1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> 4<title>Tables of Error Rates for all Functions</title> 5<link rel="stylesheet" href="../../math.css" type="text/css"> 6<meta name="generator" content="DocBook XSL Stylesheets V1.79.1"> 7<link rel="home" href="../../index.html" title="Math Toolkit 2.12.0"> 8<link rel="up" href="../logs_and_tables.html" title="Error logs and tables"> 9<link rel="prev" href="../logs_and_tables.html" title="Error logs and tables"> 10<link rel="next" href="logs.html" title="Error Logs For Error Rate Tables"> 11</head> 12<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> 13<table cellpadding="2" width="100%"><tr> 14<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> 15<td align="center"><a href="../../../../../../index.html">Home</a></td> 16<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> 17<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> 18<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> 19<td align="center"><a href="../../../../../../more/index.htm">More</a></td> 20</tr></table> 21<hr> 22<div class="spirit-nav"> 23<a accesskey="p" href="../logs_and_tables.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../logs_and_tables.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="logs.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> 24</div> 25<div class="section"> 26<div class="titlepage"><div><div><h3 class="title"> 27<a name="math_toolkit.logs_and_tables.all_table"></a><a class="link" href="all_table.html" title="Tables of Error Rates for all Functions">Tables of Error 28 Rates for all Functions</a> 29</h3></div></div></div> 30<div class="table"> 31<a name="math_toolkit.logs_and_tables.all_table.table_beta"></a><p class="title"><b>Table 23.3. Error rates for beta</b></p> 32<div class="table-contents"><table class="table" summary="Error rates for beta"> 33<colgroup> 34<col> 35<col> 36<col> 37<col> 38<col> 39</colgroup> 40<thead><tr> 41<th> 42 </th> 43<th> 44 <p> 45 GNU C++ version 7.1.0<br> linux<br> double 46 </p> 47 </th> 48<th> 49 <p> 50 GNU C++ version 7.1.0<br> linux<br> long double 51 </p> 52 </th> 53<th> 54 <p> 55 Sun compiler version 0x5150<br> Sun Solaris<br> long double 56 </p> 57 </th> 58<th> 59 <p> 60 Microsoft Visual C++ version 14.1<br> Win32<br> double 61 </p> 62 </th> 63</tr></thead> 64<tbody> 65<tr> 66<td> 67 <p> 68 Beta Function: Small Values 69 </p> 70 </td> 71<td> 72 <p> 73 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 74 2.1:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_beta_GSL_2_1_Beta_Function_Small_Values">And 75 other failures.</a>)</span><br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 76 Max = 1.14ε (Mean = 0.574ε)) 77 </p> 78 </td> 79<td> 80 <p> 81 <span class="blue">Max = 2.86ε (Mean = 1.22ε)</span><br> <br> 82 (<span class="emphasis"><em><cmath>:</em></span> Max = 364ε (Mean = 76.2ε)) 83 </p> 84 </td> 85<td> 86 <p> 87 <span class="blue">Max = 2.86ε (Mean = 1.22ε)</span> 88 </p> 89 </td> 90<td> 91 <p> 92 <span class="blue">Max = 2.23ε (Mean = 1.14ε)</span> 93 </p> 94 </td> 95</tr> 96<tr> 97<td> 98 <p> 99 Beta Function: Medium Values 100 </p> 101 </td> 102<td> 103 <p> 104 <span class="blue">Max = 0.978ε (Mean = 0.0595ε)</span><br> 105 <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.18e+03ε (Mean = 238ε))<br> 106 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.09e+03ε (Mean = 265ε)) 107 </p> 108 </td> 109<td> 110 <p> 111 <span class="blue">Max = 61.4ε (Mean = 19.4ε)</span><br> <br> 112 (<span class="emphasis"><em><cmath>:</em></span> Max = 1.07e+03ε (Mean = 264ε)) 113 </p> 114 </td> 115<td> 116 <p> 117 <span class="blue">Max = 107ε (Mean = 24.5ε)</span> 118 </p> 119 </td> 120<td> 121 <p> 122 <span class="blue">Max = 96.5ε (Mean = 22.4ε)</span> 123 </p> 124 </td> 125</tr> 126<tr> 127<td> 128 <p> 129 Beta Function: Divergent Values 130 </p> 131 </td> 132<td> 133 <p> 134 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 135 2.1:</em></span> Max = 12.1ε (Mean = 1.99ε))<br> (<span class="emphasis"><em>Rmath 136 3.2.3:</em></span> Max = 176ε (Mean = 28ε)) 137 </p> 138 </td> 139<td> 140 <p> 141 <span class="blue">Max = 8.99ε (Mean = 2.44ε)</span><br> <br> 142 (<span class="emphasis"><em><cmath>:</em></span> Max = 128ε (Mean = 23.8ε)) 143 </p> 144 </td> 145<td> 146 <p> 147 <span class="blue">Max = 18.8ε (Mean = 2.71ε)</span> 148 </p> 149 </td> 150<td> 151 <p> 152 <span class="blue">Max = 11.4ε (Mean = 2.19ε)</span> 153 </p> 154 </td> 155</tr> 156</tbody> 157</table></div> 158</div> 159<br class="table-break"><div class="table"> 160<a name="math_toolkit.logs_and_tables.all_table.table_beta_incomplete_"></a><p class="title"><b>Table 23.4. Error rates for beta (incomplete)</b></p> 161<div class="table-contents"><table class="table" summary="Error rates for beta (incomplete)"> 162<colgroup> 163<col> 164<col> 165<col> 166<col> 167<col> 168</colgroup> 169<thead><tr> 170<th> 171 </th> 172<th> 173 <p> 174 GNU C++ version 7.1.0<br> linux<br> double 175 </p> 176 </th> 177<th> 178 <p> 179 GNU C++ version 7.1.0<br> linux<br> long double 180 </p> 181 </th> 182<th> 183 <p> 184 Sun compiler version 0x5150<br> Sun Solaris<br> long double 185 </p> 186 </th> 187<th> 188 <p> 189 Microsoft Visual C++ version 14.1<br> Win32<br> double 190 </p> 191 </th> 192</tr></thead> 193<tbody> 194<tr> 195<td> 196 <p> 197 Incomplete Beta Function: Small Values 198 </p> 199 </td> 200<td> 201 <p> 202 <span class="blue">Max = 0ε (Mean = 0ε)</span> 203 </p> 204 </td> 205<td> 206 <p> 207 <span class="blue">Max = 11.1ε (Mean = 2.32ε)</span> 208 </p> 209 </td> 210<td> 211 <p> 212 <span class="blue">Max = 18.7ε (Mean = 3.19ε)</span> 213 </p> 214 </td> 215<td> 216 <p> 217 <span class="blue">Max = 9.94ε (Mean = 2.17ε)</span> 218 </p> 219 </td> 220</tr> 221<tr> 222<td> 223 <p> 224 Incomplete Beta Function: Medium Values 225 </p> 226 </td> 227<td> 228 <p> 229 <span class="blue">Max = 0.568ε (Mean = 0.0254ε)</span> 230 </p> 231 </td> 232<td> 233 <p> 234 <span class="blue">Max = 69.2ε (Mean = 13.4ε)</span> 235 </p> 236 </td> 237<td> 238 <p> 239 <span class="blue">Max = 174ε (Mean = 25ε)</span> 240 </p> 241 </td> 242<td> 243 <p> 244 <span class="blue">Max = 90ε (Mean = 12.7ε)</span> 245 </p> 246 </td> 247</tr> 248<tr> 249<td> 250 <p> 251 Incomplete Beta Function: Large and Diverse Values 252 </p> 253 </td> 254<td> 255 <p> 256 <span class="blue">Max = 0.999ε (Mean = 0.0325ε)</span> 257 </p> 258 </td> 259<td> 260 <p> 261 <span class="blue">Max = 6.84e+04ε (Mean = 2.76e+03ε)</span> 262 </p> 263 </td> 264<td> 265 <p> 266 <span class="blue">Max = 6.86e+04ε (Mean = 2.79e+03ε)</span> 267 </p> 268 </td> 269<td> 270 <p> 271 <span class="blue">Max = 633ε (Mean = 29.7ε)</span> 272 </p> 273 </td> 274</tr> 275<tr> 276<td> 277 <p> 278 Incomplete Beta Function: Small Integer Values 279 </p> 280 </td> 281<td> 282 <p> 283 <span class="blue">Max = 0.786ε (Mean = 0.0323ε)</span> 284 </p> 285 </td> 286<td> 287 <p> 288 <span class="blue">Max = 11.6ε (Mean = 3.6ε)</span> 289 </p> 290 </td> 291<td> 292 <p> 293 <span class="blue">Max = 51.8ε (Mean = 11ε)</span> 294 </p> 295 </td> 296<td> 297 <p> 298 <span class="blue">Max = 26ε (Mean = 6.28ε)</span> 299 </p> 300 </td> 301</tr> 302</tbody> 303</table></div> 304</div> 305<br class="table-break"><div class="table"> 306<a name="math_toolkit.logs_and_tables.all_table.table_betac"></a><p class="title"><b>Table 23.5. Error rates for betac</b></p> 307<div class="table-contents"><table class="table" summary="Error rates for betac"> 308<colgroup> 309<col> 310<col> 311<col> 312<col> 313<col> 314</colgroup> 315<thead><tr> 316<th> 317 </th> 318<th> 319 <p> 320 GNU C++ version 7.1.0<br> linux<br> double 321 </p> 322 </th> 323<th> 324 <p> 325 GNU C++ version 7.1.0<br> linux<br> long double 326 </p> 327 </th> 328<th> 329 <p> 330 Sun compiler version 0x5150<br> Sun Solaris<br> long double 331 </p> 332 </th> 333<th> 334 <p> 335 Microsoft Visual C++ version 14.1<br> Win32<br> double 336 </p> 337 </th> 338</tr></thead> 339<tbody> 340<tr> 341<td> 342 <p> 343 Incomplete Beta Function: Small Values 344 </p> 345 </td> 346<td> 347 <p> 348 <span class="blue">Max = 0.676ε (Mean = 0.0302ε)</span> 349 </p> 350 </td> 351<td> 352 <p> 353 <span class="blue">Max = 9.92ε (Mean = 2.3ε)</span> 354 </p> 355 </td> 356<td> 357 <p> 358 <span class="blue">Max = 11.2ε (Mean = 2.94ε)</span> 359 </p> 360 </td> 361<td> 362 <p> 363 <span class="blue">Max = 8.94ε (Mean = 2.06ε)</span> 364 </p> 365 </td> 366</tr> 367<tr> 368<td> 369 <p> 370 Incomplete Beta Function: Medium Values 371 </p> 372 </td> 373<td> 374 <p> 375 <span class="blue">Max = 0.949ε (Mean = 0.098ε)</span> 376 </p> 377 </td> 378<td> 379 <p> 380 <span class="blue">Max = 63.5ε (Mean = 13.5ε)</span> 381 </p> 382 </td> 383<td> 384 <p> 385 <span class="blue">Max = 97.6ε (Mean = 24.3ε)</span> 386 </p> 387 </td> 388<td> 389 <p> 390 <span class="blue">Max = 90.6ε (Mean = 14.8ε)</span> 391 </p> 392 </td> 393</tr> 394<tr> 395<td> 396 <p> 397 Incomplete Beta Function: Large and Diverse Values 398 </p> 399 </td> 400<td> 401 <p> 402 <span class="blue">Max = 1.12ε (Mean = 0.0458ε)</span> 403 </p> 404 </td> 405<td> 406 <p> 407 <span class="blue">Max = 1.05e+05ε (Mean = 5.45e+03ε)</span> 408 </p> 409 </td> 410<td> 411 <p> 412 <span class="blue">Max = 1.04e+05ε (Mean = 5.46e+03ε)</span> 413 </p> 414 </td> 415<td> 416 <p> 417 <span class="blue">Max = 3.72e+03ε (Mean = 113ε)</span> 418 </p> 419 </td> 420</tr> 421<tr> 422<td> 423 <p> 424 Incomplete Beta Function: Small Integer Values 425 </p> 426 </td> 427<td> 428 <p> 429 <span class="blue">Max = 0.586ε (Mean = 0.0314ε)</span> 430 </p> 431 </td> 432<td> 433 <p> 434 <span class="blue">Max = 11.1ε (Mean = 3.65ε)</span> 435 </p> 436 </td> 437<td> 438 <p> 439 <span class="blue">Max = 103ε (Mean = 17.4ε)</span> 440 </p> 441 </td> 442<td> 443 <p> 444 <span class="blue">Max = 26.2ε (Mean = 6.36ε)</span> 445 </p> 446 </td> 447</tr> 448</tbody> 449</table></div> 450</div> 451<br class="table-break"><div class="table"> 452<a name="math_toolkit.logs_and_tables.all_table.table_binomial_coefficient"></a><p class="title"><b>Table 23.6. Error rates for binomial_coefficient</b></p> 453<div class="table-contents"><table class="table" summary="Error rates for binomial_coefficient"> 454<colgroup> 455<col> 456<col> 457<col> 458<col> 459<col> 460</colgroup> 461<thead><tr> 462<th> 463 </th> 464<th> 465 <p> 466 GNU C++ version 7.1.0<br> linux<br> double 467 </p> 468 </th> 469<th> 470 <p> 471 GNU C++ version 7.1.0<br> linux<br> long double 472 </p> 473 </th> 474<th> 475 <p> 476 Sun compiler version 0x5150<br> Sun Solaris<br> long double 477 </p> 478 </th> 479<th> 480 <p> 481 Microsoft Visual C++ version 14.1<br> Win32<br> double 482 </p> 483 </th> 484</tr></thead> 485<tbody> 486<tr> 487<td> 488 <p> 489 Binomials: small arguments 490 </p> 491 </td> 492<td> 493 <p> 494 <span class="blue">Max = 1ε (Mean = 0.369ε)</span> 495 </p> 496 </td> 497<td> 498 <p> 499 <span class="blue">Max = 1.5ε (Mean = 0.339ε)</span> 500 </p> 501 </td> 502<td> 503 <p> 504 <span class="blue">Max = 1.5ε (Mean = 0.339ε)</span> 505 </p> 506 </td> 507<td> 508 <p> 509 <span class="blue">Max = 1ε (Mean = 0.369ε)</span> 510 </p> 511 </td> 512</tr> 513<tr> 514<td> 515 <p> 516 Binomials: large arguments 517 </p> 518 </td> 519<td> 520 <p> 521 <span class="blue">Max = 0.939ε (Mean = 0.314ε)</span> 522 </p> 523 </td> 524<td> 525 <p> 526 <span class="blue">Max = 26.6ε (Mean = 6.13ε)</span> 527 </p> 528 </td> 529<td> 530 <p> 531 <span class="blue">Max = 53.2ε (Mean = 10.8ε)</span> 532 </p> 533 </td> 534<td> 535 <p> 536 <span class="blue">Max = 37.2ε (Mean = 7.4ε)</span> 537 </p> 538 </td> 539</tr> 540</tbody> 541</table></div> 542</div> 543<br class="table-break"><div class="table"> 544<a name="math_toolkit.logs_and_tables.all_table.table_boost_math_powm1"></a><p class="title"><b>Table 23.7. Error rates for boost::math::powm1</b></p> 545<div class="table-contents"><table class="table" summary="Error rates for boost::math::powm1"> 546<colgroup> 547<col> 548<col> 549<col> 550<col> 551<col> 552</colgroup> 553<thead><tr> 554<th> 555 </th> 556<th> 557 <p> 558 GNU C++ version 7.1.0<br> linux<br> long double 559 </p> 560 </th> 561<th> 562 <p> 563 GNU C++ version 7.1.0<br> linux<br> double 564 </p> 565 </th> 566<th> 567 <p> 568 Sun compiler version 0x5150<br> Sun Solaris<br> long double 569 </p> 570 </th> 571<th> 572 <p> 573 Microsoft Visual C++ version 14.1<br> Win32<br> double 574 </p> 575 </th> 576</tr></thead> 577<tbody><tr> 578<td> 579 <p> 580 powm1 581 </p> 582 </td> 583<td> 584 <p> 585 (<span class="emphasis"><em><math.h>:</em></span> Max = 2.04ε (Mean = 0.493ε))<br> 586 <br> <span class="blue">Max = 2.04ε (Mean = 0.493ε)</span><br> 587 <br> (<span class="emphasis"><em><cmath>:</em></span> Max = 2.04ε (Mean = 0.493ε)) 588 </p> 589 </td> 590<td> 591 <p> 592 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.06ε (Mean = 0.425ε))<br> 593 <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.06ε (Mean = 0.425ε))<br> 594 <br> <span class="blue">Max = 1.06ε (Mean = 0.425ε)</span> 595 </p> 596 </td> 597<td> 598 <p> 599 <span class="blue">Max = 1.88ε (Mean = 0.49ε)</span><br> <br> 600 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.88ε (Mean = 0.49ε)) 601 </p> 602 </td> 603<td> 604 <p> 605 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.84ε (Mean = 0.486ε))<br> 606 <br> <span class="blue">Max = 1.84ε (Mean = 0.486ε)</span> 607 </p> 608 </td> 609</tr></tbody> 610</table></div> 611</div> 612<br class="table-break"><div class="table"> 613<a