</span> 4149 </p> 4150 </td> 4151<td> 4152 <p> 4153 <span class="blue">Max = 0.627ε (Mean = 0.237ε)</span> 4154 </p> 4155 </td> 4156</tr> 4157<tr> 4158<td> 4159 <p> 4160 Y'0 and Y'1: Random Data 4161 </p> 4162 </td> 4163<td> 4164 <p> 4165 <span class="blue">Max = 0ε (Mean = 0ε)</span> 4166 </p> 4167 </td> 4168<td> 4169 <p> 4170 <span class="blue">Max = 23.8ε (Mean = 3.69ε)</span> 4171 </p> 4172 </td> 4173<td> 4174 <p> 4175 <span class="blue">Max = 23.8ε (Mean = 3.69ε)</span> 4176 </p> 4177 </td> 4178<td> 4179 <p> 4180 <span class="blue">Max = 5.95ε (Mean = 1.36ε)</span> 4181 </p> 4182 </td> 4183</tr> 4184<tr> 4185<td> 4186 <p> 4187 Y'n: Random Data 4188 </p> 4189 </td> 4190<td> 4191 <p> 4192 <span class="blue">Max = 1.53ε (Mean = 0.0885ε)</span> 4193 </p> 4194 </td> 4195<td> 4196 <p> 4197 <span class="blue">Max = 2.35e+03ε (Mean = 136ε)</span> 4198 </p> 4199 </td> 4200<td> 4201 <p> 4202 <span class="blue">Max = 2.35e+03ε (Mean = 136ε)</span> 4203 </p> 4204 </td> 4205<td> 4206 <p> 4207 <span class="blue">Max = 621ε (Mean = 36ε)</span> 4208 </p> 4209 </td> 4210</tr> 4211<tr> 4212<td> 4213 <p> 4214 Y'v: Random Data 4215 </p> 4216 </td> 4217<td> 4218 <p> 4219 <span class="blue">Max = 56.8ε (Mean = 2.59ε)</span> 4220 </p> 4221 </td> 4222<td> 4223 <p> 4224 <span class="blue">Max = 1.16e+05ε (Mean = 5.28e+03ε)</span> 4225 </p> 4226 </td> 4227<td> 4228 <p> 4229 <span class="blue">Max = 1.16e+05ε (Mean = 5.28e+03ε)</span> 4230 </p> 4231 </td> 4232<td> 4233 <p> 4234 <span class="blue">Max = 3.23e+04ε (Mean = 1.13e+03ε)</span> 4235 </p> 4236 </td> 4237</tr> 4238</tbody> 4239</table></div> 4240</div> 4241<br class="table-break"> 4242</div> 4243<div class="section"> 4244<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 4245<a name="special_function_error_rates_rep.section_cyl_neumann_prime_integer_orders_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_neumann_prime_integer_orders_" title="cyl_neumann_prime (integer orders)">cyl_neumann_prime 4246 (integer orders)</a> 4247</h2></div></div></div> 4248<div class="table"> 4249<a name="special_function_error_rates_rep.section_cyl_neumann_prime_integer_orders_.table_cyl_neumann_prime_integer_orders_"></a><p class="title"><b>Table 23. Error rates for cyl_neumann_prime (integer orders)</b></p> 4250<div class="table-contents"><table class="table" summary="Error rates for cyl_neumann_prime (integer orders)"> 4251<colgroup> 4252<col> 4253<col> 4254<col> 4255<col> 4256<col> 4257</colgroup> 4258<thead><tr> 4259<th> 4260 </th> 4261<th> 4262 <p> 4263 GNU C++ version 7.1.0<br> linux<br> double 4264 </p> 4265 </th> 4266<th> 4267 <p> 4268 GNU C++ version 7.1.0<br> linux<br> long double 4269 </p> 4270 </th> 4271<th> 4272 <p> 4273 Sun compiler version 0x5150<br> Sun Solaris<br> long double 4274 </p> 4275 </th> 4276<th> 4277 <p> 4278 Microsoft Visual C++ version 14.1<br> Win32<br> double 4279 </p> 4280 </th> 4281</tr></thead> 4282<tbody> 4283<tr> 4284<td> 4285 <p> 4286 Y'0: Mathworld Data (Integer Version) 4287 </p> 4288 </td> 4289<td> 4290 <p> 4291 <span class="blue">Max = 0ε (Mean = 0ε)</span> 4292 </p> 4293 </td> 4294<td> 4295 <p> 4296 <span class="blue">Max = 6.33ε (Mean = 3.12ε)</span> 4297 </p> 4298 </td> 4299<td> 4300 <p> 4301 <span class="blue">Max = 6.33ε (Mean = 3.14ε)</span> 4302 </p> 4303 </td> 4304<td> 4305 <p> 4306 <span class="blue">Max = 4.75ε (Mean = 1.75ε)</span> 4307 </p> 4308 </td> 4309</tr> 4310<tr> 4311<td> 4312 <p> 4313 Y'1: Mathworld Data (Integer Version) 4314 </p> 4315 </td> 4316<td> 4317 <p> 4318 <span class="blue">Max = 0.58ε (Mean = 0.193ε)</span> 4319 </p> 4320 </td> 4321<td> 4322 <p> 4323 <span class="blue">Max = 37.1ε (Mean = 12.8ε)</span> 4324 </p> 4325 </td> 4326<td> 4327 <p> 4328 <span class="blue">Max = 34ε (Mean = 11.8ε)</span> 4329 </p> 4330 </td> 4331<td> 4332 <p> 4333 <span class="blue">Max = 3.08ε (Mean = 1.2ε)</span> 4334 </p> 4335 </td> 4336</tr> 4337<tr> 4338<td> 4339 <p> 4340 Y'n: Mathworld Data (Integer Version) 4341 </p> 4342 </td> 4343<td> 4344 <p> 4345 <span class="blue">Max = 2.05ε (Mean = 0.677ε)</span> 4346 </p> 4347 </td> 4348<td> 4349 <p> 4350 <span class="blue">Max = 56ε (Mean = 18.2ε)</span> 4351 </p> 4352 </td> 4353<td> 4354 <p> 4355 <span class="blue">Max = 56ε (Mean = 21.3ε)</span> 4356 </p> 4357 </td> 4358<td> 4359 <p> 4360 <span class="blue">Max = 563ε (Mean = 178ε)</span> 4361 </p> 4362 </td> 4363</tr> 4364</tbody> 4365</table></div> 4366</div> 4367<br class="table-break"> 4368</div> 4369<div class="section"> 4370<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 4371<a name="special_function_error_rates_rep.section_digamma"></a><a class="link" href="index.html#special_function_error_rates_rep.section_digamma" title="digamma">digamma</a> 4372</h2></div></div></div> 4373<div class="table"> 4374<a name="special_function_error_rates_rep.section_digamma.table_digamma"></a><p class="title"><b>Table 24. Error rates for digamma</b></p> 4375<div class="table-contents"><table class="table" summary="Error rates for digamma"> 4376<colgroup> 4377<col> 4378<col> 4379<col> 4380<col> 4381<col> 4382</colgroup> 4383<thead><tr> 4384<th> 4385 </th> 4386<th> 4387 <p> 4388 GNU C++ version 7.1.0<br> linux<br> double 4389 </p> 4390 </th> 4391<th> 4392 <p> 4393 GNU C++ version 7.1.0<br> linux<br> long double 4394 </p> 4395 </th> 4396<th> 4397 <p> 4398 Sun compiler version 0x5150<br> Sun Solaris<br> long double 4399 </p> 4400 </th> 4401<th> 4402 <p> 4403 Microsoft Visual C++ version 14.1<br> Win32<br> double 4404 </p> 4405 </th> 4406</tr></thead> 4407<tbody> 4408<tr> 4409<td> 4410 <p> 4411 Digamma Function: Large Values 4412 </p> 4413 </td> 4414<td> 4415 <p> 4416 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 4417 2.1:</em></span> Max = 1.84ε (Mean = 0.71ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 4418 Max = 1.18ε (Mean = 0.331ε)) 4419 </p> 4420 </td> 4421<td> 4422 <p> 4423 <span class="blue">Max = 1.39ε (Mean = 0.413ε)</span> 4424 </p> 4425 </td> 4426<td> 4427 <p> 4428 <span class="blue">Max = 1.39ε (Mean = 0.413ε)</span> 4429 </p> 4430 </td> 4431<td> 4432 <p> 4433 <span class="blue">Max = 0.98ε (Mean = 0.369ε)</span> 4434 </p> 4435 </td> 4436</tr> 4437<tr> 4438<td> 4439 <p> 4440 Digamma Function: Near the Positive Root 4441 </p> 4442 </td> 4443<td> 4444 <p> 4445 <span class="blue">Max = 0.891ε (Mean = 0.0995ε)</span><br> <br> 4446 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 135ε (Mean = 11.9ε))<br> (<span class="emphasis"><em>Rmath 4447 3.2.3:</em></span> Max = 2.02e+03ε (Mean = 256ε)) 4448 </p> 4449 </td> 4450<td> 4451 <p> 4452 <span class="blue">Max = 1.37ε (Mean = 0.477ε)</span> 4453 </p> 4454 </td> 4455<td> 4456 <p> 4457 <span class="blue">Max = 1.31ε (Mean = 0.471ε)</span> 4458 </p> 4459 </td> 4460<td> 4461 <p> 4462 <span class="blue">Max = 0.997ε (Mean = 0.527ε)</span> 4463 </p> 4464 </td> 4465</tr> 4466<tr> 4467<td> 4468 <p> 4469 Digamma Function: Near Zero 4470 </p> 4471 </td> 4472<td> 4473 <p> 4474 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 4475 2.1:</em></span> Max = 0.953ε (Mean = 0.348ε))<br> (<span class="emphasis"><em>Rmath 4476 3.2.3:</em></span> Max = 1.17ε (Mean = 0.564ε)) 4477 </p> 4478 </td> 4479<td> 4480 <p> 4481 <span class="blue">Max = 0.984ε (Mean = 0.361ε)</span> 4482 </p> 4483 </td> 4484<td> 4485 <p> 4486 <span class="blue">Max = 0.984ε (Mean = 0.361ε)</span> 4487 </p> 4488 </td> 4489<td> 4490 <p> 4491 <span class="blue">Max = 0.953ε (Mean = 0.337ε)</span> 4492 </p> 4493 </td> 4494</tr> 4495<tr> 4496<td> 4497 <p> 4498 Digamma Function: Negative Values 4499 </p> 4500 </td> 4501<td> 4502 <p> 4503 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 4504 2.1:</em></span> Max = 4.56e+04ε (Mean = 3.91e+03ε))<br> (<span class="emphasis"><em>Rmath 4505 3.2.3:</em></span> Max = 4.6e+04ε (Mean = 3.94e+03ε)) 4506 </p> 4507 </td> 4508<td> 4509 <p> 4510 <span class="blue">Max = 180ε (Mean = 13ε)</span> 4511 </p> 4512 </td> 4513<td> 4514 <p> 4515 <span class="blue">Max = 180ε (Mean = 13ε)</span> 4516 </p> 4517 </td> 4518<td> 4519 <p> 4520 <span class="blue">Max = 214ε (Mean = 16.1ε)</span> 4521 </p> 4522 </td> 4523</tr> 4524<tr> 4525<td> 4526 <p> 4527 Digamma Function: Values near 0 4528 </p> 4529 </td> 4530<td> 4531 <p> 4532 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 4533 2.1:</em></span> Max = 0.866ε (Mean = 0.387ε))<br> (<span class="emphasis"><em>Rmath 4534 3.2.3:</em></span> Max = 3.58e+05ε (Mean = 1.6e+05ε)) 4535 </p> 4536 </td> 4537<td> 4538 <p> 4539 <span class="blue">Max = 1ε (Mean = 0.592ε)</span> 4540 </p> 4541 </td> 4542<td> 4543 <p> 4544 <span class="blue">Max = 1ε (Mean = 0.592ε)</span> 4545 </p> 4546 </td> 4547<td> 4548 <p> 4549 <span class="blue">Max = 0ε (Mean = 0ε)</span> 4550 </p> 4551 </td> 4552</tr> 4553<tr> 4554<td> 4555 <p> 4556 Digamma Function: Integer arguments 4557 </p> 4558 </td> 4559<td> 4560 <p> 4561 <span class="blue">Max = 0.992ε (Mean = 0.215ε)</span><br> <br> 4562 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.18ε (Mean = 0.607ε))<br> (<span class="emphasis"><em>Rmath 4563 3.2.3:</em></span> Max = 4.33ε (Mean = 0.982ε)) 4564 </p> 4565 </td> 4566<td> 4567 <p> 4568 <span class="blue">Max = 0.888ε (Mean = 0.403ε)</span> 4569 </p> 4570 </td> 4571<td> 4572 <p> 4573 <span class="blue">Max = 0.888ε (Mean = 0.403ε)</span> 4574 </p> 4575 </td> 4576<td> 4577 <p> 4578 <span class="blue">Max = 0.992ε (Mean = 0.452ε)</span> 4579 </p> 4580 </td> 4581</tr> 4582<tr> 4583<td> 4584 <p> 4585 Digamma Function: Half integer arguments 4586 </p> 4587 </td> 4588<td> 4589 <p> 4590 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 4591 2.1:</em></span> Max = 1.09ε (Mean = 0.531ε))<br> (<span class="emphasis"><em>Rmath 4592 3.2.3:</em></span> Max = 46.2ε (Mean = 7.24ε)) 4593 </p> 4594 </td> 4595<td> 4596 <p> 4597 <span class="blue">Max = 0.906ε (Mean = 0.409ε)</span> 4598 </p> 4599 </td> 4600<td> 4601 <p> 4602 <span class="blue">Max = 0.906ε (Mean = 0.409ε)</span> 4603 </p> 4604 </td> 4605<td> 4606 <p> 4607 <span class="blue">Max = 0.78ε (Mean = 0.314ε)</span> 4608 </p> 4609 </td> 4610</tr> 4611</tbody> 4612</table></div> 4613</div> 4614<br class="table-break"> 4615</div> 4616<div class="section"> 4617<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 4618<a name="special_function_error_rates_rep.section_ellint_1"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_1" title="ellint_1">ellint_1</a> 4619</h2></div></div></div> 4620<div class="table"> 4621<a name="special_function_error_rates_rep.section_ellint_1.table_ellint_1"></a><p class="title"><b>Table 25. Error rates for ellint_1</b></p> 4622<div class="table-contents"><table class="table" summary="Error rates for ellint_1"> 4623<colgroup> 4624<col> 4625<col> 4626<col> 4627<col> 4628<col> 4629</colgroup> 4630<thead><tr> 4631<th> 4632 </th> 4633<th> 4634 <p> 4635 GNU C++ version 7.1.0<br> linux<br> long double 4636 </p> 4637 </th> 4638<th> 4639 <p> 4640 GNU C++ version 7.1.0<br> linux<br> double 4641 </p> 4642 </th> 4643<th> 4644 <p> 4645 Sun compiler version 0x5150<br> Sun Solaris<br> long double 4646 </p> 4647 </th> 4648<th> 4649 <p> 4650 Microsoft Visual C++ version 14.1<br> Win32<br> double 4651 </p> 4652 </th> 4653</tr></thead> 4654<tbody> 4655<tr> 4656<td> 4657 <p> 4658 Elliptic Integral F: Mathworld Data 4659 </p> 4660 </td> 4661<td> 4662 <p> 4663 <span class="blue">Max = 0.94ε (Mean = 0.509ε)</span><br> <br> 4664 (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = +INFε (Mean 4665 = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_1__cmath__Elliptic_Integral_F_Mathworld_Data">And 4666 other failures.</a>)</span> 4667 </p> 4668 </td> 4669<td> 4670 <p> 4671 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 4672 2.1:</em></span> Max = 0.919ε (Mean = 0.544ε)) 4673 </p> 4674 </td> 4675<td> 4676 <p> 4677 <span class="blue">Max = 0.94ε (Mean = 0.509ε)</span> 4678 </p> 4679 </td> 4680<td> 4681 <p> 4682 <span class="blue">Max = 0.919ε (Mean = 0.542ε)</span> 4683 </p> 4684 </td> 4685</tr> 4686<tr> 4687<td> 4688 <p> 4689 Elliptic Integral F: Random Data 4690 </p> 4691 </td> 4692<td> 4693 <p> 4694 <span class="blue">Max = 1.57ε (Mean = 0.56ε)</span><br> <br> 4695 (<span class="emphasis"><em><cmath>:</em></span> Max = 2.56ε (Mean = 0.816ε)) 4696 </p> 4697 </td> 4698<td> 4699 <p> 4700 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 4701 2.1:</em></span> Max = 2.99ε (Mean = 0.797ε)) 4702 </p> 4703 </td> 4704<td> 4705 <p> 4706 <span class="blue">Max = 1.57ε (Mean = 0.561ε)</span> 4707 </p> 4708 </td> 4709<td> 4710 <p> 4711 <span class="blue">Max = 2.26ε (Mean = 0.631ε)</span> 4712 </p> 4713 </td> 4714</tr> 4715</tbody> 4716</table></div> 4717</div> 4718<br class="table-break"> 4719</div> 4720<div class="section"> 4721<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 4722<a name="special_function_error_rates_rep.section_ellint_1_complete_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_1_complete_" title="ellint_1 (complete)">ellint_1 4723 (complete)</a> 4724</h2></div></div></div> 4725<div class="table"> 4726<a name="special_function_error_rates_rep.section_ellint_1_complete_.table_ellint_1_complete_"></a><p class="title"><b>Table 26. Error rates for ellint_1 (complete)</b></p> 4727<div class="table-contents"><table class="table" summary="Error rates for ellint_1 (complete)"> 4728<colgroup> 4729<col> 4730<col> 4731<col> 4732<col> 4733<col> 4734</colgroup> 4735<thead><tr> 4736<th> 4737 </th> 4738<th> 4739 <p> 4740 GNU C++ version 7.1.0<br> linux<br> long double 4741 </p> 4742 </th> 4743<th> 4744 <p> 4745 GNU C++ version 7.1.0<br> linux<br> double 4746 </p> 4747 </th> 4748<th> 4749 <p> 4750 Sun compiler version 0x5150<br> Sun Solaris<br> long double 4751 </p> 4752 </th> 4753<th> 4754 <p> 4755 Microsoft Visual C++ version 14.1<br> Win32<br> double 4756 </p> 4757 </th> 4758</tr></thead> 4759<tbody> 4760<tr> 4761<td> 4762 <p> 4763 Elliptic Integral K: Mathworld Data 4764 </p> 4765 </td> 4766<td> 4767 <p> 4768 <span class="blue">Max = 0.887ε (Mean = 0.296ε)</span><br> <br> 4769 (<span class="emphasis"><em><cmath>:</em></span> Max = 1.19ε (Mean = 0.765ε)) 4770 </p> 4771 </td> 4772<td> 4773 <p> 4774 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 4775 2.1:</em></span> Max = 0.623ε (Mean = 0.393ε)) 4776 </p> 4777 </td> 4778<td> 4779 <p> 4780 <span class="blue">Max = 0.887ε (Mean = 0.296ε)</span> 4781 </p> 4782 </td> 4783<td> 4784 <p> 4785 <span class="blue">Max = 0.915ε (Mean = 0.547ε)</span> 4786 </p> 4787 </td> 4788</tr> 4789<tr> 4790<td> 4791 <p> 4792 Elliptic Integral K: Random Data 4793 </p> 4794 </td> 4795<td> 4796 <p> 4797 <span class="blue">Max = 1.27ε (Mean = 0.473ε)</span><br> <br> 4798 (<span class="emphasis"><em><cmath>:</em></span> Max = 2.19ε (Mean = 0.694ε)) 4799 </p> 4800 </td> 4801<td> 4802 <p> 4803 <span class="blue">Max = 0.851ε (Mean = 0.0851ε)</span><br> <br> 4804 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.32ε (Mean = 0.688ε)) 4805 </p> 4806 </td> 4807<td> 4808 <p> 4809 <span class="blue">Max = 1.27ε (Mean = 0.473ε)</span> 4810 </p> 4811 </td> 4812<td> 4813 <p> 4814 <span class="blue">Max = 0.958ε (Mean = 0.408ε)</span> 4815 </p> 4816 </td> 4817</tr> 4818</tbody> 4819</table></div> 4820</div> 4821<br class="table-break"> 4822</div> 4823<div class="section"> 4824<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 4825<a name="special_function_error_rates_rep.section_ellint_2"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_2" title="ellint_2">ellint_2</a> 4826</h2></div></div></div> 4827<div class="table"> 4828<a name="special_function_error_rates_rep.section_ellint_2.table_ellint_2"></a><p class="title"><b>Table 27. Error rates for ellint_2</b></p> 4829<div class="table-contents"><table class="table" summary="Error rates for ellint_2"> 4830<colgroup> 4831<col> 4832<col> 4833<col> 4834<col> 4835<col> 4836</colgroup> 4837<thead><tr> 4838<th> 4839 </th> 4840<th> 4841 <p> 4842 GNU C++ version 7.1.0<br> linux<br> double 4843 </p> 4844 </th> 4845<th> 4846 <p> 4847 GNU C++ version 7.1.0<br> linux<br> long double 4848 </p> 4849 </th> 4850<th> 4851 <p> 4852 Sun compiler version 0x5150<br> Sun Solaris<br> long double 4853 </p> 4854 </th> 4855<th> 4856 <p> 4857 Microsoft Visual C++ version 14.1<br> Win32<br> double 4858 </p> 4859 </th> 4860</tr></thead> 4861<tbody> 4862<tr> 4863<td> 4864 <p> 4865 Elliptic Integral E: Mathworld Data 4866 </p> 4867 </td> 4868<td> 4869 <p> 4870 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 4871 2.1:</em></span> Max = 0.63ε (Mean = 0.325ε)) 4872 </p> 4873 </td> 4874<td> 4875 <p> 4876 <span class="blue">Max = 0.656ε (Mean = 0.317ε)</span><br> <br> 4877 (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = +INFε (Mean 4878 = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_2__cmath__Elliptic_Integral_E_Mathworld_Data">And 4879 other failures.</a>)</span> 4880 </p> 4881 </td> 4882<td> 4883 <p> 4884 <span class="blue">Max = 0.656ε (Mean = 0.317ε)</span> 4885 </p> 4886 </td> 4887<td> 4888 <p> 4889 <span class="blue">Max = 1.31ε (Mean = 0.727ε)</span> 4890 </p> 4891 </td> 4892</tr> 4893<tr> 4894<td> 4895 <p> 4896 Elliptic Integral E: Random Data 4897 </p> 4898 </td> 4899<td> 4900 <p> 4901 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 4902 2.1:</em></span> Max = 4.4ε (Mean = 1.16ε)) 4903 </p> 4904 </td> 4905<td> 4906 <p> 4907 <span class="blue">Max = 2.05ε (Mean = 0.632ε)</span><br> <br> 4908 (<span class="emphasis"><em><cmath>:</em></span> Max = 3.08e+04ε (Mean = 3.84e+03ε)) 4909 </p> 4910 </td> 4911<td> 4912 <p> 4913 <span class="blue">Max = 2.05ε (Mean = 0.632ε)</span> 4914 </p> 4915 </td> 4916<td> 4917 <p> 4918 <span class="blue">Max = 2.23ε (Mean = 0.639ε)</span> 4919 </p> 4920 </td> 4921</tr> 4922<tr> 4923<td> 4924 <p> 4925 Elliptic Integral E: Small Angles 4926 </p> 4927 </td> 4928<td> 4929 <p> 4930 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 4931 2.1:</em></span> Max = 0.5ε (Mean = 0.118ε)) 4932 </p> 4933 </td> 4934<td> 4935 <p> 4936 <span class="blue">Max = 1ε (Mean = 0.283ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span> 4937 Max = 2ε (Mean = 0.333ε)) 4938 </p> 4939 </td> 4940<td> 4941 <p> 4942 <span class="blue">Max = 1ε (Mean = 0.283ε)</span> 4943 </p> 4944 </td> 4945<td> 4946 <p> 4947 <span class="blue">Max = 1ε (Mean = 0.421ε)</span> 4948 </p> 4949 </td> 4950</tr> 4951</tbody> 4952</table></div> 4953</div> 4954<br class="table-break"> 4955</div> 4956<div class="section"> 4957<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 4958<a name="special_function_error_rates_rep.section_ellint_2_complete_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_2_complete_" title="ellint_2 (complete)">ellint_2 4959 (complete)</a> 4960</h2></div></div></div> 4961<div class="table"> 4962<a name="special_function_error_rates_rep.section_ellint_2_complete_.table_ellint_2_complete_"></a><p class="title"><b>Table 28. Error rates for ellint_2 (complete)</b></p> 4963<div class="table-contents"><table class="table" summary="Error rates for ellint_2 (complete)"> 4964<colgroup> 4965<col> 4966<col> 4967<col> 4968<col> 4969<col> 4970</colgroup> 4971<thead><tr> 4972<th> 4973 </th> 4974<th> 4975 <p> 4976 GNU C++ version 7.1.0<br> linux<br> double 4977 </p> 4978 </th> 4979<th> 4980 <p> 4981 GNU C++ version 7.1.0<br> linux<br> long double 4982 </p> 4983 </th> 4984<th> 4985 <p> 4986 Sun compiler version 0x5150<br> Sun Solaris<br> long double 4987 </p> 4988 </th> 4989<th> 4990 <p> 4991 Microsoft Visual C++ version 14.1<br> Win32<br> double 4992 </p> 4993 </th> 4994</tr></thead> 4995<tbody> 4996<tr> 4997<td> 4998 <p> 4999 Elliptic Integral E: Mathworld Data 5000 </p> 5001 </td> 5002<td> 5003 <p> 5004 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 5005 2.1:</em></span> Max = 3.09ε (Mean = 1.04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ellint_2_complete__GSL_2_1_Elliptic_Integral_E_Mathworld_Data">And 5006 other failures.</a>) 5007 </p> 5008 </td> 5009<td> 5010 <p> 5011 <span class="blue">Max = 0.836ε (Mean = 0.469ε)</span><br> <br> 5012 (<span class="emphasis"><em><cmath>:</em></span> Max = 170ε (Mean = 55.1ε)) 5013 </p> 5014 </td> 5015<td> 5016 <p> 5017 <span class="blue">Max = 0.836ε (Mean = 0.469ε)</span> 5018 </p> 5019 </td> 5020<td> 5021 <p> 5022 <span class="blue">Max = 1.3ε (Mean = 0.615ε)</span> 5023 </p> 5024 </td> 5025</tr> 5026<tr> 5027<td> 5028 <p> 5029 Elliptic Integral E: Random Data 5030 </p> 5031 </td> 5032<td> 5033 <p> 5034 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 5035 2.1:</em></span> Max = 4.34ε (Mean = 1.18ε)) 5036 </p> 5037 </td> 5038<td> 5039 <p> 5040 <span class="blue">Max = 1.97ε (Mean = 0.629ε)</span><br> <br> 5041 (<span class="emphasis"><em><cmath>:</em></span> Max = 2.49e+04ε (Mean = 3.39e+03ε)) 5042 </p> 5043 </td> 5044<td> 5045 <p> 5046 <span class="blue">Max = 1.97ε (Mean = 0.629ε)</span> 5047 </p> 5048 </td> 5049<td> 5050 <p> 5051 <span class="blue">Max = 1.71ε (Mean = 0.553ε)</span> 5052 </p> 5053 </td> 5054</tr> 5055</tbody> 5056</table></div> 5057</div> 5058<br class="table-break"> 5059</div> 5060<div class="section"> 5061<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 5062<a name="special_function_error_rates_rep.section_ellint_3"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_3" title="ellint_3">ellint_3</a> 5063</h2></div></div></div> 5064<div class="table"> 5065<a name="special_function_error_rates_rep.section_ellint_3.table_ellint_3"></a><p class="title"><b>Table 29. Error rates for ellint_3</b></p> 5066<div class="table-contents"><table class="table" summary="Error rates for ellint_3"> 5067<colgroup> 5068<col> 5069<col> 5070<col> 5071<col> 5072<col> 5073</colgroup> 5074<thead><tr> 5075<th> 5076 </th> 5077<th> 5078 <p> 5079 GNU C++ version 7.1.0<br> linux<br> long double 5080 </p> 5081 </th> 5082<th> 5083 <p> 5084 GNU C++ version 7.1.0<br> linux<br> double 5085 </p> 5086 </th> 5087<th> 5088 <p> 5089 Sun compiler version 0x5150<br> Sun Solaris<br> long double 5090 </p> 5091 </th> 5092<th> 5093 <p> 5094 Microsoft Visual C++ version 14.1<br> Win32<br> double 5095 </p> 5096 </th> 5097</tr></thead> 5098<tbody> 5099<tr> 5100<td> 5101 <p> 5102 Elliptic Integral PI: Mathworld Data 5103 </p> 5104 </td> 5105<td> 5106 <p> 5107 <span class="blue">Max = 475ε (Mean = 86.3ε)</span><br> <br> 5108 (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = +INFε (Mean 5109 = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Mathworld_Data">And 5110 other failures.</a>)</span> 5111 </p> 5112 </td> 5113<td> 5114 <p> 5115 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 5116 2.1:</em></span> Max = 1.48e+05ε (Mean = 2.54e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ellint_3_GSL_2_1_Elliptic_Integral_PI_Mathworld_Data">And 5117 other failures.</a>) 5118 </p> 5119 </td> 5120<td> 5121 <p> 5122 <span class="blue">Max = 475ε (Mean = 86.3ε)</span> 5123 </p> 5124 </td> 5125<td> 5126 <p> 5127 <span class="blue">Max = 565ε (Mean = 102ε)</span> 5128 </p> 5129 </td> 5130</tr> 5131<tr> 5132<td> 5133 <p> 5134 Elliptic Integral PI: Random Data 5135 </p> 5136 </td> 5137<td> 5138 <p> 5139 <span class="blue">Max = 4.54ε (Mean = 0.895ε)</span><br> <br> 5140 (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 3.37e+20ε (Mean 5141 = 3.47e+19ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Random_Data">And 5142 other failures.</a>)</span> 5143 </p> 5144 </td> 5145<td> 5146 <p> 5147 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 5148 2.1:</em></span> Max = 633ε (Mean = 50.1ε)) 5149 </p> 5150 </td> 5151<td> 5152 <p> 5153 <span class="blue">Max = 4.49ε (Mean = 0.885ε)</span> 5154 </p> 5155 </td> 5156<td> 5157 <p> 5158 <span class="blue">Max = 8.33ε (Mean = 0.971ε)</span> 5159 </p> 5160 </td> 5161</tr> 5162<tr> 5163<td> 5164 <p> 5165 Elliptic Integral PI: Large Random Data 5166 </p> 5167 </td> 5168<td> 5169 <p> 5170 <span class="blue">Max = 3.7ε (Mean = 0.893ε)</span><br> <br> 5171 (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 2.52e+18ε (Mean 5172 = 4.83e+17ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Large_Random_Data">And 5173 other failures.</a>)</span> 5174 </p> 5175 </td> 5176<td> 5177 <p> 5178 <span class="blue">Max = 0.557ε (Mean = 0.0389ε)</span><br> <br> 5179 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 40.1ε (Mean = 7.77ε)) 5180 </p> 5181 </td> 5182<td> 5183 <p> 5184 <span class="blue">Max = 3.7ε (Mean = 0.892ε)</span> 5185 </p> 5186 </td> 5187<td> 5188 <p> 5189 <span class="blue">Max = 2.86ε (Mean = 0.944ε)</span> 5190 </p> 5191 </td> 5192</tr> 5193</tbody> 5194</table></div> 5195</div> 5196<br class="table-break"> 5197</div> 5198<div class="section"> 5199<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 5200<a name="special_function_error_rates_rep.section_ellint_3_complete_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_3_complete_" title="ellint_3 (complete)">ellint_3 5201 (complete)</a> 5202</h2></div></div></div> 5203<div class="table"> 5204<a name="special_function_error_rates_rep.section_ellint_3_complete_.table_ellint_3_complete_"></a><p class="title"><b>Table 30. Error rates for ellint_3 (complete)</b></p> 5205<div class="table-contents"><table class="table" summary="Error rates for ellint_3 (complete)"> 5206<colgroup> 5207<col> 5208<col> 5209<col> 5210<col> 5211<col> 5212</colgroup> 5213<thead><tr> 5214<th> 5215 </th> 5216<th> 5217 <p> 5218 GNU C++ version 7.1.0<br> linux<br> long double 5219 </p> 5220 </th> 5221<th> 5222 <p> 5223 GNU C++ version 7.1.0<br> linux<br> double 5224 </p> 5225 </th> 5226<th> 5227 <p> 5228 Sun compiler version 0x5150<br> Sun Solaris<br> long double 5229 </p> 5230 </th> 5231<th> 5232 <p> 5233 Microsoft Visual C++ version 14.1<br> Win32<br> double 5234 </p> 5235 </th> 5236</tr></thead> 5237<tbody> 5238<tr> 5239<td> 5240 <p> 5241 Complete Elliptic Integral PI: Mathworld Data 5242 </p> 5243 </td> 5244<td> 5245 <p> 5246 <span class="blue">Max = 1.4ε (Mean = 0.575ε)</span><br> <br> 5247 (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 6.31e+20ε (Mean 5248 = 1.53e+20ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3_complete___cmath__Complete_Elliptic_Integral_PI_Mathworld_Data">And 5249 other failures.</a>)</span> 5250 </p> 5251 </td> 5252<td> 5253 <p> 5254 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 5255 2.1:</em></span> Max = 6.33e+04ε (Mean = 1.54e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ellint_3_complete__GSL_2_1_Complete_Elliptic_Integral_PI_Mathworld_Data">And 5256 other failures.</a>) 5257 </p> 5258 </td> 5259<td> 5260 <p> 5261 <span class="blue">Max = 1.4ε (Mean = 0.575ε)</span> 5262 </p> 5263 </td> 5264<td> 5265 <p> 5266 <span class="blue">Max = 0.971ε (Mean = 0.464ε)</span> 5267 </p> 5268 </td> 5269</tr> 5270<tr> 5271<td> 5272 <p> 5273 Complete Elliptic Integral PI: Random Data 5274 </p> 5275 </td> 5276<td> 5277 <p> 5278 <span class="blue">Max = 2.45ε (Mean = 0.696ε)</span><br> <br> 5279 (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 8.78e+20ε (Mean 5280 = 1.02e+20ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3_complete___cmath__Complete_Elliptic_Integral_PI_Random_Data">And 5281 other failures.</a>)</span> 5282 </p> 5283 </td> 5284<td> 5285 <p> 5286 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 5287 2.1:</em></span> Max = 24ε (Mean = 2.99ε)) 5288 </p> 5289 </td> 5290<td> 5291 <p> 5292 <span class="blue">Max = 2.4ε (Mean = 0.677ε)</span> 5293 </p> 5294 </td> 5295<td> 5296 <p> 5297 <span class="blue">Max = 2.46ε (Mean = 0.657ε)</span> 5298 </p> 5299 </td> 5300</tr> 5301</tbody> 5302</table></div> 5303</div> 5304<br class="table-break"> 5305</div> 5306<div class="section"> 5307<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 5308<a name="special_function_error_rates_rep.section_ellint_d"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_d" title="ellint_d">ellint_d</a> 5309</h2></div></div></div> 5310<div class="table"> 5311<a name="special_function_error_rates_rep.section_ellint_d.table_ellint_d"></a><p class="title"><b>Table 31. Error rates for ellint_d</b></p> 5312<div class="table-contents"><table class="table" summary="Error rates for ellint_d"> 5313<colgroup> 5314<col> 5315<col> 5316<col> 5317<col> 5318<col> 5319</colgroup> 5320<thead><tr> 5321<th> 5322 </th> 5323<th> 5324 <p> 5325 GNU C++ version 7.1.0<br> linux<br> double 5326 </p> 5327 </th> 5328<th> 5329 <p> 5330 GNU C++ version 7.1.0<br> linux<br> long double 5331 </p> 5332 </th> 5333<th> 5334 <p> 5335 Sun compiler version 0x5150<br> Sun Solaris<br> long double 5336 </p> 5337 </th> 5338<th> 5339 <p> 5340 Microsoft Visual C++ version 14.1<br> Win32<br> double 5341 </p> 5342 </th> 5343</tr></thead> 5344<tbody> 5345<tr> 5346<td> 5347 <p> 5348 Elliptic Integral E: Mathworld Data 5349 </p> 5350 </td> 5351<td> 5352 <p> 5353 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 5354 2.1:</em></span> Max = 0.862ε (Mean = 0.568ε)) 5355 </p> 5356 </td> 5357<td> 5358 <p> 5359 <span class="blue">Max = 1.3ε (Mean = 0.813ε)</span> 5360 </p> 5361 </td> 5362<td> 5363 <p> 5364 <span class="blue">Max = 1.3ε (Mean = 0.813ε)</span> 5365 </p> 5366 </td> 5367<td> 5368 <p> 5369 <span class="blue">Max = 0.862ε (Mean = 0.457ε)</span> 5370 </p> 5371 </td> 5372</tr> 5373<tr> 5374<td> 5375 <p> 5376 Elliptic Integral D: Random Data 5377 </p> 5378 </td> 5379<td> 5380 <p> 5381 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 5382 2.1:</em></span> Max = 3.01ε (Mean = 0.928ε)) 5383 </p> 5384 </td> 5385<td> 5386 <p> 5387 <span class="blue">Max = 2.51ε (Mean = 0.883ε)</span> 5388 </p> 5389 </td> 5390<td> 5391 <p> 5392 <span class="blue">Max = 2.51ε (Mean = 0.883ε)</span> 5393 </p> 5394 </td> 5395<td> 5396 <p> 5397 <span class="blue">Max = 2.87ε (Mean = 0.805ε)</span> 5398 </p> 5399 </td> 5400</tr> 5401</tbody> 5402</table></div> 5403</div> 5404<br class="table-break"> 5405</div> 5406<div class="section"> 5407<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 5408<a name="special_function_error_rates_rep.section_ellint_d_complete_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_d_complete_" title="ellint_d (complete)">ellint_d 5409 (complete)</a> 5410</h2></div></div></div> 5411<div class="table"> 5412<a name="special_function_error_rates_rep.section_ellint_d_complete_.table_ellint_d_complete_"></a><p class="title"><b>Table 32. Error rates for ellint_d (complete)</b></p> 5413<div class="table-contents"><table class="table" summary="Error rates for ellint_d (complete)"> 5414<colgroup> 5415<col> 5416<col> 5417<col> 5418<col> 5419<col> 5420</colgroup> 5421<thead><tr> 5422<th> 5423 </th> 5424<th> 5425 <p> 5426 GNU C++ version 7.1.0<br> linux<br> double 5427 </p> 5428 </th> 5429<th> 5430 <p> 5431 GNU C++ version 7.1.0<br> linux<br> long double 5432 </p> 5433 </th> 5434<th> 5435 <p> 5436 Sun compiler version 0x5150<br> Sun Solaris<br> long double 5437 </p> 5438 </th> 5439<th> 5440 <p> 5441 Microsoft Visual C++ version 14.1<br> Win32<br> double 5442 </p> 5443 </th> 5444</tr></thead> 5445<tbody> 5446<tr> 5447<td> 5448 <p> 5449 Elliptic Integral E: Mathworld Data 5450 </p> 5451 </td> 5452<td> 5453 <p> 5454 <span class="blue">Max = 0.637ε (Mean = 0.368ε)</span> 5455 </p> 5456 </td> 5457<td> 5458 <p> 5459 <span class="blue">Max = 1.27ε (Mean = 0.735ε)</span> 5460 </p> 5461 </td> 5462<td> 5463 <p> 5464 <span class="blue">Max = 1.27ε (Mean = 0.735ε)</span> 5465 </p> 5466 </td> 5467<td> 5468 <p> 5469 <span class="blue">Max = 0.637ε (Mean = 0.368ε)</span> 5470 </p> 5471 </td> 5472</tr> 5473<tr> 5474<td> 5475 <p> 5476 Elliptic Integral D: Random Data 5477 </p> 5478 </td> 5479<td> 5480 <p> 5481 <span class="blue">Max = 0ε (Mean = 0ε)</span> 5482 </p> 5483 </td> 5484<td> 5485 <p> 5486 <span class="blue">Max = 1.27ε (Mean = 0.334ε)</span> 5487 </p> 5488 </td> 5489<td> 5490 <p> 5491 <span class="blue">Max = 1.27ε (Mean = 0.334ε)</span> 5492 </p> 5493 </td> 5494<td> 5495 <p> 5496 <span class="blue">Max = 1.27ε (Mean = 0.355ε)</span> 5497 </p> 5498 </td> 5499</tr> 5500</tbody> 5501</table></div> 5502</div> 5503<br class="table-break"> 5504</div> 5505<div class="section"> 5506<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 5507<a name="special_function_error_rates_rep.section_ellint_rc"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_rc" title="ellint_rc">ellint_rc</a> 5508</h2></div></div></div> 5509<div class="table"> 5510<a name="special_function_error_rates_rep.section_ellint_rc.table_ellint_rc"></a><p class="title"><b>Table 33. Error rates for ellint_rc</b></p> 5511<div class="table-contents"><table class="table" summary="Error rates for ellint_rc"> 5512<colgroup> 5513<col> 5514<col> 5515<col> 5516<col> 5517</colgroup> 5518<thead><tr> 5519<th> 5520 </th> 5521<th> 5522 <p> 5523 GNU C++ version 7.1.0<br> linux<br> double 5524 </p> 5525 </th> 5526<th> 5527 <p> 5528 GNU C++ version 7.1.0<br> linux<br> long double 5529 </p> 5530 </th> 5531<th> 5532 <p> 5533 Microsoft Visual C++ version 14.1<br> Win32<br> double 5534 </p> 5535 </th> 5536</tr></thead> 5537<tbody><tr> 5538<td> 5539 <p> 5540 RC: Random data 5541 </p> 5542 </td> 5543<td> 5544 <p> 5545 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 5546 2.1:</em></span> Max = 2.4ε (Mean = 0.624ε)) 5547 </p> 5548 </td> 5549<td> 5550 <p> 5551 <span class="blue">Max = 0.995ε (Mean = 0.433ε)</span> 5552 </p> 5553 </td> 5554<td> 5555 <p> 5556 <span class="blue">Max = 0.962ε (Mean = 0.407ε)</span> 5557 </p> 5558 </td> 5559</tr></tbody> 5560</table></div> 5561</div> 5562<br class="table-break"> 5563</div> 5564<div class="section"> 5565<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 5566<a name="special_function_error_rates_rep.section_ellint_rd"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_rd" title="ellint_rd">ellint_rd</a> 5567</h2></div></div></div> 5568<div class="table"> 5569<a name="special_function_error_rates_rep.section_ellint_rd.table_ellint_rd"></a><p class="title"><b>Table 34. Error rates for ellint_rd</b></p> 5570<div class="table-contents"><table class="table" summary="Error rates for ellint_rd"> 5571<colgroup> 5572<col> 5573<col> 5574<col> 5575<col> 5576</colgroup> 5577<thead><tr> 5578<th> 5579 </th> 5580<th> 5581 <p> 5582 GNU C++ version 7.1.0<br> linux<br> double 5583 </p> 5584 </th> 5585<th> 5586 <p> 5587 GNU C++ version 7.1.0<br> linux<br> long double 5588 </p> 5589 </th> 5590<th> 5591 <p> 5592 Microsoft Visual C++ version 14.1<br> Win32<br> double 5593 </p> 5594 </th> 5595</tr></thead> 5596<tbody> 5597<tr> 5598<td> 5599 <p> 5600 RD: Random data 5601 </p> 5602 </td> 5603<td> 5604 <p> 5605 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 5606 2.1:</em></span> Max = 2.59ε (Mean = 0.878ε)) 5607 </p> 5608 </td> 5609<td> 5610 <p> 5611 <span class="blue">Max = 2.73ε (Mean = 0.831ε)</span> 5612 </p> 5613 </td> 5614<td> 5615 <p> 5616 <span class="blue">Max = 2.16ε (Mean = 0.803ε)</span> 5617 </p> 5618 </td> 5619</tr> 5620<tr> 5621<td> 5622 <p> 5623 RD: y = z 5624 </p> 5625 </td> 5626<td> 5627 <p> 5628 <span class="blue">Max = 0.896ε (Mean = 0.022ε)</span><br> <br> 5629 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.88ε (Mean = 0.839ε)) 5630 </p> 5631 </td> 5632<td> 5633 <p> 5634 <span class="blue">Max = 2.65ε (Mean = 0.82ε)</span> 5635 </p> 5636 </td> 5637<td> 5638 <p> 5639 <span class="blue">Max = 16.5ε (Mean = 0.843ε)</span> 5640 </p> 5641 </td> 5642</tr> 5643<tr> 5644<td> 5645 <p> 5646 RD: x = y 5647 </p> 5648 </td> 5649<td> 5650 <p> 5651 <span class="blue">Max = 0.824ε (Mean = 0.0272ε)</span><br> <br> 5652 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.74ε (Mean = 0.84ε)) 5653 </p> 5654 </td> 5655<td> 5656 <p> 5657 <span class="blue">Max = 2.85ε (Mean = 0.865ε)</span> 5658 </p> 5659 </td> 5660<td> 5661 <p> 5662 <span class="blue">Max = 3.51ε (Mean = 0.816ε)</span> 5663 </p> 5664 </td> 5665</tr> 5666<tr> 5667<td> 5668 <p> 5669 RD: x = 0, y = z 5670 </p> 5671 </td> 5672<td> 5673 <p> 5674 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 5675 2.1:</em></span> Max = 2ε (Mean = 0.656ε)) 5676 </p> 5677 </td> 5678<td> 5679 <p> 5680 <span class="blue">Max = 1.19ε (Mean = 0.522ε)</span> 5681 </p> 5682 </td> 5683<td> 5684 <p> 5685 <span class="blue">Max = 1.16ε (Mean = 0.497ε)</span> 5686 </p> 5687 </td> 5688</tr> 5689<tr> 5690<td> 5691 <p> 5692 RD: x = y = z 5693 </p> 5694 </td> 5695<td> 5696 <p> 5697 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 5698 2.1:</em></span> Max = 1.03ε (Mean = 0.418ε)) 5699 </p> 5700 </td> 5701<td> 5702 <p> 5703 <span class="blue">Max = 0.998ε (Mean = 0.387ε)</span> 5704 </p> 5705 </td> 5706<td> 5707 <p> 5708 <span class="blue">Max = 1.03ε (Mean = 0.418ε)</span> 5709 </p> 5710 </td> 5711</tr> 5712<tr> 5713<td> 5714 <p> 5715 RD: x = 0 5716 </p> 5717 </td> 5718<td> 5719 <p> 5720 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 5721 2.1:</em></span> Max = 2.85ε (Mean = 0.781ε)) 5722 </p> 5723 </td> 5724<td> 5725 <p> 5726 <span class="blue">Max = 2.79ε (Mean = 0.883ε)</span> 5727 </p> 5728 </td> 5729<td> 5730 <p> 5731 <span class="blue">Max = 2.64ε (Mean = 0.894ε)</span> 5732 </p> 5733 </td> 5734</tr> 5735</tbody> 5736</table></div> 5737</div> 5738<br class="table-break"> 5739</div> 5740<div class="section"> 5741<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 5742<a name="special_function_error_rates_rep.section_ellint_rf"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_rf" title="ellint_rf">ellint_rf</a> 5743</h2></div></div></div> 5744<div class="table"> 5745<a name="special_function_error_rates_rep.section_ellint_rf.table_ellint_rf"></a><p class="title"><b>Table 35. Error rates for ellint_rf</b></p> 5746<div class="table-contents"><table class="table" summary="Error rates for ellint_rf"> 5747<colgroup> 5748<col> 5749<col> 5750<col> 5751<col> 5752</colgroup> 5753<thead><tr> 5754<th> 5755 </th> 5756<th> 5757 <p> 5758 GNU C++ version 7.1.0<br> linux<br> double 5759 </p> 5760 </th> 5761<th> 5762 <p> 5763 GNU C++ version 7.1.0<br> linux<br> long double 5764 </p> 5765 </th> 5766<th> 5767 <p> 5768 Microsoft Visual C++ version 14.1<br> Win32<br> double 5769 </p> 5770 </th> 5771</tr></thead> 5772<tbody> 5773<tr> 5774<td> 5775 <p> 5776 RF: Random data 5777 </p> 5778 </td> 5779<td> 5780 <p> 5781 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 5782 2.1:</em></span> Max = 2.73ε (Mean = 0.804ε)) 5783 </p> 5784 </td> 5785<td> 5786 <p> 5787 <span class="blue">Max = 2.54ε (Mean = 0.674ε)</span> 5788 </p> 5789 </td> 5790<td> 5791 <p> 5792 <span class="blue">Max = 2.02ε (Mean = 0.677ε)</span> 5793 </p> 5794 </td> 5795</tr> 5796<tr> 5797<td> 5798 <p> 5799 RF: x = y = z 5800 </p> 5801 </td> 5802<td> 5803 <p> 5804 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 5805 2.1:</em></span> Max = 0.999ε (Mean = 0.34ε)) 5806 </p> 5807 </td> 5808<td> 5809 <p> 5810 <span class="blue">Max = 0.991ε (Mean = 0.345ε)</span> 5811 </p> 5812 </td> 5813<td> 5814 <p> 5815 <span class="blue">Max = 0.999ε (Mean = 0.34ε)</span> 5816 </p> 5817 </td> 5818</tr> 5819<tr> 5820<td> 5821 <p> 5822 RF: x = y or y = z or x = z 5823 </p> 5824 </td> 5825<td> 5826 <p> 5827 <span class="blue">Max = 0.536ε (Mean = 0.00658ε)</span><br> <br> 5828 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.89ε (Mean = 0.749ε)) 5829 </p> 5830 </td> 5831<td> 5832 <p> 5833 <span class="blue">Max = 1.95ε (Mean = 0.418ε)</span> 5834 </p> 5835 </td> 5836<td> 5837 <p> 5838 <span class="blue">Max = 1.21ε (Mean = 0.394ε)</span> 5839 </p> 5840 </td> 5841</tr> 5842<tr> 5843<td> 5844 <p> 5845 RF: x = 0, y = z 5846 </p> 5847 </td> 5848<td> 5849 <p> 5850 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 5851 2.1:</em></span> Max = 1.29ε (Mean = 0.527ε)) 5852 </p> 5853 </td> 5854<td> 5855 <p> 5856 <span class="blue">Max = 0.894ε (Mean = 0.338ε)</span> 5857 </p> 5858 </td> 5859<td> 5860 <p> 5861 <span class="blue">Max = 0.999ε (Mean = 0.407ε)</span> 5862 </p> 5863 </td> 5864</tr> 5865<tr> 5866<td> 5867 <p> 5868 RF: z = 0 5869 </p> 5870 </td> 5871<td> 5872 <p> 5873 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 5874 2.1:</em></span> Max = 2.54ε (Mean = 0.781ε)) 5875 </p> 5876 </td> 5877<td> 5878 <p> 5879 <span class="blue">Max = 1.7ε (Mean = 0.539ε)</span> 5880 </p> 5881 </td> 5882<td> 5883 <p> 5884 <span class="blue">Max = 1.89ε (Mean = 0.587ε)</span> 5885 </p> 5886 </td> 5887</tr> 5888</tbody> 5889</table></div> 5890</div> 5891<br class="table-break"> 5892</div> 5893<div class="section"> 5894<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 5895<a name="special_function_error_rates_rep.section_ellint_rg"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_rg" title="ellint_rg">ellint_rg</a> 5896</h2></div></div></div> 5897<div class="table"> 5898<a name="special_function_error_rates_rep.section_ellint_rg.table_ellint_rg"></a><p class="title"><b>Table 36. Error rates for ellint_rg</b></p> 5899<div class="table-contents"><table class="table" summary="Error rates for ellint_rg"> 5900<colgroup> 5901<col> 5902<col> 5903<col> 5904<col> 5905</colgroup> 5906<thead><tr> 5907<th> 5908 </th> 5909<th> 5910 <p> 5911 GNU C++ version 7.1.0<br> linux<br> double 5912 </p> 5913 </th> 5914<th> 5915 <p> 5916 GNU C++ version 7.1.0<br> linux<br> long double 5917 </p> 5918 </th> 5919<th> 5920 <p> 5921 Microsoft Visual C++ version 14.1<br> Win32<br> double 5922 </p> 5923 </th> 5924</tr></thead> 5925<tbody> 5926<tr> 5927<td> 5928 <p> 5929 RG: Random Data 5930 </p> 5931 </td> 5932<td> 5933 <p> 5934 <span class="blue">Max = 0.983ε (Mean = 0.0172ε)</span><br> <br> 5935 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.983ε (Mean = 0.0172ε)) 5936 </p> 5937 </td> 5938<td> 5939 <p> 5940 <span class="blue">Max = 3.95ε (Mean = 0.951ε)</span> 5941 </p> 5942 </td> 5943<td> 5944 <p> 5945 <span class="blue">Max = 3.65ε (Mean = 0.929ε)</span> 5946 </p> 5947 </td> 5948</tr> 5949<tr> 5950<td> 5951 <p> 5952 RG: two values 0 5953 </p> 5954 </td> 5955<td> 5956 <p> 5957 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 5958 2.1:</em></span> Max = 0ε (Mean = 0ε)) 5959 </p> 5960 </td> 5961<td> 5962 <p> 5963 <span class="blue">Max = 0ε (Mean = 0ε)</span> 5964 </p> 5965 </td> 5966<td> 5967 <p> 5968 <span class="blue">Max = 0ε (Mean = 0ε)</span> 5969 </p> 5970 </td> 5971</tr> 5972<tr> 5973<td> 5974 <p> 5975 RG: All values the same or zero 5976 </p> 5977 </td> 5978<td> 5979 <p> 5980 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 5981 2.1:</em></span> Max = 0ε (Mean = 0ε)) 5982 </p> 5983 </td> 5984<td> 5985 <p> 5986 <span class="blue">Max = 0.992ε (Mean = 0.288ε)</span> 5987 </p> 5988 </td> 5989<td> 5990 <p> 5991 <span class="blue">Max = 1.06ε (Mean = 0.348ε)</span> 5992 </p> 5993 </td> 5994</tr> 5995<tr> 5996<td> 5997 <p> 5998 RG: two values the same 5999 </p> 6000 </td> 6001<td> 6002 <p> 6003 <span class="blue">Max = 0.594ε (Mean = 0.0103ε)</span><br> <br> 6004 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.594ε (Mean = 0.0103ε)) 6005 </p> 6006 </td> 6007<td> 6008 <p> 6009 <span class="blue">Max = 1.51ε (Mean = 0.404ε)</span> 6010 </p> 6011 </td> 6012<td> 6013 <p> 6014 <span class="blue">Max = 1.96ε (Mean = 0.374ε)</span> 6015 </p> 6016 </td> 6017</tr> 6018<tr> 6019<td> 6020 <p> 6021 RG: one value zero 6022 </p> 6023 </td> 6024<td> 6025 <p> 6026 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 6027 2.1:</em></span> Max = 0ε (Mean = 0ε)) 6028 </p> 6029 </td> 6030<td> 6031 <p> 6032 <span class="blue">Max = 2.14ε (Mean = 0.722ε)</span> 6033 </p> 6034 </td> 6035<td> 6036 <p> 6037 <span class="blue">Max = 1.96ε (Mean = 0.674ε)</span> 6038 </p> 6039 </td> 6040</tr> 6041</tbody> 6042</table></div> 6043</div> 6044<br class="table-break"> 6045</div> 6046<div class="section"> 6047<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 6048<a name="special_function_error_rates_rep.section_ellint_rj"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_rj" title="ellint_rj">ellint_rj</a> 6049</h2></div></div></div> 6050<div class="table"> 6051<a name="special_function_error_rates_rep.section_ellint_rj.table_ellint_rj"></a><p class="title"><b>Table 37. Error rates for ellint_rj</b></p> 6052<div class="table-contents"><table class="table" summary="Error rates for ellint_rj"> 6053<colgroup> 6054<col> 6055<col> 6056<col> 6057<col> 6058</colgroup> 6059<thead><tr> 6060<th> 6061 </th> 6062<th> 6063 <p> 6064 GNU C++ version 7.1.0<br> linux<br> double 6065 </p> 6066 </th> 6067<th> 6068 <p> 6069 GNU C++ version 7.1.0<br> linux<br> long double 6070 </p> 6071 </th> 6072<th> 6073 <p> 6074 Microsoft Visual C++ version 14.1<br> Win32<br> double 6075 </p> 6076 </th> 6077</tr></thead> 6078<tbody> 6079<tr> 6080<td> 6081 <p> 6082 RJ: Random data 6083 </p> 6084 </td> 6085<td> 6086 <p> 6087 <span class="blue">Max = 0.52ε (Mean = 0.0184ε)</span><br> <br> 6088 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.57ε (Mean = 0.704ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ellint_rj_GSL_2_1_RJ_Random_data">And 6089 other failures.</a>) 6090 </p> 6091 </td> 6092<td> 6093 <p> 6094 <span class="blue">Max = 186ε (Mean = 6.67ε)</span> 6095 </p> 6096 </td> 6097<td> 6098 <p> 6099 <span class="blue">Max = 215ε (Mean = 7.66ε)</span> 6100 </p> 6101 </td> 6102</tr> 6103<tr> 6104<td> 6105 <p> 6106 RJ: 4 Equal Values 6107 </p> 6108 </td> 6109<td> 6110 <p> 6111 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 6112 2.1:</em></span> Max = 1.03ε (Mean = 0.418ε)) 6113 </p> 6114 </td> 6115<td> 6116 <p> 6117 <span class="blue">Max = 0.998ε (Mean = 0.387ε)</span> 6118 </p> 6119 </td> 6120<td> 6121 <p> 6122 <span class="blue">Max = 1.03ε (Mean = 0.418ε)</span> 6123 </p> 6124 </td> 6125</tr> 6126<tr> 6127<td> 6128 <p> 6129 RJ: 3 Equal Values 6130 </p> 6131 </td> 6132<td> 6133 <p> 6134 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 6135 2.1:</em></span> Max = 3.96ε (Mean = 1.06ε)) 6136 </p> 6137 </td> 6138<td> 6139 <p> 6140 <span class="blue">Max = 20.8ε (Mean = 0.986ε)</span> 6141 </p> 6142 </td> 6143<td> 6144 <p> 6145 <span class="blue">Max = 39.9ε (Mean = 1.17ε)</span> 6146 </p> 6147 </td> 6148</tr> 6149<tr> 6150<td> 6151 <p> 6152 RJ: 2 Equal Values 6153 </p> 6154 </td> 6155<td> 6156 <p> 6157 <span class="blue">Max = 0.6ε (Mean = 0.0228ε)</span><br> <br> 6158 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.57ε (Mean = 0.754ε)) 6159 </p> 6160 </td> 6161<td> 6162 <p> 6163 <span class="blue">Max = 220ε (Mean = 6.64ε)</span> 6164 </p> 6165 </td> 6166<td> 6167 <p> 6168 <span class="blue">Max = 214ε (Mean = 5.28ε)</span> 6169 </p> 6170 </td> 6171</tr> 6172<tr> 6173<td> 6174 <p> 6175 RJ: Equal z and p 6176 </p> 6177 </td> 6178<td> 6179 <p> 6180 <span class="blue">Max = 0.742ε (Mean = 0.0166ε)</span><br> <br> 6181 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.62ε (Mean = 0.699ε)) 6182 </p> 6183 </td> 6184<td> 6185 <p> 6186 <span class="blue">Max = 17.2ε (Mean = 1.16ε)</span> 6187 </p> 6188 </td> 6189<td> 6190 <p> 6191 <span class="blue">Max = 16.1ε (Mean = 1.14ε)</span> 6192 </p> 6193 </td> 6194</tr> 6195</tbody> 6196</table></div> 6197</div> 6198<br class="table-break"> 6199</div> 6200<div class="section"> 6201<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 6202<a name="special_function_error_rates_rep.section_erf"></a><a class="link" href="index.html#special_function_error_rates_rep.section_erf" title="erf">erf</a> 6203</h2></div></div></div> 6204<div class="table"> 6205<a name="special_function_error_rates_rep.section_erf.table_erf"></a><p class="title"><b>Table 38. Error rates for erf</b></p> 6206<div class="table-contents"><table class="table" summary="Error rates for erf"> 6207<colgroup> 6208<col> 6209<col> 6210<col> 6211<col> 6212<col> 6213</colgroup> 6214<thead><tr> 6215<th> 6216 </th> 6217<th> 6218 <p> 6219 GNU C++ version 7.1.0<br> linux<br> long double 6220 </p> 6221 </th> 6222<th> 6223 <p> 6224 GNU C++ version 7.1.0<br> linux<br> double 6225 </p> 6226 </th> 6227<th> 6228 <p> 6229 Sun compiler version 0x5150<br> Sun Solaris<br> long double 6230 </p> 6231 </th> 6232<th> 6233 <p> 6234 Microsoft Visual C++ version 14.1<br> Win32<br> double 6235 </p> 6236 </th> 6237</tr></thead> 6238<tbody> 6239<tr> 6240<td> 6241 <p> 6242 Erf Function: Small Values 6243 </p> 6244 </td> 6245<td> 6246 <p> 6247 <span class="blue">Max = 0.925ε (Mean = 0.193ε)</span><br> <br> 6248 (<span class="emphasis"><em><cmath>:</em></span> Max = 0.944ε (Mean = 0.191ε))<br> 6249 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.944ε (Mean = 0.191ε)) 6250 </p> 6251 </td> 6252<td> 6253 <p> 6254 <span class="blue">Max = 0.841ε (Mean = 0.0687ε)</span><br> <br> 6255 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.06ε (Mean = 0.319ε)) 6256 </p> 6257 </td> 6258<td> 6259 <p> 6260 <span class="blue">Max = 0.925ε (Mean = 0.193ε)</span><br> <br> 6261 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.944ε (Mean = 0.194ε)) 6262 </p> 6263 </td> 6264<td> 6265 <p> 6266 <span class="blue">Max = 0.996ε (Mean = 0.182ε)</span><br> <br> 6267 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.57ε (Mean = 0.317ε)) 6268 </p> 6269 </td> 6270</tr> 6271<tr> 6272<td> 6273 <p> 6274 Erf Function: Medium Values 6275 </p> 6276 </td> 6277<td> 6278 <p> 6279 <span class="blue">Max = 1.5ε (Mean = 0.193ε)</span><br> <br> 6280 (<span class="emphasis"><em><cmath>:</em></span> Max = 0.921ε (Mean = 0.0723ε))<br> 6281 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.921ε (Mean = 0.0723ε)) 6282 </p> 6283 </td> 6284<td> 6285 <p> 6286 <span class="blue">Max = 1ε (Mean = 0.119ε)</span><br> <br> (<span class="emphasis"><em>GSL 6287 2.1:</em></span> Max = 2.31ε (Mean = 0.368ε)) 6288 </p> 6289 </td> 6290<td> 6291 <p> 6292 <span class="blue">Max = 1.5ε (Mean = 0.197ε)</span><br> <br> 6293 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.921ε (Mean = 0.071ε)) 6294 </p> 6295 </td> 6296<td> 6297 <p> 6298 <span class="blue">Max = 1ε (Mean = 0.171ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span> 6299 Max = 1.19ε (Mean = 0.244ε)) 6300 </p> 6301 </td> 6302</tr> 6303<tr> 6304<td> 6305 <p> 6306 Erf Function: Large Values 6307 </p> 6308 </td> 6309<td> 6310 <p> 6311 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span> 6312 Max = 0ε (Mean = 0ε))<br> (<span class="emphasis"><em><math.h>:</em></span> Max 6313 = 0ε (Mean = 0ε)) 6314 </p> 6315 </td> 6316<td> 6317 <p> 6318 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 6319 2.1:</em></span> Max = 0ε (Mean = 0ε)) 6320 </p> 6321 </td> 6322<td> 6323 <p> 6324 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span> 6325 Max = 0ε (Mean = 0ε)) 6326 </p> 6327 </td> 6328<td> 6329 <p> 6330 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span> 6331 Max = 0ε (Mean = 0ε)) 6332 </p> 6333 </td> 6334</tr> 6335</tbody> 6336</table></div> 6337</div> 6338<br class="table-break"> 6339</div> 6340<div class="section"> 6341<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 6342<a name="special_function_error_rates_rep.section_erf_inv"></a><a class="link" href="index.html#special_function_error_rates_rep.section_erf_inv" title="erf_inv">erf_inv</a> 6343</h2></div></div></div> 6344<div class="table"> 6345<a name="special_function_error_rates_rep.section_erf_inv.table_erf_inv"></a><p class="title"><b>Table 39. Error rates for erf_inv</b></p> 6346<div class="table-contents"><table class="table" summary="Error rates for erf_inv"> 6347<colgroup> 6348<col> 6349<col> 6350<col> 6351<col> 6352<col> 6353</colgroup> 6354<thead><tr> 6355<th> 6356 </th> 6357<th> 6358 <p> 6359 GNU C++ version 7.1.0<br> linux<br> double 6360 </p> 6361 </th> 6362<th> 6363 <p> 6364 GNU C++ version 7.1.0<br> linux<br> long double 6365 </p> 6366 </th> 6367<th> 6368 <p> 6369 Sun compiler version 0x5150<br> Sun Solaris<br> long double 6370 </p> 6371 </th> 6372<th> 6373 <p> 6374 Microsoft Visual C++ version 14.1<br> Win32<br> double 6375 </p> 6376 </th> 6377</tr></thead> 6378<tbody><tr> 6379<td> 6380 <p> 6381 Inverse Erf Function 6382 </p> 6383 </td> 6384<td> 6385 <p> 6386 <span class="blue">Max = 0ε (Mean = 0ε)</span> 6387 </p> 6388 </td> 6389<td> 6390 <p> 6391 <span class="blue">Max = 0.996ε (Mean = 0.389ε)</span> 6392 </p> 6393 </td> 6394<td> 6395 <p> 6396 <span class="blue">Max = 1.08ε (Mean = 0.395ε)</span> 6397 </p> 6398 </td> 6399<td> 6400 <p> 6401 <span class="blue">Max = 1.09ε (Mean = 0.502ε)</span> 6402 </p> 6403 </td> 6404</tr></tbody> 6405</table></div> 6406</div> 6407<br class="table-break"> 6408</div> 6409<div class="section"> 6410<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 6411<a name="special_function_error_rates_rep.section_erfc"></a><a class="link" href="index.html#special_function_error_rates_rep.section_erfc" title="erfc">erfc</a> 6412</h2></div></div></div> 6413<div class="table"> 6414<a name="special_function_error_rates_rep.section_erfc.table_erfc"></a><p class="title"><b>Table 40. Error rates for erfc</b></p> 6415<div class="table-contents"><table class="table" summary="Error rates for erfc"> 6416<colgroup> 6417<col> 6418<col> 6419<col> 6420<col> 6421<col> 6422</colgroup> 6423<thead><tr> 6424<th> 6425 </th> 6426<th> 6427 <p> 6428 GNU C++ version 7.1.0<br> linux<br> long double 6429 </p> 6430 </th> 6431<th> 6432 <p> 6433 GNU C++ version 7.1.0<br> linux<br> double 6434 </p> 6435 </th> 6436<th> 6437 <p> 6438 Sun compiler version 0x5150<br> Sun Solaris<br> long double 6439 </p> 6440 </th> 6441<th> 6442 <p> 6443 Microsoft Visual C++ version 14.1<br> Win32<br> double 6444 </p> 6445 </th> 6446</tr></thead> 6447<tbody> 6448<tr> 6449<td> 6450 <p> 6451 Erf Function: Small Values 6452 </p> 6453 </td> 6454<td> 6455 <p> 6456 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span> 6457 Max = 0ε (Mean = 0ε))<br> (<span class="emphasis"><em><math.h>:</em></span> Max 6458 = 0ε (Mean = 0ε)) 6459 </p> 6460 </td> 6461<td> 6462 <p> 6463 <span class="blue">Max = 0.658ε (Mean = 0.0537ε)</span><br> <br> 6464 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.01ε (Mean = 0.485ε)) 6465 </p> 6466 </td> 6467<td> 6468 <p> 6469 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span> 6470 Max = 0ε (Mean = 0ε)) 6471 </p> 6472 </td> 6473<td> 6474 <p> 6475 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span> 6476 Max = 0ε (Mean = 0ε)) 6477 </p> 6478 </td> 6479</tr> 6480<tr> 6481<td> 6482 <p> 6483 Erf Function: Medium Values 6484 </p> 6485 </td> 6486<td> 6487 <p> 6488 <span class="blue">Max = 1.76ε (Mean = 0.365ε)</span><br> <br> 6489 (<span class="emphasis"><em><cmath>:</em></span> Max = 1.35ε (Mean = 0.307ε))<br> 6490 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.35ε (Mean = 0.307ε)) 6491 </p> 6492 </td> 6493<td> 6494 <p> 6495 <span class="blue">Max = 0.983ε (Mean = 0.213ε)</span><br> <br> 6496 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.64ε (Mean = 0.662ε)) 6497 </p> 6498 </td> 6499<td> 6500 <p> 6501 <span class="blue">Max = 1.76ε (Mean = 0.38ε)</span><br> <br> 6502 (<span class="emphasis"><em><math.h>:</em></span> Max = 2.81ε (Mean = 0.739ε)) 6503 </p> 6504 </td> 6505<td> 6506 <p> 6507 <span class="blue">Max = 1.65ε (Mean = 0.373ε)</span><br> <br> 6508 (<span class="emphasis"><em><math.h>:</em></span> Max = 2.36ε (Mean = 0.539ε)) 6509 </p> 6510 </td> 6511</tr> 6512<tr> 6513<td> 6514 <p> 6515 Erf Function: Large Values 6516 </p> 6517 </td> 6518<td> 6519 <p> 6520 <span class="blue">Max = 1.57ε (Mean = 0.542ε)</span><br> <br> 6521 (<span class="emphasis"><em><cmath>:</em></span> Max = 1.26ε (Mean = 0.441ε))<br> 6522 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.26ε (Mean = 0.441ε)) 6523 </p> 6524 </td> 6525<td> 6526 <p> 6527 <span class="blue">Max = 0.868ε (Mean = 0.147ε)</span><br> <br> 6528 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.9ε (Mean = 0.472ε)) 6529 </p> 6530 </td> 6531<td> 6532 <p> 6533 <span class="blue">Max = 1.57ε (Mean = 0.564ε)</span><br> <br> 6534 (<span class="emphasis"><em><math.h>:</em></span> Max = 4.91ε (Mean = 1.54ε)) 6535 </p> 6536 </td> 6537<td> 6538 <p> 6539 <span class="blue">Max = 1.14ε (Mean = 0.248ε)</span><br> <br> 6540 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.84ε (Mean = 0.331ε)) 6541 </p> 6542 </td> 6543</tr> 6544</tbody> 6545</table></div> 6546</div> 6547<br class="table-break"> 6548</div> 6549<div class="section"> 6550<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 6551<a name="special_function_error_rates_rep.section_erfc_inv"></a><a class="link" href="index.html#special_function_error_rates_rep.section_erfc_inv" title="erfc_inv">erfc_inv</a> 6552</h2></div></div></div> 6553<div class="table"> 6554<a name="special_function_error_rates_rep.section_erfc_inv.table_erfc_inv"></a><p class="title"><b>Table 41. Error rates for erfc_inv</b></p> 6555<div class="table-contents"><table class="table" summary="Error rates for erfc_inv"> 6556<colgroup> 6557<col> 6558<col> 6559<col> 6560<col> 6561<col> 6562</colgroup> 6563<thead><tr> 6564<th> 6565 </th> 6566<th> 6567 <p> 6568 GNU C++ version 7.1.0<br> linux<br> double 6569 </p> 6570 </th> 6571<th> 6572 <p> 6573 GNU C++ version 7.1.0<br> linux<br> long double 6574 </p> 6575 </th> 6576<th> 6577 <p> 6578 Sun compiler version 0x5150<br> Sun Solaris<br> long double 6579 </p> 6580 </th> 6581<th> 6582 <p> 6583 Microsoft Visual C++ version 14.1<br> Win32<br> double 6584 </p> 6585 </th> 6586</tr></thead> 6587<tbody> 6588<tr> 6589<td> 6590 <p> 6591 Inverse Erfc Function 6592 </p> 6593 </td> 6594<td> 6595 <p> 6596 <span class="blue">Max = 0ε (Mean = 0ε)</span> 6597 </p> 6598 </td> 6599<td> 6600 <p> 6601 <span class="blue">Max = 0.996ε (Mean = 0.397ε)</span> 6602 </p> 6603 </td> 6604<td> 6605 <p> 6606 <span class="blue">Max = 1.08ε (Mean = 0.403ε)</span> 6607 </p> 6608 </td> 6609<td> 6610 <p> 6611 <span class="blue">Max = 1ε (Mean = 0.491ε)</span> 6612 </p> 6613 </td> 6614</tr> 6615<tr> 6616<td> 6617 <p> 6618 Inverse Erfc Function: extreme values 6619 </p> 6620 </td> 6621<td> 6622 </td> 6623<td> 6624 <p> 6625 <span class="blue">Max = 1.62ε (Mean = 0.383ε)</span> 6626 </p> 6627 </td> 6628<td> 6629 <p> 6630 <span class="blue">Max = 1.62ε (Mean = 0.383ε)</span> 6631 </p> 6632 </td> 6633<td> 6634 </td> 6635</tr> 6636</tbody> 6637</table></div> 6638</div> 6639<br class="table-break"> 6640</div> 6641<div class="section"> 6642<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 6643<a name="special_function_error_rates_rep.section_expint_Ei_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_expint_Ei_" title="expint (Ei)">expint 6644 (Ei)</a> 6645</h2></div></div></div> 6646<div class="table"> 6647<a name="special_function_error_rates_rep.section_expint_Ei_.table_expint_Ei_"></a><p class="title"><b>Table 42. Error rates for expint (Ei)</b></p> 6648<div class="table-contents"><table class="table" summary="Error rates for expint (Ei)"> 6649<colgroup> 6650<col> 6651<col> 6652<col> 6653<col> 6654<col> 6655</colgroup> 6656<thead><tr> 6657<th> 6658 </th> 6659<th> 6660 <p> 6661 GNU C++ version 7.1.0<br> linux<br> long double 6662 </p> 6663 </th> 6664<th> 6665 <p> 6666 GNU C++ version 7.1.0<br> linux<br> double 6667 </p> 6668 </th> 6669<th> 6670 <p> 6671 Sun compiler version 0x5150<br> Sun Solaris<br> long double 6672 </p> 6673 </th> 6674<th> 6675 <p> 6676 Microsoft Visual C++ version 14.1<br> Win32<br> double 6677 </p> 6678 </th> 6679</tr></thead> 6680<tbody> 6681<tr> 6682<td> 6683 <p> 6684 Exponential Integral Ei 6685 </p> 6686 </td> 6687<td> 6688 <p> 6689 <span class="blue">Max = 5.05ε (Mean = 0.821ε)</span><br> <br> 6690 (<span class="emphasis"><em><cmath>:</em></span> Max = 14.1ε (Mean = 2.43ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_expint_Ei___cmath__Exponential_Integral_Ei">And 6691 other failures.</a>) 6692 </p> 6693 </td> 6694<td> 6695 <p> 6696 <span class="blue">Max = 0.994ε (Mean = 0.142ε)</span><br> <br> 6697 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.96ε (Mean = 0.703ε)) 6698 </p> 6699 </td> 6700<td> 6701 <p> 6702 <span class="blue">Max = 5.05ε (Mean = 0.835ε)</span> 6703 </p> 6704 </td> 6705<td> 6706 <p> 6707 <span class="blue">Max = 1.43ε (Mean = 0.54ε)</span> 6708 </p> 6709 </td> 6710</tr> 6711<tr> 6712<td> 6713 <p> 6714 Exponential Integral Ei: double exponent range 6715 </p> 6716 </td> 6717<td> 6718 <p> 6719 <span class="blue">Max = 1.72ε (Mean = 0.593ε)</span><br> <br> 6720 (<span class="emphasis"><em><cmath>:</em></span> Max = 3.11ε (Mean = 1.13ε)) 6721 </p> 6722 </td> 6723<td> 6724 <p> 6725 <span class="blue">Max = 0.998ε (Mean = 0.156ε)</span><br> <br> 6726 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.5ε (Mean = 0.612ε)) 6727 </p> 6728 </td> 6729<td> 6730 <p> 6731 <span class="blue">Max = 1.72ε (Mean = 0.607ε)</span> 6732 </p> 6733 </td> 6734<td> 6735 <p> 6736 <span class="blue">Max = 1.7ε (Mean = 0.66ε)</span> 6737 </p> 6738 </td> 6739</tr> 6740<tr> 6741<td> 6742 <p> 6743 Exponential Integral Ei: long exponent range 6744 </p> 6745 </td> 6746<td> 6747 <p> 6748 <span class="blue">Max = 1.98ε (Mean = 0.595ε)</span><br> <br> 6749 (<span class="emphasis"><em><cmath>:</em></span> Max = 1.93ε (Mean = 0.855ε)) 6750 </p> 6751 </td> 6752<td> 6753 </td> 6754<td> 6755 <p> 6756 <span class="blue">Max = 1.98ε (Mean = 0.575ε)</span> 6757 </p> 6758 </td> 6759<td> 6760 </td> 6761</tr> 6762</tbody> 6763</table></div> 6764</div> 6765<br class="table-break"> 6766</div> 6767<div class="section"> 6768<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 6769<a name="special_function_error_rates_rep.section_expint_En_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_expint_En_" title="expint (En)">expint 6770 (En)</a> 6771</h2></div></div></div> 6772<div class="table"> 6773<a name="special_function_error_rates_rep.section_expint_En_.table_expint_En_"></a><p class="title"><b>Table 43. Error rates for expint (En)</b></p> 6774<div class="table-contents"><table class="table" summary="Error rates for expint (En)"> 6775<colgroup> 6776<col> 6777<col> 6778<col> 6779<col> 6780<col> 6781</colgroup> 6782<thead><tr> 6783<th> 6784 </th> 6785<th> 6786 <p> 6787 GNU C++ version 7.1.0<br> linux<br> double 6788 </p> 6789 </th> 6790<th> 6791 <p> 6792 GNU C++ version 7.1.0<br> linux<br> long double 6793 </p> 6794 </th> 6795<th> 6796 <p> 6797 Sun compiler version 0x5150<br> Sun Solaris<br> long double 6798 </p> 6799 </th> 6800<th> 6801 <p> 6802 Microsoft Visual C++ version 14.1<br> Win32<br> double 6803 </p> 6804 </th> 6805</tr></thead> 6806<tbody> 6807<tr> 6808<td> 6809 <p> 6810 Exponential Integral En 6811 </p> 6812 </td> 6813<td> 6814 <p> 6815 <span class="blue">Max = 0.589ε (Mean = 0.0331ε)</span><br> <br> 6816 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 58.5ε (Mean = 17.1ε)) 6817 </p> 6818 </td> 6819<td> 6820 <p> 6821 <span class="blue">Max = 9.97ε (Mean = 2.13ε)</span> 6822 </p> 6823 </td> 6824<td> 6825 <p> 6826 <span class="blue">Max = 9.97ε (Mean = 2.13ε)</span> 6827 </p> 6828 </td> 6829<td> 6830 <p> 6831 <span class="blue">Max = 7.16ε (Mean = 1.85ε)</span> 6832 </p> 6833 </td> 6834</tr> 6835<tr> 6836<td> 6837 <p> 6838 Exponential Integral En: small z values 6839 </p> 6840 </td> 6841<td> 6842 <p> 6843 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 6844 2.1:</em></span> Max = 115ε (Mean = 23.6ε)) 6845 </p> 6846 </td> 6847<td> 6848 <p> 6849 <span class="blue">Max = 1.99ε (Mean = 0.559ε)</span> 6850 </p> 6851 </td> 6852<td> 6853 <p> 6854 <span class="blue">Max = 1.99ε (Mean = 0.559ε)</span> 6855 </p> 6856 </td> 6857<td> 6858 <p> 6859 <span class="blue">Max = 2.62ε (Mean = 0.531ε)</span> 6860 </p> 6861 </td> 6862</tr> 6863<tr> 6864<td> 6865 <p> 6866 Exponential Integral E1 6867 </p> 6868 </td> 6869<td> 6870 <p> 6871 <span class="blue">Max = 0.556ε (Mean = 0.0625ε)</span><br> <br> 6872 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.988ε (Mean = 0.469ε)) 6873 </p> 6874 </td> 6875<td> 6876 <p> 6877 <span class="blue">Max = 0.965ε (Mean = 0.414ε)</span> 6878 </p> 6879 </td> 6880<td> 6881 <p> 6882 <span class="blue">Max = 0.965ε (Mean = 0.408ε)</span> 6883 </p> 6884 </td> 6885<td> 6886 <p> 6887 <span class="blue">Max = 0.988ε (Mean = 0.486ε)</span> 6888 </p> 6889 </td> 6890</tr> 6891</tbody> 6892</table></div> 6893</div> 6894<br class="table-break"> 6895</div> 6896<div class="section"> 6897<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 6898<a name="special_function_error_rates_rep.section_expm1"></a><a class="link" href="index.html#special_function_error_rates_rep.section_expm1" title="expm1">expm1</a> 6899</h2></div></div></div> 6900<div class="table"> 6901<a name="special_function_error_rates_rep.section_expm1.table_expm1"></a><p class="title"><b>Table 44. Error rates for expm1</b></p> 6902<div class="table-contents"><table class="table" summary="Error rates for expm1"> 6903<colgroup> 6904<col> 6905<col> 6906<col> 6907<col> 6908<col> 6909</colgroup> 6910<thead><tr> 6911<th> 6912 </th> 6913<th> 6914 <p> 6915 GNU C++ version 7.1.0<br> linux<br> long double 6916 </p> 6917 </th> 6918<th> 6919 <p> 6920 GNU C++ version 7.1.0<br> linux<br> double 6921 </p> 6922 </th> 6923<th> 6924 <p> 6925 Sun compiler version 0x5150<br> Sun Solaris<br> long double 6926 </p> 6927 </th> 6928<th> 6929 <p> 6930 Microsoft Visual C++ version 14.1<br> Win32<br> double 6931 </p> 6932 </th> 6933</tr></thead> 6934<tbody><tr> 6935<td> 6936 <p> 6937 Random test data 6938 </p> 6939 </td> 6940<td> 6941 <p> 6942 <span class="blue">Max = 0.992ε (Mean = 0.402ε)</span><br> <br> 6943 (<span class="emphasis"><em><cmath>:</em></span> Max = 0.992ε (Mean = 0.402ε))<br> 6944 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.992ε (Mean = 0.402ε)) 6945 </p> 6946 </td> 6947<td> 6948 <p> 6949 <span class="blue">Max = 0.793ε (Mean = 0.126ε)</span><br> <br> 6950 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 0.793ε (Mean = 0.126ε)) 6951 </p> 6952 </td> 6953<td> 6954 <p> 6955 <span class="blue">Max = 1.31ε (Mean = 0.428ε)</span><br> <br> 6956 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.996ε (Mean = 0.426ε)) 6957 </p> 6958 </td> 6959<td> 6960 <p> 6961 <span class="blue">Max = 1.31ε (Mean = 0.496ε)</span><br> <br> 6962 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.31ε (Mean = 0.496ε)) 6963 </p> 6964 </td> 6965</tr></tbody> 6966</table></div> 6967</div> 6968<br class="table-break"> 6969</div> 6970<div class="section"> 6971<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 6972<a name="special_function_error_rates_rep.section_gamma_p"></a><a class="link" href="index.html#special_function_error_rates_rep.section_gamma_p" title="gamma_p">gamma_p</a> 6973</h2></div></div></div> 6974<div class="table"> 6975<a name="special_function_error_rates_rep.section_gamma_p.table_gamma_p"></a><p class="title"><b>Table 45. Error rates for gamma_p</b></p> 6976<div class="table-contents"><table class="table" summary="Error rates for gamma_p"> 6977<colgroup> 6978<col> 6979<col> 6980<col> 6981<col> 6982<col> 6983</colgroup> 6984<thead><tr> 6985<th> 6986 </th> 6987<th> 6988 <p> 6989 GNU C++ version 7.1.0<br> linux<br> double 6990 </p> 6991 </th> 6992<th> 6993 <p> 6994 GNU C++ version 7.1.0<br> linux<br> long double 6995 </p> 6996 </th> 6997<th> 6998 <p> 6999 Sun compiler version 0x5150<br> Sun Solaris<br> long double 7000 </p> 7001 </th> 7002<th> 7003 <p> 7004 Microsoft Visual C++ version 14.1<br> Win32<br> double 7005 </p> 7006 </th> 7007</tr></thead> 7008<tbody> 7009<tr> 7010<td> 7011 <p> 7012 tgamma(a, z) medium values 7013 </p> 7014 </td> 7015<td> 7016 <p> 7017 <span class="blue">Max = 0.955ε (Mean = 0.05ε)</span><br> <br> 7018 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 342ε (Mean = 45.8ε))<br> (<span class="emphasis"><em>Rmath 7019 3.2.3:</em></span> Max = 389ε (Mean = 44ε)) 7020 </p> 7021 </td> 7022<td> 7023 <p> 7024 <span class="blue">Max = 41.6ε (Mean = 8.09ε)</span> 7025 </p> 7026 </td> 7027<td> 7028 <p> 7029 <span class="blue">Max = 239ε (Mean = 30.2ε)</span> 7030 </p> 7031 </td> 7032<td> 7033 <p> 7034 <span class="blue">Max = 35.1ε (Mean = 6.98ε)</span> 7035 </p> 7036 </td> 7037</tr> 7038<tr> 7039<td> 7040 <p> 7041 tgamma(a, z) small values 7042 </p> 7043 </td> 7044<td> 7045 <p> 7046 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 7047 2.1:</em></span> Max = 4.82ε (Mean = 0.758ε))<br> (<span class="emphasis"><em>Rmath 7048 3.2.3:</em></span> Max = 1.01ε (Mean = 0.306ε)) 7049 </p> 7050 </td> 7051<td> 7052 <p> 7053 <span class="blue">Max = 2ε (Mean = 0.464ε)</span> 7054 </p> 7055 </td> 7056<td> 7057 <p> 7058 <span class="blue">Max = 2ε (Mean = 0.461ε)</span> 7059 </p> 7060 </td> 7061<td> 7062 <p> 7063 <span class="blue">Max = 1.54ε (Mean = 0.439ε)</span> 7064 </p> 7065 </td> 7066</tr> 7067<tr> 7068<td> 7069 <p> 7070 tgamma(a, z) large values 7071 </p> 7072 </td> 7073<td> 7074 <p> 7075 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 7076 2.1:</em></span> Max = 1.02e+03ε (Mean = 105ε))<br> (<span class="emphasis"><em>Rmath 7077 3.2.3:</em></span> Max = 1.11e+03ε (Mean = 67.5ε)) 7078 </p> 7079 </td> 7080<td> 7081 <p> 7082 <span class="blue">Max = 3.08e+04ε (Mean = 1.86e+03ε)</span> 7083 </p> 7084 </td> 7085<td> 7086 <p> 7087 <span class="blue">Max = 3.02e+04ε (Mean = 1.91e+03ε)</span> 7088 </p> 7089 </td> 7090<td> 7091 <p> 7092 <span class="blue">Max = 243ε (Mean = 20.2ε)</span> 7093 </p> 7094 </td> 7095</tr> 7096<tr> 7097<td> 7098 <p> 7099 tgamma(a, z) integer and half integer values 7100 </p> 7101 </td> 7102<td> 7103 <p> 7104 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 7105 2.1:</em></span> Max = 128ε (Mean = 22.6ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 7106 Max = 66.2ε (Mean = 12.2ε)) 7107 </p> 7108 </td> 7109<td> 7110 <p> 7111 <span class="blue">Max = 11.8ε (Mean = 2.66ε)</span> 7112 </p> 7113 </td> 7114<td> 7115 <p> 7116 <span class="blue">Max = 71.6ε (Mean = 9.47ε)</span> 7117 </p> 7118 </td> 7119<td> 7120 <p> 7121 <span class="blue">Max = 13ε (Mean = 2.97ε)</span> 7122 </p> 7123 </td> 7124</tr> 7125</tbody> 7126</table></div> 7127</div> 7128<br class="table-break"> 7129</div> 7130<div class="section"> 7131<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 7132<a name="special_function_error_rates_rep.section_gamma_p_inv"></a><a class="link" href="index.html#special_function_error_rates_rep.section_gamma_p_inv" title="gamma_p_inv">gamma_p_inv</a> 7133</h2></div></div></div> 7134<div class="table"> 7135<a name="special_function_error_rates_rep.section_gamma_p_inv.table_gamma_p_inv"></a><p class="title"><b>Table 46. Error rates for gamma_p_inv</b></p> 7136<div class="table-contents"><table class="table" summary="Error rates for gamma_p_inv"> 7137<colgroup> 7138<col> 7139<col> 7140<col> 7141<col> 7142<col> 7143</colgroup> 7144<thead><tr> 7145<th> 7146 </th> 7147<th> 7148 <p> 7149 GNU C++ version 7.1.0<br> linux<br> double 7150 </p> 7151 </th> 7152<th> 7153 <p> 7154 GNU C++ version 7.1.0<br> linux<br> long double 7155 </p> 7156 </th> 7157<th> 7158 <p> 7159 Sun compiler version 0x5150<br> Sun Solaris<br> long double 7160 </p> 7161 </th> 7162<th> 7163 <p> 7164 Microsoft Visual C++ version 14.1<br> Win32<br> double 7165 </p> 7166 </th> 7167</tr></thead> 7168<tbody> 7169<tr> 7170<td> 7171 <p> 7172 incomplete gamma inverse(a, z) medium values 7173 </p> 7174 </td> 7175<td> 7176 <p> 7177 <span class="blue">Max = 0.993ε (Mean = 0.15ε)</span><br> <br> 7178 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 4.88ε (Mean = 0.868ε)) 7179 </p> 7180 </td> 7181<td> 7182 <p> 7183 <span class="blue">Max = 1.8ε (Mean = 0.406ε)</span> 7184 </p> 7185 </td> 7186<td> 7187 <p> 7188 <span class="blue">Max = 1.89ε (Mean = 0.466ε)</span> 7189 </p> 7190 </td> 7191<td> 7192 <p> 7193 <span class="blue">Max = 1.71ε (Mean = 0.34ε)</span> 7194 </p> 7195 </td> 7196</tr> 7197<tr> 7198<td> 7199 <p> 7200 incomplete gamma inverse(a, z) large values 7201 </p> 7202 </td> 7203<td> 7204 <p> 7205 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath 7206 3.2.3:</em></span> Max = 0.816ε (Mean = 0.0874ε)) 7207 </p> 7208 </td> 7209<td> 7210 <p> 7211 <span class="blue">Max = 0.509ε (Mean = 0.0447ε)</span> 7212 </p> 7213 </td> 7214<td> 7215 <p> 7216 <span class="blue">Max = 0.509ε (Mean = 0.0447ε)</span> 7217 </p> 7218 </td> 7219<td> 7220 <p> 7221 <span class="blue">Max = 0.924ε (Mean = 0.108ε)</span> 7222 </p> 7223 </td> 7224</tr> 7225<tr> 7226<td> 7227 <p> 7228 incomplete gamma inverse(a, z) small values 7229 </p> 7230 </td> 7231<td> 7232 <p> 7233 <span class="blue">Max = 441ε (Mean = 53.9ε)</span><br> <br> 7234 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 547ε (Mean = 61.6ε)) 7235 </p> 7236 </td> 7237<td> 7238 <p> 7239 <span class="blue">Max = 9.17e+03ε (Mean = 1.45e+03ε)</span> 7240 </p> 7241 </td> 7242<td> 7243 <p> 7244 <span class="blue">Max = 1.09e+04ε (Mean = 1.3e+03ε)</span> 7245 </p> 7246 </td> 7247<td> 7248 <p> 7249 <span class="blue">Max = 1.1e+03ε (Mean = 131ε)</span> 7250 </p> 7251 </td> 7252</tr> 7253</tbody> 7254</table></div> 7255</div> 7256<br class="table-break"> 7257</div> 7258<div class="section"> 7259<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 7260<a name="special_function_error_rates_rep.section_gamma_p_inva"></a><a class="link" href="index.html#special_function_error_rates_rep.section_gamma_p_inva" title="gamma_p_inva">gamma_p_inva</a> 7261</h2></div></div></div> 7262<div class="table"> 7263<a name="special_function_error_rates_rep.section_gamma_p_inva.table_gamma_p_inva"></a><p class="title"><b>Table 47. Error rates for gamma_p_inva</b></p> 7264<div class="table-contents"><table class="table" summary="Error rates for gamma_p_inva"> 7265<colgroup> 7266<col> 7267<col> 7268<col> 7269<col> 7270<col> 7271</colgroup> 7272<thead><tr> 7273<th> 7274 </th> 7275<th> 7276 <p> 7277 GNU C++ version 7.1.0<br> linux<br> double 7278 </p> 7279 </th> 7280<th> 7281 <p> 7282 GNU C++ version 7.1.0<br> linux<br> long double 7283 </p> 7284 </th> 7285<th> 7286 <p> 7287 Sun compiler version 0x5150<br> Sun Solaris<br> long double 7288 </p> 7289 </th> 7290<th> 7291 <p> 7292 Microsoft Visual C++ version 14.1<br> Win32<br> double 7293 </p> 7294 </th> 7295</tr></thead> 7296<tbody><tr> 7297<td> 7298 <p> 7299 Incomplete gamma inverses. 7300 </p> 7301 </td> 7302<td> 7303 <p> 7304 <span class="blue">Max = 0ε (Mean = 0ε)</span> 7305 </p> 7306 </td> 7307<td> 7308 <p> 7309 <span class="blue">Max = 7.87ε (Mean = 1.15ε)</span> 7310 </p> 7311 </td> 7312<td> 7313 <p> 7314 <span class="blue">Max = 4.08ε (Mean = 1.12ε)</span> 7315 </p> 7316 </td> 7317<td> 7318 <p> 7319 <span class="blue">Max = 4.92ε (Mean = 1.03ε)</span> 7320 </p> 7321 </td> 7322</tr></tbody> 7323</table></div> 7324</div> 7325<br class="table-break"> 7326</div> 7327<div class="section"> 7328<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 7329<a name="special_function_error_rates_rep.section_gamma_q"></a><a class="link" href="index.html#special_function_error_rates_rep.section_gamma_q" title="gamma_q">gamma_q</a> 7330</h2></div></div></div> 7331<div class="table"> 7332<a name="special_function_error_rates_rep.section_gamma_q.table_gamma_q"></a><p class="title"><b>Table 48. Error rates for gamma_q</b></p> 7333<div class="table-contents"><table class="table" summary="Error rates for gamma_q"> 7334<colgroup> 7335<col> 7336<col> 7337<col> 7338<col> 7339<col> 7340</colgroup> 7341<thead><tr> 7342<th> 7343 </th> 7344<th> 7345 <p> 7346 GNU C++ version 7.1.0<br> linux<br> double 7347 </p> 7348 </th> 7349<th> 7350 <p> 7351 GNU C++ version 7.1.0<br> linux<br> long double 7352 </p> 7353 </th> 7354<th> 7355 <p> 7356 Sun compiler version 0x5150<br> Sun Solaris<br> long double 7357 </p> 7358 </th> 7359<th> 7360 <p> 7361 Microsoft Visual C++ version 14.1<br> Win32<br> double 7362 </p> 7363 </th> 7364</tr></thead> 7365<tbody> 7366<tr> 7367<td> 7368 <p> 7369 tgamma(a, z) medium values 7370 </p> 7371 </td> 7372<td> 7373 <p> 7374 <span class="blue">Max = 0.927ε (Mean = 0.035ε)</span><br> <br> 7375 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 201ε (Mean = 13.5ε))<br> (<span class="emphasis"><em>Rmath 7376 3.2.3:</em></span> Max = 131ε (Mean = 12.7ε)) 7377 </p> 7378 </td> 7379<td> 7380 <p> 7381 <span class="blue">Max = 32.3ε (Mean = 6.61ε)</span> 7382 </p> 7383 </td> 7384<td> 7385 <p> 7386 <span class="blue">Max = 199ε (Mean = 26.6ε)</span> 7387 </p> 7388 </td> 7389<td> 7390 <p> 7391 <span class="blue">Max = 23.7ε (Mean = 4ε)</span> 7392 </p> 7393 </td> 7394</tr> 7395<tr> 7396<td> 7397 <p> 7398 tgamma(a, z) small values 7399 </p> 7400 </td> 7401<td> 7402 <p> 7403 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 7404 2.1:</em></span> <span class="red">Max = 1.38e+10ε (Mean = 1.05e+09ε))</span><br> 7405 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 65.6ε (Mean = 11ε)) 7406 </p> 7407 </td> 7408<td> 7409 <p> 7410 <span class="blue">Max = 2.45ε (Mean = 0.885ε)</span> 7411 </p> 7412 </td> 7413<td> 7414 <p> 7415 <span class="blue">Max = 2.45ε (Mean = 0.819ε)</span> 7416 </p> 7417 </td> 7418<td> 7419 <p> 7420 <span class="blue">Max = 2.26ε (Mean = 0.74ε)</span> 7421 </p> 7422 </td> 7423</tr> 7424<tr> 7425<td> 7426 <p> 7427 tgamma(a, z) large values 7428 </p> 7429 </td> 7430<td> 7431 <p> 7432 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 7433 2.1:</em></span> Max = 2.71e+04ε (Mean = 2.16e+03ε))<br> (<span class="emphasis"><em>Rmath 7434 3.2.3:</em></span> Max = 1.02e+03ε (Mean = 62.7ε)) 7435 </p> 7436 </td> 7437<td> 7438 <p> 7439 <span class="blue">Max = 6.82e+03ε (Mean = 414ε)</span> 7440 </p> 7441 </td> 7442<td> 7443 <p> 7444 <span class="blue">Max = 1.15e+04ε (Mean = 733ε)</span> 7445 </p> 7446 </td> 7447<td> 7448 <p> 7449 <span class="blue">Max = 469ε (Mean = 31.5ε)</span> 7450 </p> 7451 </td> 7452</tr> 7453<tr> 7454<td> 7455 <p> 7456 tgamma(a, z) integer and half integer values 7457 </p> 7458 </td> 7459<td> 7460 <p> 7461 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 7462 2.1:</em></span> Max = 118ε (Mean = 12.5ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 7463 Max = 138ε (Mean = 16.9ε)) 7464 </p> 7465 </td> 7466<td> 7467 <p> 7468 <span class="blue">Max = 11.1ε (Mean = 2.07ε)</span> 7469 </p> 7470 </td> 7471<td> 7472 <p> 7473 <span class="blue">Max = 54.7ε (Mean = 6.16ε)</span> 7474 </p> 7475 </td> 7476<td> 7477 <p> 7478 <span class="blue">Max = 8.72ε (Mean = 1.48ε)</span> 7479 </p> 7480 </td> 7481</tr> 7482</tbody> 7483</table></div> 7484</div> 7485<br class="table-break"> 7486</div> 7487<div class="section"> 7488<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 7489<a name="special_function_error_rates_rep.section_gamma_q_inv"></a><a class="link" href="index.html#special_function_error_rates_rep.section_gamma_q_inv" title="gamma_q_inv">gamma_q_inv</a> 7490</h2></div></div></div> 7491<div class="table"> 7492<a name="special_function_error_rates_rep.section_gamma_q_inv.table_gamma_q_inv"></a><p class="title"><b>Table 49. Error rates for gamma_q_inv</b></p> 7493<div class="table-contents"><table class="table" summary="Error rates for gamma_q_inv"> 7494<colgroup> 7495<col> 7496<col> 7497<col> 7498<col> 7499<col> 7500</colgroup> 7501<thead><tr> 7502<th> 7503 </th> 7504<th> 7505 <p> 7506 GNU C++ version 7.1.0<br> linux<br> double 7507 </p> 7508 </th> 7509<th> 7510 <p> 7511 GNU C++ version 7.1.0<br> linux<br> long double 7512 </p> 7513 </th> 7514<th> 7515 <p> 7516 Sun compiler version 0x5150<br> Sun Solaris<br> long double 7517 </p> 7518 </th> 7519<th> 7520 <p> 7521 Microsoft Visual C++ version 14.1<br> Win32<br> double 7522 </p> 7523 </th> 7524</tr></thead> 7525<tbody> 7526<tr> 7527<td> 7528 <p> 7529 incomplete gamma inverse(a, z) medium values 7530 </p> 7531 </td> 7532<td> 7533 <p> 7534 <span class="blue">Max = 0.912ε (Mean = 0.154ε)</span><br> <br> 7535 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 4.66ε (Mean = 0.792ε)) 7536 </p> 7537 </td> 7538<td> 7539 <p> 7540 <span class="blue">Max = 6.2ε (Mean = 0.627ε)</span> 7541 </p> 7542 </td> 7543<td> 7544 <p> 7545 <span class="blue">Max = 6.2ε (Mean = 0.683ε)</span> 7546 </p> 7547 </td> 7548<td> 7549 <p> 7550 <span class="blue">Max = 2.88ε (Mean = 0.469ε)</span> 7551 </p> 7552 </td> 7553</tr> 7554<tr> 7555<td> 7556 <p> 7557 incomplete gamma inverse(a, z) large values 7558 </p> 7559 </td> 7560<td> 7561 <p> 7562 <span class="blue">Max = 0.894ε (Mean = 0.0915ε)</span><br> <br> 7563 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 0.894ε (Mean = 0.106ε)) 7564 </p> 7565 </td> 7566<td> 7567 <p> 7568 <span class="blue">Max = 0ε (Mean = 0ε)</span> 7569 </p> 7570 </td> 7571<td> 7572 <p> 7573 <span class="blue">Max = 0ε (Mean = 0ε)</span> 7574 </p> 7575 </td> 7576<td> 7577 <p> 7578 <span class="blue">Max = 0.814ε (Mean = 0.0856ε)</span> 7579 </p> 7580 </td> 7581</tr> 7582<tr> 7583<td> 7584 <p> 7585 incomplete gamma inverse(a, z) small values 7586 </p> 7587 </td> 7588<td> 7589 <p> 7590 <span class="blue">Max = 292ε (Mean = 36.4ε)</span><br> <br> 7591 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 415ε (Mean = 48.7ε)) 7592 </p> 7593 </td> 7594<td> 7595 <p> 7596 <span class="blue">Max = 8.28e+03ε (Mean = 1.09e+03ε)</span> 7597 </p> 7598 </td> 7599<td> 7600 <p> 7601 <span class="blue">Max = 8.98e+03ε (Mean = 877ε)</span> 7602 </p> 7603 </td> 7604<td> 7605 <p> 7606 <span class="blue">Max = 451ε (Mean = 64.7ε)</span> 7607 </p> 7608 </td> 7609</tr> 7610</tbody> 7611</table></div> 7612</div> 7613<br class="table-break"> 7614</div> 7615<div class="section"> 7616<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 7617<a name="special_function_error_rates_rep.section_gamma_q_inva"></a><a class="link" href="index.html#special_function_error_rates_rep.section_gamma_q_inva" title="gamma_q_inva">gamma_q_inva</a> 7618</h2></div></div></div> 7619<div class="table"> 7620<a name="special_function_error_rates_rep.section_gamma_q_inva.table_gamma_q_inva"></a><p class="title"><b>Table 50. Error rates for gamma_q_inva</b></p> 7621<div class="table-contents"><table class="table" summary="Error rates for gamma_q_inva"> 7622<colgroup> 7623<col> 7624<col> 7625<col> 7626<col> 7627<col> 7628</colgroup> 7629<thead><tr> 7630<th> 7631 </th> 7632<th> 7633 <p> 7634 GNU C++ version 7.1.0<br> linux<br> double 7635 </p> 7636 </th> 7637<th> 7638 <p> 7639 GNU C++ version 7.1.0<br> linux<br> long double 7640 </p> 7641 </th> 7642<th> 7643 <p> 7644 Sun compiler version 0x5150<br> Sun Solaris<br> long double 7645 </p> 7646 </th> 7647<th> 7648 <p> 7649 Microsoft Visual C++ version 14.1<br> Win32<br> double 7650 </p> 7651 </th> 7652</tr></thead> 7653<tbody><tr> 7654<td> 7655 <p> 7656 Incomplete gamma inverses. 7657 </p> 7658 </td> 7659<td> 7660 <p> 7661 <span class="blue">Max = 0ε (Mean = 0ε)</span> 7662 </p> 7663 </td> 7664<td> 7665 <p> 7666 <span class="blue">Max = 8.42ε (Mean = 1.3ε)</span> 7667 </p> 7668 </td> 7669<td> 7670 <p> 7671 <span class="blue">Max = 7.86ε (Mean = 1.24ε)</span> 7672 </p> 7673 </td> 7674<td> 7675 <p> 7676 <span class="blue">Max = 5.05ε (Mean = 1.08ε)</span> 7677 </p> 7678 </td> 7679</tr></tbody> 7680</table></div> 7681</div> 7682<br class="table-break"> 7683</div> 7684<div class="section"> 7685<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 7686<a name="special_function_error_rates_rep.section_hermite"></a><a class="link" href="index.html#special_function_error_rates_rep.section_hermite" title="hermite">hermite</a> 7687</h2></div></div></div> 7688<div class="table"> 7689<a name="special_function_error_rates_rep.section_hermite.table_hermite"></a><p class="title"><b>Table 51. Error rates for hermite</b></p> 7690<div class="table-contents"><table class="table" summary="Error rates for hermite"> 7691<colgroup> 7692<col> 7693<col> 7694<col> 7695<col> 7696<col> 7697</colgroup> 7698<thead><tr> 7699<th> 7700 </th> 7701<th> 7702 <p> 7703 GNU C++ version 7.1.0<br> linux<br> double 7704 </p> 7705 </th> 7706<th> 7707 <p> 7708 GNU C++ version 7.1.0<br> linux<br> long double 7709 </p> 7710 </th> 7711<th> 7712 <p> 7713 Sun compiler version 0x5150<br> Sun Solaris<br> long double 7714 </p> 7715 </th> 7716<th> 7717 <p> 7718 Microsoft Visual C++ version 14.1<br> Win32<br> double 7719 </p> 7720 </th> 7721</tr></thead> 7722<tbody><tr> 7723<td> 7724 <p> 7725 Hermite Polynomials 7726 </p> 7727 </td> 7728<td> 7729 <p> 7730 <span class="blue">Max = 0ε (Mean = 0ε)</span> 7731 </p> 7732 </td> 7733<td> 7734 <p> 7735 <span class="blue">Max = 6.24ε (Mean = 2.07ε)</span> 7736 </p> 7737 </td> 7738<td> 7739 <p> 7740 <span class="blue">Max = 6.24ε (Mean = 2.07ε)</span> 7741 </p> 7742 </td> 7743<td> 7744 <p> 7745 <span class="blue">Max = 4.46ε (Mean = 1.41ε)</span> 7746 </p> 7747 </td> 7748</tr></tbody> 7749</table></div> 7750</div> 7751<br class="table-break"> 7752</div> 7753<div class="section"> 7754<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 7755<a name="special_function_error_rates_rep.section_heuman_lambda"></a><a class="link" href="index.html#special_function_error_rates_rep.section_heuman_lambda" title="heuman_lambda">heuman_lambda</a> 7756</h2></div></div></div> 7757<div class="table"> 7758<a name="special_function_error_rates_rep.section_heuman_lambda.table_heuman_lambda"></a><p class="title"><b>Table 52. Error rates for heuman_lambda</b></p> 7759<div class="table-contents"><table class="table" summary="Error rates for heuman_lambda"> 7760<colgroup> 7761<col> 7762<col> 7763<col> 7764<col> 7765<col> 7766</colgroup> 7767<thead><tr> 7768<th> 7769 </th> 7770<th> 7771 <p> 7772 GNU C++ version 7.1.0<br> linux<br> double 7773 </p> 7774 </th> 7775<th> 7776 <p> 7777 GNU C++ version 7.1.0<br> linux<br> long double 7778 </p> 7779 </th> 7780<th> 7781 <p> 7782 Sun compiler version 0x5150<br> Sun Solaris<br> long double 7783 </p> 7784 </th> 7785<th> 7786 <p> 7787 Microsoft Visual C++ version 14.1<br> Win32<br> double 7788 </p> 7789 </th> 7790</tr></thead> 7791<tbody> 7792<tr> 7793<td> 7794 <p> 7795 Elliptic Integral Jacobi Zeta: Mathworld Data 7796 </p> 7797 </td> 7798<td> 7799 <p> 7800 <span class="blue">Max = 0ε (Mean = 0ε)</span> 7801 </p> 7802 </td> 7803<td> 7804 <p> 7805 <span class="blue">Max = 1.89ε (Mean = 0.887ε)</span> 7806 </p> 7807 </td> 7808<td> 7809 <p> 7810 <span class="blue">Max = 1.89ε (Mean = 0.887ε)</span> 7811 </p> 7812 </td> 7813<td> 7814 <p> 7815 <span class="blue">Max = 1.08ε (Mean = 0.734ε)</span> 7816 </p> 7817 </td> 7818</tr> 7819<tr> 7820<td> 7821 <p> 7822 Elliptic Integral Heuman Lambda: Random Data 7823 </p> 7824 </td> 7825<td> 7826 <p> 7827 <span class="blue">Max = 0ε (Mean = 0ε)</span> 7828 </p> 7829 </td> 7830<td> 7831 <p> 7832 <span class="blue">Max = 3.82ε (Mean = 0.609ε)</span> 7833 </p> 7834 </td> 7835<td> 7836 <p> 7837 <span class="blue">Max = 3.82ε (Mean = 0.608ε)</span> 7838 </p> 7839 </td> 7840<td> 7841 <p> 7842 <span class="blue">Max = 2.12ε (Mean = 0.588ε)</span> 7843 </p> 7844 </td> 7845</tr> 7846</tbody> 7847</table></div> 7848</div> 7849<br class="table-break"> 7850</div> 7851<div class="section"> 7852<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 7853<a name="special_function_error_rates_rep.section_ibeta"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ibeta" title="ibeta">ibeta</a> 7854</h2></div></div></div> 7855<div class="table"> 7856<a name="special_function_error_rates_rep.section_ibeta.table_ibeta"></a><p class="title"><b>Table 53. Error rates for ibeta</b></p> 7857<div class="table-contents"><table class="table" summary="Error rates for ibeta"> 7858<colgroup> 7859<col> 7860<col> 7861<col> 7862<col> 7863<col> 7864</colgroup> 7865<thead><tr> 7866<th> 7867 </th> 7868<th> 7869 <p> 7870 GNU C++ version 7.1.0<br> linux<br> double 7871 </p> 7872 </th> 7873<th> 7874 <p> 7875 GNU C++ version 7.1.0<br> linux<br> long double 7876 </p> 7877 </th> 7878<th> 7879 <p> 7880 Sun compiler version 0x5150<br> Sun Solaris<br> long double 7881 </p> 7882 </th> 7883<th> 7884 <p> 7885 Microsoft Visual C++ version 14.1<br> Win32<br> double 7886 </p> 7887 </th> 7888</tr></thead> 7889<tbody> 7890<tr> 7891<td> 7892 <p> 7893 Incomplete Beta Function: Small Values 7894 </p> 7895 </td> 7896<td> 7897 <p> 7898 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 7899 2.1:</em></span> Max = 682ε (Mean = 32.6ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 7900 Max = 22.9ε (Mean = 3.35ε)) 7901 </p> 7902 </td> 7903<td> 7904 <p> 7905 <span class="blue">Max = 8.97ε (Mean = 2.09ε)</span> 7906 </p> 7907 </td> 7908<td> 7909 <p> 7910 <span class="blue">Max = 21.3ε (Mean = 2.75ε)</span> 7911 </p> 7912 </td> 7913<td> 7914 <p> 7915 <span class="blue">Max = 8.4ε (Mean = 1.93ε)</span> 7916 </p> 7917 </td> 7918</tr> 7919<tr> 7920<td> 7921 <p> 7922 Incomplete Beta Function: Medium Values 7923 </p> 7924 </td> 7925<td> 7926 <p> 7927 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 7928 2.1:</em></span> Max = 690ε (Mean = 151ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 7929 Max = 232ε (Mean = 27.9ε)) 7930 </p> 7931 </td> 7932<td> 7933 <p> 7934 <span class="blue">Max = 50ε (Mean = 12.1ε)</span> 7935 </p> 7936 </td> 7937<td> 7938 <p> 7939 <span class="blue">Max = 124ε (Mean = 18.4ε)</span> 7940 </p> 7941 </td> 7942<td> 7943 <p> 7944 <span class="blue">Max = 106ε (Mean = 16.3ε)</span> 7945 </p> 7946 </td> 7947</tr> 7948<tr> 7949<td> 7950 <p> 7951 Incomplete Beta Function: Large and Diverse Values 7952 </p> 7953 </td> 7954<td> 7955 <p> 7956 <span class="blue">Max = 1.26ε (Mean = 0.063ε)</span><br> <br> 7957 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.9e+05ε (Mean = 1.82e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ibeta_GSL_2_1_Incomplete_Beta_Function_Large_and_Diverse_Values">And 7958 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 7959 Max = 574ε (Mean = 49.4ε)) 7960 </p> 7961 </td> 7962<td> 7963 <p> 7964 <span class="blue">Max = 1.96e+04ε (Mean = 997ε)</span> 7965 </p> 7966 </td> 7967<td> 7968 <p> 7969 <span class="blue">Max = 4.98e+04ε (Mean = 2.07e+03ε)</span> 7970 </p> 7971 </td> 7972<td> 7973 <p> 7974 <span class="blue">Max = 1.32e+03ε (Mean = 68.5ε)</span> 7975 </p> 7976 </td> 7977</tr> 7978<tr> 7979<td> 7980 <p> 7981 Incomplete Beta Function: Small Integer Values 7982 </p> 7983 </td> 7984<td> 7985 <p> 7986 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 7987 2.1:</em></span> Max = 254ε (Mean = 50.9ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 7988 Max = 62.2ε (Mean = 8.95ε)) 7989 </p> 7990 </td> 7991<td> 7992 <p> 7993 <span class="blue">Max = 4.45ε (Mean = 0.814ε)</span> 7994 </p> 7995 </td> 7996<td> 7997 <p> 7998 <span class="blue">Max = 44.5ε (Mean = 10.1ε)</span> 7999 </p> 8000 </td> 8001<td> 8002 <p> 8003 <span class="blue">Max = 3.85ε (Mean = 0.791ε)</span> 8004 </p> 8005 </td> 8006</tr> 8007</tbody> 8008</table></div> 8009</div> 8010<br class="table-break"> 8011</div> 8012<div class="section"> 8013<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 8014<a name="special_function_error_rates_rep.section_ibeta_inv"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ibeta_inv" title="ibeta_inv">ibeta_inv</a> 8015</h2></div></div></div> 8016<div class="table"> 8017<a name="special_function_error_rates_rep.section_ibeta_inv.table_ibeta_inv"></a><p class="title"><b>Table 54. Error rates for ibeta_inv</b></p> 8018<div class="table-contents"><table class="table" summary="Error rates for ibeta_inv"> 8019<colgroup> 8020<col> 8021<col> 8022<col> 8023<col> 8024<col> 8025</colgroup> 8026<thead><tr> 8027<th> 8028 </th> 8029<th> 8030 <p> 8031 GNU C++ version 7.1.0<br> linux<br> double 8032 </p> 8033 </th> 8034<th> 8035 <p> 8036 GNU C++ version 7.1.0<br> linux<br> long double 8037 </p> 8038 </th> 8039<th> 8040 <p> 8041 Sun compiler version 0x5150<br> Sun Solaris<br> long double 8042 </p> 8043 </th> 8044<th> 8045 <p> 8046 Microsoft Visual C++ version 14.1<br> Win32<br> double 8047 </p> 8048 </th> 8049</tr></thead> 8050<tbody><tr> 8051<td> 8052 <p> 8053 Inverse incomplete beta 8054 </p> 8055 </td> 8056<td> 8057 <p> 8058 <span class="blue">Max = 11ε (Mean = 0.345ε)</span><br> <br> 8059 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 1.14e+121ε (Mean 8060 = 3.28e+119ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ibeta_inv_Rmath_3_2_3_Inverse_incomplete_beta">And 8061 other failures.