name="math_toolkit.logs_and_tables.all_table.table_cbrt"></a><p class="title"><b>Table 23.8. Error rates for cbrt</b></p> 614<div class="table-contents"><table class="table" summary="Error rates for cbrt"> 615<colgroup> 616<col> 617<col> 618<col> 619<col> 620<col> 621</colgroup> 622<thead><tr> 623<th> 624 </th> 625<th> 626 <p> 627 GNU C++ version 7.1.0<br> linux<br> double 628 </p> 629 </th> 630<th> 631 <p> 632 GNU C++ version 7.1.0<br> linux<br> long double 633 </p> 634 </th> 635<th> 636 <p> 637 Sun compiler version 0x5150<br> Sun Solaris<br> long double 638 </p> 639 </th> 640<th> 641 <p> 642 Microsoft Visual C++ version 14.1<br> Win32<br> double 643 </p> 644 </th> 645</tr></thead> 646<tbody><tr> 647<td> 648 <p> 649 cbrt Function 650 </p> 651 </td> 652<td> 653 <p> 654 <span class="blue">Max = 0ε (Mean = 0ε)</span> 655 </p> 656 </td> 657<td> 658 <p> 659 <span class="blue">Max = 1.34ε (Mean = 0.471ε)</span><br> <br> 660 (<span class="emphasis"><em><cmath>:</em></span> Max = 1.34ε (Mean = 0.471ε))<br> 661 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.34ε (Mean = 0.471ε)) 662 </p> 663 </td> 664<td> 665 <p> 666 <span class="blue">Max = 1.34ε (Mean = 0.471ε)</span><br> <br> 667 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.34ε (Mean = 0.471ε)) 668 </p> 669 </td> 670<td> 671 <p> 672 <span class="blue">Max = 1.7ε (Mean = 0.565ε)</span><br> <br> 673 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.7ε (Mean = 0.565ε)) 674 </p> 675 </td> 676</tr></tbody> 677</table></div> 678</div> 679<br class="table-break"><div class="table"> 680<a name="math_toolkit.logs_and_tables.all_table.table_cos_pi"></a><p class="title"><b>Table 23.9. Error rates for cos_pi</b></p> 681<div class="table-contents"><table class="table" summary="Error rates for cos_pi"> 682<colgroup> 683<col> 684<col> 685<col> 686<col> 687<col> 688</colgroup> 689<thead><tr> 690<th> 691 </th> 692<th> 693 <p> 694 GNU C++ version 7.1.0<br> linux<br> double 695 </p> 696 </th> 697<th> 698 <p> 699 GNU C++ version 7.1.0<br> linux<br> long double 700 </p> 701 </th> 702<th> 703 <p> 704 Sun compiler version 0x5150<br> Sun Solaris<br> long double 705 </p> 706 </th> 707<th> 708 <p> 709 Microsoft Visual C++ version 14.1<br> Win32<br> double 710 </p> 711 </th> 712</tr></thead> 713<tbody> 714<tr> 715<td> 716 <p> 717 sin_pi and cos_pi 718 </p> 719 </td> 720<td> 721 <p> 722 <span class="blue">Max = 0ε (Mean = 0ε)</span> 723 </p> 724 </td> 725<td> 726 <p> 727 <span class="blue">Max = 0.991ε (Mean = 0.302ε)</span> 728 </p> 729 </td> 730<td> 731 <p> 732 <span class="blue">Max = 0.991ε (Mean = 0.302ε)</span> 733 </p> 734 </td> 735<td> 736 <p> 737 <span class="blue">Max = 0.996ε (Mean = 0.284ε)</span> 738 </p> 739 </td> 740</tr> 741<tr> 742<td> 743 <p> 744 sin_pi and cos_pi near integers and half integers 745 </p> 746 </td> 747<td> 748 <p> 749 <span class="blue">Max = 0ε (Mean = 0ε)</span> 750 </p> 751 </td> 752<td> 753 <p> 754 <span class="blue">Max = 0.976ε (Mean = 0.28ε)</span> 755 </p> 756 </td> 757<td> 758 <p> 759 <span class="blue">Max = 0.976ε (Mean = 0.28ε)</span> 760 </p> 761 </td> 762<td> 763 <p> 764 <span class="blue">Max = 0.996ε (Mean = 0.298ε)</span> 765 </p> 766 </td> 767</tr> 768</tbody> 769</table></div> 770</div> 771<br class="table-break"><div class="table"> 772<a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_i"></a><p class="title"><b>Table 23.10. Error rates for cyl_bessel_i</b></p> 773<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i"> 774<colgroup> 775<col> 776<col> 777<col> 778<col> 779<col> 780</colgroup> 781<thead><tr> 782<th> 783 </th> 784<th> 785 <p> 786 GNU C++ version 7.1.0<br> linux<br> double 787 </p> 788 </th> 789<th> 790 <p> 791 GNU C++ version 7.1.0<br> linux<br> long double 792 </p> 793 </th> 794<th> 795 <p> 796 Sun compiler version 0x5150<br> Sun Solaris<br> long double 797 </p> 798 </th> 799<th> 800 <p> 801 Microsoft Visual C++ version 14.1<br> Win32<br> double 802 </p> 803 </th> 804</tr></thead> 805<tbody> 806<tr> 807<td> 808 <p> 809 Bessel I0: Mathworld Data 810 </p> 811 </td> 812<td> 813 <p> 814 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 815 2.1:</em></span> Max = 270ε (Mean = 91.6ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_I0_Mathworld_Data">And 816 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 817 Max = 1.52ε (Mean = 0.622ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_I0_Mathworld_Data">And 818 other failures.</a>) 819 </p> 820 </td> 821<td> 822 <p> 823 <span class="blue">Max = 1.95ε (Mean = 0.738ε)</span><br> <br> 824 (<span class="emphasis"><em><cmath>:</em></span> Max = 8.49ε (Mean = 3.46ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_I0_Mathworld_Data">And 825 other failures.</a>) 826 </p> 827 </td> 828<td> 829 <p> 830 <span class="blue">Max = 1.95ε (Mean = 0.661ε)</span> 831 </p> 832 </td> 833<td> 834 <p> 835 <span class="blue">Max = 0.762ε (Mean = 0.329ε)</span> 836 </p> 837 </td> 838</tr> 839<tr> 840<td> 841 <p> 842 Bessel I1: Mathworld Data 843 </p> 844 </td> 845<td> 846 <p> 847 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 848 2.1:</em></span> Max = 128ε (Mean = 41ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_I1_Mathworld_Data">And 849 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 850 Max = 1.53ε (Mean = 0.483ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_I1_Mathworld_Data">And 851 other failures.</a>) 852 </p> 853 </td> 854<td> 855 <p> 856 <span class="blue">Max = 0.64ε (Mean = 0.202ε)</span><br> <br> 857 (<span class="emphasis"><em><cmath>:</em></span> Max = 5ε (Mean = 2.15ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_I1_Mathworld_Data">And 858 other failures.</a>) 859 </p> 860 </td> 861<td> 862 <p> 863 <span class="blue">Max = 0.64ε (Mean = 0.202ε)</span> 864 </p> 865 </td> 866<td> 867 <p> 868 <span class="blue">Max = 0.767ε (Mean = 0.398ε)</span> 869 </p> 870 </td> 871</tr> 872<tr> 873<td> 874 <p> 875 Bessel In: Mathworld Data 876 </p> 877 </td> 878<td> 879 <p> 880 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 881 2.1:</em></span> Max = 2.31ε (Mean = 0.838ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_In_Mathworld_Data">And 882 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 883 Max = 1.73ε (Mean = 0.601ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_In_Mathworld_Data">And 884 other failures.</a>) 885 </p> 886 </td> 887<td> 888 <p> 889 <span class="blue">Max = 1.8ε (Mean = 1.33ε)</span><br> <br> 890 (<span class="emphasis"><em><cmath>:</em></span> Max = 430ε (Mean = 163ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_In_Mathworld_Data">And 891 other failures.</a>) 892 </p> 893 </td> 894<td> 895 <p> 896 <span class="blue">Max = 463ε (Mean = 140ε)</span> 897 </p> 898 </td> 899<td> 900 <p> 901 <span class="blue">Max = 3.46ε (Mean = 1.32ε)</span> 902 </p> 903 </td> 904</tr> 905<tr> 906<td> 907 <p> 908 Bessel Iv: Mathworld Data 909 </p> 910 </td> 911<td> 912 <p> 913 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 914 2.1:</em></span> Max = 5.95ε (Mean = 2.08ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Mathworld_Data">And 915 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 916 Max = 3.53ε (Mean = 1.39ε)) 917 </p> 918 </td> 919<td> 920 <p> 921 <span class="blue">Max = 4.12ε (Mean = 1.85ε)</span><br> <br> 922 (<span class="emphasis"><em><cmath>:</em></span> Max = 616ε (Mean = 221ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Mathworld_Data">And 923 other failures.</a>) 924 </p> 925 </td> 926<td> 927 <p> 928 <span class="blue">Max = 4.12ε (Mean = 1.95ε)</span> 929 </p> 930 </td> 931<td> 932 <p> 933 <span class="blue">Max = 2.97ε (Mean = 1.24ε)</span> 934 </p> 935 </td> 936</tr> 937<tr> 938<td> 939 <p> 940 Bessel In: Random Data 941 </p> 942 </td> 943<td> 944 <p> 945 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 946 2.1:</em></span> Max = 261ε (Mean = 53.2ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_In_Random_Data">And 947 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 948 Max = 7.37ε (Mean = 2.4ε)) 949 </p> 950 </td> 951<td> 952 <p> 953 <span class="blue">Max = 4.62ε (Mean = 1.06ε)</span><br> <br> 954 (<span class="emphasis"><em><cmath>:</em></span> Max = 645ε (Mean = 132ε)) 955 </p> 956 </td> 957<td> 958 <p> 959 <span class="blue">Max = 176ε (Mean = 39.1ε)</span> 960 </p> 961 </td> 962<td> 963 <p> 964 <span class="blue">Max = 9.67ε (Mean = 1.88ε)</span> 965 </p> 966 </td> 967</tr> 968<tr> 969<td> 970 <p> 971 Bessel Iv: Random Data 972 </p> 973 </td> 974<td> 975 <p> 976 <span class="blue">Max = 0.661ε (Mean = 0.0441ε)</span><br> 977 <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 6.18e+03ε (Mean = 1.55e+03ε) 978 <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Random_Data">And 979 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 980 <span class="red">Max = 4.28e+08ε (Mean = 2.85e+07ε))</span> 981 </p> 982 </td> 983<td> 984 <p> 985 <span class="blue">Max = 8.35ε (Mean = 1.62ε)</span><br> <br> 986 (<span class="emphasis"><em><cmath>:</em></span> Max = 1.05e+03ε (Mean = 224ε) 987 <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Random_Data">And 988 other failures.</a>) 989 </p> 990 </td> 991<td> 992 <p> 993 <span class="blue">Max = 283ε (Mean = 88.4ε)</span> 994 </p> 995 </td> 996<td> 997 <p> 998 <span class="blue">Max = 7.46ε (Mean = 1.71ε)</span> 999 </p> 1000 </td> 1001</tr> 1002<tr> 1003<td> 1004 <p> 1005 Bessel Iv: Mathworld Data (large values) 1006 </p> 1007 </td> 1008<td> 1009 <p> 1010 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 1011 2.1:</em></span> Max = 37ε (Mean = 18ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Mathworld_Data_large_values_">And 1012 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 1013 <span class="red">Max = 3.77e+168ε (Mean = 2.39e+168ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_Iv_Mathworld_Data_large_values_">And 1014 other failures.</a>)</span> 1015 </p> 1016 </td> 1017<td> 1018 <p> 1019 <span class="blue">Max = 14.7ε (Mean = 6.66ε)</span><br> <br> 1020 (<span class="emphasis"><em><cmath>:</em></span> Max = 118ε (Mean = 57.2ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Mathworld_Data_large_values_">And 1021 other failures.</a>) 1022 </p> 1023 </td> 1024<td> 1025 <p> 1026 <span class="blue">Max = 14.7ε (Mean = 6.59ε)</span> 1027 </p> 1028 </td> 1029<td> 1030 <p> 1031 <span class="blue">Max = 3.67ε (Mean = 1.64ε)</span> 1032 </p> 1033 </td> 1034</tr> 1035</tbody> 1036</table></div> 1037</div> 1038<br class="table-break"><div class="table"> 1039<a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_i_integer_orders_"></a><p class="title"><b>Table 23.11. Error rates for cyl_bessel_i (integer orders)</b></p> 1040<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i (integer orders)"> 1041<colgroup> 1042<col> 1043<col> 1044<col> 1045<col> 1046<col> 1047</colgroup> 1048<thead><tr> 1049<th> 1050 </th> 1051<th> 1052 <p> 1053 GNU C++ version 7.1.0<br> linux<br> double 1054 </p> 1055 </th> 1056<th> 1057 <p> 1058 GNU C++ version 7.1.0<br> linux<br> long double 1059 </p> 1060 </th> 1061<th> 1062 <p> 1063 Sun compiler version 0x5150<br> Sun Solaris<br> long double 1064 </p> 1065 </th> 1066<th> 1067 <p> 1068 Microsoft Visual C++ version 14.1<br> Win32<br> double 1069 </p> 1070 </th> 1071</tr></thead> 1072<tbody> 1073<tr> 1074<td> 1075 <p> 1076 Bessel I0: Mathworld Data (Integer Version) 1077 </p> 1078 </td> 1079<td> 1080 <p> 1081 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 1082 2.1:</em></span> Max = 0.79ε (Mean = 0.482ε))<br> (<span class="emphasis"><em>Rmath 1083 3.2.3:</em></span> Max = 1.52ε (Mean = 0.622ε) <a class="link" href="logs.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 1084 other failures.</a>) 1085 </p> 1086 </td> 1087<td> 1088 <p> 1089 <span class="blue">Max = 1.95ε (Mean = 0.738ε)</span><br> <br> 1090 (<span class="emphasis"><em><cmath>:</em></span> Max = 8.49ε (Mean = 3.46ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_I0_Mathworld_Data_Integer_Version_">And 1091 other failures.</a>) 1092 </p> 1093 </td> 1094<td> 1095 <p> 1096 <span class="blue">Max = 1.95ε (Mean = 0.661ε)</span> 1097 </p> 1098 </td> 1099<td> 1100 <p> 1101 <span class="blue">Max = 0.762ε (Mean = 0.329ε)</span> 1102 </p> 1103 </td> 1104</tr> 1105<tr> 1106<td> 1107 <p> 1108 Bessel I1: Mathworld Data (Integer Version) 1109 </p> 1110 </td> 1111<td> 1112 <p> 1113 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 1114 2.1:</em></span> Max = 0.82ε (Mean = 0.456ε))<br> (<span class="emphasis"><em>Rmath 1115 3.2.3:</em></span> Max = 1.53ε (Mean = 0.483ε) <a class="link" href="logs.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 1116 other failures.</a>) 1117 </p> 1118 </td> 1119<td> 1120 <p> 1121 <span class="blue">Max = 0.64ε (Mean = 0.202ε)</span><br> <br> 1122 (<span class="emphasis"><em><cmath>:</em></span> Max = 5ε (Mean = 2.15ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_I1_Mathworld_Data_Integer_Version_">And 1123 other failures.</a>) 1124 </p> 1125 </td> 1126<td> 1127 <p> 1128 <span class="blue">Max = 0.64ε (Mean = 0.202ε)</span> 1129 </p> 1130 </td> 1131<td> 1132 <p> 1133 <span class="blue">Max = 0.767ε (Mean = 0.398ε)</span> 1134 </p> 1135 </td> 1136</tr> 1137<tr> 1138<td> 1139 <p> 1140 Bessel In: Mathworld Data (Integer Version) 1141 </p> 1142 </td> 1143<td> 1144 <p> 1145 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 1146 2.1:</em></span> Max = 5.15ε (Mean = 2.13ε) <a class="link" href="logs.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 1147 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 1148 Max = 1.73ε (Mean = 0.601ε) <a class="link" href="logs.