</a>)</span> 8062 </p> 8063 </td> 8064<td> 8065 <p> 8066 <span class="blue">Max = 3.8e+04ε (Mean = 2.66e+03ε)</span> 8067 </p> 8068 </td> 8069<td> 8070 <p> 8071 <span class="blue">Max = 4.07e+04ε (Mean = 2.86e+03ε)</span> 8072 </p> 8073 </td> 8074<td> 8075 <p> 8076 <span class="blue">Max = 8.59e+03ε (Mean = 277ε)</span> 8077 </p> 8078 </td> 8079</tr></tbody> 8080</table></div> 8081</div> 8082<br class="table-break"> 8083</div> 8084<div class="section"> 8085<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 8086<a name="special_function_error_rates_rep.section_ibeta_inva"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ibeta_inva" title="ibeta_inva">ibeta_inva</a> 8087</h2></div></div></div> 8088<div class="table"> 8089<a name="special_function_error_rates_rep.section_ibeta_inva.table_ibeta_inva"></a><p class="title"><b>Table 55. Error rates for ibeta_inva</b></p> 8090<div class="table-contents"><table class="table" summary="Error rates for ibeta_inva"> 8091<colgroup> 8092<col> 8093<col> 8094<col> 8095<col> 8096<col> 8097</colgroup> 8098<thead><tr> 8099<th> 8100 </th> 8101<th> 8102 <p> 8103 GNU C++ version 7.1.0<br> linux<br> double 8104 </p> 8105 </th> 8106<th> 8107 <p> 8108 GNU C++ version 7.1.0<br> linux<br> long double 8109 </p> 8110 </th> 8111<th> 8112 <p> 8113 Sun compiler version 0x5150<br> Sun Solaris<br> long double 8114 </p> 8115 </th> 8116<th> 8117 <p> 8118 Microsoft Visual C++ version 14.1<br> Win32<br> double 8119 </p> 8120 </th> 8121</tr></thead> 8122<tbody><tr> 8123<td> 8124 <p> 8125 Inverse incomplete beta 8126 </p> 8127 </td> 8128<td> 8129 <p> 8130 <span class="blue">Max = 0.602ε (Mean = 0.0239ε)</span> 8131 </p> 8132 </td> 8133<td> 8134 <p> 8135 <span class="blue">Max = 377ε (Mean = 24.4ε)</span> 8136 </p> 8137 </td> 8138<td> 8139 <p> 8140 <span class="blue">Max = 438ε (Mean = 31.3ε)</span> 8141 </p> 8142 </td> 8143<td> 8144 <p> 8145 <span class="blue">Max = 242ε (Mean = 22.9ε)</span> 8146 </p> 8147 </td> 8148</tr></tbody> 8149</table></div> 8150</div> 8151<br class="table-break"> 8152</div> 8153<div class="section"> 8154<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 8155<a name="special_function_error_rates_rep.section_ibeta_invb"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ibeta_invb" title="ibeta_invb">ibeta_invb</a> 8156</h2></div></div></div> 8157<div class="table"> 8158<a name="special_function_error_rates_rep.section_ibeta_invb.table_ibeta_invb"></a><p class="title"><b>Table 56. Error rates for ibeta_invb</b></p> 8159<div class="table-contents"><table class="table" summary="Error rates for ibeta_invb"> 8160<colgroup> 8161<col> 8162<col> 8163<col> 8164<col> 8165<col> 8166</colgroup> 8167<thead><tr> 8168<th> 8169 </th> 8170<th> 8171 <p> 8172 GNU C++ version 7.1.0<br> linux<br> double 8173 </p> 8174 </th> 8175<th> 8176 <p> 8177 GNU C++ version 7.1.0<br> linux<br> long double 8178 </p> 8179 </th> 8180<th> 8181 <p> 8182 Sun compiler version 0x5150<br> Sun Solaris<br> long double 8183 </p> 8184 </th> 8185<th> 8186 <p> 8187 Microsoft Visual C++ version 14.1<br> Win32<br> double 8188 </p> 8189 </th> 8190</tr></thead> 8191<tbody><tr> 8192<td> 8193 <p> 8194 Inverse incomplete beta 8195 </p> 8196 </td> 8197<td> 8198 <p> 8199 <span class="blue">Max = 0.765ε (Mean = 0.0422ε)</span> 8200 </p> 8201 </td> 8202<td> 8203 <p> 8204 <span class="blue">Max = 407ε (Mean = 27.2ε)</span> 8205 </p> 8206 </td> 8207<td> 8208 <p> 8209 <span class="blue">Max = 407ε (Mean = 24.4ε)</span> 8210 </p> 8211 </td> 8212<td> 8213 <p> 8214 <span class="blue">Max = 409ε (Mean = 19.3ε)</span> 8215 </p> 8216 </td> 8217</tr></tbody> 8218</table></div> 8219</div> 8220<br class="table-break"> 8221</div> 8222<div class="section"> 8223<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 8224<a name="special_function_error_rates_rep.section_ibetac"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ibetac" title="ibetac">ibetac</a> 8225</h2></div></div></div> 8226<div class="table"> 8227<a name="special_function_error_rates_rep.section_ibetac.table_ibetac"></a><p class="title"><b>Table 57. Error rates for ibetac</b></p> 8228<div class="table-contents"><table class="table" summary="Error rates for ibetac"> 8229<colgroup> 8230<col> 8231<col> 8232<col> 8233<col> 8234<col> 8235</colgroup> 8236<thead><tr> 8237<th> 8238 </th> 8239<th> 8240 <p> 8241 GNU C++ version 7.1.0<br> linux<br> double 8242 </p> 8243 </th> 8244<th> 8245 <p> 8246 GNU C++ version 7.1.0<br> linux<br> long double 8247 </p> 8248 </th> 8249<th> 8250 <p> 8251 Sun compiler version 0x5150<br> Sun Solaris<br> long double 8252 </p> 8253 </th> 8254<th> 8255 <p> 8256 Microsoft Visual C++ version 14.1<br> Win32<br> double 8257 </p> 8258 </th> 8259</tr></thead> 8260<tbody> 8261<tr> 8262<td> 8263 <p> 8264 Incomplete Beta Function: Small Values 8265 </p> 8266 </td> 8267<td> 8268 <p> 8269 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath 8270 3.2.3:</em></span> Max = 22.4ε (Mean = 3.67ε)) 8271 </p> 8272 </td> 8273<td> 8274 <p> 8275 <span class="blue">Max = 10.6ε (Mean = 2.22ε)</span> 8276 </p> 8277 </td> 8278<td> 8279 <p> 8280 <span class="blue">Max = 13.8ε (Mean = 2.68ε)</span> 8281 </p> 8282 </td> 8283<td> 8284 <p> 8285 <span class="blue">Max = 6.94ε (Mean = 1.71ε)</span> 8286 </p> 8287 </td> 8288</tr> 8289<tr> 8290<td> 8291 <p> 8292 Incomplete Beta Function: Medium Values 8293 </p> 8294 </td> 8295<td> 8296 <p> 8297 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath 8298 3.2.3:</em></span> Max = 204ε (Mean = 25.8ε)) 8299 </p> 8300 </td> 8301<td> 8302 <p> 8303 <span class="blue">Max = 73.9ε (Mean = 11.2ε)</span> 8304 </p> 8305 </td> 8306<td> 8307 <p> 8308 <span class="blue">Max = 132ε (Mean = 19.8ε)</span> 8309 </p> 8310 </td> 8311<td> 8312 <p> 8313 <span class="blue">Max = 56.7ε (Mean = 14.3ε)</span> 8314 </p> 8315 </td> 8316</tr> 8317<tr> 8318<td> 8319 <p> 8320 Incomplete Beta Function: Large and Diverse Values 8321 </p> 8322 </td> 8323<td> 8324 <p> 8325 <span class="blue">Max = 0.981ε (Mean = 0.0573ε)</span><br> <br> 8326 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 889ε (Mean = 68.4ε)) 8327 </p> 8328 </td> 8329<td> 8330 <p> 8331 <span class="blue">Max = 3.45e+04ε (Mean = 1.32e+03ε)</span> 8332 </p> 8333 </td> 8334<td> 8335 <p> 8336 <span class="blue">Max = 6.31e+04ε (Mean = 2.04e+03ε)</span> 8337 </p> 8338 </td> 8339<td> 8340 <p> 8341 <span class="blue">Max = 1.88e+03ε (Mean = 82.7ε)</span> 8342 </p> 8343 </td> 8344</tr> 8345<tr> 8346<td> 8347 <p> 8348 Incomplete Beta Function: Small Integer Values 8349 </p> 8350 </td> 8351<td> 8352 <p> 8353 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath 8354 3.2.3:</em></span> Max = 84.6ε (Mean = 18ε)) 8355 </p> 8356 </td> 8357<td> 8358 <p> 8359 <span class="blue">Max = 5.34ε (Mean = 1.11ε)</span> 8360 </p> 8361 </td> 8362<td> 8363 <p> 8364 <span class="blue">Max = 107ε (Mean = 17.1ε)</span> 8365 </p> 8366 </td> 8367<td> 8368 <p> 8369 <span class="blue">Max = 6.37ε (Mean = 1.03ε)</span> 8370 </p> 8371 </td> 8372</tr> 8373</tbody> 8374</table></div> 8375</div> 8376<br class="table-break"> 8377</div> 8378<div class="section"> 8379<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 8380<a name="special_function_error_rates_rep.section_ibetac_inv"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ibetac_inv" title="ibetac_inv">ibetac_inv</a> 8381</h2></div></div></div> 8382<div class="table"> 8383<a name="special_function_error_rates_rep.section_ibetac_inv.table_ibetac_inv"></a><p class="title"><b>Table 58. Error rates for ibetac_inv</b></p> 8384<div class="table-contents"><table class="table" summary="Error rates for ibetac_inv"> 8385<colgroup> 8386<col> 8387<col> 8388<col> 8389<col> 8390<col> 8391</colgroup> 8392<thead><tr> 8393<th> 8394 </th> 8395<th> 8396 <p> 8397 GNU C++ version 7.1.0<br> linux<br> double 8398 </p> 8399 </th> 8400<th> 8401 <p> 8402 GNU C++ version 7.1.0<br> linux<br> long double 8403 </p> 8404 </th> 8405<th> 8406 <p> 8407 Sun compiler version 0x5150<br> Sun Solaris<br> long double 8408 </p> 8409 </th> 8410<th> 8411 <p> 8412 Microsoft Visual C++ version 14.1<br> Win32<br> double 8413 </p> 8414 </th> 8415</tr></thead> 8416<tbody><tr> 8417<td> 8418 <p> 8419 Inverse incomplete beta 8420 </p> 8421 </td> 8422<td> 8423 <p> 8424 <span class="blue">Max = 0.977ε (Mean = 0.0976ε)</span><br> <br> 8425 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 3.01e+132ε (Mean 8426 = 8.65e+130ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ibetac_inv_Rmath_3_2_3_Inverse_incomplete_beta">And 8427 other failures.</a>)</span> 8428 </p> 8429 </td> 8430<td> 8431 <p> 8432 <span class="blue">Max = 4.88e+04ε (Mean = 3.16e+03ε)</span> 8433 </p> 8434 </td> 8435<td> 8436 <p> 8437 <span class="blue">Max = 5.05e+04ε (Mean = 3.33e+03ε)</span> 8438 </p> 8439 </td> 8440<td> 8441 <p> 8442 <span class="blue">Max = 2.93e+03ε (Mean = 198ε)</span> 8443 </p> 8444 </td> 8445</tr></tbody> 8446</table></div> 8447</div> 8448<br class="table-break"> 8449</div> 8450<div class="section"> 8451<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 8452<a name="special_function_error_rates_rep.section_ibetac_inva"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ibetac_inva" title="ibetac_inva">ibetac_inva</a> 8453</h2></div></div></div> 8454<div class="table"> 8455<a name="special_function_error_rates_rep.section_ibetac_inva.table_ibetac_inva"></a><p class="title"><b>Table 59. Error rates for ibetac_inva</b></p> 8456<div class="table-contents"><table class="table" summary="Error rates for ibetac_inva"> 8457<colgroup> 8458<col> 8459<col> 8460<col> 8461<col> 8462<col> 8463</colgroup> 8464<thead><tr> 8465<th> 8466 </th> 8467<th> 8468 <p> 8469 GNU C++ version 7.1.0<br> linux<br> double 8470 </p> 8471 </th> 8472<th> 8473 <p> 8474 GNU C++ version 7.1.0<br> linux<br> long double 8475 </p> 8476 </th> 8477<th> 8478 <p> 8479 Sun compiler version 0x5150<br> Sun Solaris<br> long double 8480 </p> 8481 </th> 8482<th> 8483 <p> 8484 Microsoft Visual C++ version 14.1<br> Win32<br> double 8485 </p> 8486 </th> 8487</tr></thead> 8488<tbody><tr> 8489<td> 8490 <p> 8491 Inverse incomplete beta 8492 </p> 8493 </td> 8494<td> 8495 <p> 8496 <span class="blue">Max = 0.683ε (Mean = 0.0314ε)</span> 8497 </p> 8498 </td> 8499<td> 8500 <p> 8501 <span class="blue">Max = 382ε (Mean = 22.2ε)</span> 8502 </p> 8503 </td> 8504<td> 8505 <p> 8506 <span class="blue">Max = 315ε (Mean = 23.7ε)</span> 8507 </p> 8508 </td> 8509<td> 8510 <p> 8511 <span class="blue">Max = 408ε (Mean = 26.7ε)</span> 8512 </p> 8513 </td> 8514</tr></tbody> 8515</table></div> 8516</div> 8517<br class="table-break"> 8518</div> 8519<div class="section"> 8520<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 8521<a name="special_function_error_rates_rep.section_ibetac_invb"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ibetac_invb" title="ibetac_invb">ibetac_invb</a> 8522</h2></div></div></div> 8523<div class="table"> 8524<a name="special_function_error_rates_rep.section_ibetac_invb.table_ibetac_invb"></a><p class="title"><b>Table 60. Error rates for ibetac_invb</b></p> 8525<div class="table-contents"><table class="table" summary="Error rates for ibetac_invb"> 8526<colgroup> 8527<col> 8528<col> 8529<col> 8530<col> 8531<col> 8532</colgroup> 8533<thead><tr> 8534<th> 8535 </th> 8536<th> 8537 <p> 8538 GNU C++ version 7.1.0<br> linux<br> double 8539 </p> 8540 </th> 8541<th> 8542 <p> 8543 GNU C++ version 7.1.0<br> linux<br> long double 8544 </p> 8545 </th> 8546<th> 8547 <p> 8548 Sun compiler version 0x5150<br> Sun Solaris<br> long double 8549 </p> 8550 </th> 8551<th> 8552 <p> 8553 Microsoft Visual C++ version 14.1<br> Win32<br> double 8554 </p> 8555 </th> 8556</tr></thead> 8557<tbody><tr> 8558<td> 8559 <p> 8560 Inverse incomplete beta 8561 </p> 8562 </td> 8563<td> 8564 <p> 8565 <span class="blue">Max = 0.724ε (Mean = 0.0303ε)</span> 8566 </p> 8567 </td> 8568<td> 8569 <p> 8570 <span class="blue">Max = 317ε (Mean = 19.8ε)</span> 8571 </p> 8572 </td> 8573<td> 8574 <p> 8575 <span class="blue">Max = 369ε (Mean = 22.6ε)</span> 8576 </p> 8577 </td> 8578<td> 8579 <p> 8580 <span class="blue">Max = 271ε (Mean = 16.4ε)</span> 8581 </p> 8582 </td> 8583</tr></tbody> 8584</table></div> 8585</div> 8586<br class="table-break"> 8587</div> 8588<div class="section"> 8589<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 8590<a name="special_function_error_rates_rep.section_jacobi_cn"></a><a class="link" href="index.html#special_function_error_rates_rep.section_jacobi_cn" title="jacobi_cn">jacobi_cn</a> 8591</h2></div></div></div> 8592<div class="table"> 8593<a name="special_function_error_rates_rep.section_jacobi_cn.table_jacobi_cn"></a><p class="title"><b>Table 61. Error rates for jacobi_cn</b></p> 8594<div class="table-contents"><table class="table" summary="Error rates for jacobi_cn"> 8595<colgroup> 8596<col> 8597<col> 8598<col> 8599<col> 8600<col> 8601</colgroup> 8602<thead><tr> 8603<th> 8604 </th> 8605<th> 8606 <p> 8607 GNU C++ version 7.1.0<br> linux<br> double 8608 </p> 8609 </th> 8610<th> 8611 <p> 8612 GNU C++ version 7.1.0<br> linux<br> long double 8613 </p> 8614 </th> 8615<th> 8616 <p> 8617 Sun compiler version 0x5150<br> Sun Solaris<br> long double 8618 </p> 8619 </th> 8620<th> 8621 <p> 8622 Microsoft Visual C++ version 14.1<br> Win32<br> double 8623 </p> 8624 </th> 8625</tr></thead> 8626<tbody> 8627<tr> 8628<td> 8629 <p> 8630 Jacobi Elliptic: Mathworld Data 8631 </p> 8632 </td> 8633<td> 8634 <p> 8635 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 8636 2.1:</em></span> Max = 17.3ε (Mean = 4.29ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data">And 8637 other failures.</a>) 8638 </p> 8639 </td> 8640<td> 8641 <p> 8642 <span class="blue">Max = 71.6ε (Mean = 19.3ε)</span> 8643 </p> 8644 </td> 8645<td> 8646 <p> 8647 <span class="blue">Max = 71.6ε (Mean = 19.4ε)</span> 8648 </p> 8649 </td> 8650<td> 8651 <p> 8652 <span class="blue">Max = 45.8ε (Mean = 11.4ε)</span> 8653 </p> 8654 </td> 8655</tr> 8656<tr> 8657<td> 8658 <p> 8659 Jacobi Elliptic: Random Data 8660 </p> 8661 </td> 8662<td> 8663 <p> 8664 <span class="blue">Max = 0.816ε (Mean = 0.0563ε)</span><br> <br> 8665 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.43ε (Mean = 0.803ε)) 8666 </p> 8667 </td> 8668<td> 8669 <p> 8670 <span class="blue">Max = 1.68ε (Mean = 0.443ε)</span> 8671 </p> 8672 </td> 8673<td> 8674 <p> 8675 <span class="blue">Max = 1.68ε (Mean = 0.454ε)</span> 8676 </p> 8677 </td> 8678<td> 8679 <p> 8680 <span class="blue">Max = 1.83ε (Mean = 0.455ε)</span> 8681 </p> 8682 </td> 8683</tr> 8684<tr> 8685<td> 8686 <p> 8687 Jacobi Elliptic: Random Small Values 8688 </p> 8689 </td> 8690<td> 8691 <p> 8692 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 8693 2.1:</em></span> Max = 55.2ε (Mean = 1.64ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values">And 8694 other failures.</a>) 8695 </p> 8696 </td> 8697<td> 8698 <p> 8699 <span class="blue">Max = 10.4ε (Mean = 0.594ε)</span> 8700 </p> 8701 </td> 8702<td> 8703 <p> 8704 <span class="blue">Max = 10.4ε (Mean = 0.602ε)</span> 8705 </p> 8706 </td> 8707<td> 8708 <p> 8709 <span class="blue">Max = 26.2ε (Mean = 1.17ε)</span> 8710 </p> 8711 </td> 8712</tr> 8713<tr> 8714<td> 8715 <p> 8716 Jacobi Elliptic: Modulus near 1 8717 </p> 8718 </td> 8719<td> 8720 <p> 8721 <span class="blue">Max = 0.919ε (Mean = 0.127ε)</span><br> <br> 8722 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0ε (Mean = 0ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1">And 8723 other failures.</a>) 8724 </p> 8725 </td> 8726<td> 8727 <p> 8728 <span class="blue">Max = 675ε (Mean = 87.1ε)</span> 8729 </p> 8730 </td> 8731<td> 8732 <p> 8733 <span class="blue">Max = 675ε (Mean = 86.8ε)</span> 8734 </p> 8735 </td> 8736<td> 8737 <p> 8738 <span class="blue">Max = 513ε (Mean = 126ε)</span> 8739 </p> 8740 </td> 8741</tr> 8742<tr> 8743<td> 8744 <p> 8745 Jacobi Elliptic: Large Phi 8746 </p> 8747 </td> 8748<td> 8749 <p> 8750 <span class="blue">Max = 14.2ε (Mean = 0.927ε)</span><br> <br> 8751 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 5.92e+03ε (Mean = 477ε)) 8752 </p> 8753 </td> 8754<td> 8755 <p> 8756 <span class="blue">Max = 2.97e+04ε (Mean = 1.9e+03ε)</span> 8757 </p> 8758 </td> 8759<td> 8760 <p> 8761 <span class="blue">Max = 2.97e+04ε (Mean = 1.9e+03ε)</span> 8762 </p> 8763 </td> 8764<td> 8765 <p> 8766 <span class="blue">Max = 3.27e+04ε (Mean = 1.93e+03ε)</span> 8767 </p> 8768 </td> 8769</tr> 8770</tbody> 8771</table></div> 8772</div> 8773<br class="table-break"> 8774</div> 8775<div class="section"> 8776<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 8777<a name="special_function_error_rates_rep.section_jacobi_dn"></a><a class="link" href="index.html#special_function_error_rates_rep.section_jacobi_dn" title="jacobi_dn">jacobi_dn</a> 8778</h2></div></div></div> 8779<div class="table"> 8780<a name="special_function_error_rates_rep.section_jacobi_dn.table_jacobi_dn"></a><p class="title"><b>Table 62. Error rates for jacobi_dn</b></p> 8781<div class="table-contents"><table class="table" summary="Error rates for jacobi_dn"> 8782<colgroup> 8783<col> 8784<col> 8785<col> 8786<col> 8787<col> 8788</colgroup> 8789<thead><tr> 8790<th> 8791 </th> 8792<th> 8793 <p> 8794 GNU C++ version 7.1.0<br> linux<br> double 8795 </p> 8796 </th> 8797<th> 8798 <p> 8799 GNU C++ version 7.1.0<br> linux<br> long double 8800 </p> 8801 </th> 8802<th> 8803 <p> 8804 Sun compiler version 0x5150<br> Sun Solaris<br> long double 8805 </p> 8806 </th> 8807<th> 8808 <p> 8809 Microsoft Visual C++ version 14.1<br> Win32<br> double 8810 </p> 8811 </th> 8812</tr></thead> 8813<tbody> 8814<tr> 8815<td> 8816 <p> 8817 Jacobi Elliptic: Mathworld Data 8818 </p> 8819 </td> 8820<td> 8821 <p> 8822 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 8823 2.1:</em></span> Max = 2.82ε (Mean = 1.18ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data">And 8824 other failures.</a>) 8825 </p> 8826 </td> 8827<td> 8828 <p> 8829 <span class="blue">Max = 49ε (Mean = 14ε)</span> 8830 </p> 8831 </td> 8832<td> 8833 <p> 8834 <span class="blue">Max = 49ε (Mean = 14ε)</span> 8835 </p> 8836 </td> 8837<td> 8838 <p> 8839 <span class="blue">Max = 34.3ε (Mean = 8.71ε)</span> 8840 </p> 8841 </td> 8842</tr> 8843<tr> 8844<td> 8845 <p> 8846 Jacobi Elliptic: Random Data 8847 </p> 8848 </td> 8849<td> 8850 <p> 8851 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 8852 2.1:</em></span> Max = 3ε (Mean = 0.61ε)) 8853 </p> 8854 </td> 8855<td> 8856 <p> 8857 <span class="blue">Max = 1.53ε (Mean = 0.473ε)</span> 8858 </p> 8859 </td> 8860<td> 8861 <p> 8862 <span class="blue">Max = 1.53ε (Mean = 0.481ε)</span> 8863 </p> 8864 </td> 8865<td> 8866 <p> 8867 <span class="blue">Max = 1.52ε (Mean = 0.466ε)</span> 8868 </p> 8869 </td> 8870</tr> 8871<tr> 8872<td> 8873 <p> 8874 Jacobi Elliptic: Random Small Values 8875 </p> 8876 </td> 8877<td> 8878 <p> 8879 <span class="blue">Max = 0.5ε (Mean = 0.0122ε)</span><br> <br> 8880 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.5ε (Mean = 0.391ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values">And 8881 other failures.</a>) 8882 </p> 8883 </td> 8884<td> 8885 <p> 8886 <span class="blue">Max = 22.4ε (Mean = 0.777ε)</span> 8887 </p> 8888 </td> 8889<td> 8890 <p> 8891 <span class="blue">Max = 22.4ε (Mean = 0.763ε)</span> 8892 </p> 8893 </td> 8894<td> 8895 <p> 8896 <span class="blue">Max = 16.1ε (Mean = 0.685ε)</span> 8897 </p> 8898 </td> 8899</tr> 8900<tr> 8901<td> 8902 <p> 8903 Jacobi Elliptic: Modulus near 1 8904 </p> 8905 </td> 8906<td> 8907 <p> 8908 <span class="blue">Max = 2.28ε (Mean = 0.194ε)</span><br> <br> 8909 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0ε (Mean = 0ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1">And 8910 other failures.</a>) 8911 </p> 8912 </td> 8913<td> 8914 <p> 8915 <span class="blue">Max = 3.75e+03ε (Mean = 293ε)</span> 8916 </p> 8917 </td> 8918<td> 8919 <p> 8920 <span class="blue">Max = 3.75e+03ε (Mean = 293ε)</span> 8921 </p> 8922 </td> 8923<td> 8924 <p> 8925 <span class="blue">Max = 6.24e+03ε (Mean = 482ε)</span> 8926 </p> 8927 </td> 8928</tr> 8929<tr> 8930<td> 8931 <p> 8932 Jacobi Elliptic: Large Phi 8933 </p> 8934 </td> 8935<td> 8936 <p> 8937 <span class="blue">Max = 14.1ε (Mean = 0.897ε)</span><br> <br> 8938 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 121ε (Mean = 22ε)) 8939 </p> 8940 </td> 8941<td> 8942 <p> 8943 <span class="blue">Max = 2.82e+04ε (Mean = 1.79e+03ε)</span> 8944 </p> 8945 </td> 8946<td> 8947 <p> 8948 <span class="blue">Max = 2.82e+04ε (Mean = 1.79e+03ε)</span> 8949 </p> 8950 </td> 8951<td> 8952 <p> 8953 <span class="blue">Max = 1.67e+04ε (Mean = 1e+03ε)</span> 8954 </p> 8955 </td> 8956</tr> 8957</tbody> 8958</table></div> 8959</div> 8960<br class="table-break"> 8961</div> 8962<div class="section"> 8963<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 8964<a name="special_function_error_rates_rep.section_jacobi_sn"></a><a class="link" href="index.html#special_function_error_rates_rep.section_jacobi_sn" title="jacobi_sn">jacobi_sn</a> 8965</h2></div></div></div> 8966<div class="table"> 8967<a name="special_function_error_rates_rep.section_jacobi_sn.table_jacobi_sn"></a><p class="title"><b>Table 63. Error rates for jacobi_sn</b></p> 8968<div class="table-contents"><table class="table" summary="Error rates for jacobi_sn"> 8969<colgroup> 8970<col> 8971<col> 8972<col> 8973<col> 8974<col> 8975</colgroup> 8976<thead><tr> 8977<th> 8978 </th> 8979<th> 8980 <p> 8981 GNU C++ version 7.1.0<br> linux<br> double 8982 </p> 8983 </th> 8984<th> 8985 <p> 8986 GNU C++ version 7.1.0<br> linux<br> long double 8987 </p> 8988 </th> 8989<th> 8990 <p> 8991 Sun compiler version 0x5150<br> Sun Solaris<br> long double 8992 </p> 8993 </th> 8994<th> 8995 <p> 8996 Microsoft Visual C++ version 14.1<br> Win32<br> double 8997 </p> 8998 </th> 8999</tr></thead> 9000<tbody> 9001<tr> 9002<td> 9003 <p> 9004 Jacobi Elliptic: Mathworld Data 9005 </p> 9006 </td> 9007<td> 9008 <p> 9009 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 9010 2.1:</em></span> Max = 588ε (Mean = 146ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data">And 9011 other failures.</a>) 9012 </p> 9013 </td> 9014<td> 9015 <p> 9016 <span class="blue">Max = 341ε (Mean = 80.7ε)</span> 9017 </p> 9018 </td> 9019<td> 9020 <p> 9021 <span class="blue">Max = 341ε (Mean = 80.7ε)</span> 9022 </p> 9023 </td> 9024<td> 9025 <p> 9026 <span class="blue">Max = 481ε (Mean = 113ε)</span> 9027 </p> 9028 </td> 9029</tr> 9030<tr> 9031<td> 9032 <p> 9033 Jacobi Elliptic: Random Data 9034 </p> 9035 </td> 9036<td> 9037 <p> 9038 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 9039 2.1:</em></span> Max = 4.02ε (Mean = 1.07ε)) 9040 </p> 9041 </td> 9042<td> 9043 <p> 9044 <span class="blue">Max = 2.01ε (Mean = 0.584ε)</span> 9045 </p> 9046 </td> 9047<td> 9048 <p> 9049 <span class="blue">Max = 2.01ε (Mean = 0.593ε)</span> 9050 </p> 9051 </td> 9052<td> 9053 <p> 9054 <span class="blue">Max = 1.92ε (Mean = 0.567ε)</span> 9055 </p> 9056 </td> 9057</tr> 9058<tr> 9059<td> 9060 <p> 9061 Jacobi Elliptic: Random Small Values 9062 </p> 9063 </td> 9064<td> 9065 <p> 9066 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 9067 2.1:</em></span> Max = 11.7ε (Mean = 1.65ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values">And 9068 other failures.</a>) 9069 </p> 9070 </td> 9071<td> 9072 <p> 9073 <span class="blue">Max = 1.99ε (Mean = 0.347ε)</span> 9074 </p> 9075 </td> 9076<td> 9077 <p> 9078 <span class="blue">Max = 1.99ε (Mean = 0.347ε)</span> 9079 </p> 9080 </td> 9081<td> 9082 <p> 9083 <span class="blue">Max = 2.11ε (Mean = 0.385ε)</span> 9084 </p> 9085 </td> 9086</tr> 9087<tr> 9088<td> 9089 <p> 9090 Jacobi Elliptic: Modulus near 1 9091 </p> 9092 </td> 9093<td> 9094 <p> 9095 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 9096 2.1:</em></span> Max = 0ε (Mean = 0ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1">And 9097 other failures.</a>) 9098 </p> 9099 </td> 9100<td> 9101 <p> 9102 <span class="blue">Max = 109ε (Mean = 7.35ε)</span> 9103 </p> 9104 </td> 9105<td> 9106 <p> 9107 <span class="blue">Max = 109ε (Mean = 7.38ε)</span> 9108 </p> 9109 </td> 9110<td> 9111 <p> 9112 <span class="blue">Max = 23.2ε (Mean = 1.85ε)</span> 9113 </p> 9114 </td> 9115</tr> 9116<tr> 9117<td> 9118 <p> 9119 Jacobi Elliptic: Large Phi 9120 </p> 9121 </td> 9122<td> 9123 <p> 9124 <span class="blue">Max = 12ε (Mean = 0.771ε)</span><br> <br> 9125 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 4.54e+04ε (Mean = 2.63e+03ε)) 9126 </p> 9127 </td> 9128<td> 9129 <p> 9130 <span class="blue">Max = 2.45e+04ε (Mean = 1.51e+03ε)</span> 9131 </p> 9132 </td> 9133<td> 9134 <p> 9135 <span class="blue">Max = 2.45e+04ε (Mean = 1.51e+03ε)</span> 9136 </p> 9137 </td> 9138<td> 9139 <p> 9140 <span class="blue">Max = 4.36e+04ε (Mean = 2.54e+03ε)</span> 9141 </p> 9142 </td> 9143</tr> 9144</tbody> 9145</table></div> 9146</div> 9147<br class="table-break"> 9148</div> 9149<div class="section"> 9150<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 9151<a name="special_function_error_rates_rep.section_jacobi_zeta"></a><a class="link" href="index.html#special_function_error_rates_rep.section_jacobi_zeta" title="jacobi_zeta">jacobi_zeta</a> 9152</h2></div></div></div> 9153<div class="table"> 9154<a name="special_function_error_rates_rep.section_jacobi_zeta.table_jacobi_zeta"></a><p class="title"><b>Table 64. Error rates for jacobi_zeta</b></p> 9155<div class="table-contents"><table class="table" summary="Error rates for jacobi_zeta"> 9156<colgroup> 9157<col> 9158<col> 9159<col> 9160<col> 9161<col> 9162</colgroup> 9163<thead><tr> 9164<th> 9165 </th> 9166<th> 9167 <p> 9168 GNU C++ version 7.1.0<br> linux<br> double 9169 </p> 9170 </th> 9171<th> 9172 <p> 9173 GNU C++ version 7.1.0<br> linux<br> long double 9174 </p> 9175 </th> 9176<th> 9177 <p> 9178 Sun compiler version 0x5150<br> Sun Solaris<br> long double 9179 </p> 9180 </th> 9181<th> 9182 <p> 9183 Microsoft Visual C++ version 14.1<br> Win32<br> double 9184 </p> 9185 </th> 9186</tr></thead> 9187<tbody> 9188<tr> 9189<td> 9190 <p> 9191 Elliptic Integral Jacobi Zeta: Mathworld Data 9192 </p> 9193 </td> 9194<td> 9195 <p> 9196 <span class="blue">Max = 0ε (Mean = 0ε)</span> 9197 </p> 9198 </td> 9199<td> 9200 <p> 9201 <span class="blue">Max = 1.66ε (Mean = 0.48ε)</span> 9202 </p> 9203 </td> 9204<td> 9205 <p> 9206 <span class="blue">Max = 1.66ε (Mean = 0.48ε)</span> 9207 </p> 9208 </td> 9209<td> 9210 <p> 9211 <span class="blue">Max = 1.52ε (Mean = 0.357ε)</span> 9212 </p> 9213 </td> 9214</tr> 9215<tr> 9216<td> 9217 <p> 9218 Elliptic Integral Jacobi Zeta: Random Data 9219 </p> 9220 </td> 9221<td> 9222 <p> 9223 <span class="blue">Max = 0ε (Mean = 0ε)</span> 9224 </p> 9225 </td> 9226<td> 9227 <p> 9228 <span class="blue">Max = 2.99ε (Mean = 0.824ε)</span> 9229 </p> 9230 </td> 9231<td> 9232 <p> 9233 <span class="blue">Max = 3.96ε (Mean = 1.06ε)</span> 9234 </p> 9235 </td> 9236<td> 9237 <p> 9238 <span class="blue">Max = 3.89ε (Mean = 0.824ε)</span> 9239 </p> 9240 </td> 9241</tr> 9242<tr> 9243<td> 9244 <p> 9245 Elliptic Integral Jacobi Zeta: Large Phi Values 9246 </p> 9247 </td> 9248<td> 9249 <p> 9250 <span class="blue">Max = 0ε (Mean = 0ε)</span> 9251 </p> 9252 </td> 9253<td> 9254 <p> 9255 <span class="blue">Max = 2.92ε (Mean = 0.951ε)</span> 9256 </p> 9257 </td> 9258<td> 9259 <p> 9260 <span class="blue">Max = 3.05ε (Mean = 1.13ε)</span> 9261 </p> 9262 </td> 9263<td> 9264 <p> 9265 <span class="blue">Max = 2.52ε (Mean = 0.977ε)</span> 9266 </p> 9267 </td> 9268</tr> 9269</tbody> 9270</table></div> 9271</div> 9272<br class="table-break"> 9273</div> 9274<div class="section"> 9275<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 9276<a name="special_function_error_rates_rep.section_laguerre_n_m_x_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_laguerre_n_m_x_" title="laguerre(n, m, x)">laguerre(n, 9277 m, x)</a> 9278</h2></div></div></div> 9279<div class="table"> 9280<a name="special_function_error_rates_rep.section_laguerre_n_m_x_.table_laguerre_n_m_x_"></a><p class="title"><b>Table 65. Error rates for laguerre(n, m, x)</b></p> 9281<div class="table-contents"><table class="table" summary="Error rates for laguerre(n, m, x)"> 9282<colgroup> 9283<col> 9284<col> 9285<col> 9286<col> 9287<col> 9288</colgroup> 9289<thead><tr> 9290<th> 9291 </th> 9292<th> 9293 <p> 9294 GNU C++ version 7.1.0<br> linux<br> double 9295 </p> 9296 </th> 9297<th> 9298 <p> 9299 GNU C++ version 7.1.0<br> linux<br> long double 9300 </p> 9301 </th> 9302<th> 9303 <p> 9304 Sun compiler version 0x5150<br> Sun Solaris<br> long double 9305 </p> 9306 </th> 9307<th> 9308 <p> 9309 Microsoft Visual C++ version 14.1<br> Win32<br> double 9310 </p> 9311 </th> 9312</tr></thead> 9313<tbody><tr> 9314<td> 9315 <p> 9316 Associated Laguerre Polynomials 9317 </p> 9318 </td> 9319<td> 9320 <p> 9321 <span class="blue">Max = 0.84ε (Mean = 0.0358ε)</span><br> <br> 9322 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 434ε (Mean = 10.7ε)) 9323 </p> 9324 </td> 9325<td> 9326 <p> 9327 <span class="blue">Max = 167ε (Mean = 6.38ε)</span><br> <br> 9328 (<span class="emphasis"><em><cmath>:</em></span> Max = 206ε (Mean = 6.86ε)) 9329 </p> 9330 </td> 9331<td> 9332 <p> 9333 <span class="blue">Max = 167ε (Mean = 6.38ε)</span> 9334 </p> 9335 </td> 9336<td> 9337 <p> 9338 <span class="blue">Max = 434ε (Mean = 11.1ε)</span> 9339 </p> 9340 </td> 9341</tr></tbody> 9342</table></div> 9343</div> 9344<br class="table-break"> 9345</div> 9346<div class="section"> 9347<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 9348<a name="special_function_error_rates_rep.section_laguerre_n_x_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_laguerre_n_x_" title="laguerre(n, x)">laguerre(n, 9349 x)</a> 9350</h2></div></div></div> 9351<div class="table"> 9352<a name="special_function_error_rates_rep.section_laguerre_n_x_.table_laguerre_n_x_"></a><p class="title"><b>Table 66. Error rates for laguerre(n, x)</b></p> 9353<div class="table-contents"><table class="table" summary="Error rates for laguerre(n, x)"> 9354<colgroup> 9355<col> 9356<col> 9357<col> 9358<col> 9359<col> 9360</colgroup> 9361<thead><tr> 9362<th> 9363 </th> 9364<th> 9365 <p> 9366 GNU C++ version 7.1.0<br> linux<br> double 9367 </p> 9368 </th> 9369<th> 9370 <p> 9371 GNU C++ version 7.1.0<br> linux<br> long double 9372 </p> 9373 </th> 9374<th> 9375 <p> 9376 Sun compiler version 0x5150<br> Sun Solaris<br> long double 9377 </p> 9378 </th> 9379<th> 9380 <p> 9381 Microsoft Visual C++ version 14.1<br> Win32<br> double 9382 </p> 9383 </th> 9384</tr></thead> 9385<tbody><tr> 9386<td> 9387 <p> 9388 Laguerre Polynomials 9389 </p> 9390 </td> 9391<td> 9392 <p> 9393 <span class="blue">Max = 6.82ε (Mean = 0.408ε)</span><br> <br> 9394 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.1e+03ε (Mean = 185ε)) 9395 </p> 9396 </td> 9397<td> 9398 <p> 9399 <span class="blue">Max = 1.39e+04ε (Mean = 828ε)</span><br> <br> 9400 (<span class="emphasis"><em><cmath>:</em></span> Max = 4.2e+03ε (Mean = 251ε)) 9401 </p> 9402 </td> 9403<td> 9404 <p> 9405 <span class="blue">Max = 1.39e+04ε (Mean = 828ε)</span> 9406 </p> 9407 </td> 9408<td> 9409 <p> 9410 <span class="blue">Max = 3.1e+03ε (Mean = 185ε)</span> 9411 </p> 9412 </td> 9413</tr></tbody> 9414</table></div> 9415</div> 9416<br class="table-break"> 9417</div> 9418<div class="section"> 9419<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 9420<a name="special_function_error_rates_rep.section_legendre_p"></a><a class="link" href="index.html#special_function_error_rates_rep.section_legendre_p" title="legendre_p">legendre_p</a> 9421</h2></div></div></div> 9422<div class="table"> 9423<a name="special_function_error_rates_rep.section_legendre_p.table_legendre_p"></a><p class="title"><b>Table 67. Error rates for legendre_p</b></p> 9424<div class="table-contents"><table class="table" summary="Error rates for legendre_p"> 9425<colgroup> 9426<col> 9427<col> 9428<col> 9429<col> 9430<col> 9431</colgroup> 9432<thead><tr> 9433<th> 9434 </th> 9435<th> 9436 <p> 9437 GNU C++ version 7.1.0<br> linux<br> double 9438 </p> 9439 </th> 9440<th> 9441 <p> 9442 GNU C++ version 7.1.0<br> linux<br> long double 9443 </p> 9444 </th> 9445<th> 9446 <p> 9447 Sun compiler version 0x5150<br> Sun Solaris<br> long double 9448 </p> 9449 </th> 9450<th> 9451 <p> 9452 Microsoft Visual C++ version 14.1<br> Win32<br> double 9453 </p> 9454 </th> 9455</tr></thead> 9456<tbody> 9457<tr> 9458<td> 9459 <p> 9460 Legendre Polynomials: Small Values 9461 </p> 9462 </td> 9463<td> 9464 <p> 9465 <span class="blue">Max = 0.732ε (Mean = 0.0619ε)</span><br> <br> 9466 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 211ε (Mean = 20.4ε)) 9467 </p> 9468 </td> 9469<td> 9470 <p> 9471 <span class="blue">Max = 69.2ε (Mean = 9.58ε)</span><br> <br> 9472 (<span class="emphasis"><em><cmath>:</em></span> Max = 124ε (Mean = 13.2ε)) 9473 </p> 9474 </td> 9475<td> 9476 <p> 9477 <span class="blue">Max = 69.2ε (Mean = 9.58ε)</span> 9478 </p> 9479 </td> 9480<td> 9481 <p> 9482 <span class="blue">Max = 211ε (Mean = 20.4ε)</span> 9483 </p> 9484 </td> 9485</tr> 9486<tr> 9487<td> 9488 <p> 9489 Legendre Polynomials: Large Values 9490 </p> 9491 </td> 9492<td> 9493 <p> 9494 <span class="blue">Max = 0.632ε (Mean = 0.0693ε)</span><br> <br> 9495 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 300ε (Mean = 33.2ε)) 9496 </p> 9497 </td> 9498<td> 9499 <p> 9500 <span class="blue">Max = 699ε (Mean = 59.6ε)</span><br> <br> 9501 (<span class="emphasis"><em><cmath>:</em></span> Max = 343ε (Mean = 32.1ε)) 9502 </p> 9503 </td> 9504<td> 9505 <p> 9506 <span class="blue">Max = 699ε (Mean = 59.6ε)</span> 9507 </p> 9508 </td> 9509<td> 9510 <p> 9511 <span class="blue">Max = 300ε (Mean = 33.2ε)</span> 9512 </p> 9513 </td> 9514</tr> 9515</tbody> 9516</table></div> 9517</div> 9518<br class="table-break"> 9519</div> 9520<div class="section"> 9521<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 9522<a name="special_function_error_rates_rep.section_legendre_p_associated_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_legendre_p_associated_" title="legendre_p (associated)">legendre_p 9523 (associated)</a> 9524</h2></div></div></div> 9525<div class="table"> 9526<a name="special_function_error_rates_rep.section_legendre_p_associated_.table_legendre_p_associated_"></a><p class="title"><b>Table 68. Error rates for legendre_p (associated)</b></p> 9527<div class="table-contents"><table class="table" summary="Error rates for legendre_p (associated)"> 9528<colgroup> 9529<col> 9530<col> 9531<col> 9532<col> 9533<col> 9534</colgroup> 9535<thead><tr> 9536<th> 9537 </th> 9538<th> 9539 <p> 9540 GNU C++ version 7.1.0<br> linux<br> double 9541 </p> 9542 </th> 9543<th> 9544 <p> 9545 GNU C++ version 7.1.0<br> linux<br> long double 9546 </p> 9547 </th> 9548<th> 9549 <p> 9550 Sun compiler version 0x5150<br> Sun Solaris<br> long double 9551 </p> 9552 </th> 9553<th> 9554 <p> 9555 Microsoft Visual C++ version 14.1<br> Win32<br> double 9556 </p> 9557 </th> 9558</tr></thead> 9559<tbody><tr> 9560<td> 9561 <p> 9562 Associated Legendre Polynomials: Small Values 9563 </p> 9564 </td> 9565<td> 9566 <p> 9567 <span class="blue">Max = 0.999ε (Mean = 0.05ε)</span><br> <br> 9568 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 121ε (Mean = 6.75ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_legendre_p_associated__GSL_2_1_Associated_Legendre_Polynomials_Small_Values">And 9569 other failures.</a>) 9570 </p> 9571 </td> 9572<td> 9573 <p> 9574 <span class="blue">Max = 175ε (Mean = 9.88ε)</span><br> <br> 9575 (<span class="emphasis"><em><cmath>:</em></span> Max = 175ε (Mean = 9.36ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_legendre_p_associated___cmath__Associated_Legendre_Polynomials_Small_Values">And 9576 other failures.</a>) 9577 </p> 9578 </td> 9579<td> 9580 <p> 9581 <span class="blue">Max = 77.7ε (Mean = 5.59ε)</span> 9582 </p> 9583 </td> 9584<td> 9585 <p> 9586 <span class="blue">Max = 121ε (Mean = 7.14ε)</span> 9587 </p> 9588 </td> 9589</tr></tbody> 9590</table></div> 9591</div> 9592<br class="table-break"> 9593</div> 9594<div class="section"> 9595<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 9596<a name="special_function_error_rates_rep.section_legendre_q"></a><a class="link" href="index.html#special_function_error_rates_rep.section_legendre_q" title="legendre_q">legendre_q</a> 9597</h2></div></div></div> 9598<div class="table"> 9599<a name="special_function_error_rates_rep.section_legendre_q.table_legendre_q"></a><p class="title"><b>Table 69. Error rates for legendre_q</b></p> 9600<div class="table-contents"><table class="table" summary="Error rates for legendre_q"> 9601<colgroup> 9602<col> 9603<col> 9604<col> 9605<col> 9606<col> 9607</colgroup> 9608<thead><tr> 9609<th> 9610 </th> 9611<th> 9612 <p> 9613 GNU C++ version 7.1.0<br> linux<br> double 9614 </p> 9615 </th> 9616<th> 9617 <p> 9618 GNU C++ version 7.1.0<br> linux<br> long double 9619 </p> 9620 </th> 9621<th> 9622 <p> 9623 Sun compiler version 0x5150<br> Sun Solaris<br> long double 9624 </p> 9625 </th> 9626<th> 9627 <p> 9628 Microsoft Visual C++ version 14.1<br> Win32<br> double 9629 </p> 9630 </th> 9631</tr></thead> 9632<tbody> 9633<tr> 9634<td> 9635 <p> 9636 Legendre Polynomials: Small Values 9637 </p> 9638 </td> 9639<td> 9640 <p> 9641 <span class="blue">Max = 0.612ε (Mean = 0.0517ε)</span><br> <br> 9642 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 46.4ε (Mean = 7.46ε)) 9643 </p> 9644 </td> 9645<td> 9646 <p> 9647 <span class="blue">Max = 50.9ε (Mean = 9ε)</span> 9648 </p> 9649 </td> 9650<td> 9651 <p> 9652 <span class="blue">Max = 50.9ε (Mean = 8.98ε)</span> 9653 </p> 9654 </td> 9655<td> 9656 <p> 9657 <span class="blue">Max = 46.4ε (Mean = 7.32ε)</span> 9658 </p> 9659 </td> 9660</tr> 9661<tr> 9662<td> 9663 <p> 9664 Legendre Polynomials: Large Values 9665 </p> 9666 </td> 9667<td> 9668 <p> 9669 <span class="blue">Max = 2.49ε (Mean = 0.202ε)</span><br> <br> 9670 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 4.6e+03ε (Mean = 366ε)) 9671 </p> 9672 </td> 9673<td> 9674 <p> 9675 <span class="blue">Max = 5.98e+03ε (Mean = 478ε)</span> 9676 </p> 9677 </td> 9678<td> 9679 <p> 9680 <span class="blue">Max = 5.98e+03ε (Mean = 478ε)</span> 9681 </p> 9682 </td> 9683<td> 9684 <p> 9685 <span class="blue">Max = 4.6e+03ε (Mean = 366ε)</span> 9686 </p> 9687 </td> 9688</tr> 9689</tbody> 9690</table></div> 9691</div> 9692<br class="table-break"> 9693</div> 9694<div class="section"> 9695<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 9696<a name="special_function_error_rates_rep.section_lgamma"></a><a class="link" href="index.html#special_function_error_rates_rep.section_lgamma" title="lgamma">lgamma</a> 9697</h2></div></div></div> 9698<div class="table"> 9699<a name="special_function_error_rates_rep.section_lgamma.table_lgamma"></a><p class="title"><b>Table 70. Error rates for lgamma</b></p> 9700<div class="table-contents"><table class="table" summary="Error rates for lgamma"> 9701<colgroup> 9702<col> 9703<col> 9704<col> 9705<col> 9706<col> 9707</colgroup> 9708<thead><tr> 9709<th> 9710 </th> 9711<th> 9712 <p> 9713 GNU C++ version 7.1.0<br> linux<br> double 9714 </p> 9715 </th> 9716<th> 9717 <p> 9718 GNU C++ version 7.1.0<br> linux<br> long double 9719 </p> 9720 </th> 9721<th> 9722 <p> 9723 Sun compiler version 0x5150<br> Sun Solaris<br> long double 9724 </p> 9725 </th> 9726<th> 9727 <p> 9728 Microsoft Visual C++ version 14.1<br> Win32<br> double 9729 </p> 9730 </th> 9731</tr></thead> 9732<tbody> 9733<tr> 9734<td> 9735 <p> 9736 factorials 9737 </p> 9738 </td> 9739<td> 9740 <p> 9741 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 9742 2.1:</em></span> Max = 33.6ε (Mean = 2.78ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 9743 Max = 1.55ε (Mean = 0.592ε)) 9744 </p> 9745 </td> 9746<td> 9747 <p> 9748 <span class="blue">Max = 0.991ε (Mean = 0.308ε)</span><br> <br> 9749 (<span class="emphasis"><em><cmath>:</em></span> Max = 1.67ε (Mean = 0.487ε))<br> 9750 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.67ε (Mean = 0.487ε)) 9751 </p> 9752 </td> 9753<td> 9754 <p> 9755 <span class="blue">Max = 0.991ε (Mean = 0.383ε)</span><br> <br> 9756 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.36ε (Mean = 0.476ε)) 9757 </p> 9758 </td> 9759<td> 9760 <p> 9761 <span class="blue">Max = 0.914ε (Mean = 0.175ε)</span><br> <br> 9762 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.958ε (Mean = 0.38ε)) 9763 </p> 9764 </td> 9765</tr> 9766<tr> 9767<td> 9768 <p> 9769 near 0 9770 </p> 9771 </td> 9772<td> 9773 <p> 9774 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 9775 2.1:</em></span> Max = 5.21ε (Mean = 1.57ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 9776 Max = 0ε (Mean = 0ε)) 9777 </p> 9778 </td> 9779<td> 9780 <p> 9781 <span class="blue">Max = 1.42ε (Mean = 0.566ε)</span><br> <br> 9782 (<span class="emphasis"><em><cmath>:</em></span> Max = 0.964ε (Mean = 0.543ε))<br> 9783 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.964ε (Mean = 0.543ε)) 9784 </p> 9785 </td> 9786<td> 9787 <p> 9788 <span class="blue">Max = 1.42ε (Mean = 0.566ε)</span><br> <br> 9789 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.964ε (Mean = 0.543ε)) 9790 </p> 9791 </td> 9792<td> 9793 <p> 9794 <span class="blue">Max = 0.964ε (Mean = 0.462ε)</span><br> <br> 9795 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.962ε (Mean = 0.372ε)) 9796 </p> 9797 </td> 9798</tr> 9799<tr> 9800<td> 9801 <p> 9802 near 1 9803 </p> 9804 </td> 9805<td> 9806 <p> 9807 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 9808 2.1:</em></span> Max = 442ε (Mean = 88.8ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 9809 Max = 7.99e+04ε (Mean = 1.68e+04ε)) 9810 </p> 9811 </td> 9812<td> 9813 <p> 9814 <span class="blue">Max = 0.948ε (Mean = 0.36ε)</span><br> <br> 9815 (<span class="emphasis"><em><cmath>:</em></span> Max = 0.615ε (Mean = 0.096ε))<br> 9816 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.615ε (Mean = 0.096ε)) 9817 </p> 9818 </td> 9819<td> 9820 <p> 9821 <span class="blue">Max = 0.948ε (Mean = 0.36ε)</span><br> <br> 9822 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.71ε (Mean = 0.581ε)) 9823 </p> 9824 </td> 9825<td> 9826 <p> 9827 <span class="blue">Max = 0.867ε (Mean = 0.468ε)</span><br> <br> 9828 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.906ε (Mean = 0.565ε)) 9829 </p> 9830 </td> 9831</tr> 9832<tr> 9833<td> 9834 <p> 9835 near 2 9836 </p> 9837 </td> 9838<td> 9839 <p> 9840 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 9841 2.1:</em></span> Max = 1.17e+03ε (Mean = 274ε))<br> (<span class="emphasis"><em>Rmath 9842 3.2.3:</em></span> Max = 2.63e+05ε (Mean = 5.84e+04ε)) 9843 </p> 9844 </td> 9845<td> 9846 <p> 9847 <span class="blue">Max = 0.878ε (Mean = 0.242ε)</span><br> <br> 9848 (<span class="emphasis"><em><cmath>:</em></span> Max = 0.741ε (Mean = 0.263ε))<br> 9849 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.741ε (Mean = 0.263ε)) 9850 </p> 9851 </td> 9852<td> 9853 <p> 9854 <span class="blue">Max = 0.878ε (Mean = 0.242ε)</span><br> <br> 9855 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.598ε (Mean = 0.235ε)) 9856 </p> 9857 </td> 9858<td> 9859 <p> 9860 <span class="blue">Max = 0.591ε (Mean = 0.159ε)</span><br> <br> 9861 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.741ε (Mean = 0.473ε)) 9862 </p> 9863 </td> 9864</tr> 9865<tr> 9866<td> 9867 <p> 9868 near -10 9869 </p> 9870 </td> 9871<td> 9872 <p> 9873 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 9874 2.1:</em></span> Max = 24.9ε (Mean = 4.6ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 9875 Max = 4.22ε (Mean = 1.26ε)) 9876 </p> 9877 </td> 9878<td> 9879 <p> 9880 <span class="blue">Max = 3.81ε (Mean = 1.01ε)</span><br> <br> 9881 (<span class="emphasis"><em><cmath>:</em></span> Max = 0.997ε (Mean = 0.412ε))<br> 9882 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.997ε (Mean = 0.412ε)) 9883 </p> 9884 </td> 9885<td> 9886 <p> 9887 <span class="blue">Max = 3.81ε (Mean = 1.01ε)</span><br> <br> 9888 (<span class="emphasis"><em><math.h>:</em></span> Max = 3.04ε (Mean = 1.01ε)) 9889 </p> 9890 </td> 9891<td> 9892 <p> 9893 <span class="blue">Max = 4.22ε (Mean = 1.33ε)</span><br> <br> 9894 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.997ε (Mean = 0.444ε)) 9895 </p> 9896 </td> 9897</tr> 9898<tr> 9899<td> 9900 <p> 9901 near -55 9902 </p> 9903 </td> 9904<td> 9905 <p> 9906 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 9907 2.1:</em></span> Max = 7.02ε (Mean = 1.47ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 9908 Max = 250ε (Mean = 60.9ε)) 9909 </p> 9910 </td> 9911<td> 9912 <p> 9913 <span class="blue">Max = 0.821ε (Mean = 0.513ε)</span><br> <br> 9914 (<span class="emphasis"><em><cmath>:</em></span> Max = 1.58ε (Mean = 0.672ε))<br> 9915 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.58ε (Mean = 0.672ε)) 9916 </p> 9917 </td> 9918<td> 9919 <p> 9920 <span class="blue">Max = 1.59ε (Mean = 0.587ε)</span><br> <br> 9921 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.821ε (Mean = 0.674ε)) 9922 </p> 9923 </td> 9924<td> 9925 <p> 9926 <span class="blue">Max = 0.821ε (Mean = 0.419ε)</span><br> <br> 9927 (<span class="emphasis"><em><math.h>:</em></span> Max = 249ε (Mean = 43.1ε)) 9928 </p> 9929 </td> 9930</tr> 9931</tbody> 9932</table></div> 9933</div> 9934<br class="table-break"> 9935</div> 9936<div class="section"> 9937<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 9938<a name="special_function_error_rates_rep.section_log1p"></a><a class="link" href="index.html#special_function_error_rates_rep.section_log1p" title="log1p">log1p</a> 9939</h2></div></div></div> 9940<div class="table"> 9941<a name="special_function_error_rates_rep.section_log1p.table_log1p"></a><p class="title"><b>Table 71. Error rates for log1p</b></p> 9942<div class="table-contents"><table class="table" summary="Error rates for log1p"> 9943<colgroup> 9944<col> 9945<col> 9946<col> 9947<col> 9948<col> 9949</colgroup> 9950<thead><tr> 9951<th> 9952 </th> 9953<th> 9954 <p> 9955 GNU C++ version 7.1.0<br> linux<br> long double 9956 </p> 9957 </th> 9958<th> 9959 <p> 9960 GNU C++ version 7.1.0<br> linux<br> double 9961 </p> 9962 </th> 9963<th> 9964 <p> 9965 Sun compiler version 0x5150<br> Sun Solaris<br> long double 9966 </p> 9967 </th> 9968<th> 9969 <p> 9970 Microsoft Visual C++ version 14.1<br> Win32<br> double 9971 </p> 9972 </th> 9973</tr></thead> 9974<tbody><tr> 9975<td> 9976 <p> 9977 Random test data 9978 </p> 9979 </td> 9980<td> 9981 <p> 9982 <span class="blue">Max = 0.818ε (Mean = 0.227ε)</span><br> <br> 9983 (<span class="emphasis"><em><cmath>:</em></span> Max = 0.818ε (Mean = 0.227ε))<br> 9984 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.818ε (Mean = 0.227ε)) 9985 </p> 9986 </td> 9987<td> 9988 <p> 9989 <span class="blue">Max = 0.846ε (Mean = 0.153ε)</span><br> <br> 9990 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 0.846ε (Mean = 0.153ε)) 9991 </p> 9992 </td> 9993<td> 9994 <p> 9995 <span class="blue">Max = 2.3ε (Mean = 0.66ε)</span><br> <br> 9996 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.818ε (Mean = 0.249ε)) 9997 </p> 9998 </td> 9999<td> 10000 <p> 10001 <span class="blue">Max = 0.509ε (Mean = 0.057ε)</span><br> <br> 10002 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.509ε (Mean = 0.057ε)) 10003 </p> 10004 </td> 10005</tr></tbody> 10006</table></div> 10007</div> 10008<br class="table-break"> 10009</div> 10010<div class="section"> 10011<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 10012<a name="special_function_error_rates_rep.section_non_central_beta_CDF"></a><a class="link" href="index.html#special_function_error_rates_rep.section_non_central_beta_CDF" title="non central beta CDF">non 10013 central beta CDF</a> 10014</h2></div></div></div> 10015<div class="table"> 10016<a name="special_function_error_rates_rep.section_non_central_beta_CDF.table_non_central_beta_CDF"></a><p class="title"><b>Table 72. Error rates for non central beta CDF</b></p> 10017<div class="table-contents"><table class="table" summary="Error rates for non central beta CDF"> 10018<colgroup> 10019<col> 10020<col> 10021<col> 10022<col> 10023<col> 10024</colgroup> 10025<thead><tr> 10026<th> 10027 </th> 10028<th> 10029 <p> 10030 GNU C++ version 7.1.0<br> linux<br> double 10031 </p> 10032 </th> 10033<th> 10034 <p> 10035 GNU C++ version 7.1.0<br> linux<br> long double 10036 </p> 10037 </th> 10038<th> 10039 <p> 10040 Sun compiler version 0x5150<br> Sun Solaris<br> long double 10041 </p> 10042 </th> 10043<th> 10044 <p> 10045 Microsoft Visual C++ version 14.1<br> Win32<br> double 10046 </p> 10047 </th> 10048</tr></thead> 10049<tbody> 10050<tr> 10051<td> 10052 <p> 10053 Non Central Beta, medium parameters 10054 </p> 10055 </td> 10056<td> 10057 <p> 10058 <span class="blue">Max = 0.998ε (Mean = 0.0649ε)</span><br> <br> 10059 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 1.46e+26ε (Mean 10060 = 3.5e+24ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_Rmath_3_2_3_Non_Central_Beta_medium_parameters">And 10061 other failures.</a>)</span> 10062 </p> 10063 </td> 10064<td> 10065 <p> 10066 <span class="blue">Max = 824ε (Mean = 27.4ε)</span> 10067 </p> 10068 </td> 10069<td> 10070 <p> 10071 <span class="blue">Max = 832ε (Mean = 38.1ε)</span> 10072 </p> 10073 </td> 10074<td> 10075 <p> 10076 <span class="blue">Max = 242ε (Mean = 31ε)</span> 10077 </p> 10078 </td> 10079</tr> 10080<tr> 10081<td> 10082 <p> 10083 Non Central Beta, large parameters 10084 </p> 10085 </td> 10086<td> 10087 <p> 10088 <span class="blue">Max = 1.18ε (Mean = 0.175ε)</span><br> <br> 10089 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 1.01e+36ε (Mean 10090 = 1.19e+35ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_Rmath_3_2_3_Non_Central_Beta_large_parameters">And 10091 other failures.</a>)</span> 10092 </p> 10093 </td> 10094<td> 10095 <p> 10096 <span class="blue">Max = 2.5e+04ε (Mean = 3.78e+03ε)</span> 10097 </p> 10098 </td> 10099<td> 10100 <p> 10101 <span class="blue">Max = 2.57e+04ε (Mean = 4.45e+03ε)</span> 10102 </p> 10103 </td> 10104<td> 10105 <p> 10106 <span class="blue">Max = 3.66e+03ε (Mean = 500ε)</span> 10107 </p> 10108 </td> 10109</tr> 10110</tbody> 10111</table></div> 10112</div> 10113<br class="table-break"> 10114</div> 10115<div class="section"> 10116<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 10117<a name="special_function_error_rates_rep.section_non_central_beta_CDF_complement"></a><a class="link" href="index.html#special_function_error_rates_rep.section_non_central_beta_CDF_complement" title="non central beta CDF complement">non 10118 central beta CDF complement</a> 10119</h2></div></div></div> 10120<div class="table"> 10121<a name="special_function_error_rates_rep.section_non_central_beta_CDF_complement.table_non_central_beta_CDF_complement"></a><p class="title"><b>Table 73. Error rates for non central beta CDF complement</b></p> 10122<div class="table-contents"><table class="table" summary="Error rates for non central beta CDF complement"> 10123<colgroup> 10124<col> 10125<col> 10126<col> 10127<col> 10128<col> 10129</colgroup> 10130<thead><tr> 10131<th> 10132 </th> 10133<th> 10134 <p> 10135 GNU C++ version 7.1.0<br> linux<br> double 10136 </p> 10137 </th> 10138<th> 10139 <p> 10140 GNU C++ version 7.1.0<br> linux<br> long double 10141 </p> 10142 </th> 10143<th> 10144 <p> 10145 Sun compiler version 0x5150<br> Sun Solaris<br> long double 10146 </p> 10147 </th> 10148<th> 10149 <p> 10150 Microsoft Visual C++ version 14.1<br> Win32<br> double 10151 </p> 10152 </th> 10153</tr></thead> 10154<tbody> 10155<tr> 10156<td> 10157 <p> 10158 Non Central Beta, medium parameters 10159 </p> 10160 </td> 10161<td> 10162 <p> 10163 <span class="blue">Max = 0.998ε (Mean = 0.0936ε)</span><br> <br> 10164 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 7.5e+97ε (Mean 10165 = 1.37e+96ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_complement_Rmath_3_2_3_Non_Central_Beta_medium_parameters">And 10166 other failures.</a>)</span> 10167 </p> 10168 </td> 10169<td> 10170 <p> 10171 <span class="blue">Max = 396ε (Mean = 50.7ε)</span> 10172 </p> 10173 </td> 10174<td> 10175 <p> 10176 <span class="blue">Max = 554ε (Mean = 57.2ε)</span> 10177 </p> 10178 </td> 10179<td> 10180 <p> 10181 <span class="blue">Max = 624ε (Mean = 62.7ε)</span> 10182 </p> 10183 </td> 10184</tr> 10185<tr> 10186<td> 10187 <p> 10188 Non Central Beta, large parameters 10189 </p> 10190 </td> 10191<td> 10192 <p> 10193 <span class="blue">Max = 0.986ε (Mean = 0.188ε)</span><br> <br> 10194 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = +INFε (Mean 10195 = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_complement_Rmath_3_2_3_Non_Central_Beta_large_parameters">And 10196 other failures.</a>)</span> 10197 </p> 10198 </td> 10199<td> 10200 <p> 10201 <span class="blue">Max = 6.83e+03ε (Mean = 993ε)</span> 10202 </p> 10203 </td> 10204<td> 10205 <p> 10206 <span class="blue">Max = 3.56e+03ε (Mean = 707ε)</span> 10207 </p> 10208 </td> 10209<td> 10210 <p> 10211 <span class="blue">Max = 1.25e+04ε (Mean = 1.49e+03ε)</span> 10212 </p> 10213 </td> 10214</tr> 10215</tbody> 10216</table></div> 10217</div> 10218<br class="table-break"> 10219</div> 10220<div class="section"> 10221<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 10222<a name="special_function_error_rates_rep.section_non_central_chi_squared_CDF"></a><a class="link" href="index.html#special_function_error_rates_rep.section_non_central_chi_squared_CDF" title="non central chi squared CDF">non 10223 central chi squared CDF</a> 10224</h2></div></div></div> 10225<div class="table"> 10226<a name="special_function_error_rates_rep.section_non_central_chi_squared_CDF.table_non_central_chi_squared_CDF"></a><p class="title"><b>Table 74. Error rates for non central chi squared CDF</b></p> 10227<div class="table-contents"><table class="table" summary="Error rates for non central chi squared CDF"> 10228<colgroup> 10229<col> 10230<col> 10231<col> 10232<col> 10233<col> 10234</colgroup> 10235<thead><tr> 10236<th> 10237 </th> 10238<th> 10239 <p> 10240 GNU C++ version 7.1.0<br> linux<br> double 10241 </p> 10242 </th> 10243<th> 10244 <p> 10245 GNU C++ version 7.1.0<br> linux<br> long double 10246 </p> 10247 </th> 10248<th> 10249 <p> 10250 Sun compiler version 0x5150<br> Sun Solaris<br> long double 10251 </p> 10252 </th> 10253<th> 10254 <p> 10255 Microsoft Visual C++ version 14.1<br> Win32<br> double 10256 </p> 10257 </th> 10258</tr></thead> 10259<tbody> 10260<tr> 10261<td> 10262 <p> 10263 Non Central Chi Squared, medium parameters 10264 </p> 10265 </td> 10266<td> 10267 <p> 10268 <span class="blue">Max = 0.99ε (Mean = 0.0544ε)</span><br> <br> 10269 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 727ε (Mean = 121ε)) 10270 </p> 10271 </td> 10272<td> 10273 <p> 10274 <span class="blue">Max = 46.5ε (Mean = 10.3ε)</span> 10275 </p> 10276 </td> 10277<td> 10278 <p> 10279 <span class="blue">Max = 115ε (Mean = 13.9ε)</span> 10280 </p> 10281 </td> 10282<td> 10283 <p> 10284 <span class="blue">Max = 48.9ε (Mean = 10ε)</span> 10285 </p> 10286 </td> 10287</tr> 10288<tr> 10289<td> 10290 <p> 10291 Non Central Chi Squared, large parameters 10292 </p> 10293 </td> 10294<td> 10295 <p> 10296 <span class="blue">Max = 1.07ε (Mean = 0.102ε)</span><br> <br> 10297 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 3.27e+08ε (Mean 10298 = 2.23e+07ε))</span> 10299 </p> 10300 </td> 10301<td> 10302 <p> 10303 <span class="blue">Max = 3.07e+03ε (Mean = 336ε)</span> 10304 </p> 10305 </td> 10306<td> 10307 <p> 10308 <span class="blue">Max = 6.17e+03ε (Mean = 677ε)</span> 10309 </p> 10310 </td> 10311<td> 10312 <p> 10313 <span class="blue">Max = 9.79e+03ε (Mean = 723ε)</span> 10314 </p> 10315 </td> 10316</tr> 10317</tbody> 10318</table></div> 10319</div> 10320<br class="table-break"> 10321</div> 10322<div class="section"> 10323<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 10324<a name="special_function_error_rates_rep.section_non_central_chi_squared_CDF_complement"></a><a class="link" href="index.html#special_function_error_rates_rep.section_non_central_chi_squared_CDF_complement" title="non central chi squared CDF complement">non 10325 central chi squared CDF complement</a> 10326</h2></div></div></div> 10327<div class="table"> 10328<a name="special_function_error_rates_rep.section_non_central_chi_squared_CDF_complement.table_non_central_chi_squared_CDF_complement"></a><p class="title"><b>Table 75. Error rates for non central chi squared CDF complement</b></p> 10329<div class="table-contents"><table class="table" summary="Error rates for non central chi squared CDF complement"> 10330<colgroup> 10331<col> 10332<col> 10333<col> 10334<col> 10335<col> 10336</colgroup> 10337<thead><tr> 10338<th> 10339 </th> 10340<th> 10341 <p> 10342 GNU C++ version 7.1.0<br> linux<br> double 10343 </p> 10344 </th> 10345<th> 10346 <p> 10347 GNU C++ version 7.1.0<br> linux<br> long double 10348 </p> 10349 </th> 10350<th> 10351 <p> 10352 Sun compiler version 0x5150<br> Sun Solaris<br> long double 10353 </p> 10354 </th> 10355<th> 10356 <p> 10357 Microsoft Visual C++ version 14.1<br> Win32<br> double 10358 </p> 10359 </th> 10360</tr></thead> 10361<tbody> 10362<tr> 10363<td> 10364 <p> 10365 Non Central Chi Squared, medium parameters 10366 </p> 10367 </td> 10368<td> 10369 <p> 10370 <span class="blue">Max = 0.96ε (Mean = 0.0635ε)</span><br> <br> 10371 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = +INFε (Mean 10372 = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_chi_squared_CDF_complement_Rmath_3_2_3_Non_Central_Chi_Squared_medium_parameters">And 10373 other failures.</a>)</span> 10374 </p> 10375 </td> 10376<td> 10377 <p> 10378 <span class="blue">Max = 107ε (Mean = 17.2ε)</span> 10379 </p> 10380 </td> 10381<td> 10382 <p> 10383 <span class="blue">Max = 171ε (Mean = 22.8ε)</span> 10384 </p> 10385 </td> 10386<td> 10387 <p> 10388 <span class="blue">Max = 98.6ε (Mean = 15.8ε)</span> 10389 </p> 10390 </td> 10391</tr> 10392<tr> 10393<td> 10394 <p> 10395 Non Central Chi Squared, large parameters 10396 </p> 10397 </td> 10398<td> 10399 <p> 10400 <span class="blue">Max = 2.11ε (Mean = 0.278ε)</span><br> <br> 10401 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = +INFε (Mean 10402 = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_chi_squared_CDF_complement_Rmath_3_2_3_Non_Central_Chi_Squared_large_parameters">And 10403 other failures.</a>)</span> 10404 </p> 10405 </td> 10406<td> 10407 <p> 10408 <span class="blue">Max = 5.02e+03ε (Mean = 630ε)</span> 10409 </p> 10410 </td> 10411<td> 10412 <p> 10413 <span class="blue">Max = 5.1e+03ε (Mean = 577ε)</span> 10414 </p> 10415 </td> 10416<td> 10417 <p> 10418 <span class="blue">Max = 5.43e+03ε (Mean = 705ε)</span> 10419 </p> 10420 </td> 10421</tr> 10422</tbody> 10423</table></div> 10424</div> 10425<br class="table-break"> 10426</div> 10427<div class="section"> 10428<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 10429<a name="special_function_error_rates_rep.section_non_central_t_CDF"></a><a class="link" href="index.html#special_function_error_rates_rep.section_non_central_t_CDF" title="non central t CDF">non 10430 central t CDF</a> 10431</h2></div></div></div> 10432<div class="table"> 10433<a name="special_function_error_rates_rep.section_non_central_t_CDF.table_non_central_t_CDF"></a><p class="title"><b>Table 76. Error rates for non central t CDF</b></p> 10434<div class="table-contents"><table class="table" summary="Error rates for non central t CDF"> 10435<colgroup> 10436<col> 10437<col> 10438<col> 10439<col> 10440<col> 10441</colgroup> 10442<thead><tr> 10443<th> 10444 </th> 10445<th> 10446 <p> 10447 GNU C++ version 7.1.0<br> linux<br> double 10448 </p> 10449 </th> 10450<th> 10451 <p> 10452 GNU C++ version 7.1.0<br> linux<br> long double 10453 </p> 10454 </th> 10455<th> 10456 <p> 10457 Sun compiler version 0x5150<br> Sun Solaris<br> long double 10458 </p> 10459 </th> 10460<th> 10461 <p> 10462 Microsoft Visual C++ version 14.1<br> Win32<br> double 10463 </p> 10464 </th> 10465</tr></thead> 10466<tbody> 10467<tr> 10468<td> 10469 <p> 10470 Non Central T 10471 </p> 10472 </td> 10473<td> 10474 <p> 10475 <span class="blue">Max = 0.796ε (Mean = 0.0691ε)</span><br> <br> 10476 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 5.28e+15ε (Mean 10477 = 8.49e+14ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_t_CDF_Rmath_3_2_3_Non_Central_T">And 10478 other failures.</a>)</span> 10479 </p> 10480 </td> 10481<td> 10482 <p> 10483 <span class="blue">Max = 139ε (Mean = 31ε)</span> 10484 </p> 10485 </td> 10486<td> 10487 <p> 10488 <span class="blue">Max = 145ε (Mean = 30.9ε)</span> 10489 </p> 10490 </td> 10491<td> 10492 <p> 10493 <span class="blue">Max = 135ε (Mean = 32.1ε)</span> 10494 </p> 10495 </td> 10496</tr> 10497<tr> 10498<td> 10499 <p> 10500 Non Central T (small non-centrality) 10501 </p> 10502 </td> 10503<td> 10504 <p> 10505 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath 10506 3.2.3:</em></span> Max = 2.09e+03ε (Mean = 244ε)) 10507 </p> 10508 </td> 10509<td> 10510 <p> 10511 <span class="blue">Max = 3.86ε (Mean = 1.4ε)</span> 10512 </p> 10513 </td> 10514<td> 10515 <p> 10516 <span class="blue">Max = 9.15ε (Mean = 2.13ε)</span> 10517 </p> 10518 </td> 10519<td> 10520 <p> 10521 <span class="blue">Max = 6.17ε (Mean = 1.45ε)</span> 10522 </p> 10523 </td> 10524</tr> 10525<tr> 10526<td> 10527 <p> 10528 Non Central T (large parameters) 10529 </p> 10530 </td> 10531<td> 10532 <p> 10533 <span class="blue">Max = 257ε (Mean = 72.1ε)</span><br> <br> 10534 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.46ε (Mean = 0.657ε)) 10535 </p> 10536 </td> 10537<td> 10538 <p> 10539 <span class="blue">Max = 5.26e+05ε (Mean = 1.48e+05ε)</span> 10540 </p> 10541 </td> 10542<td> 10543 <p> 10544 <span class="blue">Max = 5.24e+05ε (Mean = 1.47e+05ε)</span> 10545 </p> 10546 </td> 10547<td> 10548 <p> 10549 <span class="blue">Max = 286ε (Mean = 62.8ε)</span> 10550 </p> 10551 </td> 10552</tr> 10553</tbody> 10554</table></div> 10555</div> 10556<br class="table-break"> 10557</div> 10558<div class="section"> 10559<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 10560<a name="special_function_error_rates_rep.section_non_central_t_CDF_complement"></a><a class="link" href="index.html#special_function_error_rates_rep.section_non_central_t_CDF_complement" title="non central t CDF complement">non 10561 central t CDF complement</a> 10562</h2></div></div></div> 10563<div class="table"> 10564<a name="special_function_error_rates_rep.section_non_central_t_CDF_complement.table_non_central_t_CDF_complement"></a><p class="title"><b>Table 77. Error rates for non central t CDF complement</b></p> 10565<div class="table-contents"><table class="table" summary="Error rates for non central t CDF complement"> 10566<colgroup> 10567<col> 10568<col> 10569<col> 10570<col> 10571<col> 10572</colgroup> 10573<thead><tr> 10574<th> 10575 </th> 10576<th> 10577 <p> 10578 GNU C++ version 7.1.0<br> linux<br> double 10579 </p> 10580 </th> 10581<th> 10582 <p> 10583 GNU C++ version 7.1.0<br> linux<br> long double 10584 </p> 10585 </th> 10586<th> 10587 <p> 10588 Sun compiler version 0x5150<br> Sun Solaris<br> long double 10589 </p> 10590 </th> 10591<th> 10592 <p> 10593 Microsoft Visual C++ version 14.1<br> Win32<br> double 10594 </p> 10595 </th> 10596</tr></thead> 10597<tbody> 10598<tr> 10599<td> 10600 <p> 10601 Non Central T 10602 </p> 10603 </td> 10604<td> 10605 <p> 10606 <span class="blue">Max = 0.707ε (Mean = 0.0497ε)</span><br> <br> 10607 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 6.19e+15ε (Mean 10608 = 6.72e+14ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_t_CDF_complement_Rmath_3_2_3_Non_Central_T">And 10609 other failures.</a>)</span> 10610 </p> 10611 </td> 10612<td> 10613 <p> 10614 <span class="blue">Max = 201ε (Mean = 31.7ε)</span> 10615 </p> 10616 </td> 10617<td> 10618 <p> 10619 <span class="blue">Max = 340ε (Mean = 43.2ε)</span> 10620 </p> 10621 </td> 10622<td> 10623 <p> 10624 <span class="blue">Max = 154ε (Mean = 32.1ε)</span> 10625 </p> 10626 </td> 10627</tr> 10628<tr> 10629<td> 10630 <p> 10631 Non Central T (small non-centrality) 10632 </p> 10633 </td> 10634<td> 10635 <p> 10636 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath 10637 3.2.3:</em></span> Max = 1.87e+03ε (Mean = 263ε)) 10638 </p> 10639 </td> 10640<td> 10641 <p> 10642 <span class="blue">Max = 10.5ε (Mean = 2.13ε)</span> 10643 </p> 10644 </td> 10645<td> 10646 <p> 10647 <span class="blue">Max = 10.5ε (Mean = 2.39ε)</span> 10648 </p> 10649 </td> 10650<td> 10651 <p> 10652 <span class="blue">Max = 4.6ε (Mean = 1.63ε)</span> 10653 </p> 10654 </td> 10655</tr> 10656<tr> 10657<td> 10658 <p> 10659 Non Central T (large parameters) 10660 </p> 10661 </td> 10662<td> 10663 <p> 10664 <span class="blue">Max = 478ε (Mean = 96.3ε)</span><br> <br> 10665 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.24ε (Mean = 0.945ε)) 10666 </p> 10667 </td> 10668<td> 10669 <p> 10670 <span class="blue">Max = 9.79e+05ε (Mean = 1.97e+05ε)</span> 10671 </p> 10672 </td> 10673<td> 10674 <p> 10675 <span class="blue">Max = 9.79e+05ε (Mean = 1.97e+05ε)</span> 10676 </p> 10677 </td> 10678<td> 10679 <p> 10680 <span class="blue">Max = 227ε (Mean = 50.4ε)</span> 10681 </p> 10682 </td> 10683</tr> 10684</tbody> 10685</table></div> 10686</div> 10687<br class="table-break"> 10688</div> 10689<div class="section"> 10690<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 10691<a name="special_function_error_rates_rep.section_owens_t"></a><a class="link" href="index.html#special_function_error_rates_rep.section_owens_t" title="owens_t">owens_t</a> 10692</h2></div></div></div> 10693<div class="table"> 10694<a name="special_function_error_rates_rep.section_owens_t.table_owens_t"></a><p class="title"><b>Table 78. Error rates for owens_t</b></p> 10695<div class="table-contents"><table class="table" summary="Error rates for owens_t"> 10696<colgroup> 10697<col> 10698<col> 10699<col> 10700<col> 10701<col> 10702</colgroup> 10703<thead><tr> 10704<th> 10705 </th> 10706<th> 10707 <p> 10708 GNU C++ version 7.1.0<br> linux<br> double 10709 </p> 10710 </th> 10711<th> 10712 <p> 10713 GNU C++ version 7.1.0<br> linux<br> long double 10714 </p> 10715 </th> 10716<th> 10717 <p> 10718 Sun compiler version 0x5150<br> Sun Solaris<br> long double 10719 </p> 10720 </th> 10721<th> 10722 <p> 10723 Microsoft Visual C++ version 14.1<br> Win32<br> double 10724 </p> 10725 </th> 10726</tr></thead> 10727<tbody> 10728<tr> 10729<td> 10730 <p> 10731 Owens T (medium small values) 10732 </p> 10733 </td> 10734<td> 10735 <p> 10736 <span class="blue">Max = 0ε (Mean = 0ε)</span> 10737 </p> 10738 </td> 10739<td> 10740 <p> 10741 <span class="blue">Max = 3.34ε (Mean = 0.944ε)</span> 10742 </p> 10743 </td> 10744<td> 10745 <p> 10746 <span class="blue">Max = 3.34ε (Mean = 0.911ε)</span> 10747 </p> 10748 </td> 10749<td> 10750 <p> 10751 <span class="blue">Max = 4.37ε (Mean = 0.98ε)</span> 10752 </p> 10753 </td> 10754</tr> 10755<tr> 10756<td> 10757 <p> 10758 Owens T (large and diverse values) 10759 </p> 10760 </td> 10761<td> 10762 <p> 10763 <span class="blue">Max = 0ε (Mean = 0ε)</span> 10764 </p> 10765 </td> 10766<td> 10767 <p> 10768 <span class="blue">Max = 49ε (Mean = 2.16ε)</span> 10769 </p> 10770 </td> 10771<td> 10772 <p> 10773 <span class="blue">Max = 24.5ε (Mean = 1.39ε)</span> 10774 </p> 10775 </td> 10776<td> 10777 <p> 10778 <span class="blue">Max = 3.78ε (Mean = 0.621ε)</span> 10779 </p> 10780 </td> 10781</tr> 10782</tbody> 10783</table></div> 10784</div> 10785<br class="table-break"> 10786</div> 10787<div class="section"> 10788<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 10789<a name="special_function_error_rates_rep.section_polygamma"></a><a class="link" href="index.html#special_function_error_rates_rep.section_polygamma" title="polygamma">polygamma</a> 10790</h2></div></div></div> 10791<div class="table"> 10792<a name="special_function_error_rates_rep.section_polygamma.table_polygamma"></a><p class="title"><b>Table 79. Error rates for polygamma</b></p> 10793<div class="table-contents"><table class="table" summary="Error rates for polygamma"> 10794<colgroup> 10795<col> 10796<col> 10797<col> 10798<col> 10799<col> 10800</colgroup> 10801<thead><tr> 10802<th> 10803 </th> 10804<th> 10805 <p> 10806 GNU C++ version 7.1.0<br> linux<br> double 10807 </p> 10808 </th> 10809<th> 10810 <p> 10811 GNU C++ version 7.1.0<br> linux<br> long double 10812 </p> 10813 </th> 10814<th> 10815 <p> 10816 Sun compiler version 0x5150<br> Sun Solaris<br> long double 10817 </p> 10818 </th> 10819<th> 10820 <p> 10821 Microsoft Visual C++ version 14.1<br> Win32<br> double 10822 </p> 10823 </th> 10824</tr></thead> 10825<tbody> 10826<tr> 10827<td> 10828 <p> 10829 Mathematica Data 10830 </p> 10831 </td> 10832<td> 10833 <p> 10834 <span class="blue">Max = 0.824ε (Mean = 0.0574ε)</span><br> <br> 10835 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 62.9ε (Mean = 12.8ε))<br> (<span class="emphasis"><em>Rmath 10836 3.2.3:</em></span> Max = 108ε (Mean = 15.2ε)) 10837 </p> 10838 </td> 10839<td> 10840 <p> 10841 <span class="blue">Max = 7.38ε (Mean = 1.84ε)</span> 10842 </p> 10843 </td> 10844<td> 10845 <p> 10846 <span class="blue">Max = 34.3ε (Mean = 7.65ε)</span> 10847 </p> 10848 </td> 10849<td> 10850 <p> 10851 <span class="blue">Max = 9.32ε (Mean = 1.95ε)</span> 10852 </p> 10853 </td> 10854</tr> 10855<tr> 10856<td> 10857 <p> 10858 Mathematica Data - large arguments 10859 </p> 10860 </td> 10861<td> 10862 <p> 10863 <span class="blue">Max = 0.998ε (Mean = 0.0592ε)</span><br> <br> 10864 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 244ε (Mean = 32.8ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_large_arguments">And 10865 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 10866 <span class="red">Max = 1.71e+56ε (Mean = 1.01e+55ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_large_arguments">And 10867 other failures.</a>)</span> 10868 </p> 10869 </td> 10870<td> 10871 <p> 10872 <span class="blue">Max = 2.23ε (Mean = 0.323ε)</span> 10873 </p> 10874 </td> 10875<td> 10876 <p> 10877 <span class="blue">Max = 11.1ε (Mean = 0.848ε)</span> 10878 </p> 10879 </td> 10880<td> 10881 <p> 10882 <span class="blue">Max = 150ε (Mean = 13.9ε)</span> 10883 </p> 10884 </td> 10885</tr> 10886<tr> 10887<td> 10888 <p> 10889 Mathematica Data - negative arguments 10890 </p> 10891 </td> 10892<td> 10893 <p> 10894 <span class="blue">Max = 0.516ε (Mean = 0.022ε)</span><br> <br> 10895 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 36.6ε (Mean = 3.04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_negative_arguments">And 10896 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 10897 Max = 0ε (Mean = 0ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_negative_arguments">And 10898 other failures.</a>) 10899 </p> 10900 </td> 10901<td> 10902 <p> 10903 <span class="blue">Max = 269ε (Mean = 87.7ε)</span> 10904 </p> 10905 </td> 10906<td> 10907 <p> 10908 <span class="blue">Max = 269ε (Mean = 88.4ε)</span> 10909 </p> 10910 </td> 10911<td> 10912 <p> 10913 <span class="blue">Max = 497ε (Mean = 129ε)</span> 10914 </p> 10915 </td> 10916</tr> 10917<tr> 10918<td> 10919 <p> 10920 Mathematica Data - large negative arguments 10921 </p> 10922 </td> 10923<td> 10924 <p> 10925 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 10926 2.1:</em></span> Max = 1.79ε (Mean = 0.197ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_large_negative_arguments">And 10927 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 10928 Max = 0ε (Mean = 0ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_large_negative_arguments">And 10929 other failures.</a>) 10930 </p> 10931 </td> 10932<td> 10933 <p> 10934 <span class="blue">Max = 155ε (Mean = 96.4ε)</span> 10935 </p> 10936 </td> 10937<td> 10938 <p> 10939 <span class="blue">Max = 155ε (Mean = 96.4ε)</span> 10940 </p> 10941 </td> 10942<td> 10943 <p> 10944 <span class="blue">Max = 162ε (Mean = 101ε)</span> 10945 </p> 10946 </td> 10947</tr> 10948<tr> 10949<td> 10950 <p> 10951 Mathematica Data - small arguments 10952 </p> 10953 </td> 10954<td> 10955 <p> 10956 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 10957 2.1:</em></span> Max = 15.2ε (Mean = 5.03ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 10958 Max = 106ε (Mean = 20ε)) 10959 </p> 10960 </td> 10961<td> 10962 <p> 10963 <span class="blue">Max = 3.33ε (Mean = 0.75ε)</span> 10964 </p> 10965 </td> 10966<td> 10967 <p> 10968 <span class="blue">Max = 3.33ε (Mean = 0.75ε)</span> 10969 </p> 10970 </td> 10971<td> 10972 <p> 10973 <span class="blue">Max = 3ε (Mean = 0.496ε)</span> 10974 </p> 10975 </td> 10976</tr> 10977<tr> 10978<td> 10979 <p> 10980 Mathematica Data - Large orders and other bug cases 10981 </p> 10982 </td> 10983<td> 10984 <p> 10985 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 10986 2.1:</em></span> Max = 151ε (Mean = 39.3ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_Large_orders_and_other_bug_cases">And 10987 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 10988 <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_Large_orders_and_other_bug_cases">And 10989 other failures.