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 1149 other failures.</a>) 1150 </p> 1151 </td> 1152<td> 1153 <p> 1154 <span class="blue">Max = 1.8ε (Mean = 1.33ε)</span><br> <br> 1155 (<span class="emphasis"><em><cmath>:</em></span> Max = 430ε (Mean = 163ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_In_Mathworld_Data_Integer_Version_">And 1156 other failures.</a>) 1157 </p> 1158 </td> 1159<td> 1160 <p> 1161 <span class="blue">Max = 463ε (Mean = 140ε)</span> 1162 </p> 1163 </td> 1164<td> 1165 <p> 1166 <span class="blue">Max = 3.46ε (Mean = 1.32ε)</span> 1167 </p> 1168 </td> 1169</tr> 1170</tbody> 1171</table></div> 1172</div> 1173<br class="table-break"><div class="table"> 1174<a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_i_prime"></a><p class="title"><b>Table 23.12. Error rates for cyl_bessel_i_prime</b></p> 1175<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i_prime"> 1176<colgroup> 1177<col> 1178<col> 1179<col> 1180<col> 1181<col> 1182</colgroup> 1183<thead><tr> 1184<th> 1185 </th> 1186<th> 1187 <p> 1188 GNU C++ version 7.1.0<br> linux<br> double 1189 </p> 1190 </th> 1191<th> 1192 <p> 1193 GNU C++ version 7.1.0<br> linux<br> long double 1194 </p> 1195 </th> 1196<th> 1197 <p> 1198 Sun compiler version 0x5150<br> Sun Solaris<br> long double 1199 </p> 1200 </th> 1201<th> 1202 <p> 1203 Microsoft Visual C++ version 14.1<br> Win32<br> double 1204 </p> 1205 </th> 1206</tr></thead> 1207<tbody> 1208<tr> 1209<td> 1210 <p> 1211 Bessel I'0: Mathworld Data 1212 </p> 1213 </td> 1214<td> 1215 <p> 1216 <span class="blue">Max = 0ε (Mean = 0ε)</span> 1217 </p> 1218 </td> 1219<td> 1220 <p> 1221 <span class="blue">Max = 0.82ε (Mean = 0.259ε)</span> 1222 </p> 1223 </td> 1224<td> 1225 <p> 1226 <span class="blue">Max = 0.82ε (Mean = 0.259ε)</span> 1227 </p> 1228 </td> 1229<td> 1230 <p> 1231 <span class="blue">Max = 0.82ε (Mean = 0.354ε)</span> 1232 </p> 1233 </td> 1234</tr> 1235<tr> 1236<td> 1237 <p> 1238 Bessel I'1: Mathworld Data 1239 </p> 1240 </td> 1241<td> 1242 <p> 1243 <span class="blue">Max = 0ε (Mean = 0ε)</span> 1244 </p> 1245 </td> 1246<td> 1247 <p> 1248 <span class="blue">Max = 1.97ε (Mean = 0.757ε)</span> 1249 </p> 1250 </td> 1251<td> 1252 <p> 1253 <span class="blue">Max = 1.97ε (Mean = 0.757ε)</span> 1254 </p> 1255 </td> 1256<td> 1257 <p> 1258 <span class="blue">Max = 1.36ε (Mean = 0.782ε)</span> 1259 </p> 1260 </td> 1261</tr> 1262<tr> 1263<td> 1264 <p> 1265 Bessel I'n: Mathworld Data 1266 </p> 1267 </td> 1268<td> 1269 <p> 1270 <span class="blue">Max = 0ε (Mean = 0ε)</span> 1271 </p> 1272 </td> 1273<td> 1274 <p> 1275 <span class="blue">Max = 2.31ε (Mean = 1.41ε)</span> 1276 </p> 1277 </td> 1278<td> 1279 <p> 1280 <span class="blue">Max = 701ε (Mean = 212ε)</span> 1281 </p> 1282 </td> 1283<td> 1284 <p> 1285 <span class="blue">Max = 3.61ε (Mean = 1.22ε)</span> 1286 </p> 1287 </td> 1288</tr> 1289<tr> 1290<td> 1291 <p> 1292 Bessel I'v: Mathworld Data 1293 </p> 1294 </td> 1295<td> 1296 <p> 1297 <span class="blue">Max = 1.62ε (Mean = 0.512ε)</span> 1298 </p> 1299 </td> 1300<td> 1301 <p> 1302 <span class="blue">Max = 2.89e+03ε (Mean = 914ε)</span> 1303 </p> 1304 </td> 1305<td> 1306 <p> 1307 <span class="blue">Max = 2.89e+03ε (Mean = 914ε)</span> 1308 </p> 1309 </td> 1310<td> 1311 <p> 1312 <span class="blue">Max = 3.76e+03ε (Mean = 1.19e+03ε)</span> 1313 </p> 1314 </td> 1315</tr> 1316<tr> 1317<td> 1318 <p> 1319 Bessel I'n: Random Data 1320 </p> 1321 </td> 1322<td> 1323 <p> 1324 <span class="blue">Max = 0ε (Mean = 0ε)</span> 1325 </p> 1326 </td> 1327<td> 1328 <p> 1329 <span class="blue">Max = 3.95ε (Mean = 1.06ε)</span> 1330 </p> 1331 </td> 1332<td> 1333 <p> 1334 <span class="blue">Max = 195ε (Mean = 37.1ε)</span> 1335 </p> 1336 </td> 1337<td> 1338 <p> 1339 <span class="blue">Max = 9.85ε (Mean = 1.82ε)</span> 1340 </p> 1341 </td> 1342</tr> 1343<tr> 1344<td> 1345 <p> 1346 Bessel I'v: Random Data 1347 </p> 1348 </td> 1349<td> 1350 <p> 1351 <span class="blue">Max = 0ε (Mean = 0ε)</span> 1352 </p> 1353 </td> 1354<td> 1355 <p> 1356 <span class="blue">Max = 14.1ε (Mean = 2.93ε)</span> 1357 </p> 1358 </td> 1359<td> 1360 <p> 1361 <span class="blue">Max = 336ε (Mean = 68.5ε)</span> 1362 </p> 1363 </td> 1364<td> 1365 <p> 1366 <span class="blue">Max = 14ε (Mean = 2.5ε)</span> 1367 </p> 1368 </td> 1369</tr> 1370<tr> 1371<td> 1372 <p> 1373 Bessel I'v: Mathworld Data (large values) 1374 </p> 1375 </td> 1376<td> 1377 <p> 1378 <span class="blue">Max = 0ε (Mean = 0ε)</span> 1379 </p> 1380 </td> 1381<td> 1382 <p> 1383 <span class="blue">Max = 42.6ε (Mean = 20.2ε)</span> 1384 </p> 1385 </td> 1386<td> 1387 <p> 1388 <span class="blue">Max = 42.6ε (Mean = 20.2ε)</span> 1389 </p> 1390 </td> 1391<td> 1392 <p> 1393 <span class="blue">Max = 59.5ε (Mean = 26.6ε)</span> 1394 </p> 1395 </td> 1396</tr> 1397</tbody> 1398</table></div> 1399</div> 1400<br class="table-break"><div class="table"> 1401<a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_i_prime_integer_orders_"></a><p class="title"><b>Table 23.13. Error rates for cyl_bessel_i_prime (integer orders)</b></p> 1402<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i_prime (integer orders)"> 1403<colgroup> 1404<col> 1405<col> 1406<col> 1407<col> 1408<col> 1409</colgroup> 1410<thead><tr> 1411<th> 1412 </th> 1413<th> 1414 <p> 1415 GNU C++ version 7.1.0<br> linux<br> double 1416 </p> 1417 </th> 1418<th> 1419 <p> 1420 GNU C++ version 7.1.0<br> linux<br> long double 1421 </p> 1422 </th> 1423<th> 1424 <p> 1425 Sun compiler version 0x5150<br> Sun Solaris<br> long double 1426 </p> 1427 </th> 1428<th> 1429 <p> 1430 Microsoft Visual C++ version 14.1<br> Win32<br> double 1431 </p> 1432 </th> 1433</tr></thead> 1434<tbody> 1435<tr> 1436<td> 1437 <p> 1438 Bessel I'0: Mathworld Data (Integer Version) 1439 </p> 1440 </td> 1441<td> 1442 <p> 1443 <span class="blue">Max = 0ε (Mean = 0ε)</span> 1444 </p> 1445 </td> 1446<td> 1447 <p> 1448 <span class="blue">Max = 0.82ε (Mean = 0.259ε)</span> 1449 </p> 1450 </td> 1451<td> 1452 <p> 1453 <span class="blue">Max = 0.82ε (Mean = 0.259ε)</span> 1454 </p> 1455 </td> 1456<td> 1457 <p> 1458 <span class="blue">Max = 0.82ε (Mean = 0.354ε)</span> 1459 </p> 1460 </td> 1461</tr> 1462<tr> 1463<td> 1464 <p> 1465 Bessel I'1: Mathworld Data (Integer Version) 1466 </p> 1467 </td> 1468<td> 1469 <p> 1470 <span class="blue">Max = 0ε (Mean = 0ε)</span> 1471 </p> 1472 </td> 1473<td> 1474 <p> 1475 <span class="blue">Max = 1.97ε (Mean = 0.757ε)</span> 1476 </p> 1477 </td> 1478<td> 1479 <p> 1480 <span class="blue">Max = 1.97ε (Mean = 0.757ε)</span> 1481 </p> 1482 </td> 1483<td> 1484 <p> 1485 <span class="blue">Max = 1.36ε (Mean = 0.782ε)</span> 1486 </p> 1487 </td> 1488</tr> 1489<tr> 1490<td> 1491 <p> 1492 Bessel I'n: Mathworld Data (Integer Version) 1493 </p> 1494 </td> 1495<td> 1496 <p> 1497 <span class="blue">Max = 0ε (Mean = 0ε)</span> 1498 </p> 1499 </td> 1500<td> 1501 <p> 1502 <span class="blue">Max = 2.31ε (Mean = 1.41ε)</span> 1503 </p> 1504 </td> 1505<td> 1506 <p> 1507 <span class="blue">Max = 701ε (Mean = 212ε)</span> 1508 </p> 1509 </td> 1510<td> 1511 <p> 1512 <span class="blue">Max = 3.61ε (Mean = 1.22ε)</span> 1513 </p> 1514 </td> 1515</tr> 1516</tbody> 1517</table></div> 1518</div> 1519<br class="table-break"><div class="table"> 1520<a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_j"></a><p class="title"><b>Table 23.14. Error rates for cyl_bessel_j</b></p> 1521<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j"> 1522<colgroup> 1523<col> 1524<col> 1525<col> 1526<col> 1527<col> 1528</colgroup> 1529<thead><tr> 1530<th> 1531 </th> 1532<th> 1533 <p> 1534 GNU C++ version 7.1.0<br> linux<br> long double 1535 </p> 1536 </th> 1537<th> 1538 <p> 1539 GNU C++ version 7.1.0<br> linux<br> double 1540 </p> 1541 </th> 1542<th> 1543 <p> 1544 Sun compiler version 0x5150<br> Sun Solaris<br> long double 1545 </p> 1546 </th> 1547<th> 1548 <p> 1549 Microsoft Visual C++ version 14.1<br> Win32<br> double 1550 </p> 1551 </th> 1552</tr></thead> 1553<tbody> 1554<tr> 1555<td> 1556 <p> 1557 Bessel J0: Mathworld Data 1558 </p> 1559 </td> 1560<td> 1561 <p> 1562 <span class="blue">Max = 6.55ε (Mean = 2.86ε)</span><br> <br> 1563 (<span class="emphasis"><em><cmath>:</em></span> Max = 5.04ε (Mean = 1.78ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J0_Mathworld_Data">And 1564 other failures.</a>) 1565 </p> 1566 </td> 1567<td> 1568 <p> 1569 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 1570 2.1:</em></span> Max = 0.629ε (Mean = 0.223ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J0_Mathworld_Data">And 1571 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 1572 Max = 0.629ε (Mean = 0.223ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J0_Mathworld_Data">And 1573 other failures.</a>) 1574 </p> 1575 </td> 1576<td> 1577 <p> 1578 <span class="blue">Max = 6.55ε (Mean = 2.86ε)</span> 1579 </p> 1580 </td> 1581<td> 1582 <p> 1583 <span class="blue">Max = 2.52ε (Mean = 1.2ε)</span> 1584 </p> 1585 </td> 1586</tr> 1587<tr> 1588<td> 1589 <p> 1590 Bessel J0: Mathworld Data (Tricky cases) 1591 </p> 1592 </td> 1593<td> 1594 <p> 1595 <span class="blue">Max = 1.64e+08ε (Mean = 6.69e+07ε)</span><br> 1596 <br> (<span class="emphasis"><em><cmath>:</em></span> Max = 4.79e+08ε (Mean 1597 = 1.96e+08ε)) 1598 </p> 1599 </td> 1600<td> 1601 <p> 1602 <span class="blue">Max = 8e+04ε (Mean = 3.27e+04ε)</span><br> 1603 <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 6.5e+07ε (Mean = 2.66e+07ε))<br> 1604 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.04e+07ε (Mean = 4.29e+06ε)) 1605 </p> 1606 </td> 1607<td> 1608 <p> 1609 <span class="blue">Max = 1.64e+08ε (Mean = 6.69e+07ε)</span> 1610 </p> 1611 </td> 1612<td> 1613 <p> 1614 <span class="blue">Max = 1e+07ε (Mean = 4.09e+06ε)</span> 1615 </p> 1616 </td> 1617</tr> 1618<tr> 1619<td> 1620 <p> 1621 Bessel J1: Mathworld Data 1622 </p> 1623 </td> 1624<td> 1625 <p> 1626 <span class="blue">Max = 3.59ε (Mean = 1.33ε)</span><br> <br> 1627 (<span class="emphasis"><em><cmath>:</em></span> Max = 6.1ε (Mean = 2.95ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J1_Mathworld_Data">And 1628 other failures.</a>) 1629 </p> 1630 </td> 1631<td> 1632 <p> 1633 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 1634 2.1:</em></span> Max = 6.62ε (Mean = 2.35ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J1_Mathworld_Data">And 1635 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 1636 Max = 0.946ε (Mean = 0.39ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J1_Mathworld_Data">And 1637 other failures.</a>) 1638 </p> 1639 </td> 1640<td> 1641 <p> 1642 <span class="blue">Max = 1.44ε (Mean = 0.637ε)</span> 1643 </p> 1644 </td> 1645<td> 1646 <p> 1647 <span class="blue">Max = 1.73ε (Mean = 0.976ε)</span> 1648 </p> 1649 </td> 1650</tr> 1651<tr> 1652<td> 1653 <p> 1654 Bessel J1: Mathworld Data (tricky cases) 1655 </p> 1656 </td> 1657<td> 1658 <p> 1659 <span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span><br> 1660 <br> (<span class="emphasis"><em><cmath>:</em></span> Max = 2.15e+06ε (Mean 1661 = 1.58e+06ε)) 1662 </p> 1663 </td> 1664<td> 1665 <p> 1666 <span class="blue">Max = 106ε (Mean = 47.5ε)</span><br> <br> 1667 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.75e+05ε (Mean = 5.32e+05ε))<br> 1668 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.93e+06ε (Mean = 1.7e+06ε)) 1669 </p> 1670 </td> 1671<td> 1672 <p> 1673 <span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span> 1674 </p> 1675 </td> 1676<td> 1677 <p> 1678 <span class="blue">Max = 3.23e+04ε (Mean = 1.45e+04ε)</span> 1679 </p> 1680 </td> 1681</tr> 1682<tr> 1683<td> 1684 <p> 1685 Bessel JN: Mathworld Data 1686 </p> 1687 </td> 1688<td> 1689 <p> 1690 <span class="blue">Max = 6.85ε (Mean = 3.35ε)</span><br> <br> 1691 (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 2.13e+19ε (Mean 1692 = 5.16e+18ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_JN_Mathworld_Data">And 1693 other failures.</a>)</span> 1694 </p> 1695 </td> 1696<td> 1697 <p> 1698 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 1699 2.1:</em></span> Max = 6.9e+05ε (Mean = 2.15e+05ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_JN_Mathworld_Data">And 1700 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 1701 <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_JN_Mathworld_Data">And 1702 other failures.</a>)</span> 1703 </p> 1704 </td> 1705<td> 1706 <p> 1707 <span class="blue">Max = 463ε (Mean = 112ε)</span> 1708 </p> 1709 </td> 1710<td> 1711 <p> 1712 <span class="blue">Max = 14.7ε (Mean = 5.4ε)</span> 1713 </p> 1714 </td> 1715</tr> 1716<tr> 1717<td> 1718 <p> 1719 Bessel J: Mathworld Data 1720 </p> 1721 </td> 1722<td> 1723 <p> 1724 <span class="blue">Max = 14.7ε (Mean = 4.11ε)</span><br> <br> 1725 (<span class="emphasis"><em><cmath>:</em></span> Max = 3.49e+05ε (Mean = 8.09e+04ε) 1726 <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J_Mathworld_Data">And 1727 other failures.</a>) 1728 </p> 1729 </td> 1730<td> 1731 <p> 1732 <span class="blue">Max = 10ε (Mean = 2.24ε)</span><br> <br> 1733 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.39e+05ε (Mean = 5.37e+04ε) 1734 <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Mathworld_Data">And 1735 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 1736 <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J_Mathworld_Data">And 1737 other failures.</a>)</span> 1738 </p> 1739 </td> 1740<td> 1741 <p> 1742 <span class="blue">Max = 14.7ε (Mean = 4.22ε)</span> 1743 </p> 1744 </td> 1745<td> 1746 <p> 1747 <span class="blue">Max = 14.9ε (Mean = 3.89ε)</span> 1748 </p> 1749 </td> 1750</tr> 1751<tr> 1752<td> 1753 <p> 1754 Bessel J: Mathworld Data (large values) 1755 </p> 1756 </td> 1757<td> 1758 <p> 1759 <span class="blue">Max = 607ε (Mean = 305ε)</span><br> <br> 1760 (<span class="emphasis"><em><cmath>:</em></span> Max = 34.9ε (Mean = 17.4ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J_Mathworld_Data_large_values_">And 1761 other failures.</a>) 1762 </p> 1763 </td> 1764<td> 1765 <p> 1766 <span class="blue">Max = 0.536ε (Mean = 0.268ε)</span><br> <br> 1767 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 4.91e+03ε (Mean = 2.46e+03ε) 1768 <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Mathworld_Data_large_values_">And 1769 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 1770 Max = 5.9ε (Mean = 3.76ε)) 1771 </p> 1772 </td> 1773<td> 1774 <p> 1775 <span class="blue">Max = 607ε (Mean = 305ε)</span> 1776 </p> 1777 </td> 1778<td> 1779 <p> 1780 <span class="blue">Max = 9.31ε (Mean = 5.52ε)</span> 1781 </p> 1782 </td> 1783</tr> 1784<tr> 1785<td> 1786 <p> 1787 Bessel JN: Random Data 1788 </p> 1789 </td> 1790<td> 1791 <p> 1792 <span class="blue">Max = 50.8ε (Mean = 3.69ε)</span><br> <br> 1793 (<span class="emphasis"><em><cmath>:</em></span> Max = 1.12e+03ε (Mean = 88.7ε)) 1794 </p> 1795 </td> 1796<td> 1797 <p> 1798 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 1799 2.1:</em></span> Max = 75.7ε (Mean = 5.36ε))<br> (<span class="emphasis"><em>Rmath 1800 3.2.3:</em></span> Max = 3.93ε (Mean = 1.22ε)) 1801 </p> 1802 </td> 1803<td> 1804 <p> 1805 <span class="blue">Max = 99.6ε (Mean = 22ε)</span> 1806 </p> 1807 </td> 1808<td> 1809 <p> 1810 <span class="blue">Max = 17.5ε (Mean = 1.46ε)</span> 1811 </p> 1812 </td> 1813</tr> 1814<tr> 1815<td> 1816 <p> 1817 Bessel J: Random Data 1818 </p> 1819 </td> 1820<td> 1821 <p> 1822 <span class="blue">Max = 11.4ε (Mean = 1.68ε)</span><br> <br> 1823 (<span class="emphasis"><em><cmath>:</em></span> Max = 501ε (Mean = 52.3ε)) 1824 </p> 1825 </td> 1826<td> 1827 <p> 1828 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 1829 2.1:</em></span> Max = 15.5ε (Mean = 3.33ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Random_Data">And 1830 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 1831 Max = 6.74ε (Mean = 1.3ε)) 1832 </p> 1833 </td> 1834<td> 1835 <p> 1836 <span class="blue">Max = 260ε (Mean = 34ε)</span> 1837 </p> 1838 </td> 1839<td> 1840 <p> 1841 <span class="blue">Max = 9.24ε (Mean = 1.17ε)</span> 1842 </p> 1843 </td> 1844</tr> 1845<tr> 1846<td> 1847 <p> 1848 Bessel J: Random Data (Tricky large values) 1849 </p> 1850 </td> 1851<td> 1852 <p> 1853 <span class="blue">Max = 785ε (Mean = 94.2ε)</span><br> <br> 1854 (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 5.01e+17ε (Mean 1855 = 6.23e+16ε))</span> 1856 </p> 1857 </td> 1858<td> 1859 <p> 1860 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 1861 2.1:</em></span> Max = 2.48e+05ε (Mean = 5.11e+04ε))<br> (<span class="emphasis"><em>Rmath 1862 3.2.3:</em></span> Max = 71.6ε (Mean = 11.7ε)) 1863 </p> 1864 </td> 1865<td> 1866 <p> 1867 <span class="blue">Max = 785ε (Mean = 97.4ε)</span> 1868 </p> 1869 </td> 1870<td> 1871 <p> 1872 <span class="blue">Max = 59.2ε (Mean = 8.67ε)</span> 1873 </p> 1874 </td> 1875</tr> 1876</tbody> 1877</table></div> 1878</div> 1879<br class="table-break"><div class="table"> 1880<a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_j_integer_orders_"></a><p class="title"><b>Table 23.15. Error rates for cyl_bessel_j (integer orders)</b></p> 1881<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j (integer orders)"> 1882<colgroup> 1883<col> 1884<col> 1885<col> 1886<col> 1887<col> 1888</colgroup> 1889<thead><tr> 1890<th> 1891 </th> 1892<th> 1893 <p> 1894 GNU C++ version 7.1.0<br> linux<br> long double 1895 </p> 1896 </th> 1897<th> 1898 <p> 1899 GNU C++ version 7.1.0<br> linux<br> double 1900 </p> 1901 </th> 1902<th> 1903 <p> 1904 Sun compiler version 0x5150<br> Sun Solaris<br> long double 1905 </p> 1906 </th> 1907<th> 1908 <p> 1909 Microsoft Visual C++ version 14.1<br> Win32<br> double 1910 </p> 1911 </th> 1912</tr></thead> 1913<tbody> 1914<tr> 1915<td> 1916 <p> 1917 Bessel J0: Mathworld Data (Integer Version) 1918 </p> 1919 </td> 1920<td> 1921 <p> 1922 <span class="blue">Max = 6.55ε (Mean = 2.86ε)</span><br> <br> 1923 (<span class="emphasis"><em><cmath>:</em></span> Max = 5.04ε (Mean = 1.78ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_J0_Mathworld_Data_Integer_Version_">And 1924 other failures.</a>) 1925 </p> 1926 </td> 1927<td> 1928 <p> 1929 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 1930 2.1:</em></span> Max = 1.12ε (Mean = 0.488ε))<br> (<span class="emphasis"><em>Rmath 1931 3.2.3:</em></span> Max = 0.629ε (Mean = 0.223ε) <a class="link" href="logs.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 1932 other failures.</a>) 1933 </p> 1934 </td> 1935<td> 1936 <p> 1937 <span class="blue">Max = 6.55ε (Mean = 2.86ε)</span> 1938 </p> 1939 </td> 1940<td> 1941 <p> 1942 <span class="blue">Max = 2.52ε (Mean = 1.2ε)</span><br> <br> 1943 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.89ε (Mean = 0.988ε)) 1944 </p> 1945 </td> 1946</tr> 1947<tr> 1948<td> 1949 <p> 1950 Bessel J0: Mathworld Data (Tricky cases) (Integer Version) 1951 </p> 1952 </td> 1953<td> 1954 <p> 1955 <span class="blue">Max = 1.64e+08ε (Mean = 6.69e+07ε)</span><br> 1956 <br> (<span class="emphasis"><em><cmath>:</em></span> Max = 4.79e+08ε (Mean 1957 = 1.96e+08ε)) 1958 </p> 1959 </td> 1960<td> 1961 <p> 1962 <span class="blue">Max = 8e+04ε (Mean = 3.27e+04ε)</span><br> 1963 <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1e+07ε (Mean = 4.11e+06ε))<br> 1964 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.04e+07ε (Mean = 4.29e+06ε)) 1965 </p> 1966 </td> 1967<td> 1968 <p> 1969 <span class="blue">Max = 1.64e+08ε (Mean = 6.69e+07ε)</span> 1970 </p> 1971 </td> 1972<td> 1973 <p> 1974 <span class="blue">Max = 1e+07ε (Mean = 4.09e+06ε)</span><br> 1975 <br> (<span class="emphasis"><em><math.h>:</em></span> <span class="red">Max 1976 = 2.54e+08ε (Mean = 1.04e+08ε))</span> 1977 </p> 1978 </td> 1979</tr> 1980<tr> 1981<td> 1982 <p> 1983 Bessel J1: Mathworld Data (Integer Version) 1984 </p> 1985 </td> 1986<td> 1987 <p> 1988 <span class="blue">Max = 3.59ε (Mean = 1.33ε)</span><br> <br> 1989 (<span class="emphasis"><em><cmath>:</em></span> Max = 6.1ε (Mean = 2.95ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_J1_Mathworld_Data_Integer_Version_">And 1990 other failures.</a>) 1991 </p> 1992 </td> 1993<td> 1994 <p> 1995 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 1996 2.1:</em></span> Max = 1.89ε (Mean = 0.721ε))<br> (<span class="emphasis"><em>Rmath 1997 3.2.3:</em></span> Max = 0.946ε (Mean = 0.39ε) <a class="link" href="logs.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 1998 other failures.</a>) 1999 </p> 2000 </td> 2001<td> 2002 <p> 2003 <span class="blue">Max = 1.44ε (Mean = 0.637ε)</span> 2004 </p> 2005 </td> 2006<td> 2007 <p> 2008 <span class="blue">Max = 1.73ε (Mean = 0.976ε)</span><br> <br> 2009 (<span class="emphasis"><em><math.h>:</em></span> Max = 11.4ε (Mean = 4.15ε)) 2010 </p> 2011 </td> 2012</tr> 2013<tr> 2014<td> 2015 <p> 2016 Bessel J1: Mathworld Data (tricky cases) (Integer Version) 2017 </p> 2018 </td> 2019<td> 2020 <p> 2021 <span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span><br> 2022 <br> (<span class="emphasis"><em><cmath>:</em></span> Max = 2.15e+06ε (Mean 2023 = 1.58e+06ε)) 2024 </p> 2025 </td> 2026<td> 2027 <p> 2028 <span class="blue">Max = 106ε (Mean = 47.5ε)</span><br> <br> 2029 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.26e+06ε (Mean = 6.28e+05ε))<br> 2030 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.93e+06ε (Mean = 1.7e+06ε)) 2031 </p> 2032 </td> 2033<td> 2034 <p> 2035 <span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span> 2036 </p> 2037 </td> 2038<td> 2039 <p> 2040 <span class="blue">Max = 3.23e+04ε (Mean = 1.45e+04ε)</span><br> 2041 <br> (<span class="emphasis"><em><math.h>:</em></span> Max = 1.44e+07ε (Mean 2042 = 6.5e+06ε)) 2043 </p> 2044 </td> 2045</tr> 2046<tr> 2047<td> 2048 <p> 2049 Bessel JN: Mathworld Data (Integer Version) 2050 </p> 2051 </td> 2052<td> 2053 <p> 2054 <span class="blue">Max = 6.85ε (Mean = 3.35ε)</span><br> <br> 2055 (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 2.13e+19ε (Mean 2056 = 5.16e+18ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_JN_Mathworld_Data_Integer_Version_">And 2057 other failures.</a>)</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 = 6.9e+05ε (Mean = 2.53e+05ε) <a class="link" href="logs.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 2064 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 2065 <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.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 2066 other failures.</a>)</span> 2067 </p> 2068 </td> 2069<td> 2070 <p> 2071 <span class="blue">Max = 463ε (Mean = 112ε)</span> 2072 </p> 2073 </td> 2074<td> 2075 <p> 2076 <span class="blue">Max = 14.7ε (Mean = 5.4ε)</span><br> <br> 2077 (<span class="emphasis"><em><math.h>:</em></span> <span class="red">Max = 2078 +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_Microsoft_Visual_C_version_14_1_Win32_double_cyl_bessel_j_integer_orders___math_h__Bessel_JN_Mathworld_Data_Integer_Version_">And 2079 other failures.</a>)</span> 2080 </p> 2081 </td> 2082</tr> 2083</tbody> 2084</table></div> 2085</div> 2086<br class="table-break"><div class="table"> 2087<a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_j_prime"></a><p class="title"><b>Table 23.16. Error rates for cyl_bessel_j_prime</b></p> 2088<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j_prime"> 2089<colgroup> 2090<col> 2091<col> 2092<col> 2093<col> 2094<col> 2095</colgroup> 2096<thead><tr> 2097<th> 2098 </th> 2099<th> 2100 <p> 2101 GNU C++ version 7.1.0<br> linux<br> double 2102 </p> 2103 </th> 2104<th> 2105 <p> 2106 GNU C++ version 7.1.0<br> linux<br> long double 2107 </p> 2108 </th> 2109<th> 2110 <p> 2111 Sun compiler version 0x5150<br> Sun Solaris<br> long double 2112 </p> 2113 </th> 2114<th> 2115 <p> 2116 Microsoft Visual C++ version 14.1<br> Win32<br> double 2117 </p> 2118 </th> 2119</tr></thead> 2120<tbody> 2121<tr> 2122<td> 2123 <p> 2124 Bessel J0': Mathworld Data 2125 </p> 2126 </td> 2127<td> 2128 <p> 2129 <span class="blue">Max = 0ε (Mean = 0ε)</span> 2130 </p> 2131 </td> 2132<td> 2133 <p> 2134 <span class="blue">Max = 18.9ε (Mean = 6.82ε)</span> 2135 </p> 2136 </td> 2137<td> 2138 <p> 2139 <span class="blue">Max = 18.9ε (Mean = 6.72ε)</span> 2140 </p> 2141 </td> 2142<td> 2143 <p> 2144 <span class="blue">Max = 6.62ε (Mean = 2.55ε)</span> 2145 </p> 2146 </td> 2147</tr> 2148<tr> 2149<td> 2150 <p> 2151 Bessel J0': Mathworld Data (Tricky cases) 2152 </p> 2153 </td> 2154<td> 2155 <p> 2156 <span class="blue">Max = 0ε (Mean = 0ε)</span> 2157 </p> 2158 </td> 2159<td> 2160 <p> 2161 <span class="blue">Max = 7.44ε (Mean = 3.34ε)</span> 2162 </p> 2163 </td> 2164<td> 2165 <p> 2166 <span class="blue">Max = 7.44ε (Mean = 3.31ε)</span> 2167 </p> 2168 </td> 2169<td> 2170 <p> 2171 <span class="blue">Max = 3.67ε (Mean = 1.74ε)</span> 2172 </p> 2173 </td> 2174</tr> 2175<tr> 2176<td> 2177 <p> 2178 Bessel J1': Mathworld Data 2179 </p> 2180 </td> 2181<td> 2182 <p> 2183 <span class="blue">Max = 0ε (Mean = 0ε)</span> 2184 </p> 2185 </td> 2186<td> 2187 <p> 2188 <span class="blue">Max = 7.9ε (Mean = 3.37ε)</span> 2189 </p> 2190 </td> 2191<td> 2192 <p> 2193 <span class="blue">Max = 7.9ε (Mean = 3.37ε)</span> 2194 </p> 2195 </td> 2196<td> 2197 <p> 2198 <span class="blue">Max = 0.999ε (Mean = 0.627ε)</span> 2199 </p> 2200 </td> 2201</tr> 2202<tr> 2203<td> 2204 <p> 2205 Bessel J1': Mathworld Data (tricky cases) 2206 </p> 2207 </td> 2208<td> 2209 <p> 2210 <span class="blue">Max = 287ε (Mean = 129ε)</span> 2211 </p> 2212 </td> 2213<td> 2214 <p> 2215 <span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span> 2216 </p> 2217 </td> 2218<td> 2219 <p> 2220 <span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span> 2221 </p> 2222 </td> 2223<td> 2224 <p> 2225 <span class="blue">Max = 288ε (Mean = 129ε)</span> 2226 </p> 2227 </td> 2228</tr> 2229<tr> 2230<td> 2231 <p> 2232 Bessel JN': Mathworld Data 2233 </p> 2234 </td> 2235<td> 2236 <p> 2237 <span class="blue">Max = 0.527ε (Mean = 0.128ε)</span> 2238 </p> 2239 </td> 2240<td> 2241 <p> 2242 <span class="blue">Max = 1.29e+03ε (Mean = 312ε)</span> 2243 </p> 2244 </td> 2245<td> 2246 <p> 2247 <span class="blue">Max = 1.29e+03ε (Mean = 355ε)</span> 2248 </p> 2249 </td> 2250<td> 2251 <p> 2252 <span class="blue">Max = 14ε (Mean = 6.13ε)</span> 2253 </p> 2254 </td> 2255</tr> 2256<tr> 2257<td> 2258 <p> 2259 Bessel J': Mathworld Data 2260 </p> 2261 </td> 2262<td> 2263 <p> 2264 <span class="blue">Max = 21.5ε (Mean = 4.7ε)</span> 2265 </p> 2266 </td> 2267<td> 2268 <p> 2269 <span class="blue">Max = 42.5ε (Mean = 9.31ε)</span> 2270 </p> 2271 </td> 2272<td> 2273 <p> 2274 <span class="blue">Max = 42.5ε (Mean = 9.32ε)</span> 2275 </p> 2276 </td> 2277<td> 2278 <p> 2279 <span class="blue">Max = 23.7ε (Mean = 8ε)</span> 2280 </p> 2281 </td> 2282</tr> 2283<tr> 2284<td> 2285 <p> 2286 Bessel J': Mathworld Data (large values) 2287 </p> 2288 </td> 2289<td> 2290 <p> 2291 <span class="blue">Max = 0ε (Mean = 0ε)</span> 2292 </p> 2293 </td> 2294<td> 2295 <p> 2296 <span class="blue">Max = 989ε (Mean = 495ε)</span> 2297 </p> 2298 </td> 2299<td> 2300 <p> 2301 <span