</a>)</span> 10990 </p> 10991 </td> 10992<td> 10993 <p> 10994 <span class="blue">Max = 54.5ε (Mean = 13.3ε)</span> 10995 </p> 10996 </td> 10997<td> 10998 <p> 10999 <span class="blue">Max = 145ε (Mean = 55.9ε)</span> 11000 </p> 11001 </td> 11002<td> 11003 <p> 11004 <span class="blue">Max = 200ε (Mean = 57.2ε)</span> 11005 </p> 11006 </td> 11007</tr> 11008</tbody> 11009</table></div> 11010</div> 11011<br class="table-break"> 11012</div> 11013<div class="section"> 11014<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 11015<a name="special_function_error_rates_rep.section_powm1"></a><a class="link" href="index.html#special_function_error_rates_rep.section_powm1" title="powm1">powm1</a> 11016</h2></div></div></div> 11017<div class="table"> 11018<a name="special_function_error_rates_rep.section_powm1.table_powm1"></a><p class="title"><b>Table 80. Error rates for powm1</b></p> 11019<div class="table-contents"><table class="table" summary="Error rates for powm1"> 11020<colgroup> 11021<col> 11022<col> 11023<col> 11024<col> 11025<col> 11026</colgroup> 11027<thead><tr> 11028<th> 11029 </th> 11030<th> 11031 <p> 11032 GNU C++ version 7.1.0<br> linux<br> double 11033 </p> 11034 </th> 11035<th> 11036 <p> 11037 GNU C++ version 7.1.0<br> linux<br> long double 11038 </p> 11039 </th> 11040<th> 11041 <p> 11042 Sun compiler version 0x5150<br> Sun Solaris<br> long double 11043 </p> 11044 </th> 11045<th> 11046 <p> 11047 Microsoft Visual C++ version 14.1<br> Win32<br> double 11048 </p> 11049 </th> 11050</tr></thead> 11051<tbody><tr> 11052<td> 11053 <p> 11054 powm1 11055 </p> 11056 </td> 11057<td> 11058 <p> 11059 <span class="blue">Max = 1.06ε (Mean = 0.425ε)</span> 11060 </p> 11061 </td> 11062<td> 11063 <p> 11064 <span class="blue">Max = 2.04ε (Mean = 0.493ε)</span> 11065 </p> 11066 </td> 11067<td> 11068 <p> 11069 <span class="blue">Max = 1.88ε (Mean = 0.49ε)</span> 11070 </p> 11071 </td> 11072<td> 11073 <p> 11074 <span class="blue">Max = 1.84ε (Mean = 0.486ε)</span> 11075 </p> 11076 </td> 11077</tr></tbody> 11078</table></div> 11079</div> 11080<br class="table-break"> 11081</div> 11082<div class="section"> 11083<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 11084<a name="special_function_error_rates_rep.section_sin_pi"></a><a class="link" href="index.html#special_function_error_rates_rep.section_sin_pi" title="sin_pi">sin_pi</a> 11085</h2></div></div></div> 11086<div class="table"> 11087<a name="special_function_error_rates_rep.section_sin_pi.table_sin_pi"></a><p class="title"><b>Table 81. Error rates for sin_pi</b></p> 11088<div class="table-contents"><table class="table" summary="Error rates for sin_pi"> 11089<colgroup> 11090<col> 11091<col> 11092<col> 11093<col> 11094<col> 11095</colgroup> 11096<thead><tr> 11097<th> 11098 </th> 11099<th> 11100 <p> 11101 GNU C++ version 7.1.0<br> linux<br> double 11102 </p> 11103 </th> 11104<th> 11105 <p> 11106 GNU C++ version 7.1.0<br> linux<br> long double 11107 </p> 11108 </th> 11109<th> 11110 <p> 11111 Sun compiler version 0x5150<br> Sun Solaris<br> long double 11112 </p> 11113 </th> 11114<th> 11115 <p> 11116 Microsoft Visual C++ version 14.1<br> Win32<br> double 11117 </p> 11118 </th> 11119</tr></thead> 11120<tbody> 11121<tr> 11122<td> 11123 <p> 11124 sin_pi and cos_pi 11125 </p> 11126 </td> 11127<td> 11128 <p> 11129 <span class="blue">Max = 0ε (Mean = 0ε)</span> 11130 </p> 11131 </td> 11132<td> 11133 <p> 11134 <span class="blue">Max = 0.996ε (Mean = 0.335ε)</span> 11135 </p> 11136 </td> 11137<td> 11138 <p> 11139 <span class="blue">Max = 0.996ε (Mean = 0.336ε)</span> 11140 </p> 11141 </td> 11142<td> 11143 <p> 11144 <span class="blue">Max = 0.99ε (Mean = 0.328ε)</span> 11145 </p> 11146 </td> 11147</tr> 11148<tr> 11149<td> 11150 <p> 11151 sin_pi and cos_pi near integers and half integers 11152 </p> 11153 </td> 11154<td> 11155 <p> 11156 <span class="blue">Max = 0ε (Mean = 0ε)</span> 11157 </p> 11158 </td> 11159<td> 11160 <p> 11161 <span class="blue">Max = 0.976ε (Mean = 0.293ε)</span> 11162 </p> 11163 </td> 11164<td> 11165 <p> 11166 <span class="blue">Max = 0.976ε (Mean = 0.293ε)</span> 11167 </p> 11168 </td> 11169<td> 11170 <p> 11171 <span class="blue">Max = 0.996ε (Mean = 0.343ε)</span> 11172 </p> 11173 </td> 11174</tr> 11175</tbody> 11176</table></div> 11177</div> 11178<br class="table-break"> 11179</div> 11180<div class="section"> 11181<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 11182<a name="special_function_error_rates_rep.section_sph_bessel"></a><a class="link" href="index.html#special_function_error_rates_rep.section_sph_bessel" title="sph_bessel">sph_bessel</a> 11183</h2></div></div></div> 11184<div class="table"> 11185<a name="special_function_error_rates_rep.section_sph_bessel.table_sph_bessel"></a><p class="title"><b>Table 82. Error rates for sph_bessel</b></p> 11186<div class="table-contents"><table class="table" summary="Error rates for sph_bessel"> 11187<colgroup> 11188<col> 11189<col> 11190<col> 11191<col> 11192<col> 11193</colgroup> 11194<thead><tr> 11195<th> 11196 </th> 11197<th> 11198 <p> 11199 GNU C++ version 7.1.0<br> linux<br> long double 11200 </p> 11201 </th> 11202<th> 11203 <p> 11204 GNU C++ version 7.1.0<br> linux<br> double 11205 </p> 11206 </th> 11207<th> 11208 <p> 11209 Sun compiler version 0x5150<br> Sun Solaris<br> long double 11210 </p> 11211 </th> 11212<th> 11213 <p> 11214 Microsoft Visual C++ version 14.1<br> Win32<br> double 11215 </p> 11216 </th> 11217</tr></thead> 11218<tbody><tr> 11219<td> 11220 <p> 11221 Bessel j: Random Data 11222 </p> 11223 </td> 11224<td> 11225 <p> 11226 <span class="blue">Max = 243ε (Mean = 13.3ε)</span><br> <br> 11227 (<span class="emphasis"><em><cmath>:</em></span> Max = 1.91e+06ε (Mean = 1.09e+05ε)) 11228 </p> 11229 </td> 11230<td> 11231 <p> 11232 <span class="blue">Max = 0.978ε (Mean = 0.0445ε)</span><br> <br> 11233 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.79e+03ε (Mean = 107ε)) 11234 </p> 11235 </td> 11236<td> 11237 <p> 11238 <span class="blue">Max = 243ε (Mean = 33.7ε)</span> 11239 </p> 11240 </td> 11241<td> 11242 <p> 11243 <span class="blue">Max = 245ε (Mean = 16.3ε)</span> 11244 </p> 11245 </td> 11246</tr></tbody> 11247</table></div> 11248</div> 11249<br class="table-break"> 11250</div> 11251<div class="section"> 11252<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 11253<a name="special_function_error_rates_rep.section_sph_bessel_prime"></a><a class="link" href="index.html#special_function_error_rates_rep.section_sph_bessel_prime" title="sph_bessel_prime">sph_bessel_prime</a> 11254</h2></div></div></div> 11255<div class="table"> 11256<a name="special_function_error_rates_rep.section_sph_bessel_prime.table_sph_bessel_prime"></a><p class="title"><b>Table 83. Error rates for sph_bessel_prime</b></p> 11257<div class="table-contents"><table class="table" summary="Error rates for sph_bessel_prime"> 11258<colgroup> 11259<col> 11260<col> 11261<col> 11262<col> 11263<col> 11264</colgroup> 11265<thead><tr> 11266<th> 11267 </th> 11268<th> 11269 <p> 11270 GNU C++ version 7.1.0<br> linux<br> double 11271 </p> 11272 </th> 11273<th> 11274 <p> 11275 GNU C++ version 7.1.0<br> linux<br> long double 11276 </p> 11277 </th> 11278<th> 11279 <p> 11280 Sun compiler version 0x5150<br> Sun Solaris<br> long double 11281 </p> 11282 </th> 11283<th> 11284 <p> 11285 Microsoft Visual C++ version 14.1<br> Win32<br> double 11286 </p> 11287 </th> 11288</tr></thead> 11289<tbody><tr> 11290<td> 11291 <p> 11292 Bessel j': Random Data 11293 </p> 11294 </td> 11295<td> 11296 <p> 11297 <span class="blue">Max = 0.753ε (Mean = 0.0343ε)</span> 11298 </p> 11299 </td> 11300<td> 11301 <p> 11302 <span class="blue">Max = 167ε (Mean = 12ε)</span> 11303 </p> 11304 </td> 11305<td> 11306 <p> 11307 <span class="blue">Max = 167ε (Mean = 33.2ε)</span> 11308 </p> 11309 </td> 11310<td> 11311 <p> 11312 <span class="blue">Max = 307ε (Mean = 25.2ε)</span> 11313 </p> 11314 </td> 11315</tr></tbody> 11316</table></div> 11317</div> 11318<br class="table-break"> 11319</div> 11320<div class="section"> 11321<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 11322<a name="special_function_error_rates_rep.section_sph_neumann"></a><a class="link" href="index.html#special_function_error_rates_rep.section_sph_neumann" title="sph_neumann">sph_neumann</a> 11323</h2></div></div></div> 11324<div class="table"> 11325<a name="special_function_error_rates_rep.section_sph_neumann.table_sph_neumann"></a><p class="title"><b>Table 84. Error rates for sph_neumann</b></p> 11326<div class="table-contents"><table class="table" summary="Error rates for sph_neumann"> 11327<colgroup> 11328<col> 11329<col> 11330<col> 11331<col> 11332<col> 11333</colgroup> 11334<thead><tr> 11335<th> 11336 </th> 11337<th> 11338 <p> 11339 GNU C++ version 7.1.0<br> linux<br> long double 11340 </p> 11341 </th> 11342<th> 11343 <p> 11344 GNU C++ version 7.1.0<br> linux<br> double 11345 </p> 11346 </th> 11347<th> 11348 <p> 11349 Sun compiler version 0x5150<br> Sun Solaris<br> long double 11350 </p> 11351 </th> 11352<th> 11353 <p> 11354 Microsoft Visual C++ version 14.1<br> Win32<br> double 11355 </p> 11356 </th> 11357</tr></thead> 11358<tbody><tr> 11359<td> 11360 <p> 11361 y: Random Data 11362 </p> 11363 </td> 11364<td> 11365 <p> 11366 <span class="blue">Max = 234ε (Mean = 19.5ε)</span><br> <br> 11367 (<span class="emphasis"><em><cmath>:</em></span> Max = 1.6e+06ε (Mean = 1.4e+05ε)) 11368 </p> 11369 </td> 11370<td> 11371 <p> 11372 <span class="blue">Max = 0.995ε (Mean = 0.0665ε)</span><br> <br> 11373 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.5e+04ε (Mean = 5.33e+03ε)) 11374 </p> 11375 </td> 11376<td> 11377 <p> 11378 <span class="blue">Max = 234ε (Mean = 19.8ε)</span> 11379 </p> 11380 </td> 11381<td> 11382 <p> 11383 <span class="blue">Max = 281ε (Mean = 31.1ε)</span> 11384 </p> 11385 </td> 11386</tr></tbody> 11387</table></div> 11388</div> 11389<br class="table-break"> 11390</div> 11391<div class="section"> 11392<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 11393<a name="special_function_error_rates_rep.section_sph_neumann_prime"></a><a class="link" href="index.html#special_function_error_rates_rep.section_sph_neumann_prime" title="sph_neumann_prime">sph_neumann_prime</a> 11394</h2></div></div></div> 11395<div class="table"> 11396<a name="special_function_error_rates_rep.section_sph_neumann_prime.table_sph_neumann_prime"></a><p class="title"><b>Table 85. Error rates for sph_neumann_prime</b></p> 11397<div class="table-contents"><table class="table" summary="Error rates for sph_neumann_prime"> 11398<colgroup> 11399<col> 11400<col> 11401<col> 11402<col> 11403<col> 11404</colgroup> 11405<thead><tr> 11406<th> 11407 </th> 11408<th> 11409 <p> 11410 GNU C++ version 7.1.0<br> linux<br> double 11411 </p> 11412 </th> 11413<th> 11414 <p> 11415 GNU C++ version 7.1.0<br> linux<br> long double 11416 </p> 11417 </th> 11418<th> 11419 <p> 11420 Sun compiler version 0x5150<br> Sun Solaris<br> long double 11421 </p> 11422 </th> 11423<th> 11424 <p> 11425 Microsoft Visual C++ version 14.1<br> Win32<br> double 11426 </p> 11427 </th> 11428</tr></thead> 11429<tbody><tr> 11430<td> 11431 <p> 11432 y': Random Data 11433 </p> 11434 </td> 11435<td> 11436 <p> 11437 <span class="blue">Max = 0.988ε (Mean = 0.0869ε)</span> 11438 </p> 11439 </td> 11440<td> 11441 <p> 11442 <span class="blue">Max = 158ε (Mean = 18.8ε)</span> 11443 </p> 11444 </td> 11445<td> 11446 <p> 11447 <span class="blue">Max = 158ε (Mean = 20.2ε)</span> 11448 </p> 11449 </td> 11450<td> 11451 <p> 11452 <span class="blue">Max = 296ε (Mean = 25.6ε)</span> 11453 </p> 11454 </td> 11455</tr></tbody> 11456</table></div> 11457</div> 11458<br class="table-break"> 11459</div> 11460<div class="section"> 11461<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 11462<a name="special_function_error_rates_rep.section_spherical_harmonic_i"></a><a class="link" href="index.html#special_function_error_rates_rep.section_spherical_harmonic_i" title="spherical_harmonic_i">spherical_harmonic_i</a> 11463</h2></div></div></div> 11464<div class="table"> 11465<a name="special_function_error_rates_rep.section_spherical_harmonic_i.table_spherical_harmonic_i"></a><p class="title"><b>Table 86. Error rates for spherical_harmonic_i</b></p> 11466<div class="table-contents"><table class="table" summary="Error rates for spherical_harmonic_i"> 11467<colgroup> 11468<col> 11469<col> 11470<col> 11471<col> 11472<col> 11473</colgroup> 11474<thead><tr> 11475<th> 11476 </th> 11477<th> 11478 <p> 11479 GNU C++ version 7.1.0<br> linux<br> double 11480 </p> 11481 </th> 11482<th> 11483 <p> 11484 GNU C++ version 7.1.0<br> linux<br> long double 11485 </p> 11486 </th> 11487<th> 11488 <p> 11489 Sun compiler version 0x5150<br> Sun Solaris<br> long double 11490 </p> 11491 </th> 11492<th> 11493 <p> 11494 Microsoft Visual C++ version 14.1<br> Win32<br> double 11495 </p> 11496 </th> 11497</tr></thead> 11498<tbody><tr> 11499<td> 11500 <p> 11501 Spherical Harmonics 11502 </p> 11503 </td> 11504<td> 11505 <p> 11506 <span class="blue">Max = 1.36ε (Mean = 0.0765ε)</span> 11507 </p> 11508 </td> 11509<td> 11510 <p> 11511 <span class="blue">Max = 2.89e+03ε (Mean = 108ε)</span> 11512 </p> 11513 </td> 11514<td> 11515 <p> 11516 <span class="blue">Max = 1.03e+04ε (Mean = 327ε)</span> 11517 </p> 11518 </td> 11519<td> 11520 <p> 11521 <span class="blue">Max = 2.27e+04ε (Mean = 725ε)</span> 11522 </p> 11523 </td> 11524</tr></tbody> 11525</table></div> 11526</div> 11527<br class="table-break"> 11528</div> 11529<div class="section"> 11530<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 11531<a name="special_function_error_rates_rep.section_spherical_harmonic_r"></a><a class="link" href="index.html#special_function_error_rates_rep.section_spherical_harmonic_r" title="spherical_harmonic_r">spherical_harmonic_r</a> 11532</h2></div></div></div> 11533<div class="table"> 11534<a name="special_function_error_rates_rep.section_spherical_harmonic_r.table_spherical_harmonic_r"></a><p class="title"><b>Table 87. Error rates for spherical_harmonic_r</b></p> 11535<div class="table-contents"><table class="table" summary="Error rates for spherical_harmonic_r"> 11536<colgroup> 11537<col> 11538<col> 11539<col> 11540<col> 11541<col> 11542</colgroup> 11543<thead><tr> 11544<th> 11545 </th> 11546<th> 11547 <p> 11548 GNU C++ version 7.1.0<br> linux<br> double 11549 </p> 11550 </th> 11551<th> 11552 <p> 11553 GNU C++ version 7.1.0<br> linux<br> long double 11554 </p> 11555 </th> 11556<th> 11557 <p> 11558 Sun compiler version 0x5150<br> Sun Solaris<br> long double 11559 </p> 11560 </th> 11561<th> 11562 <p> 11563 Microsoft Visual C++ version 14.1<br> Win32<br> double 11564 </p> 11565 </th> 11566</tr></thead> 11567<tbody><tr> 11568<td> 11569 <p> 11570 Spherical Harmonics 11571 </p> 11572 </td> 11573<td> 11574 <p> 11575 <span class="blue">Max = 1.58ε (Mean = 0.0707ε)</span> 11576 </p> 11577 </td> 11578<td> 11579 <p> 11580 <span class="blue">Max = 2.89e+03ε (Mean = 108ε)</span> 11581 </p> 11582 </td> 11583<td> 11584 <p> 11585 <span class="blue">Max = 1.03e+04ε (Mean = 327ε)</span> 11586 </p> 11587 </td> 11588<td> 11589 <p> 11590 <span class="blue">Max = 2.27e+04ε (Mean = 725ε)</span> 11591 </p> 11592 </td> 11593</tr></tbody> 11594</table></div> 11595</div> 11596<br class="table-break"> 11597</div> 11598<div class="section"> 11599<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 11600<a name="special_function_error_rates_rep.section_sqrt1pm1"></a><a class="link" href="index.html#special_function_error_rates_rep.section_sqrt1pm1" title="sqrt1pm1">sqrt1pm1</a> 11601</h2></div></div></div> 11602<div class="table"> 11603<a name="special_function_error_rates_rep.section_sqrt1pm1.table_sqrt1pm1"></a><p class="title"><b>Table 88. Error rates for sqrt1pm1</b></p> 11604<div class="table-contents"><table class="table" summary="Error rates for sqrt1pm1"> 11605<colgroup> 11606<col> 11607<col> 11608<col> 11609<col> 11610<col> 11611</colgroup> 11612<thead><tr> 11613<th> 11614 </th> 11615<th> 11616 <p> 11617 GNU C++ version 7.1.0<br> linux<br> double 11618 </p> 11619 </th> 11620<th> 11621 <p> 11622 GNU C++ version 7.1.0<br> linux<br> long double 11623 </p> 11624 </th> 11625<th> 11626 <p> 11627 Sun compiler version 0x5150<br> Sun Solaris<br> long double 11628 </p> 11629 </th> 11630<th> 11631 <p> 11632 Microsoft Visual C++ version 14.1<br> Win32<br> double 11633 </p> 11634 </th> 11635</tr></thead> 11636<tbody><tr> 11637<td> 11638 <p> 11639 sqrt1pm1 11640 </p> 11641 </td> 11642<td> 11643 <p> 11644 <span class="blue">Max = 1.3ε (Mean = 0.404ε)</span> 11645 </p> 11646 </td> 11647<td> 11648 <p> 11649 <span class="blue">Max = 1.33ε (Mean = 0.404ε)</span> 11650 </p> 11651 </td> 11652<td> 11653 <p> 11654 <span class="blue">Max = 1.54ε (Mean = 0.563ε)</span> 11655 </p> 11656 </td> 11657<td> 11658 <p> 11659 <span class="blue">Max = 1.35ε (Mean = 0.497ε)</span> 11660 </p> 11661 </td> 11662</tr></tbody> 11663</table></div> 11664</div> 11665<br class="table-break"> 11666</div> 11667<div class="section"> 11668<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 11669<a name="special_function_error_rates_rep.section_tgamma"></a><a class="link" href="index.html#special_function_error_rates_rep.section_tgamma" title="tgamma">tgamma</a> 11670</h2></div></div></div> 11671<div class="table"> 11672<a name="special_function_error_rates_rep.section_tgamma.table_tgamma"></a><p class="title"><b>Table 89. Error rates for tgamma</b></p> 11673<div class="table-contents"><table class="table" summary="Error rates for tgamma"> 11674<colgroup> 11675<col> 11676<col> 11677<col> 11678<col> 11679<col> 11680</colgroup> 11681<thead><tr> 11682<th> 11683 </th> 11684<th> 11685 <p> 11686 GNU C++ version 7.1.0<br> linux<br> double 11687 </p> 11688 </th> 11689<th> 11690 <p> 11691 GNU C++ version 7.1.0<br> linux<br> long double 11692 </p> 11693 </th> 11694<th> 11695 <p> 11696 Sun compiler version 0x5150<br> Sun Solaris<br> long double 11697 </p> 11698 </th> 11699<th> 11700 <p> 11701 Microsoft Visual C++ version 14.1<br> Win32<br> double 11702 </p> 11703 </th> 11704</tr></thead> 11705<tbody> 11706<tr> 11707<td> 11708 <p> 11709 factorials 11710 </p> 11711 </td> 11712<td> 11713 <p> 11714 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 11715 2.1:</em></span> Max = 3.95ε (Mean = 0.783ε))<br> (<span class="emphasis"><em>Rmath 11716 3.2.3:</em></span> Max = 314ε (Mean = 93.4ε)) 11717 </p> 11718 </td> 11719<td> 11720 <p> 11721 <span class="blue">Max = 2.67ε (Mean = 0.617ε)</span><br> <br> 11722 (<span class="emphasis"><em><cmath>:</em></span> Max = 1.66ε (Mean = 0.584ε))<br> 11723 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.66ε (Mean = 0.584ε)) 11724 </p> 11725 </td> 11726<td> 11727 <p> 11728 <span class="blue">Max = 172ε (Mean = 41ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span> 11729 Max = 0ε (Mean = 0ε)) 11730 </p> 11731 </td> 11732<td> 11733 <p> 11734 <span class="blue">Max = 1.85ε (Mean = 0.566ε)</span><br> <br> 11735 (<span class="emphasis"><em><math.h>:</em></span> Max = 3.17ε (Mean = 0.928ε)) 11736 </p> 11737 </td> 11738</tr> 11739<tr> 11740<td> 11741 <p> 11742 near 0 11743 </p> 11744 </td> 11745<td> 11746 <p> 11747 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 11748 2.1:</em></span> Max = 4.51ε (Mean = 1.92ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 11749 Max = 1ε (Mean = 0.335ε)) 11750 </p> 11751 </td> 11752<td> 11753 <p> 11754 <span class="blue">Max = 2ε (Mean = 0.608ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span> 11755 Max = 1ε (Mean = 0.376ε))<br> (<span class="emphasis"><em><math.h>:</em></span> 11756 Max = 1ε (Mean = 0.376ε)) 11757 </p> 11758 </td> 11759<td> 11760 <p> 11761 <span class="blue">Max = 2ε (Mean = 0.647ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span> 11762 Max = 0.5ε (Mean = 0.0791ε)) 11763 </p> 11764 </td> 11765<td> 11766 <p> 11767 <span class="blue">Max = 1.5ε (Mean = 0.635ε)</span><br> <br> 11768 (<span class="emphasis"><em><math.h>:</em></span> Max = 1ε (Mean = 0.405ε)) 11769 </p> 11770 </td> 11771</tr> 11772<tr> 11773<td> 11774 <p> 11775 near 1 11776 </p> 11777 </td> 11778<td> 11779 <p> 11780 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 11781 2.1:</em></span> Max = 4.41ε (Mean = 1.81ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 11782 Max = 1ε (Mean = 0.32ε)) 11783 </p> 11784 </td> 11785<td> 11786 <p> 11787 <span class="blue">Max = 2.51ε (Mean = 1.02ε)</span><br> <br> 11788 (<span class="emphasis"><em><cmath>:</em></span> Max = 0.918ε (Mean = 0.203ε))<br> 11789 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.918ε (Mean = 0.203ε)) 11790 </p> 11791 </td> 11792<td> 11793 <p> 11794 <span class="blue">Max = 3.01ε (Mean = 1.06ε)</span><br> <br> 11795 (<span class="emphasis"><em><math.h>:</em></span> Max = 1ε (Mean = 0.175ε)) 11796 </p> 11797 </td> 11798<td> 11799 <p> 11800 <span class="blue">Max = 1.1ε (Mean = 0.59ε)</span><br> <br> 11801 (<span class="emphasis"><em><math.h>:</em></span> Max = 1ε (Mean = 0.4ε)) 11802 </p> 11803 </td> 11804</tr> 11805<tr> 11806<td> 11807 <p> 11808 near 2 11809 </p> 11810 </td> 11811<td> 11812 <p> 11813 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 11814 2.1:</em></span> Max = 7.95ε (Mean = 3.12ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 11815 Max = 1ε (Mean = 0.191ε)) 11816 </p> 11817 </td> 11818<td> 11819 <p> 11820 <span class="blue">Max = 4.1ε (Mean = 1.55ε)</span><br> <br> 11821 (<span class="emphasis"><em><cmath>:</em></span> Max = 0.558ε (Mean = 0.298ε))<br> 11822 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.558ε (Mean = 0.298ε)) 11823 </p> 11824 </td> 11825<td> 11826 <p> 11827 <span class="blue">Max = 5.01ε (Mean = 1.89ε)</span><br> <br> 11828 (<span class="emphasis"><em><math.h>:</em></span> Max = 0ε (Mean = 0ε)) 11829 </p> 11830 </td> 11831<td> 11832 <p> 11833 <span class="blue">Max = 2ε (Mean = 0.733ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span> 11834 Max = 0ε (Mean = 0ε)) 11835 </p> 11836 </td> 11837</tr> 11838<tr> 11839<td> 11840 <p> 11841 near -10 11842 </p> 11843 </td> 11844<td> 11845 <p> 11846 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 11847 2.1:</em></span> Max = 2.6ε (Mean = 1.05ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 11848 Max = 34.9ε (Mean = 9.2ε)) 11849 </p> 11850 </td> 11851<td> 11852 <p> 11853 <span class="blue">Max = 1.75ε (Mean = 0.895ε)</span><br> <br> 11854 (<span class="emphasis"><em><cmath>:</em></span> Max = 2.26ε (Mean = 1.08ε))<br> 11855 (<span class="emphasis"><em><math.h>:</em></span> Max = 2.26ε (Mean = 1.08ε)) 11856 </p> 11857 </td> 11858<td> 11859 <p> 11860 <span class="blue">Max = 1.75ε (Mean = 0.819ε)</span><br> <br> 11861 (<span class="emphasis"><em><math.h>:</em></span> Max = 0ε (Mean = 0ε)) 11862 </p> 11863 </td> 11864<td> 11865 <p> 11866 <span class="blue">Max = 1.86ε (Mean = 0.881ε)</span><br> <br> 11867 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.866ε (Mean = 0.445ε)) 11868 </p> 11869 </td> 11870</tr> 11871<tr> 11872<td> 11873 <p> 11874 near -55 11875 </p> 11876 </td> 11877<td> 11878 <p> 11879 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 11880 2.1:</em></span> Max = 1.8ε (Mean = 0.782ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 11881 Max = 3.89e+04ε (Mean = 9.52e+03ε)) 11882 </p> 11883 </td> 11884<td> 11885 <p> 11886 <span class="blue">Max = 2.69ε (Mean = 1.09ε)</span><br> <br> 11887 (<span class="emphasis"><em><cmath>:</em></span> Max = 1.79ε (Mean = 0.75ε))<br> 11888 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.79ε (Mean = 0.75ε)) 11889 </p> 11890 </td> 11891<td> 11892 <p> 11893 <span class="blue">Max = 98.5ε (Mean = 53.4ε)</span><br> <br> 11894 (<span class="emphasis"><em><math.h>:</em></span> Max = 0ε (Mean = 0ε)) 11895 </p> 11896 </td> 11897<td> 11898 <p> 11899 <span class="blue">Max = 2.7ε (Mean = 1.35ε)</span><br> <br> 11900 (<span class="emphasis"><em><math.h>:</em></span> Max = 3.87e+04ε (Mean = 6.71e+03ε)) 11901 </p> 11902 </td> 11903</tr> 11904</tbody> 11905</table></div> 11906</div> 11907<br class="table-break"> 11908</div> 11909<div class="section"> 11910<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 11911<a name="special_function_error_rates_rep.section_tgamma1pm1"></a><a class="link" href="index.html#special_function_error_rates_rep.section_tgamma1pm1" title="tgamma1pm1">tgamma1pm1</a> 11912</h2></div></div></div> 11913<div class="table"> 11914<a name="special_function_error_rates_rep.section_tgamma1pm1.table_tgamma1pm1"></a><p class="title"><b>Table 90. Error rates for tgamma1pm1</b></p> 11915<div class="table-contents"><table class="table" summary="Error rates for tgamma1pm1"> 11916<colgroup> 11917<col> 11918<col> 11919<col> 11920<col> 11921<col> 11922</colgroup> 11923<thead><tr> 11924<th> 11925 </th> 11926<th> 11927 <p> 11928 GNU C++ version 7.1.0<br> linux<br> double 11929 </p> 11930 </th> 11931<th> 11932 <p> 11933 GNU C++ version 7.1.0<br> linux<br> long double 11934 </p> 11935 </th> 11936<th> 11937 <p> 11938 Sun compiler version 0x5150<br> Sun Solaris<br> long double 11939 </p> 11940 </th> 11941<th> 11942 <p> 11943 Microsoft Visual C++ version 14.1<br> Win32<br> double 11944 </p> 11945 </th> 11946</tr></thead> 11947<tbody><tr> 11948<td> 11949 <p> 11950 tgamma1pm1(dz) 11951 </p> 11952 </td> 11953<td> 11954 <p> 11955 <span class="blue">Max = 0ε (Mean = 0ε)</span> 11956 </p> 11957 </td> 11958<td> 11959 <p> 11960 <span class="blue">Max = 1.12ε (Mean = 0.49ε)</span> 11961 </p> 11962 </td> 11963<td> 11964 <p> 11965 <span class="blue">Max = 6.61ε (Mean = 0.84ε)</span> 11966 </p> 11967 </td> 11968<td> 11969 <p> 11970 <span class="blue">Max = 3.31ε (Mean = 0.517ε)</span> 11971 </p> 11972 </td> 11973</tr></tbody> 11974</table></div> 11975</div> 11976<br class="table-break"> 11977</div> 11978<div class="section"> 11979<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 11980<a name="special_function_error_rates_rep.section_tgamma_delta_ratio"></a><a class="link" href="index.html#special_function_error_rates_rep.section_tgamma_delta_ratio" title="tgamma_delta_ratio">tgamma_delta_ratio</a> 11981</h2></div></div></div> 11982<div class="table"> 11983<a name="special_function_error_rates_rep.section_tgamma_delta_ratio.table_tgamma_delta_ratio"></a><p class="title"><b>Table 91. Error rates for tgamma_delta_ratio</b></p> 11984<div class="table-contents"><table class="table" summary="Error rates for tgamma_delta_ratio"> 11985<colgroup> 11986<col> 11987<col> 11988<col> 11989<col> 11990<col> 11991</colgroup> 11992<thead><tr> 11993<th> 11994 </th> 11995<th> 11996 <p> 11997 GNU C++ version 7.1.0<br> linux<br> double 11998 </p> 11999 </th> 12000<th> 12001 <p> 12002 GNU C++ version 7.1.0<br> linux<br> long double 12003 </p> 12004 </th> 12005<th> 12006 <p> 12007 Sun compiler version 0x5150<br> Sun Solaris<br> long double 12008 </p> 12009 </th> 12010<th> 12011 <p> 12012 Microsoft Visual C++ version 14.1<br> Win32<br> double 12013 </p> 12014 </th> 12015</tr></thead> 12016<tbody> 12017<tr> 12018<td> 12019 <p> 12020 tgamma + small delta ratios 12021 </p> 12022 </td> 12023<td> 12024 <p> 12025 <span class="blue">Max = 0ε (Mean = 0ε)</span> 12026 </p> 12027 </td> 12028<td> 12029 <p> 12030 <span class="blue">Max = 5.83ε (Mean = 1.3ε)</span> 12031 </p> 12032 </td> 12033<td> 12034 <p> 12035 <span class="blue">Max = 15.4ε (Mean = 2.09ε)</span> 12036 </p> 12037 </td> 12038<td> 12039 <p> 12040 <span class="blue">Max = 7.56ε (Mean = 1.31ε)</span> 12041 </p> 12042 </td> 12043</tr> 12044<tr> 12045<td> 12046 <p> 12047 tgamma + small delta ratios (negative delta) 12048 </p> 12049 </td> 12050<td> 12051 <p> 12052 <span class="blue">Max = 0ε (Mean = 0ε)</span> 12053 </p> 12054 </td> 12055<td> 12056 <p> 12057 <span class="blue">Max = 7.94ε (Mean = 1.4ε)</span> 12058 </p> 12059 </td> 12060<td> 12061 <p> 12062 <span class="blue">Max = 18.3ε (Mean = 2.03ε)</span> 12063 </p> 12064 </td> 12065<td> 12066 <p> 12067 <span class="blue">Max = 7.43ε (Mean = 1.42ε)</span> 12068 </p> 12069 </td> 12070</tr> 12071<tr> 12072<td> 12073 <p> 12074 tgamma + small integer ratios 12075 </p> 12076 </td> 12077<td> 12078 <p> 12079 <span class="blue">Max = 0ε (Mean = 0ε)</span> 12080 </p> 12081 </td> 12082<td> 12083 <p> 12084 <span class="blue">Max = 1.96ε (Mean = 0.677ε)</span> 12085 </p> 12086 </td> 12087<td> 12088 <p> 12089 <span class="blue">Max = 1.96ε (Mean = 0.677ε)</span> 12090 </p> 12091 </td> 12092<td> 12093 <p> 12094 <span class="blue">Max = 2.74ε (Mean = 0.736ε)</span> 12095 </p> 12096 </td> 12097</tr> 12098<tr> 12099<td> 12100 <p> 12101 tgamma + small integer ratios (negative delta) 12102 </p> 12103 </td> 12104<td> 12105 <p> 12106 <span class="blue">Max = 0ε (Mean = 0ε)</span> 12107 </p> 12108 </td> 12109<td> 12110 <p> 12111 <span class="blue">Max = 1.62ε (Mean = 0.451ε)</span> 12112 </p> 12113 </td> 12114<td> 12115 <p> 12116 <span class="blue">Max = 1.62ε (Mean = 0.451ε)</span> 12117 </p> 12118 </td> 12119<td> 12120 <p> 12121 <span class="blue">Max = 2.15ε (Mean = 0.685ε)</span> 12122 </p> 12123 </td> 12124</tr> 12125<tr> 12126<td> 12127 <p> 12128 integer tgamma ratios 12129 </p> 12130 </td> 12131<td> 12132 <p> 12133 <span class="blue">Max = 0ε (Mean = 0ε)</span> 12134 </p> 12135 </td> 12136<td> 12137 <p> 12138 <span class="blue">Max = 0.997ε (Mean = 0.4ε)</span> 12139 </p> 12140 </td> 12141<td> 12142 <p> 12143 <span class="blue">Max = 0.997ε (Mean = 0.4ε)</span> 12144 </p> 12145 </td> 12146<td> 12147 <p> 12148 <span class="blue">Max = 0.968ε (Mean = 0.386ε)</span> 12149 </p> 12150 </td> 12151</tr> 12152<tr> 12153<td> 12154 <p> 12155 integer tgamma ratios (negative delta) 12156 </p> 12157 </td> 12158<td> 12159 <p> 12160 <span class="blue">Max = 0ε (Mean = 0ε)</span> 12161 </p> 12162 </td> 12163<td> 12164 <p> 12165 <span class="blue">Max = 0.853ε (Mean = 0.176ε)</span> 12166 </p> 12167 </td> 12168<td> 12169 <p> 12170 <span class="blue">Max = 0.853ε (Mean = 0.176ε)</span> 12171 </p> 12172 </td> 12173<td> 12174 <p> 12175 <span class="blue">Max = 0.974ε (Mean = 0.175ε)</span> 12176 </p> 12177 </td> 12178</tr> 12179</tbody> 12180</table></div> 12181</div> 12182<br class="table-break"> 12183</div> 12184<div class="section"> 12185<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 12186<a name="special_function_error_rates_rep.section_tgamma_incomplete_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_tgamma_incomplete_" title="tgamma (incomplete)">tgamma 12187 (incomplete)</a> 12188</h2></div></div></div> 12189<div class="table"> 12190<a name="special_function_error_rates_rep.section_tgamma_incomplete_.table_tgamma_incomplete_"></a><p class="title"><b>Table 92. Error rates for tgamma (incomplete)</b></p> 12191<div class="table-contents"><table class="table" summary="Error rates for tgamma (incomplete)"> 12192<colgroup> 12193<col> 12194<col> 12195<col> 12196<col> 12197<col> 12198</colgroup> 12199<thead><tr> 12200<th> 12201 </th> 12202<th> 12203 <p> 12204 GNU C++ version 7.1.0<br> linux<br> double 12205 </p> 12206 </th> 12207<th> 12208 <p> 12209 GNU C++ version 7.1.0<br> linux<br> long double 12210 </p> 12211 </th> 12212<th> 12213 <p> 12214 Sun compiler version 0x5150<br> Sun Solaris<br> long double 12215 </p> 12216 </th> 12217<th> 12218 <p> 12219 Microsoft Visual C++ version 14.1<br> Win32<br> double 12220 </p> 12221 </th> 12222</tr></thead> 12223<tbody> 12224<tr> 12225<td> 12226 <p> 12227 tgamma(a, z) medium values 12228 </p> 12229 </td> 12230<td> 12231 <p> 12232 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 12233 2.1:</em></span> Max = 200ε (Mean = 13.3ε)) 12234 </p> 12235 </td> 12236<td> 12237 <p> 12238 <span class="blue">Max = 8.47ε (Mean = 1.9ε)</span> 12239 </p> 12240 </td> 12241<td> 12242 <p> 12243 <span class="blue">Max = 412ε (Mean = 95.5ε)</span> 12244 </p> 12245 </td> 12246<td> 12247 <p> 12248 <span class="blue">Max = 8.14ε (Mean = 1.76ε)</span> 12249 </p> 12250 </td> 12251</tr> 12252<tr> 12253<td> 12254 <p> 12255 tgamma(a, z) small values 12256 </p> 12257 </td> 12258<td> 12259 <p> 12260 <span class="blue">Max = 0.753ε (Mean = 0.0474ε)</span><br> <br> 12261 (<span class="emphasis"><em>GSL 2.1:</em></span> <span class="red">Max = 1.38e+10ε (Mean 12262 = 1.05e+09ε))</span> 12263 </p> 12264 </td> 12265<td> 12266 <p> 12267 <span class="blue">Max = 2.31ε (Mean = 0.775ε)</span> 12268 </p> 12269 </td> 12270<td> 12271 <p> 12272 <span class="blue">Max = 2.13ε (Mean = 0.717ε)</span> 12273 </p> 12274 </td> 12275<td> 12276 <p> 12277 <span class="blue">Max = 2.53ε (Mean = 0.66ε)</span> 12278 </p> 12279 </td> 12280</tr> 12281<tr> 12282<td> 12283 <p> 12284 tgamma(a, z) integer and half integer values 12285 </p> 12286 </td> 12287<td> 12288 <p> 12289 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 12290 2.1:</em></span> Max = 117ε (Mean = 12.5ε)) 12291 </p> 12292 </td> 12293<td> 12294 <p> 12295 <span class="blue">Max = 5.52ε (Mean = 1.48ε)</span> 12296 </p> 12297 </td> 12298<td> 12299 <p> 12300 <span class="blue">Max = 79.6ε (Mean = 20.9ε)</span> 12301 </p> 12302 </td> 12303<td> 12304 <p> 12305 <span class="blue">Max = 5.16ε (Mean = 1.33ε)</span> 12306 </p> 12307 </td> 12308</tr> 12309</tbody> 12310</table></div> 12311</div> 12312<br class="table-break"> 12313</div> 12314<div class="section"> 12315<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 12316<a name="special_function_error_rates_rep.section_tgamma_lower"></a><a class="link" href="index.html#special_function_error_rates_rep.section_tgamma_lower" title="tgamma_lower">tgamma_lower</a> 12317</h2></div></div></div> 12318<div class="table"> 12319<a name="special_function_error_rates_rep.section_tgamma_lower.table_tgamma_lower"></a><p class="title"><b>Table 93. Error rates for tgamma_lower</b></p> 12320<div class="table-contents"><table class="table" summary="Error rates for tgamma_lower"> 12321<colgroup> 12322<col> 12323<col> 12324<col> 12325<col> 12326<col> 12327</colgroup> 12328<thead><tr> 12329<th> 12330 </th> 12331<th> 12332 <p> 12333 GNU C++ version 7.1.0<br> linux<br> double 12334 </p> 12335 </th> 12336<th> 12337 <p> 12338 GNU C++ version 7.1.0<br> linux<br> long double 12339 </p> 12340 </th> 12341<th> 12342 <p> 12343 Sun compiler version 0x5150<br> Sun Solaris<br> long double 12344 </p> 12345 </th> 12346<th> 12347 <p> 12348 Microsoft Visual C++ version 14.1<br> Win32<br> double 12349 </p> 12350 </th> 12351</tr></thead> 12352<tbody> 12353<tr> 12354<td> 12355 <p> 12356 tgamma(a, z) medium values 12357 </p> 12358 </td> 12359<td> 12360 <p> 12361 <span class="blue">Max = 0.833ε (Mean = 0.0315ε)</span><br> <br> 12362 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.833ε (Mean = 0.0315ε)) 12363 </p> 12364 </td> 12365<td> 12366 <p> 12367 <span class="blue">Max = 6.79ε (Mean = 1.46ε)</span> 12368 </p> 12369 </td> 12370<td> 12371 <p> 12372 <span class="blue">Max = 363ε (Mean = 63.8ε)</span> 12373 </p> 12374 </td> 12375<td> 12376 <p> 12377 <span class="blue">Max = 5.62ε (Mean = 1.49ε)</span> 12378 </p> 12379 </td> 12380</tr> 12381<tr> 12382<td> 12383 <p> 12384 tgamma(a, z) small values 12385 </p> 12386 </td> 12387<td> 12388 <p> 12389 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 12390 2.1:</em></span> Max = 0ε (Mean = 0ε)) 12391 </p> 12392 </td> 12393<td> 12394 <p> 12395 <span class="blue">Max = 1.97ε (Mean = 0.555ε)</span> 12396 </p> 12397 </td> 12398<td> 12399 <p> 12400 <span class="blue">Max = 1.97ε (Mean = 0.558ε)</span> 12401 </p> 12402 </td> 12403<td> 12404 <p> 12405 <span class="blue">Max = 1.57ε (Mean = 0.525ε)</span> 12406 </p> 12407 </td> 12408</tr> 12409<tr> 12410<td> 12411 <p> 12412 tgamma(a, z) integer and half integer values 12413 </p> 12414 </td> 12415<td> 12416 <p> 12417 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 12418 2.1:</em></span> Max = 0ε (Mean = 0ε)) 12419 </p> 12420 </td> 12421<td> 12422 <p> 12423 <span class="blue">Max = 4.83ε (Mean = 1.15ε)</span> 12424 </p> 12425 </td> 12426<td> 12427 <p> 12428 <span class="blue">Max = 84.7ε (Mean = 17.5ε)</span> 12429 </p> 12430 </td> 12431<td> 12432 <p> 12433 <span class="blue">Max = 2.69ε (Mean = 0.849ε)</span> 12434 </p> 12435 </td> 12436</tr> 12437</tbody> 12438</table></div> 12439</div> 12440<br class="table-break"> 12441</div> 12442<div class="section"> 12443<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 12444<a name="special_function_error_rates_rep.section_tgamma_ratio"></a><a class="link" href="index.html#special_function_error_rates_rep.section_tgamma_ratio" title="tgamma_ratio">tgamma_ratio</a> 12445</h2></div></div></div> 12446<div class="table"> 12447<a name="special_function_error_rates_rep.section_tgamma_ratio.table_tgamma_ratio"></a><p class="title"><b>Table 94. Error rates for tgamma_ratio</b></p> 12448<div class="table-contents"><table class="table" summary="Error rates for tgamma_ratio"> 12449<colgroup> 12450<col> 12451<col> 12452<col> 12453<col> 12454<col> 12455</colgroup> 12456<thead><tr> 12457<th> 12458 </th> 12459<th> 12460 <p> 12461 GNU C++ version 7.1.0<br> linux<br> double 12462 </p> 12463 </th> 12464<th> 12465 <p> 12466 GNU C++ version 7.1.0<br> linux<br> long double 12467 </p> 12468 </th> 12469<th> 12470 <p> 12471 Sun compiler version 0x5150<br> Sun Solaris<br> long double 12472 </p> 12473 </th> 12474<th> 12475 <p> 12476 Microsoft Visual C++ version 14.1<br> Win32<br> double 12477 </p> 12478 </th> 12479</tr></thead> 12480<tbody><tr> 12481<td> 12482 <p> 12483 tgamma ratios 12484 </p> 12485 </td> 12486<td> 12487 <p> 12488 <span class="blue">Max = 0.694ε (Mean = 0.0347ε)</span> 12489 </p> 12490 </td> 12491<td> 12492 <p> 12493 <span class="blue">Max = 2.99ε (Mean = 1.15ε)</span> 12494 </p> 12495 </td> 12496<td> 12497 <p> 12498 <span class="blue">Max = 174ε (Mean = 61.2ε)</span> 12499 </p> 12500 </td> 12501<td> 12502 <p> 12503 <span class="blue">Max = 3.28ε (Mean = 1.12ε)</span> 12504 </p> 12505 </td> 12506</tr></tbody> 12507</table></div> 12508</div> 12509<br class="table-break"> 12510</div> 12511<div class="section"> 12512<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 12513<a name="special_function_error_rates_rep.section_trigamma"></a><a class="link" href="index.html#special_function_error_rates_rep.section_trigamma" title="trigamma">trigamma</a> 12514</h2></div></div></div> 12515<div class="table"> 12516<a name="special_function_error_rates_rep.section_trigamma.table_trigamma"></a><p class="title"><b>Table 95. Error rates for trigamma</b></p> 12517<div class="table-contents"><table class="table" summary="Error rates for trigamma"> 12518<colgroup> 12519<col> 12520<col> 12521<col> 12522<col> 12523<col> 12524</colgroup> 12525<thead><tr> 12526<th> 12527 </th> 12528<th> 12529 <p> 12530 GNU C++ version 7.1.0<br> linux<br> double 12531 </p> 12532 </th> 12533<th> 12534 <p> 12535 GNU C++ version 7.1.0<br> linux<br> long double 12536 </p> 12537 </th> 12538<th> 12539 <p> 12540 Sun compiler version 0x5150<br> Sun Solaris<br> long double 12541 </p> 12542 </th> 12543<th> 12544 <p> 12545 Microsoft Visual C++ version 14.1<br> Win32<br> double 12546 </p> 12547 </th> 12548</tr></thead> 12549<tbody><tr> 12550<td> 12551 <p> 12552 Mathematica Data 12553 </p> 12554 </td> 12555<td> 12556 <p> 12557 <span class="blue">Max = 0.998ε (Mean = 0.105ε)</span><br> <br> 12558 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.34e+04ε (Mean = 1.49e+03ε))<br> 12559 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.34e+04ε (Mean = 1.51e+03ε)) 12560 </p> 12561 </td> 12562<td> 12563 <p> 12564 <span class="blue">Max = 1.28ε (Mean = 0.449ε)</span> 12565 </p> 12566 </td> 12567<td> 12568 <p> 12569 <span class="blue">Max = 1.28ε (Mean = 0.449ε)</span> 12570 </p> 12571 </td> 12572<td> 12573 <p> 12574 <span class="blue">Max = 1ε (Mean = 0.382ε)</span> 12575 </p> 12576 </td> 12577</tr></tbody> 12578</table></div> 12579</div> 12580<br class="table-break"> 12581</div> 12582<div class="section"> 12583<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 12584<a name="special_function_error_rates_rep.section_zeta"></a><a class="link" href="index.html#special_function_error_rates_rep.section_zeta" title="zeta">zeta</a> 12585</h2></div></div></div> 12586<div class="table"> 12587<a name="special_function_error_rates_rep.section_zeta.table_zeta"></a><p class="title"><b>Table 96. Error rates for zeta</b></p> 12588<div class="table-contents"><table class="table" summary="Error rates for zeta"> 12589<colgroup> 12590<col> 12591<col> 12592<col> 12593<col> 12594<col> 12595</colgroup> 12596<thead><tr> 12597<th> 12598 </th> 12599<th> 12600 <p> 12601 GNU C++ version 7.1.0<br> linux<br> long double 12602 </p> 12603 </th> 12604<th> 12605 <p> 12606 GNU C++ version 7.1.0<br> linux<br> double 12607 </p> 12608 </th> 12609<th> 12610 <p> 12611 Sun compiler version 0x5150<br> Sun Solaris<br> long double 12612 </p> 12613 </th> 12614<th> 12615 <p> 12616 Microsoft Visual C++ version 14.1<br> Win32<br> double 12617 </p> 12618 </th> 12619</tr></thead> 12620<tbody> 12621<tr> 12622<td> 12623 <p> 12624 Zeta: Random values greater than 1 12625 </p> 12626 </td> 12627<td> 12628 <p> 12629 <span class="blue">Max = 0.846ε (Mean = 0.0833ε)</span><br> <br> 12630 (<span class="emphasis"><em><cmath>:</em></span> Max = 5.45ε (Mean = 1ε)) 12631 </p> 12632 </td> 12633<td> 12634 <p> 12635 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 12636 2.1:</em></span> Max = 8.69ε (Mean = 1.03ε)) 12637 </p> 12638 </td> 12639<td> 12640 <p> 12641 <span class="blue">Max = 0.846ε (Mean = 0.0833ε)</span> 12642 </p> 12643 </td> 12644<td> 12645 <p> 12646 <span class="blue">Max = 0.836ε (Mean = 0.093ε)</span> 12647 </p> 12648 </td> 12649</tr> 12650<tr> 12651<td> 12652 <p> 12653 Zeta: Random values less than 1 12654 </p> 12655 </td> 12656<td> 12657 <p> 12658 <span class="blue">Max = 7.03ε (Mean = 2.93ε)</span><br> <br> 12659 (<span class="emphasis"><em><cmath>:</em></span> Max = 538ε (Mean = 59.3ε)) 12660 </p> 12661 </td> 12662<td> 12663 <p> 12664 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 12665 2.1:</em></span> Max = 137ε (Mean = 13.8ε)) 12666 </p> 12667 </td> 12668<td> 12669 <p> 12670 <span class="blue">Max = 70.1ε (Mean = 17.1ε)</span> 12671 </p> 12672 </td> 12673<td> 12674 <p> 12675 <span class="blue">Max = 6.84ε (Mean = 3.12ε)</span> 12676 </p> 12677 </td> 12678</tr> 12679<tr> 12680<td> 12681 <p> 12682 Zeta: Values close to and greater than 1 12683 </p> 12684 </td> 12685<td> 12686 <p> 12687 <span class="blue">Max = 0.995ε (Mean = 0.5ε)</span><br> <br> 12688 (<span class="emphasis"><em><cmath>:</em></span> Max = 1.9e+06ε (Mean = 5.11e+05ε)) 12689 </p> 12690 </td> 12691<td> 12692 <p> 12693 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 12694 2.1:</em></span> Max = 7.73ε (Mean = 4.07ε)) 12695 </p> 12696 </td> 12697<td> 12698 <p> 12699 <span class="blue">Max = 0.995ε (Mean = 0.5ε)</span> 12700 </p> 12701 </td> 12702<td> 12703 <p> 12704 <span class="blue">Max = 0.994ε (Mean = 0.421ε)</span> 12705 </p> 12706 </td> 12707</tr> 12708<tr> 12709<td> 12710 <p> 12711 Zeta: Values close to and less than 1 12712 </p> 12713 </td> 12714<td> 12715 <p> 12716 <span class="blue">Max = 0.998ε (Mean = 0.508ε)</span><br> <br> 12717 (<span class="emphasis"><em><cmath>:</em></span> Max = 8.53e+06ε (Mean = 1.87e+06ε)) 12718 </p> 12719 </td> 12720<td> 12721 <p> 12722 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 12723 2.1:</em></span> Max = 0.991ε (Mean = 0.28ε)) 12724 </p> 12725 </td> 12726<td> 12727 <p> 12728 <span class="blue">Max = 0.998ε (Mean = 0.508ε)</span> 12729 </p> 12730 </td> 12731<td> 12732 <p> 12733 <span class="blue">Max = 0.991ε (Mean = 0.375ε)</span> 12734 </p> 12735 </td> 12736</tr> 12737<tr> 12738<td> 12739 <p> 12740 Zeta: Integer arguments 12741 </p> 12742 </td> 12743<td> 12744 <p> 12745 <span class="blue">Max = 9ε (Mean = 3.06ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span> 12746 Max = 70.3ε (Mean = 17.4ε)) 12747 </p> 12748 </td> 12749<td> 12750 <p> 12751 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 12752 2.1:</em></span> Max = 3.75ε (Mean = 1.1ε)) 12753 </p> 12754 </td> 12755<td> 12756 <p> 12757 <span class="blue">Max = 28ε (Mean = 5.62ε)</span> 12758 </p> 12759 </td> 12760<td> 12761 <p> 12762 <span class="blue">Max = 9ε (Mean = 3ε)</span> 12763 </p> 12764 </td> 12765</tr> 12766</tbody> 12767</table></div> 12768</div> 12769<br class="table-break"> 12770</div> 12771<div class="section"> 12772<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 12773<a name="special_function_error_rates_rep.error_logs"></a><a class="link" href="index.html#special_function_error_rates_rep.error_logs" title="Error Logs">Error Logs</a> 12774</h2></div></div></div> 12775<h5> 12776<a name="special_function_error_rates_rep.error_logs.h0"></a> 12777 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_in"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_in">Error 12778 Output For cyl_bessel_j (integer orders) with compiler Microsoft Visual C++ 12779 version 14.1 and library <math.h> and test data Bessel JN: Mathworld 12780 Data (Integer Version)</a> 12781 </h5> 12782<p> 12783 <a name="errors_Microsoft_Visual_C_version_14_1_Win32_double_cyl_bessel_j_integer_orders___math_h__Bessel_JN_Mathworld_Data_Integer_Version_"></a>CAUTION: 12784 Found non-finite result, when a finite value was expected at entry 16<br> 12785 Found: -nan(ind) Expected 0 Error: 1.79769e+308<br> 10, 1e-100, 0<br> CAUTION: 12786 Gross error found at entry 16.<br> Found: -nan(ind) Expected 0 Error: 1.79769e+308<br> 12787 10, 1e-100, 0<br> 12788 </p> 12789<h5> 12790<a name="special_function_error_rates_rep.error_logs.h1"></a> 12791 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_legendre_p_asso"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_legendre_p_asso">Error 12792 Output For legendre_p (associated) with compiler GNU C++ version 7.1.0 and 12793 library GSL 2.1 and test data Associated Legendre Polynomials: Small Values</a> 12794 </h5> 12795<p> 12796 <a name="errors_GNU_C_version_7_1_0_linux_double_legendre_p_associated__GSL_2_1_Associated_Legendre_Polynomials_Small_Values"></a>domain 12797 error<br> 3.75573, -3, 0.264719, 0.0186823<br> domain error<br> 3.75573, 12798 -3, 0.670017, 0.0085227<br> domain error<br> 3.75573, -3, 0.915014, 0.00136786<br> 12799 domain error<br> 3.75573, -3, 0.93539, 0.000921218<br> domain error<br> 12800 3.75573, -2, -0.804919, -0.035427<br> domain error<br> 3.75573, -2, -0.623236, 12801 -0.0476446<br> domain error<br> 3.75573, -2, 0.629447, 0.0475072<br> 12802 domain error<br> 3.75573, -2, 0.929777, 0.0157498<br> domain error<br> 12803 3.75573, -2, 0.985763, 0.0034837<br> domain error<br> 3.75573, -1, 0.093763, 12804 -0.118979<br> domain error<br> 4.28576, -4, 0.0944412, 0.00255792<br> 12805 domain error<br> 4.28576, -4, 0.670017, 0.000790849<br> domain error<br> 12806 4.28576, -3, -0.746026, -0.00458957<br> domain error<br> 4.28576, -2, -0.623236, 12807 0.0219016<br> domain error<br> 4.28576, -2, 0.629447, 0.0223081<br> domain 12808 error<br> 4.28576, -2, 0.93539, 0.0133504<br> domain error<br> 4.28576, 12809 -1, 0.915014, 0.132001<br> domain error<br> 4.28576, -1, 0.985763, 0.0787743<br> 12810 domain error<br> 4.43859, -4, 0.093763, 0.00255858<br> domain error<br> 12811 4.43859, -4, 0.811584, 0.000303404<br> domain error<br> 4.43859, -4, 0.826752, 12812 0.000260835<br> domain error<br> 4.43859, -4, 0.929777, 4.78235e-05<br> 12813 domain error<br> 4.43859, -3, -0.804919, -0.00350364<br> domain error<br> 12814 4.43859, -3, -0.729046, -0.00487043<br> domain error<br> 4.43859, -3, -0.623236, 12815 -0.00620995<br> domain error<br> 4.43859, -3, 0.93539, 0.000861698<br> 12816 domain error<br> 4.43859, -2, -0.557932, 0.0169167<br> domain error<br> 12817 4.43859, -2, -0.443004, 0.0062586<br> domain error<br> 4.43859, -2, 0.915014, 12818 0.016481<br> domain error<br> 4.43859, -1, 0.629447, -0.0138523<br> domain 12819 error<br> 5.39088, -5, 0.0944412, 0.000254649<br> domain error<br> 5.39088, 12820 -5, 0.264719, 0.000217164<br> domain error<br> 5.39088, -5, 0.670017, 5.87083e-05<br> 12821 domain error<br> 5.39088, -5, 0.915014, 2.78273e-06<br> domain error<br> 12822 5.39088, -3, 0.929777, 0.000880849<br> domain error<br> 5.39088, -2, 0.629447, 12823 0.00448021<br> domain error<br> 5.39088, -2, 0.826752, 0.01718<br> domain 12824 error<br> 5.39088, -2, 0.937736, 0.011583<br> domain error<br> 5.39088, 12825 -1, -0.804919, 0.0276144<br> domain error<br> 5.39088, -1, -0.746026, -0.0119425<br> 12826 domain error<br> 5.39088, -1, -0.443004, -0.0525987<br> domain error<br> 12827 5.39088, -1, 0.811584, 0.032475<br> domain error<br> 5.39088, -1, 0.985763, 12828 0.0759289<br> domain error<br> 5.97861, -5, -0.729046, 3.91223e-05<br> 12829 domain error<br> 5.97861, -5, -0.383666, 0.000174899<br> domain error<br> 12830 5.97861, -5, 0.93539, 1.43993e-06<br> domain error<br> 5.97861, -4, -0.623236, 12831 -0.000607048<br> domain error<br> 5.97861, -4, 0.264719, 0.00059614<br> 12832 domain error<br> 5.97861, -3, 0.629447, 0.00313497<br> domain error<br> 12833 5.97861, -3, 0.670017, 0.00323895<br> domain error<br> 5.97861, -2, 0.915014, 12834 0.0140705<br> domain error<br> 5.97861, -2, 0.992923, 0.00171356<br> 12835 domain error<br> 5.97861, -1, -0.746026, -0.0119425<br> domain error<br> 12836 5.97861, -1, 0.937736, 0.106972<br> domain error<br> 7.01297, -6, -0.443004, 12837 -4.99177e-06<br> domain error<br> 7.01297, -6, 0.629447, 3.00689e-06<br> 12838 domain error<br> 7.01297, -6, 0.811584, 7.00407e-07<br> domain error<br> 12839 7.01297, -6, 0.985763, 4.83431e-10<br> domain error<br> 7.01297, -3, 0.670017, 12840 0.000233323<br> domain error<br> 7.01297, -2, -0.804919, -0.0027739<br> 12841 domain error<br> 7.01297, -1, -0.383666, 0.0397866<br> domain error<br> 12842 7.01297, -1, 0.929777, 0.0544549<br> domain error<br> 7.54701, -7, 0.929777, 12843 1.42008e-09<br> domain error<br> 7.54701, -6, 0.992923, 6.04622e-11<br> 12844 domain error<br> 7.54701, -5, -0.804919, 1.18502e-05<br> domain error<br> 12845 7.54701, -5, -0.623236, 2.57049e-05<br> domain error<br> 7.54701, -5, -0.557932, 12846 2.60266e-05<br> domain error<br> 7.54701, -5, 0.826752, 9.64276e-06<br> 12847 domain error<br> 7.54701, -4, -0.746026, -0.0001618<br> domain error<br> 12848 7.54701, -3, 0.0944412, 0.000622493<br> domain error<br> 7.54701, -3, 0.985763, 12849 9.14782e-05<br> domain error<br> 7.54701, -1, 0.811584, -0.0376184<br> 12850 domain error<br> 11.8439, -10, -0.557932, -2.32652e-11<br> domain error<br> 12851 11.8439, -10, 0.811584, 1.01194e-12<br> domain error<br> 11.8439, -8, -0.746026, 12852 -1.34891e-09<br> domain error<br> 11.8439, -8, -0.729046, -1.5428e-09<br> 12853 domain error<br> 11.8439, -8, 0.985763, 5.90035e-14<br> domain error<br> 12854 11.8439, -4, 0.629447, -1.44723e-05<br> domain error<br> 11.8439, -4, 0.929777, 12855 1.98812e-05<br> domain error<br> 11.8439, -3, 0.670017, -4.58296e-05<br> 12856 domain error<br> 11.8439, -2, 0.826752, -0.00244759<br> domain error<br> 12857 11.8439, -2, 0.992923, 0.00151458<br> domain error<br> 11.8439, -1, -0.383666, 12858 0.00419108<br> domain error<br> 11.85, -11, 0.093763, 1.16526e-11<br> 12859 domain error<br> 11.85, -11, 0.929777, 2.05797e-16<br> domain error<br> 12860 11.85, -11, 0.93539, 1.32249e-16<br> domain error<br> *** FURTHER CONTENT 12861 HAS BEEN TRUNCATED FOR BREVITY ***<br> 12862 </p> 12863<h5> 12864<a name="special_function_error_rates_rep.error_logs.h2"></a> 12865 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_legendre_p_ass0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_legendre_p_ass0">Error 12866 Output For legendre_p (associated) with compiler GNU C++ version 7.1.0 and 12867 library <cmath> and test data Associated Legendre Polynomials: Small 12868 Values</a> 12869 </h5> 12870<p> 12871 <a name="errors_GNU_C_version_7_1_0_linux_long_double_legendre_p_associated___cmath__Associated_Legendre_Polynomials_Small_Values"></a>order 12872 parameters less than 0 not supported in TR1<br> 3.75573, -3, 0.264719, 0.0186823<br> 12873 order parameters less than 0 not supported in TR1<br> 3.75573, -3, 0.670017, 12874 0.0085227<br> order parameters less than 0 not supported in TR1<br> 3.75573, 12875 -3, 0.915014, 0.00136786<br> order parameters less than 0 not supported in 12876 TR1<br> 3.75573, -3, 0.93539, 0.000921218<br> order parameters less than 12877 0 not supported in TR1<br> 3.75573, -2, -0.804919, -0.035427<br> order 12878 parameters less than 0 not supported in TR1<br> 3.75573, -2, -0.623236, -0.0476446<br> 12879 order parameters less than 0 not supported in TR1<br> 3.75573, -2, 0.629447, 12880 0.0475072<br> order parameters less than 0 not supported in TR1<br> 3.75573, 12881 -2, 0.929777, 0.0157498<br> order parameters less than 0 not supported in 12882 TR1<br> 3.75573, -2, 0.985763, 0.0034837<br> order parameters less than 12883 0 not supported in TR1<br> 3.75573, -1, 0.093763, -0.118979<br> order parameters 12884 less than 0 not supported in TR1<br> 4.28576, -4, 0.0944412, 0.00255792<br> 12885 order parameters less than 0 not supported in TR1<br> 4.28576, -4, 0.670017, 12886 0.000790849<br> order parameters less than 0 not supported in TR1<br> 4.28576, 12887 -3, -0.746026, -0.00458957<br> order parameters less than 0 not supported 12888 in TR1<br> 4.28576, -2, -0.623236, 0.0219016<br> order parameters less 12889 than 0 not supported in TR1<br> 4.28576, -2, 0.629447, 0.0223081<br> order 12890 parameters less than 0 not supported in TR1<br> 4.28576, -2, 0.93539, 0.0133504<br> 12891 order parameters less than 0 not supported in TR1<br> 4.28576, -1, 0.915014, 12892 0.132001<br> order parameters less than 0 not supported in TR1<br> 4.28576, 12893 -1, 0.985763, 0.0787743<br> order parameters less than 0 not supported in 12894 TR1<br> 4.43859, -4, 0.093763, 0.00255858<br> order parameters less than 12895 0 not supported in TR1<br> 4.43859, -4, 0.811584, 0.000303404<br> order 12896 parameters less than 0 not supported in TR1<br> 4.43859, -4, 0.826752, 0.000260835<br> 12897 order parameters less than 0 not supported in TR1<br> 4.43859, -4, 0.929777, 12898 4.78235e-05<br> order parameters less than 0 not supported in TR1<br> 4.43859, 12899 -3, -0.804919, -0.00350364<br> order parameters less than 0 not supported 12900 in TR1<br> 4.43859, -3, -0.729046, -0.00487043<br> order parameters less 12901 than 0 not supported in TR1<br> 4.43859, -3, -0.623236, -0.00620995<br> 12902 order parameters less than 0 not supported in TR1<br> 4.43859, -3, 0.93539, 12903 0.000861698<br> order parameters less than 0 not supported in TR1<br> 4.43859, 12904 -2, -0.557932, 0.0169167<br> order parameters less than 0 not supported in 12905 TR1<br> 4.43859, -2, -0.443004, 0.0062586<br> order parameters less than 12906 0 not supported in TR1<br> 4.43859, -2, 0.915014, 0.016481<br> order parameters 12907 less than 0 not supported in TR1<br> 4.43859, -1, 0.629447, -0.0138523<br> 12908 order parameters less than 0 not supported in TR1<br> 5.39088, -5, 0.0944412, 12909 0.000254649<br> order parameters less than 0 not supported in TR1<br> 5.39088, 12910 -5, 0.264719, 0.000217164<br> order parameters less than 0 not supported 12911 in TR1<br> 5.39088, -5, 0.670017, 5.87083e-05<br> order parameters less 12912 than 0 not supported in TR1<br> 5.39088, -5, 0.915014, 2.78273e-06<br> 12913 order parameters less than 0 not supported in TR1<br> 5.39088, -3, 0.929777, 12914 0.000880849<br> order parameters less than 0 not supported in TR1<br> 5.39088, 12915 -2, 0.629447, 0.00448021<br> order parameters less than 0 not supported in 12916 TR1<br> 5.39088, -2, 0.826752, 0.01718<br> order parameters less than 0 12917 not supported in TR1<br> 5.39088, -2, 0.937736, 0.011583<br> order parameters 12918 less than 0 not supported in TR1<br> 5.39088, -1, -0.804919, 0.0276144<br> 12919 order parameters less than 0 not supported in TR1<br> 5.39088, -1, -0.746026, 12920 -0.0119425<br> order parameters less than 0 not supported in TR1<br> 5.39088, 12921 -1, -0.443004, -0.0525987<br> order parameters less than 0 not supported 12922 in TR1<br> 5.39088, -1, 0.811584, 0.032475<br> order parameters less than 12923 0 not supported in TR1<br> 5.39088, -1, 0.985763, 0.0759289<br> order parameters 12924 less than 0 not supported in TR1<br> 5.97861, -5, -0.729046, 3.91223e-05<br> 12925 order parameters less than 0 not supported in TR1<br> 5.97861, -5, -0.383666, 12926 0.000174899<br> order parameters less than 0 not supported in TR1<br> 5.97861, 12927 -5, 0.93539, 1.43993e-06<br> order parameters less than 0 not supported in 12928 TR1<br> 5.97861, -4, -0.623236, -0.000607048<br> order parameters less 12929 than 0 not supported in TR1<br> 5.97861, -4, 0.264719, 0.00059614<br> order 12930 parameters less than 0 not supported in TR1<br> 5.97861, -3, 0.629447, 0.00313497<br> 12931 *** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br> 12932 </p> 12933<h5> 12934<a name="special_function_error_rates_rep.error_logs.h3"></a> 12935 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_wi"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_wi">Error 12936 Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library Rmath 12937 3.2.3 and test data Bessel Iv: Mathworld Data (large values)</a> 12938 </h5> 12939<p> 12940 <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_Iv_Mathworld_Data_large_values_"></a>CAUTION: 12941 Gross error found at entry 0.<br> Found: 0 Expected 1.86459e-155 Error: 8.37988e+152<br> 12942 -1, 3.72917e-155, 1.86459e-155<br> CAUTION: Gross error found at entry 1.<br> 12943 Found: 0 Expected 1.86459e-155 Error: 8.37988e+152<br> 1, 3.72917e-155, 1.86459e-155<br> 12944 CAUTION: Gross error found at entry 3.<br> Found: 0 Expected 8.02269e-175 12945 Error: 3.60559e+133<br> 1.125, 3.72917e-155, 8.02269e-175<br> 12946 </p> 12947<h5> 12948<a name="special_function_error_rates_rep.error_logs.h4"></a> 12949 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_in"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_in">Error 12950 Output For cyl_bessel_i (integer orders) with compiler GNU C++ version 7.1.0 12951 and library Rmath 3.2.3 and test data Bessel In: Mathworld Data (Integer Version)</a> 12952 </h5> 12953<p> 12954 <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_In_Mathworld_Data_Integer_Version_"></a>Unsupported 12955 domain<br> -5, -1, -0.000271463<br> Unsupported domain<br> 10, -5, 0.00458004<br> 12956 Unsupported domain<br> -100, -200, 4.35275e+74<br> 12957 </p> 12958<h5> 12959<a name="special_function_error_rates_rep.error_logs.h5"></a> 12960 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i0">Error 12961 Output For cyl_bessel_i (integer orders) with compiler GNU C++ version 7.1.0 12962 and library Rmath 3.2.3 and test data Bessel I1: Mathworld Data (Integer Version)</a> 12963 </h5> 12964<p> 12965 <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_I1_Mathworld_Data_Integer_Version_"></a>Unsupported 12966 domain<br> 1, -2, -1.59064<br> Unsupported domain<br> 1, -8, -399.873<br> 12967 Unsupported domain<br> 1, -10, -2670.99<br> 12968 </p> 12969<h5> 12970<a name="special_function_error_rates_rep.error_logs.h6"></a> 12971 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i1">Error 12972 Output For cyl_bessel_i (integer orders) with compiler GNU C++ version 7.1.0 12973 and library Rmath 3.2.3 and test data Bessel I0: Mathworld Data (Integer Version)</a> 12974 </h5> 12975<p> 12976 <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_I0_Mathworld_Data_Integer_Version_"></a>Unsupported 12977 domain<br> 0, -2, 2.27959<br> Unsupported domain<br> 0, -7, 168.594<br> 12978 Unsupported domain<br> 0, -1, 1.26607<br> 12979 </p> 12980<h5> 12981<a name="special_function_error_rates_rep.error_logs.h7"></a> 12982 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w0">Error 12983 Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library Rmath 12984 3.2.3 and test data Bessel In: Mathworld Data</a> 12985 </h5> 12986<p> 12987 <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_In_Mathworld_Data"></a>Unsupported 12988 domain<br> -5, -1, -0.000271463<br> Unsupported domain<br> 10, -5, 0.00458004<br> 12989 Unsupported domain<br> -100, -200, 4.35275e+74<br> 12990 </p> 12991<h5> 12992<a name="special_function_error_rates_rep.error_logs.h8"></a> 12993 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w1">Error 12994 Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library Rmath 12995 3.2.3 and test data Bessel I1: Mathworld Data</a> 12996 </h5> 12997<p> 12998 <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_I1_Mathworld_Data"></a>Unsupported 12999 domain<br> 1, -2, -1.59064<br> Unsupported domain<br> 1, -8, -399.873<br> 13000 Unsupported domain<br> 1, -10, -2670.99<br> 13001 </p> 13002<h5> 13003<a name="special_function_error_rates_rep.error_logs.h9"></a> 13004 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w2">Error 13005 Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library Rmath 13006 3.2.3 and test data Bessel I0: Mathworld Data</a> 13007 </h5> 13008<p> 13009 <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_I0_Mathworld_Data"></a>Unsupported 13010 domain<br> 0, -2, 2.27959<br> Unsupported domain<br> 0, -7, 168.594<br> 13011 Unsupported domain<br> 0, -1, 1.26607<br> 13012 </p> 13013<h5> 13014<a name="special_function_error_rates_rep.error_logs.h10"></a> 13015 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_wi"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_wi">Error 13016 Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library Rmath 13017 3.2.3 and test data Bessel J: Mathworld Data</a> 13018 </h5> 13019<p> 13020 <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J_Mathworld_Data"></a>CAUTION: 13021 Gross error found at entry 6.<br> Found: 0 Expected -0.000747424 Error: 3.3591e+304<br> 13022 5.5, 1e+06, -0.000747424<br> CAUTION: Gross error found at entry 7.<br> 13023 Found: 0 Expected -0.0007766 Error: 3.49022e+304<br> 5.125, 1e+06, -0.0007766<br> 13024 CAUTION: Gross error found at entry 8.<br> Found: 0 Expected -0.000466323 13025 Error: 2.09576e+304<br> 5.875, 1e+06, -0.000466323<br> 13026 </p> 13027<h5> 13028<a name="special_function_error_rates_rep.error_logs.h11"></a> 13029 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i0">Error 13030 Output For cyl_bessel_j (integer orders) with compiler GNU C++ version 7.1.0 13031 and library Rmath 3.2.3 and test data Bessel JN: Mathworld Data (Integer Version)</a> 13032 </h5> 13033<p> 13034 <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_JN_Mathworld_Data_Integer_Version_"></a>Unsupported 13035 domain<br> 5, -10, 0.234062<br> CAUTION: Gross error found at entry 6.<br> 13036 Found: 0 Expected 0.000725964 Error: 3.26265e+304<br> -5, 1e+06, 0.000725964<br> 13037 CAUTION: Gross error found at entry 7.<br> Found: 0 Expected -0.000725964 13038 Error: 3.26265e+304<br> 5, 1e+06, -0.000725964<br> Unsupported domain<br> 13039 -5, -1, 0.000249758<br> Unsupported domain<br> 10, -10, 0.207486<br> 13040 Unsupported domain<br> 10, -5, 0.0014678<br> CAUTION: Gross error found 13041 at entry 12.<br> Found: 0 Expected -0.000331079 Error: 1.48795e+304<br> 13042 -10, 1e+06, -0.000331079<br> CAUTION: Gross error found at entry 13.<br> 13043 Found: 0 Expected -0.000331079 Error: 1.48795e+304<br> 10, 1e+06, -0.000331079<br> 13044 </p> 13045<h5> 13046<a name="special_function_error_rates_rep.error_logs.h12"></a> 13047 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i1">Error 13048 Output For cyl_bessel_j (integer orders) with compiler GNU C++ version 7.1.0 13049 and library Rmath 3.2.3 and test data Bessel J1: Mathworld Data (Integer Version)</a> 13050 </h5> 13051<p> 13052 <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_J1_Mathworld_Data_Integer_Version_"></a>Unsupported 13053 domain<br> 1, -2, -0.576725<br> Unsupported domain<br> 1, -8, -0.234636<br> 13054 Unsupported domain<br> 1, -10, -0.0434727<br> 13055 </p> 13056<h5> 13057<a name="special_function_error_rates_rep.error_logs.h13"></a> 13058 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i2">Error 13059 Output For cyl_bessel_j (integer orders) with compiler GNU C++ version 7.1.0 13060 and library Rmath 3.2.3 and test data Bessel J0: Mathworld Data (Integer Version)</a> 13061 </h5> 13062<p> 13063 <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_J0_Mathworld_Data_Integer_Version_"></a>Unsupported 13064 domain<br> 0, -2, 0.223891<br> Unsupported domain<br> 0, -8, 0.171651<br> 13065 Unsupported domain<br> 0, -10, -0.245936<br> 13066 </p> 13067<h5> 13068<a name="special_function_error_rates_rep.error_logs.h14"></a> 13069 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w0">Error 13070 Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library Rmath 13071 3.2.3 and test data Bessel JN: Mathworld Data</a> 13072 </h5> 13073<p> 13074 <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_JN_Mathworld_Data"></a>Unsupported 13075 domain<br> 5, -10, 0.234062<br> CAUTION: Gross error found at entry 6.<br> 13076 Found: 0 Expected 0.000725964 Error: 3.26265e+304<br> -5, 1e+06, 0.000725964<br> 13077 CAUTION: Gross error found at entry 7.<br> Found: 0 Expected -0.000725964 13078 Error: 3.26265e+304<br> 5, 1e+06, -0.000725964<br> Unsupported domain<br> 13079 -5, -1, 0.000249758<br> Unsupported domain<br> 10, -10, 0.207486<br> 13080 Unsupported domain<br> 10, -5, 0.0014678<br> CAUTION: Gross error found 13081 at entry 12.<br> Found: 0 Expected -0.000331079 Error: 1.48795e+304<br> 13082 -10, 1e+06, -0.000331079<br> CAUTION: Gross error found at entry 13.<br> 13083 Found: 0 Expected -0.000331079 Error: 1.48795e+304<br> 10, 1e+06, -0.000331079<br> 13084 </p> 13085<h5> 13086<a name="special_function_error_rates_rep.error_logs.h15"></a> 13087 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w1">Error 13088 Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library Rmath 13089 3.2.3 and test data Bessel J1: Mathworld Data</a> 13090 </h5> 13091<p> 13092 <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J1_Mathworld_Data"></a>Unsupported 13093 domain<br> 1, -2, -0.576725<br> Unsupported domain<br> 1, -8, -0.234636<br> 13094 Unsupported domain<br> 1, -10, -0.0434727<br> 13095 </p> 13096<h5> 13097<a name="special_function_error_rates_rep.error_logs.h16"></a> 13098 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w2">Error 13099 Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library Rmath 13100 3.2.3 and test data Bessel J0: Mathworld Data</a> 13101 </h5> 13102<p> 13103 <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J0_Mathworld_Data"></a>Unsupported 13104 domain<br> 0, -2, 0.223891<br> Unsupported domain<br> 0, -8, 0.171651<br> 13105 Unsupported domain<br> 0, -10, -0.245936<br> 13106 </p> 13107<h5> 13108<a name="special_function_error_rates_rep.error_logs.h17"></a> 13109 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ibetac_inv_with"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ibetac_inv_with">Error 13110 Output For ibetac_inv with compiler GNU C++ version 7.1.0 and library Rmath 13111 3.2.3 and test data Inverse incomplete beta</a> 13112 </h5> 13113<p> 13114 <a name="errors_GNU_C_version_7_1_0_linux_double_ibetac_inv_Rmath_3_2_3_Inverse_incomplete_beta"></a>CAUTION: 13115 Gross error found at entry 7.<br> Found: 3.8247e-302 Expected 0 Error: 1.71891e+06<br> 13116 1.38853e-05, 0.0497627, 0.632396, 0, 0<br> CAUTION: Gross error found at 13117 entry 71.<br> Found: 1.38362e-204 Expected 0 Error: 6.21832e+103<br> 3.77931e-05, 13118 0.0150073, 0.835025, 0, 0<br> CAUTION: Gross error found at entry 90.<br> 13119 Found: 1.09275e-303 Expected 0 Error: 49109.6<br> 4.29383e-05, 0.0428761, 13120 0.814742, 0, 0<br> CAUTION: Gross error found at entry 102.<br> Found: 13121 3.8625e-304 Expected 0 Error: 17358<br> 4.80089e-05, 0.0296236, 0.913384, 13122 0, 0<br> CAUTION: Gross error found at entry 115.<br> Found: 1.51774e-303 13123 Expected 0 Error: 68209.8<br> 0.000130387, 0.0404969, 0.814742, 0, 0<br> 13124 CAUTION: Gross error found at entry 123.<br> Found: 1.28036e-303 Expected 13125 0 Error: 57541.4<br> 0.000149328, 0.0201182, 0.905801, 5.70765e-267, 0<br> 13126 CAUTION: Gross error found at entry 133.<br> Found: 1.96732e-302 Expected 13127 0 Error: 884160<br> 0.000173563, 0.0301908, 0.913384, 4.21662e-213, 0<br> 13128 CAUTION: Gross error found at entry 159.<br> Found: 1.48697e-191 Expected 13129 0 Error: 6.68279e+116<br> 0.000260723, 0.0252933, 0.632396, 0, 0<br> CAUTION: 13130 Gross error found at entry 256.<br> Found: 9.24166e-245 Expected 0 Error: 13131 4.15342e+63<br> 0.00246975, 0.016063, 0.913384, 1, 0<br> 13132 </p> 13133<h5> 13134<a name="special_function_error_rates_rep.error_logs.h18"></a> 13135 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ibeta_inv_with_"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ibeta_inv_with_">Error 13136 Output For ibeta_inv with compiler GNU C++ version 7.1.0 and library Rmath 13137 3.2.3 and test data Inverse incomplete beta</a> 13138 </h5> 13139<p> 13140 <a name="errors_GNU_C_version_7_1_0_linux_double_ibeta_inv_Rmath_3_2_3_Inverse_incomplete_beta"></a>CAUTION: 13141 Gross error found at entry 1.<br> Found: 1.90197e-247 Expected 0 Error: 8.54789e+60<br> 13142 1.12733e-05, 0.022662, 0.135563, 0, 0<br> CAUTION: Gross error found at entry 13143 30.<br> Found: 1.36217e-301 Expected 0 Error: 6.12191e+06<br> 2.10769e-05, 13144 0.0448972, 0.221112, 0, 0<br> CAUTION: Gross error found at entry 152.<br> 13145 Found: 2.92621e-285 Expected 0 Error: 1.31511e+23<br> 0.000240381, 0.017982, 13146 0.221112, 0, 0<br> CAUTION: Gross error found at entry 184.<br> Found: 13147 5.63355e-203 Expected 0 Error: 2.53185e+105<br> 0.000348822, 0.0275467, 0.135563, 13148 0, 1.88165e-166<br> CAUTION: Gross error found at entry 205.<br> Found: 13149 5.52731e-303 Expected 0 Error: 248409<br> 0.000441212, 0.0313573, 0.127074, 13150 0, 9.07221e-121<br> 13151 </p> 13152<h5> 13153<a name="special_function_error_rates_rep.error_logs.h19"></a> 13154 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_non_central_bet"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_non_central_bet">Error 13155 Output For non central beta CDF complement with compiler GNU C++ version 7.1.0 13156 and library Rmath 3.2.3 and test data Non Central Beta, large parameters</a> 13157 </h5> 13158<p> 13159 <a name="errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_complement_Rmath_3_2_3_Non_Central_Beta_large_parameters"></a>CAUTION: 13160 Gross error found at entry 10.<br> Found: 9.76918e-10 Expected 1.61248e-15 13161 Error: 605846<br> 290.682, 72.6705, 20005.4, 0.997663, 1, 1.61248e-15<br> 13162 CAUTION: Gross error found at entry 11.<br> Found: 9.94184e-10 Expected 3.0108e-42 13163 Error: 3.30205e+32<br> 290.682, 145.341, 53489.1, 0.998663, 1, 3.0108e-42<br> 13164 CAUTION: Gross error found at entry 16.<br> Found: 8.45406e-10 Expected 4.46652e-22 13165 Error: 1.89276e+12<br> 290.682, 1162.73, 2308.07, 0.656921, 1, 4.46652e-22<br> 13166 CAUTION: Gross error found at entry 17.<br> Found: 9.41971e-10 Expected 1.7241e-50 13167 Error: 5.46356e+40<br> 290.682, 1453.41, 8064.48, 0.832237, 1, 1.7241e-50<br> 13168 CAUTION: Gross error found at entry 18.<br> Found: 9.30663e-10 Expected 2.09803e-305 13169 Error: 4.43589e+295<br> 975.766, 731.824, 232.285, 0.919742, 1, 2.09803e-305<br> 13170 CAUTION: Gross error found at entry 27.<br> Found: 9.76918e-10 Expected 9.3474e-18 13171 Error: 1.04512e+08<br> 1879.05, 187.905, 20005.4, 0.992215, 1, 9.3474e-18<br> 13172 CAUTION: Gross error found at entry 28.<br> Found: 9.94184e-10 Expected 1.8122e-90 13173 Error: 5.48607e+80<br> 1879.05, 469.762, 53489.1, 0.994618, 1, 1.8122e-90<br> 13174 CAUTION: Gross error found at entry 32.<br> Found: 9.27224e-10 Expected 3.18255e-15 13175 Error: 291345<br> 1879.05, 3758.1, 1879.05, 0.480508, 1, 3.18255e-15<br> 13176 CAUTION: Gross error found at entry 33.<br> Found: 8.45406e-10 Expected 1.10218e-77 13177 Error: 7.67029e+67<br> 1879.05, 5637.15, 2308.07, 0.458181, 1, 1.10218e-77<br> 13178 CAUTION: Gross error found at entry 34.<br> Found: 9.30663e-10 Expected 0 13179 Error: 4.18262e+298<br> 2308.07, 1154.03, 232.285, 0.919371, 1, 0<br> CAUTION: 13180 Gross error found at entry 35.<br> Found: 8.93617e-10 Expected 0 Error: 4.01612e+298<br> 13181 2308.07, 1731.05, 290.682, 0.917262, 1, 0<br> CAUTION: Gross error found 13182 at entry 43.<br> Found: 9.94184e-10 Expected 3.57283e-70 Error: 2.78262e+60<br> 13183 8064.48, 806.448, 53489.1, 0.988678, 1, 3.57283e-70<br> CAUTION: Gross error 13184 found at entry 48.<br> Found: 8.45406e-10 Expected 8.78057e-74 Error: 9.62814e+63<br> 13185 8064.48, 16129, 2308.07, 0.421531, 1, 8.78057e-74<br> CAUTION: Gross error 13186 found at entry 49.<br> Found: 9.30663e-10 Expected 0 Error: 4.18262e+298<br> 13187 15674.4, 3918.59, 232.285, 0.933726, 1, 0<br> CAUTION: Gross error found 13188 at entry 50.<br> Found: 8.93617e-10 Expected 0 Error: 4.01612e+298<br> 13189 15674.4, 7837.19, 290.682, 0.917179, 1, 0<br> CAUTION: Gross error found 13190 at entry 51.<br> Found: 8.9318e-10 Expected 0 Error: 4.01416e+298<br> 15674.4, 13191 11755.8, 975.766, 0.915784, 1, 0<br> CAUTION: Gross error found at entry 13192 63.<br> Found: 9.41971e-10 Expected 2.31296e-171 Error: 4.07258e+161<br> 13193 20005.4, 40010.8, 8064.48, 0.432094, 1, 2.31296e-171<br> CAUTION: Gross error 13194 found at entry 64.<br> Found: 9.30663e-10 Expected 0 Error: 4.18262e+298<br> 13195 53489.1, 5348.92, 232.285, 0.954635, 1, 0<br> CAUTION: Gross error found 13196 at entry 65.<br> Found: 8.93617e-10 Expected 0 Error: 4.01612e+298<br> 13197 53489.1, 13372.3, 290.682, 0.933478, 1, 0<br> CAUTION: Gross error found 13198 at entry 66.<br> Found: 8.9318e-10 Expected 0 Error: 4.01416e+298<br> 53489.1, 13199 26744.6, 975.766, 0.91717, 1, 0<br> 13200 </p> 13201<h5> 13202<a name="special_function_error_rates_rep.error_logs.h20"></a> 13203 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_non_central_be0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_non_central_be0">Error 13204 Output For non central beta CDF with compiler GNU C++ version 7.1.0 and library 13205 Rmath 3.2.3 and test data Non Central Beta, large parameters</a> 13206 </h5> 13207<p> 13208 <a name="errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_Rmath_3_2_3_Non_Central_Beta_large_parameters"></a>CAUTION: 13209 Gross error found at entry 0.<br> Found: 9.1136e-209 Expected 5.82279e-200 13210 Error: 6.38913e+08<br> 232.285, 209.056, 232.285, 0.062486, 5.82279e-200, 13211 1<br> CAUTION: Gross error found at entry 1.<br> Found: 4.08108e-115 Expected 13212 2.37643e-112 Error: 581.304<br> 232.285, 229.962, 290.682, 0.155342, 2.37643e-112, 13213 1<br> CAUTION: Gross error found at entry 2.<br> Found: 1.07549e-93 Expected 13214 9.53431e-89 Error: 88650<br> 232.285, 232.052, 975.766, 0.378086, 9.53431e-89, 13215 1<br> CAUTION: Gross error found at entry 3.<br> Found: 2.58402e-54 Expected 13216 8.27353e-53 Error: 31.0181<br> 232.285, 232.285, 1879.05, 0.625865, 8.27353e-53, 13217 1<br> CAUTION: Gross error found at entry 4.<br> Found: 1.93718e-19 Expected 13218 6.64275e-16 Error: 3428.08<br> 232.285, 232.308, 2308.07, 0.770774, 6.64275e-16, 13219 1<br> CAUTION: Gross error found at entry 21.<br> Found: 8.12962e-240 Expected 13220 1.82294e-219 Error: 2.24234e+20<br> 975.766, 974.79, 1879.05, 0.331337, 1.82294e-219, 13221 1<br> CAUTION: Gross error found at entry 22.<br> Found: 3.47274e-69 Expected 13222 1.42183e-67 Error: 39.9426<br> 975.766, 975.766, 2308.07, 0.514323, 1.42183e-67, 13223 1<br> CAUTION: Gross error found at entry 23.<br> Found: 5.86885e-50 Expected 13224 1.27896e-47 Error: 216.923<br> 975.766, 975.863, 8064.48, 0.753209, 1.27896e-47, 13225 1<br> CAUTION: Gross error found at entry 39.<br> Found: 4.82785e-230 Expected 13226 1.25446e-213 Error: 2.59838e+16<br> 2308.07, 2308.07, 8064.48, 0.54983, 1.25446e-213, 13227 1<br> CAUTION: Gross error found at entry 40.<br> Found: 1.22971e-87 Expected 13228 1.82618e-85 Error: 147.505<br> 2308.07, 2308.3, 15674.4, 0.733174, 1.82618e-85, 13229 1<br> CAUTION: Gross error found at entry 56.<br> Found: 2.97337e-127 Expected 13230 2.56068e-124 Error: 860.205<br> 15674.4, 15675.9, 20005.4, 0.55883, 2.56068e-124, 13231 1<br> 13232 </p> 13233<h5> 13234<a name="special_function_error_rates_rep.error_logs.h21"></a> 13235 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_non_central_be1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_non_central_be1">Error 13236 Output For non central beta CDF complement with compiler GNU C++ version 7.1.0 13237 and library Rmath 3.2.3 and test data Non Central Beta, medium parameters</a> 13238 </h5> 13239<p> 13240 <a name="errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_complement_Rmath_3_2_3_Non_Central_Beta_medium_parameters"></a>CAUTION: 13241 Gross error found at entry 296.<br> Found: 9.44166e-10 Expected 6.22975e-10 13242 Error: 0.515577<br> 22.9367, 114.683, 19.5081, 0.480981, 1, 6.22975e-10<br> 13243 CAUTION: Gross error found at entry 369.<br> Found: 2.52234e-10 Expected 13244 1.40246e-10 Error: 0.79851<br> 27.5277, 20.6457, 0.956697, 0.915111, 1, 1.40246e-10<br> 13245 CAUTION: Gross error found at entry 429.<br> Found: 1.18105e-09 Expected 13246 7.45745e-10 Error: 0.58372<br> 28.8063, 21.6047, 60.3826, 0.946143, 1, 7.45745e-10<br> 13247 CAUTION: Gross error found at entry 430.<br> Found: 2.44435e-09 Expected 13248 1.60695e-09 Error: 0.521115<br> 28.8063, 21.6047, 148.129, 0.965121, 1, 1.60695e-09<br> 13249 CAUTION: Gross error found at entry 477.<br> Found: 7.57435e-10 Expected 13250 7.14133e-11 Error: 9.60635<br> 28.8063, 144.032, 42.3849, 0.504845, 1, 7.14133e-11<br> 13251 CAUTION: Gross error found at entry 489.<br> Found: 4.8561e-10 Expected 5.62991e-11 13252 Error: 7.62553<br> 31.9438, 23.9579, 44.2068, 0.93835, 1, 5.62991e-11<br> 13253 CAUTION: Gross error found at entry 490.<br> Found: 8.35187e-10 Expected 13254 1.87483e-10 Error: 3.45473<br> 31.9438, 23.9579, 135.747, 0.961117, 1, 1.87483e-10<br> 13255 CAUTION: Gross error found at entry 491.<br> Found: 1.00174e-09 Expected 13256 2.38491e-10 Error: 3.20032<br> 31.9438, 23.9579, 191.501, 0.968273, 1, 2.38491e-10<br> 13257 CAUTION: Gross error found at entry 537.<br> Found: 7.29746e-10 Expected 13258 1.31223e-12 Error: 555.111<br> 31.9438, 159.719, 34.2373, 0.489796, 1, 1.31223e-12<br> 13259 CAUTION: Gross error found at entry 538.<br> Found: 2.49663e-09 Expected 13260 1.54239e-09 Error: 0.618681<br> 31.9438, 159.719, 126.472, 0.581861, 1, 1.54239e-09<br> 13261 CAUTION: Gross error found at entry 549.<br> Found: 4.16125e-10 Expected 13262 4.8536e-13 Error: 856.353<br> 38.0822, 28.5617, 34.773, 0.931853, 1, 4.8536e-13<br> 13263 CAUTION: Gross error found at entry 550.<br> Found: 9.69907e-10 Expected 13264 2.87054e-12 Error: 336.883<br> 38.0822, 28.5617, 127.953, 0.956104, 1, 2.87054e-12<br> 13265 CAUTION: Gross error found at entry 551.<br> Found: 5.90132e-10 Expected 13266 4.08361e-12 Error: 143.512<br> 38.0822, 28.5617, 183.147, 0.963764, 1, 4.08361e-12<br> 13267 CAUTION: Gross error found at entry 597.<br> Found: 4.67033e-10 Expected 13268 9.82939e-16 Error: 475139<br> 38.0822, 190.411, 27.0954, 0.475419, 1, 9.82939e-16<br> 13269 CAUTION: Gross error found at entry 598.<br> Found: 9.33207e-10 Expected 13270 4.03465e-12 Error: 230.298<br> 38.0822, 190.411, 100.733, 0.544491, 1, 4.03465e-12<br> 13271 CAUTION: Gross error found at entry 599.<br> Found: 7.4092e-10 Expected 9.53942e-11 13272 Error: 6.76693<br> 38.0822, 190.411, 169.826, 0.594614, 1, 9.53942e-11<br> 13273 CAUTION: Gross error found at entry 609.<br> Found: 5.71813e-10 Expected 13274 1.17207e-14 Error: 48785.7<br> 42.7789, 32.0842, 28.3773, 0.927814, 1, 1.17207e-14<br> 13275 CAUTION: Gross error found at entry 610.<br> Found: 5.16834e-10 Expected 13276 9.62679e-14 Error: 5367.71<br> 42.7789, 32.0842, 109.376, 0.950307, 1, 9.62679e-14<br> 13277 CAUTION: Gross error found at entry 611.<br> Found: 6.08012e-10 Expected 13278 1.7454e-13 Error: 3482.51<br> 42.7789, 32.0842, 175.686, 0.960431, 1, 1.7454e-13<br> 13279 CAUTION: Gross error found at entry 657.<br> Found: 5.59489e-10 Expected 13280 2.86344e-18 Error: 1.95391e+08<br> 42.7789, 213.895, 21.9724, 0.467166, 1, 13281 2.86344e-18<br> CAUTION: Gross error found at entry 658.<br> Found: 5.14798e-10 13282 Expected 2.50972e-14 Error: 20511.2<br> 42.7789, 213.895, 84.4175, 0.522676, 13283 1, 2.50972e-14<br> CAUTION: Gross error found at entry 659.<br> Found: 13284 8.49991e-10 Expected 2.38005e-12 Error: 356.131<br> 42.7789, 213.895, 160.056, 13285 0.576191, 1, 2.38005e-12<br> CAUTION: Gross error found at entry 671.<br> 13286 Found: 3.03281e-10 Expected 2.22036e-15 Error: 136590<br> 44.5963, 33.4472, 13287 22.4929, 0.924976, 1, 2.22036e-15<br> CAUTION: Gross error found at entry 13288 672.<br> Found: 8.40636e-10 Expected 2.22384e-14 Error: 37800.1<br> 44.5963, 13289 33.4472, 94.9517, 0.946545, 1, 2.22384e-14<br> CAUTION: Gross error found 13290 at entry 673.<br> Found: 8.15021e-10 Expected 4.75974e-14 Error: 17122.2<br> 13291 44.5963, 33.4472, 162.945, 0.95793, 1, 4.75974e-14<br> CAUTION: Gross error 13292 found at entry 716.<br> Found: 1.11988e-10 Expected 2.84965e-22 Error: 3.92989e+11<br> 13293 44.5963, 222.981, 0.956697, 0.445432, 1, 2.84965e-22<br> CAUTION: Gross error 13294 found at entry 717.<br> Found: 7.99524e-10 Expected 3.04552e-15 Error: 262523<br> 13295 44.5963, 222.981, 78.4454, 0.515267, 1, 3.04552e-15<br> CAUTION: Gross error 13296 found at entry 718.<br> Found: 8.0958e-10 Expected 5.89458e-13 Error: 1372.43<br> 13297 44.5963, 222.981, 158.441, 0.57107, 1, 5.89458e-13<br> *** FURTHER CONTENT 13298 HAS BEEN TRUNCATED FOR BREVITY ***<br> 13299 </p> 13300<h5> 13301<a name="special_function_error_rates_rep.error_logs.h22"></a> 13302 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_non_central_be2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_non_central_be2">Error 13303 Output For non central beta CDF with compiler GNU C++ version 7.1.0 and library 13304 Rmath 3.2.3 and test data Non Central Beta, medium parameters</a> 13305 </h5> 13306<p> 13307 <a name="errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_Rmath_3_2_3_Non_Central_Beta_medium_parameters"></a>CAUTION: 13308 Gross error found at entry 14.<br> Found: 4.64669e-35 Expected 7.14875e-33 13309 Error: 152.846<br> 1.45431, 1.30887, 158.441, 0.0983847, 7.14875e-33, 1<br> 13310 CAUTION: Gross error found at entry 15.<br> Found: 4.66674e-46 Expected 3.13332e-40 13311 Error: 671416<br> 1.45431, 1.30887, 196.222, 0.09869, 3.13332e-40, 1<br> 13312 CAUTION: Gross error found at entry 18.<br> Found: 5.84342e-28 Expected 3.61559e-27 13313 Error: 5.18745<br> 1.45431, 1.43976, 159.586, 0.245596, 3.61559e-27, 1<br> 13314 CAUTION: Gross error found at entry 19.<br> Found: 1.72833e-34 Expected 1.76943e-33 13315 Error: 9.2378<br> 1.45431, 1.43976, 198.576, 0.246444, 1.76943e-33, 1<br> 13316 CAUTION: Gross error found at entry 22.<br> Found: 1.76915e-19 Expected 3.69506e-18 13317 Error: 19.8861<br> 1.45431, 1.45285, 159.621, 0.491116, 3.69506e-18, 1<br> 13318 CAUTION: Gross error found at entry 23.<br> Found: 2.52007e-25 Expected 2.00482e-22 13319 Error: 794.544<br> 1.45431, 1.45285, 199.292, 0.492849, 2.00482e-22, 1<br> 13320 CAUTION: Gross error found at entry 73.<br> Found: 2.04477e-34 Expected 2.45287e-33 13321 Error: 10.9958<br> 7.62448, 6.86203, 148.129, 0.0921776, 2.45287e-33, 1<br> 13322 CAUTION: Gross error found at entry 74.<br> Found: 2.36587e-46 Expected 7.32638e-42 13323 Error: 30966<br> 7.62448, 6.86203, 193.539, 0.093784, 7.32638e-42, 1<br> 13324 CAUTION: Gross error found at entry 76.<br> Found: 3.29122e-26 Expected 7.418e-25 13325 Error: 21.5387<br> 7.62448, 7.54824, 148.626, 0.228717, 7.418e-25, 1<br> 13326 CAUTION: Gross error found at entry 77.<br> Found: 1.70126e-32 Expected 1.07666e-31 13327 Error: 5.32864<br> 7.62448, 7.54824, 193.774, 0.23303, 1.07666e-31, 1<br> 13328 CAUTION: Gross error found at entry 79.<br> Found: 1.3478e-15 Expected 4.21836e-15 13329 Error: 2.12982<br> 7.62448, 7.61686, 151.548, 0.457773, 4.21836e-15, 1<br> 13330 CAUTION: Gross error found at entry 80.<br> Found: 8.78487e-21 Expected 3.41238e-19 13331 Error: 37.8438<br> 7.62448, 7.61686, 194.119, 0.465826, 3.41238e-19, 1<br> 13332 CAUTION: Gross error found at entry 132.<br> Found: 3.85783e-23 Expected 13333 1.54142e-22 Error: 2.99555<br> 19.9593, 17.9634, 44.2068, 0.0698905, 1.54142e-22, 13334 1<br> CAUTION: Gross error found at entry 133.<br> Found: 8.6122e-39 Expected 13335 3.94361e-38 Error: 3.5791<br> 19.9593, 17.9634, 135.747, 0.0829178, 3.94361e-38, 13336 1<br> CAUTION: Gross error found at entry 134.<br> Found: 3.61781e-52 Expected 13337 3.98669e-48 Error: 11018.6<br> 19.9593, 17.9634, 191.501, 0.0864897, 3.98669e-48, 13338 1<br> CAUTION: Gross error found at entry 135.<br> Found: 2.07122e-15 Expected 13339 7.08614e-15 Error: 2.42124<br> 19.9593, 19.7597, 55.6996, 0.176444, 7.08614e-15, 13340 1<br> CAUTION: Gross error found at entry 136.<br> Found: 2.28223e-27 Expected 13341 2.16759e-25 Error: 93.977<br> 19.9593, 19.7597, 136.272, 0.20393, 2.16759e-25, 13342 1<br> CAUTION: Gross error found at entry 137.<br> Found: 6.4251e-34 Expected 13343 4.0064e-33 Error: 5.23554<br> 19.9593, 19.7597, 191.898, 0.213398, 4.0064e-33, 13344 1<br> CAUTION: Gross error found at entry 139.<br> Found: 2.1734e-14 Expected 13345 4.65637e-14 Error: 1.14243<br> 19.9593, 19.9394, 145.168, 0.410858, 4.65637e-14, 13346 1<br> CAUTION: Gross error found at entry 140.<br> Found: 2.18388e-19 Expected 13347 5.1677e-18 Error: 22.663<br> 19.9593, 19.9394, 192.978, 0.426523, 5.1677e-18, 13348 1<br> CAUTION: Gross error found at entry 192.<br> Found: 3.29537e-23 Expected 13349 8.29996e-23 Error: 1.51867<br> 22.4174, 20.1757, 34.773, 0.0661999, 8.29996e-23, 13350 1<br> CAUTION: Gross error found at entry 193.<br> Found: 7.86091e-39 Expected 13351 2.77686e-38 Error: 2.5325<br> 22.4174, 20.1757, 127.953, 0.0809614, 2.77686e-38, 13352 1<br> CAUTION: Gross error found at entry 194.<br> Found: 3.0161e-51 Expected 13353 4.5396e-48 Error: 1504.12<br> 22.4174, 20.1757, 183.147, 0.0848857, 4.5396e-48, 13354 1<br> CAUTION: Gross error found at entry 195.<br> Found: 3.08022e-14 Expected 13355 1.42713e-13 Error: 3.6332<br> 22.4174, 22.1932, 37.6764, 0.162145, 1.42713e-13, 13356 1<br> CAUTION: Gross error found at entry 196.<br> Found: 8.89935e-28 Expected 13357 2.56187e-25 Error: 286.871<br> 22.4174, 22.1932, 131.096, 0.199361, 2.56187e-25, 13358 1<br> CAUTION: Gross error found at entry 197.<br> Found: 9.34392e-34 Expected 13359 6.14831e-33 Error: 5.58001<br> 22.4174, 22.1932, 186.799, 0.209601, 6.14831e-33, 13360 1<br> CAUTION: Gross error found at entry 199.<br> Found: 2.79341e-13 Expected 13361 4.79277e-13 Error: 0.71574<br> 22.4174, 22.395, 131.148, 0.398015, 4.79277e-13, 13362 1<br> CAUTION: Gross error found at entry 200.<br> Found: 3.13989e-19 Expected 13363 7.01608e-18 Error: 21.345<br> 22.4174, 22.395, 191.433, 0.419933, 7.01608e-18, 13364 1<br> *** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br> 13365 </p> 13366<h5> 13367<a name="special_function_error_rates_rep.error_logs.h23"></a> 13368 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_non_central_chi"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_non_central_chi">Error 13369 Output For non central chi squared CDF complement with compiler GNU C++ version 13370 7.1.0 and library Rmath 3.2.3 and test data Non Central Chi Squared, large 13371 parameters</a> 13372 </h5> 13373<p> 13374 <a name="errors_GNU_C_version_7_1_0_linux_double_non_central_chi_squared_CDF_complement_Rmath_3_2_3_Non_Central_Chi_Squared_large_parameters"></a>CAUTION: 13375 Gross error found at entry 12.<br> Found: 0 Expected 1.17655e-12 Error: 5.28771e+295<br> 13376 101.815, 5236.73, 6406.25, 1, 1.17655e-12<br> CAUTION: Gross error found 13377 at entry 13.<br> Found: 0 Expected 1.79374e-44 Error: 8.06149e+263<br> 13378 101.815, 9735.22, 12788.2, 1, 1.79374e-44<br> CAUTION: Gross error found 13379 at entry 35.<br> Found: 2.58682e-14 Expected 1.84404e-61 Error: 1.4028e+47<br> 13380 107.623, 122.456, 920.317, 1, 1.84404e-61<br> CAUTION: Gross error found 13381 at entry 36.<br> Found: 0 Expected 2.30757e-102 Error: 1.03707e+206<br> 13382 107.623, 156.292, 1319.58, 1, 2.30757e-102<br> CAUTION: Gross error found 13383 at entry 52.<br> Found: 0 Expected 6.40952e-24 Error: 2.88059e+284<br> 13384 114.68, 417.884, 1065.13, 1, 6.40952e-24<br> CAUTION: Gross error found at 13385 entry 53.<br> Found: 0 Expected 1.02366e-98 Error: 4.60058e+209<br> 114.68, 13386 669.781, 2353.38, 1, 1.02366e-98<br> CAUTION: Gross error found at entry 13387 69.<br> Found: 0 Expected 6.55726e-39 Error: 2.94699e+269<br> 118.032, 13388 3168.71, 4930.11, 1, 6.55726e-39<br> CAUTION: Gross error found at entry 13389 85.<br> Found: 0 Expected 7.30688e-22 Error: 3.28388e+286<br> 163.004, 13390 9735.22, 11877.9, 1, 7.30688e-22<br> CAUTION: Gross error found at entry 13391 86.<br> Found: 0 Expected 1.17171e-111 Error: 5.26596e+196<br> 163.004, 13392 25344.1, 33159.2, 1, 1.17171e-111<br> CAUTION: Gross error found at entry 13393 108.<br> Found: 1.12355e-13 Expected 2.67349e-61 Error: 4.20255e+47<br> 13394 256.292, 122.456, 1136.25, 1, 2.67349e-61<br> CAUTION: Gross error found 13395 at entry 109.<br> Found: 1.16462e-13 Expected 8.30595e-116 Error: 1.40216e+102<br> 13396 256.292, 156.292, 1650.34, 1, 8.30595e-116<br> CAUTION: Gross error found 13397 at entry 124.<br> Found: 1.05804e-13 Expected 1.01672e-15 Error: 103.064<br> 13398 517.884, 417.884, 1403.65, 1, 1.01672e-15<br> CAUTION: Gross error found 13399 at entry 125.<br> Found: 2.00728e-13 Expected 3.50192e-56 Error: 5.73194e+42<br> 13400 517.884, 669.781, 2375.33, 1, 3.50192e-56<br> CAUTION: Gross error found 13401 at entry 141.<br> Found: 0 Expected 1.36924e-20 Error: 6.15368e+287<br> 13402 769.781, 3168.71, 5120.04, 1, 1.36924e-20<br> CAUTION: Gross error found 13403 at entry 142.<br> Found: 0 Expected 3.19215e-72 Error: 1.43463e+236<br> 13404 769.781, 5236.73, 9009.76, 1, 3.19215e-72<br> CAUTION: Gross error found 13405 at entry 157.<br> Found: 0 Expected 7.26231e-08 Error: 3.26385e+300<br> 13406 1223.88, 9735.22, 12055, 1, 7.26231e-08<br> CAUTION: Gross error found at 13407 entry 158.<br> Found: 0 Expected 4.5906e-56 Error: 2.06312e+252<br> 1223.88, 13408 25344.1, 31881.6, 1, 4.5906e-56<br> CAUTION: Gross error found at entry 194.<br> 13409 Found: 0 Expected 5.34714e-12 Error: 2.40313e+296<br> 9835.22, 122.456, 10953.4, 13410 1, 5.34714e-12<br> CAUTION: Gross error found at entry 195.<br> Found: 13411 0 Expected 4.84412e-40 Error: 2.17706e+268<br> 9835.22, 156.292, 11989.8, 13412 1, 4.84412e-40<br> CAUTION: Gross error found at entry 196.<br> Found: 13413 0 Expected 5.50199e-83 Error: 2.47272e+225<br> 9835.22, 417.884, 13329, 1, 13414 5.50199e-83<br> CAUTION: Gross error found at entry 197.<br> Found: 0 Expected 13415 1.28192e-205 Error: 5.76124e+102<br> 9835.22, 669.781, 15757.5, 1, 1.28192e-205<br> 13416 CAUTION: Gross error found at entry 211.<br> Found: 0 Expected 3.83272e-28 13417 Error: 1.72251e+280<br> 25444.1, 1123.88, 29224.8, 1, 3.83272e-28<br> CAUTION: 13418 Gross error found at entry 212.<br> Found: 0 Expected 1.69815e-101 Error: 13419 7.63188e+206<br> 25444.1, 3168.71, 34335.4, 1, 1.69815e-101<br> CAUTION: 13420 Gross error found at entry 213.<br> Found: 0 Expected 1.09245e-217 Error: 13421 4.90974e+90<br> 25444.1, 5236.73, 39885.1, 1, 1.09245e-217<br> 13422 </p> 13423<h5> 13424<a name="special_function_error_rates_rep.error_logs.h24"></a> 13425 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_non_central_ch0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_non_central_ch0">Error 13426 Output For non central chi squared CDF complement with compiler GNU C++ version 13427 7.1.0 and library Rmath 3.2.3 and test data Non Central Chi Squared, medium 13428 parameters</a> 13429 </h5> 13430<p> 13431 <a name="errors_GNU_C_version_7_1_0_linux_double_non_central_chi_squared_CDF_complement_Rmath_3_2_3_Non_Central_Chi_Squared_medium_parameters"></a>CAUTION: 13432 Gross error found at entry 36.<br> Found: 1.11022e-14 Expected 1.30043e-26 13433 Error: 8.53738e+11<br> 1.95191, 109.376, 445.313, 1, 1.30043e-26<br> CAUTION: 13434 Gross error found at entry 37.<br> Found: 0 Expected 1.45478e-39 Error: 6.53812e+268<br> 13435 1.95191, 109.444, 556.98, 1, 1.45478e-39<br> CAUTION: Gross error found at 13436 entry 54.<br> Found: 2.91989e-14 Expected 4.25949e-21 Error: 6.85501e+06<br> 13437 1.95191, 159.586, 484.613, 1, 4.25949e-21<br> CAUTION: Gross error found 13438 at entry 55.<br> Found: 0 Expected 1.33424e-37 Error: 5.99639e+270<br> 13439 1.95191, 159.621, 646.292, 1, 1.33424e-37<br> CAUTION: Gross error found 13440 at entry 56.<br> Found: 1.25455e-14 Expected 1.95903e-56 Error: 6.40393e+41<br> 13441 1.95191, 160.056, 810.04, 1, 1.95903e-56<br> CAUTION: Gross error found at 13442 entry 73.<br> Found: 0 Expected 4.34735e-25 Error: 1.9538e+283<br> 1.95191, 13443 193.539, 586.473, 1, 4.34735e-25<br> CAUTION: Gross error found at entry 13444 74.<br> Found: 0 Expected 4.66119e-45 Error: 2.09485e+263<br> 1.95191, 13445 193.774, 782.902, 1, 4.66119e-45<br> CAUTION: Gross error found at entry 13446 75.<br> Found: 4.77396e-15 Expected 8.92248e-68 Error: 5.35048e+52<br> 13447 1.95191, 194.119, 980.352, 1, 8.92248e-68<br> CAUTION: Gross error found 13448 at entry 111.<br> Found: 0 Expected 3.1064e-15 Error: 1.39609e+293<br> 13449 20.4105, 84.4175, 314.484, 1, 3.1064e-15<br> CAUTION: Gross error found at 13450 entry 112.<br> Found: 0 Expected 7.50903e-29 Error: 3.37473e+279<br> 20.4105, 13451 94.9517, 461.449, 1, 7.50903e-29<br> CAUTION: Gross error found at entry 13452 113.<br> Found: 3.77476e-15 Expected 1.74225e-43 Error: 2.1666e+28<br> 13453 20.4105, 97.0751, 587.428, 1, 1.74225e-43<br> CAUTION: Gross error found 13454 at entry 130.<br> Found: 8.88178e-16 Expected 4.13277e-23 Error: 2.14911e+07<br> 13455 20.4105, 151.548, 515.876, 1, 4.13277e-23<br> CAUTION: Gross error found 13456 at entry 131.<br> Found: 1.75415e-14 Expected 1.92146e-41 Error: 9.12928e+26<br> 13457 20.4105, 152.75, 692.642, 1, 1.92146e-41<br> CAUTION: Gross error found at 13458 entry 132.<br> Found: 1.38778e-14 Expected 7.09864e-64 Error: 1.95499e+49<br> 13459 20.4105, 158.441, 894.26, 1, 7.09864e-64<br> CAUTION: Gross error found at 13460 entry 149.<br> Found: 2.22045e-16 Expected 8.74501e-28 Error: 2.5391e+11<br> 13461 20.4105, 191.433, 635.532, 1, 8.74501e-28<br> CAUTION: Gross error found 13462 at entry 150.<br> Found: 0 Expected 6.94227e-50 Error: 3.12002e+258<br> 13463 20.4105, 191.501, 847.648, 1, 6.94227e-50<br> CAUTION: Gross error found 13464 at entry 151.<br> Found: 3.40838e-14 Expected 5.3889e-75 Error: 6.32482e+60<br> 13465 20.4105, 191.898, 1061.55, 1, 5.3889e-75<br> CAUTION: Gross error found at 13466 entry 206.<br> Found: 5.88418e-15 Expected 2.69136e-22 Error: 2.18632e+07<br> 13467 22.8625, 141.209, 492.215, 1, 2.69136e-22<br> CAUTION: Gross error found 13468 at entry 207.<br> Found: 3.60822e-14 Expected 1.64941e-40 Error: 2.18759e+26<br> 13469 22.8625, 145.168, 672.121, 1, 1.64941e-40<br> CAUTION: Gross error found 13470 at entry 208.<br> Found: 3.73035e-14 Expected 1.6094e-61 Error: 2.31784e+47<br> 13471 22.8625, 148.129, 854.96, 1, 1.6094e-61<br> CAUTION: Gross error found at 13472 entry 225.<br> Found: 0 Expected 3.73672e-27 Error: 1.67937e+281<br> 22.8625, 13473 182.675, 616.613, 1, 3.73672e-27<br> CAUTION: Gross error found at entry 13474 226.<br> Found: 0 Expected 8.85688e-49 Error: 3.98049e+259<br> 22.8625, 13475 183.147, 824.038, 1, 8.85688e-49<br> CAUTION: Gross error found at entry 13476 227.<br> Found: 0 Expected 2.29176e-74 Error: 1.02997e+234<br> 22.8625, 13477 186.799, 1048.31, 1, 2.29176e-74<br> CAUTION: Gross error found at entry 13478 282.<br> Found: 0 Expected 2.18831e-21 Error: 9.8348e+286<br> 23.3804, 13479 132.721, 468.305, 1, 2.18831e-21<br> CAUTION: Gross error found at entry 13480 283.<br> Found: 0 Expected 1.3071e-38 Error: 5.87439e+269<br> 23.3804, 13481 135.747, 636.51, 1, 1.3071e-38<br> CAUTION: Gross error found at entry 284.<br> 13482 Found: 1.84297e-14 Expected 8.27843e-58 Error: 2.22623e+43<br> 23.3804, 136.272, 13483 798.262, 1, 8.27843e-58<br> CAUTION: Gross error found at entry 301.<br> 13484 Found: 0 Expected 9.85282e-26 Error: 4.42808e+282<br> 23.3804, 169.826, 579.619, 13485 1, 9.85282e-26<br> CAUTION: Gross error found at entry 302.<br> Found: 13486 0 Expected 4.8094e-47 Error: 2.16145e+261<br> 23.3804, 174.486, 791.465, 13487 1, 4.8094e-47<br> CAUTION: Gross error found at entry 303.<br> Found: 1.11022e-16 13488 Expected 6.70476e-71 Error: 1.65587e+54<br> 23.3804, 175.686, 995.333, 1, 13489 6.70476e-71<br> CAUTION: Gross error found at entry 358.<br> Found: 0 Expected 13490 3.9702e-21 Error: 1.7843e+287<br> 26.2704, 126.472, 458.227, 1, 3.9702e-21<br> 13491 CAUTION: Gross error found at entry 359.<br> *** FURTHER CONTENT HAS BEEN 13492 TRUNCATED FOR BREVITY ***<br> 13493 </p> 13494<h5> 13495<a name="special_function_error_rates_rep.error_logs.h25"></a> 13496 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_non_central_t_c"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_non_central_t_c">Error 13497 Output For non central t CDF complement with compiler GNU C++ version 7.1.0 13498 and library Rmath 3.2.3 and test data Non Central T</a> 13499 </h5> 13500<p> 13501 <a name="errors_GNU_C_version_7_1_0_linux_double_non_central_t_CDF_complement_Rmath_3_2_3_Non_Central_T"></a>CAUTION: 13502 Gross error found at entry 56.<br> Found: 0.000186411 Expected 7.85192e-05 13503 Error: 1.37408<br> 61.6335, 46.2251, 68.8608, 0.999921, 7.85192e-05<br> 13504 CAUTION: Gross error found at entry 75.<br> Found: 0.00011439 Expected 5.05344e-05 13505 Error: 1.26361<br> 80.8418, 60.6313, 86.1278, 0.999949, 5.05344e-05<br> 13506 CAUTION: Gross error found at entry 93.<br> Found: 0.000655162 Expected 0.000423927 13507 Error: 0.545458<br> 100.733, 50.3663, 65.7619, 0.999576, 0.000423927<br> 13508 CAUTION: Gross error found at entry 112.<br> Found: 0.000518249 Expected 13509 0.00034473 Error: 0.503348<br> 127.953, 63.9764, 81.0824, 0.999655, 0.00034473<br> 13510 </p> 13511<h5> 13512<a name="special_function_error_rates_rep.error_logs.h26"></a> 13513 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_non_central_t_0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_non_central_t_0">Error 13514 Output For non central t CDF with compiler GNU C++ version 7.1.0 and library 13515 Rmath 3.2.3 and test data Non Central T</a> 13516 </h5> 13517<p> 13518 <a name="errors_GNU_C_version_7_1_0_linux_double_non_central_t_CDF_Rmath_3_2_3_Non_Central_T"></a>CAUTION: 13519 Gross error found at entry 74.<br> Found: 0.000830062 Expected 0.000522858 13520 Error: 0.587549<br> 79.7478, -39.8739, -53.8066, 0.000522858, 0.999477<br> 13521 CAUTION: Gross error found at entry 94.<br> Found: 7.69292e-05 Expected 3.54024e-05 13522 Error: 1.17299<br> 101.191, -75.8936, -104.104, 3.54024e-05, 0.999965<br> 13523 CAUTION: Gross error found at entry 113.<br> Found: 5.07713e-05 Expected 13524 2.4439e-05 Error: 1.07747<br> 128.792, -96.5942, -128.112, 2.4439e-05, 0.999976<br> 13525 CAUTION: Gross error found at entry 132.<br> Found: 4.08612e-05 Expected 13526 2.01542e-05 Error: 1.02743<br> 146.56, -109.92, -143.392, 2.01542e-05, 0.99998<br> 13527 CAUTION: Gross error found at entry 151.<br> Found: 3.55146e-05 Expected 13528 1.7803e-05 Error: 0.994869<br> 159.586, -119.689, -154.522, 1.7803e-05, 0.999982<br> 13529 CAUTION: Gross error found at entry 170.<br> Found: 3.03671e-05 Expected 13530 1.55023e-05 Error: 0.958873<br> 175.686, -131.765, -168.211, 1.55023e-05, 13531 0.999984<br> CAUTION: Gross error found at entry 189.<br> Found: 2.61339e-05 13532 Expected 1.3581e-05 Error: 0.924298<br> 192.978, -144.733, -182.834, 1.3581e-05, 13533 0.999986<br> 13534 </p> 13535<h5> 13536<a name="special_function_error_rates_rep.error_logs.h27"></a> 13537 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_polygamma_with_"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_polygamma_with_">Error 13538 Output For polygamma with compiler GNU C++ version 7.1.0 and library Rmath 13539 3.2.3 and test data Mathematica Data - Large orders and other bug cases</a> 13540 </h5> 13541<p> 13542 <a name="errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_Large_orders_and_other_bug_cases"></a>CAUTION: 13543 Found non-finite result, when a finite value was expected at entry 0<br> 13544 Found: -nan Expected 2.07309e+257 Error: 1.79769e+308<br> 171, 2, 2.07309e+257<br> 13545 CAUTION: Gross error found at entry 0.<br> Found: -nan Expected 2.07309e+257 13546 Error: 1.79769e+308<br> 171, 2, 2.07309e+257<br> CAUTION: Found non-finite 13547 result, when a finite value was expected at entry 1<br> Found: -nan Expected 13548 7.42912e+188 Error: 1.79769e+308<br> 171, 5, 7.42912e+188<br> CAUTION: 13549 Gross error found at entry 1.<br> Found: -nan Expected 7.42912e+188 Error: 13550 1.79769e+308<br> 171, 5, 7.42912e+188<br> CAUTION: Found non-finite result, 13551 when a finite value was expected at entry 2<br> Found: -nan Expected -4.81295e+247 13552 Error: 1.79769e+308<br> 166, 2, -4.81295e+247<br> CAUTION: Gross error 13553 found at entry 2.<br> Found: -nan Expected -4.81295e+247 Error: 1.79769e+308<br> 13554 166, 2, -4.81295e+247<br> CAUTION: Found non-finite result, when a finite 13555 value was expected at entry 3<br> Found: -nan Expected -1.88439e+218 Error: 13556 1.79769e+308<br> 166, 3, -1.88439e+218<br> CAUTION: Gross error found at 13557 entry 3.<br> Found: -nan Expected -1.88439e+218 Error: 1.79769e+308<br> 13558 166, 3, -1.88439e+218<br> CAUTION: Found non-finite result, when a finite 13559 value was expected at entry 4<br> Found: -nan Expected 7.53144e+74 Error: 13560 1.79769e+308<br> 171, 23, 7.53144e+74<br> CAUTION: Gross error found at 13561 entry 4.<br> Found: -nan Expected 7.53144e+74 Error: 1.79769e+308<br> 171, 13562 23, 7.53144e+74<br> CAUTION: Found non-finite result, when a finite value 13563 was expected at entry 5<br> Found: -nan Expected -6.52661e-66 Error: 1.79769e+308<br> 13564 168, 150, -6.52661e-66<br> CAUTION: Gross error found at entry 5.<br> Found: 13565 -nan Expected -6.52661e-66 Error: 1.79769e+308<br> 168, 150, -6.52661e-66<br> 13566 CAUTION: Found non-finite result, when a finite value was expected at entry 13567 6<br> Found: -nan Expected 9.2734e-88 Error: 1.79769e+308<br> 169, 202, 13568 9.2734e-88<br> CAUTION: Gross error found at entry 6.<br> Found: -nan Expected 13569 9.2734e-88 Error: 1.79769e+308<br> 169, 202, 9.2734e-88<br> Outside supported 13570 domain<br> 20, -9.5, -0.00103076<br> Outside supported domain<br> 21, 13571 -9.5, 4.28582e+26<br> Outside supported domain<br> 22, -9.5, -0.00419144<br> 13572 Outside supported domain<br> 23, -9.5, 8.6745e+29<br> Outside supported 13573 domain<br> 24, -9.5, -0.0204825<br> Outside supported domain<br> 25, 13574 -9.5, 2.08188e+33<br> Outside supported domain<br> 26, -9.5, -0.118403<br> 13575 Outside supported domain<br> 27, -9.5, 5.84592e+36<br> Outside supported 13576 domain<br> 28, -9.5, -0.798969<br> Outside supported domain<br> 29, -9.5, 13577 1.89875e+40<br> Outside supported domain<br> 30, -9.5, -6.22245<br> 13578 </p> 13579<h5> 13580<a name="special_function_error_rates_rep.error_logs.h28"></a> 13581 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_polygamma_with0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_polygamma_with0">Error 13582 Output For polygamma with compiler GNU C++ version 7.1.0 and library Rmath 13583 3.2.3 and test data Mathematica Data - large negative arguments</a> 13584 </h5> 13585<p> 13586 <a name="errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_large_negative_arguments"></a>Outside 13587 supported domain<br> 124, -1.5, 7.63705e+240<br> Outside supported domain<br> 13588 124, -2.5, 7.63705e+240<br> Outside supported domain<br> 124, -3.5, 7.63705e+240<br> 13589 Outside supported domain<br> 124, -4.5, 7.63705e+240<br> Outside supported 13590 domain<br> 124, -5.5, 7.63705e+240<br> Outside supported domain<br> 124, 13591 -6.5, 7.63705e+240<br> Outside supported domain<br> 124, -7.5, 7.63705e+240<br> 13592 Outside supported domain<br> 124, -8.5, 7.63705e+240<br> Outside supported 13593 domain<br> 124, -9.5, 7.63705e+240<br> Outside supported domain<br> 124, 13594 -10.5, 7.63705e+240<br> Outside supported domain<br> 124, -11.5, 7.63705e+240<br> 13595 Outside supported domain<br> 124, -12.5, 7.63705e+240<br> Outside supported 13596 domain<br> 124, -13.5, 7.63705e+240<br> Outside supported domain<br> 13597 124, -14.5, 7.63705e+240<br> Outside supported domain<br> 124, -15.5, 7.63705e+240<br> 13598 Outside supported domain<br> 124, -16.5, 7.63705e+240<br> Outside supported 13599 domain<br> 124, -17.5, 7.63705e+240<br> Outside supported domain<br> 13600 124, -18.5, 7.63705e+240<br> Outside supported domain<br> 124, -19.5, 7.63705e+240<br> 13601 Outside supported domain<br> 124, -20.5, 7.63705e+240<br> Outside supported 13602 domain<br> 124, -1.5, -7.63705e+240<br> Outside supported domain<br> 13603 124, -2.5, -7.63705e+240<br> Outside supported domain<br> 124, -3.5, -7.63705e+240<br> 13604 Outside supported domain<br> 124, -4.5, -7.63705e+240<br> Outside supported 13605 domain<br> 124, -5.5, -7.63705e+240<br> Outside supported domain<br> 13606 124, -6.5, -7.63705e+240<br> Outside supported domain<br> 124, -7.5, -7.63705e+240<br> 13607 Outside supported domain<br> 124, -8.5, -7.63705e+240<br> Outside supported 13608 domain<br> 124, -9.5, -7.63705e+240<br> Outside supported domain<br> 13609 124, -10.5, -7.63705e+240<br> Outside supported domain<br> 124, -11.5, 13610 -7.63705e+240<br> Outside supported domain<br> 124, -12.5, -7.63705e+240<br> 13611 Outside supported domain<br> 124, -13.5, -7.63705e+240<br> Outside supported 13612 domain<br> 124, -14.5, -7.63705e+240<br> Outside supported domain<br> 13613 124, -15.5, -7.63705e+240<br> Outside supported domain<br> 124, -16.5, 13614 -7.63705e+240<br> Outside supported domain<br> 124, -17.5, -7.63705e+240<br> 13615 Outside supported domain<br> 124, -18.5, -7.63705e+240<br> Outside supported 13616 domain<br> 124, -19.5, -7.63705e+240<br> Outside supported domain<br> 13617 124, -20.5, -7.63705e+240<br> Outside supported domain<br> 1, -0.5, 8.9348<br> 13618 Outside supported domain<br> 2, -0.5, -0.828797<br> Outside supported domain<br> 13619 3, -0.5, 193.409<br> Outside supported domain<br> 4, -0.5, -3.47425<br> 13620 Outside supported domain<br> 5, -0.5, 15371.1<br> Outside supported domain<br> 13621 6, -0.5, -43.4579<br> Outside supported domain<br> 7, -0.5, 2.58068e+06<br> 13622 Outside supported domain<br> 8, -0.5, -1059.96<br> Outside supported domain<br> 13623 9, -0.5, 7.43185e+08<br> Outside supported domain<br> 10, -0.5, -42108.9<br> 13624 Outside supported domain<br> 11, -0.5, 3.26999e+11<br> Outside supported 13625 domain<br> 12, -0.5, -2.46448e+06<br> Outside supported domain<br> 13, 13626 -0.5, 2.04047e+14<br> Outside supported domain<br> 14, -0.5, -1.9918e+08<br> 13627 Outside supported domain<br> 15, -0.5, 1.71399e+17<br> Outside supported 13628 domain<br> 16, -0.5, -2.12394e+10<br> Outside supported domain<br> 17, 13629 -0.5, 1.86483e+20<br> Outside supported domain<br> 18, -0.5, -2.88824e+12<br> 13630 Outside supported domain<br> 19, -0.5, 2.55108e+23<br> Outside supported 13631 domain<br> 20, -0.5, -4.87773e+14<br> Outside supported domain<br> 21, 13632 -0.5, 4.28582e+26<br> Outside supported domain<br> 1, -0.5, 8.9348<br> 13633 Outside supported domain<br> 2, -0.5, -0.828843<br> Outside supported domain<br> 13634 3, -0.5, 193.409<br> Outside supported domain<br> 4, -0.5, -3.47791<br> 13635 Outside supported domain<br> 5, -0.5, 15371.1<br> Outside supported domain<br> 13636 6, -0.5, -44.0732<br> Outside supported domain<br> 7, -0.5, 2.58068e+06<br> 13637 Outside supported domain<br> 8, -0.5, -1237.15<br> Outside supported domain<br> 13638 9, -0.5, 7.43185e+08<br> Outside supported domain<br> 10, -0.5, -120071<br> 13639 Outside supported domain<br> 11, -0.5, 3.26999e+11<br> Outside supported 13640 domain<br> 12, -0.5, -5.11131e+07<br> Outside supported domain<br> 13, 13641 -0.5, 2.04047e+14<br> Outside supported domain<br> 14, -0.5, -4.1064e+10<br> 13642 Outside supported domain<br> 15, -0.5, 1.71399e+17<br> Outside supported 13643 domain<br> 16, -0.5, -4.44822e+13<br> Outside supported domain<br> 17, 13644 -0.5, 1.86483e+20<br> Outside supported domain<br> 18, -0.5, -6.08254e+16<br> 13645 Outside supported domain<br> 19, -0.5, 2.55108e+23<br> Outside supported 13646 domain<br> 20, -0.5, -1.02182e+20<br> Outside supported domain<br> 21, 13647 -0.5, 4.28582e+26<br> Outside supported domain<br> 1, -0.5, 8.9348<br> 13648 Outside supported domain<br> 2, -0.5, -0.828751<br> Outside supported domain<br> 13649 3, -0.5, 193.409<br> Outside supported domain<br> 4, -0.5, -3.47059<br> 13650 Outside supported domain<br> *** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY 13651 ***<br> 13652 </p> 13653<h5> 13654<a name="special_function_error_rates_rep.error_logs.h29"></a> 13655 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_polygamma_with1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_polygamma_with1">Error 13656 Output For polygamma with compiler GNU C++ version 7.1.0 and library Rmath 13657 3.2.3 and test data Mathematica Data - negative arguments</a> 13658 </h5> 13659<p> 13660 <a name="errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_negative_arguments"></a>Outside 13661 supported domain<br> 1, -12.75, 19.6638<br> Outside supported domain<br> 13662 1, -12.25, 19.6608<br> Outside supported domain<br> 1, -11.75, 19.6576<br> 13663 Outside supported domain<br> 1, -11.25, 19.6542<br> Outside supported domain<br> 13664 1, -10.75, 19.6504<br> Outside supported domain<br> 1, -10.25, 19.6463<br> 13665 Outside supported domain<br> 1, -9.75, 19.6417<br> Outside supported domain<br> 13666 1, -9.25, 19.6367<br> Outside supported domain<br> 1, -8.75, 19.6312<br> 13667 Outside supported domain<br> 1, -8.25, 19.625<br> Outside supported domain<br> 13668 1, -7.75, 19.6181<br> Outside supported domain<br> 1, -7.25, 19.6104<br> 13669 Outside supported domain<br> 1, -6.75, 19.6015<br> Outside supported domain<br> 13670 1, -6.25, 19.5913<br> Outside supported domain<br> 1, -5.75, 19.5795<br> 13671 Outside supported domain<br> 1, -5.25, 19.5657<br> Outside supported domain<br> 13672 1, -4.75, 19.5493<br> Outside supported domain<br> 1, -4.25, 19.5294<br> 13673 Outside supported domain<br> 1, -3.75, 19.505<br> Outside supported domain<br> 13674 1, -3.25, 19.4741<br> Outside supported domain<br> 1, -2.75, 19.4339<br> 13675 Outside supported domain<br> 1, -2.25, 19.3794<br> Outside supported domain<br> 13676 1, -1.75, 19.3016<br> Outside supported domain<br> 1, -1.25, 19.1819<br> 13677 Outside supported domain<br> 1, -0.75, 18.9751<br> Outside supported domain<br> 13678 1, -0.25, 18.5419<br> Outside supported domain<br> 2, -12.75, -124.031<br> 13679 Outside supported domain<br> 2, -12.25, 124.019<br> Outside supported domain<br> 13680 2, -11.75, -124.032<br> Outside supported domain<br> 2, -11.25, 124.018<br> 13681 Outside supported domain<br> 2, -10.75, -124.033<br> Outside supported 13682 domain<br> 2, -10.25, 124.016<br> Outside supported domain<br> 2, -9.75, 13683 -124.035<br> Outside supported domain<br> 2, -9.25, 124.015<br> Outside 13684 supported domain<br> 2, -8.75, -124.037<br> Outside supported domain<br> 13685 2, -8.25, 124.012<br> Outside supported domain<br> 2, -7.75, -124.04<br> 13686 Outside supported domain<br> 2, -7.25, 124.009<br> Outside supported domain<br> 13687 2, -6.75, -124.044<br> Outside supported domain<br> 2, -6.25, 124.003<br> 13688 Outside supported domain<br> 2, -5.75, -124.051<br> Outside supported domain<br> 13689 2, -5.25, 123.995<br> Outside supported domain<br> 2, -4.75, -124.061<br> 13690 Outside supported domain<br> 2, -4.25, 123.981<br> Outside supported domain<br> 13691 2, -3.75, -124.08<br> Outside supported domain<br> 2, -3.25, 123.955<br> 13692 Outside supported domain<br> 2, -2.75, -124.118<br> Outside supported domain<br> 13693 2, -2.25, 123.897<br> Outside supported domain<br> 2, -1.75, -124.214<br> 13694 Outside supported domain<br> 2, -1.25, 123.721<br> Outside supported domain<br> 13695 2, -0.75, -124.587<br> Outside supported domain<br> 2, -0.25, 122.697<br> 13696 Outside supported domain<br> 3, -12.75, 1558.54<br> Outside supported domain<br> 13697 3, -12.25, 1558.54<br> Outside supported domain<br> 3, -11.75, 1558.54<br> 13698 Outside supported domain<br> 3, -11.25, 1558.54<br> Outside supported domain<br> 13699 3, -10.75, 1558.54<br> Outside supported domain<br> 3, -10.25, 1558.54<br> 13700 Outside supported domain<br> 3, -9.75, 1558.54<br> Outside supported domain<br> 13701 3, -9.25, 1558.54<br> Outside supported domain<br> 3, -8.75, 1558.54<br> 13702 Outside supported domain<br> 3, -8.25, 1558.54<br> Outside supported domain<br> 13703 3, -7.75, 1558.54<br> Outside supported domain<br> 3, -7.25, 1558.54<br> 13704 Outside supported domain<br> 3, -6.75, 1558.54<br> Outside supported domain<br> 13705 3, -6.25, 1558.54<br> Outside supported domain<br> 3, -5.75, 1558.54<br> 13706 Outside supported domain<br> 3, -5.25, 1558.54<br> Outside supported domain<br> 13707 3, -4.75, 1558.53<br> Outside supported domain<br> 3, -4.25, 1558.53<br> 13708 Outside supported domain<br> 3, -3.75, 1558.52<br> Outside supported domain<br> 13709 3, -3.25, 1558.51<br> Outside supported domain<br> 3, -2.75, 1558.49<br> 13710 Outside supported domain<br> 3, -2.25, 1558.46<br> Outside supported domain<br> 13711 3, -1.75, 1558.38<br> Outside supported domain<br> 3, -1.25, 1558.22<br> 13712 Outside supported domain<br> 3, -0.75, 1557.75<br> Outside supported domain<br> 13713 3, -0.25, 1555.76<br> Outside supported domain<br> 4, -12.75, -24481.6<br> 13714 Outside supported domain<br> 4, -12.25, 24481.6<br> Outside supported domain<br> 13715 4, -11.75, -24481.6<br> Outside supported domain<br> 4, -11.25, 24481.6<br> 13716 Outside supported domain<br> 4, -10.75, -24481.6<br> Outside supported 13717 domain<br> 4, -10.25, 24481.6<br> Outside supported domain<br> 4, -9.75, 13718 -24481.6<br> Outside supported domain<br> 4, -9.25, 24481.6<br> Outside 13719 supported domain<br> 4, -8.75, -24481.6<br> Outside supported domain<br> 13720 4, -8.25, 24481.6<br> Outside supported domain<br> 4, -7.75, -24481.6<br> 13721 Outside supported domain<br> 4, -7.25, 24481.6<br> Outside supported domain<br> 13722 4, -6.75, -24481.6<br> Outside supported domain<br> 4, -6.25, 24481.6<br> 13723 Outside supported domain<br> 4, -5.75, -24481.6<br> Outside supported domain<br> 13724 4, -5.25, 24481.6<br> Outside supported domain<br> *** FURTHER CONTENT 13725 HAS BEEN TRUNCATED FOR BREVITY ***<br> 13726 </p> 13727<h5> 13728<a name="special_function_error_rates_rep.error_logs.h30"></a> 13729 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_polygamma_with2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_polygamma_with2">Error 13730 Output For polygamma with compiler GNU C++ version 7.1.0 and library Rmath 13731 3.2.3 and test data Mathematica Data - large arguments</a> 13732 </h5> 13733<p> 13734 <a name="errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_large_arguments"></a>CAUTION: 13735 Gross error found at entry 211.<br> Found: -0 Expected -8.44974e-268 Error: 13736 3.79751e+40<br> 30, 8.58993e+09, -8.44974e-268<br> CAUTION: Gross error 13737 found at entry 212.<br> Found: -0 Expected -7.86943e-277 Error: 3.5367e+31<br> 13738 30, 1.71799e+10, -7.86943e-277<br> CAUTION: Gross error found at entry 213.<br> 13739 Found: -0 Expected -7.32898e-286 Error: 3.29381e+22<br> 30, 3.43597e+10, 13740 -7.32898e-286<br> CAUTION: Gross error found at entry 214.<br> Found: -0 13741 Expected -6.82564e-295 Error: 3.0676e+13<br> 30, 6.87195e+10, -6.82564e-295<br> 13742 CAUTION: Gross error found at entry 215.<br> Found: -0 Expected -6.35687e-304 13743 Error: 28568.3<br> 30, 1.37439e+11, -6.35687e-304<br> 13744 </p> 13745<h5> 13746<a name="special_function_error_rates_rep.error_logs.h31"></a> 13747 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w3"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w3">Error 13748 Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library GSL 13749 2.1 and test data Bessel Iv: Mathworld Data (large values)</a> 13750 </h5> 13751<p> 13752 <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Mathworld_Data_large_values_"></a>domain 13753 error<br> -1, 3.72917e-155, 1.86459e-155<br> domain error<br> -1.125, 13754 3.72917e-155, -1.34964e+173<br> 13755 </p> 13756<h5> 13757<a name="special_function_error_rates_rep.error_logs.h32"></a> 13758 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w4"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w4">Error 13759 Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library GSL 13760 2.1 and test data Bessel Iv: Random Data</a> 13761 </h5> 13762<p> 13763 <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Random_Data"></a>domain 13764 error<br> -80.4919, 24.7501, 4.18698e+28<br> domain error<br> -80.4919, 13765 63.7722, 2.03248e+06<br> domain error<br> -74.6026, 24.7501, 7.20977e+23<br> 13766 domain error<br> -74.6026, 63.7722, 8.7549e+08<br> domain error<br> -72.9046, 13767 24.7501, 1.04535e+22<br> domain error<br> -72.9046, 63.7722, 4.7162e+09<br> 13768 domain error<br> -62.3236, 24.7501, 3.65147e+14<br> domain error<br> 13769 -62.3236, 63.7722, 8.56683e+13<br> domain error<br> -55.7932, 24.7501, 13770 -7.70364e+09<br> domain error<br> -55.7932, 63.7722, 1.95969e+16<br> 13771 domain error<br> -44.3004, 9.50706, 2.93478e+22<br> domain error<br> 13772 -44.3004, 24.7501, 640.568<br> domain error<br> -44.3004, 63.7722, 8.05557e+19<br> 13773 domain error<br> -38.3666, 5.11399, 2.89105e+27<br> domain error<br> 13774 -38.3666, 9.50706, 8.80632e+16<br> domain error<br> -38.3666, 24.7501, 13775 0.389004<br> domain error<br> -38.3666, 63.7722, 3.06303e+21<br> underflow<br> 13776 81.1584, 0.00177219, 0<br> underflow<br> 81.1584, 0.00221773, 0<br> underflow<br> 13777 81.1584, 0.0074445, 6.08857e-319<br> underflow<br> 82.6752, 0.00177219, 13778 0<br> underflow<br> 82.6752, 0.00221773, 0<br> underflow<br> 82.6752, 13779 0.0074445, 0<br> underflow<br> 91.5014, 0.00177219, 0<br> underflow<br> 13780 91.5014, 0.00221773, 0<br> underflow<br> 91.5014, 0.0074445, 0<br> underflow<br> 13781 91.5014, 0.014336, 0<br> underflow<br> 91.5014, 0.0176092, 0<br> underflow<br> 13782 92.9777, 0.00177219, 0<br> underflow<br> 92.9777, 0.00221773, 0<br> underflow<br> 13783 92.9777, 0.0074445, 0<br> underflow<br> 92.9777, 0.014336, 0<br> underflow<br> 13784 92.9777, 0.0176092, 0<br> underflow<br> 93.539, 0.00177219, 0<br> underflow<br> 13785 93.539, 0.00221773, 0<br> underflow<br> 93.539, 0.0074445, 0<br> underflow<br> 13786 93.539, 0.014336, 0<br> underflow<br> 93.539, 0.0176092, 0<br> underflow<br> 13787 93.7736, 0.00177219, 0<br> underflow<br> 93.7736, 0.00221773, 0<br> underflow<br> 13788 93.7736, 0.0074445, 0<br> underflow<br> 93.7736, 0.014336, 0<br> underflow<br> 13789 93.7736, 0.0176092, 0<br> underflow<br> 98.5763, 0.00177219, 0<br> underflow<br> 13790 98.5763, 0.00221773, 0<br> underflow<br> 98.5763, 0.0074445, 0<br> underflow<br> 13791 98.5763, 0.014336, 0<br> underflow<br> 98.5763, 0.0176092, 0<br> underflow<br> 13792 99.2923, 0.00177219, 0<br> underflow<br> 99.2923, 0.00221773, 0<br> underflow<br> 13793 99.2923, 0.0074445, 0<br> underflow<br> 99.2923, 0.014336, 0<br> underflow<br> 13794 99.2923, 0.0176092, 0<br> 13795 </p> 13796<h5> 13797<a name="special_function_error_rates_rep.error_logs.h33"></a> 13798 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w5"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w5">Error 13799 Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library GSL 13800 2.1 and test data Bessel In: Random Data</a> 13801 </h5> 13802<p> 13803 <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_In_Random_Data"></a>underflow<br> 13804 70, 0.00177219, 1.75887e-314<br> underflow<br> 73, 0.00177219, 0<br> 13805 underflow<br> 73, 0.00221773, 4.24896e-322<br> underflow<br> 76, 0.00177219, 13806 0<br> underflow<br> 76, 0.00221773, 0<br> underflow<br> 79, 0.00177219, 13807 0<br> underflow<br> 79, 0.00221773, 0<br> underflow<br> 79, 0.0074445, 13808 1.38676e-309<br> underflow<br> 82, 0.00177219, 0<br> underflow<br> 13809 82, 0.00221773, 0<br> underflow<br> 82, 0.0074445, 1.33398e-322<br> underflow<br> 13810 85, 0.00177219, 0<br> underflow<br> 85, 0.00221773, 0<br> underflow<br> 13811 85, 0.0074445, 0<br> underflow<br> 85, 0.014336, 1.81568e-311<br> underflow<br> 13812 88, 0.00177219, 0<br> underflow<br> 88, 0.00221773, 0<br> underflow<br> 13813 88, 0.0074445, 0<br> underflow<br> 88, 0.014336, 9.88131e-324<br> underflow<br> 13814 88, 0.0176092, 7.34647e-316<br> 13815 </p> 13816<h5> 13817<a name="special_function_error_rates_rep.error_logs.h34"></a> 13818 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w6"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w6">Error 13819 Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library GSL 13820 2.1 and test data Bessel Iv: Mathworld Data</a> 13821 </h5> 13822<p> 13823 <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Mathworld_Data"></a>domain 13824 error<br> -4.99902, 2.125, 0.0267921<br> domain error<br> -5.5, 10, 597.578<br> 13825 domain error<br> -5.5, 100, 9.22363e+41<br> domain error<br> -10.0003, 13826 0.000976562, 1.41474e+35<br> domain error<br> -10.0003, 50, 1.07153e+20<br> 13827 domain error<br> -141.4, 100, 2066.28<br> 13828 </p> 13829<h5> 13830<a name="special_function_error_rates_rep.error_logs.h35"></a> 13831 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i2">Error 13832 Output For cyl_bessel_i (integer orders) with compiler GNU C++ version 7.1.0 13833 and library GSL 2.1 and test data Bessel In: Mathworld Data (Integer Version)</a> 13834 </h5> 13835<p> 13836 <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__GSL_2_1_Bessel_In_Mathworld_Data_Integer_Version_"></a>underflow<br> 13837 10, 1e-100, 0<br> 13838 </p> 13839<h5> 13840<a name="special_function_error_rates_rep.error_logs.h36"></a> 13841 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w7"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w7">Error 13842 Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library GSL 13843 2.1 and test data Bessel In: Mathworld Data</a> 13844 </h5> 13845<p> 13846 <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_In_Mathworld_Data"></a>domain 13847 error<br> -2, 0, 0<br> domain error<br> -5, 100, 9.47009e+41<br> domain 13848 error<br> -5, -1, -0.000271463<br> domain error<br> 10, -5, 0.00458004<br> 13849 domain error<br> -100, -200, 4.35275e+74<br> underflow<br> 10, 1e-100, 13850 0<br> 13851 </p> 13852<h5> 13853<a name="special_function_error_rates_rep.error_logs.h37"></a> 13854 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w8"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w8">Error 13855 Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library GSL 13856 2.1 and test data Bessel I1: Mathworld Data</a> 13857 </h5> 13858<p> 13859 <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_I1_Mathworld_Data"></a>domain 13860 error<br> 1, -2, -1.59064<br> domain error<br> 1, -8, -399.873<br> 13861 domain error<br> 1, -10, -2670.99<br> 13862 </p> 13863<h5> 13864<a name="special_function_error_rates_rep.error_logs.h38"></a> 13865 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w9"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w9">Error 13866 Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library GSL 13867 2.1 and test data Bessel I0: Mathworld Data</a> 13868 </h5> 13869<p> 13870 <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_I0_Mathworld_Data"></a>domain 13871 error<br> 0, -2, 2.27959<br> domain error<br> 0, -7, 168.594<br> domain 13872 error<br> 0, -1, 1.26607<br> 13873 </p> 13874<h5> 13875<a name="special_function_error_rates_rep.error_logs.h39"></a> 13876 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_0">Error 13877 Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library <cmath> 13878 and test data Bessel Iv: Mathworld Data (large values)</a> 13879 </h5> 13880<p> 13881 <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Mathworld_Data_large_values_"></a>Bad 13882 argument in __cyl_bessel_i.<br> -1, 3.72917e-155, 1.86459e-155<br> Bad 13883 argument in __cyl_bessel_i.<br> -1.125, 3.72917e-155, -1.34964e+173<br> 13884 </p> 13885<h5> 13886<a name="special_function_error_rates_rep.error_logs.h40"></a> 13887 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_1">Error 13888 Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library <cmath> 13889 and test data Bessel Iv: Random Data</a> 13890 </h5> 13891<p> 13892 <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Random_Data"></a>Bad 13893 argument in __cyl_bessel_i.<br> -80.4919, 24.7501, 4.18698e+28<br> Bad 13894 argument in __cyl_bessel_i.<br> -80.4919, 63.7722, 2.03248e+06<br> Bad 13895 argument in __cyl_bessel_i.<br> -74.6026, 24.7501, 7.20977e+23<br> Bad 13896 argument in __cyl_bessel_i.<br> -74.6026, 63.7722, 8.7549e+08<br> Bad argument 13897 in __cyl_bessel_i.<br> -72.9046, 24.7501, 1.04535e+22<br> Bad argument 13898 in __cyl_bessel_i.<br> -72.9046, 63.7722, 4.7162e+09<br> Bad argument in 13899 __cyl_bessel_i.<br> -62.3236, 24.7501, 3.65147e+14<br> Bad argument in 13900 __cyl_bessel_i.<br> -62.3236, 63.7722, 8.56683e+13<br> Bad argument in 13901 __cyl_bessel_i.<br> -55.7932, 24.7501, -7.70364e+09<br> Bad argument in 13902 __cyl_bessel_i.<br> -55.7932, 63.7722, 1.95969e+16<br> Bad argument in 13903 __cyl_bessel_i.<br> -44.3004, 9.50706, 2.93478e+22<br> Bad argument in 13904 __cyl_bessel_i.<br> -44.3004, 24.7501, 640.568<br> Bad argument in __cyl_bessel_i.<br> 13905 -44.3004, 63.7722, 8.05557e+19<br> Bad argument in __cyl_bessel_i.<br> 13906 -38.3666, 5.11399, 2.89105e+27<br> Bad argument in __cyl_bessel_i.<br> 13907 -38.3666, 9.50706, 8.80632e+16<br> Bad argument in __cyl_bessel_i.<br> 13908 -38.3666, 24.7501, 0.389004<br> Bad argument in __cyl_bessel_i.<br> -38.3666, 13909 63.7722, 3.06303e+21<br> 13910 </p> 13911<h5> 13912<a name="special_function_error_rates_rep.error_logs.h41"></a> 13913 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_2">Error 13914 Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library <cmath> 13915 and test data Bessel Iv: Mathworld Data</a> 13916 </h5> 13917<p> 13918 <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Mathworld_Data"></a>Bad 13919 argument in __cyl_bessel_i.<br> -4.99902, 2.125, 0.0267921<br> Bad argument 13920 in __cyl_bessel_i.<br> -5.5, 10, 597.578<br> Bad argument in __cyl_bessel_i.<br> 13921 -5.5, 100, 9.22363e+41<br> Bad argument in __cyl_bessel_i.<br> -10.0003, 13922 0.000976562, 1.41474e+35<br> Bad argument in __cyl_bessel_i.<br> -10.0003, 13923 50, 1.07153e+20<br> Bad argument in __cyl_bessel_i.<br> -141.4, 100, 2066.28<br> 13924 </p> 13925<h5> 13926<a name="special_function_error_rates_rep.error_logs.h42"></a> 13927 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i3"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i3">Error 13928 Output For cyl_bessel_i (integer orders) with compiler GNU C++ version 7.1.0 13929 and library <cmath> and test data Bessel In: Mathworld Data (Integer 13930 Version)</a> 13931 </h5> 13932<p> 13933 <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_In_Mathworld_Data_Integer_Version_"></a>Bad 13934 argument in __cyl_bessel_i.<br> -2, 0, 0<br> Bad argument in __cyl_bessel_i.<br> 13935 -5, 100, 9.47009e+41<br> Bad argument in __cyl_bessel_i.<br> -5, -1, -0.000271463<br> 13936 Bad argument in __cyl_bessel_i.<br> 10, -5, 0.00458004<br> Bad argument 13937 in __cyl_bessel_i.<br> -100, -200, 4.35275e+74<br> 13938 </p> 13939<h5> 13940<a name="special_function_error_rates_rep.error_logs.h43"></a> 13941 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i4"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i4">Error 13942 Output For cyl_bessel_i (integer orders) with compiler GNU C++ version 7.1.0 13943 and library <cmath> and test data Bessel I1: Mathworld Data (Integer 13944 Version)</a> 13945 </h5> 13946<p> 13947 <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_I1_Mathworld_Data_Integer_Version_"></a>Bad 13948 argument in __cyl_bessel_i.<br> 1, -2, -1.59064<br> Bad argument in __cyl_bessel_i.<br> 13949 1, -8, -399.873<br> Bad argument in __cyl_bessel_i.<br> 1, -10, -2670.99<br> 13950 </p> 13951<h5> 13952<a name="special_function_error_rates_rep.error_logs.h44"></a> 13953 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i5"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i5">Error 13954 Output For cyl_bessel_i (integer orders) with compiler GNU C++ version 7.1.0 13955 and library <cmath> and test data Bessel I0: Mathworld Data (Integer 13956 Version)</a> 13957 </h5> 13958<p> 13959 <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_I0_Mathworld_Data_Integer_Version_"></a>Bad 13960 argument in __cyl_bessel_i.<br> 0, -2, 2.27959<br> Bad argument in __cyl_bessel_i.<br> 13961 0, -7, 168.594<br> Bad argument in __cyl_bessel_i.<br> 0, -1, 1.26607<br> 13962 </p> 13963<h5> 13964<a name="special_function_error_rates_rep.error_logs.h45"></a> 13965 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_3"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_3">Error 13966 Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library <cmath> 13967 and test data Bessel In: Mathworld Data</a> 13968 </h5> 13969<p> 13970 <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_In_Mathworld_Data"></a>Bad 13971 argument in __cyl_bessel_i.<br> -2, 0, 0<br> Bad argument in __cyl_bessel_i.<br> 13972 -5, 100, 9.47009e+41<br> Bad argument in __cyl_bessel_i.<br> -5, -1, -0.000271463<br> 13973 Bad argument in __cyl_bessel_i.<br> 10, -5, 0.00458004<br> Bad argument 13974 in __cyl_bessel_i.<br> -100, -200, 4.35275e+74<br> 13975 </p> 13976<h5> 13977<a name="special_function_error_rates_rep.error_logs.h46"></a> 13978 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_4"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_4">Error 13979 Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library <cmath> 13980 and test data Bessel I1: Mathworld Data</a> 13981 </h5> 13982<p> 13983 <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_I1_Mathworld_Data"></a>Bad 13984 argument in __cyl_bessel_i.<br> 1, -2, -1.59064<br> Bad argument in __cyl_bessel_i.<br> 13985 1, -8, -399.873<br> Bad argument in __cyl_bessel_i.<br> 1, -10, -2670.99<br> 13986 </p> 13987<h5> 13988<a name="special_function_error_rates_rep.error_logs.h47"></a> 13989 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_5"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_5">Error 13990 Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library <cmath> 13991 and test data Bessel I0: Mathworld Data</a> 13992 </h5> 13993<p> 13994 <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_I0_Mathworld_Data"></a>Bad 13995 argument in __cyl_bessel_i.<br> 0, -2, 2.27959<br> Bad argument in __cyl_bessel_i.<br> 13996 0, -7, 168.594<br> Bad argument in __cyl_bessel_i.<br> 0, -1, 1.26607<br> 13997 </p> 13998<h5> 13999<a name="special_function_error_rates_rep.error_logs.h48"></a> 14000 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w3"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w3">Error 14001 Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library GSL 14002 2.1 and test data Bessel J: Random Data</a> 14003 </h5> 14004<p> 14005 <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Random_Data"></a>underflow<br> 14006 63.8868, 5.5381e-05, 0<br> underflow<br> 63.8868, 6.9304e-05, 0<br> underflow<br> 14007 63.8868, 0.000232641, 0<br> underflow<br> 63.8868, 0.000448, 8.39912e-323<br> 14008 underflow<br> 63.8868, 0.000550287, 4.32897e-317<br> 14009 </p> 14010<h5> 14011<a name="special_function_error_rates_rep.error_logs.h49"></a> 14012 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w4"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w4">Error 14013 Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library GSL 14014 2.1 and test data Bessel J: Mathworld Data (large values)</a> 14015 </h5> 14016<p> 14017 <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Mathworld_Data_large_values_"></a>domain 14018 error<br> -0.5, 1.2459e-206, 7.14823e+102<br> domain error<br> -256, 14019 8, 0<br> domain error<br> -2.5, 4, -0.0145679<br> 14020 </p> 14021<h5> 14022<a name="special_function_error_rates_rep.error_logs.h50"></a> 14023 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w5"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w5">Error 14024 Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library GSL 14025 2.1 and test data Bessel J: Mathworld Data</a> 14026 </h5> 14027<p> 14028 <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Mathworld_Data"></a>domain 14029 error<br> -5.5, 3.1416, -2.5582<br> domain error<br> -5.5, 10000, 0.00244984<br> 14030 domain error<br> -5.5, 10000, 0.00244984<br> domain error<br> -5.5, 1e+06, 14031 0.000279243<br> domain error<br> -0.5, 101, 0.0708185<br> domain error<br> 14032 -10.0003, 0.000976562, 1.41474e+35<br> domain error<br> -10.0003, 15, -0.0902239<br> 14033 domain error<br> -10.0003, 100, -0.0547614<br> domain error<br> -10.0003, 14034 20000, -0.00556869<br> domain error<br> -8.5, 12.5664, -0.257087<br> 14035 </p> 14036<h5> 14037<a name="special_function_error_rates_rep.error_logs.h51"></a> 14038 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i3"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i3">Error 14039 Output For cyl_bessel_j (integer orders) with compiler GNU C++ version 7.1.0 14040 and library GSL 2.1 and test data Bessel JN: Mathworld Data (Integer Version)</a> 14041 </h5> 14042<p> 14043 <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__GSL_2_1_Bessel_JN_Mathworld_Data_Integer_Version_"></a>underflow<br> 14044 10, 1e-100, 0<br> 14045 </p> 14046<h5> 14047<a name="special_function_error_rates_rep.error_logs.h52"></a> 14048 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w6"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w6">Error 14049 Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library GSL 14050 2.1 and test data Bessel JN: Mathworld Data</a> 14051 </h5> 14052<p> 14053 <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_JN_Mathworld_Data"></a>domain 14054 error<br> -1, 1.25, -0.510623<br> domain error<br> -2, 0, 0<br> domain 14055 error<br> 5, -10, 0.234062<br> domain error<br> -5, 1e+06, 0.000725964<br> 14056 domain error<br> -5, -1, 0.000249758<br> domain error<br> 10, -10, 0.207486<br> 14057 domain error<br> 10, -5, 0.0014678<br> domain error<br> -10, 1e+06, -0.000331079<br> 14058 underflow<br> 10, 1e-100, 0<br> 14059 </p> 14060<h5> 14061<a name="special_function_error_rates_rep.error_logs.h53"></a> 14062 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w7"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w7">Error 14063 Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library GSL 14064 2.1 and test data Bessel J1: Mathworld Data</a> 14065 </h5> 14066<p> 14067 <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J1_Mathworld_Data"></a>domain 14068 error<br> 1, -2, -0.576725<br> domain error<br> 1, -8, -0.234636<br> 14069 domain error<br> 1, -10, -0.0434727<br> 14070 </p> 14071<h5> 14072<a name="special_function_error_rates_rep.error_logs.h54"></a> 14073 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w8"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w8">Error 14074 Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library GSL 14075 2.1 and test data Bessel J0: Mathworld Data</a> 14076 </h5> 14077<p> 14078 <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J0_Mathworld_Data"></a>domain 14079 error<br> 0, -2, 0.223891<br> domain error<br> 0, -8, 0.171651<br> 14080 domain error<br> 0, -10, -0.245936<br> 14081 </p> 14082<h5> 14083<a name="special_function_error_rates_rep.error_logs.h55"></a> 14084 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w9"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w9">Error 14085 Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library <cmath> 14086 and test data Bessel J: Mathworld Data (large values)</a> 14087 </h5> 14088<p> 14089 <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J_Mathworld_Data_large_values_"></a>Bad 14090 argument in __cyl_bessel_j.<br> -0.5, 1.2459e-206, 7.14823e+102<br> Bad 14091 argument in __cyl_bessel_j.<br> -256, 8, 1.46866e-353<br> Bad argument 14092 in __cyl_bessel_j.<br> -2.5, 4, -0.0145679<br> 14093 </p> 14094<h5> 14095<a name="special_function_error_rates_rep.error_logs.h56"></a> 14096 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_0">Error 14097 Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library <cmath> 14098 and test data Bessel J: Mathworld Data</a> 14099 </h5> 14100<p> 14101 <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J_Mathworld_Data"></a>Bad 14102 argument in __cyl_bessel_j.<br> -5.5, 3.1416, -2.5582<br> Bad argument 14103 in __cyl_bessel_j.<br> -5.5, 10000, 0.00244984<br> Bad argument in __cyl_bessel_j.<br> 14104 -5.5, 10000, 0.00244984<br> Bad argument in __cyl_bessel_j.<br> -5.5, 1e+06, 14105 0.000279243<br> Bad argument in __cyl_bessel_j.<br> -0.5, 101, 0.0708185<br> 14106 Bad argument in __cyl_bessel_j.<br> -10.0003, 0.000976562, 1.41474e+35<br> 14107 Bad argument in __cyl_bessel_j.<br> -10.0003, 15, -0.0902239<br> Bad argument 14108 in __cyl_bessel_j.<br> -10.0003, 100, -0.0547614<br> Bad argument in __cyl_bessel_j.<br> 14109 -10.0003, 20000, -0.00556869<br> Bad argument in __cyl_bessel_j.<br> -8.5, 14110 12.5664, -0.257087<br> 14111 </p> 14112<h5> 14113<a name="special_function_error_rates_rep.error_logs.h57"></a> 14114 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i4"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i4">Error 14115 Output For cyl_bessel_j (integer orders) with compiler GNU C++ version 7.1.0 14116 and library <cmath> and test data Bessel JN: Mathworld Data (Integer 14117 Version)</a> 14118 </h5> 14119<p> 14120 <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_JN_Mathworld_Data_Integer_Version_"></a>Bad 14121 argument in __cyl_bessel_j.<br> -1, 1.25, -0.510623<br> Bad argument in 14122 __cyl_bessel_j.<br> -2, 0, 0<br> Bad argument in __cyl_bessel_j.<br> 14123 5, -10, 0.234062<br> Bad argument in __cyl_bessel_j.<br> -5, 1e+06, 0.000725964<br> 14124 Bad argument in __cyl_bessel_j.<br> -5, -1, 0.000249758<br> Bad argument 14125 in __cyl_bessel_j.<br> 10, -10, 0.207486<br> Bad argument in __cyl_bessel_j.<br> 14126 10, -5, 0.0014678<br> Bad argument in __cyl_bessel_j.<br> -10, 1e+06, -0.000331079<br> 14127 CAUTION: Gross error found at entry 15.<br> Found: 0.0042409 Expected 0.00128318 14128 Error: 2.305<br> 1000, 100000, 0.00128318<br> 14129 </p> 14130<h5> 14131<a name="special_function_error_rates_rep.error_logs.h58"></a> 14132 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i5"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i5">Error 14133 Output For cyl_bessel_j (integer orders) with compiler GNU C++ version 7.1.0 14134 and library <cmath> and test data Bessel J1: Mathworld Data (Integer 14135 Version)</a> 14136 </h5> 14137<p> 14138 <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_J1_Mathworld_Data_Integer_Version_"></a>Bad 14139 argument in __cyl_bessel_j.<br> 1, -2, -0.576725<br> Bad argument in __cyl_bessel_j.<br> 14140 1, -8, -0.234636<br> Bad argument in __cyl_bessel_j.<br> 1, -10, -0.0434727<br> 14141 </p> 14142<h5> 14143<a name="special_function_error_rates_rep.error_logs.h59"></a> 14144 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i6"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i6">Error 14145 Output For cyl_bessel_j (integer orders) with compiler GNU C++ version 7.1.0 14146 and library <cmath> and test data Bessel J0: Mathworld Data (Integer 14147 Version)</a> 14148 </h5> 14149<p> 14150 <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_J0_Mathworld_Data_Integer_Version_"></a>Bad 14151 argument in __cyl_bessel_j.<br> 0, -2, 0.223891<br> Bad argument in __cyl_bessel_j.<br> 14152 0, -8, 0.171651<br> Bad argument in __cyl_bessel_j.<br> 0, -10, -0.245936<br> 14153 </p> 14154<h5> 14155<a name="special_function_error_rates_rep.error_logs.h60"></a> 14156 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_1">Error 14157 Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library <cmath> 14158 and test data Bessel JN: Mathworld Data</a> 14159 </h5> 14160<p> 14161 <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_JN_Mathworld_Data"></a>Bad 14162 argument in __cyl_bessel_j.<br> -1, 1.25, -0.510623<br> Bad argument in 14163 __cyl_bessel_j.<br> -2, 0, 0<br> Bad argument in __cyl_bessel_j.<br> 14164 5, -10, 0.234062<br> Bad argument in __cyl_bessel_j.<br> -5, 1e+06, 0.000725964<br> 14165 Bad argument in __cyl_bessel_j.<br> -5, -1, 0.000249758<br> Bad argument 14166 in __cyl_bessel_j.<br> 10, -10, 0.207486<br> Bad argument in __cyl_bessel_j.<br> 14167 10, -5, 0.0014678<br> Bad argument in __cyl_bessel_j.<br> -10, 1e+06, -0.000331079<br> 14168 CAUTION: Gross error found at entry 15.<br> Found: 0.0042409 Expected 0.00128318 14169 Error: 2.305<br> 1000, 100000, 0.00128318<br> 14170 </p> 14171<h5> 14172<a name="special_function_error_rates_rep.error_logs.h61"></a> 14173 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_2">Error 14174 Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library <cmath> 14175 and test data Bessel J1: Mathworld Data</a> 14176 </h5> 14177<p> 14178 <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J1_Mathworld_Data"></a>Bad 14179 argument in __cyl_bessel_j.<br> 1, -2, -0.576725<br> Bad argument in __cyl_bessel_j.<br> 14180 1, -8, -0.234636<br> Bad argument in __cyl_bessel_j.<br> 1, -10, -0.0434727<br> 14181 </p> 14182<h5> 14183<a name="special_function_error_rates_rep.error_logs.h62"></a> 14184 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_3"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_3">Error 14185 Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library <cmath> 14186 and test data Bessel J0: Mathworld Data</a> 14187 </h5> 14188<p> 14189 <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J0_Mathworld_Data"></a>Bad 14190 argument in __cyl_bessel_j.<br> 0, -2, 0.223891<br> Bad argument in __cyl_bessel_j.<br> 14191 0, -8, 0.171651<br> Bad argument in __cyl_bessel_j.<br> 0, -10, -0.245936<br> 14192 </p> 14193<h5> 14194<a name="special_function_error_rates_rep.error_logs.h63"></a> 14195 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_wi"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_wi">Error 14196 Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library GSL 14197 2.1 and test data Bessel Kv: Random Data</a> 14198 </h5> 14199<p> 14200 <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Random_Data"></a>domain 14201 error<br> -80.4919, 24.7501, 6.57902e+28<br> domain error<br> -80.4919, 14202 63.7722, 2.39552e-09<br> domain error<br> -80.4919, 125.28, 3.06904e-45<br> 14203 domain error<br> -80.4919, 255.547, 2.30343e-107<br> domain error<br> 14204 -80.4919, 503.011, 1.20315e-217<br> domain error<br> -80.4919, 1007.46, 14205 0<br> domain error<br> -80.4919, 1185.4, 0<br> domain error<br> -80.4919, 14206 3534.52, 0<br> domain error<br> -80.4919, 8071.55, 0<br> domain error<br> 14207 -80.4919, 16229.2, 0<br> domain error<br> -80.4919, 32066.2, 0<br> domain 14208 error<br> -80.4919, 36367.9, 0<br> domain error<br> -74.6026, 24.7501, 14209 1.19405e+24<br> domain error<br> -74.6026, 63.7722, 5.81897e-12<br> domain 14210 error<br> -74.6026, 125.28, 9.89214e-47<br> domain error<br> -74.6026, 14211 255.547, 3.9726e-108<br> domain error<br> -74.6026, 503.011, 4.87462e-218<br> 14212 domain error<br> -74.6026, 1007.46, 0<br> domain error<br> -74.6026, 14213 1185.4, 0<br> domain error<br> -74.6026, 3534.52, 0<br> domain error<br> 14214 -74.6026, 8071.55, 0<br> domain error<br> -74.6026, 16229.2, 0<br> domain 14215 error<br> -74.6026, 32066.2, 0<br> domain error<br> -74.6026, 36367.9, 14216 0<br> domain error<br> -72.9046, 24.7501, 5.5618e+22<br> domain error<br> 14217 -72.9046, 63.7722, 1.09452e-12<br> domain error<br> -72.9046, 125.28, 3.8393e-47<br> 14218 domain error<br> -72.9046, 255.547, 2.45173e-108<br> domain error<br> 14219 -72.9046, 503.011, 3.80454e-218<br> domain error<br> -72.9046, 1007.46, 14220 0<br> domain error<br> -72.9046, 1185.4, 0<br> domain error<br> -72.9046, 14221 3534.52, 0<br> domain error<br> -72.9046, 8071.55, 0<br> domain error<br> 14222 -72.9046, 16229.2, 0<br> domain error<br> -72.9046, 32066.2, 0<br> domain 14223 error<br> -72.9046, 36367.9, 0<br> domain error<br> -62.3236, 24.7501, 14224 6.74518e+14<br> domain error<br> -62.3236, 63.7722, 6.54531e-17<br> domain 14225 error<br> -62.3236, 125.28, 1.65653e-49<br> domain error<br> -62.3236, 14226 255.547, 1.54767e-109<br> domain error<br> -62.3236, 503.011, 9.22721e-219<br> 14227 domain error<br> -62.3236, 1007.46, 0<br> domain error<br> -62.3236, 14228 1185.4, 0<br> domain error<br> -62.3236, 3534.52, 0<br> domain error<br> 14229 -62.3236, 8071.55, 0<br> domain error<br> -62.3236, 16229.2, 0<br> domain 14230 error<br> -62.3236, 32066.2, 0<br> domain error<br> -62.3236, 36367.9, 14231 0<br> domain error<br> -55.7932, 24.7501, 2.00028e+10<br> domain error<br> 14232 -55.7932, 63.7722, 3.01107e-19<br> domain error<br> -55.7932, 125.28, 8.54693e-51<br> 14233 domain error<br> -55.7932, 255.547, 3.47666e-110<br> domain error<br> 14234 -55.7932, 503.011, 4.29705e-219<br> domain error<br> -55.7932, 1007.46, 14235 0<br> domain error<br> -55.7932, 1185.4, 0<br> domain error<br> -55.7932, 14236 3534.52, 0<br> domain error<br> -55.7932, 8071.55, 0<br> domain error<br> 14237 -55.7932, 16229.2, 0<br> domain error<br> -55.7932, 32066.2, 0<br> domain 14238 error<br> -55.7932, 36367.9, 0<br> domain error<br> -44.3004, 9.50706, 14239 5.6936e+22<br> domain error<br> -44.3004, 24.7501, 1242.73<br> domain 14240 error<br> -44.3004, 63.7722, 7.99341e-23<br> domain error<br> -44.3004, 14241 125.28, 9.88149e-53<br> domain error<br> -44.3004, 255.547, 3.73007e-111<br> 14242 domain error<br> -44.3004, 503.011, 1.37367e-219<br> domain error<br> 14243 -44.3004, 1007.46, 0<br> domain error<br> -44.3004, 1185.4, 0<br> domain 14244 error<br> -44.3004, 3534.52, 0<br> domain error<br> -44.3004, 8071.55, 14245 0<br> domain error<br> -44.3004, 16229.2, 0<br> domain error<br> -44.3004, 14246 32066.2, 0<br> domain error<br> -44.3004, 36367.9, 0<br> domain error<br> 14247 -38.3666, 5.11399, 4.97154e+27<br> domain error<br> -38.3666, 9.50706, 14248 1.51436e+17<br> domain error<br> -38.3666, 24.7501, 0.639495<br> domain 14249 error<br> -38.3666, 63.7722, 2.19334e-24<br> domain error<br> -38.3666, 14250 125.28, 1.45351e-53<br> domain error<br> -38.3666, 255.547, 1.43713e-111<br> 14251 domain error<br> -38.3666, 503.011, 8.44445e-220<br> domain error<br> 14252 -38.3666, 1007.46, 0<br> domain error<br> -38.3666, 1185.4, 0<br> domain 14253 error<br> -38.3666, 3534.52, 0<br> domain error<br> -38.3666, 8071.55, 14254 0<br> domain error<br> -38.3666, 16229.2, 0<br> domain error<br> -38.3666, 14255 32066.2, 0<br> domain error<br> -38.3666, 36367.9, 0<br> underflow<br> 14256 9.3763, 1007.46, 0<br> underflow<br> 9.3763, 1185.4, 0<br> underflow<br> 14257 9.3763, 3534.52, 0<br> underflow<br> 9.3763, 8071.55, 0<br> underflow<br> 14258 9.3763, 16229.2, 0<br> underflow<br> 9.3763, 32066.2, 0<br> underflow<br> 14259 9.3763, 36367.9, 0<br> underflow<br> 9.44412, 1007.46, 0<br> underflow<br> 14260 9.44412, 1185.4, 0<br> underflow<br> 9.44412, 3534.52, 0<br> underflow<br> 14261 9.44412, 8071.55, 0<br> underflow<br> 9.44412, 16229.2, 0<br> underflow<br> 14262 9.44412, 32066.2, 0<br> underflow<br> 9.44412, 36367.9, 0<br> underflow<br> 14263 26.4719, 1007.46, 0<br> underflow<br> 26.4719, 1185.4, 0<br> underflow<br> 14264 26.4719, 3534.52, 0<br> underflow<br> 26.4719, 8071.55, 0<br> underflow<br> 14265 26.4719, 16229.2, 0<br> underflow<br> 26.4719, 32066.2, 0<br> underflow<br> 14266 26.4719, 36367.9, 0<br> underflow<br> 62.9447, 1007.46, 0<br> underflow<br> 14267 62.9447, 1185.4, 0<br> underflow<br> 62.9447, 3534.52, 0<br> underflow<br> 14268 62.9447, 8071.55, 0<br> underflow<br> 62.9447, 16229.2, 0<br> underflow<br> 14269 *** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br> 14270 </p> 14271<h5> 14272<a name="special_function_error_rates_rep.error_logs.h64"></a> 14273 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w0">Error 14274 Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library GSL 14275 2.1 and test data Bessel Kn: Random Data</a> 14276 </h5> 14277<p> 14278 <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kn_Random_Data"></a>underflow<br> 14279 0, 1007.46, 0<br> underflow<br> 0, 1185.4, 0<br> underflow<br> 0, 3534.52, 14280 0<br> underflow<br> 0, 8071.55, 0<br> underflow<br> 0, 16229.2, 0<br> 14281 underflow<br> 0, 32066.2, 0<br> underflow<br> 0, 36367.9, 0<br> underflow<br> 14282 1, 1007.46, 0<br> underflow<br> 1, 1185.4, 0<br> underflow<br> 1, 3534.52, 14283 0<br> underflow<br> 1, 8071.55, 0<br> underflow<br> 1, 16229.2, 0<br> 14284 underflow<br> 1, 32066.2, 0<br> underflow<br> 1, 36367.9, 0<br> underflow<br> 14285 4, 1007.46, 0<br> underflow<br> 4, 1185.4, 0<br> underflow<br> 4, 3534.52, 14286 0<br> underflow<br> 4, 8071.55, 0<br> underflow<br> 4, 16229.2, 0<br> 14287 underflow<br> 4, 32066.2, 0<br> underflow<br> 4, 36367.9, 0<br> underflow<br> 14288 7, 1007.46, 0<br> underflow<br> 7, 1185.4, 0<br> underflow<br> 7, 3534.52, 14289 0<br> underflow<br> 7, 8071.55, 0<br> underflow<br> 7, 16229.2, 0<br> 14290 underflow<br> 7, 32066.2, 0<br> underflow<br> 7, 36367.9, 0<br> underflow<br> 14291 10, 1007.46, 0<br> underflow<br> 10, 1185.4, 0<br> underflow<br> 10, 14292 3534.52, 0<br> underflow<br> 10, 8071.55, 0<br> underflow<br> 10, 16229.2, 14293 0<br> underflow<br> 10, 32066.2, 0<br> underflow<br> 10, 36367.9, 0<br> 14294 underflow<br> 13, 1007.46, 0<br> underflow<br> 13, 1185.4, 0<br> underflow<br> 14295 13, 3534.52, 0<br> underflow<br> 13, 8071.55, 0<br> underflow<br> 13, 14296 16229.2, 0<br> underflow<br> 13, 32066.2, 0<br> underflow<br> 13, 36367.9, 14297 0<br> underflow<br> 16, 1007.46, 0<br> underflow<br> 16, 1185.4, 0<br> 14298 underflow<br> 16, 3534.52, 0<br> underflow<br> 16, 8071.55, 0<br> underflow<br> 14299 16, 16229.2, 0<br> underflow<br> 16, 32066.2, 0<br> underflow<br> 16, 14300 36367.9, 0<br> underflow<br> 19, 1007.46, 0<br> underflow<br> 19, 1185.4, 14301 0<br> underflow<br> 19, 3534.52, 0<br> underflow<br> 19, 8071.55, 0<br> 14302 underflow<br> 19, 16229.2, 0<br> underflow<br> 19, 32066.2, 0<br> underflow<br> 14303 19, 36367.9, 0<br> underflow<br> 22, 1007.46, 0<br> underflow<br> 22, 14304 1185.4, 0<br> underflow<br> 22, 3534.52, 0<br> underflow<br> 22, 8071.55, 14305 0<br> underflow<br> 22, 16229.2, 0<br> underflow<br> 22, 32066.2, 0<br> 14306 underflow<br> 22, 36367.9, 0<br> underflow<br> 25, 1007.46, 0<br> underflow<br> 14307 25, 1185.4, 0<br> underflow<br> 25, 3534.52, 0<br> underflow<br> 25, 14308 8071.55, 0<br> underflow<br> 25, 16229.2, 0<br> underflow<br> 25, 32066.2, 14309 0<br> underflow<br> 25, 36367.9, 0<br> underflow<br> 28, 1007.46, 0<br> 14310 underflow<br> 28, 1185.4, 0<br> underflow<br> 28, 3534.52, 0<br> underflow<br> 14311 28, 8071.55, 0<br> underflow<br> 28, 16229.2, 0<br> underflow<br> 28, 14312 32066.2, 0<br> underflow<br> 28, 36367.9, 0<br> underflow<br> 31, 1007.46, 14313 0<br> underflow<br> 31, 1185.4, 0<br> underflow<br> 31, 3534.52, 0<br> 14314 underflow<br> 31, 8071.55, 0<br> underflow<br> 31, 16229.2, 0<br> underflow<br> 14315 31, 32066.2, 0<br> underflow<br> 31, 36367.9, 0<br> underflow<br> 34, 14316 1007.46, 0<br> underflow<br> 34, 1185.4, 0<br> underflow<br> 34, 3534.52, 14317 0<br> underflow<br> 34, 8071.55, 0<br> underflow<br> 34, 16229.2, 0<br> 14318 underflow<br> 34, 32066.2, 0<br> underflow<br> 34, 36367.9, 0<br> underflow<br> 14319 37, 1007.46, 0<br> underflow<br> 37, 1185.4, 0<br> underflow<br> 37, 14320 3534.52, 0<br> underflow<br> 37, 8071.55, 0<br> underflow<br> 37, 16229.2, 14321 0<br> underflow<br> 37, 32066.2, 0<br> underflow<br> 37, 36367.9, 0<br> 14322 underflow<br> 40, 1007.46, 0<br> underflow<br> 40, 1185.4, 0<br> underflow<br> 14323 40, 3534.52, 0<br> underflow<br> 40, 8071.55, 0<br> underflow<br> 40, 14324 16229.2, 0<br> underflow<br> 40, 32066.2, 0<br> underflow<br> 40, 36367.9, 14325 0<br> underflow<br> 43, 1007.46, 0<br> underflow<br> 43, 1185.4, 0<br> 14326 underflow<br> 43, 3534.52, 0<br> underflow<br> 43, 8071.55, 0<br> underflow<br> 14327 43, 16229.2, 0<br> underflow<br> 43, 32066.2, 0<br> underflow<br> 43, 14328 36367.9, 0<br> underflow<br> 46, 1007.46, 0<br> underflow<br> 46, 1185.4, 14329 0<br> underflow<br> 46, 3534.52, 0<br> underflow<br> 46, 8071.55, 0<br> 14330 underflow<br> 46, 16229.2, 0<br> underflow<br> 46, 32066.2, 0<br> underflow<br> 14331 46, 36367.9, 0<br> underflow<br> 49, 1007.46, 0<br> underflow<br> 49, 14332 1185.4, 0<br> underflow<br> 49, 3534.52, 0<br> underflow<br> 49, 8071.55, 14333 0<br> underflow<br> 49, 16229.2, 0<br> underflow<br> 49, 32066.2, 0<br> 14334 underflow<br> 49, 36367.9, 0<br> underflow<br> 52, 1007.46, 0<br> underflow<br> 14335 52, 1185.4, 0<br> underflow<br> 52, 3534.52, 0<br> underflow<br> 52, 14336 8071.55, 0<br> underflow<br> 52, 16229.2, 0<br> underflow<br> 52, 32066.2, 14337 0<br> underflow<br> 52, 36367.9, 0<br> underflow<br> 55, 1007.46, 0<br> 14338 underflow<br> 55, 1185.4, 0<br> underflow<br> 55, 3534.52, 0<br> underflow<br> 14339 55, 8071.55, 0<br> underflow<br> 55, 16229.2, 0<br> underflow<br> 55, 14340 32066.2, 0<br> underflow<br> 55, 36367.9, 0<br> underflow<br> 58, 1007.46, 14341 0<br> underflow<br> 58, 1185.4, 0<br> underflow<br> 58, 3534.52, 0<br> 14342 underflow<br> 58, 8071.55, 0<br> underflow<br> 58, 16229.2, 0<br> underflow<br> 14343 58, 32066.2, 0<br> underflow<br> 58, 36367.9, 0<br> underflow<br> 61, 14344 1007.46, 0<br> underflow<br> 61, 1185.4, 0<br> underflow<br> 61, 3534.52, 14345 0<br> underflow<br> 61, 8071.55, 0<br> underflow<br> 61, 16229.2, 0<br> 14346 underflow<br> 61, 32066.2, 0<br> underflow<br> 61, 36367.9, 0<br> underflow<br> 14347 64, 1007.46, 0<br> underflow<br> 64, 1185.4, 0<br> underflow<br> 64, 14348 3534.52, 0<br> underflow<br> 64, 8071.55, 0<br> underflow<br> 64, 16229.2, 14349 0<br> underflow<br> 64, 32066.2, 0<br> underflow<br> 64, 36367.9, 0<br> 14350 underflow<br> 67, 1007.46, 0<br> underflow<br> 67, 1185.4, 0<br> underflow<br> 14351 67, 3534.52, 0<br> underflow<br> 67, 8071.55, 0<br> underflow<br> 67, 14352 16229.2, 0<br> *** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br> 14353 </p> 14354<h5> 14355<a name="special_function_error_rates_rep.error_logs.h65"></a> 14356 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w1">Error 14357 Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library GSL 14358 2.1 and test data Bessel Kv: Mathworld Data (large values)</a> 14359 </h5> 14360<p> 14361 <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Mathworld_Data_large_values_"></a>domain 14362 error<br> -1, 3.72917e-155, 2.68156e+154<br> domain error<br> -1.125, 14363 3.72917e-155, 5.53984e+173<br> 14364 </p> 14365<h5> 14366<a name="special_function_error_rates_rep.error_logs.h66"></a> 14367 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w2">Error 14368 Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library GSL 14369 2.1 and test data Bessel Kv: Mathworld Data</a> 14370 </h5> 14371<p> 14372 <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Mathworld_Data"></a>domain 14373 error<br> -5.5, 10, 7.33045e-05<br> domain error<br> -5.5, 100, 5.41275e-45<br> 14374 domain error<br> -141.399, 50, 1.30185e+42<br> 14375 </p> 14376<h5> 14377<a name="special_function_error_rates_rep.error_logs.h67"></a> 14378 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w3"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w3">Error 14379 Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library GSL 14380 2.1 and test data Bessel Kn: Mathworld Data</a> 14381 </h5> 14382<p> 14383 <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kn_Mathworld_Data"></a>domain 14384 error<br> -5, 100, 5.27326e-45<br> domain error<br> -10, 1, 1.80713e+08<br> 14385 domain error<br> -1000, 700, 6.51562e-31<br> 14386 </p> 14387<h5> 14388<a name="special_function_error_rates_rep.error_logs.h68"></a> 14389 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w4"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w4">Error 14390 Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library <cmath> 14391 and test data Bessel Kv: Random Data</a> 14392 </h5> 14393<p> 14394 <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Random_Data"></a>Bad 14395 argument in __cyl_bessel_k.<br> -80.4919, 24.7501, 6.57902e+28<br> Bad 14396 argument in __cyl_bessel_k.<br> -80.4919, 63.7722, 2.39552e-09<br> Bad 14397 argument in __cyl_bessel_k.<br> -80.4919, 125.28, 3.06904e-45<br> Bad argument 14398 in __cyl_bessel_k.<br> -80.4919, 255.547, 2.30343e-107<br> Bad argument 14399 in __cyl_bessel_k.<br> -80.4919, 503.011, 1.20315e-217<br> Bad argument 14400 in __cyl_bessel_k.<br> -80.4919, 1007.46, 2.86537e-438<br> Bad argument 14401 in __cyl_bessel_k.<br> -80.4919, 1185.4, 8.63263e-516<br> Bad argument 14402 in __cyl_bessel_k.<br> -80.4919, 3534.52, 5.01367e-1537<br> Bad argument 14403 in __cyl_bessel_k.<br> -80.4919, 8071.55, 7.76555e-3508<br> Bad argument 14404 in __cyl_bessel_k.<br> -80.4919, 16229.2, 0<br> Bad argument in __cyl_bessel_k.<br> 14405 -80.4919, 32066.2, 0<br> Bad argument in __cyl_bessel_k.<br> -80.4919, 14406 36367.9, 0<br> Bad argument in __cyl_bessel_k.<br> -74.6026, 24.7501, 1.19405e+24<br> 14407 Bad argument in __cyl_bessel_k.<br> -74.6026, 63.7722, 5.81897e-12<br> 14408 Bad argument in __cyl_bessel_k.<br> -74.6026, 125.28, 9.89214e-47<br> Bad 14409 argument in __cyl_bessel_k.<br> -74.6026, 255.547, 3.9726e-108<br> Bad 14410 argument in __cyl_bessel_k.<br> -74.6026, 503.011, 4.87462e-218<br> Bad 14411 argument in __cyl_bessel_k.<br> -74.6026, 1007.46, 1.82221e-438<br> Bad 14412 argument in __cyl_bessel_k.<br> -74.6026, 1185.4, 5.87506e-516<br> Bad 14413 argument in __cyl_bessel_k.<br> -74.6026, 3534.52, 4.40608e-1537<br> Bad 14414 argument in __cyl_bessel_k.<br> -74.6026, 8071.55, 7.3384e-3508<br> Bad 14415 argument in __cyl_bessel_k.<br> -74.6026, 16229.2, 0<br> Bad argument in 14416 __cyl_bessel_k.<br> -74.6026, 32066.2, 0<br> Bad argument in __cyl_bessel_k.<br> 14417 -74.6026, 36367.9, 0<br> Bad argument in __cyl_bessel_k.<br> -72.9046, 14418 24.7501, 5.5618e+22<br> Bad argument in __cyl_bessel_k.<br> -72.9046, 63.7722, 14419 1.09452e-12<br> Bad argument in __cyl_bessel_k.<br> -72.9046, 125.28, 3.8393e-47<br> 14420 Bad argument in __cyl_bessel_k.<br> -72.9046, 255.547, 2.45173e-108<br> 14421 Bad argument in __cyl_bessel_k.<br> -72.9046, 503.011, 3.80454e-218<br> 14422 Bad argument in __cyl_bessel_k.<br> -72.9046, 1007.46, 1.60949e-438<br> 14423 Bad argument in __cyl_bessel_k.<br> -72.9046, 1185.4, 5.28662e-516<br> 14424 Bad argument in __cyl_bessel_k.<br> -72.9046, 3534.52, 4.25273e-1537<br> 14425 Bad argument in __cyl_bessel_k.<br> -72.9046, 8071.55, 7.22542e-3508<br> 14426 Bad argument in __cyl_bessel_k.<br> -72.9046, 16229.2, 0<br> Bad argument 14427 in __cyl_bessel_k.<br> -72.9046, 32066.2, 0<br> Bad argument in __cyl_bessel_k.<br> 14428 -72.9046, 36367.9, 0<br> Bad argument in __cyl_bessel_k.<br> -62.3236, 14429 24.7501, 6.74518e+14<br> Bad argument in __cyl_bessel_k.<br> -62.3236, 14430 63.7722, 6.54531e-17<br> Bad argument in __cyl_bessel_k.<br> -62.3236, 14431 125.28, 1.65653e-49<br> Bad argument in __cyl_bessel_k.<br> -62.3236, 255.547, 14432 1.54767e-109<br> Bad argument in __cyl_bessel_k.<br> -62.3236, 503.011, 14433 9.22721e-219<br> Bad argument in __cyl_bessel_k.<br> -62.3236, 1007.46, 14434 7.91894e-439<br> Bad argument in __cyl_bessel_k.<br> -62.3236, 1185.4, 14435 2.89281e-516<br> Bad argument in __cyl_bessel_k.<br> -62.3236, 3534.52, 14436 3.4736e-1537<br> Bad argument in __cyl_bessel_k.<br> -62.3236, 8071.55, 14437 6.6126e-3508<br> Bad argument in __cyl_bessel_k.<br> -62.3236, 16229.2, 14438 0<br> Bad argument in __cyl_bessel_k.<br> -62.3236, 32066.2, 0<br> Bad 14439 argument in __cyl_bessel_k.<br> -62.3236, 36367.9, 0<br> Bad argument in 14440 __cyl_bessel_k.<br> -55.7932, 24.7501, 2.00028e+10<br> Bad argument in 14441 __cyl_bessel_k.<br> -55.7932, 63.7722, 3.01107e-19<br> Bad argument in 14442 __cyl_bessel_k.<br> -55.7932, 125.28, 8.54693e-51<br> Bad argument in __cyl_bessel_k.<br> 14443 -55.7932, 255.547, 3.47666e-110<br> Bad argument in __cyl_bessel_k.<br> 14444 -55.7932, 503.011, 4.29705e-219<br> Bad argument in __cyl_bessel_k.<br> 14445 -55.7932, 1007.46, 5.40242e-439<br> Bad argument in __cyl_bessel_k.<br> 14446 -55.7932, 1185.4, 2.08996e-516<br> Bad argument in __cyl_bessel_k.<br> 14447 -55.7932, 3534.52, 3.11458e-1537<br> Bad argument in __cyl_bessel_k.<br> 14448 -55.7932, 8071.55, 6.30409e-3508<br> Bad argument in __cyl_bessel_k.<br> 14449 -55.7932, 16229.2, 0<br> Bad argument in __cyl_bessel_k.<br> -55.7932, 14450 32066.2, 0<br> Bad argument in __cyl_bessel_k.<br> -55.7932, 36367.9, 0<br> 14451 Bad argument in __cyl_bessel_k.<br> -44.3004, 9.50706, 5.6936e+22<br> Bad 14452 argument in __cyl_bessel_k.<br> -44.3004, 24.7501, 1242.73<br> Bad argument 14453 in __cyl_bessel_k.<br> -44.3004, 63.7722, 7.99341e-23<br> Bad argument 14454 in __cyl_bessel_k.<br> -44.3004, 125.28, 9.88149e-53<br> Bad argument in 14455 __cyl_bessel_k.<br> -44.3004, 255.547, 3.73007e-111<br> Bad argument in 14456 __cyl_bessel_k.<br> -44.3004, 503.011, 1.37367e-219<br> Bad argument in 14457 __cyl_bessel_k.<br> -44.3004, 1007.46, 3.05398e-439<br> Bad argument in 14458 __cyl_bessel_k.<br> *** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br> 14459 </p> 14460<h5> 14461<a name="special_function_error_rates_rep.error_logs.h69"></a> 14462 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w5"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w5">Error 14463 Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library <cmath> 14464 and test data Bessel Kv: Mathworld Data (large values)</a> 14465 </h5> 14466<p> 14467 <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Mathworld_Data_large_values_"></a>Bad 14468 argument in __cyl_bessel_k.<br> -1, 3.72917e-155, 2.68156e+154<br> Bad 14469 argument in __cyl_bessel_k.<br> -1.125, 3.72917e-155, 5.53984e+173<br> 14470 </p> 14471<h5> 14472<a name="special_function_error_rates_rep.error_logs.h70"></a> 14473 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w6"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w6">Error 14474 Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library <cmath> 14475 and test data Bessel Kv: Mathworld Data</a> 14476 </h5> 14477<p> 14478 <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Mathworld_Data"></a>Bad 14479 argument in __cyl_bessel_k.<br> -5.5, 10, 7.33045e-05<br> Bad argument 14480 in __cyl_bessel_k.<br> -5.5, 100, 5.41275e-45<br> Bad argument in __cyl_bessel_k.<br> 14481 -141.399, 50, 1.30185e+42<br> 14482 </p> 14483<h5> 14484<a name="special_function_error_rates_rep.error_logs.h71"></a> 14485 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_in"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_in">Error 14486 Output For cyl_bessel_k (integer orders) with compiler GNU C++ version 7.1.0 14487 and library <cmath> and test data Bessel Kn: Mathworld Data (Integer 14488 Version)</a> 14489 </h5> 14490<p> 14491 <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k_integer_orders___cmath__Bessel_Kn_Mathworld_Data_Integer_Version_"></a>Bad 14492 argument in __cyl_bessel_k.<br> -5, 100, 5.27326e-45<br> Bad argument in 14493 __cyl_bessel_k.<br> -10, 1, 1.80713e+08<br> Bad argument in __cyl_bessel_k.<br> 14494 -1000, 700, 6.51562e-31<br> 14495 </p> 14496<h5> 14497<a name="special_function_error_rates_rep.error_logs.h72"></a> 14498 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w7"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w7">Error 14499 Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library <cmath> 14500 and test data Bessel Kn: Mathworld Data</a> 14501 </h5> 14502<p> 14503 <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kn_Mathworld_Data"></a>Bad 14504 argument in __cyl_bessel_k.<br> -5, 100, 5.27326e-45<br> Bad argument in 14505 __cyl_bessel_k.<br> -10, 1, 1.80713e+08<br> Bad argument in __cyl_bessel_k.<br> 14506 -1000, 700, 6.51562e-31<br> 14507 </p> 14508<h5> 14509<a name="special_function_error_rates_rep.error_logs.h73"></a> 14510 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wit"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wit">Error 14511 Output For cyl_neumann with compiler GNU C++ version 7.1.0 and library GSL 14512 2.1 and test data Yv: Mathworld Data (large values)</a> 14513 </h5> 14514<p> 14515 <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yv_Mathworld_Data_large_values_"></a>domain 14516 error<br> -0.5, 1.2459e-206, 8.90598e-104<br> 14517 </p> 14518<h5> 14519<a name="special_function_error_rates_rep.error_logs.h74"></a> 14520 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi0">Error 14521 Output For cyl_neumann with compiler GNU C++ version 7.1.0 and library GSL 14522 2.1 and test data Yv: Mathworld Data</a> 14523 </h5> 14524<p> 14525 <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yv_Mathworld_Data"></a>domain 14526 error<br> -5.5, 3.125, -0.0274994<br> domain error<br> -5.5, 10000, -0.00759344<br> 14527 domain error<br> -10.0003, 0.000976562, -1.50382e+38<br> domain error<br> 14528 -10.0003, 100, 0.0583042<br> domain error<br> -141.75, 100, -3.8101e+09<br> 14529 domain error<br> -8.5, 12.5664, 0.0436808<br> 14530 </p> 14531<h5> 14532<a name="special_function_error_rates_rep.error_logs.h75"></a> 14533 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi1">Error 14534 Output For cyl_neumann with compiler GNU C++ version 7.1.0 and library GSL 14535 2.1 and test data Yn: Mathworld Data</a> 14536 </h5> 14537<p> 14538 <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yn_Mathworld_Data"></a>domain 14539 error<br> -5, 1e+06, 0.000331052<br> domain error<br> -10, 1e+06, 0.000725952<br> 14540 domain error<br> -1000, 700, -1.88753e+77<br> domain error<br> -25, 8, 14541 3.45114e+08<br> 14542 </p> 14543<h5> 14544<a name="special_function_error_rates_rep.error_logs.h76"></a> 14545 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi2">Error 14546 Output For cyl_neumann with compiler GNU C++ version 7.1.0 and library <cmath> 14547 and test data Yv: Random Data</a> 14548 </h5> 14549<p> 14550 <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Random_Data"></a>CAUTION: 14551 Gross error found at entry 394.<br> Found: -3.29903 Expected 0.0192842 Error: 14552 1.18973e+4932<br> 125.28, 1007.46, 0.0192842<br> CAUTION: Gross error found 14553 at entry 395.<br> Found: 1.13543 Expected 0.0230358 Error: 48.2897<br> 14554 125.28, 1185.4, 0.0230358<br> CAUTION: Gross error found at entry 396.<br> 14555 Found: 0.00119445 Expected 0.00460223 Error: 2.85302<br> 125.28, 3534.52, 14556 0.00460223<br> CAUTION: Gross error found at entry 403.<br> Found: 1068 14557 Expected -0.00270959 Error: 1.18973e+4932<br> 255.547, 1007.46, -0.00270959<br> 14558 CAUTION: Gross error found at entry 404.<br> Found: -395.006 Expected 0.00738845 14559 Error: 1.18973e+4932<br> 255.547, 1185.4, 0.00738845<br> CAUTION: Gross 14560 error found at entry 405.<br> Found: 1.08701 Expected -0.000407036 Error: 14561 1.18973e+4932<br> 255.547, 3534.52, -0.000407036<br> CAUTION: Gross error 14562 found at entry 406.<br> Found: 0.0232211 Expected 0.00886946 Error: 1.61809<br> 14563 255.547, 8071.55, 0.00886946<br> CAUTION: Gross error found at entry 411.<br> 14564 Found: 65895.7 Expected -0.0158467 Error: 1.18973e+4932<br> 503.011, 1007.46, 14565 -0.0158467<br> CAUTION: Gross error found at entry 412.<br> Found: -123316 14566 Expected 0.00594357 Error: 1.18973e+4932<br> 503.011, 1185.4, 0.00594357<br> 14567 CAUTION: Gross error found at entry 413.<br> Found: -706.209 Expected 0.010151 14568 Error: 1.18973e+4932<br> 503.011, 3534.52, 0.010151<br> CAUTION: Gross 14569 error found at entry 414.<br> Found: -21.2081 Expected 0.00888375 Error: 14570 1.18973e+4932<br> 503.011, 8071.55, 0.00888375<br> CAUTION: Gross error 14571 found at entry 415.<br> Found: 0.0272835 Expected 0.00552287 Error: 3.94008<br> 14572 503.011, 16229.2, 0.00552287<br> CAUTION: Gross error found at entry 416.<br> 14573 Found: 0.0103324 Expected 0.00445559 Error: 1.31898<br> 503.011, 32066.2, 14574 0.00445559<br> CAUTION: Gross error found at entry 417.<br> Found: 0.00540788 14575 Expected -0.00384344 Error: 1.18973e+4932<br> 503.011, 36367.9, -0.00384344<br> 14576 CAUTION: Gross error found at entry 418.<br> Found: 5.43091e+07 Expected 14577 -0.0772843 Error: 1.18973e+4932<br> 1007.46, 1007.46, -0.0772843<br> CAUTION: 14578 Gross error found at entry 419.<br> Found: -2.84383e+07 Expected 0.0304312 14579 Error: 1.18973e+4932<br> 1007.46, 1185.4, 0.0304312<br> CAUTION: Gross 14580 error found at entry 420.<br> Found: -61440.2 Expected -0.00474217 Error: 14581 1.29562e+07<br> 1007.46, 3534.52, -0.00474217<br> CAUTION: Gross error 14582 found at entry 421.<br> Found: -4126.89 Expected -0.0074205 Error: 556146<br> 14583 1007.46, 8071.55, -0.0074205<br> CAUTION: Gross error found at entry 422.<br> 14584 Found: -69.2831 Expected -0.00179572 Error: 38581.4<br> 1007.46, 16229.2, 14585 -0.00179572<br> CAUTION: Gross error found at entry 423.<br> Found: 2.32048 14586 Expected 0.000750053 Error: 3092.76<br> 1007.46, 32066.2, 0.000750053<br> 14587 CAUTION: Gross error found at entry 424.<br> Found: 3.90724 Expected 0.00305125 14588 Error: 1279.54<br> 1007.46, 36367.9, 0.00305125<br> CAUTION: Gross error 14589 found at entry 425.<br> Found: -1.83374e+08 Expected -7.25176e+28 Error: 14590 3.95463e+20<br> 1185.4, 1007.46, -7.25176e+28<br> CAUTION: Gross error 14591 found at entry 426.<br> Found: 1.09822e+08 Expected -0.0732059 Error: 1.18973e+4932<br> 14592 1185.4, 1185.4, -0.0732059<br> CAUTION: Gross error found at entry 427.<br> 14593 Found: 315632 Expected 0.000479585 Error: 6.58136e+08<br> 1185.4, 3534.52, 14594 0.000479585<br> CAUTION: Gross error found at entry 428.<br> Found: 16815.6 14595 Expected 0.00174909 Error: 9.61391e+06<br> 1185.4, 8071.55, 0.00174909<br> 14596 CAUTION: Gross error found at entry 429.<br> Found: 133.356 Expected 0.00416288 14597 Error: 32033.6<br> 1185.4, 16229.2, 0.00416288<br> CAUTION: Gross error 14598 found at entry 430.<br> Found: -1.38401 Expected -0.000320056 Error: 4323.27<br> 14599 1185.4, 32066.2, -0.000320056<br> CAUTION: Gross error found at entry 431.<br> 14600 Found: -17.7085 Expected -0.00417656 Error: 4238.96<br> 1185.4, 36367.9, 14601 -0.00417656<br> 14602 </p> 14603<h5> 14604<a name="special_function_error_rates_rep.error_logs.h77"></a> 14605 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi3"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi3">Error 14606 Output For cyl_neumann with compiler GNU C++ version 7.1.0 and library <cmath> 14607 and test data Yv: Mathworld Data (large values)</a> 14608 </h5> 14609<p> 14610 <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Mathworld_Data_large_values_"></a>Bad 14611 argument in __cyl_neumann_n.<br> -0.5, 1.2459e-206, 8.90598e-104<br> 14612 </p> 14613<h5> 14614<a name="special_function_error_rates_rep.error_logs.h78"></a> 14615 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi4"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi4">Error 14616 Output For cyl_neumann with compiler GNU C++ version 7.1.0 and library <cmath> 14617 and test data Yv: Mathworld Data</a> 14618 </h5> 14619<p> 14620 <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Mathworld_Data"></a>Bad 14621 argument in __cyl_neumann_n.<br> -5.5, 3.125, -0.0274994<br> Bad argument 14622 in __cyl_neumann_n.<br> -5.5, 10000, -0.00759344<br> Bad argument in __cyl_neumann_n.<br> 14623 -10.0003, 0.000976562, -1.50382e+38<br> Bad argument in __cyl_neumann_n.<br> 14624 -10.0003, 100, 0.0583042<br> Bad argument in __cyl_neumann_n.<br> -141.75, 14625 100, -3.8101e+09<br> Bad argument in __cyl_neumann_n.<br> -8.5, 12.5664, 14626 0.0436808<br> 14627 </p> 14628<h5> 14629<a name="special_function_error_rates_rep.error_logs.h79"></a> 14630 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_int"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_int">Error 14631 Output For cyl_neumann (integer orders) with compiler GNU C++ version 7.1.0 14632 and library <cmath> and test data Yn: Mathworld Data (Integer Version)</a> 14633 </h5> 14634<p> 14635 <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann_integer_orders___cmath__Yn_Mathworld_Data_Integer_Version_"></a>Bad 14636 argument in __cyl_neumann_n.<br> -5, 1e+06, 0.000331052<br> Bad argument 14637 in __cyl_neumann_n.<br> -10, 1e+06, 0.000725952<br> CAUTION: Gross error 14638 found at entry 7.<br> Found: 0.0540745 Expected 0.00217255 Error: 23.8899<br> 14639 1000, 100000, 0.00217255<br> Bad argument in __cyl_neumann_n.<br> -1000, 14640 700, -1.88753e+77<br> Bad argument in __cyl_neumann_n.<br> -25, 8, 3.45114e+08<br> 14641 </p> 14642<h5> 14643<a name="special_function_error_rates_rep.error_logs.h80"></a> 14644 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi5"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi5">Error 14645 Output For cyl_neumann with compiler GNU C++ version 7.1.0 and library <cmath> 14646 and test data Yn: Mathworld Data</a> 14647 </h5> 14648<p> 14649 <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yn_Mathworld_Data"></a>Bad 14650 argument in __cyl_neumann_n.<br> -5, 1e+06, 0.000331052<br> Bad argument 14651 in __cyl_neumann_n.<br> -10, 1e+06, 0.000725952<br> CAUTION: Gross error 14652 found at entry 7.<br> Found: 0.0540745 Expected 0.00217255 Error: 23.8899<br> 14653 1000, 100000, 0.00217255<br> Bad argument in __cyl_neumann_n.<br> -1000, 14654 700, -1.88753e+77<br> Bad argument in __cyl_neumann_n.<br> -25, 8, 3.45114e+08<br> 14655 </p> 14656<h5> 14657<a name="special_function_error_rates_rep.error_logs.h81"></a> 14658 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_beta_with_compi"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_beta_with_compi">Error 14659 Output For beta with compiler GNU C++ version 7.1.0 and library GSL 2.1 and 14660 test data Beta Function: Small Values</a> 14661 </h5> 14662<p> 14663 <a name="errors_GNU_C_version_7_1_0_linux_double_beta_GSL_2_1_Beta_Function_Small_Values"></a>CAUTION: 14664 Found non-finite result, when a finite value was expected at entry 22<br> 14665 Found: inf Expected 5.69832e+154 Error: 1.79769e+308<br> 2.98334e-154, 1.86459e-155, 14666 5.69832e+154<br> CAUTION: Gross error found at entry 22.<br> Found: inf 14667 Expected 5.69832e+154 Error: 1.79769e+308<br> 2.98334e-154, 1.86459e-155, 14668 5.69832e+154<br> 14669 </p> 14670<h5> 14671<a name="special_function_error_rates_rep.error_logs.h82"></a> 14672 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_rj_with_"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_rj_with_">Error 14673 Output For ellint_rj with compiler GNU C++ version 7.1.0 and library GSL 2.1 14674 and test data RJ: Random data</a> 14675 </h5> 14676<p> 14677 <a name="errors_GNU_C_version_7_1_0_linux_double_ellint_rj_GSL_2_1_RJ_Random_data"></a>domain 14678 error<br> 1.77787e-31, 1.40657e+18, 10.046, -4.8298e-10, -2.51795e-10<br> 14679 domain error<br> 3.37448e-31, 4.65772e+22, 0.469831, -4.33756e-09, -2.95865e-11<br> 14680 domain error<br> 5.25297e-31, 5.85483e+25, 2.02482e-15, -1.87347e-28, 3.36445e+07<br> 14681 domain error<br> 6.22216e-31, 3.43401e+23, 0.673005, -2.7626e-13, -7.58898e-12<br> 14682 domain error<br> 6.26875e-31, 2.62568e-13, 1.06394e+24, -1.36451e+14, -6.70372e-25<br> 14683 domain error<br> 6.84599e-31, 3.57666e-29, 1.82191e+11, -3.63292e+08, -8.35235e-13<br> 14684 domain error<br> 8.90482e-31, 1.97093e-28, 1.14939e-31, -1.26424e-12, -6.39454e+26<br> 14685 domain error<br> 1.07374e-30, 1.70005e-12, 1.88773e-25, -1.16558e-29, 4.31668e+32<br> 14686 domain error<br> 1.17141e-30, 24.2523, 3.67522e+21, -4.79065e-22, 2.2702e-05<br> 14687 domain error<br> 1.64143e-30, 2.01978e-22, 2.58942e+12, -8.52649e-12, -2.82629e+06<br> 14688 domain error<br> 1.85141e-30, 0.0386712, 2.37846e-13, -1.57357e+15, -1.38574e-13<br> 14689 domain error<br> 2.70034e-30, 4.43896e-24, 7.54576e+16, -1.1436e-14, -1.10082e+07<br> 14690 domain error<br> 4.01162e-30, 2.73343e+23, 1.32333e+13, -1.86032e-07, -4.16626e-25<br> 14691 domain error<br> 4.13665e-30, 1.08034e-30, 3.13547e-16, -5.58099e-08, -5.14643e+16<br> 14692 domain error<br> 4.3728e-30, 7.79812e+12, 8.58894e+21, -4.58312e-24, 5.28901e-09<br> 14693 domain error<br> 5.6397e-30, 1.64768e+23, 9.64423e-15, -1.82207e+20, -1.62886e-30<br> 14694 domain error<br> 9.89841e-30, 9.69731e+10, 1.03263e+21, -0.00343967, -9.62714e-22<br> 14695 domain error<br> 1.3797e-29, 6.03357e+08, 5.62497e-15, -5.87235e+16, -5.80287e-20<br> 14696 domain error<br> 1.96963e-29, 3.22384e-25, 2.92187e+23, -3.80643e+27, -8.2513e-38<br> 14697 domain error<br> 2.00927e-29, 5.6976e-05, 1.16219e+25, -1.64129e-22, 0.00318397<br> 14698 domain error<br> 7.29506e-29, 5904.94, 9.93922e+10, -19.528, -1.60795e-09<br> 14699 domain error<br> 1.19698e-28, 1.66816e-22, 28472, -1.21137e-19, -5.84699e+17<br> 14700 domain error<br> 1.64095e-28, 2.13421e-21, 7.8914e-15, -1.77584e-07, -1.70156e+15<br> 14701 domain error<br> 2.03475e-28, 4.40987e+15, 28739.1, -9624.5, -1.29418e-12<br> 14702 domain error<br> 2.73113e-28, 1.08457e+19, 4.00674e+08, -5.70043e-11, 1.092e-17<br> 14703 domain error<br> 5.52633e-28, 1.45707e-17, 1.29411e-27, -1.67255e-15, -5.84881e+24<br> 14704 domain error<br> 5.61278e-28, 9.22881e-12, 8.64222e-13, -5.6282e+23, -4.57782e-18<br> 14705 domain error<br> 6.08465e-28, 1.32249e+26, 1.25536e-30, -1.89097e-14, -223.246<br> 14706 domain error<br> 9.50943e-28, 2.49682e-18, 0.000904584, -3.1419e-12, -2.44954e+14<br> 14707 domain error<br> 1.20779e-27, 35383.2, 1.35533e-15, -4.67834e-24, 3.20581e+15<br> 14708 domain error<br> 2.29822e-27, 3.35258e-16, 2.60689e+08, -9.99161e-20, -5.4924e+11<br> 14709 domain error<br> 3.0926e-27, 3.11839e-13, 3.37883e-23, -1.94349e+26, -3.55191e-19<br> 14710 domain error<br> 3.12803e-27, 1.15118e+16, 1.52495e+10, -4.2399e+13, -3.07515e-21<br> 14711 domain error<br> 4.49747e-27, 716.685, 1.69018e-23, -1.32558e-14, -9.2291e+13<br> 14712 domain error<br> 4.84575e-27, 3.44028e-27, 3.42665e+09, -812.399, -2.12767e-06<br> 14713 domain error<br> 5.81424e-27, 3.70845e-15, 3.69338e+11, -4.15794e+06, -2.95944e-11<br> 14714 domain error<br> 6.08654e-27, 1.23742e+08, 1.09124e-26, -2.19946e+16, -4.90896e-19<br> 14715 domain error<br> 7.71967e-27, 9.46115e-26, 1.24324e+25, -522800, -5.83203e-17<br> 14716 domain error<br> 9.20037e-27, 207550, 2.45782e-17, -6.06901e+29, -2.88945e-31<br> 14717 domain error<br> 1.75502e-26, 5.81507e+16, 8.83063e+21, -1.11214e-21, 1.57697e-11<br> 14718 domain error<br> 2.29965e-26, 2.9716e-21, 1.81059e-25, -5.23972e-08, -6.23302e+18<br> 14719 domain error<br> 2.32628e-26, 0.0655133, 1.62901e-21, -7.15441e-17, -9.88586e+17<br> 14720 domain error<br> 3.49194e-26, 2.53343e+14, 756.217, -1.3359e+10, -1.275e-16<br> 14721 domain error<br> 1.009e-25, 0.0694304, 1.20267e-14, -1.55746e-22, 2.10701e+17<br> 14722 domain error<br> 3.54771e-25, 1.67999e-27, 2.3917e+24, -9.98754e+25, -1.11704e-36<br> 14723 domain error<br> 6.31714e-25, 3.4594e-28, 6.37951e-24, -1.25529e-24, -9.56292e+35<br> 14724 domain error<br> 6.74086e-25, 2.47169e+12, 1.32962e+23, -6.78845e+06, -3.32861e-24<br> 14725 domain error<br> 1.8099e-24, 4.5215e-06, 8.66937e-11, -3.70795e-08, -1.41893e+11<br> 14726 domain error<br> 2.29798e-24, 9.30454e-30, 6.56584e-17, -9890.38, -373149<br> 14727 domain error<br> 2.88161e-24, 8.82377e-05, 1.57747e+21, -4.25068e-24, 2260.61<br> 14728 domain error<br> 3.25991e-24, 1.92923e+29, 3.09752e-05, -1.00986e+11, -1.25485e-24<br> 14729 domain error<br> 6.36705e-24, 2.8074e+22, 1.75569e-13, -1.53152e+24, -4.89823e-34<br> 14730 domain error<br> 7.90772e-24, 2.11611e-30, 1.42682e-07, -0.00296297, -5.38814e+07<br> 14731 domain error<br> 1.05302e-23, 4.83473e+26, 4.43149e-30, -1.56818e+13, -3.6836e-25<br> 14732 *** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br> 14733 </p> 14734<h5> 14735<a name="special_function_error_rates_rep.error_logs.h83"></a> 14736 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_1_with_c"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_1_with_c">Error 14737 Output For ellint_1 with compiler GNU C++ version 7.1.0 and library <cmath> 14738 and test data Elliptic Integral F: Mathworld Data</a> 14739 </h5> 14740<p> 14741 <a name="errors_GNU_C_version_7_1_0_linux_long_double_ellint_1__cmath__Elliptic_Integral_F_Mathworld_Data"></a>CAUTION: 14742 Gross error found at entry 9.<br> Found: -7.02862e+09 Expected 1.04181e+20 14743 Error: 1.18973e+4932<br> 1e+20, 0.390625, 1.04181e+20<br> CAUTION: Gross 14744 error found at entry 10.<br> Found: -9.3866e+09 Expected 1.39133e+50 Error: 14745 1.18973e+4932<br> 1e+50, 0.875, 1.39133e+50<br> 14746 </p> 14747<h5> 14748<a name="special_function_error_rates_rep.error_logs.h84"></a> 14749 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_2_comple"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_2_comple">Error 14750 Output For ellint_2 (complete) with compiler GNU C++ version 7.1.0 and library 14751 GSL 2.1 and test data Elliptic Integral E: Mathworld Data</a> 14752 </h5> 14753<p> 14754 <a name="errors_GNU_C_version_7_1_0_linux_double_ellint_2_complete__GSL_2_1_Elliptic_Integral_E_Mathworld_Data"></a>domain 14755 error<br> -1, 1<br> 14756 </p> 14757<h5> 14758<a name="special_function_error_rates_rep.error_logs.h85"></a> 14759 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_2_with_c"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_2_with_c">Error 14760 Output For ellint_2 with compiler GNU C++ version 7.1.0 and library <cmath> 14761 and test data Elliptic Integral E: Mathworld Data</a> 14762 </h5> 14763<p> 14764 <a name="errors_GNU_C_version_7_1_0_linux_long_double_ellint_2__cmath__Elliptic_Integral_E_Mathworld_Data"></a>CAUTION: 14765 Gross error found at entry 7.<br> Found: -6.3027e+09 Expected 9.34215e+09 14766 Error: 1.18973e+4932<br> 1e+10, -0.5, 9.34215e+09<br> CAUTION: Gross error 14767 found at entry 8.<br> Found: -6.48129e+09 Expected 7.08861e+19 Error: 1.18973e+4932<br> 14768 7.3787e+19, 0.390625, 7.08861e+19<br> CAUTION: Gross error found at entry 14769 9.<br> Found: -5.13973e+09 Expected 7.1259e+49 Error: 1.18973e+4932<br> 14770 9.35361e+49, 0.878906, 7.1259e+49<br> 14771 </p> 14772<h5> 14773<a name="special_function_error_rates_rep.error_logs.h86"></a> 14774 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_3_comple"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_3_comple">Error 14775 Output For ellint_3 (complete) with compiler GNU C++ version 7.1.0 and library 14776 GSL 2.1 and test data Complete Elliptic Integral PI: Mathworld Data</a> 14777 </h5> 14778<p> 14779 <a name="errors_GNU_C_version_7_1_0_linux_double_ellint_3_complete__GSL_2_1_Complete_Elliptic_Integral_PI_Mathworld_Data"></a>domain 14780 error<br> -4.14952e+180, 0.5, 7.71119e-91<br> 14781 </p> 14782<h5> 14783<a name="special_function_error_rates_rep.error_logs.h87"></a> 14784 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_3_with_c"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_3_with_c">Error 14785 Output For ellint_3 with compiler GNU C++ version 7.1.0 and library GSL 2.1 14786 and test data Elliptic Integral PI: Mathworld Data</a> 14787 </h5> 14788<p> 14789 <a name="errors_GNU_C_version_7_1_0_linux_double_ellint_3_GSL_2_1_Elliptic_Integral_PI_Mathworld_Data"></a>domain 14790 error<br> 1.125, 10, 0.25, 0.662468<br> domain error<br> 1.125, 3, 0.25, 14791 -0.142697<br> domain error<br> 1.00391, 21.5, 0.125, -0.535406<br> domain 14792 error<br> 1, 2, 0.5, -2.87535<br> domain error<br> 1, -2, 0.5, 2.87535<br> 14793 domain error<br> 1, 2, 6.22302e-61, -2.18504<br> domain error<br> 1, 14794 -2, 6.22302e-61, 2.18504<br> domain error<br> 20, 3.14257, 0.5, 0.000975941<br> 14795 domain error<br> 20, -3.14257, 0.5, -0.000975941<br> domain error<br> 14796 1.01562, 1.6958, 0.5, -27.1647<br> domain error<br> 1.01562, -1.6958, 0.5, 14797 27.1647<br> 14798 </p> 14799<h5> 14800<a name="special_function_error_rates_rep.error_logs.h88"></a> 14801 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_3_compl0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_3_compl0">Error 14802 Output For ellint_3 (complete) with compiler GNU C++ version 7.1.0 and library 14803 <cmath> and test data Complete Elliptic Integral PI: Random Data</a> 14804 </h5> 14805<p> 14806 <a name="errors_GNU_C_version_7_1_0_linux_long_double_ellint_3_complete___cmath__Complete_Elliptic_Integral_PI_Random_Data"></a>Argument 14807 too small in __ellint_rj<br> -87.1743, 0.126987, 0.167413<br> Argument 14808 too small in __ellint_rj<br> -87.1743, 0.135477, 0.167431<br> Argument 14809 too small in __ellint_rj<br> -87.1743, 0.221034, 0.167683<br> Argument 14810 too small in __ellint_rj<br> -87.1743, 0.308167, 0.168078<br> Argument 14811 too small in __ellint_rj<br> -87.1743, 0.632359, 0.17122<br> Argument too 14812 small in __ellint_rj<br> -87.1743, 0.814724, 0.175341<br> Argument too 14813 small in __ellint_rj<br> -87.1743, 0.835009, 0.176056<br> Argument too 14814 small in __ellint_rj<br> -87.1743, 0.905792, 0.179501<br> Argument too 14815 small in __ellint_rj<br> -87.1743, 0.913376, 0.180014<br> Argument too 14816 small in __ellint_rj<br> -87.1743, 0.968868, 0.186162<br> Argument too 14817 small in __ellint_rj<br> -86.3168, 0.126987, 0.168233<br> Argument too 14818 small in __ellint_rj<br> -86.3168, 0.135477, 0.168252<br> Argument too 14819 small in __ellint_rj<br> -86.3168, 0.221034, 0.168506<br> Argument too 14820 small in __ellint_rj<br> -86.3168, 0.308167, 0.168905<br> Argument too 14821 small in __ellint_rj<br> -86.3168, 0.632359, 0.172077<br> Argument too 14822 small in __ellint_rj<br> -86.3168, 0.814724, 0.176237<br> Argument too 14823 small in __ellint_rj<br> -86.3168, 0.835009, 0.176958<br> Argument too 14824 small in __ellint_rj<br> -86.3168, 0.905792, 0.180437<br> Argument too 14825 small in __ellint_rj<br> -86.3168, 0.913376, 0.180955<br> Argument too 14826 small in __ellint_rj<br> -86.3168, 0.968868, 0.187163<br> Argument too 14827 small in __ellint_rj<br> -77.6756, 0.126987, 0.177238<br> Argument too 14828 small in __ellint_rj<br> -77.6756, 0.135477, 0.177258<br> Argument too 14829 small in __ellint_rj<br> -77.6756, 0.221034, 0.17754<br> Argument too small 14830 in __ellint_rj<br> -77.6756, 0.308167, 0.17798<br> Argument too small in 14831 __ellint_rj<br> -77.6756, 0.632359, 0.181485<br> Argument too small in 14832 __ellint_rj<br> -77.6756, 0.814724, 0.186089<br> Argument too small in 14833 __ellint_rj<br> -77.6756, 0.835009, 0.186888<br> Argument too small in 14834 __ellint_rj<br> -77.6756, 0.905792, 0.190742<br> Argument too small in 14835 __ellint_rj<br> -77.6756, 0.913376, 0.191315<br> Argument too small in 14836 __ellint_rj<br> -77.6756, 0.968868, 0.1982<br> Argument too small in __ellint_rj<br> 14837 -68.8751, 0.126987, 0.188077<br> Argument too small in __ellint_rj<br> 14838 -68.8751, 0.135477, 0.188099<br> Argument too small in __ellint_rj<br> 14839 -68.8751, 0.221034, 0.188414<br> Argument too small in __ellint_rj<br> 14840 -68.8751, 0.308167, 0.188907<br> Argument too small in __ellint_rj<br> 14841 -68.8751, 0.632359, 0.192834<br> Argument too small in __ellint_rj<br> 14842 -68.8751, 0.814724, 0.198<br> Argument too small in __ellint_rj<br> -68.8751, 14843 0.835009, 0.198896<br> Argument too small in __ellint_rj<br> -68.8751, 14844 0.905792, 0.203226<br> Argument too small in __ellint_rj<br> -68.8751, 14845 0.913376, 0.203871<br> Argument too small in __ellint_rj<br> -68.8751, 14846 0.968868, 0.211615<br> Argument too small in __ellint_rj<br> -36.1317, 14847 0.126987, 0.258074<br> Argument too small in __ellint_rj<br> -36.1317, 14848 0.135477, 0.258115<br> Argument too small in __ellint_rj<br> -36.1317, 14849 0.221034, 0.258686<br> Argument too small in __ellint_rj<br> -36.1317, 14850 0.308167, 0.259579<br> Argument too small in __ellint_rj<br> -36.1317, 14851 0.632359, 0.266738<br> Argument too small in __ellint_rj<br> -36.1317, 14852 0.814724, 0.276242<br> Argument too small in __ellint_rj<br> -36.1317, 14853 0.835009, 0.2779<br> Argument too small in __ellint_rj<br> -36.1317, 0.905792, 14854 0.285938<br> Argument too small in __ellint_rj<br> -36.1317, 0.913376, 14855 0.287139<br> Argument too small in __ellint_rj<br> -36.1317, 0.968868, 14856 0.301608<br> Argument too small in __ellint_rj<br> -17.7129, 0.126987, 14857 0.363673<br> Argument too small in __ellint_rj<br> -17.7129, 0.135477, 14858 0.36375<br> Argument too small in __ellint_rj<br> -17.7129, 0.221034, 0.364822<br> 14859 Argument too small in __ellint_rj<br> -17.7129, 0.308167, 0.366503<br> 14860 Argument too small in __ellint_rj<br> -17.7129, 0.632359, 0.380066<br> 14861 Argument too small in __ellint_rj<br> -17.7129, 0.814724, 0.398311<br> 14862 Argument too small in __ellint_rj<br> -17.7129, 0.835009, 0.401518<br> 14863 Argument too small in __ellint_rj<br> -17.7129, 0.905792, 0.417145<br> 14864 Argument too small in __ellint_rj<br> -17.7129, 0.913376, 0.41949<br> Argument 14865 too small in __ellint_rj<br> -17.7129, 0.968868, 0.447893<br> Argument 14866 too small in __ellint_rj<br> -15.6641, 0.126987, 0.385409<br> Argument 14867 too small in __ellint_rj<br> -15.6641, 0.135477, 0.385495<br> Argument 14868 too small in __ellint_rj<br> -15.6641, 0.221034, 0.386686<br> Argument 14869 too small in __ellint_rj<br> -15.6641, 0.308167, 0.388553<br> Argument 14870 too small in __ellint_rj<br> -15.6641, 0.632359, 0.403643<br> Argument 14871 too small in __ellint_rj<br> *** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY 14872 ***<br> 14873 </p> 14874<h5> 14875<a name="special_function_error_rates_rep.error_logs.h89"></a> 14876 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_3_compl1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_3_compl1">Error 14877 Output For ellint_3 (complete) with compiler GNU C++ version 7.1.0 and library 14878 <cmath> and test data Complete Elliptic Integral PI: Mathworld Data</a> 14879 </h5> 14880<p> 14881 <a name="errors_GNU_C_version_7_1_0_linux_long_double_ellint_3_complete___cmath__Complete_Elliptic_Integral_PI_Mathworld_Data"></a>CAUTION: 14882 Gross error found at entry 3.