class="blue">Max = 989ε (Mean = 495ε)</span> 2302 </p> 2303 </td> 2304<td> 2305 <p> 2306 <span class="blue">Max = 2.9ε (Mean = 1.61ε)</span> 2307 </p> 2308 </td> 2309</tr> 2310<tr> 2311<td> 2312 <p> 2313 Bessel JN': Random Data 2314 </p> 2315 </td> 2316<td> 2317 <p> 2318 <span class="blue">Max = 0.593ε (Mean = 0.0396ε)</span> 2319 </p> 2320 </td> 2321<td> 2322 <p> 2323 <span class="blue">Max = 11.3ε (Mean = 1.85ε)</span> 2324 </p> 2325 </td> 2326<td> 2327 <p> 2328 <span class="blue">Max = 79.4ε (Mean = 16.2ε)</span> 2329 </p> 2330 </td> 2331<td> 2332 <p> 2333 <span class="blue">Max = 6.34ε (Mean = 0.999ε)</span> 2334 </p> 2335 </td> 2336</tr> 2337<tr> 2338<td> 2339 <p> 2340 Bessel J': Random Data 2341 </p> 2342 </td> 2343<td> 2344 <p> 2345 <span class="blue">Max = 0.885ε (Mean = 0.033ε)</span> 2346 </p> 2347 </td> 2348<td> 2349 <p> 2350 <span class="blue">Max = 139ε (Mean = 6.47ε)</span> 2351 </p> 2352 </td> 2353<td> 2354 <p> 2355 <span class="blue">Max = 279ε (Mean = 27.2ε)</span> 2356 </p> 2357 </td> 2358<td> 2359 <p> 2360 <span class="blue">Max = 176ε (Mean = 9.75ε)</span> 2361 </p> 2362 </td> 2363</tr> 2364<tr> 2365<td> 2366 <p> 2367 Bessel J': Random Data (Tricky large values) 2368 </p> 2369 </td> 2370<td> 2371 <p> 2372 <span class="blue">Max = 0ε (Mean = 0ε)</span> 2373 </p> 2374 </td> 2375<td> 2376 <p> 2377 <span class="blue">Max = 474ε (Mean = 62.2ε)</span> 2378 </p> 2379 </td> 2380<td> 2381 <p> 2382 <span class="blue">Max = 474ε (Mean = 64.5ε)</span> 2383 </p> 2384 </td> 2385<td> 2386 <p> 2387 <span class="blue">Max = 379ε (Mean = 45.4ε)</span> 2388 </p> 2389 </td> 2390</tr> 2391</tbody> 2392</table></div> 2393</div> 2394<br class="table-break"><div class="table"> 2395<a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_j_prime_integer_orders_"></a><p class="title"><b>Table 23.17. Error rates for cyl_bessel_j_prime (integer orders)</b></p> 2396<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j_prime (integer orders)"> 2397<colgroup> 2398<col> 2399<col> 2400<col> 2401<col> 2402<col> 2403</colgroup> 2404<thead><tr> 2405<th> 2406 </th> 2407<th> 2408 <p> 2409 GNU C++ version 7.1.0<br> linux<br> double 2410 </p> 2411 </th> 2412<th> 2413 <p> 2414 GNU C++ version 7.1.0<br> linux<br> long double 2415 </p> 2416 </th> 2417<th> 2418 <p> 2419 Sun compiler version 0x5150<br> Sun Solaris<br> long double 2420 </p> 2421 </th> 2422<th> 2423 <p> 2424 Microsoft Visual C++ version 14.1<br> Win32<br> double 2425 </p> 2426 </th> 2427</tr></thead> 2428<tbody> 2429<tr> 2430<td> 2431 <p> 2432 Bessel J0': Mathworld Data (Integer Version) 2433 </p> 2434 </td> 2435<td> 2436 <p> 2437 <span class="blue">Max = 0ε (Mean = 0ε)</span> 2438 </p> 2439 </td> 2440<td> 2441 <p> 2442 <span class="blue">Max = 18.9ε (Mean = 6.82ε)</span> 2443 </p> 2444 </td> 2445<td> 2446 <p> 2447 <span class="blue">Max = 18.9ε (Mean = 6.72ε)</span> 2448 </p> 2449 </td> 2450<td> 2451 <p> 2452 <span class="blue">Max = 6.62ε (Mean = 2.55ε)</span> 2453 </p> 2454 </td> 2455</tr> 2456<tr> 2457<td> 2458 <p> 2459 Bessel J0': Mathworld Data (Tricky cases) (Integer Version) 2460 </p> 2461 </td> 2462<td> 2463 <p> 2464 <span class="blue">Max = 0ε (Mean = 0ε)</span> 2465 </p> 2466 </td> 2467<td> 2468 <p> 2469 <span class="blue">Max = 7.44ε (Mean = 3.34ε)</span> 2470 </p> 2471 </td> 2472<td> 2473 <p> 2474 <span class="blue">Max = 7.44ε (Mean = 3.31ε)</span> 2475 </p> 2476 </td> 2477<td> 2478 <p> 2479 <span class="blue">Max = 3.67ε (Mean = 1.74ε)</span> 2480 </p> 2481 </td> 2482</tr> 2483<tr> 2484<td> 2485 <p> 2486 Bessel J1': Mathworld Data (Integer Version) 2487 </p> 2488 </td> 2489<td> 2490 <p> 2491 <span class="blue">Max = 0ε (Mean = 0ε)</span> 2492 </p> 2493 </td> 2494<td> 2495 <p> 2496 <span class="blue">Max = 7.9ε (Mean = 3.37ε)</span> 2497 </p> 2498 </td> 2499<td> 2500 <p> 2501 <span class="blue">Max = 7.9ε (Mean = 3.37ε)</span> 2502 </p> 2503 </td> 2504<td> 2505 <p> 2506 <span class="blue">Max = 0.999ε (Mean = 0.627ε)</span> 2507 </p> 2508 </td> 2509</tr> 2510<tr> 2511<td> 2512 <p> 2513 Bessel J1': Mathworld Data (tricky cases) (Integer Version) 2514 </p> 2515 </td> 2516<td> 2517 <p> 2518 <span class="blue">Max = 287ε (Mean = 129ε)</span> 2519 </p> 2520 </td> 2521<td> 2522 <p> 2523 <span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span> 2524 </p> 2525 </td> 2526<td> 2527 <p> 2528 <span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span> 2529 </p> 2530 </td> 2531<td> 2532 <p> 2533 <span class="blue">Max = 288ε (Mean = 129ε)</span> 2534 </p> 2535 </td> 2536</tr> 2537<tr> 2538<td> 2539 <p> 2540 Bessel JN': Mathworld Data (Integer Version) 2541 </p> 2542 </td> 2543<td> 2544 <p> 2545 <span class="blue">Max = 0.527ε (Mean = 0.128ε)</span> 2546 </p> 2547 </td> 2548<td> 2549 <p> 2550 <span class="blue">Max = 1.29e+03ε (Mean = 312ε)</span> 2551 </p> 2552 </td> 2553<td> 2554 <p> 2555 <span class="blue">Max = 1.29e+03ε (Mean = 355ε)</span> 2556 </p> 2557 </td> 2558<td> 2559 <p> 2560 <span class="blue">Max = 14ε (Mean = 6.13ε)</span> 2561 </p> 2562 </td> 2563</tr> 2564</tbody> 2565</table></div> 2566</div> 2567<br class="table-break"><div class="table"> 2568<a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_k"></a><p class="title"><b>Table 23.18. Error rates for cyl_bessel_k</b></p> 2569<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k"> 2570<colgroup> 2571<col> 2572<col> 2573<col> 2574<col> 2575<col> 2576</colgroup> 2577<thead><tr> 2578<th> 2579 </th> 2580<th> 2581 <p> 2582 GNU C++ version 7.1.0<br> linux<br> long double 2583 </p> 2584 </th> 2585<th> 2586 <p> 2587 GNU C++ version 7.1.0<br> linux<br> double 2588 </p> 2589 </th> 2590<th> 2591 <p> 2592 Sun compiler version 0x5150<br> Sun Solaris<br> long double 2593 </p> 2594 </th> 2595<th> 2596 <p> 2597 Microsoft Visual C++ version 14.1<br> Win32<br> double 2598 </p> 2599 </th> 2600</tr></thead> 2601<tbody> 2602<tr> 2603<td> 2604 <p> 2605 Bessel K0: Mathworld Data 2606 </p> 2607 </td> 2608<td> 2609 <p> 2610 <span class="blue">Max = 0.833ε (Mean = 0.436ε)</span><br> <br> 2611 (<span class="emphasis"><em><cmath>:</em></span> Max = 9.33ε (Mean = 3.25ε)) 2612 </p> 2613 </td> 2614<td> 2615 <p> 2616 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 2617 2.1:</em></span> Max = 6.04ε (Mean = 2.16ε))<br> (<span class="emphasis"><em>Rmath 2618 3.2.3:</em></span> Max = 0.833ε (Mean = 0.601ε)) 2619 </p> 2620 </td> 2621<td> 2622 <p> 2623 <span class="blue">Max = 0.833ε (Mean = 0.436ε)</span> 2624 </p> 2625 </td> 2626<td> 2627 <p> 2628 <span class="blue">Max = 0.833ε (Mean = 0.552ε)</span> 2629 </p> 2630 </td> 2631</tr> 2632<tr> 2633<td> 2634 <p> 2635 Bessel K1: Mathworld Data 2636 </p> 2637 </td> 2638<td> 2639 <p> 2640 <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span><br> <br> 2641 (<span class="emphasis"><em><cmath>:</em></span> Max = 8.94ε (Mean = 3.19ε)) 2642 </p> 2643 </td> 2644<td> 2645 <p> 2646 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 2647 2.1:</em></span> Max = 6.26ε (Mean = 2.21ε))<br> (<span class="emphasis"><em>Rmath 2648 3.2.3:</em></span> Max = 0.894ε (Mean = 0.516ε)) 2649 </p> 2650 </td> 2651<td> 2652 <p> 2653 <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span> 2654 </p> 2655 </td> 2656<td> 2657 <p> 2658 <span class="blue">Max = 0.786ε (Mean = 0.39ε)</span> 2659 </p> 2660 </td> 2661</tr> 2662<tr> 2663<td> 2664 <p> 2665 Bessel Kn: Mathworld Data 2666 </p> 2667 </td> 2668<td> 2669 <p> 2670 <span class="blue">Max = 2.6ε (Mean = 1.21ε)</span><br> <br> 2671 (<span class="emphasis"><em><cmath>:</em></span> Max = 12.9ε (Mean = 4.91ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kn_Mathworld_Data">And 2672 other failures.</a>) 2673 </p> 2674 </td> 2675<td> 2676 <p> 2677 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 2678 2.1:</em></span> Max = 3.36ε (Mean = 1.43ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kn_Mathworld_Data">And 2679 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 2680 Max = 8.48ε (Mean = 2.98ε)) 2681 </p> 2682 </td> 2683<td> 2684 <p> 2685 <span class="blue">Max = 2.6ε (Mean = 1.21ε)</span> 2686 </p> 2687 </td> 2688<td> 2689 <p> 2690 <span class="blue">Max = 3.63ε (Mean = 1.46ε)</span> 2691 </p> 2692 </td> 2693</tr> 2694<tr> 2695<td> 2696 <p> 2697 Bessel Kv: Mathworld Data 2698 </p> 2699 </td> 2700<td> 2701 <p> 2702 <span class="blue">Max = 3.58ε (Mean = 2.39ε)</span><br> <br> 2703 (<span class="emphasis"><em><cmath>:</em></span> Max = 13ε (Mean = 4.81ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Mathworld_Data">And 2704 other failures.</a>) 2705 </p> 2706 </td> 2707<td> 2708 <p> 2709 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 2710 2.1:</em></span> Max = 5.47ε (Mean = 2.04ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Mathworld_Data">And 2711 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 2712 Max = 3.15ε (Mean = 1.35ε)) 2713 </p> 2714 </td> 2715<td> 2716 <p> 2717 <span class="blue">Max = 5.21ε (Mean = 2.53ε)</span> 2718 </p> 2719 </td> 2720<td> 2721 <p> 2722 <span class="blue">Max = 4.78ε (Mean = 2.19ε)</span> 2723 </p> 2724 </td> 2725</tr> 2726<tr> 2727<td> 2728 <p> 2729 Bessel Kv: Mathworld Data (large values) 2730 </p> 2731 </td> 2732<td> 2733 <p> 2734 <span class="blue">Max = 42.3ε (Mean = 21ε)</span><br> <br> 2735 (<span class="emphasis"><em><cmath>:</em></span> Max = 42.3ε (Mean = 19.8ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Mathworld_Data_large_values_">And 2736 other failures.</a>) 2737 </p> 2738 </td> 2739<td> 2740 <p> 2741 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 2742 2.1:</em></span> Max = 308ε (Mean = 142ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Mathworld_Data_large_values_">And 2743 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 2744 Max = 84.6ε (Mean = 37.8ε)) 2745 </p> 2746 </td> 2747<td> 2748 <p> 2749 <span class="blue">Max = 42.3ε (Mean = 21ε)</span> 2750 </p> 2751 </td> 2752<td> 2753 <p> 2754 <span class="blue">Max = 59.8ε (Mean = 26.9ε)</span> 2755 </p> 2756 </td> 2757</tr> 2758<tr> 2759<td> 2760 <p> 2761 Bessel Kn: Random Data 2762 </p> 2763 </td> 2764<td> 2765 <p> 2766 <span class="blue">Max = 4.55ε (Mean = 1.12ε)</span><br> <br> 2767 (<span class="emphasis"><em><cmath>:</em></span> Max = 13.9ε (Mean = 2.91ε)) 2768 </p> 2769 </td> 2770<td> 2771 <p> 2772 <span class="blue">Max = 0.764ε (Mean = 0.0348ε)</span><br> 2773 <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.71ε (Mean = 1.76ε) 2774 <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kn_Random_Data">And 2775 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 2776 Max = 7.47ε (Mean = 1.34ε)) 2777 </p> 2778 </td> 2779<td> 2780 <p> 2781 <span class="blue">Max = 4.55ε (Mean = 1.12ε)</span> 2782 </p> 2783 </td> 2784<td> 2785 <p> 2786 <span class="blue">Max = 9.34ε (Mean = 1.7ε)</span> 2787 </p> 2788 </td> 2789</tr> 2790<tr> 2791<td> 2792 <p> 2793 Bessel Kv: Random Data 2794 </p> 2795 </td> 2796<td> 2797 <p> 2798 <span class="blue">Max = 7.88ε (Mean = 1.48ε)</span><br> <br> 2799 (<span class="emphasis"><em><cmath>:</em></span> Max = 13.6ε (Mean = 2.68ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Random_Data">And 2800 other failures.</a>) 2801 </p> 2802 </td> 2803<td> 2804 <p> 2805 <span class="blue">Max = 0.507ε (Mean = 0.0313ε)</span><br> 2806 <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 9.71ε (Mean = 1.47ε) 2807 <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Random_Data">And 2808 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 2809 Max = 7.37ε (Mean = 1.49ε)) 2810 </p> 2811 </td> 2812<td> 2813 <p> 2814 <span class="blue">Max = 7.88ε (Mean = 1.47ε)</span> 2815 </p> 2816 </td> 2817<td> 2818 <p> 2819 <span class="blue">Max = 8.33ε (Mean = 1.62ε)</span> 2820 </p> 2821 </td> 2822</tr> 2823</tbody> 2824</table></div> 2825</div> 2826<br class="table-break"><div class="table"> 2827<a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_k_integer_orders_"></a><p class="title"><b>Table 23.19. Error rates for cyl_bessel_k (integer orders)</b></p> 2828<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k (integer orders)"> 2829<colgroup> 2830<col> 2831<col> 2832<col> 2833<col> 2834<col> 2835</colgroup> 2836<thead><tr> 2837<th> 2838 </th> 2839<th> 2840 <p> 2841 GNU C++ version 7.1.0<br> linux<br> long double 2842 </p> 2843 </th> 2844<th> 2845 <p> 2846 GNU C++ version 7.1.0<br> linux<br> double 2847 </p> 2848 </th> 2849<th> 2850 <p> 2851 Sun compiler version 0x5150<br> Sun Solaris<br> long double 2852 </p> 2853 </th> 2854<th> 2855 <p> 2856 Microsoft Visual C++ version 14.1<br> Win32<br> double 2857 </p> 2858 </th> 2859</tr></thead> 2860<tbody> 2861<tr> 2862<td> 2863 <p> 2864 Bessel K0: Mathworld Data (Integer Version) 2865 </p> 2866 </td> 2867<td> 2868 <p> 2869 <span class="blue">Max = 0.833ε (Mean = 0.436ε)</span><br> <br> 2870 (<span class="emphasis"><em><cmath>:</em></span> Max = 9.33ε (Mean = 3.25ε)) 2871 </p> 2872 </td> 2873<td> 2874 <p> 2875 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 2876 2.1:</em></span> Max = 1.2ε (Mean = 0.733ε))<br> (<span class="emphasis"><em>Rmath 2877 3.2.3:</em></span> Max = 0.833ε (Mean = 0.601ε)) 2878 </p> 2879 </td> 2880<td> 2881 <p> 2882 <span class="blue">Max = 0.833ε (Mean = 0.436ε)</span> 2883 </p> 2884 </td> 2885<td> 2886 <p> 2887 <span class="blue">Max = 0.833ε (Mean = 0.552ε)</span> 2888 </p> 2889 </td> 2890</tr> 2891<tr> 2892<td> 2893 <p> 2894 Bessel K1: Mathworld Data (Integer Version) 2895 </p> 2896 </td> 2897<td> 2898 <p> 2899 <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span><br> <br> 2900 (<span class="emphasis"><em><cmath>:</em></span> Max = 8.94ε (Mean = 3.19ε)) 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 = 0.626ε (Mean = 0.333ε))<br> (<span class="emphasis"><em>Rmath 2907 3.2.3:</em></span> Max = 0.894ε (Mean = 0.516ε)) 2908 </p> 2909 </td> 2910<td> 2911 <p> 2912 <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span> 2913 </p> 2914 </td> 2915<td> 2916 <p> 2917 <span class="blue">Max = 0.786ε (Mean = 0.39ε)</span> 2918 </p> 2919 </td> 2920</tr> 2921<tr> 2922<td> 2923 <p> 2924 Bessel Kn: Mathworld Data (Integer Version) 2925 </p> 2926 </td> 2927<td> 2928 <p> 2929 <span class="blue">Max = 2.6ε (Mean = 1.21ε)</span><br> <br> 2930 (<span class="emphasis"><em><cmath>:</em></span> Max = 12.9ε (Mean = 4.91ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k_integer_orders___cmath__Bessel_Kn_Mathworld_Data_Integer_Version_">And 2931 other failures.</a>) 2932 </p> 2933 </td> 2934<td> 2935 <p> 2936 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 2937 2.1:</em></span> Max = 168ε (Mean = 59.5ε))<br> (<span class="emphasis"><em>Rmath 2938 3.2.3:</em></span> Max = 8.48ε (Mean = 2.98ε)) 2939 </p> 2940 </td> 2941<td> 2942 <p> 2943 <span class="blue">Max = 2.6ε (Mean = 1.21ε)</span> 2944 </p> 2945 </td> 2946<td> 2947 <p> 2948 <span class="blue">Max = 3.63ε (Mean = 1.46ε)</span> 2949 </p> 2950 </td> 2951</tr> 2952</tbody> 2953</table></div> 2954</div> 2955<br class="table-break"><div class="table"> 2956<a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_k_prime"></a><p class="title"><b>Table 23.20. Error rates for cyl_bessel_k_prime</b></p> 2957<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k_prime"> 2958<colgroup> 2959<col> 2960<col> 2961<col> 2962<col> 2963<col> 2964</colgroup> 2965<thead><tr> 2966<th> 2967 </th> 2968<th> 2969 <p> 2970 GNU C++ version 7.1.0<br> linux<br> double 2971 </p> 2972 </th> 2973<th> 2974 <p> 2975 GNU C++ version 7.1.0<br> linux<br> long double 2976 </p> 2977 </th> 2978<th> 2979 <p> 2980 Sun compiler version 0x5150<br> Sun Solaris<br> long double 2981 </p> 2982 </th> 2983<th> 2984 <p> 2985 Microsoft Visual C++ version 14.1<br> Win32<br> double 2986 </p> 2987 </th> 2988</tr></thead> 2989<tbody> 2990<tr> 2991<td> 2992 <p> 2993 Bessel K'0: Mathworld Data 2994 </p> 2995 </td> 2996<td> 2997 <p> 2998 <span class="blue">Max = 0ε (Mean = 0ε)</span> 2999 </p> 3000 </td> 3001<td> 3002 <p> 3003 <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span> 3004 </p> 3005 </td> 3006<td> 3007 <p> 3008 <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span> 3009 </p> 3010 </td> 3011<td> 3012 <p> 3013 <span class="blue">Max = 0.786ε (Mean = 0.39ε)</span> 3014 </p> 3015 </td> 3016</tr> 3017<tr> 3018<td> 3019 <p> 3020 Bessel K'1: Mathworld Data 3021 </p> 3022 </td> 3023<td> 3024 <p> 3025 <span class="blue">Max = 0ε (Mean = 0ε)</span> 3026 </p> 3027 </td> 3028<td> 3029 <p> 3030 <span class="blue">Max = 0.736ε (Mean = 0.389ε)</span> 3031 </p> 3032 </td> 3033<td> 3034 <p> 3035 <span class="blue">Max = 0.736ε (Mean = 0.389ε)</span> 3036 </p> 3037 </td> 3038<td> 3039 <p> 3040 <span class="blue">Max = 0.761ε (Mean = 0.444ε)</span> 3041 </p> 3042 </td> 3043</tr> 3044<tr> 3045<td> 3046 <p> 3047 Bessel K'n: Mathworld Data 3048 </p> 3049 </td> 3050<td> 3051 <p> 3052 <span class="blue">Max = 0ε (Mean = 0ε)</span> 3053 </p> 3054 </td> 3055<td> 3056 <p> 3057 <span class="blue">Max = 2.16ε (Mean = 1.08ε)</span> 3058 </p> 3059 </td> 3060<td> 3061 <p> 3062 <span class="blue">Max = 2.16ε (Mean = 1.08ε)</span> 3063 </p> 3064 </td> 3065<td> 3066 <p> 3067 <span class="blue">Max = 4.17ε (Mean = 1.75ε)</span> 3068 </p> 3069 </td> 3070</tr> 3071<tr> 3072<td> 3073 <p> 3074 Bessel K'v: Mathworld Data 3075 </p> 3076 </td> 3077<td> 3078 <p> 3079 <span class="blue">Max = 0ε (Mean = 0ε)</span> 3080 </p> 3081 </td> 3082<td> 3083 <p> 3084 <span class="blue">Max = 3.94ε (Mean = 2.44ε)</span> 3085 </p> 3086 </td> 3087<td> 3088 <p> 3089 <span class="blue">Max = 3.94ε (Mean = 2.34ε)</span> 3090 </p> 3091 </td> 3092<td> 3093 <p> 3094 <span class="blue">Max = 3.94ε (Mean = 1.47ε)</span> 3095 </p> 3096 </td> 3097</tr> 3098<tr> 3099<td> 3100 <p> 3101 Bessel K'v: Mathworld Data (large values) 3102 </p> 3103 </td> 3104<td> 3105 <p> 3106 <span class="blue">Max = 0ε (Mean = 0ε)</span> 3107 </p> 3108 </td> 3109<td> 3110 <p> 3111 <span class="blue">Max = 59.2ε (Mean = 42.9ε)</span> 3112 </p> 3113 </td> 3114<td> 3115 <p> 3116 <span class="blue">Max = 58.7ε (Mean = 42.6ε)</span> 3117 </p> 3118 </td> 3119<td> 3120 <p> 3121 <span class="blue">Max = 18.6ε (Mean = 11.8ε)</span> 3122 </p> 3123 </td> 3124</tr> 3125<tr> 3126<td> 3127 <p> 3128 Bessel K'n: Random Data 3129 </p> 3130 </td> 3131<td> 3132 <p> 3133 <span class="blue">Max = 0ε (Mean = 0ε)</span> 3134 </p> 3135 </td> 3136<td> 3137 <p> 3138 <span class="blue">Max = 4.45ε (Mean = 1.19ε)</span> 3139 </p> 3140 </td> 3141<td> 3142 <p> 3143 <span class="blue">Max = 4.45ε (Mean = 1.19ε)</span> 3144 </p> 3145 </td> 3146<td> 3147 <p> 3148 <span class="blue">Max = 9.67ε (Mean = 1.73ε)</span> 3149 </p> 3150 </td> 3151</tr> 3152<tr> 3153<td> 3154 <p> 3155 Bessel K'v: Random Data 3156 </p> 3157 </td> 3158<td> 3159 <p> 3160 <span class="blue">Max = 0ε (Mean = 0ε)</span> 3161 </p> 3162 </td> 3163<td> 3164 <p> 3165 <span class="blue">Max = 7.95ε (Mean = 1.53ε)</span> 3166 </p> 3167 </td> 3168<td> 3169 <p> 3170 <span class="blue">Max = 7.95ε (Mean = 1.52ε)</span> 3171 </p> 3172 </td> 3173<td> 3174 <p> 3175 <span class="blue">Max = 8.32ε (Mean = 1.65ε)</span> 3176 </p> 3177 </td> 3178</tr> 3179</tbody> 3180</table></div> 3181</div> 3182<br class="table-break"><div class="table"> 3183<a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_k_prime_integer_orders_"></a><p class="title"><b>Table 23.21. Error rates for cyl_bessel_k_prime (integer orders)</b></p> 3184<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k_prime (integer orders)"> 3185<colgroup> 3186<col> 3187<col> 3188<col> 3189<col> 3190<col> 3191</colgroup> 3192<thead><tr> 3193<th> 3194 </th> 3195<th> 3196 <p> 3197 GNU C++ version 7.1.0<br> linux<br> double 3198 </p> 3199 </th> 3200<th> 3201 <p> 3202 GNU C++ version 7.1.0<br> linux<br> long double 3203 </p> 3204 </th> 3205<th> 3206 <p> 3207 Sun compiler version 0x5150<br> Sun Solaris<br> long double 3208 </p> 3209 </th> 3210<th> 3211 <p> 3212 Microsoft Visual C++ version 14.1<br> Win32<br> double 3213 </p> 3214 </th> 3215</tr></thead> 3216<tbody> 3217<tr> 3218<td> 3219 <p> 3220 Bessel K'0: Mathworld Data (Integer Version) 3221 </p> 3222 </td> 3223<td> 3224 <p> 3225 <span class="blue">Max = 0ε (Mean = 0ε)</span> 3226 </p> 3227 </td> 3228<td> 3229 <p> 3230 <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span> 3231 </p> 3232 </td> 3233<td> 3234 <p> 3235 <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span> 3236 </p> 3237 </td> 3238<td> 3239 <p> 3240 <span class="blue">Max = 0.786ε (Mean = 0.39ε)</span> 3241 </p> 3242 </td> 3243</tr> 3244<tr> 3245<td> 3246 <p> 3247 Bessel K'1: Mathworld Data (Integer Version) 3248 </p> 3249 </td> 3250<td> 3251 <p> 3252 <span class="blue">Max = 0ε (Mean = 0ε)</span> 3253 </p> 3254 </td> 3255<td> 3256 <p> 3257 <span class="blue">Max = 0.736ε (Mean = 0.389ε)</span> 3258 </p> 3259 </td> 3260<td> 3261 <p> 3262 <span class="blue">Max = 0.736ε (Mean = 0.389ε)</span> 3263 </p> 3264 </td> 3265<td> 3266 <p> 3267 <span class="blue">Max = 0.761ε (Mean = 0.444ε)</span> 3268 </p> 3269 </td> 3270</tr> 3271<tr> 3272<td> 3273 <p> 3274 Bessel K'n: Mathworld Data (Integer Version) 3275 </p> 3276 </td> 3277<td> 3278 <p> 3279 <span class="blue">Max = 0ε (Mean = 0ε)</span> 3280 </p> 3281 </td> 3282<td> 3283 <p> 3284 <span class="blue">Max = 2.16ε (Mean = 1.08ε)</span> 3285 </p> 3286 </td> 3287<td> 3288 <p> 3289 <span class="blue">Max = 2.16ε (Mean = 1.08ε)</span> 3290 </p> 3291 </td> 3292<td> 3293 <p> 3294 <span class="blue">Max = 4.17ε (Mean = 1.75ε)</span> 3295 </p> 3296 </td> 3297</tr> 3298</tbody> 3299</table></div> 3300</div> 3301<br class="table-break"><div class="table"> 3302<a name="math_toolkit.logs_and_tables.all_table.table_cyl_neumann"></a><p class="title"><b>Table 23.22. Error rates for cyl_neumann</b></p> 3303<div class="table-contents"><table class="table" summary="Error rates for cyl_neumann"> 3304<colgroup> 3305<col> 3306<col> 3307<col> 3308<col> 3309<col> 3310</colgroup> 3311<thead><tr> 3312<th> 3313 </th> 3314<th> 3315 <p> 3316 GNU C++ version 7.1.0<br> linux<br> long double 3317 </p> 3318 </th> 3319<th> 3320 <p> 3321 GNU C++ version 7.1.0<br> linux<br> double 3322 </p> 3323 </th> 3324<th> 3325 <p> 3326 Sun compiler version 0x5150<br> Sun Solaris<br> long double 3327 </p> 3328 </th> 3329<th> 3330 <p> 3331 Microsoft Visual C++ version 14.1<br> Win32<br> double 3332 </p> 3333 </th> 3334</tr></thead> 3335<tbody> 3336<tr> 3337<td> 3338 <p> 3339 Y0: Mathworld Data 3340 </p> 3341 </td> 3342<td> 3343 <p> 3344 <span class="blue">Max = 5.53ε (Mean = 2.4ε)</span><br> <br> 3345 (<span class="emphasis"><em><cmath>:</em></span> Max = 2.05e+05ε (Mean = 6.87e+04ε)) 3346 </p> 3347 </td> 3348<td> 3349 <p> 3350 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 3351 2.1:</em></span> Max = 60.9ε (Mean = 20.4ε))<br> (<span class="emphasis"><em>Rmath 3352 3.2.3:</em></span> Max = 167ε (Mean = 56.5ε)) 3353 </p> 3354 </td> 3355<td> 3356 <p> 3357 <span class="blue">Max = 5.53ε (Mean = 2.4ε)</span> 3358 </p> 3359 </td> 3360<td> 3361 <p> 3362 <span class="blue">Max = 4.61ε (Mean = 2.29ε)</span> 3363 </p> 3364 </td> 3365</tr> 3366<tr> 3367<td> 3368 <p> 3369 Y1: Mathworld Data 3370 </p> 3371 </td> 3372<td> 3373 <p> 3374 <span class="blue">Max = 6.33ε (Mean = 2.25ε)</span><br> <br> 3375 (<span class="emphasis"><em><cmath>:</em></span> Max = 9.71e+03ε (Mean = 4.08e+03ε)) 3376 </p> 3377 </td> 3378<td> 3379 <p> 3380 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 3381 2.1:</em></span> Max = 23.4ε (Mean = 8.1ε))<br> (<span class="emphasis"><em>Rmath 3382 3.2.3:</em></span> Max = 193ε (Mean = 64.4ε)) 3383 </p> 3384 </td> 3385<td> 3386 <p> 3387 <span class="blue">Max = 6.33ε (Mean = 2.29ε)</span> 3388 </p> 3389 </td> 3390<td> 3391 <p> 3392 <span class="blue">Max = 4.75ε (Mean = 1.72ε)</span> 3393 </p> 3394 </td> 3395</tr> 3396<tr> 3397<td> 3398 <p> 3399 Yn: Mathworld Data 3400 </p> 3401 </td> 3402<td> 3403 <p> 3404 <span class="blue">Max = 55.2ε (Mean = 17.8ε)</span><br> <br> 3405 (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 2.2e+20ε (Mean 3406 = 6.97e+19ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yn_Mathworld_Data">And 3407 other failures.</a>)</span> 3408 </p> 3409 </td> 3410<td> 3411 <p> 3412 <span class="blue">Max = 0.993ε (Mean = 0.314ε)</span><br> <br> 3413 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.41e+05ε (Mean = 7.62e+04ε) 3414 <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yn_Mathworld_Data">And 3415 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 3416 Max = 1.24e+04ε (Mean = 4e+03ε)) 3417 </p> 3418 </td> 3419<td> 3420 <p> 3421 <span class="blue">Max = 55.2ε (Mean = 17.8ε)</span> 3422 </p> 3423 </td> 3424<td> 3425 <p> 3426 <span class="blue">Max = 35ε (Mean = 11.9ε)</span> 3427 </p> 3428 </td> 3429</tr> 3430<tr> 3431<td> 3432 <p> 3433 Yv: Mathworld Data 3434 </p> 3435 </td> 3436<td> 3437 <p> 3438 <span class="blue">Max = 10.7ε (Mean = 4.93ε)</span><br> <br> 3439 (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 3.49e+15ε (Mean 3440 = 1.05e+15ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Mathworld_Data">And 3441 other failures.</a>)</span> 3442 </p> 3443 </td> 3444<td> 3445 <p> 3446 <span class="blue">Max = 10ε (Mean = 3.02ε)</span><br> <br> 3447 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.07e+05ε (Mean = 3.22e+04ε) 3448 <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yv_Mathworld_Data">And 3449 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 3450 Max = 243ε (Mean = 73.9ε)) 3451 </p> 3452 </td> 3453<td> 3454 <p> 3455 <span class="blue">Max = 10.7ε (Mean = 5.1ε)</span> 3456 </p> 3457 </td> 3458<td> 3459 <p> 3460 <span class="blue">Max = 7.89ε (Mean = 3.27ε)</span> 3461 </p> 3462 </td> 3463</tr> 3464<tr> 3465<td> 3466 <p> 3467 Yv: Mathworld Data (large values) 3468 </p> 3469 </td> 3470<td> 3471 <p> 3472 <span class="blue">Max = 1.7ε (Mean = 1.33ε)</span><br> <br> 3473 (<span class="emphasis"><em><cmath>:</em></span> Max = 43.2ε (Mean = 16.3ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Mathworld_Data_large_values_">And 3474 other failures.