<br> Found: 1.28255 Expected 2.22144 Error: 14883 0.732051<br> 0.5, 0, 2.22144<br> Argument too small in __ellint_rj<br> 14884 -4, 0.3, 0.712709<br> Argument too small in __ellint_rj<br> -100000, -0.5, 14885 0.00496945<br> Argument too small in __ellint_rj<br> -1e+10, -0.75, 1.5708e-05<br> 14886 CAUTION: Gross error found at entry 8.<br> Found: 1.45615 Expected 101.045 14887 Error: 68.3919<br> 0.999023, -0.875, 101.045<br> Argument too small in 14888 __ellint_rj<br> -4.14952e+180, 0.5, 7.71119e-91<br> 14889 </p> 14890<h5> 14891<a name="special_function_error_rates_rep.error_logs.h90"></a> 14892 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_3_with_0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_3_with_0">Error 14893 Output For ellint_3 with compiler GNU C++ version 7.1.0 and library <cmath> 14894 and test data Elliptic Integral PI: Large Random Data</a> 14895 </h5> 14896<p> 14897 <a name="errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Large_Random_Data"></a>Argument 14898 too small in __ellint_rj<br> -88.2952, -8.04919, 0.814724, -0.874724<br> 14899 Argument too small in __ellint_rj<br> -88.2952, -7.46026, 0.135477, -0.827189<br> 14900 Argument too small in __ellint_rj<br> -88.2952, -7.29046, 0.905792, -0.877476<br> 14901 Argument too small in __ellint_rj<br> -88.2952, -6.23236, 0.835009, -0.652152<br> 14902 Argument too small in __ellint_rj<br> -88.2952, -5.57932, 0.126987, -0.512276<br> 14903 Argument too small in __ellint_rj<br> -88.2952, -4.43004, 0.968868, -0.543324<br> 14904 Argument too small in __ellint_rj<br> -88.2952, -3.83666, 0.913376, -0.513389<br> 14905 Argument too small in __ellint_rj<br> -88.2952, 0.93763, 0.221034, 0.158243<br> 14906 Argument too small in __ellint_rj<br> -88.2952, 0.944412, 0.632359, 0.160101<br> 14907 Argument too small in __ellint_rj<br> -88.2952, 2.64719, 0.308167, 0.188127<br> 14908 Argument too small in __ellint_rj<br> -88.2952, 6.29447, 0.0975404, 0.676465<br> 14909 Argument too small in __ellint_rj<br> -88.2952, 6.70017, 0.547221, 0.817785<br> 14910 Argument too small in __ellint_rj<br> -88.2952, 8.11584, 0.278498, 0.837452<br> 14911 Argument too small in __ellint_rj<br> -88.2952, 8.26752, 0.188382, 0.837571<br> 14912 Argument too small in __ellint_rj<br> -88.2952, 9.15014, 0.546881, 0.885365<br> 14913 Argument too small in __ellint_rj<br> -88.2952, 9.29777, 0.992881, 1.06701<br> 14914 Argument too small in __ellint_rj<br> -88.2952, 9.3539, 0.957507, 1.03573<br> 14915 Argument too small in __ellint_rj<br> -88.2952, 9.37736, 0.996461, 1.13933<br> 14916 Argument too small in __ellint_rj<br> -88.2952, 9.85763, 0.964889, 1.24906<br> 14917 Argument too small in __ellint_rj<br> -88.2952, 9.92923, 0.967695, 1.25621<br> 14918 Argument too small in __ellint_rj<br> -86.8166, -8.04919, 0.157613, -0.841405<br> 14919 Argument too small in __ellint_rj<br> -86.8166, -7.46026, 0.725839, -0.859877<br> 14920 Argument too small in __ellint_rj<br> -86.8166, -7.29046, 0.970593, -0.914439<br> 14921 Argument too small in __ellint_rj<br> -86.8166, -6.23236, 0.98111, -0.710627<br> 14922 Argument too small in __ellint_rj<br> -86.8166, -5.57932, 0.957167, -0.58106<br> 14923 Argument too small in __ellint_rj<br> -86.8166, -4.43004, 0.109862, -0.499839<br> 14924 Argument too small in __ellint_rj<br> -86.8166, -3.83666, 0.485376, -0.494286<br> 14925 Argument too small in __ellint_rj<br> -86.8166, 0.93763, 0.798106, 0.162644<br> 14926 Argument too small in __ellint_rj<br> -86.8166, 0.944412, 0.80028, 0.16282<br> 14927 Argument too small in __ellint_rj<br> -86.8166, 2.64719, 0.297029, 0.18978<br> 14928 Argument too small in __ellint_rj<br> -86.8166, 6.29447, 0.141886, 0.682392<br> 14929 Argument too small in __ellint_rj<br> -86.8166, 6.70017, 0.00478348, 0.812885<br> 14930 Argument too small in __ellint_rj<br> -86.8166, 8.11584, 0.421761, 0.849249<br> 14931 Argument too small in __ellint_rj<br> -86.8166, 8.26752, 0.112465, 0.843648<br> 14932 Argument too small in __ellint_rj<br> -86.8166, 9.15014, 0.915736, 0.953733<br> 14933 Argument too small in __ellint_rj<br> -86.8166, 9.29777, 0.639763, 0.936743<br> 14934 Argument too small in __ellint_rj<br> -86.8166, 9.3539, 0.792207, 0.987359<br> 14935 Argument too small in __ellint_rj<br> -86.8166, 9.37736, 0.878431, 1.02525<br> 14936 Argument too small in __ellint_rj<br> -86.8166, 9.85763, 0.959492, 1.25508<br> 14937 Argument too small in __ellint_rj<br> -86.8166, 9.92923, 0.503663, 1.16735<br> 14938 Argument too small in __ellint_rj<br> -84.7616, -8.04919, 0.655741, -0.873305<br> 14939 Argument too small in __ellint_rj<br> -84.7616, -7.46026, 0.797929, -0.879044<br> 14940 Argument too small in __ellint_rj<br> -84.7616, -7.29046, 0.0357117, -0.840785<br> 14941 Argument too small in __ellint_rj<br> -84.7616, -6.23236, 0.361294, -0.635502<br> 14942 Argument too small in __ellint_rj<br> -84.7616, -5.57932, 0.849129, -0.558231<br> 14943 Argument too small in __ellint_rj<br> -84.7616, -4.43004, 0.211924, -0.506533<br> 14944 Argument too small in __ellint_rj<br> -84.7616, -3.83666, 0.933993, -0.527681<br> 14945 Argument too small in __ellint_rj<br> -84.7616, 0.93763, 0.68136, 0.163458<br> 14946 Argument too small in __ellint_rj<br> -84.7616, 0.944412, 0.678735, 0.163582<br> 14947 Argument too small in __ellint_rj<br> -84.7616, 2.64719, 0.398739, 0.193458<br> 14948 Argument too small in __ellint_rj<br> -84.7616, 6.29447, 0.75774, 0.716086<br> 14949 Argument too small in __ellint_rj<br> -84.7616, 6.70017, 0.740647, 0.847849<br> 14950 Argument too small in __ellint_rj<br> -84.7616, 8.11584, 0.743132, 0.883827<br> 14951 Argument too small in __ellint_rj<br> -84.7616, 8.26752, 0.474759, 0.864181<br> 14952 Argument too small in __ellint_rj<br> -84.7616, 9.15014, 0.392227, 0.895646<br> 14953 Argument too small in __ellint_rj<br> -84.7616, 9.29777, 0.422088, 0.933423<br> 14954 Argument too small in __ellint_rj<br> *** FURTHER CONTENT HAS BEEN TRUNCATED 14955 FOR BREVITY ***<br> 14956 </p> 14957<h5> 14958<a name="special_function_error_rates_rep.error_logs.h91"></a> 14959 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_3_with_1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_3_with_1">Error 14960 Output For ellint_3 with compiler GNU C++ version 7.1.0 and library <cmath> 14961 and test data Elliptic Integral PI: Random Data</a> 14962 </h5> 14963<p> 14964 <a name="errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Random_Data"></a>CAUTION: 14965 Gross error found at entry 150.<br> Found: 1.09748 Expected 1.76311 Error: 14966 0.606506<br> 0.546881, 1.27977, 0.349984, 1.76311<br> CAUTION: Gross error 14967 found at entry 151.<br> Found: 1.39529 Expected 2.4686 Error: 0.769232<br> 14968 0.546881, 1.31163, 0.907365, 2.4686<br> CAUTION: Gross error found at entry 14969 152.<br> Found: 1.17627 Expected 2.03097 Error: 0.726615<br> 0.546881, 14970 1.42281, 0.196595, 2.03097<br> CAUTION: Gross error found at entry 153.<br> 14971 Found: 1.47192 Expected 2.76894 Error: 0.881179<br> 0.546881, 1.43473, 0.848468, 14972 2.76894<br> CAUTION: Gross error found at entry 154.<br> Found: 1.23674 14973 Expected 2.22733 Error: 0.800966<br> 0.546881, 1.50405, 0.251084, 2.22733<br> 14974 CAUTION: Gross error found at entry 155.<br> Found: 1.87704 Expected 3.98415 14975 Error: 1.12257<br> 0.546881, 1.51564, 0.955018, 3.98415<br> CAUTION: Gross 14976 error found at entry 156.<br> Found: 1.35817 Expected 2.53989 Error: 0.870091<br> 14977 0.546881, 1.52005, 0.616045, 2.53989<br> CAUTION: Gross error found at entry 14978 157.<br> Found: 1.48427 Expected 2.87082 Error: 0.934166<br> 0.546881, 14979 1.52189, 0.778898, 2.87082<br> CAUTION: Gross error found at entry 158.<br> 14980 Found: 1.32687 Expected 2.48679 Error: 0.874176<br> 0.546881, 1.55961, 0.473289, 14981 2.48679<br> CAUTION: Gross error found at entry 159.<br> Found: 2.37485 14982 Expected 5.58805 Error: 1.35301<br> 0.546881, 1.56524, 0.98746, 5.58805<br> 14983 CAUTION: Gross error found at entry 170.<br> Found: 1.08889 Expected 1.74565 14984 Error: 0.603142<br> 0.547221, 1.27977, 0.285839, 1.74565<br> CAUTION: Gross 14985 error found at entry 171.<br> Found: 1.21346 Expected 2.03956 Error: 0.680778<br> 14986 0.547221, 1.31163, 0.67982, 2.03956<br> CAUTION: Gross error found at entry 14987 172.<br> Found: 1.36407 Expected 2.48392 Error: 0.820965<br> 0.547221, 14988 1.42281, 0.7572, 2.48392<br> CAUTION: Gross error found at entry 173.<br> 14989 Found: 1.21442 Expected 2.12881 Error: 0.752947<br> 0.547221, 1.43473, 0.39232, 14990 2.12881<br> CAUTION: Gross error found at entry 174.<br> Found: 1.4409 14991 Expected 2.74399 Error: 0.904352<br> 0.547221, 1.50405, 0.753729, 2.74399<br> 14992 CAUTION: Gross error found at entry 175.<br> Found: 1.32796 Expected 2.46156 14993 Error: 0.853642<br> 0.547221, 1.51564, 0.561557, 2.46156<br> CAUTION: Gross 14994 error found at entry 176.<br> Found: 1.27163 Expected 2.32413 Error: 0.82767<br> 14995 0.547221, 1.52005, 0.380446, 2.32413<br> CAUTION: Gross error found at entry 14996 177.<br> Found: 1.24298 Expected 2.25511 Error: 0.814274<br> 0.547221, 14997 1.52189, 0.208068, 2.25511<br> CAUTION: Gross error found at entry 178.<br> 14998 Found: 1.36528 Expected 2.58635 Error: 0.894379<br> 0.547221, 1.55961, 0.567822, 14999 2.58635<br> CAUTION: Gross error found at entry 179.<br> Found: 1.35151 15000 Expected 2.55463 Error: 0.890206<br> 0.547221, 1.56524, 0.527371, 2.55463<br> 15001 CAUTION: Gross error found at entry 189.<br> Found: 1.01047 Expected 1.52344 15002 Error: 0.507658<br> 0.632359, 0.993308, 0.964966, 1.52344<br> CAUTION: 15003 Gross error found at entry 190.<br> Found: 1.05231 Expected 1.84135 Error: 15004 0.749817<br> 0.632359, 1.27977, 0.129906, 1.84135<br> CAUTION: Gross error 15005 found at entry 191.<br> Found: 1.07393 Expected 1.92224 Error: 0.789918<br> 15006 0.632359, 1.31163, 0.154438, 1.92224<br> CAUTION: Gross error found at entry 15007 192.<br> Found: 1.22616 Expected 2.43657 Error: 0.987156<br> 0.632359, 15008 1.42281, 0.568824, 2.43657<br> CAUTION: Gross error found at entry 193.<br> 15009 Found: 1.18462 Expected 2.33142 Error: 0.968083<br> 0.632359, 1.43473, 0.394908, 15010 2.33142<br> CAUTION: Gross error found at entry 194.<br> Found: 1.25094 15011 Expected 2.59169 Error: 1.0718<br> 0.632359, 1.50405, 0.469391, 2.59169<br> 15012 CAUTION: Gross error found at entry 195.<br> Found: 1.23693 Expected 2.56158 15013 Error: 1.07091<br> 0.632359, 1.51564, 0.387296, 2.56158<br> CAUTION: Gross 15014 error found at entry 196.<br> Found: 1.19839 Expected 2.45293 Error: 1.04685<br> 15015 0.632359, 1.52005, 0.0119021, 2.45293<br> CAUTION: Gross error found at entry 15016 197.<br> Found: 1.39415 Expected 3.05228 Error: 1.18935<br> 0.632359, 1.52189, 15017 0.726955, 3.05228<br> CAUTION: Gross error found at entry 198.<br> Found: 15018 1.25489 Expected 2.6569 Error: 1.11723<br> 0.632359, 1.55961, 0.337123, 2.6569<br> 15019 CAUTION: Gross error found at entry 199.<br> Found: 1.27021 Expected 2.70857 15020 Error: 1.13237<br> 0.632359, 1.56524, 0.38857, 2.70857<br> CAUTION: Gross 15021 error found at entry 209.<br> Found: 0.83304 Expected 1.35947 Error: 0.631944<br> 15022 0.814724, 0.993308, 0.119547, 1.35947<br> CAUTION: Gross error found at entry 15023 210.<br> Found: 1.07764 Expected 2.50291 Error: 1.32258<br> *** FURTHER 15024 CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br> 15025 </p> 15026<h5> 15027<a name="special_function_error_rates_rep.error_logs.h92"></a> 15028 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_3_with_2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_3_with_2">Error 15029 Output For ellint_3 with compiler GNU C++ version 7.1.0 and library <cmath> 15030 and test data Elliptic Integral PI: Mathworld Data</a> 15031 </h5> 15032<p> 15033 <a name="errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Mathworld_Data"></a>CAUTION: 15034 Gross error found at entry 0.<br> Found: -0.809353 Expected -1.55741 Error: 15035 0.924263<br> 1, -1, 0, -1.55741<br> CAUTION: Gross error found at entry 15036 11.<br> Found: 1.07555 Expected 13.2822 Error: 11.3492<br> 0.999023, 1.5, 15037 0, 13.2822<br> CAUTION: Gross error found at entry 13.<br> Found: -5.86896e+09 15038 Expected 1.53659e+10 Error: 1.18973e+4932<br> 0.5, 1e+10, 0.5, 1.53659e+10<br> 15039 Argument too small in __ellint_rj<br> -100000, 10, 0.75, 0.0347926<br> 15040 Argument too small in __ellint_rj<br> -1e+10, 10, 0.875, 0.000109956<br> 15041 Argument too small in __ellint_rj<br> -1e+10, 1e+20, 0.875, 1.00001e+15<br> 15042 Argument too small in __ellint_rj<br> -1e+10, 1.57031, 0.875, 1.57081e-05<br> 15043 CAUTION: Gross error found at entry 18.<br> Found: -6.25413e+09 Expected 15044 6.43274e+21 Error: 1.18973e+4932<br> 0.999023, 1e+20, 0.875, 6.43274e+21<br> 15045 CAUTION: Gross error found at entry 19.<br> Found: 0.102424 Expected 0.196321 15046 Error: 0.916748<br> 50, 0.125, 0.25, 0.196321<br> CAUTION: Gross error 15047 found at entry 20.<br> Found: 0.798807 Expected 1.773 Error: 1.21956<br> 15048 1.125, 1, 0.25, 1.773<br> CAUTION: Gross error found at entry 21.<br> Found: 15049 7.07138 Expected 0.662468 Error: 9.6743<br> 1.125, 10, 0.25, 0.662468<br> 15050 CAUTION: Gross error found at entry 22.<br> Found: 2.04288 Expected -0.142697 15051 Error: 1.18973e+4932<br> 1.125, 3, 0.25, -0.142697<br> CAUTION: Gross error 15052 found at entry 23.<br> Found: 1.07762 Expected 22.2699 Error: 19.6659<br> 15053 1.00391, 1.5, 0.125, 22.2699<br> CAUTION: Gross error found at entry 24.<br> 15054 Found: 15.1275 Expected -0.535406 Error: 1.18973e+4932<br> 1.00391, 21.5, 15055 0.125, -0.535406<br> CAUTION: Gross error found at entry 41.<br> Found: 15056 1.57454 Expected 3.0338 Error: 0.926787<br> 0.5, 2, 0, 3.0338<br> CAUTION: 15057 Gross error found at entry 42.<br> Found: 3.0338 Expected 1.57454 Error: 15058 0.926787<br> -0.5, 2, 0, 1.57454<br> CAUTION: Gross error found at entry 15059 43.<br> Found: -1.57454 Expected -3.0338 Error: 0.926787<br> 0.5, -2, 0, 15060 -3.0338<br> CAUTION: Gross error found at entry 44.<br> Found: -3.0338 15061 Expected -1.57454 Error: 0.926787<br> -0.5, -2, 0, -1.57454<br> CAUTION: 15062 Found non-finite result, when a finite value was expected at entry 51<br> 15063 Found: inf Expected -2.87535 Error: 1.18973e+4932<br> 1, 2, 0.5, -2.87535<br> 15064 CAUTION: Gross error found at entry 51.<br> Found: inf Expected -2.87535 15065 Error: 1.18973e+4932<br> 1, 2, 0.5, -2.87535<br> CAUTION: Found non-finite 15066 result, when a finite value was expected at entry 52<br> Found: -inf Expected 15067 2.87535 Error: 1.18973e+4932<br> 1, -2, 0.5, 2.87535<br> CAUTION: Gross 15068 error found at entry 52.<br> Found: -inf Expected 2.87535 Error: 1.18973e+4932<br> 15069 1, -2, 0.5, 2.87535<br> CAUTION: Found non-finite result, when a finite value 15070 was expected at entry 53<br> Found: inf Expected -2.18504 Error: 1.18973e+4932<br> 15071 1, 2, 6.22302e-61, -2.18504<br> CAUTION: Gross error found at entry 53.<br> 15072 Found: inf Expected -2.18504 Error: 1.18973e+4932<br> 1, 2, 6.22302e-61, 15073 -2.18504<br> CAUTION: Found non-finite result, when a finite value was expected 15074 at entry 54<br> Found: -inf Expected 2.18504 Error: 1.18973e+4932<br> 1, 15075 -2, 6.22302e-61, 2.18504<br> CAUTION: Gross error found at entry 54.<br> 15076 Found: -inf Expected 2.18504 Error: 1.18973e+4932<br> 1, -2, 6.22302e-61, 15077 2.18504<br> CAUTION: Gross error found at entry 57.<br> Found: 0.703907 15078 Expected 0.000975941 Error: 720.259<br> 20, 3.14257, 0.5, 0.000975941<br> 15079 CAUTION: Gross error found at entry 58.<br> Found: -0.703907 Expected -0.000975941 15080 Error: 720.259<br> 20, -3.14257, 0.5, -0.000975941<br> CAUTION: Gross error 15081 found at entry 59.<br> Found: 1.24445 Expected -27.1647 Error: 1.18973e+4932<br> 15082 1.01562, 1.6958, 0.5, -27.1647<br> CAUTION: Gross error found at entry 60.<br> 15083 Found: -1.24445 Expected 27.1647 Error: 1.18973e+4932<br> 1.01562, -1.6958, 15084 0.5, 27.1647<br> 15085 </p> 15086<h5> 15087<a name="special_function_error_rates_rep.error_logs.h93"></a> 15088 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_expint_ei_with_"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_expint_ei_with_">Error 15089 Output For expint (Ei) with compiler GNU C++ version 7.1.0 and library <cmath> 15090 and test data Exponential Integral Ei</a> 15091 </h5> 15092<p> 15093 <a name="errors_GNU_C_version_7_1_0_linux_long_double_expint_Ei___cmath__Exponential_Integral_Ei"></a>Continued 15094 fraction failed in __expint_En_cont_frac.<br> -1.30539, -0.134326<br> 15095 </p> 15096<h5> 15097<a name="special_function_error_rates_rep.error_logs.h94"></a> 15098 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ibeta_with_comp"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ibeta_with_comp">Error 15099 Output For ibeta with compiler GNU C++ version 7.1.0 and library GSL 2.1 and 15100 test data Incomplete Beta Function: Large and Diverse Values</a> 15101 </h5> 15102<p> 15103 <a name="errors_GNU_C_version_7_1_0_linux_double_ibeta_GSL_2_1_Incomplete_Beta_Function_Large_and_Diverse_Values"></a>underflow<br> 15104 1.04761e-05, 39078.2, 0.913384, 95444.4, 0, 1, 0<br> underflow<br> 1.2158e-05, 15105 24110.5, 0.135563, 82239.7, 0, 1, 0<br> underflow<br> 1.30342e-05, 26168.3, 15106 0.127074, 76710.7, 0, 1, 0<br> underflow<br> 1.51962e-05, 16177.5, 0.814742, 15107 65795.4, 0, 1, 0<br> underflow<br> 1.64873e-05, 470997, 0.127074, 60639.1, 15108 0, 1, 0<br> underflow<br> 1.66259e-05, 147819, 0.632396, 60134.5, 0, 1, 15109 0<br> underflow<br> 1.78638e-05, 439.387, 0.835025, 55972.4, 0, 1, 0<br> 15110 underflow<br> 2.00434e-05, 482.007, 0.905801, 49885.1, 0, 1, 0<br> underflow<br> 15111 2.05189e-05, 236088, 0.835025, 48722.7, 0, 1, 0<br> underflow<br> 2.14336e-05, 15112 3719.28, 0.814742, 46647, 0, 1, 0<br> underflow<br> 2.24486e-05, 445071, 15113 0.221112, 44532.6, 0, 1, 0<br> underflow<br> 2.34849e-05, 25542.8, 0.968871, 15114 42569.8, 0, 1, 0<br> underflow<br> 2.39993e-05, 462.946, 0.814742, 41661.1, 15115 0, 1, 0<br> underflow<br> 2.52178e-05, 1832.27, 0.913384, 39646.4, 0, 1, 15116 0<br> underflow<br> 2.87756e-05, 25491.8, 0.905801, 34740.9, 0, 1, 0<br> 15117 underflow<br> 2.89316e-05, 494.984, 0.968871, 34557.6, 0, 1, 0<br> underflow<br> 15118 3.11413e-05, 348144, 0.308236, 32098.3, 0, 1, 0<br> underflow<br> 3.12319e-05, 15119 33713, 0.221112, 32007.5, 0, 1, 0<br> underflow<br> 3.19889e-05, 3931.19, 15120 0.308236, 31251.9, 0, 1, 0<br> underflow<br> 3.27129e-05, 3109.49, 0.968871, 15121 30560.4, 0, 1, 0<br> underflow<br> 3.27529e-05, 25796.3, 0.835025, 30520.9, 15122 0, 1, 0<br> underflow<br> 3.34106e-05, 3378.01, 0.221112, 29922, 0, 1, 15123 0<br> underflow<br> 3.40793e-05, 288783, 0.814742, 29330.2, 0, 1, 0<br> 15124 underflow<br> 3.46418e-05, 411.559, 0.913384, 28860.3, 0, 1, 0<br> underflow<br> 15125 3.61632e-05, 311937, 0.905801, 27639.2, 0, 1, 0<br> underflow<br> 3.75686e-05, 15126 386440, 0.913384, 26604.5, 0, 1, 0<br> underflow<br> 3.99261e-05, 495352, 15127 0.968871, 25032.6, 0, 1, 0<br> underflow<br> 4.01492e-05, 3246.23, 0.905801, 15128 24898.5, 0, 1, 0<br> underflow<br> 4.0288e-05, 2569.28, 0.835025, 24812.9, 15129 0, 1, 0<br> underflow<br> 4.11667e-05, 24253.8, 0.308236, 24280.8, 0, 1, 15130 0<br> underflow<br> 4.17714e-05, 274447, 0.135563, 23926.7, 0, 1, 0<br> 15131 underflow<br> 4.66877e-05, 3780.93, 0.632396, 21410.1, 0, 1, 0<br> underflow<br> 15132 4.73604e-05, 48598.7, 0.632396, 21103.3, 0, 1, 0<br> underflow<br> 0.00013245, 15133 251.768, 0.968871, 7543.9, 0, 1, 0<br> underflow<br> 0.000168283, 195801, 15134 0.905801, 5929.61, 0, 1, 0<br> underflow<br> 0.000177906, 276489, 0.814742, 15135 5607.86, 0, 1, 0<br> underflow<br> 0.000183097, 316055, 0.127074, 5448.36, 15136 0, 1, 0<br> underflow<br> 0.000190369, 159132, 0.835025, 5240.42, 0, 1, 15137 0<br> underflow<br> 0.000191066, 419861, 0.913384, 5220.29, 0, 1, 0<br> 15138 underflow<br> 0.000192195, 177798, 0.308236, 5190.39, 0, 1, 0<br> underflow<br> 15139 0.000220499, 107380, 0.135563, 4523.03, 0, 1, 0<br> underflow<br> 0.00022254, 15140 1432.25, 0.814742, 4485.74, 0, 1, 0<br> underflow<br> 0.000240291, 49604.4, 15141 0.632396, 4150.25, 0, 1, 0<br> underflow<br> 0.000251444, 15605.8, 0.135563, 15142 3966.81, 0, 1, 0<br> underflow<br> 0.000274279, 289206, 0.968871, 3632.79, 15143 0, 1, 0<br> underflow<br> 0.000274343, 2954.47, 0.308236, 3636.51, 0, 1, 15144 0<br> underflow<br> 0.000278714, 4023.16, 0.632396, 3579.05, 0, 1, 0<br> 15145 underflow<br> 0.000288369, 460073, 0.221112, 3454.19, 0, 1, 0<br> underflow<br> 15146 0.000294717, 4642.26, 0.221112, 3384.08, 0, 1, 0<br> underflow<br> 0.000303403, 15147 2574.36, 0.835025, 3287.52, 0, 1, 0<br> underflow<br> 0.000304309, 4480.75, 15148 0.905801, 3277.17, 0, 1, 0<br> underflow<br> 0.00031313, 47957, 0.308236, 15149 3182.22, 0, 1, 0<br> underflow<br> 0.000320063, 25544.6, 0.905801, 3113.68, 15150 0, 1, 0<br> underflow<br> 0.000334818, 29065.5, 0.968871, 2975.86, 0, 1, 15151 0<br> underflow<br> 0.00034899, 41187.6, 0.913384, 2854.23, 0, 1, 0<br> 15152 underflow<br> 0.000350247, 426.308, 0.905801, 2848.5, 0, 1, 0<br> underflow<br> 15153 0.000357727, 31752.2, 0.127074, 2784.5, 0, 1, 0<br> underflow<br> 0.000412091, 15154 367.714, 0.913384, 2420.17, 0, 1, 0<br> underflow<br> 0.000417933, 4668.47, 15155 0.968871, 2383.72, 0, 1, 0<br> underflow<br> 0.000424632, 17994.9, 0.221112, 15156 2344.63, 0, 1, 0<br> underflow<br> 0.000427051, 2443.44, 0.913384, 2333.28, 15157 0, 1, 0<br> underflow<br> 0.000437724, 454399, 0.632396, 2270.98, 0, 1, 15158 0<br> underflow<br> 0.000450377, 10660.8, 0.835025, 2210.53, 0, 1, 0<br> 15159 underflow<br> 0.000475601, 19603, 0.814742, 2092.17, 0, 1, 0<br> underflow<br> 15160 0.00116972, 4487.22, 0.221112, 845.964, 0, 1, 0<br> underflow<br> 0.00124188, 15161 211066, 0.632396, 792.493, 0, 1, 0<br> underflow<br> 0.00128578, 4738.41, 15162 0.308236, 768.75, 0, 1, 0<br> underflow<br> 0.00133388, 46277.8, 0.913384, 15163 738.46, 0, 1, 0<br> underflow<br> 0.00138692, 2158.76, 0.814742, 712.816, 15164 0, 1, 0<br> underflow<br> 0.00153268, 13060.2, 0.968871, 642.474, 0, 1, 15165 0<br> underflow<br> 0.00159946, 1780.43, 0.968871, 617.202, 0, 1, 0<br> 15166 *** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br> 15167 </p> 15168<h5> 15169<a name="special_function_error_rates_rep.error_logs.h95"></a> 15170 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_jacobi_dn_with_"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_jacobi_dn_with_">Error 15171 Output For jacobi_dn with compiler GNU C++ version 7.1.0 and library GSL 2.1 15172 and test data Jacobi Elliptic: Modulus near 1</a> 15173 </h5> 15174<p> 15175 <a name="errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1"></a>|m| 15176 > 1.0<br> -4.0246, 1, -0.999361, 0.0357365, 0.0357231<br> |m| > 1.0<br> 15177 -4.0246, 1, -0.999361, 0.0357497, 0.0357097<br> |m| > 1.0<br> -4.0246, 15178 1, -0.99936, 0.0357762, 0.0356829<br> |m| > 1.0<br> -4.0246, 1, -0.999359, 15179 0.0357895, 0.0356695<br> |m| > 1.0<br> -4.0246, 1.00001, -0.999354, 15180 0.0359354, 0.0355222<br> |m| > 1.0<br> -4.0246, 1.00003, -0.999347, 15181 0.0361343, 0.0353212<br> |m| > 1.0<br> -4.0246, 1.00004, -0.999343, 15182 0.036247, 0.0352073<br> |m| > 1.0<br> -4.0246, 1.0001, -0.999311, 0.0371157, 15183 0.0343296<br> |m| > 1.0<br> -4.0246, 1.00016, -0.99928, 0.0379513, 0.0334851<br> 15184 |m| > 1.0<br> -4.0246, 1.00027, -0.999221, 0.0394571, 0.0319634<br> 15185 |m| > 1.0<br> -4.0246, 1.00076, -0.99893, 0.0462407, 0.0251046<br> |m| 15186 > 1.0<br> -4.0246, 1.00125, -0.998589, 0.0531109, 0.0181532<br> |m| 15187 > 1.0<br> -4.0246, 1.00232, -0.99768, 0.0680761, 0.0029944<br> |m| > 15188 1.0<br> -4.0246, 1.00604, -0.992752, 0.120179, -0.049966<br> |m| > 1.0<br> 15189 -4.0246, 1.01557, -0.967356, 0.25342, -0.186698<br> |m| > 1.0<br> -4.0246, 15190 1.03059, -0.890373, 0.455232, -0.397492<br> |m| > 1.0<br> -4.0246, 1.06239, 15191 -0.607191, 0.794556, -0.76412<br> |m| > 1.0<br> -3.73013, 1, -0.998849, 15192 0.0479567, 0.0479467<br> |m| > 1.0<br> -3.73013, 1, -0.998849, 0.0479665, 15193 0.0479367<br> |m| > 1.0<br> -3.73013, 1, -0.998848, 0.0479862, 0.0479167<br> 15194 |m| > 1.0<br> -3.73013, 1, -0.998848, 0.047996, 0.0479067<br> |m| > 15195 1.0<br> -3.73013, 1.00001, -0.998842, 0.0481042, 0.0477966<br> |m| > 15196 1.0<br> -3.73013, 1.00003, -0.998835, 0.0482517, 0.0476465<br> |m| > 15197 1.0<br> -3.73013, 1.00004, -0.998831, 0.0483354, 0.0475615<br> |m| > 15198 1.0<br> -3.73013, 1.0001, -0.9988, 0.0489797, 0.0469059<br> |m| > 1.0<br> 15199 -3.73013, 1.00016, -0.998769, 0.0495995, 0.0462752<br> |m| > 1.0<br> 15200 -3.73013, 1.00027, -0.998713, 0.0507164, 0.0451386<br> |m| > 1.0<br> 15201 -3.73013, 1.00076, -0.998445, 0.0557477, 0.0400164<br> |m| > 1.0<br> 15202 -3.73013, 1.00125, -0.998147, 0.0608429, 0.0348257<br> |m| > 1.0<br> 15203 -3.73013, 1.00232, -0.997409, 0.0719406, 0.0235071<br> |m| > 1.0<br> 15204 -3.73013, 1.00604, -0.993866, 0.110593, -0.016048<br> |m| > 1.0<br> 15205 -3.73013, 1.01557, -0.977708, 0.209971, -0.118704<br> |m| > 1.0<br> 15206 -3.73013, 1.03059, -0.931162, 0.364606, -0.281224<br> |m| > 1.0<br> 15207 -3.73013, 1.06239, -0.753495, 0.657453, -0.599326<br> |m| > 1.0<br> 15208 -3.64523, 1, -0.998637, 0.0521997, 0.0521906<br> |m| > 1.0<br> -3.64523, 15209 1, -0.998636, 0.0522087, 0.0521814<br> |m| > 1.0<br> -3.64523, 1, -0.998635, 15210 0.0522268, 0.052163<br> |m| > 1.0<br> -3.64523, 1, -0.998635, 0.0522358, 15211 0.0521538<br> |m| > 1.0<br> -3.64523, 1.00001, -0.99863, 0.052335, 0.0520526<br> 15212 |m| > 1.0<br> -3.64523, 1.00003, -0.998622, 0.0524703, 0.0519145<br> 15213 |m| > 1.0<br> -3.64523, 1.00004, -0.998618, 0.052547, 0.0518363<br> 15214 |m| > 1.0<br> -3.64523, 1.0001, -0.998587, 0.0531379, 0.0512335<br> 15215 |m| > 1.0<br> -3.64523, 1.00016, -0.998557, 0.0537063, 0.0506536<br> 15216 |m| > 1.0<br> -3.64523, 1.00027, -0.998501, 0.0547305, 0.0496084<br> 15217 |m| > 1.0<br> -3.64523, 1.00076, -0.998238, 0.0593443, 0.0448986<br> 15218 |m| > 1.0<br> -3.64523, 1.00125, -0.997949, 0.0640165, 0.0401258<br> 15219 |m| > 1.0<br> -3.64523, 1.00232, -0.997244, 0.0741927, 0.0297191<br> 15220 |m| > 1.0<br> -3.64523, 1.00604, -0.993972, 0.109636, -0.00664888<br> 15221 |m| > 1.0<br> -3.64523, 1.01557, -0.979623, 0.200844, -0.101111<br> 15222 |m| > 1.0<br> -3.64523, 1.03059, -0.939163, 0.343472, -0.251382<br> 15223 |m| > 1.0<br> -3.64523, 1.06239, -0.784719, 0.619852, -0.552253<br> 15224 |m| > 1.0<br> -3.11618, 1, -0.996078, 0.0884811, 0.0884757<br> |m| > 15225 1.0<br> -3.11618, 1, -0.996077, 0.0884863, 0.0884702<br> |m| > 1.0<br> 15226 -3.11618, 1, -0.996076, 0.0884967, 0.0884593<br> |m| > 1.0<br> -3.11618, 15227 1, -0.996076, 0.0885019, 0.0884538<br> |m| > 1.0<br> -3.11618, 1.00001, 15228 -0.996071, 0.0885593, 0.0883936<br> |m| > 1.0<br> -3.11618, 1.00003, 15229 -0.996064, 0.0886376, 0.0883114<br> |m| > 1.0<br> -3.11618, 1.00004, 15230 -0.99606, 0.0886819, 0.0882648<br> |m| > 1.0<br> -3.11618, 1.0001, -0.99603, 15231 0.0890236, 0.0879059<br> |m| > 1.0<br> -3.11618, 1.00016, -0.996, 0.0893523, 15232 0.0875607<br> |m| > 1.0<br> -3.11618, 1.00027, -0.995947, 0.0899445, 15233 0.0869386<br> |m| > 1.0<br> -3.11618, 1.00076, -0.995702, 0.092612, 15234 0.0841353<br> |m| > 1.0<br> -3.11618, 1.00125, -0.995447, 0.0953126, 15235 0.0812953<br> |m| > 1.0<br> -3.11618, 1.00232, -0.994867, 0.101193, 15236 0.0751049<br> |m| > 1.0<br> -3.11618, 1.00604, -0.992571, 0.121667, 15237 0.0534858<br> |m| > 1.0<br> -3.11618, 1.01557, -0.984666, 0.174451, 15238 -0.00273723<br> |m| > 1.0<br> -3.11618, 1.03059, -0.966077, 0.258253, 15239 -0.0934336<br> |m| > 1.0<br> -3.11618, 1.06239, -0.901067, 0.433681, 15240 -0.289151<br> |m| > 1.0<br> -2.78966, 1, -0.992478, 0.122424, 0.12242<br> 15241 |m| > 1.0<br> -2.78966, 1, -0.992477, 0.122428, 0.122416<br> *** FURTHER 15242 CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br> 15243 </p> 15244<h5> 15245<a name="special_function_error_rates_rep.error_logs.h96"></a> 15246 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_jacobi_cn_with_"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_jacobi_cn_with_">Error 15247 Output For jacobi_cn with compiler GNU C++ version 7.1.0 and library GSL 2.1 15248 and test data Jacobi Elliptic: Modulus near 1</a> 15249 </h5> 15250<p> 15251 <a name="errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1"></a>|m| 15252 > 1.0<br> -4.0246, 1, -0.999361, 0.0357365, 0.0357231<br> |m| > 1.0<br> 15253 -4.0246, 1, -0.999361, 0.0357497, 0.0357097<br> |m| > 1.0<br> -4.0246, 15254 1, -0.99936, 0.0357762, 0.0356829<br> |m| > 1.0<br> -4.0246, 1, -0.999359, 15255 0.0357895, 0.0356695<br> |m| > 1.0<br> -4.0246, 1.00001, -0.999354, 15256 0.0359354, 0.0355222<br> |m| > 1.0<br> -4.0246, 1.00003, -0.999347, 15257 0.0361343, 0.0353212<br> |m| > 1.0<br> -4.0246, 1.00004, -0.999343, 15258 0.036247, 0.0352073<br> |m| > 1.0<br> -4.0246, 1.0001, -0.999311, 0.0371157, 15259 0.0343296<br> |m| > 1.0<br> -4.0246, 1.00016, -0.99928, 0.0379513, 0.0334851<br> 15260 |m| > 1.0<br> -4.0246, 1.00027, -0.999221, 0.0394571, 0.0319634<br> 15261 |m| > 1.0<br> -4.0246, 1.00076, -0.99893, 0.0462407, 0.0251046<br> |m| 15262 > 1.0<br> -4.0246, 1.00125, -0.998589, 0.0531109, 0.0181532<br> |m| 15263 > 1.0<br> -4.0246, 1.00232, -0.99768, 0.0680761, 0.0029944<br> |m| > 15264 1.0<br> -4.0246, 1.00604, -0.992752, 0.120179, -0.049966<br> |m| > 1.0<br> 15265 -4.0246, 1.01557, -0.967356, 0.25342, -0.186698<br> |m| > 1.0<br> -4.0246, 15266 1.03059, -0.890373, 0.455232, -0.397492<br> |m| > 1.0<br> -4.0246, 1.06239, 15267 -0.607191, 0.794556, -0.76412<br> |m| > 1.0<br> -3.73013, 1, -0.998849, 15268 0.0479567, 0.0479467<br> |m| > 1.0<br> -3.73013, 1, -0.998849, 0.0479665, 15269 0.0479367<br> |m| > 1.0<br> -3.73013, 1, -0.998848, 0.0479862, 0.0479167<br> 15270 |m| > 1.0<br> -3.73013, 1, -0.998848, 0.047996, 0.0479067<br> |m| > 15271 1.0<br> -3.73013, 1.00001, -0.998842, 0.0481042, 0.0477966<br> |m| > 15272 1.0<br> -3.73013, 1.00003, -0.998835, 0.0482517, 0.0476465<br> |m| > 15273 1.0<br> -3.73013, 1.00004, -0.998831, 0.0483354, 0.0475615<br> |m| > 15274 1.0<br> -3.73013, 1.0001, -0.9988, 0.0489797, 0.0469059<br> |m| > 1.0<br> 15275 -3.73013, 1.00016, -0.998769, 0.0495995, 0.0462752<br> |m| > 1.0<br> 15276 -3.73013, 1.00027, -0.998713, 0.0507164, 0.0451386<br> |m| > 1.0<br> 15277 -3.73013, 1.00076, -0.998445, 0.0557477, 0.0400164<br> |m| > 1.0<br> 15278 -3.73013, 1.00125, -0.998147, 0.0608429, 0.0348257<br> |m| > 1.0<br> 15279 -3.73013, 1.00232, -0.997409, 0.0719406, 0.0235071<br> |m| > 1.0<br> 15280 -3.73013, 1.00604, -0.993866, 0.110593, -0.016048<br> |m| > 1.0<br> 15281 -3.73013, 1.01557, -0.977708, 0.209971, -0.118704<br> |m| > 1.0<br> 15282 -3.73013, 1.03059, -0.931162, 0.364606, -0.281224<br> |m| > 1.0<br> 15283 -3.73013, 1.06239, -0.753495, 0.657453, -0.599326<br> |m| > 1.0<br> 15284 -3.64523, 1, -0.998637, 0.0521997, 0.0521906<br> |m| > 1.0<br> -3.64523, 15285 1, -0.998636, 0.0522087, 0.0521814<br> |m| > 1.0<br> -3.64523, 1, -0.998635, 15286 0.0522268, 0.052163<br> |m| > 1.0<br> -3.64523, 1, -0.998635, 0.0522358, 15287 0.0521538<br> |m| > 1.0<br> -3.64523, 1.00001, -0.99863, 0.052335, 0.0520526<br> 15288 |m| > 1.0<br> -3.64523, 1.00003, -0.998622, 0.0524703, 0.0519145<br> 15289 |m| > 1.0<br> -3.64523, 1.00004, -0.998618, 0.052547, 0.0518363<br> 15290 |m| > 1.0<br> -3.64523, 1.0001, -0.998587, 0.0531379, 0.0512335<br> 15291 |m| > 1.0<br> -3.64523, 1.00016, -0.998557, 0.0537063, 0.0506536<br> 15292 |m| > 1.0<br> -3.64523, 1.00027, -0.998501, 0.0547305, 0.0496084<br> 15293 |m| > 1.0<br> -3.64523, 1.00076, -0.998238, 0.0593443, 0.0448986<br> 15294 |m| > 1.0<br> -3.64523, 1.00125, -0.997949, 0.0640165, 0.0401258<br> 15295 |m| > 1.0<br> -3.64523, 1.00232, -0.997244, 0.0741927, 0.0297191<br> 15296 |m| > 1.0<br> -3.64523, 1.00604, -0.993972, 0.109636, -0.00664888<br> 15297 |m| > 1.0<br> -3.64523, 1.01557, -0.979623, 0.200844, -0.101111<br> 15298 |m| > 1.0<br> -3.64523, 1.03059, -0.939163, 0.343472, -0.251382<br> 15299 |m| > 1.0<br> -3.64523, 1.06239, -0.784719, 0.619852, -0.552253<br> 15300 |m| > 1.0<br> -3.11618, 1, -0.996078, 0.0884811, 0.0884757<br> |m| > 15301 1.0<br> -3.11618, 1, -0.996077, 0.0884863, 0.0884702<br> |m| > 1.0<br> 15302 -3.11618, 1, -0.996076, 0.0884967, 0.0884593<br> |m| > 1.0<br> -3.11618, 15303 1, -0.996076, 0.0885019, 0.0884538<br> |m| > 1.0<br> -3.11618, 1.00001, 15304 -0.996071, 0.0885593, 0.0883936<br> |m| > 1.0<br> -3.11618, 1.00003, 15305 -0.996064, 0.0886376, 0.0883114<br> |m| > 1.0<br> -3.11618, 1.00004, 15306 -0.99606, 0.0886819, 0.0882648<br> |m| > 1.0<br> -3.11618, 1.0001, -0.99603, 15307 0.0890236, 0.0879059<br> |m| > 1.0<br> -3.11618, 1.00016, -0.996, 0.0893523, 15308 0.0875607<br> |m| > 1.0<br> -3.11618, 1.00027, -0.995947, 0.0899445, 15309 0.0869386<br> |m| > 1.0<br> -3.11618, 1.00076, -0.995702, 0.092612, 15310 0.0841353<br> |m| > 1.0<br> -3.11618, 1.00125, -0.995447, 0.0953126, 15311 0.0812953<br> |m| > 1.0<br> -3.11618, 1.00232, -0.994867, 0.101193, 15312 0.0751049<br> |m| > 1.0<br> -3.11618, 1.00604, -0.992571, 0.121667, 15313 0.0534858<br> |m| > 1.0<br> -3.11618, 1.01557, -0.984666, 0.174451, 15314 -0.00273723<br> |m| > 1.0<br> -3.11618, 1.03059, -0.966077, 0.258253, 15315 -0.0934336<br> |m| > 1.0<br> -3.11618, 1.06239, -0.901067, 0.433681, 15316 -0.289151<br> |m| > 1.0<br> -2.78966, 1, -0.992478, 0.122424, 0.12242<br> 15317 |m| > 1.0<br> -2.78966, 1, -0.992477, 0.122428, 0.122416<br> *** FURTHER 15318 CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br> 15319 </p> 15320<h5> 15321<a name="special_function_error_rates_rep.error_logs.h97"></a> 15322 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_jacobi_sn_with_"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_jacobi_sn_with_">Error 15323 Output For jacobi_sn with compiler GNU C++ version 7.1.0 and library GSL 2.1 15324 and test data Jacobi Elliptic: Modulus near 1</a> 15325 </h5> 15326<p> 15327 <a name="errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1"></a>|m| 15328 > 1.0<br> -4.0246, 1, -0.999361, 0.0357365, 0.0357231<br> |m| > 1.0<br> 15329 -4.0246, 1, -0.999361, 0.0357497, 0.0357097<br> |m| > 1.0<br> -4.0246, 15330 1, -0.99936, 0.0357762, 0.0356829<br> |m| > 1.0<br> -4.0246, 1, -0.999359, 15331 0.0357895, 0.0356695<br> |m| > 1.0<br> -4.0246, 1.00001, -0.999354, 15332 0.0359354, 0.0355222<br> |m| > 1.0<br> -4.0246, 1.00003, -0.999347, 15333 0.0361343, 0.0353212<br> |m| > 1.0<br> -4.0246, 1.00004, -0.999343, 15334 0.036247, 0.0352073<br> |m| > 1.0<br> -4.0246, 1.0001, -0.999311, 0.0371157, 15335 0.0343296<br> |m| > 1.0<br> -4.0246, 1.00016, -0.99928, 0.0379513, 0.0334851<br> 15336 |m| > 1.0<br> -4.0246, 1.00027, -0.999221, 0.0394571, 0.0319634<br> 15337 |m| > 1.0<br> -4.0246, 1.00076, -0.99893, 0.0462407, 0.0251046<br> |m| 15338 > 1.0<br> -4.0246, 1.00125, -0.998589, 0.0531109, 0.0181532<br> |m| 15339 > 1.0<br> -4.0246, 1.00232, -0.99768, 0.0680761, 0.0029944<br> |m| > 15340 1.0<br> -4.0246, 1.00604, -0.992752, 0.120179, -0.049966<br> |m| > 1.0<br> 15341 -4.0246, 1.01557, -0.967356, 0.25342, -0.186698<br> |m| > 1.0<br> -4.0246, 15342 1.03059, -0.890373, 0.455232, -0.397492<br> |m| > 1.0<br> -4.0246, 1.06239, 15343 -0.607191, 0.794556, -0.76412<br> |m| > 1.0<br> -3.73013, 1, -0.998849, 15344 0.0479567, 0.0479467<br> |m| > 1.0<br> -3.73013, 1, -0.998849, 0.0479665, 15345 0.0479367<br> |m| > 1.0<br> -3.73013, 1, -0.998848, 0.0479862, 0.0479167<br> 15346 |m| > 1.0<br> -3.73013, 1, -0.998848, 0.047996, 0.0479067<br> |m| > 15347 1.0<br> -3.73013, 1.00001, -0.998842, 0.0481042, 0.0477966<br> |m| > 15348 1.0<br> -3.73013, 1.00003, -0.998835, 0.0482517, 0.0476465<br> |m| > 15349 1.0<br> -3.73013, 1.00004, -0.998831, 0.0483354, 0.0475615<br> |m| > 15350 1.0<br> -3.73013, 1.0001, -0.9988, 0.0489797, 0.0469059<br> |m| > 1.0<br> 15351 -3.73013, 1.00016, -0.998769, 0.0495995, 0.0462752<br> |m| > 1.0<br> 15352 -3.73013, 1.00027, -0.998713, 0.0507164, 0.0451386<br> |m| > 1.0<br> 15353 -3.73013, 1.00076, -0.998445, 0.0557477, 0.0400164<br> |m| > 1.0<br> 15354 -3.73013, 1.00125, -0.998147, 0.0608429, 0.0348257<br> |m| > 1.0<br> 15355 -3.73013, 1.00232, -0.997409, 0.0719406, 0.0235071<br> |m| > 1.0<br> 15356 -3.73013, 1.00604, -0.993866, 0.110593, -0.016048<br> |m| > 1.0<br> 15357 -3.73013, 1.01557, -0.977708, 0.209971, -0.118704<br> |m| > 1.0<br> 15358 -3.73013, 1.03059, -0.931162, 0.364606, -0.281224<br> |m| > 1.0<br> 15359 -3.73013, 1.06239, -0.753495, 0.657453, -0.599326<br> |m| > 1.0<br> 15360 -3.64523, 1, -0.998637, 0.0521997, 0.0521906<br> |m| > 1.0<br> -3.64523, 15361 1, -0.998636, 0.0522087, 0.0521814<br> |m| > 1.0<br> -3.64523, 1, -0.998635, 15362 0.0522268, 0.052163<br> |m| > 1.0<br> -3.64523, 1, -0.998635, 0.0522358, 15363 0.0521538<br> |m| > 1.0<br> -3.64523, 1.00001, -0.99863, 0.052335, 0.0520526<br> 15364 |m| > 1.0<br> -3.64523, 1.00003, -0.998622, 0.0524703, 0.0519145<br> 15365 |m| > 1.0<br> -3.64523, 1.00004, -0.998618, 0.052547, 0.0518363<br> 15366 |m| > 1.0<br> -3.64523, 1.0001, -0.998587, 0.0531379, 0.0512335<br> 15367 |m| > 1.0<br> -3.64523, 1.00016, -0.998557, 0.0537063, 0.0506536<br> 15368 |m| > 1.0<br> -3.64523, 1.00027, -0.998501, 0.0547305, 0.0496084<br> 15369 |m| > 1.0<br> -3.64523, 1.00076, -0.998238, 0.0593443, 0.0448986<br> 15370 |m| > 1.0<br> -3.64523, 1.00125, -0.997949, 0.0640165, 0.0401258<br> 15371 |m| > 1.0<br> -3.64523, 1.00232, -0.997244, 0.0741927, 0.0297191<br> 15372 |m| > 1.0<br> -3.64523, 1.00604, -0.993972, 0.109636, -0.00664888<br> 15373 |m| > 1.0<br> -3.64523, 1.01557, -0.979623, 0.200844, -0.101111<br> 15374 |m| > 1.0<br> -3.64523, 1.03059, -0.939163, 0.343472, -0.251382<br> 15375 |m| > 1.0<br> -3.64523, 1.06239, -0.784719, 0.619852, -0.552253<br> 15376 |m| > 1.0<br> -3.11618, 1, -0.996078, 0.0884811, 0.0884757<br> |m| > 15377 1.0<br> -3.11618, 1, -0.996077, 0.0884863, 0.0884702<br> |m| > 1.0<br> 15378 -3.11618, 1, -0.996076, 0.0884967, 0.0884593<br> |m| > 1.0<br> -3.11618, 15379 1, -0.996076, 0.0885019, 0.0884538<br> |m| > 1.0<br> -3.11618, 1.00001, 15380 -0.996071, 0.0885593, 0.0883936<br> |m| > 1.0<br> -3.11618, 1.00003, 15381 -0.996064, 0.0886376, 0.0883114<br> |m| > 1.0<br> -3.11618, 1.00004, 15382 -0.99606, 0.0886819, 0.0882648<br> |m| > 1.0<br> -3.11618, 1.0001, -0.99603, 15383 0.0890236, 0.0879059<br> |m| > 1.0<br> -3.11618, 1.00016, -0.996, 0.0893523, 15384 0.0875607<br> |m| > 1.0<br> -3.11618, 1.00027, -0.995947, 0.0899445, 15385 0.0869386<br> |m| > 1.0<br> -3.11618, 1.00076, -0.995702, 0.092612, 15386 0.0841353<br> |m| > 1.0<br> -3.11618, 1.00125, -0.995447, 0.0953126, 15387 0.0812953<br> |m| > 1.0<br> -3.11618, 1.00232, -0.994867, 0.101193, 15388 0.0751049<br> |m| > 1.0<br> -3.11618, 1.00604, -0.992571, 0.121667, 15389 0.0534858<br> |m| > 1.0<br> -3.11618, 1.01557, -0.984666, 0.174451, 15390 -0.00273723<br> |m| > 1.0<br> -3.11618, 1.03059, -0.966077, 0.258253, 15391 -0.0934336<br> |m| > 1.0<br> -3.11618, 1.06239, -0.901067, 0.433681, 15392 -0.289151<br> |m| > 1.0<br> -2.78966, 1, -0.992478, 0.122424, 0.12242<br> 15393 |m| > 1.0<br> -2.78966, 1, -0.992477, 0.122428, 0.122416<br> *** FURTHER 15394 CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br> 15395 </p> 15396<h5> 15397<a name="special_function_error_rates_rep.error_logs.h98"></a> 15398 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_jacobi_dn_with0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_jacobi_dn_with0">Error 15399 Output For jacobi_dn with compiler GNU C++ version 7.1.0 and library GSL 2.1 15400 and test data Jacobi Elliptic: Random Small Values</a> 15401 </h5> 15402<p> 15403 <a name="errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values"></a>|m| 15404 > 1.0<br> 1.65048e-12, 1.65574, 1.65048e-12, 1, 1<br> |m| > 1.0<br> 15405 2.06542e-12, 1.65574, 2.06542e-12, 1, 1<br> |m| > 1.0<br> 6.93323e-12, 15406 1.65574, 6.93323e-12, 1, 1<br> |m| > 1.0<br> 1.33514e-11, 1.65574, 1.33514e-11, 15407 1, 1<br> |m| > 1.0<br> 1.63998e-11, 1.65574, 1.63998e-11, 1, 1<br> 15408 |m| > 1.0<br> 5.73016e-11, 1.65574, 5.73016e-11, 1, 1<br> |m| > 1.0<br> 15409 1.11373e-10, 1.65574, 1.11373e-10, 1, 1<br> |m| > 1.0<br> 1.42147e-10, 15410 1.65574, 1.42147e-10, 1, 1<br> |m| > 1.0<br> 3.80063e-10, 1.65574, 3.80063e-10, 15411 1, 1<br> |m| > 1.0<br> 6.09163e-10, 1.65574, 6.09163e-10, 1, 1<br> 15412 |m| > 1.0<br> 1.02216e-09, 1.65574, 1.02216e-09, 1, 1<br> |m| > 1.0<br> 15413 2.88192e-09, 1.65574, 2.88192e-09, 1, 1<br> |m| > 1.0<br> 4.76278e-09, 15414 1.65574, 4.76278e-09, 1, 1<br> |m| > 1.0<br> 8.85413e-09, 1.65574, 8.85413e-09, 15415 1, 1<br> |m| > 1.0<br> 2.30503e-08, 1.65574, 2.30503e-08, 1, 1<br> 15416 |m| > 1.0<br> 5.93925e-08, 1.65574, 5.93925e-08, 1, 1<br> |m| > 1.0<br> 15417 1.16676e-07, 1.65574, 1.16676e-07, 1, 1<br> |m| > 1.0<br> 2.37997e-07, 15418 1.65574, 2.37997e-07, 1, 1<br> |m| > 1.0<br> 4.68466e-07, 1.65574, 4.68466e-07, 15419 1, 1<br> |m| > 1.0<br> 9.3827e-07, 1.65574, 9.3827e-07, 1, 1<br> |m| 15420 > 1.0<br> 1.10399e-06, 1.65574, 1.10399e-06, 1, 1<br> |m| > 1.0<br> 15421 3.29178e-06, 1.65574, 3.29178e-06, 1, 1<br> |m| > 1.0<br> 7.51721e-06, 15422 1.65574, 7.51721e-06, 1, 1<br> |m| > 1.0<br> 1.51147e-05, 1.65574, 1.51147e-05, 15423 1, 1<br> |m| > 1.0<br> 2.9864e-05, 1.65574, 2.9864e-05, 1, 1<br> |m| 15424 > 1.0<br> 3.38703e-05, 1.65574, 3.38703e-05, 1, 1<br> |m| > 1.0<br> 15425 9.06601e-05, 1.65574, 9.06601e-05, 1, 1<br> |m| > 1.0<br> 0.000219495, 15426 1.65574, 0.000219495, 1, 1<br> |m| > 1.0<br> 0.000439522, 1.65574, 0.000439521, 15427 1, 1<br> |m| > 1.0<br> 0.000633315, 1.65574, 0.000633315, 1, 0.999999<br> 15428 |m| > 1.0<br> 0.00111512, 1.65574, 0.00111512, 0.999999, 0.999998<br> 15429 |m| > 1.0<br> 0.00196247, 1.65574, 0.00196246, 0.999998, 0.999995<br> 15430 |m| > 1.0<br> 0.00555375, 1.65574, 0.00555365, 0.999985, 0.999958<br> 15431 |m| > 1.0<br> 0.00869113, 1.65574, 0.00869072, 0.999962, 0.999896<br> 15432 |m| > 1.0<br> 0.0299334, 1.65574, 0.0299166, 0.999552, 0.998772<br> 15433 |m| > 1.0<br> 0.0512426, 1.65574, 0.0511588, 0.998691, 0.996406<br> 15434 |m| > 1.0<br> 0.112013, 1.65574, 0.111143, 0.993804, 0.982922<br> |m| 15435 > 1.0<br> 0.234804, 1.65574, 0.227, 0.973895, 0.926679<br> |m| > 15436 1.0<br> 0.489873, 1.65574, 0.425971, 0.904737, 0.708912<br> |m| > 1.0<br> 15437 0.751831, 1.65574, 0.553446, 0.832885, 0.400346<br> |m| > 1.0<br> 1.65574, 15438 1.65574, 0.408154, 0.912913, -0.737088<br> 15439 </p> 15440<h5> 15441<a name="special_function_error_rates_rep.error_logs.h99"></a> 15442 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_jacobi_cn_with0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_jacobi_cn_with0">Error 15443 Output For jacobi_cn with compiler GNU C++ version 7.1.0 and library GSL 2.1 15444 and test data Jacobi Elliptic: Random Small Values</a> 15445 </h5> 15446<p> 15447 <a name="errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values"></a>|m| 15448 > 1.0<br> 1.65048e-12, 1.65574, 1.65048e-12, 1, 1<br> |m| > 1.0<br> 15449 2.06542e-12, 1.65574, 2.06542e-12, 1, 1<br> |m| > 1.0<br> 6.93323e-12, 15450 1.65574, 6.93323e-12, 1, 1<br> |m| > 1.0<br> 1.33514e-11, 1.65574, 1.33514e-11, 15451 1, 1<br> |m| > 1.0<br> 1.63998e-11, 1.65574, 1.63998e-11, 1, 1<br> 15452 |m| > 1.0<br> 5.73016e-11, 1.65574, 5.73016e-11, 1, 1<br> |m| > 1.0<br> 15453 1.11373e-10, 1.65574, 1.11373e-10, 1, 1<br> |m| > 1.0<br> 1.42147e-10, 15454 1.65574, 1.42147e-10, 1, 1<br> |m| > 1.0<br> 3.80063e-10, 1.65574, 3.80063e-10, 15455 1, 1<br> |m| > 1.0<br> 6.09163e-10, 1.65574, 6.09163e-10, 1, 1<br> 15456 |m| > 1.0<br> 1.02216e-09, 1.65574, 1.02216e-09, 1, 1<br> |m| > 1.0<br> 15457 2.88192e-09, 1.65574, 2.88192e-09, 1, 1<br> |m| > 1.0<br> 4.76278e-09, 15458 1.65574, 4.76278e-09, 1, 1<br> |m| > 1.0<br> 8.85413e-09, 1.65574, 8.85413e-09, 15459 1, 1<br> |m| > 1.0<br> 2.30503e-08, 1.65574, 2.30503e-08, 1, 1<br> 15460 |m| > 1.0<br> 5.93925e-08, 1.65574, 5.93925e-08, 1, 1<br> |m| > 1.0<br> 15461 1.16676e-07, 1.65574, 1.16676e-07, 1, 1<br> |m| > 1.0<br> 2.37997e-07, 15462 1.65574, 2.37997e-07, 1, 1<br> |m| > 1.0<br> 4.68466e-07, 1.65574, 4.68466e-07, 15463 1, 1<br> |m| > 1.0<br> 9.3827e-07, 1.65574, 9.3827e-07, 1, 1<br> |m| 15464 > 1.0<br> 1.10399e-06, 1.65574, 1.10399e-06, 1, 1<br> |m| > 1.0<br> 15465 3.29178e-06, 1.65574, 3.29178e-06, 1, 1<br> |m| > 1.0<br> 7.51721e-06, 15466 1.65574, 7.51721e-06, 1, 1<br> |m| > 1.0<br> 1.51147e-05, 1.65574, 1.51147e-05, 15467 1, 1<br> |m| > 1.0<br> 2.9864e-05, 1.65574, 2.9864e-05, 1, 1<br> |m| 15468 > 1.0<br> 3.38703e-05, 1.65574, 3.38703e-05, 1, 1<br> |m| > 1.0<br> 15469 9.06601e-05, 1.65574, 9.06601e-05, 1, 1<br> |m| > 1.0<br> 0.000219495, 15470 1.65574, 0.000219495, 1, 1<br> |m| > 1.0<br> 0.000439522, 1.65574, 0.000439521, 15471 1, 1<br> |m| > 1.0<br> 0.000633315, 1.65574, 0.000633315, 1, 0.999999<br> 15472 |m| > 1.0<br> 0.00111512, 1.65574, 0.00111512, 0.999999, 0.999998<br> 15473 |m| > 1.0<br> 0.00196247, 1.65574, 0.00196246, 0.999998, 0.999995<br> 15474 |m| > 1.0<br> 0.00555375, 1.65574, 0.00555365, 0.999985, 0.999958<br> 15475 |m| > 1.0<br> 0.00869113, 1.65574, 0.00869072, 0.999962, 0.999896<br> 15476 |m| > 1.0<br> 0.0299334, 1.65574, 0.0299166, 0.999552, 0.998772<br> 15477 |m| > 1.0<br> 0.0512426, 1.65574, 0.0511588, 0.998691, 0.996406<br> 15478 |m| > 1.0<br> 0.112013, 1.65574, 0.111143, 0.993804, 0.982922<br> |m| 15479 > 1.0<br> 0.234804, 1.65574, 0.227, 0.973895, 0.926679<br> |m| > 15480 1.0<br> 0.489873, 1.65574, 0.425971, 0.904737, 0.708912<br> |m| > 1.0<br> 15481 0.751831, 1.65574, 0.553446, 0.832885, 0.400346<br> |m| > 1.0<br> 1.65574, 15482 1.65574, 0.408154, 0.912913, -0.737088<br> 15483 </p> 15484<h5> 15485<a name="special_function_error_rates_rep.error_logs.h100"></a> 15486 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_jacobi_sn_with0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_jacobi_sn_with0">Error 15487 Output For jacobi_sn with compiler GNU C++ version 7.1.0 and library GSL 2.1 15488 and test data Jacobi Elliptic: Random Small Values</a> 15489 </h5> 15490<p> 15491 <a name="errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values"></a>|m| 15492 > 1.0<br> 1.65048e-12, 1.65574, 1.65048e-12, 1, 1<br> |m| > 1.0<br> 15493 2.06542e-12, 1.65574, 2.06542e-12, 1, 1<br> |m| > 1.0<br> 6.93323e-12, 15494 1.65574, 6.93323e-12, 1, 1<br> |m| > 1.0<br> 1.33514e-11, 1.65574, 1.33514e-11, 15495 1, 1<br> |m| > 1.0<br> 1.63998e-11, 1.65574, 1.63998e-11, 1, 1<br> 15496 |m| > 1.0<br> 5.73016e-11, 1.65574, 5.73016e-11, 1, 1<br> |m| > 1.0<br> 15497 1.11373e-10, 1.65574, 1.11373e-10, 1, 1<br> |m| > 1.0<br> 1.42147e-10, 15498 1.65574, 1.42147e-10, 1, 1<br> |m| > 1.0<br> 3.80063e-10, 1.65574, 3.80063e-10, 15499 1, 1<br> |m| > 1.0<br> 6.09163e-10, 1.65574, 6.09163e-10, 1, 1<br> 15500 |m| > 1.0<br> 1.02216e-09, 1.65574, 1.02216e-09, 1, 1<br> |m| > 1.0<br> 15501 2.88192e-09, 1.65574, 2.88192e-09, 1, 1<br> |m| > 1.0<br> 4.76278e-09, 15502 1.65574, 4.76278e-09, 1, 1<br> |m| > 1.0<br> 8.85413e-09, 1.65574, 8.85413e-09, 15503 1, 1<br> |m| > 1.0<br> 2.30503e-08, 1.65574, 2.30503e-08, 1, 1<br> 15504 |m| > 1.0<br> 5.93925e-08, 1.65574, 5.93925e-08, 1, 1<br> |m| > 1.0<br> 15505 1.16676e-07, 1.65574, 1.16676e-07, 1, 1<br> |m| > 1.0<br> 2.37997e-07, 15506 1.65574, 2.37997e-07, 1, 1<br> |m| > 1.0<br> 4.68466e-07, 1.65574, 4.68466e-07, 15507 1, 1<br> |m| > 1.0<br> 9.3827e-07, 1.65574, 9.3827e-07, 1, 1<br> |m| 15508 > 1.0<br> 1.10399e-06, 1.65574, 1.10399e-06, 1, 1<br> |m| > 1.0<br> 15509 3.29178e-06, 1.65574, 3.29178e-06, 1, 1<br> |m| > 1.0<br> 7.51721e-06, 15510 1.65574, 7.51721e-06, 1, 1<br> |m| > 1.0<br> 1.51147e-05, 1.65574, 1.51147e-05, 15511 1, 1<br> |m| > 1.0<br> 2.9864e-05, 1.65574, 2.9864e-05, 1, 1<br> |m| 15512 > 1.0<br> 3.38703e-05, 1.65574, 3.38703e-05, 1, 1<br> |m| > 1.0<br> 15513 9.06601e-05, 1.65574, 9.06601e-05, 1, 1<br> |m| > 1.0<br> 0.000219495, 15514 1.65574, 0.000219495, 1, 1<br> |m| > 1.0<br> 0.000439522, 1.65574, 0.000439521, 15515 1, 1<br> |m| > 1.0<br> 0.000633315, 1.65574, 0.000633315, 1, 0.999999<br> 15516 |m| > 1.0<br> 0.00111512, 1.65574, 0.00111512, 0.999999, 0.999998<br> 15517 |m| > 1.0<br> 0.00196247, 1.65574, 0.00196246, 0.999998, 0.999995<br> 15518 |m| > 1.0<br> 0.00555375, 1.65574, 0.00555365, 0.999985, 0.999958<br> 15519 |m| > 1.0<br> 0.00869113, 1.65574, 0.00869072, 0.999962, 0.999896<br> 15520 |m| > 1.0<br> 0.0299334, 1.65574, 0.0299166, 0.999552, 0.998772<br> 15521 |m| > 1.0<br> 0.0512426, 1.65574, 0.0511588, 0.998691, 0.996406<br> 15522 |m| > 1.0<br> 0.112013, 1.65574, 0.111143, 0.993804, 0.982922<br> |m| 15523 > 1.0<br> 0.234804, 1.65574, 0.227, 0.973895, 0.926679<br> |m| > 15524 1.0<br> 0.489873, 1.65574, 0.425971, 0.904737, 0.708912<br> |m| > 1.0<br> 15525 0.751831, 1.65574, 0.553446, 0.832885, 0.400346<br> |m| > 1.0<br> 1.65574, 15526 1.65574, 0.408154, 0.912913, -0.737088<br> 15527 </p> 15528<h5> 15529<a name="special_function_error_rates_rep.error_logs.h101"></a> 15530 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_jacobi_dn_with1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_jacobi_dn_with1">Error 15531 Output For jacobi_dn with compiler GNU C++ version 7.1.0 and library GSL 2.1 15532 and test data Jacobi Elliptic: Mathworld Data</a> 15533 </h5> 15534<p> 15535 <a name="errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data"></a>|m| 15536 > 1.0<br> 2.98023e-08, 1.5, 2.98023e-08, 1, 1<br> |m| > 1.0<br> 15537 -2.98023e-08, 1.5, -2.98023e-08, 1, 1<br> |m| > 1.0<br> 0.25, 1.5, 0.24183, 15538 0.970319, 0.931888<br> |m| > 1.0<br> -0.25, 1.5, -0.24183, 0.970319, 15539 0.931888<br> |m| > 1.0<br> 1.25, 1.5, 0.665876, 0.746063, -0.0486921<br> 15540 |m| > 1.0<br> -1.25, 1.5, -0.665876, 0.746063, -0.0486921<br> |m| > 15541 1.0<br> 25, 1.5, 0.618665, 0.785655, 0.372585<br> |m| > 1.0<br> -25, 15542 1.5, -0.618665, 0.785655, 0.372585<br> 15543 </p> 15544<h5> 15545<a name="special_function_error_rates_rep.error_logs.h102"></a> 15546 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_jacobi_cn_with1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_jacobi_cn_with1">Error 15547 Output For jacobi_cn with compiler GNU C++ version 7.1.0 and library GSL 2.1 15548 and test data Jacobi Elliptic: Mathworld Data</a> 15549 </h5> 15550<p> 15551 <a name="errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data"></a>|m| 15552 > 1.0<br> 2.98023e-08, 1.5, 2.98023e-08, 1, 1<br> |m| > 1.0<br> 15553 -2.98023e-08, 1.5, -2.98023e-08, 1, 1<br> |m| > 1.0<br> 0.25, 1.5, 0.24183, 15554 0.970319, 0.931888<br> |m| > 1.0<br> -0.25, 1.5, -0.24183, 0.970319, 15555 0.931888<br> |m| > 1.0<br> 1.25, 1.5, 0.665876, 0.746063, -0.0486921<br> 15556 |m| > 1.0<br> -1.25, 1.5, -0.665876, 0.746063, -0.0486921<br> |m| > 15557 1.0<br> 25, 1.5, 0.618665, 0.785655, 0.372585<br> |m| > 1.0<br> -25, 15558 1.5, -0.618665, 0.785655, 0.372585<br> 15559 </p> 15560<h5> 15561<a name="special_function_error_rates_rep.error_logs.h103"></a> 15562 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_jacobi_sn_with1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_jacobi_sn_with1">Error 15563 Output For jacobi_sn with compiler GNU C++ version 7.1.0 and library GSL 2.1 15564 and test data Jacobi Elliptic: Mathworld Data</a> 15565 </h5> 15566<p> 15567 <a name="errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data"></a>|m| 15568 > 1.0<br> 2.98023e-08, 1.5, 2.98023e-08, 1, 1<br> |m| > 1.0<br> 15569 -2.98023e-08, 1.5, -2.98023e-08, 1, 1<br> |m| > 1.0<br> 0.25, 1.5, 0.24183, 15570 0.970319, 0.931888<br> |m| > 1.0<br> -0.25, 1.5, -0.24183, 0.970319, 15571 0.931888<br> |m| > 1.0<br> 1.25, 1.5, 0.665876, 0.746063, -0.0486921<br> 15572 |m| > 1.0<br> -1.25, 1.5, -0.665876, 0.746063, -0.0486921<br> |m| > 15573 1.0<br> 25, 1.5, 0.618665, 0.785655, 0.372585<br> |m| > 1.0<br> -25, 15574 1.5, -0.618665, 0.785655, 0.372585<br> 15575 </p> 15576<h5> 15577<a name="special_function_error_rates_rep.error_logs.h104"></a> 15578 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_polygamma_with3"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_polygamma_with3">Error 15579 Output For polygamma with compiler GNU C++ version 7.1.0 and library GSL 2.1 15580 and test data Mathematica Data - Large orders and other bug cases</a> 15581 </h5> 15582<p> 15583 <a name="errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_Large_orders_and_other_bug_cases"></a>underflow<br> 15584 168, 150, -6.52661e-66<br> underflow<br> 169, 202, 9.2734e-88<br> domain 15585 error<br> 20, -9.5, -0.00103076<br> domain error<br> 21, -9.5, 4.28582e+26<br> 15586 domain error<br> 22, -9.5, -0.00419144<br> domain error<br> 23, -9.5, 15587 8.6745e+29<br> domain error<br> 24, -9.5, -0.0204825<br> domain error<br> 15588 25, -9.5, 2.08188e+33<br> domain error<br> 26, -9.5, -0.118403<br> domain 15589 error<br> 27, -9.5, 5.84592e+36<br> domain error<br> 28, -9.5, -0.798969<br> 15590 domain error<br> 29, -9.5, 1.89875e+40<br> domain error<br> 30, -9.5, 15591 -6.22245<br> underflow<br> 10, 1.32923e+36, -0<br> underflow<br> 15, 15592 1.32923e+36, 0<br> 15593 </p> 15594<h5> 15595<a name="special_function_error_rates_rep.error_logs.h105"></a> 15596 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_polygamma_with4"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_polygamma_with4">Error 15597 Output For polygamma with compiler GNU C++ version 7.1.0 and library GSL 2.1 15598 and test data Mathematica Data - large negative arguments</a> 15599 </h5> 15600<p> 15601 <a name="errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_large_negative_arguments"></a>domain 15602 error<br> 124, -1.5, 7.63705e+240<br> domain error<br> 124, -2.5, 7.63705e+240<br> 15603 domain error<br> 124, -3.5, 7.63705e+240<br> domain error<br> 124, -4.5, 15604 7.63705e+240<br> domain error<br> 124, -5.5, 7.63705e+240<br> domain 15605 error<br> 124, -6.5, 7.63705e+240<br> domain error<br> 124, -7.5, 7.63705e+240<br> 15606 domain error<br> 124, -8.5, 7.63705e+240<br> domain error<br> 124, -9.5, 15607 7.63705e+240<br> domain error<br> 124, -10.5, 7.63705e+240<br> domain 15608 error<br> 124, -11.5, 7.63705e+240<br> domain error<br> 124, -12.5, 7.63705e+240<br> 15609 domain error<br> 124, -13.5, 7.63705e+240<br> domain error<br> 124, -14.5, 15610 7.63705e+240<br> domain error<br> 124, -15.5, 7.63705e+240<br> domain 15611 error<br> 124, -16.5, 7.63705e+240<br> domain error<br> 124, -17.5, 7.63705e+240<br> 15612 domain error<br> 124, -18.5, 7.63705e+240<br> domain error<br> 124, -19.5, 15613 7.63705e+240<br> domain error<br> 124, -20.5, 7.63705e+240<br> domain 15614 error<br> 124, -1.5, -7.63705e+240<br> domain error<br> 124, -2.5, -7.63705e+240<br> 15615 domain error<br> 124, -3.5, -7.63705e+240<br> domain error<br> 124, -4.5, 15616 -7.63705e+240<br> domain error<br> 124, -5.5, -7.63705e+240<br> domain 15617 error<br> 124, -6.5, -7.63705e+240<br> domain error<br> 124, -7.5, -7.63705e+240<br> 15618 domain error<br> 124, -8.5, -7.63705e+240<br> domain error<br> 124, -9.5, 15619 -7.63705e+240<br> domain error<br> 124, -10.5, -7.63705e+240<br> domain 15620 error<br> 124, -11.5, -7.63705e+240<br> domain error<br> 124, -12.5, 15621 -7.63705e+240<br> domain error<br> 124, -13.5, -7.63705e+240<br> domain 15622 error<br> 124, -14.5, -7.63705e+240<br> domain error<br> 124, -15.5, 15623 -7.63705e+240<br> domain error<br> 124, -16.5, -7.63705e+240<br> domain 15624 error<br> 124, -17.5, -7.63705e+240<br> domain error<br> 124, -18.5, 15625 -7.63705e+240<br> domain error<br> 124, -19.5, -7.63705e+240<br> domain 15626 error<br> 124, -20.5, -7.63705e+240<br> domain error<br> 2, -0.5, -0.828797<br> 15627 domain error<br> 3, -0.5, 193.409<br> domain error<br> 4, -0.5, -3.47425<br> 15628 domain error<br> 5, -0.5, 15371.1<br> domain error<br> 6, -0.5, -43.4579<br> 15629 domain error<br> 7, -0.5, 2.58068e+06<br> domain error<br> 8, -0.5, -1059.96<br> 15630 domain error<br> 9, -0.5, 7.43185e+08<br> domain error<br> 10, -0.5, 15631 -42108.9<br> domain error<br> 11, -0.5, 3.26999e+11<br> domain error<br> 15632 12, -0.5, -2.46448e+06<br> domain error<br> 13, -0.5, 2.04047e+14<br> 15633 domain error<br> 14, -0.5, -1.9918e+08<br> domain error<br> 15, -0.5, 15634 1.71399e+17<br> domain error<br> 16, -0.5, -2.12394e+10<br> domain error<br> 15635 17, -0.5, 1.86483e+20<br> domain error<br> 18, -0.5, -2.88824e+12<br> 15636 domain error<br> 19, -0.5, 2.55108e+23<br> domain error<br> 20, -0.5, 15637 -4.87773e+14<br> domain error<br> 21, -0.5, 4.28582e+26<br> domain error<br> 15638 2, -0.5, -0.828843<br> domain error<br> 3, -0.5, 193.409<br> domain error<br> 15639 4, -0.5, -3.47791<br> domain error<br> 5, -0.5, 15371.1<br> domain error<br> 15640 6, -0.5, -44.0732<br> domain error<br> 7, -0.5, 2.58068e+06<br> domain 15641 error<br> 8, -0.5, -1237.15<br> domain error<br> 9, -0.5, 7.43185e+08<br> 15642 domain error<br> 10, -0.5, -120071<br> domain error<br> 11, -0.5, 3.26999e+11<br> 15643 domain error<br> 12, -0.5, -5.11131e+07<br> domain error<br> 13, -0.5, 15644 2.04047e+14<br> domain error<br> 14, -0.5, -4.1064e+10<br> domain error<br> 15645 15, -0.5, 1.71399e+17<br> domain error<br> 16, -0.5, -4.44822e+13<br> 15646 domain error<br> 17, -0.5, 1.86483e+20<br> domain error<br> 18, -0.5, 15647 -6.08254e+16<br> domain error<br> 19, -0.5, 2.55108e+23<br> domain error<br> 15648 20, -0.5, -1.02182e+20<br> domain error<br> 21, -0.5, 4.28582e+26<br> 15649 domain error<br> 2, -0.5, -0.828751<br> domain error<br> 3, -0.5, 193.409<br> 15650 domain error<br> 4, -0.5, -3.47059<br> domain error<br> 5, -0.5, 15371.1<br> 15651 domain error<br> 6, -0.5, -42.8426<br> domain error<br> 7, -0.5, 2.58068e+06<br> 15652 domain error<br> 8, -0.5, -882.773<br> domain error<br> 9, -0.5, 7.43185e+08<br> 15653 domain error<br> 10, -0.5, 35853.7<br> domain error<br> 11, -0.5, 3.26999e+11<br> 15654 domain error<br> 12, -0.5, 4.61841e+07<br> domain error<br> 13, -0.5, 15655 2.04047e+14<br> domain error<br> 14, -0.5, 4.06656e+10<br> domain error<br> 15656 15, -0.5, 1.71399e+17<br> domain error<br> 16, -0.5, 4.44397e+13<br> 15657 domain error<br> 17, -0.5, 1.86483e+20<br> domain error<br> 18, -0.5, 15658 6.08197e+16<br> domain error<br> 19, -0.5, 2.55108e+23<br> domain error<br> 15659 20, -0.5, 1.02181e+20<br> domain error<br> 21, -0.5, 4.28582e+26<br> 15660 </p> 15661<h5> 15662<a name="special_function_error_rates_rep.error_logs.h106"></a> 15663 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_polygamma_with5"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_polygamma_with5">Error 15664 Output For polygamma with compiler GNU C++ version 7.1.0 and library GSL 2.1 15665 and test data Mathematica Data - negative arguments</a> 15666 </h5> 15667<p> 15668 <a name="errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_negative_arguments"></a>domain 15669 error<br> 2, -12.75, -124.031<br> domain error<br> 2, -12.25, 124.019<br> 15670 domain error<br> 2, -11.75, -124.032<br> domain error<br> 2, -11.25, 15671 124.018<br> domain error<br> 2, -10.75, -124.033<br> domain error<br> 15672 2, -10.25, 124.016<br> domain error<br> 2, -9.75, -124.035<br> domain 15673 error<br> 2, -9.25, 124.015<br> domain error<br> 2, -8.75, -124.037<br> 15674 domain error<br> 2, -8.25, 124.012<br> domain error<br> 2, -7.75, -124.04<br> 15675 domain error<br> 2, -7.25, 124.009<br> domain error<br> 2, -6.75, -124.044<br> 15676 domain error<br> 2, -6.25, 124.003<br> domain error<br> 2, -5.75, -124.051<br> 15677 domain error<br> 2, -5.25, 123.995<br> domain error<br> 2, -4.75, -124.061<br> 15678 domain error<br> 2, -4.25, 123.981<br> domain error<br> 2, -3.75, -124.08<br> 15679 domain error<br> 2, -3.25, 123.955<br> domain error<br> 2, -2.75, -124.118<br> 15680 domain error<br> 2, -2.25, 123.897<br> domain error<br> 2, -1.75, -124.214<br> 15681 domain error<br> 2, -1.25, 123.721<br> domain error<br> 2, -0.75, -124.587<br> 15682 domain error<br> 2, -0.25, 122.697<br> domain error<br> 3, -12.75, 1558.54<br> 15683 domain error<br> 3, -12.25, 1558.54<br> domain error<br> 3, -11.75, 1558.54<br> 15684 domain error<br> 3, -11.25, 1558.54<br> domain error<br> 3, -10.75, 1558.54<br> 15685 domain error<br> 3, -10.25, 1558.54<br> domain error<br> 3, -9.75, 1558.54<br> 15686 domain error<br> 3, -9.25, 1558.54<br> domain error<br> 3, -8.75, 1558.54<br> 15687 domain error<br> 3, -8.25, 1558.54<br> domain error<br> 3, -7.75, 1558.54<br> 15688 domain error<br> 3, -7.25, 1558.54<br> domain error<br> 3, -6.75, 1558.54<br> 15689 domain error<br> 3, -6.25, 1558.54<br> domain error<br> 3, -5.75, 1558.54<br> 15690 domain error<br> 3, -5.25, 1558.54<br> domain error<br> 3, -4.75, 1558.53<br> 15691 domain error<br> 3, -4.25, 1558.53<br> domain error<br> 3, -3.75, 1558.52<br> 15692 domain error<br> 3, -3.25, 1558.51<br> domain error<br> 3, -2.75, 1558.49<br> 15693 domain error<br> 3, -2.25, 1558.46<br> domain error<br> 3, -1.75, 1558.38<br> 15694 domain error<br> 3, -1.25, 1558.22<br> domain error<br> 3, -0.75, 1557.75<br> 15695 domain error<br> 3, -0.25, 1555.76<br> domain error<br> 4, -12.75, -24481.6<br> 15696 domain error<br> 4, -12.25, 24481.6<br> domain error<br> 4, -11.75, -24481.6<br> 15697 domain error<br> 4, -11.25, 24481.6<br> domain error<br> 4, -10.75, -24481.6<br> 15698 domain error<br> 4, -10.25, 24481.6<br> domain error<br> 4, -9.75, -24481.6<br> 15699 domain error<br> 4, -9.25, 24481.6<br> domain error<br> 4, -8.75, -24481.6<br> 15700 domain error<br> 4, -8.25, 24481.6<br> domain error<br> 4, -7.75, -24481.6<br> 15701 domain error<br> 4, -7.25, 24481.6<br> domain error<br> 4, -6.75, -24481.6<br> 15702 domain error<br> 4, -6.25, 24481.6<br> domain error<br> 4, -5.75, -24481.6<br> 15703 domain error<br> 4, -5.25, 24481.6<br> domain error<br> 4, -4.75, -24481.6<br> 15704 domain error<br> 4, -4.25, 24481.6<br> domain error<br> 4, -3.75, -24481.6<br> 15705 domain error<br> 4, -3.25, 24481.5<br> domain error<br> 4, -2.75, -24481.6<br> 15706 domain error<br> 4, -2.25, 24481.5<br> domain error<br> 4, -1.75, -24481.8<br> 15707 domain error<br> 4, -1.25, 24481.1<br> domain error<br> 4, -0.75, -24483.2<br> 15708 domain error<br> 4, -0.25, 24473.2<br> domain error<br> 5, -12.75, 492231<br> 15709 domain error<br> 5, -12.25, 492231<br> domain error<br> 5, -11.75, 492231<br> 15710 domain error<br> 5, -11.25, 492231<br> domain error<br> 5, -10.75, 492231<br> 15711 domain error<br> 5, -10.25, 492231<br> domain error<br> 5, -9.75, 492231<br> 15712 domain error<br> 5, -9.25, 492231<br> domain error<br> 5, -8.75, 492231<br> 15713 domain error<br> 5, -8.25, 492231<br> domain error<br> 5, -7.75, 492231<br> 15714 domain error<br> 5, -7.25, 492231<br> domain error<br> 5, -6.75, 492231<br> 15715 domain error<br> 5, -6.25, 492231<br> domain error<br> 5, -5.75, 492231<br> 15716 domain error<br> 5, -5.25, 492231<br> domain error<br> 5, -4.75, 492231<br> 15717 domain error<br> 5, -4.25, 492231<br> domain error<br> 5, -3.75, 492231<br> 15718 domain error<br> 5, -3.25, 492231<br> domain error<br> 5, -2.75, 492231<br> 15719 domain error<br> 5, -2.25, 492231<br> domain error<br> 5, -1.75, 492231<br> 15720 domain error<br> 5, -1.25, 492230<br> domain error<br> 5, -0.75, 492227<br> 15721 domain error<br> 5, -0.25, 492199<br> domain error<br> 6, -12.75, -1.17912e+07<br> 15722 domain error<br> 6, -12.25, 1.17912e+07<br> domain error<br> 6, -11.75, 15723 -1.17912e+07<br> domain error<br> 6, -11.25, 1.17912e+07<br> domain error<br> 15724 6, -10.75, -1.17912e+07<br> domain error<br> 6, -10.25, 1.17912e+07<br> 15725 domain error<br> 6, -9.75, -1.17912e+07<br> domain error<br> 6, -9.25, 15726 1.17912e+07<br> domain error<br> 6, -8.75, -1.17912e+07<br> domain error<br> 15727 6, -8.25, 1.17912e+07<br> domain error<br> 6, -7.75, -1.17912e+07<br> 15728 domain error<br> 6, -7.25, 1.17912e+07<br> domain error<br> 6, -6.75, 15729 -1.17912e+07<br> domain error<br> 6, -6.25, 1.17912e+07<br> domain error<br> 15730 6, -5.75, -1.17912e+07<br> domain error<br> 6, -5.25, 1.17912e+07<br> 15731 domain error<br> 6, -4.75, -1.17912e+07<br> domain error<br> 6, -4.25, 15732 1.17912e+07<br> domain error<br> 6, -3.75, -1.17912e+07<br> domain error<br> 15733 6, -3.25, 1.17912e+07<br> domain error<br> 6, -2.75, -1.17912e+07<br> 15734 domain error<br> 6, -2.25, 1.17912e+07<br> domain error<br> 6, -1.75, 15735 -1.17912e+07<br> domain error<br> 6, -1.25, 1.17912e+07<br> *** FURTHER 15736 CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br> 15737 </p> 15738<h5> 15739<a name="special_function_error_rates_rep.error_logs.h107"></a> 15740 <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_polygamma_with6"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_polygamma_with6">Error 15741 Output For polygamma with compiler GNU C++ version 7.1.0 and library GSL 2.1 15742 and test data Mathematica Data - large arguments</a> 15743 </h5> 15744<p> 15745 <a name="errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_large_arguments"></a>underflow<br> 15746 30, 8.58993e+09, -8.44974e-268<br> underflow<br> 30, 1.71799e+10, -7.86943e-277<br> 15747 underflow<br> 30, 3.43597e+10, -7.32898e-286<br> underflow<br> 30, 6.87195e+10, 15748 -6.82564e-295<br> underflow<br> 30, 1.37439e+11, -6.35687e-304<br> underflow<br> 15749 30, 2.74878e+11, -5.9203e-313<br> underflow<br> 30, 5.49756e+11, -5.53354e-322<br> 15750 underflow<br> 30, 1.09951e+12, -0<br> underflow<br> 30, 2.19902e+12, 15751 -0<br> underflow<br> 30, 4.39805e+12, -0<br> underflow<br> 30, 8.79609e+12, 15752 -0<br> underflow<br> 30, 1.75922e+13, -0<br> underflow<br> 30, 3.51844e+13, 15753 -0<br> underflow<br> 30, 7.03687e+13, -0<br> underflow<br> 30, 1.40737e+14, 15754 -0<br> underflow<br> 30, 2.81475e+14, -0<br> underflow<br> 30, 5.6295e+14, 15755 -0<br> underflow<br> 30, 1.1259e+15, -0<br> underflow<br> 30, 2.2518e+15, 15756 -0<br> underflow<br> 30, 4.5036e+15, -0<br> underflow<br> 30, 9.0072e+15, 15757 -0<br> underflow<br> 30, 1.80144e+16, -0<br> underflow<br> 30, 3.60288e+16, 15758 -0<br> underflow<br> 30, 7.20576e+16, -0<br> underflow<br> 30, 1.44115e+17, 15759 -0<br> underflow<br> 30, 2.8823e+17, -0<br> underflow<br> 30, 5.76461e+17, 15760 -0<br> underflow<br> 30, 1.15292e+18, -0<br> underflow<br> 30, 2.30584e+18, 15761 -0<br> underflow<br> 30, 4.61169e+18, -0<br> underflow<br> 30, 9.22337e+18, 15762 -0<br> underflow<br> 30, 1.84467e+19, -0<br> underflow<br> 30, 3.68935e+19, 15763 -0<br> underflow<br> 30, 7.3787e+19, -0<br> underflow<br> 30, 1.47574e+20, 15764 -0<br> underflow<br> 30, 2.95148e+20, -0<br> underflow<br> 30, 5.90296e+20, 15765 -0<br> underflow<br> 30, 1.18059e+21, -0<br> underflow<br> 30, 2.36118e+21, 15766 -0<br> underflow<br> 30, 4.72237e+21, -0<br> underflow<br> 30, 9.44473e+21, 15767 -0<br> underflow<br> 30, 1.88895e+22, -0<br> underflow<br> 30, 3.77789e+22, 15768 -0<br> underflow<br> 30, 7.55579e+22, -0<br> underflow<br> 30, 1.51116e+23, 15769 -0<br> underflow<br> 30, 3.02231e+23, -0<br> underflow<br> 30, 6.04463e+23, 15770 -0<br> underflow<br> 30, 1.20893e+24, -0<br> underflow<br> 30, 2.41785e+24, 15771 -0<br> underflow<br> 30, 4.8357e+24, -0<br> underflow<br> 30, 9.67141e+24, 15772 -0<br> underflow<br> 30, 1.93428e+25, -0<br> underflow<br> 30, 3.86856e+25, 15773 -0<br> underflow<br> 30, 7.73713e+25, -0<br> underflow<br> 30, 1.54743e+26, 15774 -0<br> underflow<br> 30, 3.09485e+26, -0<br> underflow<br> 30, 6.1897e+26, 15775 -0<br> underflow<br> 30, 1.23794e+27, -0<br> underflow<br> 30, 2.47588e+27, 15776 -0<br> underflow<br> 30, 4.95176e+27, -0<br> underflow<br> 30, 9.90352e+27, 15777 -0<br> underflow<br> 30, 1.9807e+28, -0<br> underflow<br> 30, 3.96141e+28, 15778 -0<br> underflow<br> 30, 7.92282e+28, -0<br> underflow<br> 30, 1.58456e+29, 15779 -0<br> underflow<br> 30, 3.16913e+29, -0<br> underflow<br> 30, 6.33825e+29, 15780 -0<br> underflow<br> 30, 1.26765e+30, -0<br> 15781 </p> 15782</div> 15783<div class="section"> 15784<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 15785<a name="special_function_error_rates_rep.all_the_tables"></a><a class="link" href="index.html#special_function_error_rates_rep.all_the_tables" title="Tables">Tables</a> 15786</h2></div></div></div> 15787<div class="table"> 15788<a name="special_function_error_rates_rep.all_the_tables.table_beta"></a><p class="title"><b>Table 97. Error rates for beta</b></p> 15789<div class="table-contents"><table class="table" summary="Error rates for beta"> 15790<colgroup> 15791<col> 15792<col> 15793<col> 15794<col> 15795<col> 15796</colgroup> 15797<thead><tr> 15798<th> 15799 </th> 15800<th> 15801 <p> 15802 GNU C++ version 7.1.0<br> linux<br> double 15803 </p> 15804 </th> 15805<th> 15806 <p> 15807 GNU C++ version 7.1.0<br> linux<br> long double 15808 </p> 15809 </th> 15810<th> 15811 <p> 15812 Sun compiler version 0x5150<br> Sun Solaris<br> long double 15813 </p> 15814 </th> 15815<th> 15816 <p> 15817 Microsoft Visual C++ version 14.1<br> Win32<br> double 15818 </p> 15819 </th> 15820</tr></thead> 15821<tbody> 15822<tr> 15823<td> 15824 <p> 15825 Beta Function: Small Values 15826 </p> 15827 </td> 15828<td> 15829 <p> 15830 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 15831 2.1:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_beta_GSL_2_1_Beta_Function_Small_Values">And 15832 other failures.</a>)</span><br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 15833 Max = 1.14ε (Mean = 0.574ε)) 15834 </p> 15835 </td> 15836<td> 15837 <p> 15838 <span class="blue">Max = 2.86ε (Mean = 1.22ε)</span><br> <br> 15839 (<span class="emphasis"><em><cmath>:</em></span> Max = 364ε (Mean = 76.2ε)) 15840 </p> 15841 </td> 15842<td> 15843 <p> 15844 <span class="blue">Max = 2.86ε (Mean = 1.22ε)</span> 15845 </p> 15846 </td> 15847<td> 15848 <p> 15849 <span class="blue">Max = 2.23ε (Mean = 1.14ε)</span> 15850 </p> 15851 </td> 15852</tr> 15853<tr> 15854<td> 15855 <p> 15856 Beta Function: Medium Values 15857 </p> 15858 </td> 15859<td> 15860 <p> 15861 <span class="blue">Max = 0.978ε (Mean = 0.0595ε)</span><br> <br> 15862 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.18e+03ε (Mean = 238ε))<br> 15863 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.09e+03ε (Mean = 265ε)) 15864 </p> 15865 </td> 15866<td> 15867 <p> 15868 <span class="blue">Max = 61.4ε (Mean = 19.4ε)</span><br> <br> 15869 (<span class="emphasis"><em><cmath>:</em></span> Max = 1.07e+03ε (Mean = 264ε)) 15870 </p> 15871 </td> 15872<td> 15873 <p> 15874 <span class="blue">Max = 107ε (Mean = 24.5ε)</span> 15875 </p> 15876 </td> 15877<td> 15878 <p> 15879 <span class="blue">Max = 96.5ε (Mean = 22.4ε)</span> 15880 </p> 15881 </td> 15882</tr> 15883<tr> 15884<td> 15885 <p> 15886 Beta Function: Divergent Values 15887 </p> 15888 </td> 15889<td> 15890 <p> 15891 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 15892 2.1:</em></span> Max = 12.1ε (Mean = 1.99ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 15893 Max = 176ε (Mean = 28ε)) 15894 </p> 15895 </td> 15896<td> 15897 <p> 15898 <span class="blue">Max = 8.99ε (Mean = 2.44ε)</span><br> <br> 15899 (<span class="emphasis"><em><cmath>:</em></span> Max = 128ε (Mean = 23.8ε)) 15900 </p> 15901 </td> 15902<td> 15903 <p> 15904 <span class="blue">Max = 18.8ε (Mean = 2.71ε)</span> 15905 </p> 15906 </td> 15907<td> 15908 <p> 15909 <span class="blue">Max = 11.4ε (Mean = 2.19ε)</span> 15910 </p> 15911 </td> 15912</tr> 15913</tbody> 15914</table></div> 15915</div> 15916<br class="table-break"><div class="table"> 15917<a name="special_function_error_rates_rep.all_the_tables.table_beta_incomplete_"></a><p class="title"><b>Table 98. Error rates for beta (incomplete)</b></p> 15918<div class="table-contents"><table class="table" summary="Error rates for beta (incomplete)"> 15919<colgroup> 15920<col> 15921<col> 15922<col> 15923<col> 15924<col> 15925</colgroup> 15926<thead><tr> 15927<th> 15928 </th> 15929<th> 15930 <p> 15931 GNU C++ version 7.1.0<br> linux<br> double 15932 </p> 15933 </th> 15934<th> 15935 <p> 15936 GNU C++ version 7.1.0<br> linux<br> long double 15937 </p> 15938 </th> 15939<th> 15940 <p> 15941 Sun compiler version 0x5150<br> Sun Solaris<br> long double 15942 </p> 15943 </th> 15944<th> 15945 <p> 15946 Microsoft Visual C++ version 14.1<br> Win32<br> double 15947 </p> 15948 </th> 15949</tr></thead> 15950<tbody> 15951<tr> 15952<td> 15953 <p> 15954 Incomplete Beta Function: Small Values 15955 </p> 15956 </td> 15957<td> 15958 <p> 15959 <span class="blue">Max = 0ε (Mean = 0ε)</span> 15960 </p> 15961 </td> 15962<td> 15963 <p> 15964 <span class="blue">Max = 11.1ε (Mean = 2.32ε)</span> 15965 </p> 15966 </td> 15967<td> 15968 <p> 15969 <span class="blue">Max = 18.7ε (Mean = 3.19ε)</span> 15970 </p> 15971 </td> 15972<td> 15973 <p> 15974 <span class="blue">Max = 9.94ε (Mean = 2.17ε)</span> 15975 </p> 15976 </td> 15977</tr> 15978<tr> 15979<td> 15980 <p> 15981 Incomplete Beta Function: Medium Values 15982 </p> 15983 </td> 15984<td> 15985 <p> 15986 <span class="blue">Max = 0.568ε (Mean = 0.0254ε)</span> 15987 </p> 15988 </td> 15989<td> 15990 <p> 15991 <span class="blue">Max = 69.2ε (Mean = 13.4ε)</span> 15992 </p> 15993 </td> 15994<td> 15995 <p> 15996 <span class="blue">Max = 174ε (Mean = 25ε)</span> 15997 </p> 15998 </td> 15999<td> 16000 <p> 16001 <span class="blue">Max = 90ε (Mean = 12.7ε)</span> 16002 </p> 16003 </td> 16004</tr> 16005<tr> 16006<td> 16007 <p> 16008 Incomplete Beta Function: Large and Diverse Values 16009 </p> 16010 </td> 16011<td> 16012 <p> 16013 <span class="blue">Max = 0.999ε (Mean = 0.0325ε)</span> 16014 </p> 16015 </td> 16016<td> 16017 <p> 16018 <span class="blue">Max = 6.84e+04ε (Mean = 2.76e+03ε)</span> 16019 </p> 16020 </td> 16021<td> 16022 <p> 16023 <span class="blue">Max = 6.86e+04ε (Mean = 2.79e+03ε)</span> 16024 </p> 16025 </td> 16026<td> 16027 <p> 16028 <span class="blue">Max = 633ε (Mean = 29.7ε)</span> 16029 </p> 16030 </td> 16031</tr> 16032<tr> 16033<td> 16034 <p> 16035 Incomplete Beta Function: Small Integer Values 16036 </p> 16037 </td> 16038<td> 16039 <p> 16040 <span class="blue">Max = 0.786ε (Mean = 0.0323ε)</span> 16041 </p> 16042 </td> 16043<td> 16044 <p> 16045 <span class="blue">Max = 11.6ε (Mean = 3.6ε)</span> 16046 </p> 16047 </td> 16048<td> 16049 <p> 16050 <span class="blue">Max = 51.8ε (Mean = 11ε)</span> 16051 </p> 16052 </td> 16053<td> 16054 <p> 16055 <span class="blue">Max = 26ε (Mean = 6.28ε)</span> 16056 </p> 16057 </td> 16058</tr> 16059</tbody> 16060</table></div> 16061</div> 16062<br class="table-break"><div class="table"> 16063<a name="special_function_error_rates_rep.all_the_tables.table_betac"></a><p class="title"><b>Table 99. Error rates for betac</b></p> 16064<div class="table-contents"><table class="table" summary="Error rates for betac"> 16065<colgroup> 16066<col> 16067<col> 16068<col> 16069<col> 16070<col> 16071</colgroup> 16072<thead><tr> 16073<th> 16074 </th> 16075<th> 16076 <p> 16077 GNU C++ version 7.1.0<br> linux<br> double 16078 </p> 16079 </th> 16080<th> 16081 <p> 16082 GNU C++ version 7.1.0<br> linux<br> long double 16083 </p> 16084 </th> 16085<th> 16086 <p> 16087 Sun compiler version 0x5150<br> Sun Solaris<br> long double 16088 </p> 16089 </th> 16090<th> 16091 <p> 16092 Microsoft Visual C++ version 14.1<br> Win32<br> double 16093 </p> 16094 </th> 16095</tr></thead> 16096<tbody> 16097<tr> 16098<td> 16099 <p> 16100 Incomplete Beta Function: Small Values 16101 </p> 16102 </td> 16103<td> 16104 <p> 16105 <span class="blue">Max = 0.676ε (Mean = 0.0302ε)</span> 16106 </p> 16107 </td> 16108<td> 16109 <p> 16110 <span class="blue">Max = 9.92ε (Mean = 2.3ε)</span> 16111 </p> 16112 </td> 16113<td> 16114 <p> 16115 <span class="blue">Max = 11.2ε (Mean = 2.94ε)</span> 16116 </p> 16117 </td> 16118<td> 16119 <p> 16120 <span class="blue">Max = 8.94ε (Mean = 2.06ε)</span> 16121 </p> 16122 </td> 16123</tr> 16124<tr> 16125<td> 16126 <p> 16127 Incomplete Beta Function: Medium Values 16128 </p> 16129 </td> 16130<td> 16131 <p> 16132 <span class="blue">Max = 0.949ε (Mean = 0.098ε)</span> 16133 </p> 16134 </td> 16135<td> 16136 <p> 16137 <span class="blue">Max = 63.5ε (Mean = 13.5ε)</span> 16138 </p> 16139 </td> 16140<td> 16141 <p> 16142 <span class="blue">Max = 97.6ε (Mean = 24.3ε)</span> 16143 </p> 16144 </td> 16145<td> 16146 <p> 16147 <span class="blue">Max = 90.6ε (Mean = 14.8ε)</span> 16148 </p> 16149 </td> 16150</tr> 16151<tr> 16152<td> 16153 <p> 16154 Incomplete Beta Function: Large and Diverse Values 16155 </p> 16156 </td> 16157<td> 16158 <p> 16159 <span class="blue">Max = 1.12ε (Mean = 0.0458ε)</span> 16160 </p> 16161 </td> 16162<td> 16163 <p> 16164 <span class="blue">Max = 1.05e+05ε (Mean = 5.45e+03ε)</span> 16165 </p> 16166 </td> 16167<td> 16168 <p> 16169 <span class="blue">Max = 1.04e+05ε (Mean = 5.46e+03ε)</span> 16170 </p> 16171 </td> 16172<td> 16173 <p> 16174 <span class="blue">Max = 3.72e+03ε (Mean = 113ε)</span> 16175 </p> 16176 </td> 16177</tr> 16178<tr> 16179<td> 16180 <p> 16181 Incomplete Beta Function: Small Integer Values 16182 </p> 16183 </td> 16184<td> 16185 <p> 16186 <span class="blue">Max = 0.586ε (Mean = 0.0314ε)</span> 16187 </p> 16188 </td> 16189<td> 16190 <p> 16191 <span class="blue">Max = 11.1ε (Mean = 3.65ε)</span> 16192 </p> 16193 </td> 16194<td> 16195 <p> 16196 <span class="blue">Max = 103ε (Mean = 17.4ε)</span> 16197 </p> 16198 </td> 16199<td> 16200 <p> 16201 <span class="blue">Max = 26.2ε (Mean = 6.36ε)</span> 16202 </p> 16203 </td> 16204</tr> 16205</tbody> 16206</table></div> 16207</div> 16208<br class="table-break"><div class="table"> 16209<a name="special_function_error_rates_rep.all_the_tables.table_binomial_coefficient"></a><p class="title"><b>Table 100. Error rates for binomial_coefficient</b></p> 16210<div class="table-contents"><table class="table" summary="Error rates for binomial_coefficient"> 16211<colgroup> 16212<col> 16213<col> 16214<col> 16215<col> 16216<col> 16217</colgroup> 16218<thead><tr> 16219<th> 16220 </th> 16221<th> 16222 <p> 16223 GNU C++ version 7.1.0<br> linux<br> double 16224 </p> 16225 </th> 16226<th> 16227 <p> 16228 GNU C++ version 7.1.0<br> linux<br> long double 16229 </p> 16230 </th> 16231<th> 16232 <p> 16233 Sun compiler version 0x5150<br> Sun Solaris<br> long double 16234 </p> 16235 </th> 16236<th> 16237 <p> 16238 Microsoft Visual C++ version 14.1<br> Win32<br> double 16239 </p> 16240 </th> 16241</tr></thead> 16242<tbody> 16243<tr> 16244<td> 16245 <p> 16246 Binomials: small arguments 16247 </p> 16248 </td> 16249<td> 16250 <p> 16251 <span class="blue">Max = 1ε (Mean = 0.369ε)</span> 16252 </p> 16253 </td> 16254<td> 16255 <p> 16256 <span class="blue">Max = 1.5ε (Mean = 0.339ε)</span> 16257 </p> 16258 </td> 16259<td> 16260 <p> 16261 <span class="blue">Max = 1.5ε (Mean = 0.339ε)</span> 16262 </p> 16263 </td> 16264<td> 16265 <p> 16266 <span class="blue">Max = 1ε (Mean = 0.369ε)</span> 16267 </p> 16268 </td> 16269</tr> 16270<tr> 16271<td> 16272 <p> 16273 Binomials: large arguments 16274 </p> 16275 </td> 16276<td> 16277 <p> 16278 <span class="blue">Max = 0.939ε (Mean = 0.314ε)</span> 16279 </p> 16280 </td> 16281<td> 16282 <p> 16283 <span class="blue">Max = 26.6ε (Mean = 6.13ε)</span> 16284 </p> 16285 </td> 16286<td> 16287 <p> 16288 <span class="blue">Max = 53.2ε (Mean = 10.8ε)</span> 16289 </p> 16290 </td> 16291<td> 16292 <p> 16293 <span class="blue">Max = 37.2ε (Mean = 7.4ε)</span> 16294 </p> 16295 </td> 16296</tr> 16297</tbody> 16298</table></div> 16299</div> 16300<br class="table-break"><div class="table"> 16301<a name="special_function_error_rates_rep.all_the_tables.table_boost_math_powm1"></a><p class="title"><b>Table 101. Error rates for boost::math::powm1</b></p> 16302<div class="table-contents"><table class="table" summary="Error rates for boost::math::powm1"> 16303<colgroup> 16304<col> 16305<col> 16306<col> 16307<col> 16308<col> 16309</colgroup> 16310<thead><tr> 16311<th> 16312 </th> 16313<th> 16314 <p> 16315 GNU C++ version 7.1.0<br> linux<br> long double 16316 </p> 16317 </th> 16318<th> 16319 <p> 16320 GNU C++ version 7.1.0<br> linux<br> double 16321 </p> 16322 </th> 16323<th> 16324 <p> 16325 Sun compiler version 0x5150<br> Sun Solaris<br> long double 16326 </p> 16327 </th> 16328<th> 16329 <p> 16330 Microsoft Visual C++ version 14.1<br> Win32<br> double 16331 </p> 16332 </th> 16333</tr></thead> 16334<tbody><tr> 16335<td> 16336 <p> 16337 powm1 16338 </p> 16339 </td> 16340<td> 16341 <p> 16342 (<span class="emphasis"><em><math.h>:</em></span> Max = 2.04ε (Mean = 0.493ε))<br> 16343 <br> <span class="blue">Max = 2.04ε (Mean = 0.493ε)</span><br> 16344 <br> (<span class="emphasis"><em><cmath>:</em></span> Max = 2.04ε (Mean = 0.493ε)) 16345 </p> 16346 </td> 16347<td> 16348 <p> 16349 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.06ε (Mean = 0.425ε))<br> 16350 <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.06ε (Mean = 0.425ε))<br> 16351 <br> <span class="blue">Max = 1.06ε (Mean = 0.425ε)</span> 16352 </p> 16353 </td> 16354<td> 16355 <p> 16356 <span class="blue">Max = 1.88ε (Mean = 0.49ε)</span><br> <br> 16357 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.88ε (Mean = 0.49ε)) 16358 </p> 16359 </td> 16360<td> 16361 <p> 16362 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.84ε (Mean = 0.486ε))<br> 16363 <br> <span class="blue">Max = 1.84ε (Mean = 0.486ε)</span> 16364 </p> 16365 </td> 16366</tr></tbody> 16367</table></div> 16368</div> 16369<br class="table-break"><div class="table"> 16370<a name="special_function_error_rates_rep.all_the_tables.table_cbrt"></a><p class="title"><b>Table 102. Error rates for cbrt</b></p> 16371<div class="table-contents"><table class="table" summary="Error rates for cbrt"> 16372<colgroup> 16373<col> 16374<col> 16375<col> 16376<col> 16377<col> 16378</colgroup> 16379<thead><tr> 16380<th> 16381 </th> 16382<th> 16383 <p> 16384 GNU C++ version 7.1.0<br> linux<br> double 16385 </p> 16386 </th> 16387<th> 16388 <p> 16389 GNU C++ version 7.1.0<br> linux<br> long double 16390 </p> 16391 </th> 16392<th> 16393 <p> 16394 Sun compiler version 0x5150<br> Sun Solaris<br> long double 16395 </p> 16396 </th> 16397<th> 16398 <p> 16399 Microsoft Visual C++ version 14.1<br> Win32<br> double 16400 </p> 16401 </th> 16402</tr></thead> 16403<tbody><tr> 16404<td> 16405 <p> 16406 cbrt Function 16407 </p> 16408 </td> 16409<td> 16410 <p> 16411 <span class="blue">Max = 0ε (Mean = 0ε)</span> 16412 </p> 16413 </td> 16414<td> 16415 <p> 16416 <span class="blue">Max = 1.34ε (Mean = 0.471ε)</span><br> <br> 16417 (<span class="emphasis"><em><cmath>:</em></span> Max = 1.34ε (Mean = 0.471ε))<br> 16418 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.34ε (Mean = 0.471ε)) 16419 </p> 16420 </td> 16421<td> 16422 <p> 16423 <span class="blue">Max = 1.34ε (Mean = 0.471ε)</span><br> <br> 16424 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.34ε (Mean = 0.471ε)) 16425 </p> 16426 </td> 16427<td> 16428 <p> 16429 <span class="blue">Max = 1.7ε (Mean = 0.565ε)</span><br> <br> 16430 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.7ε (Mean = 0.565ε)) 16431 </p> 16432 </td> 16433</tr></tbody> 16434</table></div> 16435</div> 16436<br class="table-break"><div class="table"> 16437<a name="special_function_error_rates_rep.all_the_tables.table_cos_pi"></a><p class="title"><b>Table 103. Error rates for cos_pi</b></p> 16438<div class="table-contents"><table class="table" summary="Error rates for cos_pi"> 16439<colgroup> 16440<col> 16441<col> 16442<col> 16443<col> 16444<col> 16445</colgroup> 16446<thead><tr> 16447<th> 16448 </th> 16449<th> 16450 <p> 16451 GNU C++ version 7.1.0<br> linux<br> double 16452 </p> 16453 </th> 16454<th> 16455 <p> 16456 GNU C++ version 7.1.0<br> linux<br> long double 16457 </p> 16458 </th> 16459<th> 16460 <p> 16461 Sun compiler version 0x5150<br> Sun Solaris<br> long double 16462 </p> 16463 </th> 16464<th> 16465 <p> 16466 Microsoft Visual C++ version 14.1<br> Win32<br> double 16467 </p> 16468 </th> 16469</tr></thead> 16470<tbody> 16471<tr> 16472<td> 16473 <p> 16474 sin_pi and cos_pi 16475 </p> 16476 </td> 16477<td> 16478 <p> 16479 <span class="blue">Max = 0ε (Mean = 0ε)</span> 16480 </p> 16481 </td> 16482<td> 16483 <p> 16484 <span class="blue">Max = 0.991ε (Mean = 0.302ε)</span> 16485 </p> 16486 </td> 16487<td> 16488 <p> 16489 <span class="blue">Max = 0.991ε (Mean = 0.302ε)</span> 16490 </p> 16491 </td> 16492<td> 16493 <p> 16494 <span class="blue">Max = 0.996ε (Mean = 0.284ε)</span> 16495 </p> 16496 </td> 16497</tr> 16498<tr> 16499<td> 16500 <p> 16501 sin_pi and cos_pi near integers and half integers 16502 </p> 16503 </td> 16504<td> 16505 <p> 16506 <span class="blue">Max = 0ε (Mean = 0ε)</span> 16507 </p> 16508 </td> 16509<td> 16510 <p> 16511 <span class="blue">Max = 0.976ε (Mean = 0.28ε)</span> 16512 </p> 16513 </td> 16514<td> 16515 <p> 16516 <span class="blue">Max = 0.976ε (Mean = 0.28ε)</span> 16517 </p> 16518 </td> 16519<td> 16520 <p> 16521 <span class="blue">Max = 0.996ε (Mean = 0.298ε)</span> 16522 </p> 16523 </td> 16524</tr> 16525</tbody> 16526</table></div> 16527</div> 16528<br class="table-break"><div class="table"> 16529<a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_i"></a><p class="title"><b>Table 104. Error rates for cyl_bessel_i</b></p> 16530<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i"> 16531<colgroup> 16532<col> 16533<col> 16534<col> 16535<col> 16536<col> 16537</colgroup> 16538<thead><tr> 16539<th> 16540 </th> 16541<th> 16542 <p> 16543 GNU C++ version 7.1.0<br> linux<br> double 16544 </p> 16545 </th> 16546<th> 16547 <p> 16548 GNU C++ version 7.1.0<br> linux<br> long double 16549 </p> 16550 </th> 16551<th> 16552 <p> 16553 Sun compiler version 0x5150<br> Sun Solaris<br> long double 16554 </p> 16555 </th> 16556<th> 16557 <p> 16558 Microsoft Visual C++ version 14.1<br> Win32<br> double 16559 </p> 16560 </th> 16561</tr></thead> 16562<tbody> 16563<tr> 16564<td> 16565 <p> 16566 Bessel I0: Mathworld Data 16567 </p> 16568 </td> 16569<td> 16570 <p> 16571 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 16572 2.1:</em></span> Max = 270ε (Mean = 91.6ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_I0_Mathworld_Data">And 16573 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 16574 Max = 1.52ε (Mean = 0.622ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_I0_Mathworld_Data">And 16575 other failures.</a>) 16576 </p> 16577 </td> 16578<td> 16579 <p> 16580 <span class="blue">Max = 1.95ε (Mean = 0.738ε)</span><br> <br> 16581 (<span class="emphasis"><em><cmath>:</em></span> Max = 8.49ε (Mean = 3.46ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_I0_Mathworld_Data">And 16582 other failures.</a>) 16583 </p> 16584 </td> 16585<td> 16586 <p> 16587 <span class="blue">Max = 1.95ε (Mean = 0.661ε)</span> 16588 </p> 16589 </td> 16590<td> 16591 <p> 16592 <span class="blue">Max = 0.762ε (Mean = 0.329ε)</span> 16593 </p> 16594 </td> 16595</tr> 16596<tr> 16597<td> 16598 <p> 16599 Bessel I1: Mathworld Data 16600 </p> 16601 </td> 16602<td> 16603 <p> 16604 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 16605 2.1:</em></span> Max = 128ε (Mean = 41ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_I1_Mathworld_Data">And 16606 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 16607 Max = 1.53ε (Mean = 0.483ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_I1_Mathworld_Data">And 16608 other failures.</a>) 16609 </p> 16610 </td> 16611<td> 16612 <p> 16613 <span class="blue">Max = 0.64ε (Mean = 0.202ε)</span><br> <br> 16614 (<span class="emphasis"><em><cmath>:</em></span> Max = 5ε (Mean = 2.15ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_I1_Mathworld_Data">And 16615 other failures.</a>) 16616 </p> 16617 </td> 16618<td> 16619 <p> 16620 <span class="blue">Max = 0.64ε (Mean = 0.202ε)</span> 16621 </p> 16622 </td> 16623<td> 16624 <p> 16625 <span class="blue">Max = 0.767ε (Mean = 0.398ε)</span> 16626 </p> 16627 </td> 16628</tr> 16629<tr> 16630<td> 16631 <p> 16632 Bessel In: Mathworld Data 16633 </p> 16634 </td> 16635<td> 16636 <p> 16637 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 16638 2.1:</em></span> Max = 2.31ε (Mean = 0.838ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_In_Mathworld_Data">And 16639 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 16640 Max = 1.73ε (Mean = 0.601ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_In_Mathworld_Data">And 16641 other failures.</a>) 16642 </p> 16643 </td> 16644<td> 16645 <p> 16646 <span class="blue">Max = 1.8ε (Mean = 1.33ε)</span><br> <br> 16647 (<span class="emphasis"><em><cmath>:</em></span> Max = 430ε (Mean = 163ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_In_Mathworld_Data">And 16648 other failures.</a>) 16649 </p> 16650 </td> 16651<td> 16652 <p> 16653 <span class="blue">Max = 463ε (Mean = 140ε)</span> 16654 </p> 16655 </td> 16656<td> 16657 <p> 16658 <span class="blue">Max = 3.46ε (Mean = 1.32ε)</span> 16659 </p> 16660 </td> 16661</tr> 16662<tr> 16663<td> 16664 <p> 16665 Bessel Iv: Mathworld Data 16666 </p> 16667 </td> 16668<td> 16669 <p> 16670 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 16671 2.1:</em></span> Max = 5.95ε (Mean = 2.08ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Mathworld_Data">And 16672 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 16673 Max = 3.53ε (Mean = 1.39ε)) 16674 </p> 16675 </td> 16676<td> 16677 <p> 16678 <span class="blue">Max = 4.12ε (Mean = 1.85ε)</span><br> <br> 16679 (<span class="emphasis"><em><cmath>:</em></span> Max = 616ε (Mean = 221ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Mathworld_Data">And 16680 other failures.</a>) 16681 </p> 16682 </td> 16683<td> 16684 <p> 16685 <span class="blue">Max = 4.12ε (Mean = 1.95ε)</span> 16686 </p> 16687 </td> 16688<td> 16689 <p> 16690 <span class="blue">Max = 2.97ε (Mean = 1.24ε)</span> 16691 </p> 16692 </td> 16693</tr> 16694<tr> 16695<td> 16696 <p> 16697 Bessel In: Random Data 16698 </p> 16699 </td> 16700<td> 16701 <p> 16702 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 16703 2.1:</em></span> Max = 261ε (Mean = 53.2ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_In_Random_Data">And 16704 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 16705 Max = 7.37ε (Mean = 2.4ε)) 16706 </p> 16707 </td> 16708<td> 16709 <p> 16710 <span class="blue">Max = 4.62ε (Mean = 1.06ε)</span><br> <br> 16711 (<span class="emphasis"><em><cmath>:</em></span> Max = 645ε (Mean = 132ε)) 16712 </p> 16713 </td> 16714<td> 16715 <p> 16716 <span class="blue">Max = 176ε (Mean = 39.1ε)</span> 16717 </p> 16718 </td> 16719<td> 16720 <p> 16721 <span class="blue">Max = 9.67ε (Mean = 1.88ε)</span> 16722 </p> 16723 </td> 16724</tr> 16725<tr> 16726<td> 16727 <p> 16728 Bessel Iv: Random Data 16729 </p> 16730 </td> 16731<td> 16732 <p> 16733 <span class="blue">Max = 0.661ε (Mean = 0.0441ε)</span><br> <br> 16734 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 6.18e+03ε (Mean = 1.55e+03ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Random_Data">And 16735 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 16736 <span class="red">Max = 4.28e+08ε (Mean = 2.85e+07ε))</span> 16737 </p> 16738 </td> 16739<td> 16740 <p> 16741 <span class="blue">Max = 8.35ε (Mean = 1.62ε)</span><br> <br> 16742 (<span class="emphasis"><em><cmath>:</em></span> Max = 1.05e+03ε (Mean = 224ε) 16743 <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Random_Data">And 16744 other failures.</a>) 16745 </p> 16746 </td> 16747<td> 16748 <p> 16749 <span class="blue">Max = 283ε (Mean = 88.4ε)</span> 16750 </p> 16751 </td> 16752<td> 16753 <p> 16754 <span class="blue">Max = 7.46ε (Mean = 1.71ε)</span> 16755 </p> 16756 </td> 16757</tr> 16758<tr> 16759<td> 16760 <p> 16761 Bessel Iv: Mathworld Data (large values) 16762 </p> 16763 </td> 16764<td> 16765 <p> 16766 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 16767 2.1:</em></span> Max = 37ε (Mean = 18ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Mathworld_Data_large_values_">And 16768 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 16769 <span class="red">Max = 3.77e+168ε (Mean = 2.39e+168ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_Iv_Mathworld_Data_large_values_">And 16770 other failures.</a>)</span> 16771 </p> 16772 </td> 16773<td> 16774 <p> 16775 <span class="blue">Max = 14.7ε (Mean = 6.66ε)</span><br> <br> 16776 (<span class="emphasis"><em><cmath>:</em></span> Max = 118ε (Mean = 57.2ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Mathworld_Data_large_values_">And 16777 other failures.</a>) 16778 </p> 16779 </td> 16780<td> 16781 <p> 16782 <span class="blue">Max = 14.7ε (Mean = 6.59ε)</span> 16783 </p> 16784 </td> 16785<td> 16786 <p> 16787 <span class="blue">Max = 3.67ε (Mean = 1.64ε)</span> 16788 </p> 16789 </td> 16790</tr> 16791</tbody> 16792</table></div> 16793</div> 16794<br class="table-break"><div class="table"> 16795<a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_i_integer_orders_"></a><p class="title"><b>Table 105. Error rates for cyl_bessel_i (integer orders)</b></p> 16796<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i (integer orders)"> 16797<colgroup> 16798<col> 16799<col> 16800<col> 16801<col> 16802<col> 16803</colgroup> 16804<thead><tr> 16805<th> 16806 </th> 16807<th> 16808 <p> 16809 GNU C++ version 7.1.0<br> linux<br> double 16810 </p> 16811 </th> 16812<th> 16813 <p> 16814 GNU C++ version 7.1.0<br> linux<br> long double 16815 </p> 16816 </th> 16817<th> 16818 <p> 16819 Sun compiler version 0x5150<br> Sun Solaris<br> long double 16820 </p> 16821 </th> 16822<th> 16823 <p> 16824 Microsoft Visual C++ version 14.1<br> Win32<br> double 16825 </p> 16826 </th> 16827</tr></thead> 16828<tbody> 16829<tr> 16830<td> 16831 <p> 16832 Bessel I0: Mathworld Data (Integer Version) 16833 </p> 16834 </td> 16835<td> 16836 <p> 16837 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 16838 2.1:</em></span> Max = 0.79ε (Mean = 0.482ε))<br> (<span class="emphasis"><em>Rmath 16839 3.2.3:</em></span> Max = 1.52ε (Mean = 0.622ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_I0_Mathworld_Data_Integer_Version_">And 16840 other failures.</a>) 16841 </p> 16842 </td> 16843<td> 16844 <p> 16845 <span class="blue">Max = 1.95ε (Mean = 0.738ε)</span><br> <br> 16846 (<span class="emphasis"><em><cmath>:</em></span> Max = 8.49ε (Mean = 3.46ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_I0_Mathworld_Data_Integer_Version_">And 16847 other failures.</a>) 16848 </p> 16849 </td> 16850<td> 16851 <p> 16852 <span class="blue">Max = 1.95ε (Mean = 0.661ε)</span> 16853 </p> 16854 </td> 16855<td> 16856 <p> 16857 <span class="blue">Max = 0.762ε (Mean = 0.329ε)</span> 16858 </p> 16859 </td> 16860</tr> 16861<tr> 16862<td> 16863 <p> 16864 Bessel I1: Mathworld Data (Integer Version) 16865 </p> 16866 </td> 16867<td> 16868 <p> 16869 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 16870 2.1:</em></span> Max = 0.82ε (Mean = 0.456ε))<br> (<span class="emphasis"><em>Rmath 16871 3.2.3:</em></span> Max = 1.53ε (Mean = 0.483ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_I1_Mathworld_Data_Integer_Version_">And 16872 other failures.</a>) 16873 </p> 16874 </td> 16875<td> 16876 <p> 16877 <span class="blue">Max = 0.64ε (Mean = 0.202ε)</span><br> <br> 16878 (<span class="emphasis"><em><cmath>:</em></span> Max = 5ε (Mean = 2.15ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_I1_Mathworld_Data_Integer_Version_">And 16879 other failures.</a>) 16880 </p> 16881 </td> 16882<td> 16883 <p> 16884 <span class="blue">Max = 0.64ε (Mean = 0.202ε)</span> 16885 </p> 16886 </td> 16887<td> 16888 <p> 16889 <span class="blue">Max = 0.767ε (Mean = 0.398ε)</span> 16890 </p> 16891 </td> 16892</tr> 16893<tr> 16894<td> 16895 <p> 16896 Bessel In: Mathworld Data (Integer Version) 16897 </p> 16898 </td> 16899<td> 16900 <p> 16901 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 16902 2.1:</em></span> Max = 5.15ε (Mean = 2.13ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__GSL_2_1_Bessel_In_Mathworld_Data_Integer_Version_">And 16903 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 16904 Max = 1.73ε (Mean = 0.601ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_In_Mathworld_Data_Integer_Version_">And 16905 other failures.</a>) 16906 </p> 16907 </td> 16908<td> 16909 <p> 16910 <span class="blue">Max = 1.8ε (Mean = 1.33ε)</span><br> <br> 16911 (<span class="emphasis"><em><cmath>:</em></span> Max = 430ε (Mean = 163ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_In_Mathworld_Data_Integer_Version_">And 16912 other failures.</a>) 16913 </p> 16914 </td> 16915<td> 16916 <p> 16917 <span class="blue">Max = 463ε (Mean = 140ε)</span> 16918 </p> 16919 </td> 16920<td> 16921 <p> 16922 <span class="blue">Max = 3.46ε (Mean = 1.32ε)</span> 16923 </p> 16924 </td> 16925</tr> 16926</tbody> 16927</table></div> 16928</div> 16929<br class="table-break"><div class="table"> 16930<a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_i_prime"></a><p class="title"><b>Table 106. Error rates for cyl_bessel_i_prime</b></p> 16931<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i_prime"> 16932<colgroup> 16933<col> 16934<col> 16935<col> 16936<col> 16937<col> 16938</colgroup> 16939<thead><tr> 16940<th> 16941 </th> 16942<th> 16943 <p> 16944 GNU C++ version 7.1.0<br> linux<br> double 16945 </p> 16946 </th> 16947<th> 16948 <p> 16949 GNU C++ version 7.1.0<br> linux<br> long double 16950 </p> 16951 </th> 16952<th> 16953 <p> 16954 Sun compiler version 0x5150<br> Sun Solaris<br> long double 16955 </p> 16956 </th> 16957<th> 16958 <p> 16959 Microsoft Visual C++ version 14.1<br> Win32<br> double 16960 </p> 16961 </th> 16962</tr></thead> 16963<tbody> 16964<tr> 16965<td> 16966 <p> 16967 Bessel I'0: Mathworld Data 16968 </p> 16969 </td> 16970<td> 16971 <p> 16972 <span class="blue">Max = 0ε (Mean = 0ε)</span> 16973 </p> 16974 </td> 16975<td> 16976 <p> 16977 <span class="blue">Max = 0.82ε (Mean = 0.259ε)</span> 16978 </p> 16979 </td> 16980<td> 16981 <p> 16982 <span class="blue">Max = 0.82ε (Mean = 0.259ε)</span> 16983 </p> 16984 </td> 16985<td> 16986 <p> 16987 <span class="blue">Max = 0.82ε (Mean = 0.354ε)</span> 16988 </p> 16989 </td> 16990</tr> 16991<tr> 16992<td> 16993 <p> 16994 Bessel I'1: Mathworld Data 16995 </p> 16996 </td> 16997<td> 16998 <p> 16999 <span class="blue">Max = 0ε (Mean = 0ε)</span> 17000 </p> 17001 </td> 17002<td> 17003 <p> 17004 <span class="blue">Max = 1.97ε (Mean = 0.757ε)</span> 17005 </p> 17006 </td> 17007<td> 17008 <p> 17009 <span class="blue">Max = 1.97ε (Mean = 0.757ε)</span> 17010 </p> 17011 </td> 17012<td> 17013 <p> 17014 <span class="blue">Max = 1.36ε (Mean = 0.782ε)</span> 17015 </p> 17016 </td> 17017</tr> 17018<tr> 17019<td> 17020 <p> 17021 Bessel I'n: Mathworld Data 17022 </p> 17023 </td> 17024<td> 17025 <p> 17026 <span class="blue">Max = 0ε (Mean = 0ε)</span> 17027 </p> 17028 </td> 17029<td> 17030 <p> 17031 <span class="blue">Max = 2.31ε (Mean = 1.41ε)</span> 17032 </p> 17033 </td> 17034<td> 17035 <p> 17036 <span class="blue">Max = 701ε (Mean = 212ε)</span> 17037 </p> 17038 </td> 17039<td> 17040 <p> 17041 <span class="blue">Max = 3.61ε (Mean = 1.22ε)</span> 17042 </p> 17043 </td> 17044</tr> 17045<tr> 17046<td> 17047 <p> 17048 Bessel I'v: Mathworld Data 17049 </p> 17050 </td> 17051<td> 17052 <p> 17053 <span class="blue">Max = 1.62ε (Mean = 0.512ε)</span> 17054 </p> 17055 </td> 17056<td> 17057 <p> 17058 <span class="blue">Max = 2.89e+03ε (Mean = 914ε)</span> 17059 </p> 17060 </td> 17061<td> 17062 <p> 17063 <span class="blue">Max = 2.89e+03ε (Mean = 914ε)</span> 17064 </p> 17065 </td> 17066<td> 17067 <p> 17068 <span class="blue">Max = 3.76e+03ε (Mean = 1.19e+03ε)</span> 17069 </p> 17070 </td> 17071</tr> 17072<tr> 17073<td> 17074 <p> 17075 Bessel I'n: Random Data 17076 </p> 17077 </td> 17078<td> 17079 <p> 17080 <span class="blue">Max = 0ε (Mean = 0ε)</span> 17081 </p> 17082 </td> 17083<td> 17084 <p> 17085 <span class="blue">Max = 3.95ε (Mean = 1.06ε)</span> 17086 </p> 17087 </td> 17088<td> 17089 <p> 17090 <span class="blue">Max = 195ε (Mean = 37.1ε)</span> 17091 </p> 17092 </td> 17093<td> 17094 <p> 17095 <span class="blue">Max = 9.85ε (Mean = 1.82ε)</span> 17096 </p> 17097 </td> 17098</tr> 17099<tr> 17100<td> 17101 <p> 17102 Bessel I'v: Random Data 17103 </p> 17104 </td> 17105<td> 17106 <p> 17107 <span class="blue">Max = 0ε (Mean = 0ε)</span> 17108 </p> 17109 </td> 17110<td> 17111 <p> 17112 <span class="blue">Max = 14.1ε (Mean = 2.93ε)</span> 17113 </p> 17114 </td> 17115<td> 17116 <p> 17117 <span class="blue">Max = 336ε (Mean = 68.5ε)</span> 17118 </p> 17119 </td> 17120<td> 17121 <p> 17122 <span class="blue">Max = 14ε (Mean = 2.5ε)</span> 17123 </p> 17124 </td> 17125</tr> 17126<tr> 17127<td> 17128 <p> 17129 Bessel I'v: Mathworld Data (large values) 17130 </p> 17131 </td> 17132<td> 17133 <p> 17134 <span class="blue">Max = 0ε (Mean = 0ε)</span> 17135 </p> 17136 </td> 17137<td> 17138 <p> 17139 <span class="blue">Max = 42.6ε (Mean = 20.2ε)</span> 17140 </p> 17141 </td> 17142<td> 17143 <p> 17144 <span class="blue">Max = 42.6ε (Mean = 20.2ε)</span> 17145 </p> 17146 </td> 17147<td> 17148 <p> 17149 <span class="blue">Max = 59.5ε (Mean = 26.6ε)</span> 17150 </p> 17151 </td> 17152</tr> 17153</tbody> 17154</table></div> 17155</div> 17156<br class="table-break"><div class="table"> 17157<a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_i_prime_integer_orders_"></a><p class="title"><b>Table 107. Error rates for cyl_bessel_i_prime (integer orders)</b></p> 17158<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i_prime (integer orders)"> 17159<colgroup> 17160<col> 17161<col> 17162<col> 17163<col> 17164<col> 17165</colgroup> 17166<thead><tr> 17167<th> 17168 </th> 17169<th> 17170 <p> 17171 GNU C++ version 7.1.0<br> linux<br> double 17172 </p> 17173 </th> 17174<th> 17175 <p> 17176 GNU C++ version 7.1.0<br> linux<br> long double 17177 </p> 17178 </th> 17179<th> 17180 <p> 17181 Sun compiler version 0x5150<br> Sun Solaris<br> long double 17182 </p> 17183 </th> 17184<th> 17185 <p> 17186 Microsoft Visual C++ version 14.1<br> Win32<br> double 17187 </p> 17188 </th> 17189</tr></thead> 17190<tbody> 17191<tr> 17192<td> 17193 <p> 17194 Bessel I'0: Mathworld Data (Integer Version) 17195 </p> 17196 </td> 17197<td> 17198 <p> 17199 <span class="blue">Max = 0ε (Mean = 0ε)</span> 17200 </p> 17201 </td> 17202<td> 17203 <p> 17204 <span class="blue">Max = 0.82ε (Mean = 0.259ε)</span> 17205 </p> 17206 </td> 17207<td> 17208 <p> 17209 <span class="blue">Max = 0.82ε (Mean = 0.259ε)</span> 17210 </p> 17211 </td> 17212<td> 17213 <p> 17214 <span class="blue">Max = 0.82ε (Mean = 0.354ε)</span> 17215 </p> 17216 </td> 17217</tr> 17218<tr> 17219<td> 17220 <p> 17221 Bessel I'1: Mathworld Data (Integer Version) 17222 </p> 17223 </td> 17224<td> 17225 <p> 17226 <span class="blue">Max = 0ε (Mean = 0ε)</span> 17227 </p> 17228 </td> 17229<td> 17230 <p> 17231 <span class="blue">Max = 1.97ε (Mean = 0.757ε)</span> 17232 </p> 17233 </td> 17234<td> 17235 <p> 17236 <span class="blue">Max = 1.97ε (Mean = 0.757ε)</span> 17237 </p> 17238 </td> 17239<td> 17240 <p> 17241 <span class="blue">Max = 1.36ε (Mean = 0.782ε)</span> 17242 </p> 17243 </td> 17244</tr> 17245<tr> 17246<td> 17247 <p> 17248 Bessel I'n: Mathworld Data (Integer Version) 17249 </p> 17250 </td> 17251<td> 17252 <p> 17253 <span class="blue">Max = 0ε (Mean = 0ε)</span> 17254 </p> 17255 </td> 17256<td> 17257 <p> 17258 <span class="blue">Max = 2.31ε (Mean = 1.41ε)</span> 17259 </p> 17260 </td> 17261<td> 17262 <p> 17263 <span class="blue">Max = 701ε (Mean = 212ε)</span> 17264 </p> 17265 </td> 17266<td> 17267 <p> 17268 <span class="blue">Max = 3.61ε (Mean = 1.22ε)</span> 17269 </p> 17270 </td> 17271</tr> 17272</tbody> 17273</table></div> 17274</div> 17275<br class="table-break"><div class="table"> 17276<a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_j"></a><p class="title"><b>Table 108. Error rates for cyl_bessel_j</b></p> 17277<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j"> 17278<colgroup> 17279<col> 17280<col> 17281<col> 17282<col> 17283<col> 17284</colgroup> 17285<thead><tr> 17286<th> 17287 </th> 17288<th> 17289 <p> 17290 GNU C++ version 7.1.0<br> linux<br> long double 17291 </p> 17292 </th> 17293<th> 17294 <p> 17295 GNU C++ version 7.1.0<br> linux<br> double 17296 </p> 17297 </th> 17298<th> 17299 <p> 17300 Sun compiler version 0x5150<br> Sun Solaris<br> long double 17301 </p> 17302 </th> 17303<th> 17304 <p> 17305 Microsoft Visual C++ version 14.1<br> Win32<br> double 17306 </p> 17307 </th> 17308</tr></thead> 17309<tbody> 17310<tr> 17311<td> 17312 <p> 17313 Bessel J0: Mathworld Data 17314 </p> 17315 </td> 17316<td> 17317 <p> 17318 <span class="blue">Max = 6.55ε (Mean = 2.86ε)</span><br> <br> 17319 (<span class="emphasis"><em><cmath>:</em></span> Max = 5.04ε (Mean = 1.78ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J0_Mathworld_Data">And 17320 other failures.</a>) 17321 </p> 17322 </td> 17323<td> 17324 <p> 17325 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 17326 2.1:</em></span> Max = 0.629ε (Mean = 0.223ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J0_Mathworld_Data">And 17327 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 17328 Max = 0.629ε (Mean = 0.223ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J0_Mathworld_Data">And 17329 other failures.</a>) 17330 </p> 17331 </td> 17332<td> 17333 <p> 17334 <span class="blue">Max = 6.55ε (Mean = 2.86ε)</span> 17335 </p> 17336 </td> 17337<td> 17338 <p> 17339 <span class="blue">Max = 2.52ε (Mean = 1.2ε)</span> 17340 </p> 17341 </td> 17342</tr> 17343<tr> 17344<td> 17345 <p> 17346 Bessel J0: Mathworld Data (Tricky cases) 17347 </p> 17348 </td> 17349<td> 17350 <p> 17351 <span class="blue">Max = 1.64e+08ε (Mean = 6.69e+07ε)</span><br> 17352 <br> (<span class="emphasis"><em><cmath>:</em></span> Max = 4.79e+08ε (Mean = 17353 1.96e+08ε)) 17354 </p> 17355 </td> 17356<td> 17357 <p> 17358 <span class="blue">Max = 8e+04ε (Mean = 3.27e+04ε)</span><br> 17359 <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 6.5e+07ε (Mean = 2.66e+07ε))<br> 17360 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.04e+07ε (Mean = 4.29e+06ε)) 17361 </p> 17362 </td> 17363<td> 17364 <p> 17365 <span class="blue">Max = 1.64e+08ε (Mean = 6.69e+07ε)</span> 17366 </p> 17367 </td> 17368<td> 17369 <p> 17370 <span class="blue">Max = 1e+07ε (Mean = 4.09e+06ε)</span> 17371 </p> 17372 </td> 17373</tr> 17374<tr> 17375<td> 17376 <p> 17377 Bessel J1: Mathworld Data 17378 </p> 17379 </td> 17380<td> 17381 <p> 17382 <span class="blue">Max = 3.59ε (Mean = 1.33ε)</span><br> <br> 17383 (<span class="emphasis"><em><cmath>:</em></span> Max = 6.1ε (Mean = 2.95ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J1_Mathworld_Data">And 17384 other failures.</a>) 17385 </p> 17386 </td> 17387<td> 17388 <p> 17389 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 17390 2.1:</em></span> Max = 6.62ε (Mean = 2.35ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J1_Mathworld_Data">And 17391 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 17392 Max = 0.946ε (Mean = 0.39ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J1_Mathworld_Data">And 17393 other failures.</a>) 17394 </p> 17395 </td> 17396<td> 17397 <p> 17398 <span class="blue">Max = 1.44ε (Mean = 0.637ε)</span> 17399 </p> 17400 </td> 17401<td> 17402 <p> 17403 <span class="blue">Max = 1.73ε (Mean = 0.976ε)</span> 17404 </p> 17405 </td> 17406</tr> 17407<tr> 17408<td> 17409 <p> 17410 Bessel J1: Mathworld Data (tricky cases) 17411 </p> 17412 </td> 17413<td> 17414 <p> 17415 <span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span><br> 17416 <br> (<span class="emphasis"><em><cmath>:</em></span> Max = 2.15e+06ε (Mean = 17417 1.58e+06ε)) 17418 </p> 17419 </td> 17420<td> 17421 <p> 17422 <span class="blue">Max = 106ε (Mean = 47.5ε)</span><br> <br> 17423 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.75e+05ε (Mean = 5.32e+05ε))<br> 17424 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.93e+06ε (Mean = 1.7e+06ε)) 17425 </p> 17426 </td> 17427<td> 17428 <p> 17429 <span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span> 17430 </p> 17431 </td> 17432<td> 17433 <p> 17434 <span class="blue">Max = 3.23e+04ε (Mean = 1.45e+04ε)</span> 17435 </p> 17436 </td> 17437</tr> 17438<tr> 17439<td> 17440 <p> 17441 Bessel JN: Mathworld Data 17442 </p> 17443 </td> 17444<td> 17445 <p> 17446 <span class="blue">Max = 6.85ε (Mean = 3.35ε)</span><br> <br> 17447 (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 2.13e+19ε (Mean 17448 = 5.16e+18ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_JN_Mathworld_Data">And 17449 other failures.</a>)</span> 17450 </p> 17451 </td> 17452<td> 17453 <p> 17454 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 17455 2.1:</em></span> Max = 6.9e+05ε (Mean = 2.15e+05ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_JN_Mathworld_Data">And 17456 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 17457 <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_JN_Mathworld_Data">And 17458 other failures.</a>)</span> 17459 </p> 17460 </td> 17461<td> 17462 <p> 17463 <span class="blue">Max = 463ε (Mean = 112ε)</span> 17464 </p> 17465 </td> 17466<td> 17467 <p> 17468 <span class="blue">Max = 14.7ε (Mean = 5.4ε)</span> 17469 </p> 17470 </td> 17471</tr> 17472<tr> 17473<td> 17474 <p> 17475 Bessel J: Mathworld Data 17476 </p> 17477 </td> 17478<td> 17479 <p> 17480 <span class="blue">Max = 14.7ε (Mean = 4.11ε)</span><br> <br> 17481 (<span class="emphasis"><em><cmath>:</em></span> Max = 3.49e+05ε (Mean = 8.09e+04ε) 17482 <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J_Mathworld_Data">And 17483 other failures.</a>) 17484 </p> 17485 </td> 17486<td> 17487 <p> 17488 <span class="blue">Max = 10ε (Mean = 2.24ε)</span><br> <br> (<span class="emphasis"><em>GSL 17489 2.1:</em></span> Max = 2.39e+05ε (Mean = 5.37e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Mathworld_Data">And 17490 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 17491 <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J_Mathworld_Data">And 17492 other failures.</a>)</span> 17493 </p> 17494 </td> 17495<td> 17496 <p> 17497 <span class="blue">Max = 14.7ε (Mean = 4.22ε)</span> 17498 </p> 17499 </td> 17500<td> 17501 <p> 17502 <span class="blue">Max = 14.9ε (Mean = 3.89ε)</span> 17503 </p> 17504 </td> 17505</tr> 17506<tr> 17507<td> 17508 <p> 17509 Bessel J: Mathworld Data (large values) 17510 </p> 17511 </td> 17512<td> 17513 <p> 17514 <span class="blue">Max = 607ε (Mean = 305ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span> 17515 Max = 34.9ε (Mean = 17.4ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J_Mathworld_Data_large_values_">And 17516 other failures.</a>) 17517 </p> 17518 </td> 17519<td> 17520 <p> 17521 <span class="blue">Max = 0.536ε (Mean = 0.268ε)</span><br> <br> 17522 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 4.91e+03ε (Mean = 2.46e+03ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Mathworld_Data_large_values_">And 17523 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 17524 Max = 5.9ε (Mean = 3.76ε)) 17525 </p> 17526 </td> 17527<td> 17528 <p> 17529 <span class="blue">Max = 607ε (Mean = 305ε)</span> 17530 </p> 17531 </td> 17532<td> 17533 <p> 17534 <span class="blue">Max = 9.31ε (Mean = 5.52ε)</span> 17535 </p> 17536 </td> 17537</tr> 17538<tr> 17539<td> 17540 <p> 17541 Bessel JN: Random Data 17542 </p> 17543 </td> 17544<td> 17545 <p> 17546 <span class="blue">Max = 50.8ε (Mean = 3.69ε)</span><br> <br> 17547 (<span class="emphasis"><em><cmath>:</em></span> Max = 1.12e+03ε (Mean = 88.7ε)) 17548 </p> 17549 </td> 17550<td> 17551 <p> 17552 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 17553 2.1:</em></span> Max = 75.7ε (Mean = 5.36ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 17554 Max = 3.93ε (Mean = 1.22ε)) 17555 </p> 17556 </td> 17557<td> 17558 <p> 17559 <span class="blue">Max = 99.6ε (Mean = 22ε)</span> 17560 </p> 17561 </td> 17562<td> 17563 <p> 17564 <span class="blue">Max = 17.5ε (Mean = 1.46ε)</span> 17565 </p> 17566 </td> 17567</tr> 17568<tr> 17569<td> 17570 <p> 17571 Bessel J: Random Data 17572 </p> 17573 </td> 17574<td> 17575 <p> 17576 <span class="blue">Max = 11.4ε (Mean = 1.68ε)</span><br> <br> 17577 (<span class="emphasis"><em><cmath>:</em></span> Max = 501ε (Mean = 52.3ε)) 17578 </p> 17579 </td> 17580<td> 17581 <p> 17582 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 17583 2.1:</em></span> Max = 15.5ε (Mean = 3.33ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Random_Data">And 17584 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 17585 Max = 6.74ε (Mean = 1.3ε)) 17586 </p> 17587 </td> 17588<td> 17589 <p> 17590 <span class="blue">Max = 260ε (Mean = 34ε)</span> 17591 </p> 17592 </td> 17593<td> 17594 <p> 17595 <span class="blue">Max = 9.24ε (Mean = 1.17ε)</span> 17596 </p> 17597 </td> 17598</tr> 17599<tr> 17600<td> 17601 <p> 17602 Bessel J: Random Data (Tricky large values) 17603 </p> 17604 </td> 17605<td> 17606 <p> 17607 <span class="blue">Max = 785ε (Mean = 94.2ε)</span><br> <br> 17608 (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 5.01e+17ε (Mean 17609 = 6.23e+16ε))</span> 17610 </p> 17611 </td> 17612<td> 17613 <p> 17614 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 17615 2.1:</em></span> Max = 2.48e+05ε (Mean = 5.11e+04ε))<br> (<span class="emphasis"><em>Rmath 17616 3.2.3:</em></span> Max = 71.6ε (Mean = 11.7ε)) 17617 </p> 17618 </td> 17619<td> 17620 <p> 17621 <span class="blue">Max = 785ε (Mean = 97.4ε)</span> 17622 </p> 17623 </td> 17624<td> 17625 <p> 17626 <span class="blue">Max = 59.2ε (Mean = 8.67ε)</span> 17627 </p> 17628 </td> 17629</tr> 17630</tbody> 17631</table></div> 17632</div> 17633<br class="table-break"><div class="table"> 17634<a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_j_integer_orders_"></a><p class="title"><b>Table 109. Error rates for cyl_bessel_j (integer orders)</b></p> 17635<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j (integer orders)"> 17636<colgroup> 17637<col> 17638<col> 17639<col> 17640<col> 17641<col> 17642</colgroup> 17643<thead><tr> 17644<th> 17645 </th> 17646<th> 17647 <p> 17648 GNU C++ version 7.1.0<br> linux<br> long double 17649 </p> 17650 </th> 17651<th> 17652 <p> 17653 GNU C++ version 7.1.0<br> linux<br> double 17654 </p> 17655 </th> 17656<th> 17657 <p> 17658 Sun compiler version 0x5150<br> Sun Solaris<br> long double 17659 </p> 17660 </th> 17661<th> 17662 <p> 17663 Microsoft Visual C++ version 14.1<br> Win32<br> double 17664 </p> 17665 </th> 17666</tr></thead> 17667<tbody> 17668<tr> 17669<td> 17670 <p> 17671 Bessel J0: Mathworld Data (Integer Version) 17672 </p> 17673 </td> 17674<td> 17675 <p> 17676 <span class="blue">Max = 6.55ε (Mean = 2.86ε)</span><br> <br> 17677 (<span class="emphasis"><em><cmath>:</em></span> Max = 5.04ε (Mean = 1.78ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_J0_Mathworld_Data_Integer_Version_">And 17678 other failures.</a>) 17679 </p> 17680 </td> 17681<td> 17682 <p> 17683 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 17684 2.1:</em></span> Max = 1.12ε (Mean = 0.488ε))<br> (<span class="emphasis"><em>Rmath 17685 3.2.3:</em></span> Max = 0.629ε (Mean = 0.223ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_J0_Mathworld_Data_Integer_Version_">And 17686 other failures.</a>) 17687 </p> 17688 </td> 17689<td> 17690 <p> 17691 <span class="blue">Max = 6.55ε (Mean = 2.86ε)</span> 17692 </p> 17693 </td> 17694<td> 17695 <p> 17696 <span class="blue">Max = 2.52ε (Mean = 1.2ε)</span><br> <br> 17697 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.89ε (Mean = 0.988ε)) 17698 </p> 17699 </td> 17700</tr> 17701<tr> 17702<td> 17703 <p> 17704 Bessel J0: Mathworld Data (Tricky cases) (Integer Version) 17705 </p> 17706 </td> 17707<td> 17708 <p> 17709 <span class="blue">Max = 1.64e+08ε (Mean = 6.69e+07ε)</span><br> 17710 <br> (<span class="emphasis"><em><cmath>:</em></span> Max = 4.79e+08ε (Mean = 17711 1.96e+08ε)) 17712 </p> 17713 </td> 17714<td> 17715 <p> 17716 <span class="blue">Max = 8e+04ε (Mean = 3.27e+04ε)</span><br> 17717 <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1e+07ε (Mean = 4.11e+06ε))<br> 17718 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.04e+07ε (Mean = 4.29e+06ε)) 17719 </p> 17720 </td> 17721<td> 17722 <p> 17723 <span class="blue">Max = 1.64e+08ε (Mean = 6.69e+07ε)</span> 17724 </p> 17725 </td> 17726<td> 17727 <p> 17728 <span class="blue">Max = 1e+07ε (Mean = 4.09e+06ε)</span><br> 17729 <br> (<span class="emphasis"><em><math.h>:</em></span> <span class="red">Max 17730 = 2.54e+08ε (Mean = 1.04e+08ε))</span> 17731 </p> 17732 </td> 17733</tr> 17734<tr> 17735<td> 17736 <p> 17737 Bessel J1: Mathworld Data (Integer Version) 17738 </p> 17739 </td> 17740<td> 17741 <p> 17742 <span class="blue">Max = 3.59ε (Mean = 1.33ε)</span><br> <br> 17743 (<span class="emphasis"><em><cmath>:</em></span> Max = 6.1ε (Mean = 2.95ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_J1_Mathworld_Data_Integer_Version_">And 17744 other failures.</a>) 17745 </p> 17746 </td> 17747<td> 17748 <p> 17749 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 17750 2.1:</em></span> Max = 1.89ε (Mean = 0.721ε))<br> (<span class="emphasis"><em>Rmath 17751 3.2.3:</em></span> Max = 0.946ε (Mean = 0.39ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_J1_Mathworld_Data_Integer_Version_">And 17752 other failures.</a>) 17753 </p> 17754 </td> 17755<td> 17756 <p> 17757 <span class="blue">Max = 1.44ε (Mean = 0.637ε)</span> 17758 </p> 17759 </td> 17760<td> 17761 <p> 17762 <span class="blue">Max = 1.73ε (Mean = 0.976ε)</span><br> <br> 17763 (<span class="emphasis"><em><math.h>:</em></span> Max = 11.4ε (Mean = 4.15ε)) 17764 </p> 17765 </td> 17766</tr> 17767<tr> 17768<td> 17769 <p> 17770 Bessel J1: Mathworld Data (tricky cases) (Integer Version) 17771 </p> 17772 </td> 17773<td> 17774 <p> 17775 <span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span><br> 17776 <br> (<span class="emphasis"><em><cmath>:</em></span> Max = 2.15e+06ε (Mean = 17777 1.58e+06ε)) 17778 </p> 17779 </td> 17780<td> 17781 <p> 17782 <span class="blue">Max = 106ε (Mean = 47.5ε)</span><br> <br> 17783 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.26e+06ε (Mean = 6.28e+05ε))<br> 17784 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.93e+06ε (Mean = 1.7e+06ε)) 17785 </p> 17786 </td> 17787<td> 17788 <p> 17789 <span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span> 17790 </p> 17791 </td> 17792<td> 17793 <p> 17794 <span class="blue">Max = 3.23e+04ε (Mean = 1.45e+04ε)</span><br> 17795 <br> (<span class="emphasis"><em><math.h>:</em></span> Max = 1.44e+07ε (Mean 17796 = 6.5e+06ε)) 17797 </p> 17798 </td> 17799</tr> 17800<tr> 17801<td> 17802 <p> 17803 Bessel JN: Mathworld Data (Integer Version) 17804 </p> 17805 </td> 17806<td> 17807 <p> 17808 <span class="blue">Max = 6.85ε (Mean = 3.35ε)</span><br> <br> 17809 (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 2.13e+19ε (Mean 17810 = 5.16e+18ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_JN_Mathworld_Data_Integer_Version_">And 17811 other failures.</a>)</span> 17812 </p> 17813 </td> 17814<td> 17815 <p> 17816 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 17817 2.1:</em></span> Max = 6.9e+05ε (Mean = 2.53e+05ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__GSL_2_1_Bessel_JN_Mathworld_Data_Integer_Version_">And 17818 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 17819 <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_JN_Mathworld_Data_Integer_Version_">And 17820 other failures.</a>)</span> 17821 </p> 17822 </td> 17823<td> 17824 <p> 17825 <span class="blue">Max = 463ε (Mean = 112ε)</span> 17826 </p> 17827 </td> 17828<td> 17829 <p> 17830 <span class="blue">Max = 14.7ε (Mean = 5.4ε)</span><br> <br> 17831 (<span class="emphasis"><em><math.h>:</em></span> <span class="red">Max = +INFε (Mean 17832 = +INFε) <a class="link" href="index.html#errors_Microsoft_Visual_C_version_14_1_Win32_double_cyl_bessel_j_integer_orders___math_h__Bessel_JN_Mathworld_Data_Integer_Version_">And 17833 other failures.</a>)</span> 17834 </p> 17835 </td> 17836</tr> 17837</tbody> 17838</table></div> 17839</div> 17840<br class="table-break"><div class="table"> 17841<a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_j_prime"></a><p class="title"><b>Table 110. Error rates for cyl_bessel_j_prime</b></p> 17842<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j_prime"> 17843<colgroup> 17844<col> 17845<col> 17846<col> 17847<col> 17848<col> 17849</colgroup> 17850<thead><tr> 17851<th> 17852 </th> 17853<th> 17854 <p> 17855 GNU C++ version 7.1.0<br> linux<br> double 17856 </p> 17857 </th> 17858<th> 17859 <p> 17860 GNU C++ version 7.1.0<br> linux<br> long double 17861 </p> 17862 </th> 17863<th> 17864 <p> 17865 Sun compiler version 0x5150<br> Sun Solaris<br> long double 17866 </p> 17867 </th> 17868<th> 17869 <p> 17870 Microsoft Visual C++ version 14.1<br> Win32<br> double 17871 </p> 17872 </th> 17873</tr></thead> 17874<tbody> 17875<tr> 17876<td> 17877 <p> 17878 Bessel J0': Mathworld Data 17879 </p> 17880 </td> 17881<td> 17882 <p> 17883 <span class="blue">Max = 0ε (Mean = 0ε)</span> 17884 </p> 17885 </td> 17886<td> 17887 <p> 17888 <span class="blue">Max = 18.9ε (Mean = 6.82ε)</span> 17889 </p> 17890 </td> 17891<td> 17892 <p> 17893 <span class="blue">Max = 18.9ε (Mean = 6.72ε)</span> 17894 </p> 17895 </td> 17896<td> 17897 <p> 17898 <span class="blue">Max = 6.62ε (Mean = 2.55ε)</span> 17899 </p> 17900 </td> 17901</tr> 17902<tr> 17903<td> 17904 <p> 17905 Bessel J0': Mathworld Data (Tricky cases) 17906 </p> 17907 </td> 17908<td> 17909 <p> 17910 <span class="blue">Max = 0ε (Mean = 0ε)</span> 17911 </p> 17912 </td> 17913<td> 17914 <p> 17915 <span class="blue">Max = 7.44ε (Mean = 3.34ε)</span> 17916 </p> 17917 </td> 17918<td> 17919 <p> 17920 <span class="blue">Max = 7.44ε (Mean = 3.31ε)</span> 17921 </p> 17922 </td> 17923<td> 17924 <p> 17925 <span class="blue">Max = 3.67ε (Mean = 1.74ε)</span> 17926 </p> 17927 </td> 17928</tr> 17929<tr> 17930<td> 17931 <p> 17932 Bessel J1': Mathworld Data 17933 </p> 17934 </td> 17935<td> 17936 <p> 17937 <span class="blue">Max = 0ε (Mean = 0ε)</span> 17938 </p> 17939 </td> 17940<td> 17941 <p> 17942 <span class="blue">Max = 7.9ε (Mean = 3.37ε)</span> 17943 </p> 17944 </td> 17945<td> 17946 <p> 17947 <span class="blue">Max = 7.9ε (Mean = 3.37ε)</span> 17948 </p> 17949 </td> 17950<td> 17951 <p> 17952 <span class="blue">Max = 0.999ε (Mean = 0.627ε)</span> 17953 </p> 17954 </td> 17955</tr> 17956<tr> 17957<td> 17958 <p> 17959 Bessel J1': Mathworld Data (tricky cases) 17960 </p> 17961 </td> 17962<td> 17963 <p> 17964 <span class="blue">Max = 287ε (Mean = 129ε)</span> 17965 </p> 17966 </td> 17967<td> 17968 <p> 17969 <span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span> 17970 </p> 17971 </td> 17972<td> 17973 <p> 17974 <span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span> 17975 </p> 17976 </td> 17977<td> 17978 <p> 17979 <span class="blue">Max = 288ε (Mean = 129ε)</span> 17980 </p> 17981 </td> 17982</tr> 17983<tr> 17984<td> 17985 <p> 17986 Bessel JN': Mathworld Data 17987 </p> 17988 </td> 17989<td> 17990 <p> 17991 <span class="blue">Max = 0.527ε (Mean = 0.128ε)</span> 17992 </p> 17993 </td> 17994<td> 17995 <p> 17996 <span class="blue">Max = 1.29e+03ε (Mean = 312ε)</span> 17997 </p> 17998 </td> 17999<td> 18000 <p> 18001 <span class="blue">Max = 1.29e+03ε (Mean = 355ε)</span> 18002 </p> 18003 </td> 18004<td> 18005 <p> 18006 <span class="blue">Max = 14ε (Mean = 6.13ε)</span> 18007 </p> 18008 </td> 18009</tr> 18010<tr> 18011<td> 18012 <p> 18013 Bessel J': Mathworld Data 18014 </p> 18015 </td> 18016<td> 18017 <p> 18018 <span class="blue">Max = 21.5ε (Mean = 4.7ε)</span> 18019 </p> 18020 </td> 18021<td> 18022 <p> 18023 <span class="blue">Max = 42.5ε (Mean = 9.31ε)</span> 18024 </p> 18025 </td> 18026<td> 18027 <p> 18028 <span class="blue">Max = 42.5ε (Mean = 9.32ε)</span> 18029 </p> 18030 </td> 18031<td> 18032 <p> 18033 <span class="blue">Max = 23.7ε (Mean = 8ε)</span> 18034 </p> 18035 </td> 18036</tr> 18037<tr> 18038<td> 18039 <p> 18040 Bessel J': Mathworld Data (large values) 18041 </p> 18042 </td> 18043<td> 18044 <p> 18045 <span class="blue">Max = 0ε (Mean = 0ε)</span> 18046 </p> 18047 </td> 18048<td> 18049 <p> 18050 <span class="blue">Max = 989ε (Mean = 495ε)</span> 18051 </p> 18052 </td> 18053<td> 18054 <p> 18055 <span class="blue">Max = 989ε (Mean = 495ε)</span> 18056 </p> 18057 </td> 18058<td> 18059 <p> 18060 <span class="blue">Max = 2.9ε (Mean = 1.61ε)</span> 18061 </p> 18062 </td> 18063</tr> 18064<tr> 18065<td> 18066 <p> 18067 Bessel JN': Random Data 18068 </p> 18069 </td> 18070<td> 18071 <p> 18072 <span class="blue">Max = 0.593ε (Mean = 0.0396ε)</span> 18073 </p> 18074 </td> 18075<td> 18076 <p> 18077 <span class="blue">Max = 11.3ε (Mean = 1.85ε)</span> 18078 </p> 18079 </td> 18080<td> 18081 <p> 18082 <span class="blue">Max = 79.4ε (Mean = 16.2ε)</span> 18083 </p> 18084 </td> 18085<td> 18086 <p> 18087 <span class="blue">Max = 6.34ε (Mean = 0.999ε)</span> 18088 </p> 18089 </td> 18090</tr> 18091<tr> 18092<td> 18093 <p> 18094 Bessel J': Random Data 18095 </p> 18096 </td> 18097<td> 18098 <p> 18099 <span class="blue">Max = 0.885ε (Mean = 0.033ε)</span> 18100 </p> 18101 </td> 18102<td> 18103 <p> 18104 <span class="blue">Max = 139ε (Mean = 6.47ε)</span> 18105 </p> 18106 </td> 18107<td> 18108 <p> 18109 <span class="blue">Max = 279ε (Mean = 27.2ε)</span> 18110 </p> 18111 </td> 18112<td> 18113 <p> 18114 <span class="blue">Max = 176ε (Mean = 9.75ε)</span> 18115 </p> 18116 </td> 18117</tr> 18118<tr> 18119<td> 18120 <p> 18121 Bessel J': Random Data (Tricky large values) 18122 </p> 18123 </td> 18124<td> 18125 <p> 18126 <span class="blue">Max = 0ε (Mean = 0ε)</span> 18127 </p> 18128 </td> 18129<td> 18130 <p> 18131 <span class="blue">Max = 474ε (Mean = 62.2ε)</span> 18132 </p> 18133 </td> 18134<td> 18135 <p> 18136 <span class="blue">Max = 474ε (Mean = 64.5ε)</span> 18137 </p> 18138 </td> 18139<td> 18140 <p> 18141 <span class="blue">Max = 379ε (Mean = 45.4ε)</span> 18142 </p> 18143 </td> 18144</tr> 18145</tbody> 18146</table></div> 18147</div> 18148<br class="table-break"><div class="table"> 18149<a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_j_prime_integer_orders_"></a><p class="title"><b>Table 111. Error rates for cyl_bessel_j_prime (integer orders)</b></p> 18150<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j_prime (integer orders)"> 18151<colgroup> 18152<col> 18153<col> 18154<col> 18155<col> 18156<col> 18157</colgroup> 18158<thead><tr> 18159<th> 18160 </th> 18161<th> 18162 <p> 18163 GNU C++ version 7.1.0<br> linux<br> double 18164 </p> 18165 </th> 18166<th> 18167 <p> 18168 GNU C++ version 7.1.0<br> linux<br> long double 18169 </p> 18170 </th> 18171<th> 18172 <p> 18173 Sun compiler version 0x5150<br> Sun Solaris<br> long double 18174 </p> 18175 </th> 18176<th> 18177 <p> 18178 Microsoft Visual C++ version 14.1<br> Win32<br> double 18179 </p> 18180 </th> 18181</tr></thead> 18182<tbody> 18183<tr> 18184<td> 18185 <p> 18186 Bessel J0': Mathworld Data (Integer Version) 18187 </p> 18188 </td> 18189<td> 18190 <p> 18191 <span class="blue">Max = 0ε (Mean = 0ε)</span> 18192 </p> 18193 </td> 18194<td> 18195 <p> 18196 <span class="blue">Max = 18.9ε (Mean = 6.82ε)</span> 18197 </p> 18198 </td> 18199<td> 18200 <p> 18201 <span class="blue">Max = 18.9ε (Mean = 6.72ε)</span> 18202 </p> 18203 </td> 18204<td> 18205 <p> 18206 <span class="blue">Max = 6.62ε (Mean = 2.55ε)</span> 18207 </p> 18208 </td> 18209</tr> 18210<tr> 18211<td> 18212 <p> 18213 Bessel J0': Mathworld Data (Tricky cases) (Integer Version) 18214 </p> 18215 </td> 18216<td> 18217 <p> 18218 <span class="blue">Max = 0ε (Mean = 0ε)</span> 18219 </p> 18220 </td> 18221<td> 18222 <p> 18223 <span class="blue">Max = 7.44ε (Mean = 3.34ε)</span> 18224 </p> 18225 </td> 18226<td> 18227 <p> 18228 <span class="blue">Max = 7.44ε (Mean = 3.31ε)</span> 18229 </p> 18230 </td> 18231<td> 18232 <p> 18233 <span class="blue">Max = 3.67ε (Mean = 1.74ε)</span> 18234 </p> 18235 </td> 18236</tr> 18237<tr> 18238<td> 18239 <p> 18240 Bessel J1': Mathworld Data (Integer Version) 18241 </p> 18242 </td> 18243<td> 18244 <p> 18245 <span class="blue">Max = 0ε (Mean = 0ε)</span> 18246 </p> 18247 </td> 18248<td> 18249 <p> 18250 <span class="blue">Max = 7.9ε (Mean = 3.37ε)</span> 18251 </p> 18252 </td> 18253<td> 18254 <p> 18255 <span class="blue">Max = 7.9ε (Mean = 3.37ε)</span> 18256 </p> 18257 </td> 18258<td> 18259 <p> 18260 <span class="blue">Max = 0.999ε (Mean = 0.627ε)</span> 18261 </p> 18262 </td> 18263</tr> 18264<tr> 18265<td> 18266 <p> 18267 Bessel J1': Mathworld Data (tricky cases) (Integer Version) 18268 </p> 18269 </td> 18270<td> 18271 <p> 18272 <span class="blue">Max = 287ε (Mean = 129ε)</span> 18273 </p> 18274 </td> 18275<td> 18276 <p> 18277 <span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span> 18278 </p> 18279 </td> 18280<td> 18281 <p> 18282 <span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span> 18283 </p> 18284 </td> 18285<td> 18286 <p> 18287 <span class="blue">Max = 288ε (Mean = 129ε)</span> 18288 </p> 18289 </td> 18290</tr> 18291<tr> 18292<td> 18293 <p> 18294 Bessel JN': Mathworld Data (Integer Version) 18295 </p> 18296 </td> 18297<td> 18298 <p> 18299 <span class="blue">Max = 0.527ε (Mean = 0.128ε)</span> 18300 </p> 18301 </td> 18302<td> 18303 <p> 18304 <span class="blue">Max = 1.29e+03ε (Mean = 312ε)</span> 18305 </p> 18306 </td> 18307<td> 18308 <p> 18309 <span class="blue">Max = 1.29e+03ε (Mean = 355ε)</span> 18310 </p> 18311 </td> 18312<td> 18313 <p> 18314 <span class="blue">Max = 14ε (Mean = 6.13ε)</span> 18315 </p> 18316 </td> 18317</tr> 18318</tbody> 18319</table></div> 18320</div> 18321<br class="table-break"><div class="table"> 18322<a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_k"></a><p class="title"><b>Table 112. Error rates for cyl_bessel_k</b></p> 18323<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k"> 18324<colgroup> 18325<col> 18326<col> 18327<col> 18328<col> 18329<col> 18330</colgroup> 18331<thead><tr> 18332<th> 18333 </th> 18334<th> 18335 <p> 18336 GNU C++ version 7.1.0<br> linux<br> long double 18337 </p> 18338 </th> 18339<th> 18340 <p> 18341 GNU C++ version 7.1.0<br> linux<br> double 18342 </p> 18343 </th> 18344<th> 18345 <p> 18346 Sun compiler version 0x5150<br> Sun Solaris<br> long double 18347 </p> 18348 </th> 18349<th> 18350 <p> 18351 Microsoft Visual C++ version 14.1<br> Win32<br> double 18352 </p> 18353 </th> 18354</tr></thead> 18355<tbody> 18356<tr> 18357<td> 18358 <p> 18359 Bessel K0: Mathworld Data 18360 </p> 18361 </td> 18362<td> 18363 <p> 18364 <span class="blue">Max = 0.833ε (Mean = 0.436ε)</span><br> <br> 18365 (<span class="emphasis"><em><cmath>:</em></span> Max = 9.33ε (Mean = 3.25ε)) 18366 </p> 18367 </td> 18368<td> 18369 <p> 18370 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 18371 2.1:</em></span> Max = 6.04ε (Mean = 2.16ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 18372 Max = 0.833ε (Mean = 0.601ε)) 18373 </p> 18374 </td> 18375<td> 18376 <p> 18377 <span class="blue">Max = 0.833ε (Mean = 0.436ε)</span> 18378 </p> 18379 </td> 18380<td> 18381 <p> 18382 <span class="blue">Max = 0.833ε (Mean = 0.552ε)</span> 18383 </p> 18384 </td> 18385</tr> 18386<tr> 18387<td> 18388 <p> 18389 Bessel K1: Mathworld Data 18390 </p> 18391 </td> 18392<td> 18393 <p> 18394 <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span><br> <br> 18395 (<span class="emphasis"><em><cmath>:</em></span> Max = 8.94ε (Mean = 3.19ε)) 18396 </p> 18397 </td> 18398<td> 18399 <p> 18400 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 18401 2.1:</em></span> Max = 6.26ε (Mean = 2.21ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 18402 Max = 0.894ε (Mean = 0.516ε)) 18403 </p> 18404 </td> 18405<td> 18406 <p> 18407 <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span> 18408 </p> 18409 </td> 18410<td> 18411 <p> 18412 <span class="blue">Max = 0.786ε (Mean = 0.39ε)</span> 18413 </p> 18414 </td> 18415</tr> 18416<tr> 18417<td> 18418 <p> 18419 Bessel Kn: Mathworld Data 18420 </p> 18421 </td> 18422<td> 18423 <p> 18424 <span class="blue">Max = 2.6ε (Mean = 1.21ε)</span><br> <br> 18425 (<span class="emphasis"><em><cmath>:</em></span> Max = 12.9ε (Mean = 4.91ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kn_Mathworld_Data">And 18426 other failures.</a>) 18427 </p> 18428 </td> 18429<td> 18430 <p> 18431 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 18432 2.1:</em></span> Max = 3.36ε (Mean = 1.43ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kn_Mathworld_Data">And 18433 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 18434 Max = 8.48ε (Mean = 2.98ε)) 18435 </p> 18436 </td> 18437<td> 18438 <p> 18439 <span class="blue">Max = 2.6ε (Mean = 1.21ε)</span> 18440 </p> 18441 </td> 18442<td> 18443 <p> 18444 <span class="blue">Max = 3.63ε (Mean = 1.46ε)</span> 18445 </p> 18446 </td> 18447</tr> 18448<tr> 18449<td> 18450 <p> 18451 Bessel Kv: Mathworld Data 18452 </p> 18453 </td> 18454<td> 18455 <p> 18456 <span class="blue">Max = 3.58ε (Mean = 2.39ε)</span><br> <br> 18457 (<span class="emphasis"><em><cmath>:</em></span> Max = 13ε (Mean = 4.81ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Mathworld_Data">And 18458 other failures.</a>) 18459 </p> 18460 </td> 18461<td> 18462 <p> 18463 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 18464 2.1:</em></span> Max = 5.47ε (Mean = 2.04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Mathworld_Data">And 18465 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 18466 Max = 3.15ε (Mean = 1.35ε)) 18467 </p> 18468 </td> 18469<td> 18470 <p> 18471 <span class="blue">Max = 5.21ε (Mean = 2.53ε)</span> 18472 </p> 18473 </td> 18474<td> 18475 <p> 18476 <span class="blue">Max = 4.78ε (Mean = 2.19ε)</span> 18477 </p> 18478 </td> 18479</tr> 18480<tr> 18481<td> 18482 <p> 18483 Bessel Kv: Mathworld Data (large values) 18484 </p> 18485 </td> 18486<td> 18487 <p> 18488 <span class="blue">Max = 42.3ε (Mean = 21ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span> 18489 Max = 42.3ε (Mean = 19.8ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Mathworld_Data_large_values_">And 18490 other failures.</a>) 18491 </p> 18492 </td> 18493<td> 18494 <p> 18495 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 18496 2.1:</em></span> Max = 308ε (Mean = 142ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Mathworld_Data_large_values_">And 18497 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 18498 Max = 84.6ε (Mean = 37.8ε)) 18499 </p> 18500 </td> 18501<td> 18502 <p> 18503 <span class="blue">Max = 42.3ε (Mean = 21ε)</span> 18504 </p> 18505 </td> 18506<td> 18507 <p> 18508 <span class="blue">Max = 59.8ε (Mean = 26.9ε)</span> 18509 </p> 18510 </td> 18511</tr> 18512<tr> 18513<td> 18514 <p> 18515 Bessel Kn: Random Data 18516 </p> 18517 </td> 18518<td> 18519 <p> 18520 <span class="blue">Max = 4.55ε (Mean = 1.12ε)</span><br> <br> 18521 (<span class="emphasis"><em><cmath>:</em></span> Max = 13.9ε (Mean = 2.91ε)) 18522 </p> 18523 </td> 18524<td> 18525 <p> 18526 <span class="blue">Max = 0.764ε (Mean = 0.0348ε)</span><br> <br> 18527 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.71ε (Mean = 1.76ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kn_Random_Data">And 18528 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 18529 Max = 7.47ε (Mean = 1.34ε)) 18530 </p> 18531 </td> 18532<td> 18533 <p> 18534 <span class="blue">Max = 4.55ε (Mean = 1.12ε)</span> 18535 </p> 18536 </td> 18537<td> 18538 <p> 18539 <span class="blue">Max = 9.34ε (Mean = 1.7ε)</span> 18540 </p> 18541 </td> 18542</tr> 18543<tr> 18544<td> 18545 <p> 18546 Bessel Kv: Random Data 18547 </p> 18548 </td> 18549<td> 18550 <p> 18551 <span class="blue">Max = 7.88ε (Mean = 1.48ε)</span><br> <br> 18552 (<span class="emphasis"><em><cmath>:</em></span> Max = 13.6ε (Mean = 2.68ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Random_Data">And 18553 other failures.</a>) 18554 </p> 18555 </td> 18556<td> 18557 <p> 18558 <span class="blue">Max = 0.507ε (Mean = 0.0313ε)</span><br> <br> 18559 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 9.71ε (Mean = 1.47ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Random_Data">And 18560 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 18561 Max = 7.37ε (Mean = 1.49ε)) 18562 </p> 18563 </td> 18564<td> 18565 <p> 18566 <span class="blue">Max = 7.88ε (Mean = 1.47ε)</span> 18567 </p> 18568 </td> 18569<td> 18570 <p> 18571 <span class="blue">Max = 8.33ε (Mean = 1.62ε)</span> 18572 </p> 18573 </td> 18574</tr> 18575</tbody> 18576</table></div> 18577</div> 18578<br class="table-break"><div class="table"> 18579<a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_k_integer_orders_"></a><p class="title"><b>Table 113. Error rates for cyl_bessel_k (integer orders)</b></p> 18580<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k (integer orders)"> 18581<colgroup> 18582<col> 18583<col> 18584<col> 18585<col> 18586<col> 18587</colgroup> 18588<thead><tr> 18589<th> 18590 </th> 18591<th> 18592 <p> 18593 GNU C++ version 7.1.0<br> linux<br> long double 18594 </p> 18595 </th> 18596<th> 18597 <p> 18598 GNU C++ version 7.1.0<br> linux<br> double 18599 </p> 18600 </th> 18601<th> 18602 <p> 18603 Sun compiler version 0x5150<br> Sun Solaris<br> long double 18604 </p> 18605 </th> 18606<th> 18607 <p> 18608 Microsoft Visual C++ version 14.1<br> Win32<br> double 18609 </p> 18610 </th> 18611</tr></thead> 18612<tbody> 18613<tr> 18614<td> 18615 <p> 18616 Bessel K0: Mathworld Data (Integer Version) 18617 </p> 18618 </td> 18619<td> 18620 <p> 18621 <span class="blue">Max = 0.833ε (Mean = 0.436ε)</span><br> <br> 18622 (<span class="emphasis"><em><cmath>:</em></span> Max = 9.33ε (Mean = 3.25ε)) 18623 </p> 18624 </td> 18625<td> 18626 <p> 18627 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 18628 2.1:</em></span> Max = 1.2ε (Mean = 0.733ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 18629 Max = 0.833ε (Mean = 0.601ε)) 18630 </p> 18631 </td> 18632<td> 18633 <p> 18634 <span class="blue">Max = 0.833ε (Mean = 0.436ε)</span> 18635 </p> 18636 </td> 18637<td> 18638 <p> 18639 <span class="blue">Max = 0.833ε (Mean = 0.552ε)</span> 18640 </p> 18641 </td> 18642</tr> 18643<tr> 18644<td> 18645 <p> 18646 Bessel K1: Mathworld Data (Integer Version) 18647 </p> 18648 </td> 18649<td> 18650 <p> 18651 <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span><br> <br> 18652 (<span class="emphasis"><em><cmath>:</em></span> Max = 8.94ε (Mean = 3.19ε)) 18653 </p> 18654 </td> 18655<td> 18656 <p> 18657 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 18658 2.1:</em></span> Max = 0.626ε (Mean = 0.333ε))<br> (<span class="emphasis"><em>Rmath 18659 3.2.3:</em></span> Max = 0.894ε (Mean = 0.516ε)) 18660 </p> 18661 </td> 18662<td> 18663 <p> 18664 <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span> 18665 </p> 18666 </td> 18667<td> 18668 <p> 18669 <span class="blue">Max = 0.786ε (Mean = 0.39ε)</span> 18670 </p> 18671 </td> 18672</tr> 18673<tr> 18674<td> 18675 <p> 18676 Bessel Kn: Mathworld Data (Integer Version) 18677 </p> 18678 </td> 18679<td> 18680 <p> 18681 <span class="blue">Max = 2.6ε (Mean = 1.21ε)</span><br> <br> 18682 (<span class="emphasis"><em><cmath>:</em></span> Max = 12.9ε (Mean = 4.91ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k_integer_orders___cmath__Bessel_Kn_Mathworld_Data_Integer_Version_">And 18683 other failures.</a>) 18684 </p> 18685 </td> 18686<td> 18687 <p> 18688 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 18689 2.1:</em></span> Max = 168ε (Mean = 59.5ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 18690 Max = 8.48ε (Mean = 2.98ε)) 18691 </p> 18692 </td> 18693<td> 18694 <p> 18695 <span class="blue">Max = 2.6ε (Mean = 1.21ε)</span> 18696 </p> 18697 </td> 18698<td> 18699 <p> 18700 <span class="blue">Max = 3.63ε (Mean = 1.46ε)</span> 18701 </p> 18702 </td> 18703</tr> 18704</tbody> 18705</table></div> 18706</div> 18707<br class="table-break"><div class="table"> 18708<a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_k_prime"></a><p class="title"><b>Table 114. Error rates for cyl_bessel_k_prime</b></p> 18709<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k_prime"> 18710<colgroup> 18711<col> 18712<col> 18713<col> 18714<col> 18715<col> 18716</colgroup> 18717<thead><tr> 18718<th> 18719 </th> 18720<th> 18721 <p> 18722 GNU C++ version 7.1.0<br> linux<br> double 18723 </p> 18724 </th> 18725<th> 18726 <p> 18727 GNU C++ version 7.1.0<br> linux<br> long double 18728 </p> 18729 </th> 18730<th> 18731 <p> 18732 Sun compiler version 0x5150<br> Sun Solaris<br> long double 18733 </p> 18734 </th> 18735<th> 18736 <p> 18737 Microsoft Visual C++ version 14.1<br> Win32<br> double 18738 </p> 18739 </th> 18740</tr></thead> 18741<tbody> 18742<tr> 18743<td> 18744 <p> 18745 Bessel K'0: Mathworld Data 18746 </p> 18747 </td> 18748<td> 18749 <p> 18750 <span class="blue">Max = 0ε (Mean = 0ε)</span> 18751 </p> 18752 </td> 18753<td> 18754 <p> 18755 <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span> 18756 </p> 18757 </td> 18758<td> 18759 <p> 18760 <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span> 18761 </p> 18762 </td> 18763<td> 18764 <p> 18765 <span class="blue">Max = 0.786ε (Mean = 0.39ε)</span> 18766 </p> 18767 </td> 18768</tr> 18769<tr> 18770<td> 18771 <p> 18772 Bessel K'1: Mathworld Data 18773 </p> 18774 </td> 18775<td> 18776 <p> 18777 <span class="blue">Max = 0ε (Mean = 0ε)</span> 18778 </p> 18779 </td> 18780<td> 18781 <p> 18782 <span class="blue">Max = 0.736ε (Mean = 0.389ε)</span> 18783 </p> 18784 </td> 18785<td> 18786 <p> 18787 <span class="blue">Max = 0.736ε (Mean = 0.389ε)</span> 18788 </p> 18789 </td> 18790<td> 18791 <p> 18792 <span class="blue">Max = 0.761ε (Mean = 0.444ε)</span> 18793 </p> 18794 </td> 18795</tr> 18796<tr> 18797<td> 18798 <p> 18799 Bessel K'n: Mathworld Data 18800 </p> 18801 </td> 18802<td> 18803 <p> 18804 <span class="blue">Max = 0ε (Mean = 0ε)</span> 18805 </p> 18806 </td> 18807<td> 18808 <p> 18809 <span class="blue">Max = 2.16ε (Mean = 1.08ε)</span> 18810 </p> 18811 </td> 18812<td> 18813 <p> 18814 <span class="blue">Max = 2.16ε (Mean = 1.08ε)</span> 18815 </p> 18816 </td> 18817<td> 18818 <p> 18819 <span class="blue">Max = 4.17ε (Mean = 1.75ε)</span> 18820 </p> 18821 </td> 18822</tr> 18823<tr> 18824<td> 18825 <p> 18826 Bessel K'v: Mathworld Data 18827 </p> 18828 </td> 18829<td> 18830 <p> 18831 <span class="blue">Max = 0ε (Mean = 0ε)</span> 18832 </p> 18833 </td> 18834<td> 18835 <p> 18836 <span class="blue">Max = 3.94ε (Mean = 2.44ε)</span> 18837 </p> 18838 </td> 18839<td> 18840 <p> 18841 <span class="blue">Max = 3.94ε (Mean = 2.34ε)</span> 18842 </p> 18843 </td> 18844<td> 18845 <p> 18846 <span class="blue">Max = 3.94ε (Mean = 1.47ε)</span> 18847 </p> 18848 </td> 18849</tr> 18850<tr> 18851<td> 18852 <p> 18853 Bessel K'v: Mathworld Data (large values) 18854 </p> 18855 </td> 18856<td> 18857 <p> 18858 <span class="blue">Max = 0ε (Mean = 0ε)</span> 18859 </p> 18860 </td> 18861<td> 18862 <p> 18863 <span class="blue">Max = 59.2ε (Mean = 42.9ε)</span> 18864 </p> 18865 </td> 18866<td> 18867 <p> 18868 <span class="blue">Max = 58.7ε (Mean = 42.6ε)</span> 18869 </p> 18870 </td> 18871<td> 18872 <p> 18873 <span class="blue">Max = 18.6ε (Mean = 11.8ε)</span> 18874 </p> 18875 </td> 18876</tr> 18877<tr> 18878<td> 18879 <p> 18880 Bessel K'n: Random Data 18881 </p> 18882 </td> 18883<td> 18884 <p> 18885 <span class="blue">Max = 0ε (Mean = 0ε)</span> 18886 </p> 18887 </td> 18888<td> 18889 <p> 18890 <span class="blue">Max = 4.45ε (Mean = 1.19ε)</span> 18891 </p> 18892 </td> 18893<td> 18894 <p> 18895 <span class="blue">Max = 4.45ε (Mean = 1.19ε)</span> 18896 </p> 18897 </td> 18898<td> 18899 <p> 18900 <span class="blue">Max = 9.67ε (Mean = 1.73ε)</span> 18901 </p> 18902 </td> 18903</tr> 18904<tr> 18905<td> 18906 <p> 18907 Bessel K'v: Random Data 18908 </p> 18909 </td> 18910<td> 18911 <p> 18912 <span class="blue">Max = 0ε (Mean = 0ε)</span> 18913 </p> 18914 </td> 18915<td> 18916 <p> 18917 <span class="blue">Max = 7.95ε (Mean = 1.53ε)</span> 18918 </p> 18919 </td> 18920<td> 18921 <p> 18922 <span class="blue">Max = 7.95ε (Mean = 1.52ε)</span> 18923 </p> 18924 </td> 18925<td> 18926 <p> 18927 <span class="blue">Max = 8.32ε (Mean = 1.65ε)</span> 18928 </p> 18929 </td> 18930</tr> 18931</tbody> 18932</table></div> 18933</div> 18934<br class="table-break"><div class="table"> 18935<a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_k_prime_integer_orders_"></a><p class="title"><b>Table 115. Error rates for cyl_bessel_k_prime (integer orders)</b></p> 18936<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k_prime (integer orders)"> 18937<colgroup> 18938<col> 18939<col> 18940<col> 18941<col> 18942<col> 18943</colgroup> 18944<thead><tr> 18945<th> 18946 </th> 18947<th> 18948 <p> 18949 GNU C++ version 7.1.0<br> linux<br> double 18950 </p> 18951 </th> 18952<th> 18953 <p> 18954 GNU C++ version 7.1.0<br> linux<br> long double 18955 </p> 18956 </th> 18957<th> 18958 <p> 18959 Sun compiler version 0x5150<br> Sun Solaris<br> long double 18960 </p> 18961 </th> 18962<th> 18963 <p> 18964 Microsoft Visual C++ version 14.1<br> Win32<br> double 18965 </p> 18966 </th> 18967</tr></thead> 18968<tbody> 18969<tr> 18970<td> 18971 <p> 18972 Bessel K'0: Mathworld Data (Integer Version) 18973 </p> 18974 </td> 18975<td> 18976 <p> 18977 <span class="blue">Max = 0ε (Mean = 0ε)</span> 18978 </p> 18979 </td> 18980<td> 18981 <p> 18982 <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span> 18983 </p> 18984 </td> 18985<td> 18986 <p> 18987 <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span> 18988 </p> 18989 </td> 18990<td> 18991 <p> 18992 <span class="blue">Max = 0.786ε (Mean = 0.39ε)</span> 18993 </p> 18994 </td> 18995</tr> 18996<tr> 18997<td> 18998 <p> 18999 Bessel K'1: Mathworld Data (Integer Version) 19000 </p> 19001 </td> 19002<td> 19003 <p> 19004 <span class="blue">Max = 0ε (Mean = 0ε)</span> 19005 </p> 19006 </td> 19007<td> 19008 <p> 19009 <span class="blue">Max = 0.736ε (Mean = 0.389ε)</span> 19010 </p> 19011 </td> 19012<td> 19013 <p> 19014 <span class="blue">Max = 0.736ε (Mean = 0.389ε)</span> 19015 </p> 19016 </td> 19017<td> 19018 <p> 19019 <span class="blue">Max = 0.761ε (Mean = 0.444ε)</span> 19020 </p> 19021 </td> 19022</tr> 19023<tr> 19024<td> 19025 <p> 19026 Bessel K'n: Mathworld Data (Integer Version) 19027 </p> 19028 </td> 19029<td> 19030 <p> 19031 <span class="blue">Max = 0ε (Mean = 0ε)</span> 19032 </p> 19033 </td> 19034<td> 19035 <p> 19036 <span class="blue">Max = 2.16ε (Mean = 1.08ε)</span> 19037 </p> 19038 </td> 19039<td> 19040 <p> 19041 <span class="blue">Max = 2.16ε (Mean = 1.08ε)</span> 19042 </p> 19043 </td> 19044<td> 19045 <p> 19046 <span class="blue">Max = 4.17ε (Mean = 1.75ε)</span> 19047 </p> 19048 </td> 19049</tr> 19050</tbody> 19051</table></div> 19052</div> 19053<br class="table-break"><div class="table"> 19054<a name="special_function_error_rates_rep.all_the_tables.table_cyl_neumann"></a><p class="title"><b>Table 116. Error rates for cyl_neumann</b></p> 19055<div class="table-contents"><table class="table" summary="Error rates for cyl_neumann"> 19056<colgroup> 19057<col> 19058<col> 19059<col> 19060<col> 19061<col> 19062</colgroup> 19063<thead><tr> 19064<th> 19065 </th> 19066<th> 19067 <p> 19068 GNU C++ version 7.1.0<br> linux<br> long double 19069 </p> 19070 </th> 19071<th> 19072 <p> 19073 GNU C++ version 7.1.0<br> linux<br> double 19074 </p> 19075 </th> 19076<th> 19077 <p> 19078 Sun compiler version 0x5150<br> Sun Solaris<br> long double 19079 </p> 19080 </th> 19081<th> 19082 <p> 19083 Microsoft Visual C++ version 14.1<br> Win32<br> double 19084 </p> 19085 </th> 19086</tr></thead> 19087<tbody> 19088<tr> 19089<td> 19090 <p> 19091 Y0: Mathworld Data 19092 </p> 19093 </td> 19094<td> 19095 <p> 19096 <span class="blue">Max = 5.53ε (Mean = 2.4ε)</span><br> <br> 19097 (<span class="emphasis"><em><cmath>:</em></span> Max = 2.05e+05ε (Mean = 6.87e+04ε)) 19098 </p> 19099 </td> 19100<td> 19101 <p> 19102 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 19103 2.1:</em></span> Max = 60.9ε (Mean = 20.4ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 19104 Max = 167ε (Mean = 56.5ε)) 19105 </p> 19106 </td> 19107<td> 19108 <p> 19109 <span class="blue">Max = 5.53ε (Mean = 2.4ε)</span> 19110 </p> 19111 </td> 19112<td> 19113 <p> 19114 <span class="blue">Max = 4.61ε (Mean = 2.29ε)</span> 19115 </p> 19116 </td> 19117</tr> 19118<tr> 19119<td> 19120 <p> 19121 Y1: Mathworld Data 19122 </p> 19123 </td> 19124<td> 19125 <p> 19126 <span class="blue">Max = 6.33ε (Mean = 2.25ε)</span><br> <br> 19127 (<span class="emphasis"><em><cmath>:</em></span> Max = 9.71e+03ε (Mean = 4.08e+03ε)) 19128 </p> 19129 </td> 19130<td> 19131 <p> 19132 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 19133 2.1:</em></span> Max = 23.4ε (Mean = 8.1ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 19134 Max = 193ε (Mean = 64.4ε)) 19135 </p> 19136 </td> 19137<td> 19138 <p> 19139 <span class="blue">Max = 6.33ε (Mean = 2.29ε)</span> 19140 </p> 19141 </td> 19142<td> 19143 <p> 19144 <span class="blue">Max = 4.75ε (Mean = 1.72ε)</span> 19145 </p> 19146 </td> 19147</tr> 19148<tr> 19149<td> 19150 <p> 19151 Yn: Mathworld Data 19152 </p> 19153 </td> 19154<td> 19155 <p> 19156 <span class="blue">Max = 55.2ε (Mean = 17.8ε)</span><br> <br> 19157 (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 2.2e+20ε (Mean 19158 = 6.97e+19ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yn_Mathworld_Data">And 19159 other failures.</a>)</span> 19160 </p> 19161 </td> 19162<td> 19163 <p> 19164 <span class="blue">Max = 0.993ε (Mean = 0.314ε)</span><br> <br> 19165 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.41e+05ε (Mean = 7.62e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yn_Mathworld_Data">And 19166 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 19167 Max = 1.24e+04ε (Mean = 4e+03ε)) 19168 </p> 19169 </td> 19170<td> 19171 <p> 19172 <span class="blue">Max = 55.2ε (Mean = 17.8ε)</span> 19173 </p> 19174 </td> 19175<td> 19176 <p> 19177 <span class="blue">Max = 35ε (Mean = 11.9ε)</span> 19178 </p> 19179 </td> 19180</tr> 19181<tr> 19182<td> 19183 <p> 19184 Yv: Mathworld Data 19185 </p> 19186 </td> 19187<td> 19188 <p> 19189 <span class="blue">Max = 10.7ε (Mean = 4.93ε)</span><br> <br> 19190 (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 3.49e+15ε (Mean 19191 = 1.05e+15ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Mathworld_Data">And 19192 other failures.</a>)</span> 19193 </p> 19194 </td> 19195<td> 19196 <p> 19197 <span class="blue">Max = 10ε (Mean = 3.02ε)</span><br> <br> (<span class="emphasis"><em>GSL 19198 2.1:</em></span> Max = 1.07e+05ε (Mean = 3.22e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yv_Mathworld_Data">And 19199 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 19200 Max = 243ε (Mean = 73.9ε)) 19201 </p> 19202 </td> 19203<td> 19204 <p> 19205 <span class="blue">Max = 10.7ε (Mean = 5.1ε)</span> 19206 </p> 19207 </td> 19208<td> 19209 <p> 19210 <span class="blue">Max = 7.89ε (Mean = 3.27ε)</span> 19211 </p> 19212 </td> 19213</tr> 19214<tr> 19215<td> 19216 <p> 19217 Yv: Mathworld Data (large values) 19218 </p> 19219 </td> 19220<td> 19221 <p> 19222 <span class="blue">Max = 1.7ε (Mean = 1.33ε)</span><br> <br> 19223 (<span class="emphasis"><em><cmath>:</em></span> Max = 43.2ε (Mean = 16.3ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Mathworld_Data_large_values_">And 19224 other failures.</a>) 19225 </p> 19226 </td> 19227<td> 19228 <p> 19229 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 19230 2.1:</em></span> Max = 60.8ε (Mean = 23ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yv_Mathworld_Data_large_values_">And 19231 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 19232 Max = 0.682ε (Mean = 0.335ε)) 19233 </p> 19234 </td> 19235<td> 19236 <p> 19237 <span class="blue">Max = 1.7ε (Mean = 1.33ε)</span> 19238 </p> 19239 </td> 19240<td> 19241 <p> 19242 <span class="blue">Max = 0.682ε (Mean = 0.423ε)</span> 19243 </p> 19244 </td> 19245</tr> 19246<tr> 19247<td> 19248 <p> 19249 Y0 and Y1: Random Data 19250 </p> 19251 </td> 19252<td> 19253 <p> 19254 <span class="blue">Max = 10.8ε (Mean = 3.04ε)</span><br> <br> 19255 (<span class="emphasis"><em><cmath>:</em></span> Max = 2.59e+03ε (Mean = 500ε)) 19256 </p> 19257 </td> 19258<td> 19259 <p> 19260 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 19261 2.1:</em></span> Max = 34.4ε (Mean = 8.9ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 19262 Max = 83ε (Mean = 14.2ε)) 19263 </p> 19264 </td> 19265<td> 19266 <p> 19267 <span class="blue">Max = 10.8ε (Mean = 3.04ε)</span> 19268 </p> 19269 </td> 19270<td> 19271 <p> 19272 <span class="blue">Max = 4.17ε (Mean = 1.24ε)</span> 19273 </p> 19274 </td> 19275</tr> 19276<tr> 19277<td> 19278 <p> 19279 Yn: Random Data 19280 </p> 19281 </td> 19282<td> 19283 <p> 19284 <span class="blue">Max = 338ε (Mean = 27.5ε)</span><br> <br> 19285 (<span class="emphasis"><em><cmath>:</em></span> Max = 4.01e+03ε (Mean = 348ε)) 19286 </p> 19287 </td> 19288<td> 19289 <p> 19290 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 19291 2.1:</em></span> Max = 500ε (Mean = 47.8ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 19292 Max = 691ε (Mean = 67.9ε)) 19293 </p> 19294 </td> 19295<td> 19296 <p> 19297 <span class="blue">Max = 338ε (Mean = 27.5ε)</span> 19298 </p> 19299 </td> 19300<td> 19301 <p> 19302 <span class="blue">Max = 117ε (Mean = 10.2ε)</span> 19303 </p> 19304 </td> 19305</tr> 19306<tr> 19307<td> 19308 <p> 19309 Yv: Random Data 19310 </p> 19311 </td> 19312<td> 19313 <p> 19314 <span class="blue">Max = 2.08e+03ε (Mean = 149ε)</span><br> <br> 19315 (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = +INFε (Mean 19316 = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Random_Data">And 19317 other failures.</a>)</span> 19318 </p> 19319 </td> 19320<td> 19321 <p> 19322 <span class="blue">Max = 1.53ε (Mean = 0.102ε)</span><br> <br> 19323 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.41e+06ε (Mean = 7.67e+04ε))<br> 19324 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.79e+05ε (Mean = 9.64e+03ε)) 19325 </p> 19326 </td> 19327<td> 19328 <p> 19329 <span class="blue">Max = 2.08e+03ε (Mean = 149ε)</span> 19330 </p> 19331 </td> 19332<td> 19333 <p> 19334 <span class="blue">Max = 1.23e+03ε (Mean = 69.9ε)</span> 19335 </p> 19336 </td> 19337</tr> 19338</tbody> 19339</table></div> 19340</div> 19341<br class="table-break"><div class="table"> 19342<a name="special_function_error_rates_rep.all_the_tables.table_cyl_neumann_integer_orders_"></a><p class="title"><b>Table 117. Error rates for cyl_neumann (integer orders)</b></p> 19343<div class="table-contents"><table class="table" summary="Error rates for cyl_neumann (integer orders)"> 19344<colgroup> 19345<col> 19346<col> 19347<col> 19348<col> 19349<col> 19350</colgroup> 19351<thead><tr> 19352<th> 19353 </th> 19354<th> 19355 <p> 19356 GNU C++ version 7.1.0<br> linux<br> long double 19357 </p> 19358 </th> 19359<th> 19360 <p> 19361 GNU C++ version 7.1.0<br> linux<br> double 19362 </p> 19363 </th> 19364<th> 19365 <p> 19366 Sun compiler version 0x5150<br> Sun Solaris<br> long double 19367 </p> 19368 </th> 19369<th> 19370 <p> 19371 Microsoft Visual C++ version 14.1<br> Win32<br> double 19372 </p> 19373 </th> 19374</tr></thead> 19375<tbody> 19376<tr> 19377<td> 19378 <p> 19379 Y0: Mathworld Data (Integer Version) 19380 </p> 19381 </td> 19382<td> 19383 <p> 19384 <span class="blue">Max = 5.53ε (Mean = 2.4ε)</span><br> <br> 19385 (<span class="emphasis"><em><cmath>:</em></span> Max = 2.05e+05ε (Mean = 6.87e+04ε)) 19386 </p> 19387 </td> 19388<td> 19389 <p> 19390 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 19391 2.1:</em></span> Max = 6.46ε (Mean = 2.38ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 19392 Max = 167ε (Mean = 56.5ε)) 19393 </p> 19394 </td> 19395<td> 19396 <p> 19397 <span class="blue">Max = 5.53ε (Mean = 2.4ε)</span> 19398 </p> 19399 </td> 19400<td> 19401 <p> 19402 <span class="blue">Max = 4.61ε (Mean = 2.29ε)</span><br> <br> 19403 (<span class="emphasis"><em><math.h>:</em></span> Max = 5.37e+03ε (Mean = 1.81e+03ε)) 19404 </p> 19405 </td> 19406</tr> 19407<tr> 19408<td> 19409 <p> 19410 Y1: Mathworld Data (Integer Version) 19411 </p> 19412 </td> 19413<td> 19414 <p> 19415 <span class="blue">Max = 6.33ε (Mean = 2.25ε)</span><br> <br> 19416 (<span class="emphasis"><em><cmath>:</em></span> Max = 9.71e+03ε (Mean = 4.08e+03ε)) 19417 </p> 19418 </td> 19419<td> 19420 <p> 19421 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 19422 2.1:</em></span> Max = 1.51ε (Mean = 0.839ε))<br> (<span class="emphasis"><em>Rmath 19423 3.2.3:</em></span> Max = 193ε (Mean = 64.4ε)) 19424 </p> 19425 </td> 19426<td> 19427 <p> 19428 <span class="blue">Max = 6.33ε (Mean = 2.29ε)</span> 19429 </p> 19430 </td> 19431<td> 19432 <p> 19433 <span class="blue">Max = 4.75ε (Mean = 1.72ε)</span><br> <br> 19434 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.86e+04ε (Mean = 6.2e+03ε)) 19435 </p> 19436 </td> 19437</tr> 19438<tr> 19439<td> 19440 <p> 19441 Yn: Mathworld Data (Integer Version) 19442 </p> 19443 </td> 19444<td> 19445 <p> 19446 <span class="blue">Max = 55.2ε (Mean = 17.8ε)</span><br> <br> 19447 (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 2.2e+20ε (Mean 19448 = 6.97e+19ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann_integer_orders___cmath__Yn_Mathworld_Data_Integer_Version_">And 19449 other failures.</a>)</span> 19450 </p> 19451 </td> 19452<td> 19453 <p> 19454 <span class="blue">Max = 0.993ε (Mean = 0.314ε)</span><br> <br> 19455 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.41e+05ε (Mean = 7.62e+04ε))<br> 19456 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.24e+04ε (Mean = 4e+03ε)) 19457 </p> 19458 </td> 19459<td> 19460 <p> 19461 <span class="blue">Max = 55.2ε (Mean = 17.8ε)</span> 19462 </p> 19463 </td> 19464<td> 19465 <p> 19466 <span class="blue">Max = 35ε (Mean = 11.9ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span> 19467 Max = 2.49e+05ε (Mean = 8.14e+04ε)) 19468 </p> 19469 </td> 19470</tr> 19471</tbody> 19472</table></div> 19473</div> 19474<br class="table-break"><div class="table"> 19475<a name="special_function_error_rates_rep.all_the_tables.table_cyl_neumann_prime"></a><p class="title"><b>Table 118. Error rates for cyl_neumann_prime</b></p> 19476<div class="table-contents"><table class="table" summary="Error rates for cyl_neumann_prime"> 19477<colgroup> 19478<col> 19479<col> 19480<col> 19481<col> 19482<col> 19483</colgroup> 19484<thead><tr> 19485<th> 19486 </th> 19487<th> 19488 <p> 19489 GNU C++ version 7.1.0<br> linux<br> double 19490 </p> 19491 </th> 19492<th> 19493 <p> 19494 GNU C++ version 7.1.0<br> linux<br> long double 19495 </p> 19496 </th> 19497<th> 19498 <p> 19499 Sun compiler version 0x5150<br> Sun Solaris<br> long double 19500 </p> 19501 </th> 19502<th> 19503 <p> 19504 Microsoft Visual C++ version 14.1<br> Win32<br> double 19505 </p> 19506 </th> 19507</tr></thead> 19508<tbody> 19509<tr> 19510<td> 19511 <p> 19512 Y'0: Mathworld Data 19513 </p> 19514 </td> 19515<td> 19516 <p> 19517 <span class="blue">Max = 0ε (Mean = 0ε)</span> 19518 </p> 19519 </td> 19520<td> 19521 <p> 19522 <span class="blue">Max = 6.33ε (Mean = 3.12ε)</span> 19523 </p> 19524 </td> 19525<td> 19526 <p> 19527 <span class="blue">Max = 6.33ε (Mean = 3.14ε)</span> 19528 </p> 19529 </td> 19530<td> 19531 <p> 19532 <span class="blue">Max = 4.75ε (Mean = 1.75ε)</span> 19533 </p> 19534 </td> 19535</tr> 19536<tr> 19537<td> 19538 <p> 19539 Y'1: Mathworld Data 19540 </p> 19541 </td> 19542<td> 19543 <p> 19544 <span class="blue">Max = 0.58ε (Mean = 0.193ε)</span> 19545 </p> 19546 </td> 19547<td> 19548 <p> 19549 <span class="blue">Max = 37.1ε (Mean = 12.8ε)</span> 19550 </p> 19551 </td> 19552<td> 19553 <p> 19554 <span class="blue">Max = 34ε (Mean = 11.8ε)</span> 19555 </p> 19556 </td> 19557<td> 19558 <p> 19559 <span class="blue">Max = 3.08ε (Mean = 1.2ε)</span> 19560 </p> 19561 </td> 19562</tr> 19563<tr> 19564<td> 19565 <p> 19566 Y'n: Mathworld Data 19567 </p> 19568 </td> 19569<td> 19570 <p> 19571 <span class="blue">Max = 2.05ε (Mean = 0.677ε)</span> 19572 </p> 19573 </td> 19574<td> 19575 <p> 19576 <span class="blue">Max = 56ε (Mean = 18.2ε)</span> 19577 </p> 19578 </td> 19579<td> 19580 <p> 19581 <span class="blue">Max = 56ε (Mean = 21.3ε)</span> 19582 </p> 19583 </td> 19584<td> 19585 <p> 19586 <span class="blue">Max = 563ε (Mean = 178ε)</span> 19587 </p> 19588 </td> 19589</tr> 19590<tr> 19591<td> 19592 <p> 19593 Y'v: Mathworld Data 19594 </p> 19595 </td> 19596<td> 19597 <p> 19598 <span class="blue">Max = 21.5ε (Mean = 6.49ε)</span> 19599 </p> 19600 </td> 19601<td> 19602 <p> 19603 <span class="blue">Max = 42.5ε (Mean = 13.4ε)</span> 19604 </p> 19605 </td> 19606<td> 19607 <p> 19608 <span class="blue">Max = 42.5ε (Mean = 13.6ε)</span> 19609 </p> 19610 </td> 19611<td> 19612 <p> 19613 <span class="blue">Max = 23.7ε (Mean = 10.1ε)</span> 19614 </p> 19615 </td> 19616</tr> 19617<tr> 19618<td> 19619 <p> 19620 Y'v: Mathworld Data (large values) 19621 </p> 19622 </td> 19623<td> 19624 <p> 19625 <span class="blue">Max = 0ε (Mean = 0ε)</span> 19626 </p> 19627 </td> 19628<td> 19629 <p> 19630 <span class="blue">Max = 1.57ε (Mean = 1.24ε)</span> 19631 </p> 19632 </td> 19633<td> 19634 <p> 19635 <span class="blue">Max = 1.57ε (Mean = 1.24ε)</span> 19636 </p> 19637 </td> 19638<td> 19639 <p> 19640 <span class="blue">Max = 0.627ε (Mean = 0.237ε)</span> 19641 </p> 19642 </td> 19643</tr> 19644<tr> 19645<td> 19646 <p> 19647 Y'0 and Y'1: Random Data 19648 </p> 19649 </td> 19650<td> 19651 <p> 19652 <span class="blue">Max = 0ε (Mean = 0ε)</span> 19653 </p> 19654 </td> 19655<td> 19656 <p> 19657 <span class="blue">Max = 23.8ε (Mean = 3.69ε)</span> 19658 </p> 19659 </td> 19660<td> 19661 <p> 19662 <span class="blue">Max = 23.8ε (Mean = 3.69ε)</span> 19663 </p> 19664 </td> 19665<td> 19666 <p> 19667 <span class="blue">Max = 5.95ε (Mean = 1.36ε)</span> 19668 </p> 19669 </td> 19670</tr> 19671<tr> 19672<td> 19673 <p> 19674 Y'n: Random Data 19675 </p> 19676 </td> 19677<td> 19678 <p> 19679 <span class="blue">Max = 1.53ε (Mean = 0.0885ε)</span> 19680 </p> 19681 </td> 19682<td> 19683 <p> 19684 <span class="blue">Max = 2.35e+03ε (Mean = 136ε)</span> 19685 </p> 19686 </td> 19687<td> 19688 <p> 19689 <span class="blue">Max = 2.35e+03ε (Mean = 136ε)</span> 19690 </p> 19691 </td> 19692<td> 19693 <p> 19694 <span class="blue">Max = 621ε (Mean = 36ε)</span> 19695 </p> 19696 </td> 19697</tr> 19698<tr> 19699<td> 19700 <p> 19701 Y'v: Random Data 19702 </p> 19703 </td> 19704<td> 19705 <p> 19706 <span class="blue">Max = 56.8ε (Mean = 2.59ε)</span> 19707 </p> 19708 </td> 19709<td> 19710 <p> 19711 <span class="blue">Max = 1.16e+05ε (Mean = 5.28e+03ε)</span> 19712 </p> 19713 </td> 19714<td> 19715 <p> 19716 <span class="blue">Max = 1.16e+05ε (Mean = 5.28e+03ε)</span> 19717 </p> 19718 </td> 19719<td> 19720 <p> 19721 <span class="blue">Max = 3.23e+04ε (Mean = 1.13e+03ε)</span> 19722 </p> 19723 </td> 19724</tr> 19725</tbody> 19726</table></div> 19727</div> 19728<br class="table-break"><div class="table"> 19729<a name="special_function_error_rates_rep.all_the_tables.table_cyl_neumann_prime_integer_orders_"></a><p class="title"><b>Table 119. Error rates for cyl_neumann_prime (integer orders)</b></p> 19730<div class="table-contents"><table class="table" summary="Error rates for cyl_neumann_prime (integer orders)"> 19731<colgroup> 19732<col> 19733<col> 19734<col> 19735<col> 19736<col> 19737</colgroup> 19738<thead><tr> 19739<th> 19740 </th> 19741<th> 19742 <p> 19743 GNU C++ version 7.1.0<br> linux<br> double 19744 </p> 19745 </th> 19746<th> 19747 <p> 19748 GNU C++ version 7.1.0<br> linux<br> long double 19749 </p> 19750 </th> 19751<th> 19752 <p> 19753 Sun compiler version 0x5150<br> Sun Solaris<br> long double 19754 </p> 19755 </th> 19756<th> 19757 <p> 19758 Microsoft Visual C++ version 14.1<br> Win32<br> double 19759 </p> 19760 </th> 19761</tr></thead> 19762<tbody> 19763<tr> 19764<td> 19765 <p> 19766 Y'0: Mathworld Data (Integer Version) 19767 </p> 19768 </td> 19769<td> 19770 <p> 19771 <span class="blue">Max = 0ε (Mean = 0ε)</span> 19772 </p> 19773 </td> 19774<td> 19775 <p> 19776 <span class="blue">Max = 6.33ε (Mean = 3.12ε)</span> 19777 </p> 19778 </td> 19779<td> 19780 <p> 19781 <span class="blue">Max = 6.33ε (Mean = 3.14ε)</span> 19782 </p> 19783 </td> 19784<td> 19785 <p> 19786 <span class="blue">Max = 4.75ε (Mean = 1.75ε)</span> 19787 </p> 19788 </td> 19789</tr> 19790<tr> 19791<td> 19792 <p> 19793 Y'1: Mathworld Data (Integer Version) 19794 </p> 19795 </td> 19796<td> 19797 <p> 19798 <span class="blue">Max = 0.58ε (Mean = 0.193ε)</span> 19799 </p> 19800 </td> 19801<td> 19802 <p> 19803 <span class="blue">Max = 37.1ε (Mean = 12.8ε)</span> 19804 </p> 19805 </td> 19806<td> 19807 <p> 19808 <span class="blue">Max = 34ε (Mean = 11.8ε)</span> 19809 </p> 19810 </td> 19811<td> 19812 <p> 19813 <span class="blue">Max = 3.08ε (Mean = 1.2ε)</span> 19814 </p> 19815 </td> 19816</tr> 19817<tr> 19818<td> 19819 <p> 19820 Y'n: Mathworld Data (Integer Version) 19821 </p> 19822 </td> 19823<td> 19824 <p> 19825 <span class="blue">Max = 2.05ε (Mean = 0.677ε)</span> 19826 </p> 19827 </td> 19828<td> 19829 <p> 19830 <span class="blue">Max = 56ε (Mean = 18.2ε)</span> 19831 </p> 19832 </td> 19833<td> 19834 <p> 19835 <span class="blue">Max = 56ε (Mean = 21.3ε)</span> 19836 </p> 19837 </td> 19838<td> 19839 <p> 19840 <span class="blue">Max = 563ε (Mean = 178ε)</span> 19841 </p> 19842 </td> 19843</tr> 19844</tbody> 19845</table></div> 19846</div> 19847<br class="table-break"><div class="table"> 19848<a name="special_function_error_rates_rep.all_the_tables.table_digamma"></a><p class="title"><b>Table 120. Error rates for digamma</b></p> 19849<div class="table-contents"><table class="table" summary="Error rates for digamma"> 19850<colgroup> 19851<col> 19852<col> 19853<col> 19854<col> 19855<col> 19856</colgroup> 19857<thead><tr> 19858<th> 19859 </th> 19860<th> 19861 <p> 19862 GNU C++ version 7.1.0<br> linux<br> double 19863 </p> 19864 </th> 19865<th> 19866 <p> 19867 GNU C++ version 7.1.0<br> linux<br> long double 19868 </p> 19869 </th> 19870<th> 19871 <p> 19872 Sun compiler version 0x5150<br> Sun Solaris<br> long double 19873 </p> 19874 </th> 19875<th> 19876 <p> 19877 Microsoft Visual C++ version 14.1<br> Win32<br> double 19878 </p> 19879 </th> 19880</tr></thead> 19881<tbody> 19882<tr> 19883<td> 19884 <p> 19885 Digamma Function: Large Values 19886 </p> 19887 </td> 19888<td> 19889 <p> 19890 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 19891 2.1:</em></span> Max = 1.84ε (Mean = 0.71ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 19892 Max = 1.18ε (Mean = 0.331ε)) 19893 </p> 19894 </td> 19895<td> 19896 <p> 19897 <span class="blue">Max = 1.39ε (Mean = 0.413ε)</span> 19898 </p> 19899 </td> 19900<td> 19901 <p> 19902 <span class="blue">Max = 1.39ε (Mean = 0.413ε)</span> 19903 </p> 19904 </td> 19905<td> 19906 <p> 19907 <span class="blue">Max = 0.98ε (Mean = 0.369ε)</span> 19908 </p> 19909 </td> 19910</tr> 19911<tr> 19912<td> 19913 <p> 19914 Digamma Function: Near the Positive Root 19915 </p> 19916 </td> 19917<td> 19918 <p> 19919 <span class="blue">Max = 0.891ε (Mean = 0.0995ε)</span><br> <br> 19920 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 135ε (Mean = 11.9ε))<br> (<span class="emphasis"><em>Rmath 19921 3.2.3:</em></span> Max = 2.02e+03ε (Mean = 256ε)) 19922 </p> 19923 </td> 19924<td> 19925 <p> 19926 <span class="blue">Max = 1.37ε (Mean = 0.477ε)</span> 19927 </p> 19928 </td> 19929<td> 19930 <p> 19931 <span class="blue">Max = 1.31ε (Mean = 0.471ε)</span> 19932 </p> 19933 </td> 19934<td> 19935 <p> 19936 <span class="blue">Max = 0.997ε (Mean = 0.527ε)</span> 19937 </p> 19938 </td> 19939</tr> 19940<tr> 19941<td> 19942 <p> 19943 Digamma Function: Near Zero 19944 </p> 19945 </td> 19946<td> 19947 <p> 19948 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 19949 2.1:</em></span> Max = 0.953ε (Mean = 0.348ε))<br> (<span class="emphasis"><em>Rmath 19950 3.2.3:</em></span> Max = 1.17ε (Mean = 0.564ε)) 19951 </p> 19952 </td> 19953<td> 19954 <p> 19955 <span class="blue">Max = 0.984ε (Mean = 0.361ε)</span> 19956 </p> 19957 </td> 19958<td> 19959 <p> 19960 <span class="blue">Max = 0.984ε (Mean = 0.361ε)</span> 19961 </p> 19962 </td> 19963<td> 19964 <p> 19965 <span class="blue">Max = 0.953ε (Mean = 0.337ε)</span> 19966 </p> 19967 </td> 19968</tr> 19969<tr> 19970<td> 19971 <p> 19972 Digamma Function: Negative Values 19973 </p> 19974 </td> 19975<td> 19976 <p> 19977 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 19978 2.1:</em></span> Max = 4.56e+04ε (Mean = 3.91e+03ε))<br> (<span class="emphasis"><em>Rmath 19979 3.2.3:</em></span> Max = 4.6e+04ε (Mean = 3.94e+03ε)) 19980 </p> 19981 </td> 19982<td> 19983 <p> 19984 <span class="blue">Max = 180ε (Mean = 13ε)</span> 19985 </p> 19986 </td> 19987<td> 19988 <p> 19989 <span class="blue">Max = 180ε (Mean = 13ε)</span> 19990 </p> 19991 </td> 19992<td> 19993 <p> 19994 <span class="blue">Max = 214ε (Mean = 16.1ε)</span> 19995 </p> 19996 </td> 19997</tr> 19998<tr> 19999<td> 20000 <p> 20001 Digamma Function: Values near 0 20002 </p> 20003 </td> 20004<td> 20005 <p> 20006 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 20007 2.1:</em></span> Max = 0.866ε (Mean = 0.387ε))<br> (<span class="emphasis"><em>Rmath 20008 3.2.3:</em></span> Max = 3.58e+05ε (Mean = 1.6e+05ε)) 20009 </p> 20010 </td> 20011<td> 20012 <p> 20013 <span class="blue">Max = 1ε (Mean = 0.592ε)</span> 20014 </p> 20015 </td> 20016<td> 20017 <p> 20018 <span class="blue">Max = 1ε (Mean = 0.592ε)</span> 20019 </p> 20020 </td> 20021<td> 20022 <p> 20023 <span class="blue">Max = 0ε (Mean = 0ε)</span> 20024 </p> 20025 </td> 20026</tr> 20027<tr> 20028<td> 20029 <p> 20030 Digamma Function: Integer arguments 20031 </p> 20032 </td> 20033<td> 20034 <p> 20035 <span class="blue">Max = 0.992ε (Mean = 0.215ε)</span><br> <br> 20036 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.18ε (Mean = 0.607ε))<br> (<span class="emphasis"><em>Rmath 20037 3.2.3:</em></span> Max = 4.33ε (Mean = 0.982ε)) 20038 </p> 20039 </td> 20040<td> 20041 <p> 20042 <span class="blue">Max = 0.888ε (Mean = 0.403ε)</span> 20043 </p> 20044 </td> 20045<td> 20046 <p> 20047 <span class="blue">Max = 0.888ε (Mean = 0.403ε)</span> 20048 </p> 20049 </td> 20050<td> 20051 <p> 20052 <span class="blue">Max = 0.992ε (Mean = 0.452ε)</span> 20053 </p> 20054 </td> 20055</tr> 20056<tr> 20057<td> 20058 <p> 20059 Digamma Function: Half integer arguments 20060 </p> 20061 </td> 20062<td> 20063 <p> 20064 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 20065 2.1:</em></span> Max = 1.09ε (Mean = 0.531ε))<br> (<span class="emphasis"><em>Rmath 20066 3.2.3:</em></span> Max = 46.2ε (Mean = 7.24ε)) 20067 </p> 20068 </td> 20069<td> 20070 <p> 20071 <span class="blue">Max = 0.906ε (Mean = 0.409ε)</span> 20072 </p> 20073 </td> 20074<td> 20075 <p> 20076 <span class="blue">Max = 0.906ε (Mean = 0.409ε)</span> 20077 </p> 20078 </td> 20079<td> 20080 <p> 20081 <span class="blue">Max = 0.78ε (Mean = 0.314ε)</span> 20082 </p> 20083 </td> 20084</tr> 20085</tbody> 20086</table></div> 20087</div> 20088<br class="table-break"><div class="table"> 20089<a name="special_function_error_rates_rep.all_the_tables.table_ellint_1"></a><p class="title"><b>Table 121. Error rates for ellint_1</b></p> 20090<div class="table-contents"><table class="table" summary="Error rates for ellint_1"> 20091<colgroup> 20092<col> 20093<col> 20094<col> 20095<col> 20096<col> 20097</colgroup> 20098<thead><tr> 20099<th> 20100 </th> 20101<th> 20102 <p> 20103 GNU C++ version 7.1.0<br> linux<br> long double 20104 </p> 20105 </th> 20106<th> 20107 <p> 20108 GNU C++ version 7.1.0<br> linux<br> double 20109 </p> 20110 </th> 20111<th> 20112 <p> 20113 Sun compiler version 0x5150<br> Sun Solaris<br> long double 20114 </p> 20115 </th> 20116<th> 20117 <p> 20118 Microsoft Visual C++ version 14.1<br> Win32<br> double 20119 </p> 20120 </th> 20121</tr></thead> 20122<tbody> 20123<tr> 20124<td> 20125 <p> 20126 Elliptic Integral F: Mathworld Data 20127 </p> 20128 </td> 20129<td> 20130 <p> 20131 <span class="blue">Max = 0.94ε (Mean = 0.509ε)</span><br> <br> 20132 (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = +INFε (Mean 20133 = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_1__cmath__Elliptic_Integral_F_Mathworld_Data">And 20134 other failures.</a>)</span> 20135 </p> 20136 </td> 20137<td> 20138 <p> 20139 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 20140 2.1:</em></span> Max = 0.919ε (Mean = 0.544ε)) 20141 </p> 20142 </td> 20143<td> 20144 <p> 20145 <span class="blue">Max = 0.94ε (Mean = 0.509ε)</span> 20146 </p> 20147 </td> 20148<td> 20149 <p> 20150 <span class="blue">Max = 0.919ε (Mean = 0.542ε)</span> 20151 </p> 20152 </td> 20153</tr> 20154<tr> 20155<td> 20156 <p> 20157 Elliptic Integral F: Random Data 20158 </p> 20159 </td> 20160<td> 20161 <p> 20162 <span class="blue">Max = 1.57ε (Mean = 0.56ε)</span><br> <br> 20163 (<span class="emphasis"><em><cmath>:</em></span> Max = 2.56ε (Mean = 0.816ε)) 20164 </p> 20165 </td> 20166<td> 20167 <p> 20168 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 20169 2.1:</em></span> Max = 2.99ε (Mean = 0.797ε)) 20170 </p> 20171 </td> 20172<td> 20173 <p> 20174 <span class="blue">Max = 1.57ε (Mean = 0.561ε)</span> 20175 </p> 20176 </td> 20177<td> 20178 <p> 20179 <span class="blue">Max = 2.26ε (Mean = 0.631ε)</span> 20180 </p> 20181 </td> 20182</tr> 20183</tbody> 20184</table></div> 20185</div> 20186<br class="table-break"><div class="table"> 20187<a name="special_function_error_rates_rep.all_the_tables.table_ellint_1_complete_"></a><p class="title"><b>Table 122. Error rates for ellint_1 (complete)</b></p> 20188<div class="table-contents"><table class="table" summary="Error rates for ellint_1 (complete)"> 20189<colgroup> 20190<col> 20191<col> 20192<col> 20193<col> 20194<col> 20195</colgroup> 20196<thead><tr> 20197<th> 20198 </th> 20199<th> 20200 <p> 20201 GNU C++ version 7.1.0<br> linux<br> long double 20202 </p> 20203 </th> 20204<th> 20205 <p> 20206 GNU C++ version 7.1.0<br> linux<br> double 20207 </p> 20208 </th> 20209<th> 20210 <p> 20211 Sun compiler version 0x5150<br> Sun Solaris<br> long double 20212 </p> 20213 </th> 20214<th> 20215 <p> 20216 Microsoft Visual C++ version 14.1<br> Win32<br> double 20217 </p> 20218 </th> 20219</tr></thead> 20220<tbody> 20221<tr> 20222<td> 20223 <p> 20224 Elliptic Integral K: Mathworld Data 20225 </p> 20226 </td> 20227<td> 20228 <p> 20229 <span class="blue">Max = 0.887ε (Mean = 0.296ε)</span><br> <br> 20230 (<span class="emphasis"><em><cmath>:</em></span> Max = 1.19ε (Mean = 0.765ε)) 20231 </p> 20232 </td> 20233<td> 20234 <p> 20235 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 20236 2.1:</em></span> Max = 0.623ε (Mean = 0.393ε)) 20237 </p> 20238 </td> 20239<td> 20240 <p> 20241 <span class="blue">Max = 0.887ε (Mean = 0.296ε)</span> 20242 </p> 20243 </td> 20244<td> 20245 <p> 20246 <span class="blue">Max = 0.915ε (Mean = 0.547ε)</span> 20247 </p> 20248 </td> 20249</tr> 20250<tr> 20251<td> 20252 <p> 20253 Elliptic Integral K: Random Data 20254 </p> 20255 </td> 20256<td> 20257 <p> 20258 <span class="blue">Max = 1.27ε (Mean = 0.473ε)</span><br> <br> 20259 (<span class="emphasis"><em><cmath>:</em></span> Max = 2.19ε (Mean = 0.694ε)) 20260 </p> 20261 </td> 20262<td> 20263 <p> 20264 <span class="blue">Max = 0.851ε (Mean = 0.0851ε)</span><br> <br> 20265 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.32ε (Mean = 0.688ε)) 20266 </p> 20267 </td> 20268<td> 20269 <p> 20270 <span class="blue">Max = 1.27ε (Mean = 0.473ε)</span> 20271 </p> 20272 </td> 20273<td> 20274 <p> 20275 <span class="blue">Max = 0.958ε (Mean = 0.408ε)</span> 20276 </p> 20277 </td> 20278</tr> 20279</tbody> 20280</table></div> 20281</div> 20282<br class="table-break"><div class="table"> 20283<a name="special_function_error_rates_rep.all_the_tables.table_ellint_2"></a><p class="title"><b>Table 123. Error rates for ellint_2</b></p> 20284<div class="table-contents"><table class="table" summary="Error rates for ellint_2"> 20285<colgroup> 20286<col> 20287<col> 20288<col> 20289<col> 20290<col> 20291</colgroup> 20292<thead><tr> 20293<th> 20294 </th> 20295<th> 20296 <p> 20297 GNU C++ version 7.1.0<br> linux<br> double 20298 </p> 20299 </th> 20300<th> 20301 <p> 20302 GNU C++ version 7.1.0<br> linux<br> long double 20303 </p> 20304 </th> 20305<th> 20306 <p> 20307 Sun compiler version 0x5150<br> Sun Solaris<br> long double 20308 </p> 20309 </th> 20310<th> 20311 <p> 20312 Microsoft Visual C++ version 14.1<br> Win32<br> double 20313 </p> 20314 </th> 20315</tr></thead> 20316<tbody> 20317<tr> 20318<td> 20319 <p> 20320 Elliptic Integral E: Mathworld Data 20321 </p> 20322 </td> 20323<td> 20324 <p> 20325 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 20326 2.1:</em></span> Max = 0.63ε (Mean = 0.325ε)) 20327 </p> 20328 </td> 20329<td> 20330 <p> 20331 <span class="blue">Max = 0.656ε (Mean = 0.317ε)</span><br> <br> 20332 (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = +INFε (Mean 20333 = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_2__cmath__Elliptic_Integral_E_Mathworld_Data">And 20334 other failures.