</a>) 3475 </p> 3476 </td> 3477<td> 3478 <p> 3479 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 3480 2.1:</em></span> Max = 60.8ε (Mean = 23ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yv_Mathworld_Data_large_values_">And 3481 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 3482 Max = 0.682ε (Mean = 0.335ε)) 3483 </p> 3484 </td> 3485<td> 3486 <p> 3487 <span class="blue">Max = 1.7ε (Mean = 1.33ε)</span> 3488 </p> 3489 </td> 3490<td> 3491 <p> 3492 <span class="blue">Max = 0.682ε (Mean = 0.423ε)</span> 3493 </p> 3494 </td> 3495</tr> 3496<tr> 3497<td> 3498 <p> 3499 Y0 and Y1: Random Data 3500 </p> 3501 </td> 3502<td> 3503 <p> 3504 <span class="blue">Max = 10.8ε (Mean = 3.04ε)</span><br> <br> 3505 (<span class="emphasis"><em><cmath>:</em></span> Max = 2.59e+03ε (Mean = 500ε)) 3506 </p> 3507 </td> 3508<td> 3509 <p> 3510 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 3511 2.1:</em></span> Max = 34.4ε (Mean = 8.9ε))<br> (<span class="emphasis"><em>Rmath 3512 3.2.3:</em></span> Max = 83ε (Mean = 14.2ε)) 3513 </p> 3514 </td> 3515<td> 3516 <p> 3517 <span class="blue">Max = 10.8ε (Mean = 3.04ε)</span> 3518 </p> 3519 </td> 3520<td> 3521 <p> 3522 <span class="blue">Max = 4.17ε (Mean = 1.24ε)</span> 3523 </p> 3524 </td> 3525</tr> 3526<tr> 3527<td> 3528 <p> 3529 Yn: Random Data 3530 </p> 3531 </td> 3532<td> 3533 <p> 3534 <span class="blue">Max = 338ε (Mean = 27.5ε)</span><br> <br> 3535 (<span class="emphasis"><em><cmath>:</em></span> Max = 4.01e+03ε (Mean = 348ε)) 3536 </p> 3537 </td> 3538<td> 3539 <p> 3540 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 3541 2.1:</em></span> Max = 500ε (Mean = 47.8ε))<br> (<span class="emphasis"><em>Rmath 3542 3.2.3:</em></span> Max = 691ε (Mean = 67.9ε)) 3543 </p> 3544 </td> 3545<td> 3546 <p> 3547 <span class="blue">Max = 338ε (Mean = 27.5ε)</span> 3548 </p> 3549 </td> 3550<td> 3551 <p> 3552 <span class="blue">Max = 117ε (Mean = 10.2ε)</span> 3553 </p> 3554 </td> 3555</tr> 3556<tr> 3557<td> 3558 <p> 3559 Yv: Random Data 3560 </p> 3561 </td> 3562<td> 3563 <p> 3564 <span class="blue">Max = 2.08e+03ε (Mean = 149ε)</span><br> 3565 <br> (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max 3566 = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Random_Data">And 3567 other failures.</a>)</span> 3568 </p> 3569 </td> 3570<td> 3571 <p> 3572 <span class="blue">Max = 1.53ε (Mean = 0.102ε)</span><br> <br> 3573 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.41e+06ε (Mean = 7.67e+04ε))<br> 3574 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.79e+05ε (Mean = 9.64e+03ε)) 3575 </p> 3576 </td> 3577<td> 3578 <p> 3579 <span class="blue">Max = 2.08e+03ε (Mean = 149ε)</span> 3580 </p> 3581 </td> 3582<td> 3583 <p> 3584 <span class="blue">Max = 1.23e+03ε (Mean = 69.9ε)</span> 3585 </p> 3586 </td> 3587</tr> 3588</tbody> 3589</table></div> 3590</div> 3591<br class="table-break"><div class="table"> 3592<a name="math_toolkit.logs_and_tables.all_table.table_cyl_neumann_integer_orders_"></a><p class="title"><b>Table 23.23. Error rates for cyl_neumann (integer orders)</b></p> 3593<div class="table-contents"><table class="table" summary="Error rates for cyl_neumann (integer orders)"> 3594<colgroup> 3595<col> 3596<col> 3597<col> 3598<col> 3599<col> 3600</colgroup> 3601<thead><tr> 3602<th> 3603 </th> 3604<th> 3605 <p> 3606 GNU C++ version 7.1.0<br> linux<br> long double 3607 </p> 3608 </th> 3609<th> 3610 <p> 3611 GNU C++ version 7.1.0<br> linux<br> double 3612 </p> 3613 </th> 3614<th> 3615 <p> 3616 Sun compiler version 0x5150<br> Sun Solaris<br> long double 3617 </p> 3618 </th> 3619<th> 3620 <p> 3621 Microsoft Visual C++ version 14.1<br> Win32<br> double 3622 </p> 3623 </th> 3624</tr></thead> 3625<tbody> 3626<tr> 3627<td> 3628 <p> 3629 Y0: Mathworld Data (Integer Version) 3630 </p> 3631 </td> 3632<td> 3633 <p> 3634 <span class="blue">Max = 5.53ε (Mean = 2.4ε)</span><br> <br> 3635 (<span class="emphasis"><em><cmath>:</em></span> Max = 2.05e+05ε (Mean = 6.87e+04ε)) 3636 </p> 3637 </td> 3638<td> 3639 <p> 3640 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 3641 2.1:</em></span> Max = 6.46ε (Mean = 2.38ε))<br> (<span class="emphasis"><em>Rmath 3642 3.2.3:</em></span> Max = 167ε (Mean = 56.5ε)) 3643 </p> 3644 </td> 3645<td> 3646 <p> 3647 <span class="blue">Max = 5.53ε (Mean = 2.4ε)</span> 3648 </p> 3649 </td> 3650<td> 3651 <p> 3652 <span class="blue">Max = 4.61ε (Mean = 2.29ε)</span><br> <br> 3653 (<span class="emphasis"><em><math.h>:</em></span> Max = 5.37e+03ε (Mean = 1.81e+03ε)) 3654 </p> 3655 </td> 3656</tr> 3657<tr> 3658<td> 3659 <p> 3660 Y1: Mathworld Data (Integer Version) 3661 </p> 3662 </td> 3663<td> 3664 <p> 3665 <span class="blue">Max = 6.33ε (Mean = 2.25ε)</span><br> <br> 3666 (<span class="emphasis"><em><cmath>:</em></span> Max = 9.71e+03ε (Mean = 4.08e+03ε)) 3667 </p> 3668 </td> 3669<td> 3670 <p> 3671 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 3672 2.1:</em></span> Max = 1.51ε (Mean = 0.839ε))<br> (<span class="emphasis"><em>Rmath 3673 3.2.3:</em></span> Max = 193ε (Mean = 64.4ε)) 3674 </p> 3675 </td> 3676<td> 3677 <p> 3678 <span class="blue">Max = 6.33ε (Mean = 2.29ε)</span> 3679 </p> 3680 </td> 3681<td> 3682 <p> 3683 <span class="blue">Max = 4.75ε (Mean = 1.72ε)</span><br> <br> 3684 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.86e+04ε (Mean = 6.2e+03ε)) 3685 </p> 3686 </td> 3687</tr> 3688<tr> 3689<td> 3690 <p> 3691 Yn: Mathworld Data (Integer Version) 3692 </p> 3693 </td> 3694<td> 3695 <p> 3696 <span class="blue">Max = 55.2ε (Mean = 17.8ε)</span><br> <br> 3697 (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 2.2e+20ε (Mean 3698 = 6.97e+19ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann_integer_orders___cmath__Yn_Mathworld_Data_Integer_Version_">And 3699 other failures.</a>)</span> 3700 </p> 3701 </td> 3702<td> 3703 <p> 3704 <span class="blue">Max = 0.993ε (Mean = 0.314ε)</span><br> <br> 3705 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.41e+05ε (Mean = 7.62e+04ε))<br> 3706 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.24e+04ε (Mean = 4e+03ε)) 3707 </p> 3708 </td> 3709<td> 3710 <p> 3711 <span class="blue">Max = 55.2ε (Mean = 17.8ε)</span> 3712 </p> 3713 </td> 3714<td> 3715 <p> 3716 <span class="blue">Max = 35ε (Mean = 11.9ε)</span><br> <br> 3717 (<span class="emphasis"><em><math.h>:</em></span> Max = 2.49e+05ε (Mean = 8.14e+04ε)) 3718 </p> 3719 </td> 3720</tr> 3721</tbody> 3722</table></div> 3723</div> 3724<br class="table-break"><div class="table"> 3725<a name="math_toolkit.logs_and_tables.all_table.table_cyl_neumann_prime"></a><p class="title"><b>Table 23.24. Error rates for cyl_neumann_prime</b></p> 3726<div class="table-contents"><table class="table" summary="Error rates for cyl_neumann_prime"> 3727<colgroup> 3728<col> 3729<col> 3730<col> 3731<col> 3732<col> 3733</colgroup> 3734<thead><tr> 3735<th> 3736 </th> 3737<th> 3738 <p> 3739 GNU C++ version 7.1.0<br> linux<br> double 3740 </p> 3741 </th> 3742<th> 3743 <p> 3744 GNU C++ version 7.1.0<br> linux<br> long double 3745 </p> 3746 </th> 3747<th> 3748 <p> 3749 Sun compiler version 0x5150<br> Sun Solaris<br> long double 3750 </p> 3751 </th> 3752<th> 3753 <p> 3754 Microsoft Visual C++ version 14.1<br> Win32<br> double 3755 </p> 3756 </th> 3757</tr></thead> 3758<tbody> 3759<tr> 3760<td> 3761 <p> 3762 Y'0: Mathworld Data 3763 </p> 3764 </td> 3765<td> 3766 <p> 3767 <span class="blue">Max = 0ε (Mean = 0ε)</span> 3768 </p> 3769 </td> 3770<td> 3771 <p> 3772 <span class="blue">Max = 6.33ε (Mean = 3.12ε)</span> 3773 </p> 3774 </td> 3775<td> 3776 <p> 3777 <span class="blue">Max = 6.33ε (Mean = 3.14ε)</span> 3778 </p> 3779 </td> 3780<td> 3781 <p> 3782 <span class="blue">Max = 4.75ε (Mean = 1.75ε)</span> 3783 </p> 3784 </td> 3785</tr> 3786<tr> 3787<td> 3788 <p> 3789 Y'1: Mathworld Data 3790 </p> 3791 </td> 3792<td> 3793 <p> 3794 <span class="blue">Max = 0.58ε (Mean = 0.193ε)</span> 3795 </p> 3796 </td> 3797<td> 3798 <p> 3799 <span class="blue">Max = 37.1ε (Mean = 12.8ε)</span> 3800 </p> 3801 </td> 3802<td> 3803 <p> 3804 <span class="blue">Max = 34ε (Mean = 11.8ε)</span> 3805 </p> 3806 </td> 3807<td> 3808 <p> 3809 <span class="blue">Max = 3.08ε (Mean = 1.2ε)</span> 3810 </p> 3811 </td> 3812</tr> 3813<tr> 3814<td> 3815 <p> 3816 Y'n: Mathworld Data 3817 </p> 3818 </td> 3819<td> 3820 <p> 3821 <span class="blue">Max = 2.05ε (Mean = 0.677ε)</span> 3822 </p> 3823 </td> 3824<td> 3825 <p> 3826 <span class="blue">Max = 56ε (Mean = 18.2ε)</span> 3827 </p> 3828 </td> 3829<td> 3830 <p> 3831 <span class="blue">Max = 56ε (Mean = 21.3ε)</span> 3832 </p> 3833 </td> 3834<td> 3835 <p> 3836 <span class="blue">Max = 563ε (Mean = 178ε)</span> 3837 </p> 3838 </td> 3839</tr> 3840<tr> 3841<td> 3842 <p> 3843 Y'v: Mathworld Data 3844 </p> 3845 </td> 3846<td> 3847 <p> 3848 <span class="blue">Max = 21.5ε (Mean = 6.49ε)</span> 3849 </p> 3850 </td> 3851<td> 3852 <p> 3853 <span class="blue">Max = 42.5ε (Mean = 13.4ε)</span> 3854 </p> 3855 </td> 3856<td> 3857 <p> 3858 <span class="blue">Max = 42.5ε (Mean = 13.6ε)</span> 3859 </p> 3860 </td> 3861<td> 3862 <p> 3863 <span class="blue">Max = 23.7ε (Mean = 10.1ε)</span> 3864 </p> 3865 </td> 3866</tr> 3867<tr> 3868<td> 3869 <p> 3870 Y'v: Mathworld Data (large values) 3871 </p> 3872 </td> 3873<td> 3874 <p> 3875 <span class="blue">Max = 0ε (Mean = 0ε)</span> 3876 </p> 3877 </td> 3878<td> 3879 <p> 3880 <span class="blue">Max = 1.57ε (Mean = 1.24ε)</span> 3881 </p> 3882 </td> 3883<td> 3884 <p> 3885 <span class="blue">Max = 1.57ε (Mean = 1.24ε)</span> 3886 </p> 3887 </td> 3888<td> 3889 <p> 3890 <span class="blue">Max = 0.627ε (Mean = 0.237ε)</span> 3891 </p> 3892 </td> 3893</tr> 3894<tr> 3895<td> 3896 <p> 3897 Y'0 and Y'1: Random Data 3898 </p> 3899 </td> 3900<td> 3901 <p> 3902 <span class="blue">Max = 0ε (Mean = 0ε)</span> 3903 </p> 3904 </td> 3905<td> 3906 <p> 3907 <span class="blue">Max = 23.8ε (Mean = 3.69ε)</span> 3908 </p> 3909 </td> 3910<td> 3911 <p> 3912 <span class="blue">Max = 23.8ε (Mean = 3.69ε)</span> 3913 </p> 3914 </td> 3915<td> 3916 <p> 3917 <span class="blue">Max = 5.95ε (Mean = 1.36ε)</span> 3918 </p> 3919 </td> 3920</tr> 3921<tr> 3922<td> 3923 <p> 3924 Y'n: Random Data 3925 </p> 3926 </td> 3927<td> 3928 <p> 3929 <span class="blue">Max = 1.53ε (Mean = 0.0885ε)</span> 3930 </p> 3931 </td> 3932<td> 3933 <p> 3934 <span class="blue">Max = 2.35e+03ε (Mean = 136ε)</span> 3935 </p> 3936 </td> 3937<td> 3938 <p> 3939 <span class="blue">Max = 2.35e+03ε (Mean = 136ε)</span> 3940 </p> 3941 </td> 3942<td> 3943 <p> 3944 <span class="blue">Max = 621ε (Mean = 36ε)</span> 3945 </p> 3946 </td> 3947</tr> 3948<tr> 3949<td> 3950 <p> 3951 Y'v: Random Data 3952 </p> 3953 </td> 3954<td> 3955 <p> 3956 <span class="blue">Max = 56.8ε (Mean = 2.59ε)</span> 3957 </p> 3958 </td> 3959<td> 3960 <p> 3961 <span class="blue">Max = 1.16e+05ε (Mean = 5.28e+03ε)</span> 3962 </p> 3963 </td> 3964<td> 3965 <p> 3966 <span class="blue">Max = 1.16e+05ε (Mean = 5.28e+03ε)</span> 3967 </p> 3968 </td> 3969<td> 3970 <p> 3971 <span class="blue">Max = 3.23e+04ε (Mean = 1.13e+03ε)</span> 3972 </p> 3973 </td> 3974</tr> 3975</tbody> 3976</table></div> 3977</div> 3978<br class="table-break"><div class="table"> 3979<a name="math_toolkit.logs_and_tables.all_table.table_cyl_neumann_prime_integer_orders_"></a><p class="title"><b>Table 23.25. Error rates for cyl_neumann_prime (integer orders)</b></p> 3980<div class="table-contents"><table class="table" summary="Error rates for cyl_neumann_prime (integer orders)"> 3981<colgroup> 3982<col> 3983<col> 3984<col> 3985<col> 3986<col> 3987</colgroup> 3988<thead><tr> 3989<th> 3990 </th> 3991<th> 3992 <p> 3993 GNU C++ version 7.1.0<br> linux<br> double 3994 </p> 3995 </th> 3996<th> 3997 <p> 3998 GNU C++ version 7.1.0<br> linux<br> long double 3999 </p> 4000 </th> 4001<th> 4002 <p> 4003 Sun compiler version 0x5150<br> Sun Solaris<br> long double 4004 </p> 4005 </th> 4006<th> 4007 <p> 4008 Microsoft Visual C++ version 14.1<br> Win32<br> double 4009 </p> 4010 </th> 4011</tr></thead> 4012<tbody> 4013<tr> 4014<td> 4015 <p> 4016 Y'0: Mathworld Data (Integer Version) 4017 </p> 4018 </td> 4019<td> 4020 <p> 4021 <span class="blue">Max = 0ε (Mean = 0ε)</span> 4022 </p> 4023 </td> 4024<td> 4025 <p> 4026 <span class="blue">Max = 6.33ε (Mean = 3.12ε)</span> 4027 </p> 4028 </td> 4029<td> 4030 <p> 4031 <span class="blue">Max = 6.33ε (Mean = 3.14ε)</span> 4032 </p> 4033 </td> 4034<td> 4035 <p> 4036 <span class="blue">Max = 4.75ε (Mean = 1.75ε)</span> 4037 </p> 4038 </td> 4039</tr> 4040<tr> 4041<td> 4042 <p> 4043 Y'1: Mathworld Data (Integer Version) 4044 </p> 4045 </td> 4046<td> 4047 <p> 4048 <span class="blue">Max = 0.58ε (Mean = 0.193ε)</span> 4049 </p> 4050 </td> 4051<td> 4052 <p> 4053 <span class="blue">Max = 37.1ε (Mean = 12.8ε)</span> 4054 </p> 4055 </td> 4056<td> 4057 <p> 4058 <span class="blue">Max = 34ε (Mean = 11.8ε)</span> 4059 </p> 4060 </td> 4061<td> 4062 <p> 4063 <span class="blue">Max = 3.08ε (Mean = 1.2ε)</span> 4064 </p> 4065 </td> 4066</tr> 4067<tr> 4068<td> 4069 <p> 4070 Y'n: Mathworld Data (Integer Version) 4071 </p> 4072 </td> 4073<td> 4074 <p> 4075 <span class="blue">Max = 2.05ε (Mean = 0.677ε)</span> 4076 </p> 4077 </td> 4078<td> 4079 <p> 4080 <span class="blue">Max = 56ε (Mean = 18.2ε)</span> 4081 </p> 4082 </td> 4083<td> 4084 <p> 4085 <span class="blue">Max = 56ε (Mean = 21.3ε)</span> 4086 </p> 4087 </td> 4088<td> 4089 <p> 4090 <span class="blue">Max = 563ε (Mean = 178ε)</span> 4091 </p> 4092 </td> 4093</tr> 4094</tbody> 4095</table></div> 4096</div> 4097<br class="table-break"><div class="table"> 4098<a name="math_toolkit.logs_and_tables.all_table.table_digamma"></a><p class="title"><b>Table 23.26. Error rates for digamma</b></p> 4099<div class="table-contents"><table class="table" summary="Error rates for digamma"> 4100<colgroup> 4101<col> 4102<col> 4103<col> 4104<col> 4105<col> 4106</colgroup> 4107<thead><tr> 4108<th> 4109 </th> 4110<th> 4111 <p> 4112 GNU C++ version 7.1.0<br> linux<br> double 4113 </p> 4114 </th> 4115<th> 4116 <p> 4117 GNU C++ version 7.1.0<br> linux<br> long double 4118 </p> 4119 </th> 4120<th> 4121 <p> 4122 Sun compiler version 0x5150<br> Sun Solaris<br> long double 4123 </p> 4124 </th> 4125<th> 4126 <p> 4127 Microsoft Visual C++ version 14.1<br> Win32<br> double 4128 </p> 4129 </th> 4130</tr></thead> 4131<tbody> 4132<tr> 4133<td> 4134 <p> 4135 Digamma Function: Large Values 4136 </p> 4137 </td> 4138<td> 4139 <p> 4140 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 4141 2.1:</em></span> Max = 1.84ε (Mean = 0.71ε))<br> (<span class="emphasis"><em>Rmath 4142 3.2.3:</em></span> Max = 1.18ε (Mean = 0.331ε)) 4143 </p> 4144 </td> 4145<td> 4146 <p> 4147 <span