</a>)</span> 20335 </p> 20336 </td> 20337<td> 20338 <p> 20339 <span class="blue">Max = 0.656ε (Mean = 0.317ε)</span> 20340 </p> 20341 </td> 20342<td> 20343 <p> 20344 <span class="blue">Max = 1.31ε (Mean = 0.727ε)</span> 20345 </p> 20346 </td> 20347</tr> 20348<tr> 20349<td> 20350 <p> 20351 Elliptic Integral E: Random Data 20352 </p> 20353 </td> 20354<td> 20355 <p> 20356 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 20357 2.1:</em></span> Max = 4.4ε (Mean = 1.16ε)) 20358 </p> 20359 </td> 20360<td> 20361 <p> 20362 <span class="blue">Max = 2.05ε (Mean = 0.632ε)</span><br> <br> 20363 (<span class="emphasis"><em><cmath>:</em></span> Max = 3.08e+04ε (Mean = 3.84e+03ε)) 20364 </p> 20365 </td> 20366<td> 20367 <p> 20368 <span class="blue">Max = 2.05ε (Mean = 0.632ε)</span> 20369 </p> 20370 </td> 20371<td> 20372 <p> 20373 <span class="blue">Max = 2.23ε (Mean = 0.639ε)</span> 20374 </p> 20375 </td> 20376</tr> 20377<tr> 20378<td> 20379 <p> 20380 Elliptic Integral E: Small Angles 20381 </p> 20382 </td> 20383<td> 20384 <p> 20385 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 20386 2.1:</em></span> Max = 0.5ε (Mean = 0.118ε)) 20387 </p> 20388 </td> 20389<td> 20390 <p> 20391 <span class="blue">Max = 1ε (Mean = 0.283ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span> 20392 Max = 2ε (Mean = 0.333ε)) 20393 </p> 20394 </td> 20395<td> 20396 <p> 20397 <span class="blue">Max = 1ε (Mean = 0.283ε)</span> 20398 </p> 20399 </td> 20400<td> 20401 <p> 20402 <span class="blue">Max = 1ε (Mean = 0.421ε)</span> 20403 </p> 20404 </td> 20405</tr> 20406</tbody> 20407</table></div> 20408</div> 20409<br class="table-break"><div class="table"> 20410<a name="special_function_error_rates_rep.all_the_tables.table_ellint_2_complete_"></a><p class="title"><b>Table 124. Error rates for ellint_2 (complete)</b></p> 20411<div class="table-contents"><table class="table" summary="Error rates for ellint_2 (complete)"> 20412<colgroup> 20413<col> 20414<col> 20415<col> 20416<col> 20417<col> 20418</colgroup> 20419<thead><tr> 20420<th> 20421 </th> 20422<th> 20423 <p> 20424 GNU C++ version 7.1.0<br> linux<br> double 20425 </p> 20426 </th> 20427<th> 20428 <p> 20429 GNU C++ version 7.1.0<br> linux<br> long double 20430 </p> 20431 </th> 20432<th> 20433 <p> 20434 Sun compiler version 0x5150<br> Sun Solaris<br> long double 20435 </p> 20436 </th> 20437<th> 20438 <p> 20439 Microsoft Visual C++ version 14.1<br> Win32<br> double 20440 </p> 20441 </th> 20442</tr></thead> 20443<tbody> 20444<tr> 20445<td> 20446 <p> 20447 Elliptic Integral E: Mathworld Data 20448 </p> 20449 </td> 20450<td> 20451 <p> 20452 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 20453 2.1:</em></span> Max = 3.09ε (Mean = 1.04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ellint_2_complete__GSL_2_1_Elliptic_Integral_E_Mathworld_Data">And 20454 other failures.</a>) 20455 </p> 20456 </td> 20457<td> 20458 <p> 20459 <span class="blue">Max = 0.836ε (Mean = 0.469ε)</span><br> <br> 20460 (<span class="emphasis"><em><cmath>:</em></span> Max = 170ε (Mean = 55.1ε)) 20461 </p> 20462 </td> 20463<td> 20464 <p> 20465 <span class="blue">Max = 0.836ε (Mean = 0.469ε)</span> 20466 </p> 20467 </td> 20468<td> 20469 <p> 20470 <span class="blue">Max = 1.3ε (Mean = 0.615ε)</span> 20471 </p> 20472 </td> 20473</tr> 20474<tr> 20475<td> 20476 <p> 20477 Elliptic Integral E: Random Data 20478 </p> 20479 </td> 20480<td> 20481 <p> 20482 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 20483 2.1:</em></span> Max = 4.34ε (Mean = 1.18ε)) 20484 </p> 20485 </td> 20486<td> 20487 <p> 20488 <span class="blue">Max = 1.97ε (Mean = 0.629ε)</span><br> <br> 20489 (<span class="emphasis"><em><cmath>:</em></span> Max = 2.49e+04ε (Mean = 3.39e+03ε)) 20490 </p> 20491 </td> 20492<td> 20493 <p> 20494 <span class="blue">Max = 1.97ε (Mean = 0.629ε)</span> 20495 </p> 20496 </td> 20497<td> 20498 <p> 20499 <span class="blue">Max = 1.71ε (Mean = 0.553ε)</span> 20500 </p> 20501 </td> 20502</tr> 20503</tbody> 20504</table></div> 20505</div> 20506<br class="table-break"><div class="table"> 20507<a name="special_function_error_rates_rep.all_the_tables.table_ellint_3"></a><p class="title"><b>Table 125. Error rates for ellint_3</b></p> 20508<div class="table-contents"><table class="table" summary="Error rates for ellint_3"> 20509<colgroup> 20510<col> 20511<col> 20512<col> 20513<col> 20514<col> 20515</colgroup> 20516<thead><tr> 20517<th> 20518 </th> 20519<th> 20520 <p> 20521 GNU C++ version 7.1.0<br> linux<br> long double 20522 </p> 20523 </th> 20524<th> 20525 <p> 20526 GNU C++ version 7.1.0<br> linux<br> double 20527 </p> 20528 </th> 20529<th> 20530 <p> 20531 Sun compiler version 0x5150<br> Sun Solaris<br> long double 20532 </p> 20533 </th> 20534<th> 20535 <p> 20536 Microsoft Visual C++ version 14.1<br> Win32<br> double 20537 </p> 20538 </th> 20539</tr></thead> 20540<tbody> 20541<tr> 20542<td> 20543 <p> 20544 Elliptic Integral PI: Mathworld Data 20545 </p> 20546 </td> 20547<td> 20548 <p> 20549 <span class="blue">Max = 475ε (Mean = 86.3ε)</span><br> <br> 20550 (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = +INFε (Mean 20551 = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Mathworld_Data">And 20552 other failures.</a>)</span> 20553 </p> 20554 </td> 20555<td> 20556 <p> 20557 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 20558 2.1:</em></span> Max = 1.48e+05ε (Mean = 2.54e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ellint_3_GSL_2_1_Elliptic_Integral_PI_Mathworld_Data">And 20559 other failures.</a>) 20560 </p> 20561 </td> 20562<td> 20563 <p> 20564 <span class="blue">Max = 475ε (Mean = 86.3ε)</span> 20565 </p> 20566 </td> 20567<td> 20568 <p> 20569 <span class="blue">Max = 565ε (Mean = 102ε)</span> 20570 </p> 20571 </td> 20572</tr> 20573<tr> 20574<td> 20575 <p> 20576 Elliptic Integral PI: Random Data 20577 </p> 20578 </td> 20579<td> 20580 <p> 20581 <span class="blue">Max = 4.54ε (Mean = 0.895ε)</span><br> <br> 20582 (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 3.37e+20ε (Mean 20583 = 3.47e+19ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Random_Data">And 20584 other failures.</a>)</span> 20585 </p> 20586 </td> 20587<td> 20588 <p> 20589 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 20590 2.1:</em></span> Max = 633ε (Mean = 50.1ε)) 20591 </p> 20592 </td> 20593<td> 20594 <p> 20595 <span class="blue">Max = 4.49ε (Mean = 0.885ε)</span> 20596 </p> 20597 </td> 20598<td> 20599 <p> 20600 <span class="blue">Max = 8.33ε (Mean = 0.971ε)</span> 20601 </p> 20602 </td> 20603</tr> 20604<tr> 20605<td> 20606 <p> 20607 Elliptic Integral PI: Large Random Data 20608 </p> 20609 </td> 20610<td> 20611 <p> 20612 <span class="blue">Max = 3.7ε (Mean = 0.893ε)</span><br> <br> 20613 (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 2.52e+18ε (Mean 20614 = 4.83e+17ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Large_Random_Data">And 20615 other failures.</a>)</span> 20616 </p> 20617 </td> 20618<td> 20619 <p> 20620 <span class="blue">Max = 0.557ε (Mean = 0.0389ε)</span><br> <br> 20621 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 40.1ε (Mean = 7.77ε)) 20622 </p> 20623 </td> 20624<td> 20625 <p> 20626 <span class="blue">Max = 3.7ε (Mean = 0.892ε)</span> 20627 </p> 20628 </td> 20629<td> 20630 <p> 20631 <span class="blue">Max = 2.86ε (Mean = 0.944ε)</span> 20632 </p> 20633 </td> 20634</tr> 20635</tbody> 20636</table></div> 20637</div> 20638<br class="table-break"><div class="table"> 20639<a name="special_function_error_rates_rep.all_the_tables.table_ellint_3_complete_"></a><p class="title"><b>Table 126. Error rates for ellint_3 (complete)</b></p> 20640<div class="table-contents"><table class="table" summary="Error rates for ellint_3 (complete)"> 20641<colgroup> 20642<col> 20643<col> 20644<col> 20645<col> 20646<col> 20647</colgroup> 20648<thead><tr> 20649<th> 20650 </th> 20651<th> 20652 <p> 20653 GNU C++ version 7.1.0<br> linux<br> long double 20654 </p> 20655 </th> 20656<th> 20657 <p> 20658 GNU C++ version 7.1.0<br> linux<br> double 20659 </p> 20660 </th> 20661<th> 20662 <p> 20663 Sun compiler version 0x5150<br> Sun Solaris<br> long double 20664 </p> 20665 </th> 20666<th> 20667 <p> 20668 Microsoft Visual C++ version 14.1<br> Win32<br> double 20669 </p> 20670 </th> 20671</tr></thead> 20672<tbody> 20673<tr> 20674<td> 20675 <p> 20676 Complete Elliptic Integral PI: Mathworld Data 20677 </p> 20678 </td> 20679<td> 20680 <p> 20681 <span class="blue">Max = 1.4ε (Mean = 0.575ε)</span><br> <br> 20682 (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 6.31e+20ε (Mean 20683 = 1.53e+20ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3_complete___cmath__Complete_Elliptic_Integral_PI_Mathworld_Data">And 20684 other failures.</a>)</span> 20685 </p> 20686 </td> 20687<td> 20688 <p> 20689 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 20690 2.1:</em></span> Max = 6.33e+04ε (Mean = 1.54e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ellint_3_complete__GSL_2_1_Complete_Elliptic_Integral_PI_Mathworld_Data">And 20691 other failures.</a>) 20692 </p> 20693 </td> 20694<td> 20695 <p> 20696 <span class="blue">Max = 1.4ε (Mean = 0.575ε)</span> 20697 </p> 20698 </td> 20699<td> 20700 <p> 20701 <span class="blue">Max = 0.971ε (Mean = 0.464ε)</span> 20702 </p> 20703 </td> 20704</tr> 20705<tr> 20706<td> 20707 <p> 20708 Complete Elliptic Integral PI: Random Data 20709 </p> 20710 </td> 20711<td> 20712 <p> 20713 <span class="blue">Max = 2.45ε (Mean = 0.696ε)</span><br> <br> 20714 (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 8.78e+20ε (Mean 20715 = 1.02e+20ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3_complete___cmath__Complete_Elliptic_Integral_PI_Random_Data">And 20716 other failures.</a>)</span> 20717 </p> 20718 </td> 20719<td> 20720 <p> 20721 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 20722 2.1:</em></span> Max = 24ε (Mean = 2.99ε)) 20723 </p> 20724 </td> 20725<td> 20726 <p> 20727 <span class="blue">Max = 2.4ε (Mean = 0.677ε)</span> 20728 </p> 20729 </td> 20730<td> 20731 <p> 20732 <span class="blue">Max = 2.46ε (Mean = 0.657ε)</span> 20733 </p> 20734 </td> 20735</tr> 20736</tbody> 20737</table></div> 20738</div> 20739<br class="table-break"><div class="table"> 20740<a name="special_function_error_rates_rep.all_the_tables.table_ellint_d"></a><p class="title"><b>Table 127. Error rates for ellint_d</b></p> 20741<div class="table-contents"><table class="table" summary="Error rates for ellint_d"> 20742<colgroup> 20743<col> 20744<col> 20745<col> 20746<col> 20747<col> 20748</colgroup> 20749<thead><tr> 20750<th> 20751 </th> 20752<th> 20753 <p> 20754 GNU C++ version 7.1.0<br> linux<br> double 20755 </p> 20756 </th> 20757<th> 20758 <p> 20759 GNU C++ version 7.1.0<br> linux<br> long double 20760 </p> 20761 </th> 20762<th> 20763 <p> 20764 Sun compiler version 0x5150<br> Sun Solaris<br> long double 20765 </p> 20766 </th> 20767<th> 20768 <p> 20769 Microsoft Visual C++ version 14.1<br> Win32<br> double 20770 </p> 20771 </th> 20772</tr></thead> 20773<tbody> 20774<tr> 20775<td> 20776 <p> 20777 Elliptic Integral E: Mathworld Data 20778 </p> 20779 </td> 20780<td> 20781 <p> 20782 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 20783 2.1:</em></span> Max = 0.862ε (Mean = 0.568ε)) 20784 </p> 20785 </td> 20786<td> 20787 <p> 20788 <span class="blue">Max = 1.3ε (Mean = 0.813ε)</span> 20789 </p> 20790 </td> 20791<td> 20792 <p> 20793 <span class="blue">Max = 1.3ε (Mean = 0.813ε)</span> 20794 </p> 20795 </td> 20796<td> 20797 <p> 20798 <span class="blue">Max = 0.862ε (Mean = 0.457ε)</span> 20799 </p> 20800 </td> 20801</tr> 20802<tr> 20803<td> 20804 <p> 20805 Elliptic Integral D: Random Data 20806 </p> 20807 </td> 20808<td> 20809 <p> 20810 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 20811 2.1:</em></span> Max = 3.01ε (Mean = 0.928ε)) 20812 </p> 20813 </td> 20814<td> 20815 <p> 20816 <span class="blue">Max = 2.51ε (Mean = 0.883ε)</span> 20817 </p> 20818 </td> 20819<td> 20820 <p> 20821 <span class="blue">Max = 2.51ε (Mean = 0.883ε)</span> 20822 </p> 20823 </td> 20824<td> 20825 <p> 20826 <span class="blue">Max = 2.87ε (Mean = 0.805ε)</span> 20827 </p> 20828 </td> 20829</tr> 20830</tbody> 20831</table></div> 20832</div> 20833<br class="table-break"><div class="table"> 20834<a name="special_function_error_rates_rep.all_the_tables.table_ellint_d_complete_"></a><p class="title"><b>Table 128. Error rates for ellint_d (complete)</b></p> 20835<div class="table-contents"><table class="table" summary="Error rates for ellint_d (complete)"> 20836<colgroup> 20837<col> 20838<col> 20839<col> 20840<col> 20841<col> 20842</colgroup> 20843<thead><tr> 20844<th> 20845 </th> 20846<th> 20847 <p> 20848 GNU C++ version 7.1.0<br> linux<br> double 20849 </p> 20850 </th> 20851<th> 20852 <p> 20853 GNU C++ version 7.1.0<br> linux<br> long double 20854 </p> 20855 </th> 20856<th> 20857 <p> 20858 Sun compiler version 0x5150<br> Sun Solaris<br> long double 20859 </p> 20860 </th> 20861<th> 20862 <p> 20863 Microsoft Visual C++ version 14.1<br> Win32<br> double 20864 </p> 20865 </th> 20866</tr></thead> 20867<tbody> 20868<tr> 20869<td> 20870 <p> 20871 Elliptic Integral E: Mathworld Data 20872 </p> 20873 </td> 20874<td> 20875 <p> 20876 <span class="blue">Max = 0.637ε (Mean = 0.368ε)</span> 20877 </p> 20878 </td> 20879<td> 20880 <p> 20881 <span class="blue">Max = 1.27ε (Mean = 0.735ε)</span> 20882 </p> 20883 </td> 20884<td> 20885 <p> 20886 <span class="blue">Max = 1.27ε (Mean = 0.735ε)</span> 20887 </p> 20888 </td> 20889<td> 20890 <p> 20891 <span class="blue">Max = 0.637ε (Mean = 0.368ε)</span> 20892 </p> 20893 </td> 20894</tr> 20895<tr> 20896<td> 20897 <p> 20898 Elliptic Integral D: Random Data 20899 </p> 20900 </td> 20901<td> 20902 <p> 20903 <span class="blue">Max = 0ε (Mean = 0ε)</span> 20904 </p> 20905 </td> 20906<td> 20907 <p> 20908 <span class="blue">Max = 1.27ε (Mean = 0.334ε)</span> 20909 </p> 20910 </td> 20911<td> 20912 <p> 20913 <span class="blue">Max = 1.27ε (Mean = 0.334ε)</span> 20914 </p> 20915 </td> 20916<td> 20917 <p> 20918 <span class="blue">Max = 1.27ε (Mean = 0.355ε)</span> 20919 </p> 20920 </td> 20921</tr> 20922</tbody> 20923</table></div> 20924</div> 20925<br class="table-break"><div class="table"> 20926<a name="special_function_error_rates_rep.all_the_tables.table_ellint_rc"></a><p class="title"><b>Table 129. Error rates for ellint_rc</b></p> 20927<div class="table-contents"><table class="table" summary="Error rates for ellint_rc"> 20928<colgroup> 20929<col> 20930<col> 20931<col> 20932<col> 20933</colgroup> 20934<thead><tr> 20935<th> 20936 </th> 20937<th> 20938 <p> 20939 GNU C++ version 7.1.0<br> linux<br> double 20940 </p> 20941 </th> 20942<th> 20943 <p> 20944 GNU C++ version 7.1.0<br> linux<br> long double 20945 </p> 20946 </th> 20947<th> 20948 <p> 20949 Microsoft Visual C++ version 14.1<br> Win32<br> double 20950 </p> 20951 </th> 20952</tr></thead> 20953<tbody><tr> 20954<td> 20955 <p> 20956 RC: Random data 20957 </p> 20958 </td> 20959<td> 20960 <p> 20961 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 20962 2.1:</em></span> Max = 2.4ε (Mean = 0.624ε)) 20963 </p> 20964 </td> 20965<td> 20966 <p> 20967 <span class="blue">Max = 0.995ε (Mean = 0.433ε)</span> 20968 </p> 20969 </td> 20970<td> 20971 <p> 20972 <span class="blue">Max = 0.962ε (Mean = 0.407ε)</span> 20973 </p> 20974 </td> 20975</tr></tbody> 20976</table></div> 20977</div> 20978<br class="table-break"><div class="table"> 20979<a name="special_function_error_rates_rep.all_the_tables.table_ellint_rd"></a><p class="title"><b>Table 130. Error rates for ellint_rd</b></p> 20980<div class="table-contents"><table class="table" summary="Error rates for ellint_rd"> 20981<colgroup> 20982<col> 20983<col> 20984<col> 20985<col> 20986</colgroup> 20987<thead><tr> 20988<th> 20989 </th> 20990<th> 20991 <p> 20992 GNU C++ version 7.1.0<br> linux<br> double 20993 </p> 20994 </th> 20995<th> 20996 <p> 20997 GNU C++ version 7.1.0<br> linux<br> long double 20998 </p> 20999 </th> 21000<th> 21001 <p> 21002 Microsoft Visual C++ version 14.1<br> Win32<br> double 21003 </p> 21004 </th> 21005</tr></thead> 21006<tbody> 21007<tr> 21008<td> 21009 <p> 21010 RD: Random data 21011 </p> 21012 </td> 21013<td> 21014 <p> 21015 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 21016 2.1:</em></span> Max = 2.59ε (Mean = 0.878ε)) 21017 </p> 21018 </td> 21019<td> 21020 <p> 21021 <span class="blue">Max = 2.73ε (Mean = 0.831ε)</span> 21022 </p> 21023 </td> 21024<td> 21025 <p> 21026 <span class="blue">Max = 2.16ε (Mean = 0.803ε)</span> 21027 </p> 21028 </td> 21029</tr> 21030<tr> 21031<td> 21032 <p> 21033 RD: y = z 21034 </p> 21035 </td> 21036<td> 21037 <p> 21038 <span class="blue">Max = 0.896ε (Mean = 0.022ε)</span><br> <br> 21039 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.88ε (Mean = 0.839ε)) 21040 </p> 21041 </td> 21042<td> 21043 <p> 21044 <span class="blue">Max = 2.65ε (Mean = 0.82ε)</span> 21045 </p> 21046 </td> 21047<td> 21048 <p> 21049 <span class="blue">Max = 16.5ε (Mean = 0.843ε)</span> 21050 </p> 21051 </td> 21052</tr> 21053<tr> 21054<td> 21055 <p> 21056 RD: x = y 21057 </p> 21058 </td> 21059<td> 21060 <p> 21061 <span class="blue">Max = 0.824ε (Mean = 0.0272ε)</span><br> <br> 21062 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.74ε (Mean = 0.84ε)) 21063 </p> 21064 </td> 21065<td> 21066 <p> 21067 <span class="blue">Max = 2.85ε (Mean = 0.865ε)</span> 21068 </p> 21069 </td> 21070<td> 21071 <p> 21072 <span class="blue">Max = 3.51ε (Mean = 0.816ε)</span> 21073 </p> 21074 </td> 21075</tr> 21076<tr> 21077<td> 21078 <p> 21079 RD: x = 0, y = z 21080 </p> 21081 </td> 21082<td> 21083 <p> 21084 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 21085 2.1:</em></span> Max = 2ε (Mean = 0.656ε)) 21086 </p> 21087 </td> 21088<td> 21089 <p> 21090 <span class="blue">Max = 1.19ε (Mean = 0.522ε)</span> 21091 </p> 21092 </td> 21093<td> 21094 <p> 21095 <span class="blue">Max = 1.16ε (Mean = 0.497ε)</span> 21096 </p> 21097 </td> 21098</tr> 21099<tr> 21100<td> 21101 <p> 21102 RD: x = y = z 21103 </p> 21104 </td> 21105<td> 21106 <p> 21107 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 21108 2.1:</em></span> Max = 1.03ε (Mean = 0.418ε)) 21109 </p> 21110 </td> 21111<td> 21112 <p> 21113 <span class="blue">Max = 0.998ε (Mean = 0.387ε)</span> 21114 </p> 21115 </td> 21116<td> 21117 <p> 21118 <span class="blue">Max = 1.03ε (Mean = 0.418ε)</span> 21119 </p> 21120 </td> 21121</tr> 21122<tr> 21123<td> 21124 <p> 21125 RD: x = 0 21126 </p> 21127 </td> 21128<td> 21129 <p> 21130 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 21131 2.1:</em></span> Max = 2.85ε (Mean = 0.781ε)) 21132 </p> 21133 </td> 21134<td> 21135 <p> 21136 <span class="blue">Max = 2.79ε (Mean = 0.883ε)</span> 21137 </p> 21138 </td> 21139<td> 21140 <p> 21141 <span class="blue">Max = 2.64ε (Mean = 0.894ε)</span> 21142 </p> 21143 </td> 21144</tr> 21145</tbody> 21146</table></div> 21147</div> 21148<br class="table-break"><div class="table"> 21149<a name="special_function_error_rates_rep.all_the_tables.table_ellint_rf"></a><p class="title"><b>Table 131. Error rates for ellint_rf</b></p> 21150<div class="table-contents"><table class="table" summary="Error rates for ellint_rf"> 21151<colgroup> 21152<col> 21153<col> 21154<col> 21155<col> 21156</colgroup> 21157<thead><tr> 21158<th> 21159 </th> 21160<th> 21161 <p> 21162 GNU C++ version 7.1.0<br> linux<br> double 21163 </p> 21164 </th> 21165<th> 21166 <p> 21167 GNU C++ version 7.1.0<br> linux<br> long double 21168 </p> 21169 </th> 21170<th> 21171 <p> 21172 Microsoft Visual C++ version 14.1<br> Win32<br> double 21173 </p> 21174 </th> 21175</tr></thead> 21176<tbody> 21177<tr> 21178<td> 21179 <p> 21180 RF: Random data 21181 </p> 21182 </td> 21183<td> 21184 <p> 21185 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 21186 2.1:</em></span> Max = 2.73ε (Mean = 0.804ε)) 21187 </p> 21188 </td> 21189<td> 21190 <p> 21191 <span class="blue">Max = 2.54ε (Mean = 0.674ε)</span> 21192 </p> 21193 </td> 21194<td> 21195 <p> 21196 <span class="blue">Max = 2.02ε (Mean = 0.677ε)</span> 21197 </p> 21198 </td> 21199</tr> 21200<tr> 21201<td> 21202 <p> 21203 RF: x = y = z 21204 </p> 21205 </td> 21206<td> 21207 <p> 21208 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 21209 2.1:</em></span> Max = 0.999ε (Mean = 0.34ε)) 21210 </p> 21211 </td> 21212<td> 21213 <p> 21214 <span class="blue">Max = 0.991ε (Mean = 0.345ε)</span> 21215 </p> 21216 </td> 21217<td> 21218 <p> 21219 <span class="blue">Max = 0.999ε (Mean = 0.34ε)</span> 21220 </p> 21221 </td> 21222</tr> 21223<tr> 21224<td> 21225 <p> 21226 RF: x = y or y = z or x = z 21227 </p> 21228 </td> 21229<td> 21230 <p> 21231 <span class="blue">Max = 0.536ε (Mean = 0.00658ε)</span><br> <br> 21232 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.89ε (Mean = 0.749ε)) 21233 </p> 21234 </td> 21235<td> 21236 <p> 21237 <span class="blue">Max = 1.95ε (Mean = 0.418ε)</span> 21238 </p> 21239 </td> 21240<td> 21241 <p> 21242 <span class="blue">Max = 1.21ε (Mean = 0.394ε)</span> 21243 </p> 21244 </td> 21245</tr> 21246<tr> 21247<td> 21248 <p> 21249 RF: x = 0, y = z 21250 </p> 21251 </td> 21252<td> 21253 <p> 21254 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 21255 2.1:</em></span> Max = 1.29ε (Mean = 0.527ε)) 21256 </p> 21257 </td> 21258<td> 21259 <p> 21260 <span class="blue">Max = 0.894ε (Mean = 0.338ε)</span> 21261 </p> 21262 </td> 21263<td> 21264 <p> 21265 <span class="blue">Max = 0.999ε (Mean = 0.407ε)</span> 21266 </p> 21267 </td> 21268</tr> 21269<tr> 21270<td> 21271 <p> 21272 RF: z = 0 21273 </p> 21274 </td> 21275<td> 21276 <p> 21277 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 21278 2.1:</em></span> Max = 2.54ε (Mean = 0.781ε)) 21279 </p> 21280 </td> 21281<td> 21282 <p> 21283 <span class="blue">Max = 1.7ε (Mean = 0.539ε)</span> 21284 </p> 21285 </td> 21286<td> 21287 <p> 21288 <span class="blue">Max = 1.89ε (Mean = 0.587ε)</span> 21289 </p> 21290 </td> 21291</tr> 21292</tbody> 21293</table></div> 21294</div> 21295<br class="table-break"><div class="table"> 21296<a name="special_function_error_rates_rep.all_the_tables.table_ellint_rg"></a><p class="title"><b>Table 132. Error rates for ellint_rg</b></p> 21297<div class="table-contents"><table class="table" summary="Error rates for ellint_rg"> 21298<colgroup> 21299<col> 21300<col> 21301<col> 21302<col> 21303</colgroup> 21304<thead><tr> 21305<th> 21306 </th> 21307<th> 21308 <p> 21309 GNU C++ version 7.1.0<br> linux<br> double 21310 </p> 21311 </th> 21312<th> 21313 <p> 21314 GNU C++ version 7.1.0<br> linux<br> long double 21315 </p> 21316 </th> 21317<th> 21318 <p> 21319 Microsoft Visual C++ version 14.1<br> Win32<br> double 21320 </p> 21321 </th> 21322</tr></thead> 21323<tbody> 21324<tr> 21325<td> 21326 <p> 21327 RG: Random Data 21328 </p> 21329 </td> 21330<td> 21331 <p> 21332 <span class="blue">Max = 0.983ε (Mean = 0.0172ε)</span><br> <br> 21333 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.983ε (Mean = 0.0172ε)) 21334 </p> 21335 </td> 21336<td> 21337 <p> 21338 <span class="blue">Max = 3.95ε (Mean = 0.951ε)</span> 21339 </p> 21340 </td> 21341<td> 21342 <p> 21343 <span class="blue">Max = 3.65ε (Mean = 0.929ε)</span> 21344 </p> 21345 </td> 21346</tr> 21347<tr> 21348<td> 21349 <p> 21350 RG: two values 0 21351 </p> 21352 </td> 21353<td> 21354 <p> 21355 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 21356 2.1:</em></span> Max = 0ε (Mean = 0ε)) 21357 </p> 21358 </td> 21359<td> 21360 <p> 21361 <span class="blue">Max = 0ε (Mean = 0ε)</span> 21362 </p> 21363 </td> 21364<td> 21365 <p> 21366 <span class="blue">Max = 0ε (Mean = 0ε)</span> 21367 </p> 21368 </td> 21369</tr> 21370<tr> 21371<td> 21372 <p> 21373 RG: All values the same or zero 21374 </p> 21375 </td> 21376<td> 21377 <p> 21378 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 21379 2.1:</em></span> Max = 0ε (Mean = 0ε)) 21380 </p> 21381 </td> 21382<td> 21383 <p> 21384 <span class="blue">Max = 0.992ε (Mean = 0.288ε)</span> 21385 </p> 21386 </td> 21387<td> 21388 <p> 21389 <span class="blue">Max = 1.06ε (Mean = 0.348ε)</span> 21390 </p> 21391 </td> 21392</tr> 21393<tr> 21394<td> 21395 <p> 21396 RG: two values the same 21397 </p> 21398 </td> 21399<td> 21400 <p> 21401 <span class="blue">Max = 0.594ε (Mean = 0.0103ε)</span><br> <br> 21402 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.594ε (Mean = 0.0103ε)) 21403 </p> 21404 </td> 21405<td> 21406 <p> 21407 <span class="blue">Max = 1.51ε (Mean = 0.404ε)</span> 21408 </p> 21409 </td> 21410<td> 21411 <p> 21412 <span class="blue">Max = 1.96ε (Mean = 0.374ε)</span> 21413 </p> 21414 </td> 21415</tr> 21416<tr> 21417<td> 21418 <p> 21419 RG: one value zero 21420 </p> 21421 </td> 21422<td> 21423 <p> 21424 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 21425 2.1:</em></span> Max = 0ε (Mean = 0ε)) 21426 </p> 21427 </td> 21428<td> 21429 <p> 21430 <span class="blue">Max = 2.14ε (Mean = 0.722ε)</span> 21431 </p> 21432 </td> 21433<td> 21434 <p> 21435 <span class="blue">Max = 1.96ε (Mean = 0.674ε)</span> 21436 </p> 21437 </td> 21438</tr> 21439</tbody> 21440</table></div> 21441</div> 21442<br class="table-break"><div class="table"> 21443<a name="special_function_error_rates_rep.all_the_tables.table_ellint_rj"></a><p class="title"><b>Table 133. Error rates for ellint_rj</b></p> 21444<div class="table-contents"><table class="table" summary="Error rates for ellint_rj"> 21445<colgroup> 21446<col> 21447<col> 21448<col> 21449<col> 21450</colgroup> 21451<thead><tr> 21452<th> 21453 </th> 21454<th> 21455 <p> 21456 GNU C++ version 7.1.0<br> linux<br> double 21457 </p> 21458 </th> 21459<th> 21460 <p> 21461 GNU C++ version 7.1.0<br> linux<br> long double 21462 </p> 21463 </th> 21464<th> 21465 <p> 21466 Microsoft Visual C++ version 14.1<br> Win32<br> double 21467 </p> 21468 </th> 21469</tr></thead> 21470<tbody> 21471<tr> 21472<td> 21473 <p> 21474 RJ: Random data 21475 </p> 21476 </td> 21477<td> 21478 <p> 21479 <span class="blue">Max = 0.52ε (Mean = 0.0184ε)</span><br> <br> 21480 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.57ε (Mean = 0.704ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ellint_rj_GSL_2_1_RJ_Random_data">And 21481 other failures.</a>) 21482 </p> 21483 </td> 21484<td> 21485 <p> 21486 <span class="blue">Max = 186ε (Mean = 6.67ε)</span> 21487 </p> 21488 </td> 21489<td> 21490 <p> 21491 <span class="blue">Max = 215ε (Mean = 7.66ε)</span> 21492 </p> 21493 </td> 21494</tr> 21495<tr> 21496<td> 21497 <p> 21498 RJ: 4 Equal Values 21499 </p> 21500 </td> 21501<td> 21502 <p> 21503 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 21504 2.1:</em></span> Max = 1.03ε (Mean = 0.418ε)) 21505 </p> 21506 </td> 21507<td> 21508 <p> 21509 <span class="blue">Max = 0.998ε (Mean = 0.387ε)</span> 21510 </p> 21511 </td> 21512<td> 21513 <p> 21514 <span class="blue">Max = 1.03ε (Mean = 0.418ε)</span> 21515 </p> 21516 </td> 21517</tr> 21518<tr> 21519<td> 21520 <p> 21521 RJ: 3 Equal Values 21522 </p> 21523 </td> 21524<td> 21525 <p> 21526 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 21527 2.1:</em></span> Max = 3.96ε (Mean = 1.06ε)) 21528 </p> 21529 </td> 21530<td> 21531 <p> 21532 <span class="blue">Max = 20.8ε (Mean = 0.986ε)</span> 21533 </p> 21534 </td> 21535<td> 21536 <p> 21537 <span class="blue">Max = 39.9ε (Mean = 1.17ε)</span> 21538 </p> 21539 </td> 21540</tr> 21541<tr> 21542<td> 21543 <p> 21544 RJ: 2 Equal Values 21545 </p> 21546 </td> 21547<td> 21548 <p> 21549 <span class="blue">Max = 0.6ε (Mean = 0.0228ε)</span><br> <br> 21550 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.57ε (Mean = 0.754ε)) 21551 </p> 21552 </td> 21553<td> 21554 <p> 21555 <span class="blue">Max = 220ε (Mean = 6.64ε)</span> 21556 </p> 21557 </td> 21558<td> 21559 <p> 21560 <span class="blue">Max = 214ε (Mean = 5.28ε)</span> 21561 </p> 21562 </td> 21563</tr> 21564<tr> 21565<td> 21566 <p> 21567 RJ: Equal z and p 21568 </p> 21569 </td> 21570<td> 21571 <p> 21572 <span class="blue">Max = 0.742ε (Mean = 0.0166ε)</span><br> <br> 21573 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.62ε (Mean = 0.699ε)) 21574 </p> 21575 </td> 21576<td> 21577 <p> 21578 <span class="blue">Max = 17.2ε (Mean = 1.16ε)</span> 21579 </p> 21580 </td> 21581<td> 21582 <p> 21583 <span class="blue">Max = 16.1ε (Mean = 1.14ε)</span> 21584 </p> 21585 </td> 21586</tr> 21587</tbody> 21588</table></div> 21589</div> 21590<br class="table-break"><div class="table"> 21591<a name="special_function_error_rates_rep.all_the_tables.table_erf"></a><p class="title"><b>Table 134. Error rates for erf</b></p> 21592<div class="table-contents"><table class="table" summary="Error rates for erf"> 21593<colgroup> 21594<col> 21595<col> 21596<col> 21597<col> 21598<col> 21599</colgroup> 21600<thead><tr> 21601<th> 21602 </th> 21603<th> 21604 <p> 21605 GNU C++ version 7.1.0<br> linux<br> long double 21606 </p> 21607 </th> 21608<th> 21609 <p> 21610 GNU C++ version 7.1.0<br> linux<br> double 21611 </p> 21612 </th> 21613<th> 21614 <p> 21615 Sun compiler version 0x5150<br> Sun Solaris<br> long double 21616 </p> 21617 </th> 21618<th> 21619 <p> 21620 Microsoft Visual C++ version 14.1<br> Win32<br> double 21621 </p> 21622 </th> 21623</tr></thead> 21624<tbody> 21625<tr> 21626<td> 21627 <p> 21628 Erf Function: Small Values 21629 </p> 21630 </td> 21631<td> 21632 <p> 21633 <span class="blue">Max = 0.925ε (Mean = 0.193ε)</span><br> <br> 21634 (<span class="emphasis"><em><cmath>:</em></span> Max = 0.944ε (Mean = 0.191ε))<br> 21635 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.944ε (Mean = 0.191ε)) 21636 </p> 21637 </td> 21638<td> 21639 <p> 21640 <span class="blue">Max = 0.841ε (Mean = 0.0687ε)</span><br> <br> 21641 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.06ε (Mean = 0.319ε)) 21642 </p> 21643 </td> 21644<td> 21645 <p> 21646 <span class="blue">Max = 0.925ε (Mean = 0.193ε)</span><br> <br> 21647 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.944ε (Mean = 0.194ε)) 21648 </p> 21649 </td> 21650<td> 21651 <p> 21652 <span class="blue">Max = 0.996ε (Mean = 0.182ε)</span><br> <br> 21653 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.57ε (Mean = 0.317ε)) 21654 </p> 21655 </td> 21656</tr> 21657<tr> 21658<td> 21659 <p> 21660 Erf Function: Medium Values 21661 </p> 21662 </td> 21663<td> 21664 <p> 21665 <span class="blue">Max = 1.5ε (Mean = 0.193ε)</span><br> <br> 21666 (<span class="emphasis"><em><cmath>:</em></span> Max = 0.921ε (Mean = 0.0723ε))<br> 21667 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.921ε (Mean = 0.0723ε)) 21668 </p> 21669 </td> 21670<td> 21671 <p> 21672 <span class="blue">Max = 1ε (Mean = 0.119ε)</span><br> <br> (<span class="emphasis"><em>GSL 21673 2.1:</em></span> Max = 2.31ε (Mean = 0.368ε)) 21674 </p> 21675 </td> 21676<td> 21677 <p> 21678 <span class="blue">Max = 1.5ε (Mean = 0.197ε)</span><br> <br> 21679 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.921ε (Mean = 0.071ε)) 21680 </p> 21681 </td> 21682<td> 21683 <p> 21684 <span class="blue">Max = 1ε (Mean = 0.171ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span> 21685 Max = 1.19ε (Mean = 0.244ε)) 21686 </p> 21687 </td> 21688</tr> 21689<tr> 21690<td> 21691 <p> 21692 Erf Function: Large Values 21693 </p> 21694 </td> 21695<td> 21696 <p> 21697 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span> 21698 Max = 0ε (Mean = 0ε))<br> (<span class="emphasis"><em><math.h>:</em></span> Max 21699 = 0ε (Mean = 0ε)) 21700 </p> 21701 </td> 21702<td> 21703 <p> 21704 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 21705 2.1:</em></span> Max = 0ε (Mean = 0ε)) 21706 </p> 21707 </td> 21708<td> 21709 <p> 21710 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span> 21711 Max = 0ε (Mean = 0ε)) 21712 </p> 21713 </td> 21714<td> 21715 <p> 21716 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span> 21717 Max = 0ε (Mean = 0ε)) 21718 </p> 21719 </td> 21720</tr> 21721</tbody> 21722</table></div> 21723</div> 21724<br class="table-break"><div class="table"> 21725<a name="special_function_error_rates_rep.all_the_tables.table_erf_inv"></a><p class="title"><b>Table 135. Error rates for erf_inv</b></p> 21726<div class="table-contents"><table class="table" summary="Error rates for erf_inv"> 21727<colgroup> 21728<col> 21729<col> 21730<col> 21731<col> 21732<col> 21733</colgroup> 21734<thead><tr> 21735<th> 21736 </th> 21737<th> 21738 <p> 21739 GNU C++ version 7.1.0<br> linux<br> double 21740 </p> 21741 </th> 21742<th> 21743 <p> 21744 GNU C++ version 7.1.0<br> linux<br> long double 21745 </p> 21746 </th> 21747<th> 21748 <p> 21749 Sun compiler version 0x5150<br> Sun Solaris<br> long double 21750 </p> 21751 </th> 21752<th> 21753 <p> 21754 Microsoft Visual C++ version 14.1<br> Win32<br> double 21755 </p> 21756 </th> 21757</tr></thead> 21758<tbody><tr> 21759<td> 21760 <p> 21761 Inverse Erf Function 21762 </p> 21763 </td> 21764<td> 21765 <p> 21766 <span class="blue">Max = 0ε (Mean = 0ε)</span> 21767 </p> 21768 </td> 21769<td> 21770 <p> 21771 <span class="blue">Max = 0.996ε (Mean = 0.389ε)</span> 21772 </p> 21773 </td> 21774<td> 21775 <p> 21776 <span class="blue">Max = 1.08ε (Mean = 0.395ε)</span> 21777 </p> 21778 </td> 21779<td> 21780 <p> 21781 <span class="blue">Max = 1.09ε (Mean = 0.502ε)</span> 21782 </p> 21783 </td> 21784</tr></tbody> 21785</table></div> 21786</div> 21787<br class="table-break"><div class="table"> 21788<a name="special_function_error_rates_rep.all_the_tables.table_erfc"></a><p class="title"><b>Table 136. Error rates for erfc</b></p> 21789<div class="table-contents"><table class="table" summary="Error rates for erfc"> 21790<colgroup> 21791<col> 21792<col> 21793<col> 21794<col> 21795<col> 21796</colgroup> 21797<thead><tr> 21798<th> 21799 </th> 21800<th> 21801 <p> 21802 GNU C++ version 7.1.0<br> linux<br> long double 21803 </p> 21804 </th> 21805<th> 21806 <p> 21807 GNU C++ version 7.1.0<br> linux<br> double 21808 </p> 21809 </th> 21810<th> 21811 <p> 21812 Sun compiler version 0x5150<br> Sun Solaris<br> long double 21813 </p> 21814 </th> 21815<th> 21816 <p> 21817 Microsoft Visual C++ version 14.1<br> Win32<br> double 21818 </p> 21819 </th> 21820</tr></thead> 21821<tbody> 21822<tr> 21823<td> 21824 <p> 21825 Erf Function: Small Values 21826 </p> 21827 </td> 21828<td> 21829 <p> 21830 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span> 21831 Max = 0ε (Mean = 0ε))<br> (<span class="emphasis"><em><math.h>:</em></span> Max 21832 = 0ε (Mean = 0ε)) 21833 </p> 21834 </td> 21835<td> 21836 <p> 21837 <span class="blue">Max = 0.658ε (Mean = 0.0537ε)</span><br> <br> 21838 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.01ε (Mean = 0.485ε)) 21839 </p> 21840 </td> 21841<td> 21842 <p> 21843 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span> 21844 Max = 0ε (Mean = 0ε)) 21845 </p> 21846 </td> 21847<td> 21848 <p> 21849 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span> 21850 Max = 0ε (Mean = 0ε)) 21851 </p> 21852 </td> 21853</tr> 21854<tr> 21855<td> 21856 <p> 21857 Erf Function: Medium Values 21858 </p> 21859 </td> 21860<td> 21861 <p> 21862 <span class="blue">Max = 1.76ε (Mean = 0.365ε)</span><br> <br> 21863 (<span class="emphasis"><em><cmath>:</em></span> Max = 1.35ε (Mean = 0.307ε))<br> 21864 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.35ε (Mean = 0.307ε)) 21865 </p> 21866 </td> 21867<td> 21868 <p> 21869 <span class="blue">Max = 0.983ε (Mean = 0.213ε)</span><br> <br> 21870 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.64ε (Mean = 0.662ε)) 21871 </p> 21872 </td> 21873<td> 21874 <p> 21875 <span class="blue">Max = 1.76ε (Mean = 0.38ε)</span><br> <br> 21876 (<span class="emphasis"><em><math.h>:</em></span> Max = 2.81ε (Mean = 0.739ε)) 21877 </p> 21878 </td> 21879<td> 21880 <p> 21881 <span class="blue">Max = 1.65ε (Mean = 0.373ε)</span><br> <br> 21882 (<span class="emphasis"><em><math.h>:</em></span> Max = 2.36ε (Mean = 0.539ε)) 21883 </p> 21884 </td> 21885</tr> 21886<tr> 21887<td> 21888 <p> 21889 Erf Function: Large Values 21890 </p> 21891 </td> 21892<td> 21893 <p> 21894 <span class="blue">Max = 1.57ε (Mean = 0.542ε)</span><br> <br> 21895 (<span class="emphasis"><em><cmath>:</em></span> Max = 1.26ε (Mean = 0.441ε))<br> 21896 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.26ε (Mean = 0.441ε)) 21897 </p> 21898 </td> 21899<td> 21900 <p> 21901 <span class="blue">Max = 0.868ε (Mean = 0.147ε)</span><br> <br> 21902 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.9ε (Mean = 0.472ε)) 21903 </p> 21904 </td> 21905<td> 21906 <p> 21907 <span class="blue">Max = 1.57ε (Mean = 0.564ε)</span><br> <br> 21908 (<span class="emphasis"><em><math.h>:</em></span> Max = 4.91ε (Mean = 1.54ε)) 21909 </p> 21910 </td> 21911<td> 21912 <p> 21913 <span class="blue">Max = 1.14ε (Mean = 0.248ε)</span><br> <br> 21914 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.84ε (Mean = 0.331ε)) 21915 </p> 21916 </td> 21917</tr> 21918</tbody> 21919</table></div> 21920</div> 21921<br class="table-break"><div class="table"> 21922<a name="special_function_error_rates_rep.all_the_tables.table_erfc_inv"></a><p class="title"><b>Table 137. Error rates for erfc_inv</b></p> 21923<div class="table-contents"><table class="table" summary="Error rates for erfc_inv"> 21924<colgroup> 21925<col> 21926<col> 21927<col> 21928<col> 21929<col> 21930</colgroup> 21931<thead><tr> 21932<th> 21933 </th> 21934<th> 21935 <p> 21936 GNU C++ version 7.1.0<br> linux<br> double 21937 </p> 21938 </th> 21939<th> 21940 <p> 21941 GNU C++ version 7.1.0<br> linux<br> long double 21942 </p> 21943 </th> 21944<th> 21945 <p> 21946 Sun compiler version 0x5150<br> Sun Solaris<br> long double 21947 </p> 21948 </th> 21949<th> 21950 <p> 21951 Microsoft Visual C++ version 14.1<br> Win32<br> double 21952 </p> 21953 </th> 21954</tr></thead> 21955<tbody> 21956<tr> 21957<td> 21958 <p> 21959 Inverse Erfc Function 21960 </p> 21961 </td> 21962<td> 21963 <p> 21964 <span class="blue">Max = 0ε (Mean = 0ε)</span> 21965 </p> 21966 </td> 21967<td> 21968 <p> 21969 <span class="blue">Max = 0.996ε (Mean = 0.397ε)</span> 21970 </p> 21971 </td> 21972<td> 21973 <p> 21974 <span class="blue">Max = 1.08ε (Mean = 0.403ε)</span> 21975 </p> 21976 </td> 21977<td> 21978 <p> 21979 <span class="blue">Max = 1ε (Mean = 0.491ε)</span> 21980 </p> 21981 </td> 21982</tr> 21983<tr> 21984<td> 21985 <p> 21986 Inverse Erfc Function: extreme values 21987 </p> 21988 </td> 21989<td> 21990 </td> 21991<td> 21992 <p> 21993 <span class="blue">Max = 1.62ε (Mean = 0.383ε)</span> 21994 </p> 21995 </td> 21996<td> 21997 <p> 21998 <span class="blue">Max = 1.62ε (Mean = 0.383ε)</span> 21999 </p> 22000 </td> 22001<td> 22002 </td> 22003</tr> 22004</tbody> 22005</table></div> 22006</div> 22007<br class="table-break"><div class="table"> 22008<a name="special_function_error_rates_rep.all_the_tables.table_expint_Ei_"></a><p class="title"><b>Table 138. Error rates for expint (Ei)</b></p> 22009<div class="table-contents"><table class="table" summary="Error rates for expint (Ei)"> 22010<colgroup> 22011<col> 22012<col> 22013<col> 22014<col> 22015<col> 22016</colgroup> 22017<thead><tr> 22018<th> 22019 </th> 22020<th> 22021 <p> 22022 GNU C++ version 7.1.0<br> linux<br> long double 22023 </p> 22024 </th> 22025<th> 22026 <p> 22027 GNU C++ version 7.1.0<br> linux<br> double 22028 </p> 22029 </th> 22030<th> 22031 <p> 22032 Sun compiler version 0x5150<br> Sun Solaris<br> long double 22033 </p> 22034 </th> 22035<th> 22036 <p> 22037 Microsoft Visual C++ version 14.1<br> Win32<br> double 22038 </p> 22039 </th> 22040</tr></thead> 22041<tbody> 22042<tr> 22043<td> 22044 <p> 22045 Exponential Integral Ei 22046 </p> 22047 </td> 22048<td> 22049 <p> 22050 <span class="blue">Max = 5.05ε (Mean = 0.821ε)</span><br> <br> 22051 (<span class="emphasis"><em><cmath>:</em></span> Max = 14.1ε (Mean = 2.43ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_expint_Ei___cmath__Exponential_Integral_Ei">And 22052 other failures.</a>) 22053 </p> 22054 </td> 22055<td> 22056 <p> 22057 <span class="blue">Max = 0.994ε (Mean = 0.142ε)</span><br> <br> 22058 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.96ε (Mean = 0.703ε)) 22059 </p> 22060 </td> 22061<td> 22062 <p> 22063 <span class="blue">Max = 5.05ε (Mean = 0.835ε)</span> 22064 </p> 22065 </td> 22066<td> 22067 <p> 22068 <span class="blue">Max = 1.43ε (Mean = 0.54ε)</span> 22069 </p> 22070 </td> 22071</tr> 22072<tr> 22073<td> 22074 <p> 22075 Exponential Integral Ei: double exponent range 22076 </p> 22077 </td> 22078<td> 22079 <p> 22080 <span class="blue">Max = 1.72ε (Mean = 0.593ε)</span><br> <br> 22081 (<span class="emphasis"><em><cmath>:</em></span> Max = 3.11ε (Mean = 1.13ε)) 22082 </p> 22083 </td> 22084<td> 22085 <p> 22086 <span class="blue">Max = 0.998ε (Mean = 0.156ε)</span><br> <br> 22087 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.5ε (Mean = 0.612ε)) 22088 </p> 22089 </td> 22090<td> 22091 <p> 22092 <span class="blue">Max = 1.72ε (Mean = 0.607ε)</span> 22093 </p> 22094 </td> 22095<td> 22096 <p> 22097 <span class="blue">Max = 1.7ε (Mean = 0.66ε)</span> 22098 </p> 22099 </td> 22100</tr> 22101<tr> 22102<td> 22103 <p> 22104 Exponential Integral Ei: long exponent range 22105 </p> 22106 </td> 22107<td> 22108 <p> 22109 <span class="blue">Max = 1.98ε (Mean = 0.595ε)</span><br> <br> 22110 (<span class="emphasis"><em><cmath>:</em></span> Max = 1.93ε (Mean = 0.855ε)) 22111 </p> 22112 </td> 22113<td> 22114 </td> 22115<td> 22116 <p> 22117 <span class="blue">Max = 1.98ε (Mean = 0.575ε)</span> 22118 </p> 22119 </td> 22120<td> 22121 </td> 22122</tr> 22123</tbody> 22124</table></div> 22125</div> 22126<br class="table-break"><div class="table"> 22127<a name="special_function_error_rates_rep.all_the_tables.table_expint_En_"></a><p class="title"><b>Table 139. Error rates for expint (En)</b></p> 22128<div class="table-contents"><table class="table" summary="Error rates for expint (En)"> 22129<colgroup> 22130<col> 22131<col> 22132<col> 22133<col> 22134<col> 22135</colgroup> 22136<thead><tr> 22137<th> 22138 </th> 22139<th> 22140 <p> 22141 GNU C++ version 7.1.0<br> linux<br> double 22142 </p> 22143 </th> 22144<th> 22145 <p> 22146 GNU C++ version 7.1.0<br> linux<br> long double 22147 </p> 22148 </th> 22149<th> 22150 <p> 22151 Sun compiler version 0x5150<br> Sun Solaris<br> long double 22152 </p> 22153 </th> 22154<th> 22155 <p> 22156 Microsoft Visual C++ version 14.1<br> Win32<br> double 22157 </p> 22158 </th> 22159</tr></thead> 22160<tbody> 22161<tr> 22162<td> 22163 <p> 22164 Exponential Integral En 22165 </p> 22166 </td> 22167<td> 22168 <p> 22169 <span class="blue">Max = 0.589ε (Mean = 0.0331ε)</span><br> <br> 22170 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 58.5ε (Mean = 17.1ε)) 22171 </p> 22172 </td> 22173<td> 22174 <p> 22175 <span class="blue">Max = 9.97ε (Mean = 2.13ε)</span> 22176 </p> 22177 </td> 22178<td> 22179 <p> 22180 <span class="blue">Max = 9.97ε (Mean = 2.13ε)</span> 22181 </p> 22182 </td> 22183<td> 22184 <p> 22185 <span class="blue">Max = 7.16ε (Mean = 1.85ε)</span> 22186 </p> 22187 </td> 22188</tr> 22189<tr> 22190<td> 22191 <p> 22192 Exponential Integral En: small z values 22193 </p> 22194 </td> 22195<td> 22196 <p> 22197 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 22198 2.1:</em></span> Max = 115ε (Mean = 23.6ε)) 22199 </p> 22200 </td> 22201<td> 22202 <p> 22203 <span class="blue">Max = 1.99ε (Mean = 0.559ε)</span> 22204 </p> 22205 </td> 22206<td> 22207 <p> 22208 <span class="blue">Max = 1.99ε (Mean = 0.559ε)</span> 22209 </p> 22210 </td> 22211<td> 22212 <p> 22213 <span class="blue">Max = 2.62ε (Mean = 0.531ε)</span> 22214 </p> 22215 </td> 22216</tr> 22217<tr> 22218<td> 22219 <p> 22220 Exponential Integral E1 22221 </p> 22222 </td> 22223<td> 22224 <p> 22225 <span class="blue">Max = 0.556ε (Mean = 0.0625ε)</span><br> <br> 22226 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.988ε (Mean = 0.469ε)) 22227 </p> 22228 </td> 22229<td> 22230 <p> 22231 <span class="blue">Max = 0.965ε (Mean = 0.414ε)</span> 22232 </p> 22233 </td> 22234<td> 22235 <p> 22236 <span class="blue">Max = 0.965ε (Mean = 0.408ε)</span> 22237 </p> 22238 </td> 22239<td> 22240 <p> 22241 <span class="blue">Max = 0.988ε (Mean = 0.486ε)</span> 22242 </p> 22243 </td> 22244</tr> 22245</tbody> 22246</table></div> 22247</div> 22248<br class="table-break"><div class="table"> 22249<a name="special_function_error_rates_rep.all_the_tables.table_expm1"></a><p class="title"><b>Table 140. Error rates for expm1</b></p> 22250<div class="table-contents"><table class="table" summary="Error rates for expm1"> 22251<colgroup> 22252<col> 22253<col> 22254<col> 22255<col> 22256<col> 22257</colgroup> 22258<thead><tr> 22259<th> 22260 </th> 22261<th> 22262 <p> 22263 GNU C++ version 7.1.0<br> linux<br> long double 22264 </p> 22265 </th> 22266<th> 22267 <p> 22268 GNU C++ version 7.1.0<br> linux<br> double 22269 </p> 22270 </th> 22271<th> 22272 <p> 22273 Sun compiler version 0x5150<br> Sun Solaris<br> long double 22274 </p> 22275 </th> 22276<th> 22277 <p> 22278 Microsoft Visual C++ version 14.1<br> Win32<br> double 22279 </p> 22280 </th> 22281</tr></thead> 22282<tbody><tr> 22283<td> 22284 <p> 22285 Random test data 22286 </p> 22287 </td> 22288<td> 22289 <p> 22290 <span class="blue">Max = 0.992ε (Mean = 0.402ε)</span><br> <br> 22291 (<span class="emphasis"><em><cmath>:</em></span> Max = 0.992ε (Mean = 0.402ε))<br> 22292 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.992ε (Mean = 0.402ε)) 22293 </p> 22294 </td> 22295<td> 22296 <p> 22297 <span class="blue">Max = 0.793ε (Mean = 0.126ε)</span><br> <br> 22298 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 0.793ε (Mean = 0.126ε)) 22299 </p> 22300 </td> 22301<td> 22302 <p> 22303 <span class="blue">Max = 1.31ε (Mean = 0.428ε)</span><br> <br> 22304 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.996ε (Mean = 0.426ε)) 22305 </p> 22306 </td> 22307<td> 22308 <p> 22309 <span class="blue">Max = 1.31ε (Mean = 0.496ε)</span><br> <br> 22310 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.31ε (Mean = 0.496ε)) 22311 </p> 22312 </td> 22313</tr></tbody> 22314</table></div> 22315</div> 22316<br class="table-break"><div class="table"> 22317<a name="special_function_error_rates_rep.all_the_tables.table_gamma_p"></a><p class="title"><b>Table 141. Error rates for gamma_p</b></p> 22318<div class="table-contents"><table class="table" summary="Error rates for gamma_p"> 22319<colgroup> 22320<col> 22321<col> 22322<col> 22323<col> 22324<col> 22325</colgroup> 22326<thead><tr> 22327<th> 22328 </th> 22329<th> 22330 <p> 22331 GNU C++ version 7.1.0<br> linux<br> double 22332 </p> 22333 </th> 22334<th> 22335 <p> 22336 GNU C++ version 7.1.0<br> linux<br> long double 22337 </p> 22338 </th> 22339<th> 22340 <p> 22341 Sun compiler version 0x5150<br> Sun Solaris<br> long double 22342 </p> 22343 </th> 22344<th> 22345 <p> 22346 Microsoft Visual C++ version 14.1<br> Win32<br> double 22347 </p> 22348 </th> 22349</tr></thead> 22350<tbody> 22351<tr> 22352<td> 22353 <p> 22354 tgamma(a, z) medium values 22355 </p> 22356 </td> 22357<td> 22358 <p> 22359 <span class="blue">Max = 0.955ε (Mean = 0.05ε)</span><br> <br> 22360 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 342ε (Mean = 45.8ε))<br> (<span class="emphasis"><em>Rmath 22361 3.2.3:</em></span> Max = 389ε (Mean = 44ε)) 22362 </p> 22363 </td> 22364<td> 22365 <p> 22366 <span class="blue">Max = 41.6ε (Mean = 8.09ε)</span> 22367 </p> 22368 </td> 22369<td> 22370 <p> 22371 <span class="blue">Max = 239ε (Mean = 30.2ε)</span> 22372 </p> 22373 </td> 22374<td> 22375 <p> 22376 <span class="blue">Max = 35.1ε (Mean = 6.98ε)</span> 22377 </p> 22378 </td> 22379</tr> 22380<tr> 22381<td> 22382 <p> 22383 tgamma(a, z) small values 22384 </p> 22385 </td> 22386<td> 22387 <p> 22388 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 22389 2.1:</em></span> Max = 4.82ε (Mean = 0.758ε))<br> (<span class="emphasis"><em>Rmath 22390 3.2.3:</em></span> Max = 1.01ε (Mean = 0.306ε)) 22391 </p> 22392 </td> 22393<td> 22394 <p> 22395 <span class="blue">Max = 2ε (Mean = 0.464ε)</span> 22396 </p> 22397 </td> 22398<td> 22399 <p> 22400 <span class="blue">Max = 2ε (Mean = 0.461ε)</span> 22401 </p> 22402 </td> 22403<td> 22404 <p> 22405 <span class="blue">Max = 1.54ε (Mean = 0.439ε)</span> 22406 </p> 22407 </td> 22408</tr> 22409<tr> 22410<td> 22411 <p> 22412 tgamma(a, z) large values 22413 </p> 22414 </td> 22415<td> 22416 <p> 22417 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 22418 2.1:</em></span> Max = 1.02e+03ε (Mean = 105ε))<br> (<span class="emphasis"><em>Rmath 22419 3.2.3:</em></span> Max = 1.11e+03ε (Mean = 67.5ε)) 22420 </p> 22421 </td> 22422<td> 22423 <p> 22424 <span class="blue">Max = 3.08e+04ε (Mean = 1.86e+03ε)</span> 22425 </p> 22426 </td> 22427<td> 22428 <p> 22429 <span class="blue">Max = 3.02e+04ε (Mean = 1.91e+03ε)</span> 22430 </p> 22431 </td> 22432<td> 22433 <p> 22434 <span class="blue">Max = 243ε (Mean = 20.2ε)</span> 22435 </p> 22436 </td> 22437</tr> 22438<tr> 22439<td> 22440 <p> 22441 tgamma(a, z) integer and half integer values 22442 </p> 22443 </td> 22444<td> 22445 <p> 22446 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 22447 2.1:</em></span> Max = 128ε (Mean = 22.6ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 22448 Max = 66.2ε (Mean = 12.2ε)) 22449 </p> 22450 </td> 22451<td> 22452 <p> 22453 <span class="blue">Max = 11.8ε (Mean = 2.66ε)</span> 22454 </p> 22455 </td> 22456<td> 22457 <p> 22458 <span class="blue">Max = 71.6ε (Mean = 9.47ε)</span> 22459 </p> 22460 </td> 22461<td> 22462 <p> 22463 <span class="blue">Max = 13ε (Mean = 2.97ε)</span> 22464 </p> 22465 </td> 22466</tr> 22467</tbody> 22468</table></div> 22469</div> 22470<br class="table-break"><div class="table"> 22471<a name="special_function_error_rates_rep.all_the_tables.table_gamma_p_inv"></a><p class="title"><b>Table 142. Error rates for gamma_p_inv</b></p> 22472<div class="table-contents"><table class="table" summary="Error rates for gamma_p_inv"> 22473<colgroup> 22474<col> 22475<col> 22476<col> 22477<col> 22478<col> 22479</colgroup> 22480<thead><tr> 22481<th> 22482 </th> 22483<th> 22484 <p> 22485 GNU C++ version 7.1.0<br> linux<br> double 22486 </p> 22487 </th> 22488<th> 22489 <p> 22490 GNU C++ version 7.1.0<br> linux<br> long double 22491 </p> 22492 </th> 22493<th> 22494 <p> 22495 Sun compiler version 0x5150<br> Sun Solaris<br> long double 22496 </p> 22497 </th> 22498<th> 22499 <p> 22500 Microsoft Visual C++ version 14.1<br> Win32<br> double 22501 </p> 22502 </th> 22503</tr></thead> 22504<tbody> 22505<tr> 22506<td> 22507 <p> 22508 incomplete gamma inverse(a, z) medium values 22509 </p> 22510 </td> 22511<td> 22512 <p> 22513 <span class="blue">Max = 0.993ε (Mean = 0.15ε)</span><br> <br> 22514 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 4.88ε (Mean = 0.868ε)) 22515 </p> 22516 </td> 22517<td> 22518 <p> 22519 <span class="blue">Max = 1.8ε (Mean = 0.406ε)</span> 22520 </p> 22521 </td> 22522<td> 22523 <p> 22524 <span class="blue">Max = 1.89ε (Mean = 0.466ε)</span> 22525 </p> 22526 </td> 22527<td> 22528 <p> 22529 <span class="blue">Max = 1.71ε (Mean = 0.34ε)</span> 22530 </p> 22531 </td> 22532</tr> 22533<tr> 22534<td> 22535 <p> 22536 incomplete gamma inverse(a, z) large values 22537 </p> 22538 </td> 22539<td> 22540 <p> 22541 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath 22542 3.2.3:</em></span> Max = 0.816ε (Mean = 0.0874ε)) 22543 </p> 22544 </td> 22545<td> 22546 <p> 22547 <span class="blue">Max = 0.509ε (Mean = 0.0447ε)</span> 22548 </p> 22549 </td> 22550<td> 22551 <p> 22552 <span class="blue">Max = 0.509ε (Mean = 0.0447ε)</span> 22553 </p> 22554 </td> 22555<td> 22556 <p> 22557 <span class="blue">Max = 0.924ε (Mean = 0.108ε)</span> 22558 </p> 22559 </td> 22560</tr> 22561<tr> 22562<td> 22563 <p> 22564 incomplete gamma inverse(a, z) small values 22565 </p> 22566 </td> 22567<td> 22568 <p> 22569 <span class="blue">Max = 441ε (Mean = 53.9ε)</span><br> <br> 22570 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 547ε (Mean = 61.6ε)) 22571 </p> 22572 </td> 22573<td> 22574 <p> 22575 <span class="blue">Max = 9.17e+03ε (Mean = 1.45e+03ε)</span> 22576 </p> 22577 </td> 22578<td> 22579 <p> 22580 <span class="blue">Max = 1.09e+04ε (Mean = 1.3e+03ε)</span> 22581 </p> 22582 </td> 22583<td> 22584 <p> 22585 <span class="blue">Max = 1.1e+03ε (Mean = 131ε)</span> 22586 </p> 22587 </td> 22588</tr> 22589</tbody> 22590</table></div> 22591</div> 22592<br class="table-break"><div class="table"> 22593<a name="special_function_error_rates_rep.all_the_tables.table_gamma_p_inva"></a><p class="title"><b>Table 143. Error rates for gamma_p_inva</b></p> 22594<div class="table-contents"><table class="table" summary="Error rates for gamma_p_inva"> 22595<colgroup> 22596<col> 22597<col> 22598<col> 22599<col> 22600<col> 22601</colgroup> 22602<thead><tr> 22603<th> 22604 </th> 22605<th> 22606 <p> 22607 GNU C++ version 7.1.0<br> linux<br> double 22608 </p> 22609 </th> 22610<th> 22611 <p> 22612 GNU C++ version 7.1.0<br> linux<br> long double 22613 </p> 22614 </th> 22615<th> 22616 <p> 22617 Sun compiler version 0x5150<br> Sun Solaris<br> long double 22618 </p> 22619 </th> 22620<th> 22621 <p> 22622 Microsoft Visual C++ version 14.1<br> Win32<br> double 22623 </p> 22624 </th> 22625</tr></thead> 22626<tbody><tr> 22627<td> 22628 <p> 22629 Incomplete gamma inverses. 22630 </p> 22631 </td> 22632<td> 22633 <p> 22634 <span class="blue">Max = 0ε (Mean = 0ε)</span> 22635 </p> 22636 </td> 22637<td> 22638 <p> 22639 <span class="blue">Max = 7.87ε (Mean = 1.15ε)</span> 22640 </p> 22641 </td> 22642<td> 22643 <p> 22644 <span class="blue">Max = 4.08ε (Mean = 1.12ε)</span> 22645 </p> 22646 </td> 22647<td> 22648 <p> 22649 <span class="blue">Max = 4.92ε (Mean = 1.03ε)</span> 22650 </p> 22651 </td> 22652</tr></tbody> 22653</table></div> 22654</div> 22655<br class="table-break"><div class="table"> 22656<a name="special_function_error_rates_rep.all_the_tables.table_gamma_q"></a><p class="title"><b>Table 144. Error rates for gamma_q</b></p> 22657<div class="table-contents"><table class="table" summary="Error rates for gamma_q"> 22658<colgroup> 22659<col> 22660<col> 22661<col> 22662<col> 22663<col> 22664</colgroup> 22665<thead><tr> 22666<th> 22667 </th> 22668<th> 22669 <p> 22670 GNU C++ version 7.1.0<br> linux<br> double 22671 </p> 22672 </th> 22673<th> 22674 <p> 22675 GNU C++ version 7.1.0<br> linux<br> long double 22676 </p> 22677 </th> 22678<th> 22679 <p> 22680 Sun compiler version 0x5150<br> Sun Solaris<br> long double 22681 </p> 22682 </th> 22683<th> 22684 <p> 22685 Microsoft Visual C++ version 14.1<br> Win32<br> double 22686 </p> 22687 </th> 22688</tr></thead> 22689<tbody> 22690<tr> 22691<td> 22692 <p> 22693 tgamma(a, z) medium values 22694 </p> 22695 </td> 22696<td> 22697 <p> 22698 <span class="blue">Max = 0.927ε (Mean = 0.035ε)</span><br> <br> 22699 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 201ε (Mean = 13.5ε))<br> (<span class="emphasis"><em>Rmath 22700 3.2.3:</em></span> Max = 131ε (Mean = 12.7ε)) 22701 </p> 22702 </td> 22703<td> 22704 <p> 22705 <span class="blue">Max = 32.3ε (Mean = 6.61ε)</span> 22706 </p> 22707 </td> 22708<td> 22709 <p> 22710 <span class="blue">Max = 199ε (Mean = 26.6ε)</span> 22711 </p> 22712 </td> 22713<td> 22714 <p> 22715 <span class="blue">Max = 23.7ε (Mean = 4ε)</span> 22716 </p> 22717 </td> 22718</tr> 22719<tr> 22720<td> 22721 <p> 22722 tgamma(a, z) small values 22723 </p> 22724 </td> 22725<td> 22726 <p> 22727 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 22728 2.1:</em></span> <span class="red">Max = 1.38e+10ε (Mean = 1.05e+09ε))</span><br> 22729 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 65.6ε (Mean = 11ε)) 22730 </p> 22731 </td> 22732<td> 22733 <p> 22734 <span class="blue">Max = 2.45ε (Mean = 0.885ε)</span> 22735 </p> 22736 </td> 22737<td> 22738 <p> 22739 <span class="blue">Max = 2.45ε (Mean = 0.819ε)</span> 22740 </p> 22741 </td> 22742<td> 22743 <p> 22744 <span class="blue">Max = 2.26ε (Mean = 0.74ε)</span> 22745 </p> 22746 </td> 22747</tr> 22748<tr> 22749<td> 22750 <p> 22751 tgamma(a, z) large values 22752 </p> 22753 </td> 22754<td> 22755 <p> 22756 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 22757 2.1:</em></span> Max = 2.71e+04ε (Mean = 2.16e+03ε))<br> (<span class="emphasis"><em>Rmath 22758 3.2.3:</em></span> Max = 1.02e+03ε (Mean = 62.7ε)) 22759 </p> 22760 </td> 22761<td> 22762 <p> 22763 <span class="blue">Max = 6.82e+03ε (Mean = 414ε)</span> 22764 </p> 22765 </td> 22766<td> 22767 <p> 22768 <span class="blue">Max = 1.15e+04ε (Mean = 733ε)</span> 22769 </p> 22770 </td> 22771<td> 22772 <p> 22773 <span class="blue">Max = 469ε (Mean = 31.5ε)</span> 22774 </p> 22775 </td> 22776</tr> 22777<tr> 22778<td> 22779 <p> 22780 tgamma(a, z) integer and half integer values 22781 </p> 22782 </td> 22783<td> 22784 <p> 22785 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 22786 2.1:</em></span> Max = 118ε (Mean = 12.5ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 22787 Max = 138ε (Mean = 16.9ε)) 22788 </p> 22789 </td> 22790<td> 22791 <p> 22792 <span class="blue">Max = 11.1ε (Mean = 2.07ε)</span> 22793 </p> 22794 </td> 22795<td> 22796 <p> 22797 <span class="blue">Max = 54.7ε (Mean = 6.16ε)</span> 22798 </p> 22799 </td> 22800<td> 22801 <p> 22802 <span class="blue">Max = 8.72ε (Mean = 1.48ε)</span> 22803 </p> 22804 </td> 22805</tr> 22806</tbody> 22807</table></div> 22808</div> 22809<br class="table-break"><div class="table"> 22810<a name="special_function_error_rates_rep.all_the_tables.table_gamma_q_inv"></a><p class="title"><b>Table 145. Error rates for gamma_q_inv</b></p> 22811<div class="table-contents"><table class="table" summary="Error rates for gamma_q_inv"> 22812<colgroup> 22813<col> 22814<col> 22815<col> 22816<col> 22817<col> 22818</colgroup> 22819<thead><tr> 22820<th> 22821 </th> 22822<th> 22823 <p> 22824 GNU C++ version 7.1.0<br> linux<br> double 22825 </p> 22826 </th> 22827<th> 22828 <p> 22829 GNU C++ version 7.1.0<br> linux<br> long double 22830 </p> 22831 </th> 22832<th> 22833 <p> 22834 Sun compiler version 0x5150<br> Sun Solaris<br> long double 22835 </p> 22836 </th> 22837<th> 22838 <p> 22839 Microsoft Visual C++ version 14.1<br> Win32<br> double 22840 </p> 22841 </th> 22842</tr></thead> 22843<tbody> 22844<tr> 22845<td> 22846 <p> 22847 incomplete gamma inverse(a, z) medium values 22848 </p> 22849 </td> 22850<td> 22851 <p> 22852 <span class="blue">Max = 0.912ε (Mean = 0.154ε)</span><br> <br> 22853 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 4.66ε (Mean = 0.792ε)) 22854 </p> 22855 </td> 22856<td> 22857 <p> 22858 <span class="blue">Max = 6.2ε (Mean = 0.627ε)</span> 22859 </p> 22860 </td> 22861<td> 22862 <p> 22863 <span class="blue">Max = 6.2ε (Mean = 0.683ε)</span> 22864 </p> 22865 </td> 22866<td> 22867 <p> 22868 <span class="blue">Max = 2.88ε (Mean = 0.469ε)</span> 22869 </p> 22870 </td> 22871</tr> 22872<tr> 22873<td> 22874 <p> 22875 incomplete gamma inverse(a, z) large values 22876 </p> 22877 </td> 22878<td> 22879 <p> 22880 <span class="blue">Max = 0.894ε (Mean = 0.0915ε)</span><br> <br> 22881 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 0.894ε (Mean = 0.106ε)) 22882 </p> 22883 </td> 22884<td> 22885 <p> 22886 <span class="blue">Max = 0ε (Mean = 0ε)</span> 22887 </p> 22888 </td> 22889<td> 22890 <p> 22891 <span class="blue">Max = 0ε (Mean = 0ε)</span> 22892 </p> 22893 </td> 22894<td> 22895 <p> 22896 <span class="blue">Max = 0.814ε (Mean = 0.0856ε)</span> 22897 </p> 22898 </td> 22899</tr> 22900<tr> 22901<td> 22902 <p> 22903 incomplete gamma inverse(a, z) small values 22904 </p> 22905 </td> 22906<td> 22907 <p> 22908 <span class="blue">Max = 292ε (Mean = 36.4ε)</span><br> <br> 22909 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 415ε (Mean = 48.7ε)) 22910 </p> 22911 </td> 22912<td> 22913 <p> 22914 <span class="blue">Max = 8.28e+03ε (Mean = 1.09e+03ε)</span> 22915 </p> 22916 </td> 22917<td> 22918 <p> 22919 <span class="blue">Max = 8.98e+03ε (Mean = 877ε)</span> 22920 </p> 22921 </td> 22922<td> 22923 <p> 22924 <span class="blue">Max = 451ε (Mean = 64.7ε)</span> 22925 </p> 22926 </td> 22927</tr> 22928</tbody> 22929</table></div> 22930</div> 22931<br class="table-break"><div class="table"> 22932<a name="special_function_error_rates_rep.all_the_tables.table_gamma_q_inva"></a><p class="title"><b>Table 146. Error rates for gamma_q_inva</b></p> 22933<div class="table-contents"><table class="table" summary="Error rates for gamma_q_inva"> 22934<colgroup> 22935<col> 22936<col> 22937<col> 22938<col> 22939<col> 22940</colgroup> 22941<thead><tr> 22942<th> 22943 </th> 22944<th> 22945 <p> 22946 GNU C++ version 7.1.0<br> linux<br> double 22947 </p> 22948 </th> 22949<th> 22950 <p> 22951 GNU C++ version 7.1.0<br> linux<br> long double 22952 </p> 22953 </th> 22954<th> 22955 <p> 22956 Sun compiler version 0x5150<br> Sun Solaris<br> long double 22957 </p> 22958 </th> 22959<th> 22960 <p> 22961 Microsoft Visual C++ version 14.1<br> Win32<br> double 22962 </p> 22963 </th> 22964</tr></thead> 22965<tbody><tr> 22966<td> 22967 <p> 22968 Incomplete gamma inverses. 22969 </p> 22970 </td> 22971<td> 22972 <p> 22973 <span class="blue">Max = 0ε (Mean = 0ε)</span> 22974 </p> 22975 </td> 22976<td> 22977 <p> 22978 <span class="blue">Max = 8.42ε (Mean = 1.3ε)</span> 22979 </p> 22980 </td> 22981<td> 22982 <p> 22983 <span class="blue">Max = 7.86ε (Mean = 1.24ε)</span> 22984 </p> 22985 </td> 22986<td> 22987 <p> 22988 <span class="blue">Max = 5.05ε (Mean = 1.08ε)</span> 22989 </p> 22990 </td> 22991</tr></tbody> 22992</table></div> 22993</div> 22994<br class="table-break"><div class="table"> 22995<a name="special_function_error_rates_rep.all_the_tables.table_hermite"></a><p class="title"><b>Table 147. Error rates for hermite</b></p> 22996<div class="table-contents"><table class="table" summary="Error rates for hermite"> 22997<colgroup> 22998<col> 22999<col> 23000<col> 23001<col> 23002<col> 23003</colgroup> 23004<thead><tr> 23005<th> 23006 </th> 23007<th> 23008 <p> 23009 GNU C++ version 7.1.0<br> linux<br> double 23010 </p> 23011 </th> 23012<th> 23013 <p> 23014 GNU C++ version 7.1.0<br> linux<br> long double 23015 </p> 23016 </th> 23017<th> 23018 <p> 23019 Sun compiler version 0x5150<br> Sun Solaris<br> long double 23020 </p> 23021 </th> 23022<th> 23023 <p> 23024 Microsoft Visual C++ version 14.1<br> Win32<br> double 23025 </p> 23026 </th> 23027</tr></thead> 23028<tbody><tr> 23029<td> 23030 <p> 23031 Hermite Polynomials 23032 </p> 23033 </td> 23034<td> 23035 <p> 23036 <span class="blue">Max = 0ε (Mean = 0ε)</span> 23037 </p> 23038 </td> 23039<td> 23040 <p> 23041 <span class="blue">Max = 6.24ε (Mean = 2.07ε)</span> 23042 </p> 23043 </td> 23044<td> 23045 <p> 23046 <span class="blue">Max = 6.24ε (Mean = 2.07ε)</span> 23047 </p> 23048 </td> 23049<td> 23050 <p> 23051 <span class="blue">Max = 4.46ε (Mean = 1.41ε)</span> 23052 </p> 23053 </td> 23054</tr></tbody> 23055</table></div> 23056</div> 23057<br class="table-break"><div class="table"> 23058<a name="special_function_error_rates_rep.all_the_tables.table_heuman_lambda"></a><p class="title"><b>Table 148. Error rates for heuman_lambda</b></p> 23059<div class="table-contents"><table class="table" summary="Error rates for heuman_lambda"> 23060<colgroup> 23061<col> 23062<col> 23063<col> 23064<col> 23065<col> 23066</colgroup> 23067<thead><tr> 23068<th> 23069 </th> 23070<th> 23071 <p> 23072 GNU C++ version 7.1.0<br> linux<br> double 23073 </p> 23074 </th> 23075<th> 23076 <p> 23077 GNU C++ version 7.1.0<br> linux<br> long double 23078 </p> 23079 </th> 23080<th> 23081 <p> 23082 Sun compiler version 0x5150<br> Sun Solaris<br> long double 23083 </p> 23084 </th> 23085<th> 23086 <p> 23087 Microsoft Visual C++ version 14.1<br> Win32<br> double 23088 </p> 23089 </th> 23090</tr></thead> 23091<tbody> 23092<tr> 23093<td> 23094 <p> 23095 Elliptic Integral Jacobi Zeta: Mathworld Data 23096 </p> 23097 </td> 23098<td> 23099 <p> 23100 <span class="blue">Max = 0ε (Mean = 0ε)</span> 23101 </p> 23102 </td> 23103<td> 23104 <p> 23105 <span class="blue">Max = 1.89ε (Mean = 0.887ε)</span> 23106 </p> 23107 </td> 23108<td> 23109 <p> 23110 <span class="blue">Max = 1.89ε (Mean = 0.887ε)</span> 23111 </p> 23112 </td> 23113<td> 23114 <p> 23115 <span class="blue">Max = 1.08ε (Mean = 0.734ε)</span> 23116 </p> 23117 </td> 23118</tr> 23119<tr> 23120<td> 23121 <p> 23122 Elliptic Integral Heuman Lambda: Random Data 23123 </p> 23124 </td> 23125<td> 23126 <p> 23127 <span class="blue">Max = 0ε (Mean = 0ε)</span> 23128 </p> 23129 </td> 23130<td> 23131 <p> 23132 <span class="blue">Max = 3.82ε (Mean = 0.609ε)</span> 23133 </p> 23134 </td> 23135<td> 23136 <p> 23137 <span class="blue">Max = 3.82ε (Mean = 0.608ε)</span> 23138 </p> 23139 </td> 23140<td> 23141 <p> 23142 <span class="blue">Max = 2.12ε (Mean = 0.588ε)</span> 23143 </p> 23144 </td> 23145</tr> 23146</tbody> 23147</table></div> 23148</div> 23149<br class="table-break"><div class="table"> 23150<a name="special_function_error_rates_rep.all_the_tables.table_ibeta"></a><p class="title"><b>Table 149. Error rates for ibeta</b></p> 23151<div class="table-contents"><table class="table" summary="Error rates for ibeta"> 23152<colgroup> 23153<col> 23154<col> 23155<col> 23156<col> 23157<col> 23158</colgroup> 23159<thead><tr> 23160<th> 23161 </th> 23162<th> 23163 <p> 23164 GNU C++ version 7.1.0<br> linux<br> double 23165 </p> 23166 </th> 23167<th> 23168 <p> 23169 GNU C++ version 7.1.0<br> linux<br> long double 23170 </p> 23171 </th> 23172<th> 23173 <p> 23174 Sun compiler version 0x5150<br> Sun Solaris<br> long double 23175 </p> 23176 </th> 23177<th> 23178 <p> 23179 Microsoft Visual C++ version 14.1<br> Win32<br> double 23180 </p> 23181 </th> 23182</tr></thead> 23183<tbody> 23184<tr> 23185<td> 23186 <p> 23187 Incomplete Beta Function: Small Values 23188 </p> 23189 </td> 23190<td> 23191 <p> 23192 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 23193 2.1:</em></span> Max = 682ε (Mean = 32.6ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 23194 Max = 22.9ε (Mean = 3.35ε)) 23195 </p> 23196 </td> 23197<td> 23198 <p> 23199 <span class="blue">Max = 8.97ε (Mean = 2.09ε)</span> 23200 </p> 23201 </td> 23202<td> 23203 <p> 23204 <span class="blue">Max = 21.3ε (Mean = 2.75ε)</span> 23205 </p> 23206 </td> 23207<td> 23208 <p> 23209 <span class="blue">Max = 8.4ε (Mean = 1.93ε)</span> 23210 </p> 23211 </td> 23212</tr> 23213<tr> 23214<td> 23215 <p> 23216 Incomplete Beta Function: Medium Values 23217 </p> 23218 </td> 23219<td> 23220 <p> 23221 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 23222 2.1:</em></span> Max = 690ε (Mean = 151ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 23223 Max = 232ε (Mean = 27.9ε)) 23224 </p> 23225 </td> 23226<td> 23227 <p> 23228 <span class="blue">Max = 50ε (Mean = 12.1ε)</span> 23229 </p> 23230 </td> 23231<td> 23232 <p> 23233 <span class="blue">Max = 124ε (Mean = 18.4ε)</span> 23234 </p> 23235 </td> 23236<td> 23237 <p> 23238 <span class="blue">Max = 106ε (Mean = 16.3ε)</span> 23239 </p> 23240 </td> 23241</tr> 23242<tr> 23243<td> 23244 <p> 23245 Incomplete Beta Function: Large and Diverse Values 23246 </p> 23247 </td> 23248<td> 23249 <p> 23250 <span class="blue">Max = 1.26ε (Mean = 0.063ε)</span><br> <br> 23251 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.9e+05ε (Mean = 1.82e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ibeta_GSL_2_1_Incomplete_Beta_Function_Large_and_Diverse_Values">And 23252 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 23253 Max = 574ε (Mean = 49.4ε)) 23254 </p> 23255 </td> 23256<td> 23257 <p> 23258 <span class="blue">Max = 1.96e+04ε (Mean = 997ε)</span> 23259 </p> 23260 </td> 23261<td> 23262 <p> 23263 <span class="blue">Max = 4.98e+04ε (Mean = 2.07e+03ε)</span> 23264 </p> 23265 </td> 23266<td> 23267 <p> 23268 <span class="blue">Max = 1.32e+03ε (Mean = 68.5ε)</span> 23269 </p> 23270 </td> 23271</tr> 23272<tr> 23273<td> 23274 <p> 23275 Incomplete Beta Function: Small Integer Values 23276 </p> 23277 </td> 23278<td> 23279 <p> 23280 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 23281 2.1:</em></span> Max = 254ε (Mean = 50.9ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 23282 Max = 62.2ε (Mean = 8.95ε)) 23283 </p> 23284 </td> 23285<td> 23286 <p> 23287 <span class="blue">Max = 4.45ε (Mean = 0.814ε)</span> 23288 </p> 23289 </td> 23290<td> 23291 <p> 23292 <span class="blue">Max = 44.5ε (Mean = 10.1ε)</span> 23293 </p> 23294 </td> 23295<td> 23296 <p> 23297 <span class="blue">Max = 3.85ε (Mean = 0.791ε)</span> 23298 </p> 23299 </td> 23300</tr> 23301</tbody> 23302</table></div> 23303</div> 23304<br class="table-break"><div class="table"> 23305<a name="special_function_error_rates_rep.all_the_tables.table_ibeta_inv"></a><p class="title"><b>Table 150. Error rates for ibeta_inv</b></p> 23306<div class="table-contents"><table class="table" summary="Error rates for ibeta_inv"> 23307<colgroup> 23308<col> 23309<col> 23310<col> 23311<col> 23312<col> 23313</colgroup> 23314<thead><tr> 23315<th> 23316 </th> 23317<th> 23318 <p> 23319 GNU C++ version 7.1.0<br> linux<br> double 23320 </p> 23321 </th> 23322<th> 23323 <p> 23324 GNU C++ version 7.1.0<br> linux<br> long double 23325 </p> 23326 </th> 23327<th> 23328 <p> 23329 Sun compiler version 0x5150<br> Sun Solaris<br> long double 23330 </p> 23331 </th> 23332<th> 23333 <p> 23334 Microsoft Visual C++ version 14.1<br> Win32<br> double 23335 </p> 23336 </th> 23337</tr></thead> 23338<tbody><tr> 23339<td> 23340 <p> 23341 Inverse incomplete beta 23342 </p> 23343 </td> 23344<td> 23345 <p> 23346 <span class="blue">Max = 11ε (Mean = 0.345ε)</span><br> <br> 23347 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 1.14e+121ε (Mean 23348 = 3.28e+119ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ibeta_inv_Rmath_3_2_3_Inverse_incomplete_beta">And 23349 other failures.</a>)</span> 23350 </p> 23351 </td> 23352<td> 23353 <p> 23354 <span class="blue">Max = 3.8e+04ε (Mean = 2.66e+03ε)</span> 23355 </p> 23356 </td> 23357<td> 23358 <p> 23359 <span class="blue">Max = 4.07e+04ε (Mean = 2.86e+03ε)</span> 23360 </p> 23361 </td> 23362<td> 23363 <p> 23364 <span class="blue">Max = 8.59e+03ε (Mean = 277ε)</span> 23365 </p> 23366 </td> 23367</tr></tbody> 23368</table></div> 23369</div> 23370<br class="table-break"><div class="table"> 23371<a name="special_function_error_rates_rep.all_the_tables.table_ibeta_inva"></a><p class="title"><b>Table 151. Error rates for ibeta_inva</b></p> 23372<div class="table-contents"><table class="table" summary="Error rates for ibeta_inva"> 23373<colgroup> 23374<col> 23375<col> 23376<col> 23377<col> 23378<col> 23379</colgroup> 23380<thead><tr> 23381<th> 23382 </th> 23383<th> 23384 <p> 23385 GNU C++ version 7.1.0<br> linux<br> double 23386 </p> 23387 </th> 23388<th> 23389 <p> 23390 GNU C++ version 7.1.0<br> linux<br> long double 23391 </p> 23392 </th> 23393<th> 23394 <p> 23395 Sun compiler version 0x5150<br> Sun Solaris<br> long double 23396 </p> 23397 </th> 23398<th> 23399 <p> 23400 Microsoft Visual C++ version 14.1<br> Win32<br> double 23401 </p> 23402 </th> 23403</tr></thead> 23404<tbody><tr> 23405<td> 23406 <p> 23407 Inverse incomplete beta 23408 </p> 23409 </td> 23410<td> 23411 <p> 23412 <span class="blue">Max = 0.602ε (Mean = 0.0239ε)</span> 23413 </p> 23414 </td> 23415<td> 23416 <p> 23417 <span class="blue">Max = 377ε (Mean = 24.4ε)</span> 23418 </p> 23419 </td> 23420<td> 23421 <p> 23422 <span class="blue">Max = 438ε (Mean = 31.3ε)</span> 23423 </p> 23424 </td> 23425<td> 23426 <p> 23427 <span class="blue">Max = 242ε (Mean = 22.9ε)</span> 23428 </p> 23429 </td> 23430</tr></tbody> 23431</table></div> 23432</div> 23433<br class="table-break"><div class="table"> 23434<a name="special_function_error_rates_rep.all_the_tables.table_ibeta_invb"></a><p class="title"><b>Table 152. Error rates for ibeta_invb</b></p> 23435<div class="table-contents"><table class="table" summary="Error rates for ibeta_invb"> 23436<colgroup> 23437<col> 23438<col> 23439<col> 23440<col> 23441<col> 23442</colgroup> 23443<thead><tr> 23444<th> 23445 </th> 23446<th> 23447 <p> 23448 GNU C++ version 7.1.0<br> linux<br> double 23449 </p> 23450 </th> 23451<th> 23452 <p> 23453 GNU C++ version 7.1.0<br> linux<br> long double 23454 </p> 23455 </th> 23456<th> 23457 <p> 23458 Sun compiler version 0x5150<br> Sun Solaris<br> long double 23459 </p> 23460 </th> 23461<th> 23462 <p> 23463 Microsoft Visual C++ version 14.1<br> Win32<br> double 23464 </p> 23465 </th> 23466</tr></thead> 23467<tbody><tr> 23468<td> 23469 <p> 23470 Inverse incomplete beta 23471 </p> 23472 </td> 23473<td> 23474 <p> 23475 <span class="blue">Max = 0.765ε (Mean = 0.0422ε)</span> 23476 </p> 23477 </td> 23478<td> 23479 <p> 23480 <span class="blue">Max = 407ε (Mean = 27.2ε)</span> 23481 </p> 23482 </td> 23483<td> 23484 <p> 23485 <span class="blue">Max = 407ε (Mean = 24.4ε)</span> 23486 </p> 23487 </td> 23488<td> 23489 <p> 23490 <span class="blue">Max = 409ε (Mean = 19.3ε)</span> 23491 </p> 23492 </td> 23493</tr></tbody> 23494</table></div> 23495</div> 23496<br class="table-break"><div class="table"> 23497<a name="special_function_error_rates_rep.all_the_tables.table_ibetac"></a><p class="title"><b>Table 153. Error rates for ibetac</b></p> 23498<div class="table-contents"><table class="table" summary="Error rates for ibetac"> 23499<colgroup> 23500<col> 23501<col> 23502<col> 23503<col> 23504<col> 23505</colgroup> 23506<thead><tr> 23507<th> 23508 </th> 23509<th> 23510 <p> 23511 GNU C++ version 7.1.0<br> linux<br> double 23512 </p> 23513 </th> 23514<th> 23515 <p> 23516 GNU C++ version 7.1.0<br> linux<br> long double 23517 </p> 23518 </th> 23519<th> 23520 <p> 23521 Sun compiler version 0x5150<br> Sun Solaris<br> long double 23522 </p> 23523 </th> 23524<th> 23525 <p> 23526 Microsoft Visual C++ version 14.1<br> Win32<br> double 23527 </p> 23528 </th> 23529</tr></thead> 23530<tbody> 23531<tr> 23532<td> 23533 <p> 23534 Incomplete Beta Function: Small Values 23535 </p> 23536 </td> 23537<td> 23538 <p> 23539 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath 23540 3.2.3:</em></span> Max = 22.4ε (Mean = 3.67ε)) 23541 </p> 23542 </td> 23543<td> 23544 <p> 23545 <span class="blue">Max = 10.6ε (Mean = 2.22ε)</span> 23546 </p> 23547 </td> 23548<td> 23549 <p> 23550 <span class="blue">Max = 13.8ε (Mean = 2.68ε)</span> 23551 </p> 23552 </td> 23553<td> 23554 <p> 23555 <span class="blue">Max = 6.94ε (Mean = 1.71ε)</span> 23556 </p> 23557 </td> 23558</tr> 23559<tr> 23560<td> 23561 <p> 23562 Incomplete Beta Function: Medium Values 23563 </p> 23564 </td> 23565<td> 23566 <p> 23567 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath 23568 3.2.3:</em></span> Max = 204ε (Mean = 25.8ε)) 23569 </p> 23570 </td> 23571<td> 23572 <p> 23573 <span class="blue">Max = 73.9ε (Mean = 11.2ε)</span> 23574 </p> 23575 </td> 23576<td> 23577 <p> 23578 <span class="blue">Max = 132ε (Mean = 19.8ε)</span> 23579 </p> 23580 </td> 23581<td> 23582 <p> 23583 <span class="blue">Max = 56.7ε (Mean = 14.3ε)</span> 23584 </p> 23585 </td> 23586</tr> 23587<tr> 23588<td> 23589 <p> 23590 Incomplete Beta Function: Large and Diverse Values 23591 </p> 23592 </td> 23593<td> 23594 <p> 23595 <span class="blue">Max = 0.981ε (Mean = 0.0573ε)</span><br> <br> 23596 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 889ε (Mean = 68.4ε)) 23597 </p> 23598 </td> 23599<td> 23600 <p> 23601 <span class="blue">Max = 3.45e+04ε (Mean = 1.32e+03ε)</span> 23602 </p> 23603 </td> 23604<td> 23605 <p> 23606 <span class="blue">Max = 6.31e+04ε (Mean = 2.04e+03ε)</span> 23607 </p> 23608 </td> 23609<td> 23610 <p> 23611 <span class="blue">Max = 1.88e+03ε (Mean = 82.7ε)</span> 23612 </p> 23613 </td> 23614</tr> 23615<tr> 23616<td> 23617 <p> 23618 Incomplete Beta Function: Small Integer Values 23619 </p> 23620 </td> 23621<td> 23622 <p> 23623 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath 23624 3.2.3:</em></span> Max = 84.6ε (Mean = 18ε)) 23625 </p> 23626 </td> 23627<td> 23628 <p> 23629 <span class="blue">Max = 5.34ε (Mean = 1.11ε)</span> 23630 </p> 23631 </td> 23632<td> 23633 <p> 23634 <span class="blue">Max = 107ε (Mean = 17.1ε)</span> 23635 </p> 23636 </td> 23637<td> 23638 <p> 23639 <span class="blue">Max = 6.37ε (Mean = 1.03ε)</span> 23640 </p> 23641 </td> 23642</tr> 23643</tbody> 23644</table></div> 23645</div> 23646<br class="table-break"><div class="table"> 23647<a name="special_function_error_rates_rep.all_the_tables.table_ibetac_inv"></a><p class="title"><b>Table 154. Error rates for ibetac_inv</b></p> 23648<div class="table-contents"><table class="table" summary="Error rates for ibetac_inv"> 23649<colgroup> 23650<col> 23651<col> 23652<col> 23653<col> 23654<col> 23655</colgroup> 23656<thead><tr> 23657<th> 23658 </th> 23659<th> 23660 <p> 23661 GNU C++ version 7.1.0<br> linux<br> double 23662 </p> 23663 </th> 23664<th> 23665 <p> 23666 GNU C++ version 7.1.0<br> linux<br> long double 23667 </p> 23668 </th> 23669<th> 23670 <p> 23671 Sun compiler version 0x5150<br> Sun Solaris<br> long double 23672 </p> 23673 </th> 23674<th> 23675 <p> 23676 Microsoft Visual C++ version 14.1<br> Win32<br> double 23677 </p> 23678 </th> 23679</tr></thead> 23680<tbody><tr> 23681<td> 23682 <p> 23683 Inverse incomplete beta 23684 </p> 23685 </td> 23686<td> 23687 <p> 23688 <span class="blue">Max = 0.977ε (Mean = 0.0976ε)</span><br> <br> 23689 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 3.01e+132ε (Mean 23690 = 8.65e+130ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ibetac_inv_Rmath_3_2_3_Inverse_incomplete_beta">And 23691 other failures.</a>)</span> 23692 </p> 23693 </td> 23694<td> 23695 <p> 23696 <span class="blue">Max = 4.88e+04ε (Mean = 3.16e+03ε)</span> 23697 </p> 23698 </td> 23699<td> 23700 <p> 23701 <span class="blue">Max = 5.05e+04ε (Mean = 3.33e+03ε)</span> 23702 </p> 23703 </td> 23704<td> 23705 <p> 23706 <span class="blue">Max = 2.93e+03ε (Mean = 198ε)</span> 23707 </p> 23708 </td> 23709</tr></tbody> 23710</table></div> 23711</div> 23712<br class="table-break"><div class="table"> 23713<a name="special_function_error_rates_rep.all_the_tables.table_ibetac_inva"></a><p class="title"><b>Table 155. Error rates for ibetac_inva</b></p> 23714<div class="table-contents"><table class="table" summary="Error rates for ibetac_inva"> 23715<colgroup> 23716<col> 23717<col> 23718<col> 23719<col> 23720<col> 23721</colgroup> 23722<thead><tr> 23723<th> 23724 </th> 23725<th> 23726 <p> 23727 GNU C++ version 7.1.0<br> linux<br> double 23728 </p> 23729 </th> 23730<th> 23731 <p> 23732 GNU C++ version 7.1.0<br> linux<br> long double 23733 </p> 23734 </th> 23735<th> 23736 <p> 23737 Sun compiler version 0x5150<br> Sun Solaris<br> long double 23738 </p> 23739 </th> 23740<th> 23741 <p> 23742 Microsoft Visual C++ version 14.1<br> Win32<br> double 23743 </p> 23744 </th> 23745</tr></thead> 23746<tbody><tr> 23747<td> 23748 <p> 23749 Inverse incomplete beta 23750 </p> 23751 </td> 23752<td> 23753 <p> 23754 <span class="blue">Max = 0.683ε (Mean = 0.0314ε)</span> 23755 </p> 23756 </td> 23757<td> 23758 <p> 23759 <span class="blue">Max = 382ε (Mean = 22.2ε)</span> 23760 </p> 23761 </td> 23762<td> 23763 <p> 23764 <span class="blue">Max = 315ε (Mean = 23.7ε)</span> 23765 </p> 23766 </td> 23767<td> 23768 <p> 23769 <span class="blue">Max = 408ε (Mean = 26.7ε)</span> 23770 </p> 23771 </td> 23772</tr></tbody> 23773</table></div> 23774</div> 23775<br class="table-break"><div class="table"> 23776<a name="special_function_error_rates_rep.all_the_tables.table_ibetac_invb"></a><p class="title"><b>Table 156. Error rates for ibetac_invb</b></p> 23777<div class="table-contents"><table class="table" summary="Error rates for ibetac_invb"> 23778<colgroup> 23779<col> 23780<col> 23781<col> 23782<col> 23783<col> 23784</colgroup> 23785<thead><tr> 23786<th> 23787 </th> 23788<th> 23789 <p> 23790 GNU C++ version 7.1.0<br> linux<br> double 23791 </p> 23792 </th> 23793<th> 23794 <p> 23795 GNU C++ version 7.1.0<br> linux<br> long double 23796 </p> 23797 </th> 23798<th> 23799 <p> 23800 Sun compiler version 0x5150<br> Sun Solaris<br> long double 23801 </p> 23802 </th> 23803<th> 23804 <p> 23805 Microsoft Visual C++ version 14.1<br> Win32<br> double 23806 </p> 23807 </th> 23808</tr></thead> 23809<tbody><tr> 23810<td> 23811 <p> 23812 Inverse incomplete beta 23813 </p> 23814 </td> 23815<td> 23816 <p> 23817 <span class="blue">Max = 0.724ε (Mean = 0.0303ε)</span> 23818 </p> 23819 </td> 23820<td> 23821 <p> 23822 <span class="blue">Max = 317ε (Mean = 19.8ε)</span> 23823 </p> 23824 </td> 23825<td> 23826 <p> 23827 <span class="blue">Max = 369ε (Mean = 22.6ε)</span> 23828 </p> 23829 </td> 23830<td> 23831 <p> 23832 <span class="blue">Max = 271ε (Mean = 16.4ε)</span> 23833 </p> 23834 </td> 23835</tr></tbody> 23836</table></div> 23837</div> 23838<br class="table-break"><div class="table"> 23839<a name="special_function_error_rates_rep.all_the_tables.table_jacobi_cn"></a><p class="title"><b>Table 157. Error rates for jacobi_cn</b></p> 23840<div class="table-contents"><table class="table" summary="Error rates for jacobi_cn"> 23841<colgroup> 23842<col> 23843<col> 23844<col> 23845<col> 23846<col> 23847</colgroup> 23848<thead><tr> 23849<th> 23850 </th> 23851<th> 23852 <p> 23853 GNU C++ version 7.1.0<br> linux<br> double 23854 </p> 23855 </th> 23856<th> 23857 <p> 23858 GNU C++ version 7.1.0<br> linux<br> long double 23859 </p> 23860 </th> 23861<th> 23862 <p> 23863 Sun compiler version 0x5150<br> Sun Solaris<br> long double 23864 </p> 23865 </th> 23866<th> 23867 <p> 23868 Microsoft Visual C++ version 14.1<br> Win32<br> double 23869 </p> 23870 </th> 23871</tr></thead> 23872<tbody> 23873<tr> 23874<td> 23875 <p> 23876 Jacobi Elliptic: Mathworld Data 23877 </p> 23878 </td> 23879<td> 23880 <p> 23881 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 23882 2.1:</em></span> Max = 17.3ε (Mean = 4.29ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data">And 23883 other failures.</a>) 23884 </p> 23885 </td> 23886<td> 23887 <p> 23888 <span class="blue">Max = 71.6ε (Mean = 19.3ε)</span> 23889 </p> 23890 </td> 23891<td> 23892 <p> 23893 <span class="blue">Max = 71.6ε (Mean = 19.4ε)</span> 23894 </p> 23895 </td> 23896<td> 23897 <p> 23898 <span class="blue">Max = 45.8ε (Mean = 11.4ε)</span> 23899 </p> 23900 </td> 23901</tr> 23902<tr> 23903<td> 23904 <p> 23905 Jacobi Elliptic: Random Data 23906 </p> 23907 </td> 23908<td> 23909 <p> 23910 <span class="blue">Max = 0.816ε (Mean = 0.0563ε)</span><br> <br> 23911 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.43ε (Mean = 0.803ε)) 23912 </p> 23913 </td> 23914<td> 23915 <p> 23916 <span class="blue">Max = 1.68ε (Mean = 0.443ε)</span> 23917 </p> 23918 </td> 23919<td> 23920 <p> 23921 <span class="blue">Max = 1.68ε (Mean = 0.454ε)</span> 23922 </p> 23923 </td> 23924<td> 23925 <p> 23926 <span class="blue">Max = 1.83ε (Mean = 0.455ε)</span> 23927 </p> 23928 </td> 23929</tr> 23930<tr> 23931<td> 23932 <p> 23933 Jacobi Elliptic: Random Small Values 23934 </p> 23935 </td> 23936<td> 23937 <p> 23938 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 23939 2.1:</em></span> Max = 55.2ε (Mean = 1.64ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values">And 23940 other failures.</a>) 23941 </p> 23942 </td> 23943<td> 23944 <p> 23945 <span class="blue">Max = 10.4ε (Mean = 0.594ε)</span> 23946 </p> 23947 </td> 23948<td> 23949 <p> 23950 <span class="blue">Max = 10.4ε (Mean = 0.602ε)</span> 23951 </p> 23952 </td> 23953<td> 23954 <p> 23955 <span class="blue">Max = 26.2ε (Mean = 1.17ε)</span> 23956 </p> 23957 </td> 23958</tr> 23959<tr> 23960<td> 23961 <p> 23962 Jacobi Elliptic: Modulus near 1 23963 </p> 23964 </td> 23965<td> 23966 <p> 23967 <span class="blue">Max = 0.919ε (Mean = 0.127ε)</span><br> <br> 23968 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0ε (Mean = 0ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1">And 23969 other failures.</a>) 23970 </p> 23971 </td> 23972<td> 23973 <p> 23974 <span class="blue">Max = 675ε (Mean = 87.1ε)</span> 23975 </p> 23976 </td> 23977<td> 23978 <p> 23979 <span class="blue">Max = 675ε (Mean = 86.8ε)</span> 23980 </p> 23981 </td> 23982<td> 23983 <p> 23984 <span class="blue">Max = 513ε (Mean = 126ε)</span> 23985 </p> 23986 </td> 23987</tr> 23988<tr> 23989<td> 23990 <p> 23991 Jacobi Elliptic: Large Phi 23992 </p> 23993 </td> 23994<td> 23995 <p> 23996 <span class="blue">Max = 14.2ε (Mean = 0.927ε)</span><br> <br> 23997 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 5.92e+03ε (Mean = 477ε)) 23998 </p> 23999 </td> 24000<td> 24001 <p> 24002 <span class="blue">Max = 2.97e+04ε (Mean = 1.9e+03ε)</span> 24003 </p> 24004 </td> 24005<td> 24006 <p> 24007 <span class="blue">Max = 2.97e+04ε (Mean = 1.9e+03ε)</span> 24008 </p> 24009 </td> 24010<td> 24011 <p> 24012 <span class="blue">Max = 3.27e+04ε (Mean = 1.93e+03ε)</span> 24013 </p> 24014 </td> 24015</tr> 24016</tbody> 24017</table></div> 24018</div> 24019<br class="table-break"><div class="table"> 24020<a name="special_function_error_rates_rep.all_the_tables.table_jacobi_dn"></a><p class="title"><b>Table 158. Error rates for jacobi_dn</b></p> 24021<div class="table-contents"><table class="table" summary="Error rates for jacobi_dn"> 24022<colgroup> 24023<col> 24024<col> 24025<col> 24026<col> 24027<col> 24028</colgroup> 24029<thead><tr> 24030<th> 24031 </th> 24032<th> 24033 <p> 24034 GNU C++ version 7.1.0<br> linux<br> double 24035 </p> 24036 </th> 24037<th> 24038 <p> 24039 GNU C++ version 7.1.0<br> linux<br> long double 24040 </p> 24041 </th> 24042<th> 24043 <p> 24044 Sun compiler version 0x5150<br> Sun Solaris<br> long double 24045 </p> 24046 </th> 24047<th> 24048 <p> 24049 Microsoft Visual C++ version 14.1<br> Win32<br> double 24050 </p> 24051 </th> 24052</tr></thead> 24053<tbody> 24054<tr> 24055<td> 24056 <p> 24057 Jacobi Elliptic: Mathworld Data 24058 </p> 24059 </td> 24060<td> 24061 <p> 24062 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 24063 2.1:</em></span> Max = 2.82ε (Mean = 1.18ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data">And 24064 other failures.</a>) 24065 </p> 24066 </td> 24067<td> 24068 <p> 24069 <span class="blue">Max = 49ε (Mean = 14ε)</span> 24070 </p> 24071 </td> 24072<td> 24073 <p> 24074 <span class="blue">Max = 49ε (Mean = 14ε)</span> 24075 </p> 24076 </td> 24077<td> 24078 <p> 24079 <span class="blue">Max = 34.3ε (Mean = 8.71ε)</span> 24080 </p> 24081 </td> 24082</tr> 24083<tr> 24084<td> 24085 <p> 24086 Jacobi Elliptic: Random Data 24087 </p> 24088 </td> 24089<td> 24090 <p> 24091 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 24092 2.1:</em></span> Max = 3ε (Mean = 0.61ε)) 24093 </p> 24094 </td> 24095<td> 24096 <p> 24097 <span class="blue">Max = 1.53ε (Mean = 0.473ε)</span> 24098 </p> 24099 </td> 24100<td> 24101 <p> 24102 <span class="blue">Max = 1.53ε (Mean = 0.481ε)</span> 24103 </p> 24104 </td> 24105<td> 24106 <p> 24107 <span class="blue">Max = 1.52ε (Mean = 0.466ε)</span> 24108 </p> 24109 </td> 24110</tr> 24111<tr> 24112<td> 24113 <p> 24114 Jacobi Elliptic: Random Small Values 24115 </p> 24116 </td> 24117<td> 24118 <p> 24119 <span class="blue">Max = 0.5ε (Mean = 0.0122ε)</span><br> <br> 24120 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.5ε (Mean = 0.391ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values">And 24121 other failures.</a>) 24122 </p> 24123 </td> 24124<td> 24125 <p> 24126 <span class="blue">Max = 22.4ε (Mean = 0.777ε)</span> 24127 </p> 24128 </td> 24129<td> 24130 <p> 24131 <span class="blue">Max = 22.4ε (Mean = 0.763ε)</span> 24132 </p> 24133 </td> 24134<td> 24135 <p> 24136 <span class="blue">Max = 16.1ε (Mean = 0.685ε)</span> 24137 </p> 24138 </td> 24139</tr> 24140<tr> 24141<td> 24142 <p> 24143 Jacobi Elliptic: Modulus near 1 24144 </p> 24145 </td> 24146<td> 24147 <p> 24148 <span class="blue">Max = 2.28ε (Mean = 0.194ε)</span><br> <br> 24149 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0ε (Mean = 0ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1">And 24150 other failures.</a>) 24151 </p> 24152 </td> 24153<td> 24154 <p> 24155 <span class="blue">Max = 3.75e+03ε (Mean = 293ε)</span> 24156 </p> 24157 </td> 24158<td> 24159 <p> 24160 <span class="blue">Max = 3.75e+03ε (Mean = 293ε)</span> 24161 </p> 24162 </td> 24163<td> 24164 <p> 24165 <span class="blue">Max = 6.24e+03ε (Mean = 482ε)</span> 24166 </p> 24167 </td> 24168</tr> 24169<tr> 24170<td> 24171 <p> 24172 Jacobi Elliptic: Large Phi 24173 </p> 24174 </td> 24175<td> 24176 <p> 24177 <span class="blue">Max = 14.1ε (Mean = 0.897ε)</span><br> <br> 24178 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 121ε (Mean = 22ε)) 24179 </p> 24180 </td> 24181<td> 24182 <p> 24183 <span class="blue">Max = 2.82e+04ε (Mean = 1.79e+03ε)</span> 24184 </p> 24185 </td> 24186<td> 24187 <p> 24188 <span class="blue">Max = 2.82e+04ε (Mean = 1.79e+03ε)</span> 24189 </p> 24190 </td> 24191<td> 24192 <p> 24193 <span class="blue">Max = 1.67e+04ε (Mean = 1e+03ε)</span> 24194 </p> 24195 </td> 24196</tr> 24197</tbody> 24198</table></div> 24199</div> 24200<br class="table-break"><div class="table"> 24201<a name="special_function_error_rates_rep.all_the_tables.table_jacobi_sn"></a><p class="title"><b>Table 159. Error rates for jacobi_sn</b></p> 24202<div class="table-contents"><table class="table" summary="Error rates for jacobi_sn"> 24203<colgroup> 24204<col> 24205<col> 24206<col> 24207<col> 24208<col> 24209</colgroup> 24210<thead><tr> 24211<th> 24212 </th> 24213<th> 24214 <p> 24215 GNU C++ version 7.1.0<br> linux<br> double 24216 </p> 24217 </th> 24218<th> 24219 <p> 24220 GNU C++ version 7.1.0<br> linux<br> long double 24221 </p> 24222 </th> 24223<th> 24224 <p> 24225 Sun compiler version 0x5150<br> Sun Solaris<br> long double 24226 </p> 24227 </th> 24228<th> 24229 <p> 24230 Microsoft Visual C++ version 14.1<br> Win32<br> double 24231 </p> 24232 </th> 24233</tr></thead> 24234<tbody> 24235<tr> 24236<td> 24237 <p> 24238 Jacobi Elliptic: Mathworld Data 24239 </p> 24240 </td> 24241<td> 24242 <p> 24243 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 24244 2.1:</em></span> Max = 588ε (Mean = 146ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data">And 24245 other failures.</a>) 24246 </p> 24247 </td> 24248<td> 24249 <p> 24250 <span class="blue">Max = 341ε (Mean = 80.7ε)</span> 24251 </p> 24252 </td> 24253<td> 24254 <p> 24255 <span class="blue">Max = 341ε (Mean = 80.7ε)</span> 24256 </p> 24257 </td> 24258<td> 24259 <p> 24260 <span class="blue">Max = 481ε (Mean = 113ε)</span> 24261 </p> 24262 </td> 24263</tr> 24264<tr> 24265<td> 24266 <p> 24267 Jacobi Elliptic: Random Data 24268 </p> 24269 </td> 24270<td> 24271 <p> 24272 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 24273 2.1:</em></span> Max = 4.02ε (Mean = 1.07ε)) 24274 </p> 24275 </td> 24276<td> 24277 <p> 24278 <span class="blue">Max = 2.01ε (Mean = 0.584ε)</span> 24279 </p> 24280 </td> 24281<td> 24282 <p> 24283 <span class="blue">Max = 2.01ε (Mean = 0.593ε)</span> 24284 </p> 24285 </td> 24286<td> 24287 <p> 24288 <span class="blue">Max = 1.92ε (Mean = 0.567ε)</span> 24289 </p> 24290 </td> 24291</tr> 24292<tr> 24293<td> 24294 <p> 24295 Jacobi Elliptic: Random Small Values 24296 </p> 24297 </td> 24298<td> 24299 <p> 24300 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 24301 2.1:</em></span> Max = 11.7ε (Mean = 1.65ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values">And 24302 other failures.</a>) 24303 </p> 24304 </td> 24305<td> 24306 <p> 24307 <span class="blue">Max = 1.99ε (Mean = 0.347ε)</span> 24308 </p> 24309 </td> 24310<td> 24311 <p> 24312 <span class="blue">Max = 1.99ε (Mean = 0.347ε)</span> 24313 </p> 24314 </td> 24315<td> 24316 <p> 24317 <span class="blue">Max = 2.11ε (Mean = 0.385ε)</span> 24318 </p> 24319 </td> 24320</tr> 24321<tr> 24322<td> 24323 <p> 24324 Jacobi Elliptic: Modulus near 1 24325 </p> 24326 </td> 24327<td> 24328 <p> 24329 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 24330 2.1:</em></span> Max = 0ε (Mean = 0ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1">And 24331 other failures.</a>) 24332 </p> 24333 </td> 24334<td> 24335 <p> 24336 <span class="blue">Max = 109ε (Mean = 7.35ε)</span> 24337 </p> 24338 </td> 24339<td> 24340 <p> 24341 <span class="blue">Max = 109ε (Mean = 7.38ε)</span> 24342 </p> 24343 </td> 24344<td> 24345 <p> 24346 <span class="blue">Max = 23.2ε (Mean = 1.85ε)</span> 24347 </p> 24348 </td> 24349</tr> 24350<tr> 24351<td> 24352 <p> 24353 Jacobi Elliptic: Large Phi 24354 </p> 24355 </td> 24356<td> 24357 <p> 24358 <span class="blue">Max = 12ε (Mean = 0.771ε)</span><br> <br> 24359 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 4.54e+04ε (Mean = 2.63e+03ε)) 24360 </p> 24361 </td> 24362<td> 24363 <p> 24364 <span class="blue">Max = 2.45e+04ε (Mean = 1.51e+03ε)</span> 24365 </p> 24366 </td> 24367<td> 24368 <p> 24369 <span class="blue">Max = 2.45e+04ε (Mean = 1.51e+03ε)</span> 24370 </p> 24371 </td> 24372<td> 24373 <p> 24374 <span class="blue">Max = 4.36e+04ε (Mean = 2.54e+03ε)</span> 24375 </p> 24376 </td> 24377</tr> 24378</tbody> 24379</table></div> 24380</div> 24381<br class="table-break"><div class="table"> 24382<a name="special_function_error_rates_rep.all_the_tables.table_jacobi_zeta"></a><p class="title"><b>Table 160. Error rates for jacobi_zeta</b></p> 24383<div class="table-contents"><table class="table" summary="Error rates for jacobi_zeta"> 24384<colgroup> 24385<col> 24386<col> 24387<col> 24388<col> 24389<col> 24390</colgroup> 24391<thead><tr> 24392<th> 24393 </th> 24394<th> 24395 <p> 24396 GNU C++ version 7.1.0<br> linux<br> double 24397 </p> 24398 </th> 24399<th> 24400 <p> 24401 GNU C++ version 7.1.0<br> linux<br> long double 24402 </p> 24403 </th> 24404<th> 24405 <p> 24406 Sun compiler version 0x5150<br> Sun Solaris<br> long double 24407 </p> 24408 </th> 24409<th> 24410 <p> 24411 Microsoft Visual C++ version 14.1<br> Win32<br> double 24412 </p> 24413 </th> 24414</tr></thead> 24415<tbody> 24416<tr> 24417<td> 24418 <p> 24419 Elliptic Integral Jacobi Zeta: Mathworld Data 24420 </p> 24421 </td> 24422<td> 24423 <p> 24424 <span class="blue">Max = 0ε (Mean = 0ε)</span> 24425 </p> 24426 </td> 24427<td> 24428 <p> 24429 <span class="blue">Max = 1.66ε (Mean = 0.48ε)</span> 24430 </p> 24431 </td> 24432<td> 24433 <p> 24434 <span class="blue">Max = 1.66ε (Mean = 0.48ε)</span> 24435 </p> 24436 </td> 24437<td> 24438 <p> 24439 <span class="blue">Max = 1.52ε (Mean = 0.357ε)</span> 24440 </p> 24441 </td> 24442</tr> 24443<tr> 24444<td> 24445 <p> 24446 Elliptic Integral Jacobi Zeta: Random Data 24447 </p> 24448 </td> 24449<td> 24450 <p> 24451 <span class="blue">Max = 0ε (Mean = 0ε)</span> 24452 </p> 24453 </td> 24454<td> 24455 <p> 24456 <span class="blue">Max = 2.99ε (Mean = 0.824ε)</span> 24457 </p> 24458 </td> 24459<td> 24460 <p> 24461 <span class="blue">Max = 3.96ε (Mean = 1.06ε)</span> 24462 </p> 24463 </td> 24464<td> 24465 <p> 24466 <span class="blue">Max = 3.89ε (Mean = 0.824ε)</span> 24467 </p> 24468 </td> 24469</tr> 24470<tr> 24471<td> 24472 <p> 24473 Elliptic Integral Jacobi Zeta: Large Phi Values 24474 </p> 24475 </td> 24476<td> 24477 <p> 24478 <span class="blue">Max = 0ε (Mean = 0ε)</span> 24479 </p> 24480 </td> 24481<td> 24482 <p> 24483 <span class="blue">Max = 2.92ε (Mean = 0.951ε)</span> 24484 </p> 24485 </td> 24486<td> 24487 <p> 24488 <span class="blue">Max = 3.05ε (Mean = 1.13ε)</span> 24489 </p> 24490 </td> 24491<td> 24492 <p> 24493 <span class="blue">Max = 2.52ε (Mean = 0.977ε)</span> 24494 </p> 24495 </td> 24496</tr> 24497</tbody> 24498</table></div> 24499</div> 24500<br class="table-break"><div class="table"> 24501<a name="special_function_error_rates_rep.all_the_tables.table_laguerre_n_m_x_"></a><p class="title"><b>Table 161. Error rates for laguerre(n, m, x)</b></p> 24502<div class="table-contents"><table class="table" summary="Error rates for laguerre(n, m, x)"> 24503<colgroup> 24504<col> 24505<col> 24506<col> 24507<col> 24508<col> 24509</colgroup> 24510<thead><tr> 24511<th> 24512 </th> 24513<th> 24514 <p> 24515 GNU C++ version 7.1.0<br> linux<br> double 24516 </p> 24517 </th> 24518<th> 24519 <p> 24520 GNU C++ version 7.1.0<br> linux<br> long double 24521 </p> 24522 </th> 24523<th> 24524 <p> 24525 Sun compiler version 0x5150<br> Sun Solaris<br> long double 24526 </p> 24527 </th> 24528<th> 24529 <p> 24530 Microsoft Visual C++ version 14.1<br> Win32<br> double 24531 </p> 24532 </th> 24533</tr></thead> 24534<tbody><tr> 24535<td> 24536 <p> 24537 Associated Laguerre Polynomials 24538 </p> 24539 </td> 24540<td> 24541 <p> 24542 <span class="blue">Max = 0.84ε (Mean = 0.0358ε)</span><br> <br> 24543 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 434ε (Mean = 10.7ε)) 24544 </p> 24545 </td> 24546<td> 24547 <p> 24548 <span class="blue">Max = 167ε (Mean = 6.38ε)</span><br> <br> 24549 (<span class="emphasis"><em><cmath>:</em></span> Max = 206ε (Mean = 6.86ε)) 24550 </p> 24551 </td> 24552<td> 24553 <p> 24554 <span class="blue">Max = 167ε (Mean = 6.38ε)</span> 24555 </p> 24556 </td> 24557<td> 24558 <p> 24559 <span class="blue">Max = 434ε (Mean = 11.1ε)</span> 24560 </p> 24561 </td> 24562</tr></tbody> 24563</table></div> 24564</div> 24565<br class="table-break"><div class="table"> 24566<a name="special_function_error_rates_rep.all_the_tables.table_laguerre_n_x_"></a><p class="title"><b>Table 162. Error rates for laguerre(n, x)</b></p> 24567<div class="table-contents"><table class="table" summary="Error rates for laguerre(n, x)"> 24568<colgroup> 24569<col> 24570<col> 24571<col> 24572<col> 24573<col> 24574</colgroup> 24575<thead><tr> 24576<th> 24577 </th> 24578<th> 24579 <p> 24580 GNU C++ version 7.1.0<br> linux<br> double 24581 </p> 24582 </th> 24583<th> 24584 <p> 24585 GNU C++ version 7.1.0<br> linux<br> long double 24586 </p> 24587 </th> 24588<th> 24589 <p> 24590 Sun compiler version 0x5150<br> Sun Solaris<br> long double 24591 </p> 24592 </th> 24593<th> 24594 <p> 24595 Microsoft Visual C++ version 14.1<br> Win32<br> double 24596 </p> 24597 </th> 24598</tr></thead> 24599<tbody><tr> 24600<td> 24601 <p> 24602 Laguerre Polynomials 24603 </p> 24604 </td> 24605<td> 24606 <p> 24607 <span class="blue">Max = 6.82ε (Mean = 0.408ε)</span><br> <br> 24608 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.1e+03ε (Mean = 185ε)) 24609 </p> 24610 </td> 24611<td> 24612 <p> 24613 <span class="blue">Max = 1.39e+04ε (Mean = 828ε)</span><br> <br> 24614 (<span class="emphasis"><em><cmath>:</em></span> Max = 4.2e+03ε (Mean = 251ε)) 24615 </p> 24616 </td> 24617<td> 24618 <p> 24619 <span class="blue">Max = 1.39e+04ε (Mean = 828ε)</span> 24620 </p> 24621 </td> 24622<td> 24623 <p> 24624 <span class="blue">Max = 3.1e+03ε (Mean = 185ε)</span> 24625 </p> 24626 </td> 24627</tr></tbody> 24628</table></div> 24629</div> 24630<br class="table-break"><div class="table"> 24631<a name="special_function_error_rates_rep.all_the_tables.table_legendre_p"></a><p class="title"><b>Table 163. Error rates for legendre_p</b></p> 24632<div class="table-contents"><table class="table" summary="Error rates for legendre_p"> 24633<colgroup> 24634<col> 24635<col> 24636<col> 24637<col> 24638<col> 24639</colgroup> 24640<thead><tr> 24641<th> 24642 </th> 24643<th> 24644 <p> 24645 GNU C++ version 7.1.0<br> linux<br> double 24646 </p> 24647 </th> 24648<th> 24649 <p> 24650 GNU C++ version 7.1.0<br> linux<br> long double 24651 </p> 24652 </th> 24653<th> 24654 <p> 24655 Sun compiler version 0x5150<br> Sun Solaris<br> long double 24656 </p> 24657 </th> 24658<th> 24659 <p> 24660 Microsoft Visual C++ version 14.1<br> Win32<br> double 24661 </p> 24662 </th> 24663</tr></thead> 24664<tbody> 24665<tr> 24666<td> 24667 <p> 24668 Legendre Polynomials: Small Values 24669 </p> 24670 </td> 24671<td> 24672 <p> 24673 <span class="blue">Max = 0.732ε (Mean = 0.0619ε)</span><br> <br> 24674 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 211ε (Mean = 20.4ε)) 24675 </p> 24676 </td> 24677<td> 24678 <p> 24679 <span class="blue">Max = 69.2ε (Mean = 9.58ε)</span><br> <br> 24680 (<span class="emphasis"><em><cmath>:</em></span> Max = 124ε (Mean = 13.2ε)) 24681 </p> 24682 </td> 24683<td> 24684 <p> 24685 <span class="blue">Max = 69.2ε (Mean = 9.58ε)</span> 24686 </p> 24687 </td> 24688<td> 24689 <p> 24690 <span class="blue">Max = 211ε (Mean = 20.4ε)</span> 24691 </p> 24692 </td> 24693</tr> 24694<tr> 24695<td> 24696 <p> 24697 Legendre Polynomials: Large Values 24698 </p> 24699 </td> 24700<td> 24701 <p> 24702 <span class="blue">Max = 0.632ε (Mean = 0.0693ε)</span><br> <br> 24703 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 300ε (Mean = 33.2ε)) 24704 </p> 24705 </td> 24706<td> 24707 <p> 24708 <span class="blue">Max = 699ε (Mean = 59.6ε)</span><br> <br> 24709 (<span class="emphasis"><em><cmath>:</em></span> Max = 343ε (Mean = 32.1ε)) 24710 </p> 24711 </td> 24712<td> 24713 <p> 24714 <span class="blue">Max = 699ε (Mean = 59.6ε)</span> 24715 </p> 24716 </td> 24717<td> 24718 <p> 24719 <span class="blue">Max = 300ε (Mean = 33.2ε)</span> 24720 </p> 24721 </td> 24722</tr> 24723</tbody> 24724</table></div> 24725</div> 24726<br class="table-break"><div class="table"> 24727<a name="special_function_error_rates_rep.all_the_tables.table_legendre_p_associated_"></a><p class="title"><b>Table 164. Error rates for legendre_p (associated)</b></p> 24728<div class="table-contents"><table class="table" summary="Error rates for legendre_p (associated)"> 24729<colgroup> 24730<col> 24731<col> 24732<col> 24733<col> 24734<col> 24735</colgroup> 24736<thead><tr> 24737<th> 24738 </th> 24739<th> 24740 <p> 24741 GNU C++ version 7.1.0<br> linux<br> double 24742 </p> 24743 </th> 24744<th> 24745 <p> 24746 GNU C++ version 7.1.0<br> linux<br> long double 24747 </p> 24748 </th> 24749<th> 24750 <p> 24751 Sun compiler version 0x5150<br> Sun Solaris<br> long double 24752 </p> 24753 </th> 24754<th> 24755 <p> 24756 Microsoft Visual C++ version 14.1<br> Win32<br> double 24757 </p> 24758 </th> 24759</tr></thead> 24760<tbody><tr> 24761<td> 24762 <p> 24763 Associated Legendre Polynomials: Small Values 24764 </p> 24765 </td> 24766<td> 24767 <p> 24768 <span class="blue">Max = 0.999ε (Mean = 0.05ε)</span><br> <br> 24769 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 121ε (Mean = 6.75ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_legendre_p_associated__GSL_2_1_Associated_Legendre_Polynomials_Small_Values">And 24770 other failures.</a>) 24771 </p> 24772 </td> 24773<td> 24774 <p> 24775 <span class="blue">Max = 175ε (Mean = 9.88ε)</span><br> <br> 24776 (<span class="emphasis"><em><cmath>:</em></span> Max = 175ε (Mean = 9.36ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_legendre_p_associated___cmath__Associated_Legendre_Polynomials_Small_Values">And 24777 other failures.</a>) 24778 </p> 24779 </td> 24780<td> 24781 <p> 24782 <span class="blue">Max = 77.7ε (Mean = 5.59ε)</span> 24783 </p> 24784 </td> 24785<td> 24786 <p> 24787 <span class="blue">Max = 121ε (Mean = 7.14ε)</span> 24788 </p> 24789 </td> 24790</tr></tbody> 24791</table></div> 24792</div> 24793<br class="table-break"><div class="table"> 24794<a name="special_function_error_rates_rep.all_the_tables.table_legendre_q"></a><p class="title"><b>Table 165. Error rates for legendre_q</b></p> 24795<div class="table-contents"><table class="table" summary="Error rates for legendre_q"> 24796<colgroup> 24797<col> 24798<col> 24799<col> 24800<col> 24801<col> 24802</colgroup> 24803<thead><tr> 24804<th> 24805 </th> 24806<th> 24807 <p> 24808 GNU C++ version 7.1.0<br> linux<br> double 24809 </p> 24810 </th> 24811<th> 24812 <p> 24813 GNU C++ version 7.1.0<br> linux<br> long double 24814 </p> 24815 </th> 24816<th> 24817 <p> 24818 Sun compiler version 0x5150<br> Sun Solaris<br> long double 24819 </p> 24820 </th> 24821<th> 24822 <p> 24823 Microsoft Visual C++ version 14.1<br> Win32<br> double 24824 </p> 24825 </th> 24826</tr></thead> 24827<tbody> 24828<tr> 24829<td> 24830 <p> 24831 Legendre Polynomials: Small Values 24832 </p> 24833 </td> 24834<td> 24835 <p> 24836 <span class="blue">Max = 0.612ε (Mean = 0.0517ε)</span><br> <br> 24837 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 46.4ε (Mean = 7.46ε)) 24838 </p> 24839 </td> 24840<td> 24841 <p> 24842 <span class="blue">Max = 50.9ε (Mean = 9ε)</span> 24843 </p> 24844 </td> 24845<td> 24846 <p> 24847 <span class="blue">Max = 50.9ε (Mean = 8.98ε)</span> 24848 </p> 24849 </td> 24850<td> 24851 <p> 24852 <span class="blue">Max = 46.4ε (Mean = 7.32ε)</span> 24853 </p> 24854 </td> 24855</tr> 24856<tr> 24857<td> 24858 <p> 24859 Legendre Polynomials: Large Values 24860 </p> 24861 </td> 24862<td> 24863 <p> 24864 <span class="blue">Max = 2.49ε (Mean = 0.202ε)</span><br> <br> 24865 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 4.6e+03ε (Mean = 366ε)) 24866 </p> 24867 </td> 24868<td> 24869 <p> 24870 <span class="blue">Max = 5.98e+03ε (Mean = 478ε)</span> 24871 </p> 24872 </td> 24873<td> 24874 <p> 24875 <span class="blue">Max = 5.98e+03ε (Mean = 478ε)</span> 24876 </p> 24877 </td> 24878<td> 24879 <p> 24880 <span class="blue">Max = 4.6e+03ε (Mean = 366ε)</span> 24881 </p> 24882 </td> 24883</tr> 24884</tbody> 24885</table></div> 24886</div> 24887<br class="table-break"><div class="table"> 24888<a name="special_function_error_rates_rep.all_the_tables.table_lgamma"></a><p class="title"><b>Table 166. Error rates for lgamma</b></p> 24889<div class="table-contents"><table class="table" summary="Error rates for lgamma"> 24890<colgroup> 24891<col> 24892<col> 24893<col> 24894<col> 24895<col> 24896</colgroup> 24897<thead><tr> 24898<th> 24899 </th> 24900<th> 24901 <p> 24902 GNU C++ version 7.1.0<br> linux<br> double 24903 </p> 24904 </th> 24905<th> 24906 <p> 24907 GNU C++ version 7.1.0<br> linux<br> long double 24908 </p> 24909 </th> 24910<th> 24911 <p> 24912 Sun compiler version 0x5150<br> Sun Solaris<br> long double 24913 </p> 24914 </th> 24915<th> 24916 <p> 24917 Microsoft Visual C++ version 14.1<br> Win32<br> double 24918 </p> 24919 </th> 24920</tr></thead> 24921<tbody> 24922<tr> 24923<td> 24924 <p> 24925 factorials 24926 </p> 24927 </td> 24928<td> 24929 <p> 24930 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 24931 2.1:</em></span> Max = 33.6ε (Mean = 2.78ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 24932 Max = 1.55ε (Mean = 0.592ε)) 24933 </p> 24934 </td> 24935<td> 24936 <p> 24937 <span class="blue">Max = 0.991ε (Mean = 0.308ε)</span><br> <br> 24938 (<span class="emphasis"><em><cmath>:</em></span> Max = 1.67ε (Mean = 0.487ε))<br> 24939 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.67ε (Mean = 0.487ε)) 24940 </p> 24941 </td> 24942<td> 24943 <p> 24944 <span class="blue">Max = 0.991ε (Mean = 0.383ε)</span><br> <br> 24945 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.36ε (Mean = 0.476ε)) 24946 </p> 24947 </td> 24948<td> 24949 <p> 24950 <span class="blue">Max = 0.914ε (Mean = 0.175ε)</span><br> <br> 24951 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.958ε (Mean = 0.38ε)) 24952 </p> 24953 </td> 24954</tr> 24955<tr> 24956<td> 24957 <p> 24958 near 0 24959 </p> 24960 </td> 24961<td> 24962 <p> 24963 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 24964 2.1:</em></span> Max = 5.21ε (Mean = 1.57ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 24965 Max = 0ε (Mean = 0ε)) 24966 </p> 24967 </td> 24968<td> 24969 <p> 24970 <span class="blue">Max = 1.42ε (Mean = 0.566ε)</span><br> <br> 24971 (<span class="emphasis"><em><cmath>:</em></span> Max = 0.964ε (Mean = 0.543ε))<br> 24972 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.964ε (Mean = 0.543ε)) 24973 </p> 24974 </td> 24975<td> 24976 <p> 24977 <span class="blue">Max = 1.42ε (Mean = 0.566ε)</span><br> <br> 24978 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.964ε (Mean = 0.543ε)) 24979 </p> 24980 </td> 24981<td> 24982 <p> 24983 <span class="blue">Max = 0.964ε (Mean = 0.462ε)</span><br> <br> 24984 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.962ε (Mean = 0.372ε)) 24985 </p> 24986 </td> 24987</tr> 24988<tr> 24989<td> 24990 <p> 24991 near 1 24992 </p> 24993 </td> 24994<td> 24995 <p> 24996 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 24997 2.1:</em></span> Max = 442ε (Mean = 88.8ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 24998 Max = 7.99e+04ε (Mean = 1.68e+04ε)) 24999 </p> 25000 </td> 25001<td> 25002 <p> 25003 <span class="blue">Max = 0.948ε (Mean = 0.36ε)</span><br> <br> 25004 (<span class="emphasis"><em><cmath>:</em></span> Max = 0.615ε (Mean = 0.096ε))<br> 25005 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.615ε (Mean = 0.096ε)) 25006 </p> 25007 </td> 25008<td> 25009 <p> 25010 <span class="blue">Max = 0.948ε (Mean = 0.36ε)</span><br> <br> 25011 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.71ε (Mean = 0.581ε)) 25012 </p> 25013 </td> 25014<td> 25015 <p> 25016 <span class="blue">Max = 0.867ε (Mean = 0.468ε)</span><br> <br> 25017 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.906ε (Mean = 0.565ε)) 25018 </p> 25019 </td> 25020</tr> 25021<tr> 25022<td> 25023 <p> 25024 near 2 25025 </p> 25026 </td> 25027<td> 25028 <p> 25029 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 25030 2.1:</em></span> Max = 1.17e+03ε (Mean = 274ε))<br> (<span class="emphasis"><em>Rmath 25031 3.2.3:</em></span> Max = 2.63e+05ε (Mean = 5.84e+04ε)) 25032 </p> 25033 </td> 25034<td> 25035 <p> 25036 <span class="blue">Max = 0.878ε (Mean = 0.242ε)</span><br> <br> 25037 (<span class="emphasis"><em><cmath>:</em></span> Max = 0.741ε (Mean = 0.263ε))<br> 25038 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.741ε (Mean = 0.263ε)) 25039 </p> 25040 </td> 25041<td> 25042 <p> 25043 <span class="blue">Max = 0.878ε (Mean = 0.242ε)</span><br> <br> 25044 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.598ε (Mean = 0.235ε)) 25045 </p> 25046 </td> 25047<td> 25048 <p> 25049 <span class="blue">Max = 0.591ε (Mean = 0.159ε)</span><br> <br> 25050 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.741ε (Mean = 0.473ε)) 25051 </p> 25052 </td> 25053</tr> 25054<tr> 25055<td> 25056 <p> 25057 near -10 25058 </p> 25059 </td> 25060<td> 25061 <p> 25062 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 25063 2.1:</em></span> Max = 24.9ε (Mean = 4.6ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 25064 Max = 4.22ε (Mean = 1.26ε)) 25065 </p> 25066 </td> 25067<td> 25068 <p> 25069 <span class="blue">Max = 3.81ε (Mean = 1.01ε)</span><br> <br> 25070 (<span class="emphasis"><em><cmath>:</em></span> Max = 0.997ε (Mean = 0.412ε))<br> 25071 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.997ε (Mean = 0.412ε)) 25072 </p> 25073 </td> 25074<td> 25075 <p> 25076 <span class="blue">Max = 3.81ε (Mean = 1.01ε)</span><br> <br> 25077 (<span class="emphasis"><em><math.h>:</em></span> Max = 3.04ε (Mean = 1.01ε)) 25078 </p> 25079 </td> 25080<td> 25081 <p> 25082 <span class="blue">Max = 4.22ε (Mean = 1.33ε)</span><br> <br> 25083 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.997ε (Mean = 0.444ε)) 25084 </p> 25085 </td> 25086</tr> 25087<tr> 25088<td> 25089 <p> 25090 near -55 25091 </p> 25092 </td> 25093<td> 25094 <p> 25095 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 25096 2.1:</em></span> Max = 7.02ε (Mean = 1.47ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 25097 Max = 250ε (Mean = 60.9ε)) 25098 </p> 25099 </td> 25100<td> 25101 <p> 25102 <span class="blue">Max = 0.821ε (Mean = 0.513ε)</span><br> <br> 25103 (<span class="emphasis"><em><cmath>:</em></span> Max = 1.58ε (Mean = 0.672ε))<br> 25104 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.58ε (Mean = 0.672ε)) 25105 </p> 25106 </td> 25107<td> 25108 <p> 25109 <span class="blue">Max = 1.59ε (Mean = 0.587ε)</span><br> <br> 25110 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.821ε (Mean = 0.674ε)) 25111 </p> 25112 </td> 25113<td> 25114 <p> 25115 <span class="blue">Max = 0.821ε (Mean = 0.419ε)</span><br> <br> 25116 (<span class="emphasis"><em><math.h>:</em></span> Max = 249ε (Mean = 43.1ε)) 25117 </p> 25118 </td> 25119</tr> 25120</tbody> 25121</table></div> 25122</div> 25123<br class="table-break"><div class="table"> 25124<a name="special_function_error_rates_rep.all_the_tables.table_log1p"></a><p class="title"><b>Table 167. Error rates for log1p</b></p> 25125<div class="table-contents"><table class="table" summary="Error rates for log1p"> 25126<colgroup> 25127<col> 25128<col> 25129<col> 25130<col> 25131<col> 25132</colgroup> 25133<thead><tr> 25134<th> 25135 </th> 25136<th> 25137 <p> 25138 GNU C++ version 7.1.0<br> linux<br> long double 25139 </p> 25140 </th> 25141<th> 25142 <p> 25143 GNU C++ version 7.1.0<br> linux<br> double 25144 </p> 25145 </th> 25146<th> 25147 <p> 25148 Sun compiler version 0x5150<br> Sun Solaris<br> long double 25149 </p> 25150 </th> 25151<th> 25152 <p> 25153 Microsoft Visual C++ version 14.1<br> Win32<br> double 25154 </p> 25155 </th> 25156</tr></thead> 25157<tbody><tr> 25158<td> 25159 <p> 25160 Random test data 25161 </p> 25162 </td> 25163<td> 25164 <p> 25165 <span class="blue">Max = 0.818ε (Mean = 0.227ε)</span><br> <br> 25166 (<span class="emphasis"><em><cmath>:</em></span> Max = 0.818ε (Mean = 0.227ε))<br> 25167 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.818ε (Mean = 0.227ε)) 25168 </p> 25169 </td> 25170<td> 25171 <p> 25172 <span class="blue">Max = 0.846ε (Mean = 0.153ε)</span><br> <br> 25173 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 0.846ε (Mean = 0.153ε)) 25174 </p> 25175 </td> 25176<td> 25177 <p> 25178 <span class="blue">Max = 2.3ε (Mean = 0.66ε)</span><br> <br> 25179 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.818ε (Mean = 0.249ε)) 25180 </p> 25181 </td> 25182<td> 25183 <p> 25184 <span class="blue">Max = 0.509ε (Mean = 0.057ε)</span><br> <br> 25185 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.509ε (Mean = 0.057ε)) 25186 </p> 25187 </td> 25188</tr></tbody> 25189</table></div> 25190</div> 25191<br class="table-break"><div class="table"> 25192<a name="special_function_error_rates_rep.all_the_tables.table_non_central_beta_CDF"></a><p class="title"><b>Table 168. Error rates for non central beta CDF</b></p> 25193<div class="table-contents"><table class="table" summary="Error rates for non central beta CDF"> 25194<colgroup> 25195<col> 25196<col> 25197<col> 25198<col> 25199<col> 25200</colgroup> 25201<thead><tr> 25202<th> 25203 </th> 25204<th> 25205 <p> 25206 GNU C++ version 7.1.0<br> linux<br> double 25207 </p> 25208 </th> 25209<th> 25210 <p> 25211 GNU C++ version 7.1.0<br> linux<br> long double 25212 </p> 25213 </th> 25214<th> 25215 <p> 25216 Sun compiler version 0x5150<br> Sun Solaris<br> long double 25217 </p> 25218 </th> 25219<th> 25220 <p> 25221 Microsoft Visual C++ version 14.1<br> Win32<br> double 25222 </p> 25223 </th> 25224</tr></thead> 25225<tbody> 25226<tr> 25227<td> 25228 <p> 25229 Non Central Beta, medium parameters 25230 </p> 25231 </td> 25232<td> 25233 <p> 25234 <span class="blue">Max = 0.998ε (Mean = 0.0649ε)</span><br> <br> 25235 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 1.46e+26ε (Mean 25236 = 3.5e+24ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_Rmath_3_2_3_Non_Central_Beta_medium_parameters">And 25237 other failures.</a>)</span> 25238 </p> 25239 </td> 25240<td> 25241 <p> 25242 <span class="blue">Max = 824ε (Mean = 27.4ε)</span> 25243 </p> 25244 </td> 25245<td> 25246 <p> 25247 <span class="blue">Max = 832ε (Mean = 38.1ε)</span> 25248 </p> 25249 </td> 25250<td> 25251 <p> 25252 <span class="blue">Max = 242ε (Mean = 31ε)</span> 25253 </p> 25254 </td> 25255</tr> 25256<tr> 25257<td> 25258 <p> 25259 Non Central Beta, large parameters 25260 </p> 25261 </td> 25262<td> 25263 <p> 25264 <span class="blue">Max = 1.18ε (Mean = 0.175ε)</span><br> <br> 25265 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 1.01e+36ε (Mean 25266 = 1.19e+35ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_Rmath_3_2_3_Non_Central_Beta_large_parameters">And 25267 other failures.</a>)</span> 25268 </p> 25269 </td> 25270<td> 25271 <p> 25272 <span class="blue">Max = 2.5e+04ε (Mean = 3.78e+03ε)</span> 25273 </p> 25274 </td> 25275<td> 25276 <p> 25277 <span class="blue">Max = 2.57e+04ε (Mean = 4.45e+03ε)</span> 25278 </p> 25279 </td> 25280<td> 25281 <p> 25282 <span class="blue">Max = 3.66e+03ε (Mean = 500ε)</span> 25283 </p> 25284 </td> 25285</tr> 25286</tbody> 25287</table></div> 25288</div> 25289<br class="table-break"><div class="table"> 25290<a name="special_function_error_rates_rep.all_the_tables.table_non_central_beta_CDF_complement"></a><p class="title"><b>Table 169. Error rates for non central beta CDF complement</b></p> 25291<div class="table-contents"><table class="table" summary="Error rates for non central beta CDF complement"> 25292<colgroup> 25293<col> 25294<col> 25295<col> 25296<col> 25297<col> 25298</colgroup> 25299<thead><tr> 25300<th> 25301 </th> 25302<th> 25303 <p> 25304 GNU C++ version 7.1.0<br> linux<br> double 25305 </p> 25306 </th> 25307<th> 25308 <p> 25309 GNU C++ version 7.1.0<br> linux<br> long double 25310 </p> 25311 </th> 25312<th> 25313 <p> 25314 Sun compiler version 0x5150<br> Sun Solaris<br> long double 25315 </p> 25316 </th> 25317<th> 25318 <p> 25319 Microsoft Visual C++ version 14.1<br> Win32<br> double 25320 </p> 25321 </th> 25322</tr></thead> 25323<tbody> 25324<tr> 25325<td> 25326 <p> 25327 Non Central Beta, medium parameters 25328 </p> 25329 </td> 25330<td> 25331 <p> 25332 <span class="blue">Max = 0.998ε (Mean = 0.0936ε)</span><br> <br> 25333 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 7.5e+97ε (Mean 25334 = 1.37e+96ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_complement_Rmath_3_2_3_Non_Central_Beta_medium_parameters">And 25335 other failures.</a>)</span> 25336 </p> 25337 </td> 25338<td> 25339 <p> 25340 <span class="blue">Max = 396ε (Mean = 50.7ε)</span> 25341 </p> 25342 </td> 25343<td> 25344 <p> 25345 <span class="blue">Max = 554ε (Mean = 57.2ε)</span> 25346 </p> 25347 </td> 25348<td> 25349 <p> 25350 <span class="blue">Max = 624ε (Mean = 62.7ε)</span> 25351 </p> 25352 </td> 25353</tr> 25354<tr> 25355<td> 25356 <p> 25357 Non Central Beta, large parameters 25358 </p> 25359 </td> 25360<td> 25361 <p> 25362 <span class="blue">Max = 0.986ε (Mean = 0.188ε)</span><br> <br> 25363 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = +INFε (Mean 25364 = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_complement_Rmath_3_2_3_Non_Central_Beta_large_parameters">And 25365 other failures.</a>)</span> 25366 </p> 25367 </td> 25368<td> 25369 <p> 25370 <span class="blue">Max = 6.83e+03ε (Mean = 993ε)</span> 25371 </p> 25372 </td> 25373<td> 25374 <p> 25375 <span class="blue">Max = 3.56e+03ε (Mean = 707ε)</span> 25376 </p> 25377 </td> 25378<td> 25379 <p> 25380 <span class="blue">Max = 1.25e+04ε (Mean = 1.49e+03ε)</span> 25381 </p> 25382 </td> 25383</tr> 25384</tbody> 25385</table></div> 25386</div> 25387<br class="table-break"><div class="table"> 25388<a name="special_function_error_rates_rep.all_the_tables.table_non_central_chi_squared_CDF"></a><p class="title"><b>Table 170. Error rates for non central chi squared CDF</b></p> 25389<div class="table-contents"><table class="table" summary="Error rates for non central chi squared CDF"> 25390<colgroup> 25391<col> 25392<col> 25393<col> 25394<col> 25395<col> 25396</colgroup> 25397<thead><tr> 25398<th> 25399 </th> 25400<th> 25401 <p> 25402 GNU C++ version 7.1.0<br> linux<br> double 25403 </p> 25404 </th> 25405<th> 25406 <p> 25407 GNU C++ version 7.1.0<br> linux<br> long double 25408 </p> 25409 </th> 25410<th> 25411 <p> 25412 Sun compiler version 0x5150<br> Sun Solaris<br> long double 25413 </p> 25414 </th> 25415<th> 25416 <p> 25417 Microsoft Visual C++ version 14.1<br> Win32<br> double 25418 </p> 25419 </th> 25420</tr></thead> 25421<tbody> 25422<tr> 25423<td> 25424 <p> 25425 Non Central Chi Squared, medium parameters 25426 </p> 25427 </td> 25428<td> 25429 <p> 25430 <span class="blue">Max = 0.99ε (Mean = 0.0544ε)</span><br> <br> 25431 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 727ε (Mean = 121ε)) 25432 </p> 25433 </td> 25434<td> 25435 <p> 25436 <span class="blue">Max = 46.5ε (Mean = 10.3ε)</span> 25437 </p> 25438 </td> 25439<td> 25440 <p> 25441 <span class="blue">Max = 115ε (Mean = 13.9ε)</span> 25442 </p> 25443 </td> 25444<td> 25445 <p> 25446 <span class="blue">Max = 48.9ε (Mean = 10ε)</span> 25447 </p> 25448 </td> 25449</tr> 25450<tr> 25451<td> 25452 <p> 25453 Non Central Chi Squared, large parameters 25454 </p> 25455 </td> 25456<td> 25457 <p> 25458 <span class="blue">Max = 1.07ε (Mean = 0.102ε)</span><br> <br> 25459 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 3.27e+08ε (Mean 25460 = 2.23e+07ε))</span> 25461 </p> 25462 </td> 25463<td> 25464 <p> 25465 <span class="blue">Max = 3.07e+03ε (Mean = 336ε)</span> 25466 </p> 25467 </td> 25468<td> 25469 <p> 25470 <span class="blue">Max = 6.17e+03ε (Mean = 677ε)</span> 25471 </p> 25472 </td> 25473<td> 25474 <p> 25475 <span class="blue">Max = 9.79e+03ε (Mean = 723ε)</span> 25476 </p> 25477 </td> 25478</tr> 25479</tbody> 25480</table></div> 25481</div> 25482<br class="table-break"><div class="table"> 25483<a name="special_function_error_rates_rep.all_the_tables.table_non_central_chi_squared_CDF_complement"></a><p class="title"><b>Table 171. Error rates for non central chi squared CDF complement</b></p> 25484<div class="table-contents"><table class="table" summary="Error rates for non central chi squared CDF complement"> 25485<colgroup> 25486<col> 25487<col> 25488<col> 25489<col> 25490<col> 25491</colgroup> 25492<thead><tr> 25493<th> 25494 </th> 25495<th> 25496 <p> 25497 GNU C++ version 7.1.0<br> linux<br> double 25498 </p> 25499 </th> 25500<th> 25501 <p> 25502 GNU C++ version 7.1.0<br> linux<br> long double 25503 </p> 25504 </th> 25505<th> 25506 <p> 25507 Sun compiler version 0x5150<br> Sun Solaris<br> long double 25508 </p> 25509 </th> 25510<th> 25511 <p> 25512 Microsoft Visual C++ version 14.1<br> Win32<br> double 25513 </p> 25514 </th> 25515</tr></thead> 25516<tbody> 25517<tr> 25518<td> 25519 <p> 25520 Non Central Chi Squared, medium parameters 25521 </p> 25522 </td> 25523<td> 25524 <p> 25525 <span class="blue">Max = 0.96ε (Mean = 0.0635ε)</span><br> <br> 25526 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = +INFε (Mean 25527 = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_chi_squared_CDF_complement_Rmath_3_2_3_Non_Central_Chi_Squared_medium_parameters">And 25528 other failures.</a>)</span> 25529 </p> 25530 </td> 25531<td> 25532 <p> 25533 <span class="blue">Max = 107ε (Mean = 17.2ε)</span> 25534 </p> 25535 </td> 25536<td> 25537 <p> 25538 <span class="blue">Max = 171ε (Mean = 22.8ε)</span> 25539 </p> 25540 </td> 25541<td> 25542 <p> 25543 <span class="blue">Max = 98.6ε (Mean = 15.8ε)</span> 25544 </p> 25545 </td> 25546</tr> 25547<tr> 25548<td> 25549 <p> 25550 Non Central Chi Squared, large parameters 25551 </p> 25552 </td> 25553<td> 25554 <p> 25555 <span class="blue">Max = 2.11ε (Mean = 0.278ε)</span><br> <br> 25556 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = +INFε (Mean 25557 = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_chi_squared_CDF_complement_Rmath_3_2_3_Non_Central_Chi_Squared_large_parameters">And 25558 other failures.</a>)</span> 25559 </p> 25560 </td> 25561<td> 25562 <p> 25563 <span class="blue">Max = 5.02e+03ε (Mean = 630ε)</span> 25564 </p> 25565 </td> 25566<td> 25567 <p> 25568 <span class="blue">Max = 5.1e+03ε (Mean = 577ε)</span> 25569 </p> 25570 </td> 25571<td> 25572 <p> 25573 <span class="blue">Max = 5.43e+03ε (Mean = 705ε)</span> 25574 </p> 25575 </td> 25576</tr> 25577</tbody> 25578</table></div> 25579</div> 25580<br class="table-break"><div class="table"> 25581<a name="special_function_error_rates_rep.all_the_tables.table_non_central_t_CDF"></a><p class="title"><b>Table 172. Error rates for non central t CDF</b></p> 25582<div class="table-contents"><table class="table" summary="Error rates for non central t CDF"> 25583<colgroup> 25584<col> 25585<col> 25586<col> 25587<col> 25588<col> 25589</colgroup> 25590<thead><tr> 25591<th> 25592 </th> 25593<th> 25594 <p> 25595 GNU C++ version 7.1.0<br> linux<br> double 25596 </p> 25597 </th> 25598<th> 25599 <p> 25600 GNU C++ version 7.1.0<br> linux<br> long double 25601 </p> 25602 </th> 25603<th> 25604 <p> 25605 Sun compiler version 0x5150<br> Sun Solaris<br> long double 25606 </p> 25607 </th> 25608<th> 25609 <p> 25610 Microsoft Visual C++ version 14.1<br> Win32<br> double 25611 </p> 25612 </th> 25613</tr></thead> 25614<tbody> 25615<tr> 25616<td> 25617 <p> 25618 Non Central T 25619 </p> 25620 </td> 25621<td> 25622 <p> 25623 <span class="blue">Max = 0.796ε (Mean = 0.0691ε)</span><br> <br> 25624 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 5.28e+15ε (Mean 25625 = 8.49e+14ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_t_CDF_Rmath_3_2_3_Non_Central_T">And 25626 other failures.</a>)</span> 25627 </p> 25628 </td> 25629<td> 25630 <p> 25631 <span class="blue">Max = 139ε (Mean = 31ε)</span> 25632 </p> 25633 </td> 25634<td> 25635 <p> 25636 <span class="blue">Max = 145ε (Mean = 30.9ε)</span> 25637 </p> 25638 </td> 25639<td> 25640 <p> 25641 <span class="blue">Max = 135ε (Mean = 32.1ε)</span> 25642 </p> 25643 </td> 25644</tr> 25645<tr> 25646<td> 25647 <p> 25648 Non Central T (small non-centrality) 25649 </p> 25650 </td> 25651<td> 25652 <p> 25653 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath 25654 3.2.3:</em></span> Max = 2.09e+03ε (Mean = 244ε)) 25655 </p> 25656 </td> 25657<td> 25658 <p> 25659 <span class="blue">Max = 3.86ε (Mean = 1.4ε)</span> 25660 </p> 25661 </td> 25662<td> 25663 <p> 25664 <span class="blue">Max = 9.15ε (Mean = 2.13ε)</span> 25665 </p> 25666 </td> 25667<td> 25668 <p> 25669 <span class="blue">Max = 6.17ε (Mean = 1.45ε)</span> 25670 </p> 25671 </td> 25672</tr> 25673<tr> 25674<td> 25675 <p> 25676 Non Central T (large parameters) 25677 </p> 25678 </td> 25679<td> 25680 <p> 25681 <span class="blue">Max = 257ε (Mean = 72.1ε)</span><br> <br> 25682 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.46ε (Mean = 0.657ε)) 25683 </p> 25684 </td> 25685<td> 25686 <p> 25687 <span class="blue">Max = 5.26e+05ε (Mean = 1.48e+05ε)</span> 25688 </p> 25689 </td> 25690<td> 25691 <p> 25692 <span class="blue">Max = 5.24e+05ε (Mean = 1.47e+05ε)</span> 25693 </p> 25694 </td> 25695<td> 25696 <p> 25697 <span class="blue">Max = 286ε (Mean = 62.8ε)</span> 25698 </p> 25699 </td> 25700</tr> 25701</tbody> 25702</table></div> 25703</div> 25704<br class="table-break"><div class="table"> 25705<a name="special_function_error_rates_rep.all_the_tables.table_non_central_t_CDF_complement"></a><p class="title"><b>Table 173. Error rates for non central t CDF complement</b></p> 25706<div class="table-contents"><table class="table" summary="Error rates for non central t CDF complement"> 25707<colgroup> 25708<col> 25709<col> 25710<col> 25711<col> 25712<col> 25713</colgroup> 25714<thead><tr> 25715<th> 25716 </th> 25717<th> 25718 <p> 25719 GNU C++ version 7.1.0<br> linux<br> double 25720 </p> 25721 </th> 25722<th> 25723 <p> 25724 GNU C++ version 7.1.0<br> linux<br> long double 25725 </p> 25726 </th> 25727<th> 25728 <p> 25729 Sun compiler version 0x5150<br> Sun Solaris<br> long double 25730 </p> 25731 </th> 25732<th> 25733 <p> 25734 Microsoft Visual C++ version 14.1<br> Win32<br> double 25735 </p> 25736 </th> 25737</tr></thead> 25738<tbody> 25739<tr> 25740<td> 25741 <p> 25742 Non Central T 25743 </p> 25744 </td> 25745<td> 25746 <p> 25747 <span class="blue">Max = 0.707ε (Mean = 0.0497ε)</span><br> <br> 25748 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 6.19e+15ε (Mean 25749 = 6.72e+14ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_t_CDF_complement_Rmath_3_2_3_Non_Central_T">And 25750 other failures.</a>)</span> 25751 </p> 25752 </td> 25753<td> 25754 <p> 25755 <span class="blue">Max = 201ε (Mean = 31.7ε)</span> 25756 </p> 25757 </td> 25758<td> 25759 <p> 25760 <span class="blue">Max = 340ε (Mean = 43.2ε)</span> 25761 </p> 25762 </td> 25763<td> 25764 <p> 25765 <span class="blue">Max = 154ε (Mean = 32.1ε)</span> 25766 </p> 25767 </td> 25768</tr> 25769<tr> 25770<td> 25771 <p> 25772 Non Central T (small non-centrality) 25773 </p> 25774 </td> 25775<td> 25776 <p> 25777 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath 25778 3.2.3:</em></span> Max = 1.87e+03ε (Mean = 263ε)) 25779 </p> 25780 </td> 25781<td> 25782 <p> 25783 <span class="blue">Max = 10.5ε (Mean = 2.13ε)</span> 25784 </p> 25785 </td> 25786<td> 25787 <p> 25788 <span class="blue">Max = 10.5ε (Mean = 2.39ε)</span> 25789 </p> 25790 </td> 25791<td> 25792 <p> 25793 <span class="blue">Max = 4.6ε (Mean = 1.63ε)</span> 25794 </p> 25795 </td> 25796</tr> 25797<tr> 25798<td> 25799 <p> 25800 Non Central T (large parameters) 25801 </p> 25802 </td> 25803<td> 25804 <p> 25805 <span class="blue">Max = 478ε (Mean = 96.3ε)</span><br> <br> 25806 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.24ε (Mean = 0.945ε)) 25807 </p> 25808 </td> 25809<td> 25810 <p> 25811 <span class="blue">Max = 9.79e+05ε (Mean = 1.97e+05ε)</span> 25812 </p> 25813 </td> 25814<td> 25815 <p> 25816 <span class="blue">Max = 9.79e+05ε (Mean = 1.97e+05ε)</span> 25817 </p> 25818 </td> 25819<td> 25820 <p> 25821 <span class="blue">Max = 227ε (Mean = 50.4ε)</span> 25822 </p> 25823 </td> 25824</tr> 25825</tbody> 25826</table></div> 25827</div> 25828<br class="table-break"><div class="table"> 25829<a name="special_function_error_rates_rep.all_the_tables.table_owens_t"></a><p class="title"><b>Table 174. Error rates for owens_t</b></p> 25830<div class="table-contents"><table class="table" summary="Error rates for owens_t"> 25831<colgroup> 25832<col> 25833<col> 25834<col> 25835<col> 25836<col> 25837</colgroup> 25838<thead><tr> 25839<th> 25840 </th> 25841<th> 25842 <p> 25843 GNU C++ version 7.1.0<br> linux<br> double 25844 </p> 25845 </th> 25846<th> 25847 <p> 25848 GNU C++ version 7.1.0<br> linux<br> long double 25849 </p> 25850 </th> 25851<th> 25852 <p> 25853 Sun compiler version 0x5150<br> Sun Solaris<br> long double 25854 </p> 25855 </th> 25856<th> 25857 <p> 25858 Microsoft Visual C++ version 14.1<br> Win32<br> double 25859 </p> 25860 </th> 25861</tr></thead> 25862<tbody> 25863<tr> 25864<td> 25865 <p> 25866 Owens T (medium small values) 25867 </p> 25868 </td> 25869<td> 25870 <p> 25871 <span class="blue">Max = 0ε (Mean = 0ε)</span> 25872 </p> 25873 </td> 25874<td> 25875 <p> 25876 <span class="blue">Max = 3.34ε (Mean = 0.944ε)</span> 25877 </p> 25878 </td> 25879<td> 25880 <p> 25881 <span class="blue">Max = 3.34ε (Mean = 0.911ε)</span> 25882 </p> 25883 </td> 25884<td> 25885 <p> 25886 <span class="blue">Max = 4.37ε (Mean = 0.98ε)</span> 25887 </p> 25888 </td> 25889</tr> 25890<tr> 25891<td> 25892 <p> 25893 Owens T (large and diverse values) 25894 </p> 25895 </td> 25896<td> 25897 <p> 25898 <span class="blue">Max = 0ε (Mean = 0ε)</span> 25899 </p> 25900 </td> 25901<td> 25902 <p> 25903 <span class="blue">Max = 49ε (Mean = 2.16ε)</span> 25904 </p> 25905 </td> 25906<td> 25907 <p> 25908 <span class="blue">Max = 24.5ε (Mean = 1.39ε)</span> 25909 </p> 25910 </td> 25911<td> 25912 <p> 25913 <span class="blue">Max = 3.78ε (Mean = 0.621ε)</span> 25914 </p> 25915 </td> 25916</tr> 25917</tbody> 25918</table></div> 25919</div> 25920<br class="table-break"><div class="table"> 25921<a name="special_function_error_rates_rep.all_the_tables.table_polygamma"></a><p class="title"><b>Table 175. Error rates for polygamma</b></p> 25922<div class="table-contents"><table class="table" summary="Error rates for polygamma"> 25923<colgroup> 25924<col> 25925<col> 25926<col> 25927<col> 25928<col> 25929</colgroup> 25930<thead><tr> 25931<th> 25932 </th> 25933<th> 25934 <p> 25935 GNU C++ version 7.1.0<br> linux<br> double 25936 </p> 25937 </th> 25938<th> 25939 <p> 25940 GNU C++ version 7.1.0<br> linux<br> long double 25941 </p> 25942 </th> 25943<th> 25944 <p> 25945 Sun compiler version 0x5150<br> Sun Solaris<br> long double 25946 </p> 25947 </th> 25948<th> 25949 <p> 25950 Microsoft Visual C++ version 14.1<br> Win32<br> double 25951 </p> 25952 </th> 25953</tr></thead> 25954<tbody> 25955<tr> 25956<td> 25957 <p> 25958 Mathematica Data 25959 </p> 25960 </td> 25961<td> 25962 <p> 25963 <span class="blue">Max = 0.824ε (Mean = 0.0574ε)</span><br> <br> 25964 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 62.9ε (Mean = 12.8ε))<br> (<span class="emphasis"><em>Rmath 25965 3.2.3:</em></span> Max = 108ε (Mean = 15.2ε)) 25966 </p> 25967 </td> 25968<td> 25969 <p> 25970 <span class="blue">Max = 7.38ε (Mean = 1.84ε)</span> 25971 </p> 25972 </td> 25973<td> 25974 <p> 25975 <span class="blue">Max = 34.3ε (Mean = 7.65ε)</span> 25976 </p> 25977 </td> 25978<td> 25979 <p> 25980 <span class="blue">Max = 9.32ε (Mean = 1.95ε)</span> 25981 </p> 25982 </td> 25983</tr> 25984<tr> 25985<td> 25986 <p> 25987 Mathematica Data - large arguments 25988 </p> 25989 </td> 25990<td> 25991 <p> 25992 <span class="blue">Max = 0.998ε (Mean = 0.0592ε)</span><br> <br> 25993 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 244ε (Mean = 32.8ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_large_arguments">And 25994 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 25995 <span class="red">Max = 1.71e+56ε (Mean = 1.01e+55ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_large_arguments">And 25996 other failures.</a>)</span> 25997 </p> 25998 </td> 25999<td> 26000 <p> 26001 <span class="blue">Max = 2.23ε (Mean = 0.323ε)</span> 26002 </p> 26003 </td> 26004<td> 26005 <p> 26006 <span class="blue">Max = 11.1ε (Mean = 0.848ε)</span> 26007 </p> 26008 </td> 26009<td> 26010 <p> 26011 <span class="blue">Max = 150ε (Mean = 13.9ε)</span> 26012 </p> 26013 </td> 26014</tr> 26015<tr> 26016<td> 26017 <p> 26018 Mathematica Data - negative arguments 26019 </p> 26020 </td> 26021<td> 26022 <p> 26023 <span class="blue">Max = 0.516ε (Mean = 0.022ε)</span><br> <br> 26024 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 36.6ε (Mean = 3.04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_negative_arguments">And 26025 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 26026 Max = 0ε (Mean = 0ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_negative_arguments">And 26027 other failures.</a>) 26028 </p> 26029 </td> 26030<td> 26031 <p> 26032 <span class="blue">Max = 269ε (Mean = 87.7ε)</span> 26033 </p> 26034 </td> 26035<td> 26036 <p> 26037 <span class="blue">Max = 269ε (Mean = 88.4ε)</span> 26038 </p> 26039 </td> 26040<td> 26041 <p> 26042 <span class="blue">Max = 497ε (Mean = 129ε)</span> 26043 </p> 26044 </td> 26045</tr> 26046<tr> 26047<td> 26048 <p> 26049 Mathematica Data - large negative arguments 26050 </p> 26051 </td> 26052<td> 26053 <p> 26054 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 26055 2.1:</em></span> Max = 1.79ε (Mean = 0.197ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_large_negative_arguments">And 26056 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 26057 Max = 0ε (Mean = 0ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_large_negative_arguments">And 26058 other failures.</a>) 26059 </p> 26060 </td> 26061<td> 26062 <p> 26063 <span class="blue">Max = 155ε (Mean = 96.4ε)</span> 26064 </p> 26065 </td> 26066<td> 26067 <p> 26068 <span class="blue">Max = 155ε (Mean = 96.4ε)</span> 26069 </p> 26070 </td> 26071<td> 26072 <p> 26073 <span class="blue">Max = 162ε (Mean = 101ε)</span> 26074 </p> 26075 </td> 26076</tr> 26077<tr> 26078<td> 26079 <p> 26080 Mathematica Data - small arguments 26081 </p> 26082 </td> 26083<td> 26084 <p> 26085 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 26086 2.1:</em></span> Max = 15.2ε (Mean = 5.03ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 26087 Max = 106ε (Mean = 20ε)) 26088 </p> 26089 </td> 26090<td> 26091 <p> 26092 <span class="blue">Max = 3.33ε (Mean = 0.75ε)</span> 26093 </p> 26094 </td> 26095<td> 26096 <p> 26097 <span class="blue">Max = 3.33ε (Mean = 0.75ε)</span> 26098 </p> 26099 </td> 26100<td> 26101 <p> 26102 <span class="blue">Max = 3ε (Mean = 0.496ε)</span> 26103 </p> 26104 </td> 26105</tr> 26106<tr> 26107<td> 26108 <p> 26109 Mathematica Data - Large orders and other bug cases 26110 </p> 26111 </td> 26112<td> 26113 <p> 26114 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 26115 2.1:</em></span> Max = 151ε (Mean = 39.3ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_Large_orders_and_other_bug_cases">And 26116 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 26117 <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_Large_orders_and_other_bug_cases">And 26118 other failures.</a>)</span> 26119 </p> 26120 </td> 26121<td> 26122 <p> 26123 <span class="blue">Max = 54.5ε (Mean = 13.3ε)</span> 26124 </p> 26125 </td> 26126<td> 26127 <p> 26128 <span class="blue">Max = 145ε (Mean = 55.9ε)</span> 26129 </p> 26130 </td> 26131<td> 26132 <p> 26133 <span class="blue">Max = 200ε (Mean = 57.2ε)</span> 26134 </p> 26135 </td> 26136</tr> 26137</tbody> 26138</table></div> 26139</div> 26140<br class="table-break"><div class="table"> 26141<a name="special_function_error_rates_rep.all_the_tables.table_powm1"></a><p class="title"><b>Table 176. Error rates for powm1</b></p> 26142<div class="table-contents"><table class="table" summary="Error rates for powm1"> 26143<colgroup> 26144<col> 26145<col> 26146<col> 26147<col> 26148<col> 26149</colgroup> 26150<thead><tr> 26151<th> 26152 </th> 26153<th> 26154 <p> 26155 GNU C++ version 7.1.0<br> linux<br> double 26156 </p> 26157 </th> 26158<th> 26159 <p> 26160 GNU C++ version 7.1.0<br> linux<br> long double 26161 </p> 26162 </th> 26163<th> 26164 <p> 26165 Sun compiler version 0x5150<br> Sun Solaris<br> long double 26166 </p> 26167 </th> 26168<th> 26169 <p> 26170 Microsoft Visual C++ version 14.1<br> Win32<br> double 26171 </p> 26172 </th> 26173</tr></thead> 26174<tbody><tr> 26175<td> 26176 <p> 26177 powm1 26178 </p> 26179 </td> 26180<td> 26181 <p> 26182 <span class="blue">Max = 1.06ε (Mean = 0.425ε)</span> 26183 </p> 26184 </td> 26185<td> 26186 <p> 26187 <span class="blue">Max = 2.04ε (Mean = 0.493ε)</span> 26188 </p> 26189 </td> 26190<td> 26191 <p> 26192 <span class="blue">Max = 1.88ε (Mean = 0.49ε)</span> 26193 </p> 26194 </td> 26195<td> 26196 <p> 26197 <span class="blue">Max = 1.84ε (Mean = 0.486ε)</span> 26198 </p> 26199 </td> 26200</tr></tbody> 26201</table></div> 26202</div> 26203<br class="table-break"><div class="table"> 26204<a name="special_function_error_rates_rep.all_the_tables.table_sin_pi"></a><p class="title"><b>Table 177. Error rates for sin_pi</b></p> 26205<div class="table-contents"><table class="table" summary="Error rates for sin_pi"> 26206<colgroup> 26207<col> 26208<col> 26209<col> 26210<col> 26211<col> 26212</colgroup> 26213<thead><tr> 26214<th> 26215 </th> 26216<th> 26217 <p> 26218 GNU C++ version 7.1.0<br> linux<br> double 26219 </p> 26220 </th> 26221<th> 26222 <p> 26223 GNU C++ version 7.1.0<br> linux<br> long double 26224 </p> 26225 </th> 26226<th> 26227 <p> 26228 Sun compiler version 0x5150<br> Sun Solaris<br> long double 26229 </p> 26230 </th> 26231<th> 26232 <p> 26233 Microsoft Visual C++ version 14.1<br> Win32<br> double 26234 </p> 26235 </th> 26236</tr></thead> 26237<tbody> 26238<tr> 26239<td> 26240 <p> 26241 sin_pi and cos_pi 26242 </p> 26243 </td> 26244<td> 26245 <p> 26246 <span class="blue">Max = 0ε (Mean = 0ε)</span> 26247 </p> 26248 </td> 26249<td> 26250 <p> 26251 <span class="blue">Max = 0.996ε (Mean = 0.335ε)</span> 26252 </p> 26253 </td> 26254<td> 26255 <p> 26256 <span class="blue">Max = 0.996ε (Mean = 0.336ε)</span> 26257 </p> 26258 </td> 26259<td> 26260 <p> 26261 <span class="blue">Max = 0.99ε (Mean = 0.328ε)</span> 26262 </p> 26263 </td> 26264</tr> 26265<tr> 26266<td> 26267 <p> 26268 sin_pi and cos_pi near integers and half integers 26269 </p> 26270 </td> 26271<td> 26272 <p> 26273 <span class="blue">Max = 0ε (Mean = 0ε)</span> 26274 </p> 26275 </td> 26276<td> 26277 <p> 26278 <span class="blue">Max = 0.976ε (Mean = 0.293ε)</span> 26279 </p> 26280 </td> 26281<td> 26282 <p> 26283 <span class="blue">Max = 0.976ε (Mean = 0.293ε)</span> 26284 </p> 26285 </td> 26286<td> 26287 <p> 26288 <span class="blue">Max = 0.996ε (Mean = 0.343ε)</span> 26289 </p> 26290 </td> 26291</tr> 26292</tbody> 26293</table></div> 26294</div> 26295<br class="table-break"><div class="table"> 26296<a name="special_function_error_rates_rep.all_the_tables.table_sph_bessel"></a><p class="title"><b>Table 178. Error rates for sph_bessel</b></p> 26297<div class="table-contents"><table class="table" summary="Error rates for sph_bessel"> 26298<colgroup> 26299<col> 26300<col> 26301<col> 26302<col> 26303<col> 26304</colgroup> 26305<thead><tr> 26306<th> 26307 </th> 26308<th> 26309 <p> 26310 GNU C++ version 7.1.0<br> linux<br> long double 26311 </p> 26312 </th> 26313<th> 26314 <p> 26315 GNU C++ version 7.1.0<br> linux<br> double 26316 </p> 26317 </th> 26318<th> 26319 <p> 26320 Sun compiler version 0x5150<br> Sun Solaris<br> long double 26321 </p> 26322 </th> 26323<th> 26324 <p> 26325 Microsoft Visual C++ version 14.1<br> Win32<br> double 26326 </p> 26327 </th> 26328</tr></thead> 26329<tbody><tr> 26330<td> 26331 <p> 26332 Bessel j: Random Data 26333 </p> 26334 </td> 26335<td> 26336 <p> 26337 <span class="blue">Max = 243ε (Mean = 13.3ε)</span><br> <br> 26338 (<span class="emphasis"><em><cmath>:</em></span> Max = 1.91e+06ε (Mean = 1.09e+05ε)) 26339 </p> 26340 </td> 26341<td> 26342 <p> 26343 <span class="blue">Max = 0.978ε (Mean = 0.0445ε)</span><br> <br> 26344 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.79e+03ε (Mean = 107ε)) 26345 </p> 26346 </td> 26347<td> 26348 <p> 26349 <span class="blue">Max = 243ε (Mean = 33.7ε)</span> 26350 </p> 26351 </td> 26352<td> 26353 <p> 26354 <span class="blue">Max = 245ε (Mean = 16.3ε)</span> 26355 </p> 26356 </td> 26357</tr></tbody> 26358</table></div> 26359</div> 26360<br class="table-break"><div class="table"> 26361<a name="special_function_error_rates_rep.all_the_tables.table_sph_bessel_prime"></a><p class="title"><b>Table 179. Error rates for sph_bessel_prime</b></p> 26362<div class="table-contents"><table class="table" summary="Error rates for sph_bessel_prime"> 26363<colgroup> 26364<col> 26365<col> 26366<col> 26367<col> 26368<col> 26369</colgroup> 26370<thead><tr> 26371<th> 26372 </th> 26373<th> 26374 <p> 26375 GNU C++ version 7.1.0<br> linux<br> double 26376 </p> 26377 </th> 26378<th> 26379 <p> 26380 GNU C++ version 7.1.0<br> linux<br> long double 26381 </p> 26382 </th> 26383<th> 26384 <p> 26385 Sun compiler version 0x5150<br> Sun Solaris<br> long double 26386 </p> 26387 </th> 26388<th> 26389 <p> 26390 Microsoft Visual C++ version 14.1<br> Win32<br> double 26391 </p> 26392 </th> 26393</tr></thead> 26394<tbody><tr> 26395<td> 26396 <p> 26397 Bessel j': Random Data 26398 </p> 26399 </td> 26400<td> 26401 <p> 26402 <span class="blue">Max = 0.753ε (Mean = 0.0343ε)</span> 26403 </p> 26404 </td> 26405<td> 26406 <p> 26407 <span class="blue">Max = 167ε (Mean = 12ε)</span> 26408 </p> 26409 </td> 26410<td> 26411 <p> 26412 <span class="blue">Max = 167ε (Mean = 33.2ε)</span> 26413 </p> 26414 </td> 26415<td> 26416 <p> 26417 <span class="blue">Max = 307ε (Mean = 25.2ε)</span> 26418 </p> 26419 </td> 26420</tr></tbody> 26421</table></div> 26422</div> 26423<br class="table-break"><div class="table"> 26424<a name="special_function_error_rates_rep.all_the_tables.table_sph_neumann"></a><p class="title"><b>Table 180. Error rates for sph_neumann</b></p> 26425<div class="table-contents"><table class="table" summary="Error rates for sph_neumann"> 26426<colgroup> 26427<col> 26428<col> 26429<col> 26430<col> 26431<col> 26432</colgroup> 26433<thead><tr> 26434<th> 26435 </th> 26436<th> 26437 <p> 26438 GNU C++ version 7.1.0<br> linux<br> long double 26439 </p> 26440 </th> 26441<th> 26442 <p> 26443 GNU C++ version 7.1.0<br> linux<br> double 26444 </p> 26445 </th> 26446<th> 26447 <p> 26448 Sun compiler version 0x5150<br> Sun Solaris<br> long double 26449 </p> 26450 </th> 26451<th> 26452 <p> 26453 Microsoft Visual C++ version 14.1<br> Win32<br> double 26454 </p> 26455 </th> 26456</tr></thead> 26457<tbody><tr> 26458<td> 26459 <p> 26460 y: Random Data 26461 </p> 26462 </td> 26463<td> 26464 <p> 26465 <span class="blue">Max = 234ε (Mean = 19.5ε)</span><br> <br> 26466 (<span class="emphasis"><em><cmath>:</em></span> Max = 1.6e+06ε (Mean = 1.4e+05ε)) 26467 </p> 26468 </td> 26469<td> 26470 <p> 26471 <span class="blue">Max = 0.995ε (Mean = 0.0665ε)</span><br> <br> 26472 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.5e+04ε (Mean = 5.33e+03ε)) 26473 </p> 26474 </td> 26475<td> 26476 <p> 26477 <span class="blue">Max = 234ε (Mean = 19.8ε)</span> 26478 </p> 26479 </td> 26480<td> 26481 <p> 26482 <span class="blue">Max = 281ε (Mean = 31.1ε)</span> 26483 </p> 26484 </td> 26485</tr></tbody> 26486</table></div> 26487</div> 26488<br class="table-break"><div class="table"> 26489<a name="special_function_error_rates_rep.all_the_tables.table_sph_neumann_prime"></a><p class="title"><b>Table 181. Error rates for sph_neumann_prime</b></p> 26490<div class="table-contents"><table class="table" summary="Error rates for sph_neumann_prime"> 26491<colgroup> 26492<col> 26493<col> 26494<col> 26495<col> 26496<col> 26497</colgroup> 26498<thead><tr> 26499<th> 26500 </th> 26501<th> 26502 <p> 26503 GNU C++ version 7.1.0<br> linux<br> double 26504 </p> 26505 </th> 26506<th> 26507 <p> 26508 GNU C++ version 7.1.0<br> linux<br> long double 26509 </p> 26510 </th> 26511<th> 26512 <p> 26513 Sun compiler version 0x5150<br> Sun Solaris<br> long double 26514 </p> 26515 </th> 26516<th> 26517 <p> 26518 Microsoft Visual C++ version 14.1<br> Win32<br> double 26519 </p> 26520 </th> 26521</tr></thead> 26522<tbody><tr> 26523<td> 26524 <p> 26525 y': Random Data 26526 </p> 26527 </td> 26528<td> 26529 <p> 26530 <span class="blue">Max = 0.988ε (Mean = 0.0869ε)</span> 26531 </p> 26532 </td> 26533<td> 26534 <p> 26535 <span class="blue">Max = 158ε (Mean = 18.8ε)</span> 26536 </p> 26537 </td> 26538<td> 26539 <p> 26540 <span class="blue">Max = 158ε (Mean = 20.2ε)</span> 26541 </p> 26542 </td> 26543<td> 26544 <p> 26545 <span class="blue">Max = 296ε (Mean = 25.6ε)</span> 26546 </p> 26547 </td> 26548</tr></tbody> 26549</table></div> 26550</div> 26551<br class="table-break"><div class="table"> 26552<a name="special_function_error_rates_rep.all_the_tables.table_spherical_harmonic_i"></a><p class="title"><b>Table 182. Error rates for spherical_harmonic_i</b></p> 26553<div class="table-contents"><table class="table" summary="Error rates for spherical_harmonic_i"> 26554<colgroup> 26555<col> 26556<col> 26557<col> 26558<col> 26559<col> 26560</colgroup> 26561<thead><tr> 26562<th> 26563 </th> 26564<th> 26565 <p> 26566 GNU C++ version 7.1.0<br> linux<br> double 26567 </p> 26568 </th> 26569<th> 26570 <p> 26571 GNU C++ version 7.1.0<br> linux<br> long double 26572 </p> 26573 </th> 26574<th> 26575 <p> 26576 Sun compiler version 0x5150<br> Sun Solaris<br> long double 26577 </p> 26578 </th> 26579<th> 26580 <p> 26581 Microsoft Visual C++ version 14.1<br> Win32<br> double 26582 </p> 26583 </th> 26584</tr></thead> 26585<tbody><tr> 26586<td> 26587 <p> 26588 Spherical Harmonics 26589 </p> 26590 </td> 26591<td> 26592 <p> 26593 <span class="blue">Max = 1.36ε (Mean = 0.0765ε)</span> 26594 </p> 26595 </td> 26596<td> 26597 <p> 26598 <span class="blue">Max = 2.89e+03ε (Mean = 108ε)</span> 26599 </p> 26600 </td> 26601<td> 26602 <p> 26603 <span class="blue">Max = 1.03e+04ε (Mean = 327ε)</span> 26604 </p> 26605 </td> 26606<td> 26607 <p> 26608 <span class="blue">Max = 2.27e+04ε (Mean = 725ε)</span> 26609 </p> 26610 </td> 26611</tr></tbody> 26612</table></div> 26613</div> 26614<br class="table-break"><div class="table"> 26615<a name="special_function_error_rates_rep.all_the_tables.table_spherical_harmonic_r"></a><p class="title"><b>Table 183. Error rates for spherical_harmonic_r</b></p> 26616<div class="table-contents"><table class="table" summary="Error rates for spherical_harmonic_r"> 26617<colgroup> 26618<col> 26619<col> 26620<col> 26621<col> 26622<col> 26623</colgroup> 26624<thead><tr> 26625<th> 26626 </th> 26627<th> 26628 <p> 26629 GNU C++ version 7.1.0<br> linux<br> double 26630 </p> 26631 </th> 26632<th> 26633 <p> 26634 GNU C++ version 7.1.0<br> linux<br> long double 26635 </p> 26636 </th> 26637<th> 26638 <p> 26639 Sun compiler version 0x5150<br> Sun Solaris<br> long double 26640 </p> 26641 </th> 26642<th> 26643 <p> 26644 Microsoft Visual C++ version 14.1<br> Win32<br> double 26645 </p> 26646 </th> 26647</tr></thead> 26648<tbody><tr> 26649<td> 26650 <p> 26651 Spherical Harmonics 26652 </p> 26653 </td> 26654<td> 26655 <p> 26656 <span class="blue">Max = 1.58ε (Mean = 0.0707ε)</span> 26657 </p> 26658 </td> 26659<td> 26660 <p> 26661 <span class="blue">Max = 2.89e+03ε (Mean = 108ε)</span> 26662 </p> 26663 </td> 26664<td> 26665 <p> 26666 <span class="blue">Max = 1.03e+04ε (Mean = 327ε)</span> 26667 </p> 26668 </td> 26669<td> 26670 <p> 26671 <span class="blue">Max = 2.27e+04ε (Mean = 725ε)</span> 26672 </p> 26673 </td> 26674</tr></tbody> 26675</table></div> 26676</div> 26677<br class="table-break"><div class="table"> 26678<a name="special_function_error_rates_rep.all_the_tables.table_sqrt1pm1"></a><p class="title"><b>Table 184. Error rates for sqrt1pm1</b></p> 26679<div class="table-contents"><table class="table" summary="Error rates for sqrt1pm1"> 26680<colgroup> 26681<col> 26682<col> 26683<col> 26684<col> 26685<col> 26686</colgroup> 26687<thead><tr> 26688<th> 26689 </th> 26690<th> 26691 <p> 26692 GNU C++ version 7.1.0<br> linux<br> double 26693 </p> 26694 </th> 26695<th> 26696 <p> 26697 GNU C++ version 7.1.0<br> linux<br> long double 26698 </p> 26699 </th> 26700<th> 26701 <p> 26702 Sun compiler version 0x5150<br> Sun Solaris<br> long double 26703 </p> 26704 </th> 26705<th> 26706 <p> 26707 Microsoft Visual C++ version 14.1<br> Win32<br> double 26708 </p> 26709 </th> 26710</tr></thead> 26711<tbody><tr> 26712<td> 26713 <p> 26714 sqrt1pm1 26715 </p> 26716 </td> 26717<td> 26718 <p> 26719 <span class="blue">Max = 1.3ε (Mean = 0.404ε)</span> 26720 </p> 26721 </td> 26722<td> 26723 <p> 26724 <span class="blue">Max = 1.33ε (Mean = 0.404ε)</span> 26725 </p> 26726 </td> 26727<td> 26728 <p> 26729 <span class="blue">Max = 1.54ε (Mean = 0.563ε)</span> 26730 </p> 26731 </td> 26732<td> 26733 <p> 26734 <span class="blue">Max = 1.35ε (Mean = 0.497ε)</span> 26735 </p> 26736 </td> 26737</tr></tbody> 26738</table></div> 26739</div> 26740<br class="table-break"><div class="table"> 26741<a name="special_function_error_rates_rep.all_the_tables.table_tgamma"></a><p class="title"><b>Table 185. Error rates for tgamma</b></p> 26742<div class="table-contents"><table class="table" summary="Error rates for tgamma"> 26743<colgroup> 26744<col> 26745<col> 26746<col> 26747<col> 26748<col> 26749</colgroup> 26750<thead><tr> 26751<th> 26752 </th> 26753<th> 26754 <p> 26755 GNU C++ version 7.1.0<br> linux<br> double 26756 </p> 26757 </th> 26758<th> 26759 <p> 26760 GNU C++ version 7.1.0<br> linux<br> long double 26761 </p> 26762 </th> 26763<th> 26764 <p> 26765 Sun compiler version 0x5150<br> Sun Solaris<br> long double 26766 </p> 26767 </th> 26768<th> 26769 <p> 26770 Microsoft Visual C++ version 14.1<br> Win32<br> double 26771 </p> 26772 </th> 26773</tr></thead> 26774<tbody> 26775<tr> 26776<td> 26777 <p> 26778 factorials 26779 </p> 26780 </td> 26781<td> 26782 <p> 26783 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 26784 2.1:</em></span> Max = 3.95ε (Mean = 0.783ε))<br> (<span class="emphasis"><em>Rmath 26785 3.2.3:</em></span> Max = 314ε (Mean = 93.4ε)) 26786 </p> 26787 </td> 26788<td> 26789 <p> 26790 <span class="blue">Max = 2.67ε (Mean = 0.617ε)</span><br> <br> 26791 (<span class="emphasis"><em><cmath>:</em></span> Max = 1.66ε (Mean = 0.584ε))<br> 26792 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.66ε (Mean = 0.584ε)) 26793 </p> 26794 </td> 26795<td> 26796 <p> 26797 <span class="blue">Max = 172ε (Mean = 41ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span> 26798 Max = 0ε (Mean = 0ε)) 26799 </p> 26800 </td> 26801<td> 26802 <p> 26803 <span class="blue">Max = 1.85ε (Mean = 0.566ε)</span><br> <br> 26804 (<span class="emphasis"><em><math.h>:</em></span> Max = 3.17ε (Mean = 0.928ε)) 26805 </p> 26806 </td> 26807</tr> 26808<tr> 26809<td> 26810 <p> 26811 near 0 26812 </p> 26813 </td> 26814<td> 26815 <p> 26816 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 26817 2.1:</em></span> Max = 4.51ε (Mean = 1.92ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 26818 Max = 1ε (Mean = 0.335ε)) 26819 </p> 26820 </td> 26821<td> 26822 <p> 26823 <span class="blue">Max = 2ε (Mean = 0.608ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span> 26824 Max = 1ε (Mean = 0.376ε))<br> (<span class="emphasis"><em><math.h>:</em></span> 26825 Max = 1ε (Mean = 0.376ε)) 26826 </p> 26827 </td> 26828<td> 26829 <p> 26830 <span class="blue">Max = 2ε (Mean = 0.647ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span> 26831 Max = 0.5ε (Mean = 0.0791ε)) 26832 </p> 26833 </td> 26834<td> 26835 <p> 26836 <span class="blue">Max = 1.5ε (Mean = 0.635ε)</span><br> <br> 26837 (<span class="emphasis"><em><math.h>:</em></span> Max = 1ε (Mean = 0.405ε)) 26838 </p> 26839 </td> 26840</tr> 26841<tr> 26842<td> 26843 <p> 26844 near 1 26845 </p> 26846 </td> 26847<td> 26848 <p> 26849 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 26850 2.1:</em></span> Max = 4.41ε (Mean = 1.81ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 26851 Max = 1ε (Mean = 0.32ε)) 26852 </p> 26853 </td> 26854<td> 26855 <p> 26856 <span class="blue">Max = 2.51ε (Mean = 1.02ε)</span><br> <br> 26857 (<span class="emphasis"><em><cmath>:</em></span> Max = 0.918ε (Mean = 0.203ε))<br> 26858 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.918ε (Mean = 0.203ε)) 26859 </p> 26860 </td> 26861<td> 26862 <p> 26863 <span class="blue">Max = 3.01ε (Mean = 1.06ε)</span><br> <br> 26864 (<span class="emphasis"><em><math.h>:</em></span> Max = 1ε (Mean = 0.175ε)) 26865 </p> 26866 </td> 26867<td> 26868 <p> 26869 <span class="blue">Max = 1.1ε (Mean = 0.59ε)</span><br> <br> 26870 (<span class="emphasis"><em><math.h>:</em></span> Max = 1ε (Mean = 0.4ε)) 26871 </p> 26872 </td> 26873</tr> 26874<tr> 26875<td> 26876 <p> 26877 near 2 26878 </p> 26879 </td> 26880<td> 26881 <p> 26882 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 26883 2.1:</em></span> Max = 7.95ε (Mean = 3.12ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 26884 Max = 1ε (Mean = 0.191ε)) 26885 </p> 26886 </td> 26887<td> 26888 <p> 26889 <span class="blue">Max = 4.1ε (Mean = 1.55ε)</span><br> <br> 26890 (<span class="emphasis"><em><cmath>:</em></span> Max = 0.558ε (Mean = 0.298ε))<br> 26891 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.558ε (Mean = 0.298ε)) 26892 </p> 26893 </td> 26894<td> 26895 <p> 26896 <span class="blue">Max = 5.01ε (Mean = 1.89ε)</span><br> <br> 26897 (<span class="emphasis"><em><math.h>:</em></span> Max = 0ε (Mean = 0ε)) 26898 </p> 26899 </td> 26900<td> 26901 <p> 26902 <span class="blue">Max = 2ε (Mean = 0.733ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span> 26903 Max = 0ε (Mean = 0ε)) 26904 </p> 26905 </td> 26906</tr> 26907<tr> 26908<td> 26909 <p> 26910 near -10 26911 </p> 26912 </td> 26913<td> 26914 <p> 26915 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 26916 2.1:</em></span> Max = 2.6ε (Mean = 1.05ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 26917 Max = 34.9ε (Mean = 9.2ε)) 26918 </p> 26919 </td> 26920<td> 26921 <p> 26922 <span class="blue">Max = 1.75ε (Mean = 0.895ε)</span><br> <br> 26923 (<span class="emphasis"><em><cmath>:</em></span> Max = 2.26ε (Mean = 1.08ε))<br> 26924 (<span class="emphasis"><em><math.h>:</em></span> Max = 2.26ε (Mean = 1.08ε)) 26925 </p> 26926 </td> 26927<td> 26928 <p> 26929 <span class="blue">Max = 1.75ε (Mean = 0.819ε)</span><br> <br> 26930 (<span class="emphasis"><em><math.h>:</em></span> Max = 0ε (Mean = 0ε)) 26931 </p> 26932 </td> 26933<td> 26934 <p> 26935 <span class="blue">Max = 1.86ε (Mean = 0.881ε)</span><br> <br> 26936 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.866ε (Mean = 0.445ε)) 26937 </p> 26938 </td> 26939</tr> 26940<tr> 26941<td> 26942 <p> 26943 near -55 26944 </p> 26945 </td> 26946<td> 26947 <p> 26948 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 26949 2.1:</em></span> Max = 1.8ε (Mean = 0.782ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 26950 Max = 3.89e+04ε (Mean = 9.52e+03ε)) 26951 </p> 26952 </td> 26953<td> 26954 <p> 26955 <span class="blue">Max = 2.69ε (Mean = 1.09ε)</span><br> <br> 26956 (<span class="emphasis"><em><cmath>:</em></span> Max = 1.79ε (Mean = 0.75ε))<br> 26957 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.79ε (Mean = 0.75ε)) 26958 </p> 26959 </td> 26960<td> 26961 <p> 26962 <span class="blue">Max = 98.5ε (Mean = 53.4ε)</span><br> <br> 26963 (<span class="emphasis"><em><math.h>:</em></span> Max = 0ε (Mean = 0ε)) 26964 </p> 26965 </td> 26966<td> 26967 <p> 26968 <span class="blue">Max = 2.7ε (Mean = 1.35ε)</span><br> <br> 26969 (<span class="emphasis"><em><math.h>:</em></span> Max = 3.87e+04ε (Mean = 6.71e+03ε)) 26970 </p> 26971 </td> 26972</tr> 26973</tbody> 26974</table></div> 26975</div> 26976<br class="table-break"><div class="table"> 26977<a name="special_function_error_rates_rep.all_the_tables.table_tgamma1pm1"></a><p class="title"><b>Table 186. Error rates for tgamma1pm1</b></p> 26978<div class="table-contents"><table class="table" summary="Error rates for tgamma1pm1"> 26979<colgroup> 26980<col> 26981<col> 26982<col> 26983<col> 26984<col> 26985</colgroup> 26986<thead><tr> 26987<th> 26988 </th> 26989<th> 26990 <p> 26991 GNU C++ version 7.1.0<br> linux<br> double 26992 </p> 26993 </th> 26994<th> 26995 <p> 26996 GNU C++ version 7.1.0<br> linux<br> long double 26997 </p> 26998 </th> 26999<th> 27000 <p> 27001 Sun compiler version 0x5150<br> Sun Solaris<br> long double 27002 </p> 27003 </th> 27004<th> 27005 <p> 27006 Microsoft Visual C++ version 14.1<br> Win32<br> double 27007 </p> 27008 </th> 27009</tr></thead> 27010<tbody><tr> 27011<td> 27012 <p> 27013 tgamma1pm1(dz) 27014 </p> 27015 </td> 27016<td> 27017 <p> 27018 <span class="blue">Max = 0ε (Mean = 0ε)</span> 27019 </p> 27020 </td> 27021<td> 27022 <p> 27023 <span class="blue">Max = 1.12ε (Mean = 0.49ε)</span> 27024 </p> 27025 </td> 27026<td> 27027 <p> 27028 <span class="blue">Max = 6.61ε (Mean = 0.84ε)</span> 27029 </p> 27030 </td> 27031<td> 27032 <p> 27033 <span class="blue">Max = 3.31ε (Mean = 0.517ε)</span> 27034 </p> 27035 </td> 27036</tr></tbody> 27037</table></div> 27038</div> 27039<br class="table-break"><div class="table"> 27040<a name="special_function_error_rates_rep.all_the_tables.table_tgamma_delta_ratio"></a><p class="title"><b>Table 187. Error rates for tgamma_delta_ratio</b></p> 27041<div class="table-contents"><table class="table" summary="Error rates for tgamma_delta_ratio"> 27042<colgroup> 27043<col> 27044<col> 27045<col> 27046<col> 27047<col> 27048</colgroup> 27049<thead><tr> 27050<th> 27051 </th> 27052<th> 27053 <p> 27054 GNU C++ version 7.1.0<br> linux<br> double 27055 </p> 27056 </th> 27057<th> 27058 <p> 27059 GNU C++ version 7.1.0<br> linux<br> long double 27060 </p> 27061 </th> 27062<th> 27063 <p> 27064 Sun compiler version 0x5150<br> Sun Solaris<br> long double 27065 </p> 27066 </th> 27067<th> 27068 <p> 27069 Microsoft Visual C++ version 14.1<br> Win32<br> double 27070 </p> 27071 </th> 27072</tr></thead> 27073<tbody> 27074<tr> 27075<td> 27076 <p> 27077 tgamma + small delta ratios 27078 </p> 27079 </td> 27080<td> 27081 <p> 27082 <span class="blue">Max = 0ε (Mean = 0ε)</span> 27083 </p> 27084 </td> 27085<td> 27086 <p> 27087 <span class="blue">Max = 5.83ε (Mean = 1.3ε)</span> 27088 </p> 27089 </td> 27090<td> 27091 <p> 27092 <span class="blue">Max = 15.4ε (Mean = 2.09ε)</span> 27093 </p> 27094 </td> 27095<td> 27096 <p> 27097 <span class="blue">Max = 7.56ε (Mean = 1.31ε)</span> 27098 </p> 27099 </td> 27100</tr> 27101<tr> 27102<td> 27103 <p> 27104 tgamma + small delta ratios (negative delta) 27105 </p> 27106 </td> 27107<td> 27108 <p> 27109 <span class="blue">Max = 0ε (Mean = 0ε)</span> 27110 </p> 27111 </td> 27112<td> 27113 <p> 27114 <span class="blue">Max = 7.94ε (Mean = 1.4ε)</span> 27115 </p> 27116 </td> 27117<td> 27118 <p> 27119 <span class="blue">Max = 18.3ε (Mean = 2.03ε)</span> 27120 </p> 27121 </td> 27122<td> 27123 <p> 27124 <span class="blue">Max = 7.43ε (Mean = 1.42ε)</span> 27125 </p> 27126 </td> 27127</tr> 27128<tr> 27129<td> 27130 <p> 27131 tgamma + small integer ratios 27132 </p> 27133 </td> 27134<td> 27135 <p> 27136 <span class="blue">Max = 0ε (Mean = 0ε)</span> 27137 </p> 27138 </td> 27139<td> 27140 <p> 27141 <span class="blue">Max = 1.96ε (Mean = 0.677ε)</span> 27142 </p> 27143 </td> 27144<td> 27145 <p> 27146 <span class="blue">Max = 1.96ε (Mean = 0.677ε)</span> 27147 </p> 27148 </td> 27149<td> 27150 <p> 27151 <span class="blue">Max = 2.74ε (Mean = 0.736ε)</span> 27152 </p> 27153 </td> 27154</tr> 27155<tr> 27156<td> 27157 <p> 27158 tgamma + small integer ratios (negative delta) 27159 </p> 27160 </td> 27161<td> 27162 <p> 27163 <span class="blue">Max = 0ε (Mean = 0ε)</span> 27164 </p> 27165 </td> 27166<td> 27167 <p> 27168 <span class="blue">Max = 1.62ε (Mean = 0.451ε)</span> 27169 </p> 27170 </td> 27171<td> 27172 <p> 27173 <span class="blue">Max = 1.62ε (Mean = 0.451ε)</span> 27174 </p> 27175 </td> 27176<td> 27177 <p> 27178 <span class="blue">Max = 2.15ε (Mean = 0.685ε)</span> 27179 </p> 27180 </td> 27181</tr> 27182<tr> 27183<td> 27184 <p> 27185 integer tgamma ratios 27186 </p> 27187 </td> 27188<td> 27189 <p> 27190 <span class="blue">Max = 0ε (Mean = 0ε)</span> 27191 </p> 27192 </td> 27193<td> 27194 <p> 27195 <span class="blue">Max = 0.997ε (Mean = 0.4ε)</span> 27196 </p> 27197 </td> 27198<td> 27199 <p> 27200 <span class="blue">Max = 0.997ε (Mean = 0.4ε)</span> 27201 </p> 27202 </td> 27203<td> 27204 <p> 27205 <span class="blue">Max = 0.968ε (Mean = 0.386ε)</span> 27206 </p> 27207 </td> 27208</tr> 27209<tr> 27210<td> 27211 <p> 27212 integer tgamma ratios (negative delta) 27213 </p> 27214 </td> 27215<td> 27216 <p> 27217 <span class="blue">Max = 0ε (Mean = 0ε)</span> 27218 </p> 27219 </td> 27220<td> 27221 <p> 27222 <span class="blue">Max = 0.853ε (Mean = 0.176ε)</span> 27223 </p> 27224 </td> 27225<td> 27226 <p> 27227 <span class="blue">Max = 0.853ε (Mean = 0.176ε)</span> 27228 </p> 27229 </td> 27230<td> 27231 <p> 27232 <span class="blue">Max = 0.974ε (Mean = 0.175ε)</span> 27233 </p> 27234 </td> 27235</tr> 27236</tbody> 27237</table></div> 27238</div> 27239<br class="table-break"><div class="table"> 27240<a name="special_function_error_rates_rep.all_the_tables.table_tgamma_incomplete_"></a><p class="title"><b>Table 188. Error rates for tgamma (incomplete)</b></p> 27241<div class="table-contents"><table class="table" summary="Error rates for tgamma (incomplete)"> 27242<colgroup> 27243<col> 27244<col> 27245<col> 27246<col> 27247<col> 27248</colgroup> 27249<thead><tr> 27250<th> 27251 </th> 27252<th> 27253 <p> 27254 GNU C++ version 7.1.0<br> linux<br> double 27255 </p> 27256 </th> 27257<th> 27258 <p> 27259 GNU C++ version 7.1.0<br> linux<br> long double 27260 </p> 27261 </th> 27262<th> 27263 <p> 27264 Sun compiler version 0x5150<br> Sun Solaris<br> long double 27265 </p> 27266 </th> 27267<th> 27268 <p> 27269 Microsoft Visual C++ version 14.1<br> Win32<br> double 27270 </p> 27271 </th> 27272</tr></thead> 27273<tbody> 27274<tr> 27275<td> 27276 <p> 27277 tgamma(a, z) medium values 27278 </p> 27279 </td> 27280<td> 27281 <p> 27282 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 27283 2.1:</em></span> Max = 200ε (Mean = 13.3ε)) 27284 </p> 27285 </td> 27286<td> 27287 <p> 27288 <span class="blue">Max = 8.47ε (Mean = 1.9ε)</span> 27289 </p> 27290 </td> 27291<td> 27292 <p> 27293 <span class="blue">Max = 412ε (Mean = 95.5ε)</span> 27294 </p> 27295 </td> 27296<td> 27297 <p> 27298 <span class="blue">Max = 8.14ε (Mean = 1.76ε)</span> 27299 </p> 27300 </td> 27301</tr> 27302<tr> 27303<td> 27304 <p> 27305 tgamma(a, z) small values 27306 </p> 27307 </td> 27308<td> 27309 <p> 27310 <span class="blue">Max = 0.753ε (Mean = 0.0474ε)</span><br> <br> 27311 (<span class="emphasis"><em>GSL 2.1:</em></span> <span class="red">Max = 1.38e+10ε (Mean 27312 = 1.05e+09ε))</span> 27313 </p> 27314 </td> 27315<td> 27316 <p> 27317 <span class="blue">Max = 2.31ε (Mean = 0.775ε)</span> 27318 </p> 27319 </td> 27320<td> 27321 <p> 27322 <span class="blue">Max = 2.13ε (Mean = 0.717ε)</span> 27323 </p> 27324 </td> 27325<td> 27326 <p> 27327 <span class="blue">Max = 2.53ε (Mean = 0.66ε)</span> 27328 </p> 27329 </td> 27330</tr> 27331<tr> 27332<td> 27333 <p> 27334 tgamma(a, z) integer and half integer values 27335 </p> 27336 </td> 27337<td> 27338 <p> 27339 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 27340 2.1:</em></span> Max = 117ε (Mean = 12.5ε)) 27341 </p> 27342 </td> 27343<td> 27344 <p> 27345 <span class="blue">Max = 5.52ε (Mean = 1.48ε)</span> 27346 </p> 27347 </td> 27348<td> 27349 <p> 27350 <span class="blue">Max = 79.6ε (Mean = 20.9ε)</span> 27351 </p> 27352 </td> 27353<td> 27354 <p> 27355 <span class="blue">Max = 5.16ε (Mean = 1.33ε)</span> 27356 </p> 27357 </td> 27358</tr> 27359</tbody> 27360</table></div> 27361</div> 27362<br class="table-break"><div class="table"> 27363<a name="special_function_error_rates_rep.all_the_tables.table_tgamma_lower"></a><p class="title"><b>Table 189. Error rates for tgamma_lower</b></p> 27364<div class="table-contents"><table class="table" summary="Error rates for tgamma_lower"> 27365<colgroup> 27366<col> 27367<col> 27368<col> 27369<col> 27370<col> 27371</colgroup> 27372<thead><tr> 27373<th> 27374 </th> 27375<th> 27376 <p> 27377 GNU C++ version 7.1.0<br> linux<br> double 27378 </p> 27379 </th> 27380<th> 27381 <p> 27382 GNU C++ version 7.1.0<br> linux<br> long double 27383 </p> 27384 </th> 27385<th> 27386 <p> 27387 Sun compiler version 0x5150<br> Sun Solaris<br> long double 27388 </p> 27389 </th> 27390<th> 27391 <p> 27392 Microsoft Visual C++ version 14.1<br> Win32<br> double 27393 </p> 27394 </th> 27395</tr></thead> 27396<tbody> 27397<tr> 27398<td> 27399 <p> 27400 tgamma(a, z) medium values 27401 </p> 27402 </td> 27403<td> 27404 <p> 27405 <span class="blue">Max = 0.833ε (Mean = 0.0315ε)</span><br> <br> 27406 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.833ε (Mean = 0.0315ε)) 27407 </p> 27408 </td> 27409<td> 27410 <p> 27411 <span class="blue">Max = 6.79ε (Mean = 1.46ε)</span> 27412 </p> 27413 </td> 27414<td> 27415 <p> 27416 <span class="blue">Max = 363ε (Mean = 63.8ε)</span> 27417 </p> 27418 </td> 27419<td> 27420 <p> 27421 <span class="blue">Max = 5.62ε (Mean = 1.49ε)</span> 27422 </p> 27423 </td> 27424</tr> 27425<tr> 27426<td> 27427 <p> 27428 tgamma(a, z) small values 27429 </p> 27430 </td> 27431<td> 27432 <p> 27433 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 27434 2.1:</em></span> Max = 0ε (Mean = 0ε)) 27435 </p> 27436 </td> 27437<td> 27438 <p> 27439 <span class="blue">Max = 1.97ε (Mean = 0.555ε)</span> 27440 </p> 27441 </td> 27442<td> 27443 <p> 27444 <span class="blue">Max = 1.97ε (Mean = 0.558ε)</span> 27445 </p> 27446 </td> 27447<td> 27448 <p> 27449 <span class="blue">Max = 1.57ε (Mean = 0.525ε)</span> 27450 </p> 27451 </td> 27452</tr> 27453<tr> 27454<td> 27455 <p> 27456 tgamma(a, z) integer and half integer values 27457 </p> 27458 </td> 27459<td> 27460 <p> 27461 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 27462 2.1:</em></span> Max = 0ε (Mean = 0ε)) 27463 </p> 27464 </td> 27465<td> 27466 <p> 27467 <span class="blue">Max = 4.83ε (Mean = 1.15ε)</span> 27468 </p> 27469 </td> 27470<td> 27471 <p> 27472 <span class="blue">Max = 84.7ε (Mean = 17.5ε)</span> 27473 </p> 27474 </td> 27475<td> 27476 <p> 27477 <span class="blue">Max = 2.69ε (Mean = 0.849ε)</span> 27478 </p> 27479 </td> 27480</tr> 27481</tbody> 27482</table></div> 27483</div> 27484<br class="table-break"><div class="table"> 27485<a name="special_function_error_rates_rep.all_the_tables.table_tgamma_ratio"></a><p class="title"><b>Table 190. Error rates for tgamma_ratio</b></p> 27486<div class="table-contents"><table class="table" summary="Error rates for tgamma_ratio"> 27487<colgroup> 27488<col> 27489<col> 27490<col> 27491<col> 27492<col> 27493</colgroup> 27494<thead><tr> 27495<th> 27496 </th> 27497<th> 27498 <p> 27499 GNU C++ version 7.1.0<br> linux<br> double 27500 </p> 27501 </th> 27502<th> 27503 <p> 27504 GNU C++ version 7.1.0<br> linux<br> long double 27505 </p> 27506 </th> 27507<th> 27508 <p> 27509 Sun compiler version 0x5150<br> Sun Solaris<br> long double 27510 </p> 27511 </th> 27512<th> 27513 <p> 27514 Microsoft Visual C++ version 14.1<br> Win32<br> double 27515 </p> 27516 </th> 27517</tr></thead> 27518<tbody><tr> 27519<td> 27520 <p> 27521 tgamma ratios 27522 </p> 27523 </td> 27524<td> 27525 <p> 27526 <span class="blue">Max = 0.694ε (Mean = 0.0347ε)</span> 27527 </p> 27528 </td> 27529<td> 27530 <p> 27531 <span class="blue">Max = 2.99ε (Mean = 1.15ε)</span> 27532 </p> 27533 </td> 27534<td> 27535 <p> 27536 <span class="blue">Max = 174ε (Mean = 61.2ε)</span> 27537 </p> 27538 </td> 27539<td> 27540 <p> 27541 <span class="blue">Max = 3.28ε (Mean = 1.12ε)</span> 27542 </p> 27543 </td> 27544</tr></tbody> 27545</table></div> 27546</div> 27547<br class="table-break"><div class="table"> 27548<a name="special_function_error_rates_rep.all_the_tables.table_trigamma"></a><p class="title"><b>Table 191. Error rates for trigamma</b></p> 27549<div class="table-contents"><table class="table" summary="Error rates for trigamma"> 27550<colgroup> 27551<col> 27552<col> 27553<col> 27554<col> 27555<col> 27556</colgroup> 27557<thead><tr> 27558<th> 27559 </th> 27560<th> 27561 <p> 27562 GNU C++ version 7.1.0<br> linux<br> double 27563 </p> 27564 </th> 27565<th> 27566 <p> 27567 GNU C++ version 7.1.0<br> linux<br> long double 27568 </p> 27569 </th> 27570<th> 27571 <p> 27572 Sun compiler version 0x5150<br> Sun Solaris<br> long double 27573 </p> 27574 </th> 27575<th> 27576 <p> 27577 Microsoft Visual C++ version 14.1<br> Win32<br> double 27578 </p> 27579 </th> 27580</tr></thead> 27581<tbody><tr> 27582<td> 27583 <p> 27584 Mathematica Data 27585 </p> 27586 </td> 27587<td> 27588 <p> 27589 <span class="blue">Max = 0.998ε (Mean = 0.105ε)</span><br> <br> 27590 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.34e+04ε (Mean = 1.49e+03ε))<br> 27591 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.34e+04ε (Mean = 1.51e+03ε)) 27592 </p> 27593 </td> 27594<td> 27595 <p> 27596 <span class="blue">Max = 1.28ε (Mean = 0.449ε)</span> 27597 </p> 27598 </td> 27599<td> 27600 <p> 27601 <span class="blue">Max = 1.28ε (Mean = 0.449ε)</span> 27602 </p> 27603 </td> 27604<td> 27605 <p> 27606 <span class="blue">Max = 1ε (Mean = 0.382ε)</span> 27607 </p> 27608 </td> 27609</tr></tbody> 27610</table></div> 27611</div> 27612<br class="table-break"><div class="table"> 27613<a name="special_function_error_rates_rep.all_the_tables.table_zeta"></a><p class="title"><b>Table 192. Error rates for zeta</b></p> 27614<div class="table-contents"><table class="table" summary="Error rates for zeta"> 27615<colgroup> 27616<col> 27617<col> 27618<col> 27619<col> 27620<col> 27621</colgroup> 27622<thead><tr> 27623<th> 27624 </th> 27625<th> 27626 <p> 27627 GNU C++ version 7.1.0<br> linux<br> long double 27628 </p> 27629 </th> 27630<th> 27631 <p> 27632 GNU C++ version 7.1.0<br> linux<br> double 27633 </p> 27634 </th> 27635<th> 27636 <p> 27637 Sun compiler version 0x5150<br> Sun Solaris<br> long double 27638 </p> 27639 </th> 27640<th> 27641 <p> 27642 Microsoft Visual C++ version 14.1<br> Win32<br> double 27643 </p> 27644 </th> 27645</tr></thead> 27646<tbody> 27647<tr> 27648<td> 27649 <p> 27650 Zeta: Random values greater than 1 27651 </p> 27652 </td> 27653<td> 27654 <p> 27655 <span class="blue">Max = 0.846ε (Mean = 0.0833ε)</span><br> <br> 27656 (<span class="emphasis"><em><cmath>:</em></span> Max = 5.45ε (Mean = 1ε)) 27657 </p> 27658 </td> 27659<td> 27660 <p> 27661 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 27662 2.1:</em></span> Max = 8.69ε (Mean = 1.03ε)) 27663 </p> 27664 </td> 27665<td> 27666 <p> 27667 <span class="blue">Max = 0.846ε (Mean = 0.0833ε)</span> 27668 </p> 27669 </td> 27670<td> 27671 <p> 27672 <span class="blue">Max = 0.836ε (Mean = 0.093ε)</span> 27673 </p> 27674 </td> 27675</tr> 27676<tr> 27677<td> 27678 <p> 27679 Zeta: Random values less than 1 27680 </p> 27681 </td> 27682<td> 27683 <p> 27684 <span class="blue">Max = 7.03ε (Mean = 2.93ε)</span><br> <br> 27685 (<span class="emphasis"><em><cmath>:</em></span> Max = 538ε (Mean = 59.3ε)) 27686 </p> 27687 </td> 27688<td> 27689 <p> 27690 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 27691 2.1:</em></span> Max = 137ε (Mean = 13.8ε)) 27692 </p> 27693 </td> 27694<td> 27695 <p> 27696 <span class="blue">Max = 70.1ε (Mean = 17.1ε)</span> 27697 </p> 27698 </td> 27699<td> 27700 <p> 27701 <span class="blue">Max = 6.84ε (Mean = 3.12ε)</span> 27702 </p> 27703 </td> 27704</tr> 27705<tr> 27706<td> 27707 <p> 27708 Zeta: Values close to and greater than 1 27709 </p> 27710 </td> 27711<td> 27712 <p> 27713 <span class="blue">Max = 0.995ε (Mean = 0.5ε)</span><br> <br> 27714 (<span class="emphasis"><em><cmath>:</em></span> Max = 1.9e+06ε (Mean = 5.11e+05ε)) 27715 </p> 27716 </td> 27717<td> 27718 <p> 27719 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 27720 2.1:</em></span> Max = 7.73ε (Mean = 4.07ε)) 27721 </p> 27722 </td> 27723<td> 27724 <p> 27725 <span class="blue">Max = 0.995ε (Mean = 0.5ε)</span> 27726 </p> 27727 </td> 27728<td> 27729 <p> 27730 <span class="blue">Max = 0.994ε (Mean = 0.421ε)</span> 27731 </p> 27732 </td> 27733</tr> 27734<tr> 27735<td> 27736 <p> 27737 Zeta: Values close to and less than 1 27738 </p> 27739 </td> 27740<td> 27741 <p> 27742 <span class="blue">Max = 0.998ε (Mean = 0.508ε)</span><br> <br> 27743 (<span class="emphasis"><em><cmath>:</em></span> Max = 8.53e+06ε (Mean = 1.87e+06ε)) 27744 </p> 27745 </td> 27746<td> 27747 <p> 27748 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 27749 2.1:</em></span> Max = 0.991ε (Mean = 0.28ε)) 27750 </p> 27751 </td> 27752<td> 27753 <p> 27754 <span class="blue">Max = 0.998ε (Mean = 0.508ε)</span> 27755 </p> 27756 </td> 27757<td> 27758 <p> 27759 <span class="blue">Max = 0.991ε (Mean = 0.375ε)</span> 27760 </p> 27761 </td> 27762</tr> 27763<tr> 27764<td> 27765 <p> 27766 Zeta: Integer arguments 27767 </p> 27768 </td> 27769<td> 27770 <p> 27771 <span class="blue">Max = 9ε (Mean = 3.06ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span> 27772 Max = 70.3ε (Mean = 17.4ε)) 27773 </p> 27774 </td> 27775<td> 27776 <p> 27777 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 27778 2.1:</em></span> Max = 3.75ε (Mean = 1.1ε)) 27779 </p> 27780 </td> 27781<td> 27782 <p> 27783 <span class="blue">Max = 28ε (Mean = 5.62ε)</span> 27784 </p> 27785 </td> 27786<td> 27787 <p> 27788 <span class="blue">Max = 9ε (Mean = 3ε)</span> 27789 </p> 27790 </td> 27791</tr> 27792</tbody> 27793</table></div> 27794</div> 27795<br class="table-break"> 27796</div> 27797</div> 27798<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> 27799<td align="left"><p><small>Last revised: March 09, 2018 at 13:43:44 GMT</small></p></td> 27800<td align="right"><div class="copyright-footer"></div></td> 27801</tr></table> 27802<hr> 27803<div class="spirit-nav"></div> 27804</body> 27805</html> 27806