class="blue">Max = 1.39ε (Mean = 0.413ε)</span> 4148 </p> 4149 </td> 4150<td> 4151 <p> 4152 <span class="blue">Max = 1.39ε (Mean = 0.413ε)</span> 4153 </p> 4154 </td> 4155<td> 4156 <p> 4157 <span class="blue">Max = 0.98ε (Mean = 0.369ε)</span> 4158 </p> 4159 </td> 4160</tr> 4161<tr> 4162<td> 4163 <p> 4164 Digamma Function: Near the Positive Root 4165 </p> 4166 </td> 4167<td> 4168 <p> 4169 <span class="blue">Max = 0.891ε (Mean = 0.0995ε)</span><br> 4170 <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 135ε (Mean = 11.9ε))<br> 4171 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.02e+03ε (Mean = 256ε)) 4172 </p> 4173 </td> 4174<td> 4175 <p> 4176 <span class="blue">Max = 1.37ε (Mean = 0.477ε)</span> 4177 </p> 4178 </td> 4179<td> 4180 <p> 4181 <span class="blue">Max = 1.31ε (Mean = 0.471ε)</span> 4182 </p> 4183 </td> 4184<td> 4185 <p> 4186 <span class="blue">Max = 0.997ε (Mean = 0.527ε)</span> 4187 </p> 4188 </td> 4189</tr> 4190<tr> 4191<td> 4192 <p> 4193 Digamma Function: Near Zero 4194 </p> 4195 </td> 4196<td> 4197 <p> 4198 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 4199 2.1:</em></span> Max = 0.953ε (Mean = 0.348ε))<br> (<span class="emphasis"><em>Rmath 4200 3.2.3:</em></span> Max = 1.17ε (Mean = 0.564ε)) 4201 </p> 4202 </td> 4203<td> 4204 <p> 4205 <span class="blue">Max = 0.984ε (Mean = 0.361ε)</span> 4206 </p> 4207 </td> 4208<td> 4209 <p> 4210 <span class="blue">Max = 0.984ε (Mean = 0.361ε)</span> 4211 </p> 4212 </td> 4213<td> 4214 <p> 4215 <span class="blue">Max = 0.953ε (Mean = 0.337ε)</span> 4216 </p> 4217 </td> 4218</tr> 4219<tr> 4220<td> 4221 <p> 4222 Digamma Function: Negative Values 4223 </p> 4224 </td> 4225<td> 4226 <p> 4227 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 4228 2.1:</em></span> Max = 4.56e+04ε (Mean = 3.91e+03ε))<br> (<span class="emphasis"><em>Rmath 4229 3.2.3:</em></span> Max = 4.6e+04ε (Mean = 3.94e+03ε)) 4230 </p> 4231 </td> 4232<td> 4233 <p> 4234 <span class="blue">Max = 180ε (Mean = 13ε)</span> 4235 </p> 4236 </td> 4237<td> 4238 <p> 4239 <span class="blue">Max = 180ε (Mean = 13ε)</span> 4240 </p> 4241 </td> 4242<td> 4243 <p> 4244 <span class="blue">Max = 214ε (Mean = 16.1ε)</span> 4245 </p> 4246 </td> 4247</tr> 4248<tr> 4249<td> 4250 <p> 4251 Digamma Function: Values near 0 4252 </p> 4253 </td> 4254<td> 4255 <p> 4256 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 4257 2.1:</em></span> Max = 0.866ε (Mean = 0.387ε))<br> (<span class="emphasis"><em>Rmath 4258 3.2.3:</em></span> Max = 3.58e+05ε (Mean = 1.6e+05ε)) 4259 </p> 4260 </td> 4261<td> 4262 <p> 4263 <span class="blue">Max = 1ε (Mean = 0.592ε)</span> 4264 </p> 4265 </td> 4266<td> 4267 <p> 4268 <span class="blue">Max = 1ε (Mean = 0.592ε)</span> 4269 </p> 4270 </td> 4271<td> 4272 <p> 4273 <span class="blue">Max = 0ε (Mean = 0ε)</span> 4274 </p> 4275 </td> 4276</tr> 4277<tr> 4278<td> 4279 <p> 4280 Digamma Function: Integer arguments 4281 </p> 4282 </td> 4283<td> 4284 <p> 4285 <span class="blue">Max = 0.992ε (Mean = 0.215ε)</span><br> <br> 4286 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.18ε (Mean = 0.607ε))<br> 4287 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 4.33ε (Mean = 0.982ε)) 4288 </p> 4289 </td> 4290<td> 4291 <p> 4292 <span class="blue">Max = 0.888ε (Mean = 0.403ε)</span> 4293 </p> 4294 </td> 4295<td> 4296 <p> 4297 <span class="blue">Max = 0.888ε (Mean = 0.403ε)</span> 4298 </p> 4299 </td> 4300<td> 4301 <p> 4302 <span class="blue">Max = 0.992ε (Mean = 0.452ε)</span> 4303 </p> 4304 </td> 4305</tr> 4306<tr> 4307<td> 4308 <p> 4309 Digamma Function: Half integer arguments 4310 </p> 4311 </td> 4312<td> 4313 <p> 4314 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 4315 2.1:</em></span> Max = 1.09ε (Mean = 0.531ε))<br> (<span class="emphasis"><em>Rmath 4316 3.2.3:</em></span> Max = 46.2ε (Mean = 7.24ε)) 4317 </p> 4318 </td> 4319<td> 4320 <p> 4321 <span class="blue">Max = 0.906ε (Mean = 0.409ε)</span> 4322 </p> 4323 </td> 4324<td> 4325 <p> 4326 <span class="blue">Max = 0.906ε (Mean = 0.409ε)</span> 4327 </p> 4328 </td> 4329<td> 4330 <p> 4331 <span class="blue">Max = 0.78ε (Mean = 0.314ε)</span> 4332 </p> 4333 </td> 4334</tr> 4335</tbody> 4336</table></div> 4337</div> 4338<br class="table-break"><div class="table"> 4339<a name="math_toolkit.logs_and_tables.all_table.table_ellint_1"></a><p class="title"><b>Table 23.27. Error rates for ellint_1</b></p> 4340<div class="table-contents"><table class="table" summary="Error rates for ellint_1"> 4341<colgroup> 4342<col> 4343<col> 4344<col> 4345<col> 4346<col> 4347</colgroup> 4348<thead><tr> 4349<th> 4350 </th> 4351<th> 4352 <p> 4353 GNU C++ version 7.1.0<br> linux<br> long double 4354 </p> 4355 </th> 4356<th> 4357 <p> 4358 GNU C++ version 7.1.0<br> linux<br> double 4359 </p> 4360 </th> 4361<th> 4362 <p> 4363 Sun compiler version 0x5150<br> Sun Solaris<br> long double 4364 </p> 4365 </th> 4366<th> 4367 <p> 4368 Microsoft Visual C++ version 14.1<br> Win32<br> double 4369 </p> 4370 </th> 4371</tr></thead> 4372<tbody> 4373<tr> 4374<td> 4375 <p> 4376 Elliptic Integral F: Mathworld Data 4377 </p> 4378 </td> 4379<td> 4380 <p> 4381 <span class="blue">Max = 0.94ε (Mean = 0.509ε)</span><br> <br> 4382 (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = +INFε (Mean 4383 = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_1__cmath__Elliptic_Integral_F_Mathworld_Data">And 4384 other failures.</a>)</span> 4385 </p> 4386 </td> 4387<td> 4388 <p> 4389 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 4390 2.1:</em></span> Max = 0.919ε (Mean = 0.544ε)) 4391 </p> 4392 </td> 4393<td> 4394 <p> 4395 <span class="blue">Max = 0.94ε (Mean = 0.509ε)</span> 4396 </p> 4397 </td> 4398<td> 4399 <p> 4400 <span class="blue">Max = 0.919ε (Mean = 0.542ε)</span> 4401 </p> 4402 </td> 4403</tr> 4404<tr> 4405<td> 4406 <p> 4407 Elliptic Integral F: Random Data 4408 </p> 4409 </td> 4410<td> 4411 <p> 4412 <span class="blue">Max = 1.57ε (Mean = 0.56ε)</span><br> <br> 4413 (<span class="emphasis"><em><cmath>:</em></span> Max = 2.56ε (Mean = 0.816ε)) 4414 </p> 4415 </td> 4416<td> 4417 <p> 4418 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 4419 2.1:</em></span> Max = 2.99ε (Mean = 0.797ε)) 4420 </p> 4421 </td> 4422<td> 4423 <p> 4424 <span class="blue">Max = 1.57ε (Mean = 0.561ε)</span> 4425 </p> 4426 </td> 4427<td> 4428 <p> 4429 <span class="blue">Max = 2.26ε (Mean = 0.631ε)</span> 4430 </p> 4431 </td> 4432</tr> 4433</tbody> 4434</table></div> 4435</div> 4436<br class="table-break"><div class="table"> 4437<a name="math_toolkit.logs_and_tables.all_table.table_ellint_1_complete_"></a><p class="title"><b>Table 23.28. Error rates for ellint_1 (complete)</b></p> 4438<div class="table-contents"><table class="table" summary="Error rates for ellint_1 (complete)"> 4439<colgroup> 4440<col> 4441<col> 4442<col> 4443<col> 4444<col> 4445</colgroup> 4446<thead><tr> 4447<th> 4448 </th> 4449<th> 4450 <p> 4451 GNU C++ version 7.1.0<br> linux<br> long double 4452 </p> 4453 </th> 4454<th> 4455 <p> 4456 GNU C++ version 7.1.0<br> linux<br> double 4457 </p> 4458 </th> 4459<th> 4460 <p> 4461 Sun compiler version 0x5150<br> Sun Solaris<br> long double 4462 </p> 4463 </th> 4464<th> 4465 <p> 4466 Microsoft Visual C++ version 14.1<br> Win32<br> double 4467 </p> 4468 </th> 4469</tr></thead> 4470<tbody> 4471<tr> 4472<td> 4473 <p> 4474 Elliptic Integral K: Mathworld Data 4475 </p> 4476 </td> 4477<td> 4478 <p> 4479 <span class="blue">Max = 0.887ε (Mean = 0.296ε)</span><br> <br> 4480 (<span class="emphasis"><em><cmath>:</em></span> Max = 1.19ε (Mean = 0.765ε)) 4481 </p> 4482 </td> 4483<td> 4484 <p> 4485 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 4486 2.1:</em></span> Max = 0.623ε (Mean = 0.393ε)) 4487 </p> 4488 </td> 4489<td> 4490 <p> 4491 <span class="blue">Max = 0.887ε (Mean = 0.296ε)</span> 4492 </p> 4493 </td> 4494<td> 4495 <p> 4496 <span class="blue">Max = 0.915ε (Mean = 0.547ε)</span> 4497 </p> 4498 </td> 4499</tr> 4500<tr> 4501<td> 4502 <p> 4503 Elliptic Integral K: Random Data 4504 </p> 4505 </td> 4506<td> 4507 <p> 4508 <span class="blue">Max = 1.27ε (Mean = 0.473ε)</span><br> <br> 4509 (<span class="emphasis"><em><cmath>:</em></span> Max = 2.19ε (Mean = 0.694ε)) 4510 </p> 4511 </td> 4512<td> 4513 <p> 4514 <span class="blue">Max = 0.851ε (Mean = 0.0851ε)</span><br> 4515 <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.32ε (Mean = 0.688ε)) 4516 </p> 4517 </td> 4518<td> 4519 <p> 4520 <span class="blue">Max = 1.27ε (Mean = 0.473ε)</span> 4521 </p> 4522 </td> 4523<td> 4524 <p> 4525 <span class="blue">Max = 0.958ε (Mean = 0.408ε)</span> 4526 </p> 4527 </td> 4528</tr> 4529</tbody> 4530</table></div> 4531</div> 4532<br class="table-break"><div class="table"> 4533<a name="math_toolkit.logs_and_tables.all_table.table_ellint_2"></a><p class="title"><b>Table 23.29. Error rates for ellint_2</b></p> 4534<div class="table-contents"><table class="table" summary="Error rates for ellint_2"> 4535<colgroup> 4536<col> 4537<col> 4538<col> 4539<col> 4540<col> 4541</colgroup> 4542<thead><tr> 4543<th> 4544 </th> 4545<th> 4546 <p> 4547 GNU C++ version 7.1.0<br> linux<br> double 4548 </p> 4549 </th> 4550<th> 4551 <p> 4552 GNU C++ version 7.1.0<br> linux<br> long double 4553 </p> 4554 </th> 4555<th> 4556 <p> 4557 Sun compiler version 0x5150<br> Sun Solaris<br> long double 4558 </p> 4559 </th> 4560<th> 4561 <p> 4562 Microsoft Visual C++ version 14.1<br> Win32<br> double 4563 </p> 4564 </th> 4565</tr></thead> 4566<tbody> 4567<tr> 4568<td> 4569 <p> 4570 Elliptic Integral E: Mathworld Data 4571 </p> 4572 </td> 4573<td> 4574 <p> 4575 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 4576 2.1:</em></span> Max = 0.63ε (Mean = 0.325ε)) 4577 </p> 4578 </td> 4579<td> 4580 <p> 4581 <span class="blue">Max = 0.656ε (Mean = 0.317ε)</span><br> <br> 4582 (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = +INFε (Mean 4583 = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_2__cmath__Elliptic_Integral_E_Mathworld_Data">And 4584 other failures.</a>)</span> 4585 </p> 4586 </td> 4587<td> 4588 <p> 4589 <span class="blue">Max = 0.656ε (Mean = 0.317ε)</span> 4590 </p> 4591 </td> 4592<td> 4593 <p> 4594 <span class="blue">Max = 1.31ε (Mean = 0.727ε)</span> 4595 </p> 4596 </td> 4597</tr> 4598<tr> 4599<td> 4600 <p> 4601 Elliptic Integral E: Random Data 4602 </p> 4603 </td> 4604<td> 4605 <p> 4606 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 4607 2.1:</em></span> Max = 4.4ε (Mean = 1.16ε)) 4608 </p> 4609 </td> 4610<td> 4611 <p> 4612 <span class="blue">Max = 2.05ε (Mean = 0.632ε)</span><br> <br> 4613 (<span class="emphasis"><em><cmath>:</em></span> Max = 3.08e+04ε (Mean = 3.84e+03ε)) 4614 </p> 4615 </td> 4616<td> 4617 <p> 4618 <span class="blue">Max = 2.05ε (Mean = 0.632ε)</span> 4619 </p> 4620 </td> 4621<td> 4622 <p> 4623 <span class="blue">Max = 2.23ε (Mean = 0.639ε)</span> 4624 </p> 4625 </td> 4626</tr> 4627<tr> 4628<td> 4629 <p> 4630 Elliptic Integral E: Small Angles 4631 </p> 4632 </td> 4633<td> 4634 <p> 4635 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 4636 2.1:</em></span> Max = 0.5ε (Mean = 0.118ε)) 4637 </p> 4638 </td> 4639<td> 4640 <p> 4641 <span class="blue">Max = 1ε (Mean = 0.283ε)</span><br> <br> 4642 (<span class="emphasis"><em><cmath>:</em></span> Max = 2ε (Mean = 0.333ε)) 4643 </p> 4644 </td> 4645<td> 4646 <p> 4647 <span class="blue">Max = 1ε (Mean = 0.283ε)</span> 4648 </p> 4649 </td> 4650<td> 4651 <p> 4652 <span class="blue">Max = 1ε (Mean = 0.421ε)</span> 4653 </p> 4654 </td> 4655</tr> 4656</tbody> 4657</table></div> 4658</div> 4659<br class="table-break"><div class="table"> 4660<a name="math_toolkit.logs_and_tables.all_table.table_ellint_2_complete_"></a><p class="title"><b>Table 23.30. Error rates for ellint_2 (complete)</b></p> 4661<div class="table-contents"><table class="table" summary="Error rates for ellint_2 (complete)"> 4662<colgroup> 4663<col> 4664<col> 4665<col> 4666<col> 4667<col> 4668</colgroup> 4669<thead><tr> 4670<th> 4671 </th> 4672<th> 4673 <p> 4674 GNU C++ version 7.1.0<br> linux<br> double 4675 </p> 4676 </th> 4677<th> 4678 <p> 4679 GNU C++ version 7.1.0<br> linux<br> long double 4680 </p> 4681 </th> 4682<th> 4683 <p> 4684 Sun compiler version 0x5150<br> Sun Solaris<br> long double 4685 </p> 4686 </th> 4687<th> 4688 <p> 4689 Microsoft Visual C++ version 14.1<br> Win32<br> double 4690 </p> 4691 </th> 4692</tr></thead> 4693<tbody> 4694<tr> 4695<td> 4696 <p> 4697 Elliptic Integral E: Mathworld Data 4698 </p> 4699 </td> 4700<td> 4701 <p> 4702 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 4703 2.1:</em></span> Max = 3.09ε (Mean = 1.04ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_ellint_2_complete__GSL_2_1_Elliptic_Integral_E_Mathworld_Data">And 4704 other failures.</a>) 4705 </p> 4706 </td> 4707<td> 4708 <p> 4709 <span class="blue">Max = 0.836ε (Mean = 0.469ε)</span><br> <br> 4710 (<span class="emphasis"><em><cmath>:</em></span> Max = 170ε (Mean = 55.1ε)) 4711 </p> 4712 </td> 4713<td> 4714 <p> 4715 <span class="blue">Max = 0.836ε (Mean = 0.469ε)</span> 4716 </p> 4717 </td> 4718<td> 4719 <p> 4720 <span class="blue">Max = 1.3ε (Mean = 0.615ε)</span> 4721 </p> 4722 </td> 4723</tr> 4724<tr> 4725<td> 4726 <p> 4727 Elliptic Integral E: Random Data 4728 </p> 4729 </td> 4730<td> 4731 <p> 4732 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 4733 2.1:</em></span> Max = 4.34ε (Mean = 1.18ε)) 4734 </p> 4735 </td> 4736<td> 4737 <p> 4738 <span class="blue">Max = 1.97ε (Mean = 0.629ε)</span><br> <br> 4739 (<span class="emphasis"><em><cmath>:</em></span> Max = 2.49e+04ε (Mean = 3.39e+03ε)) 4740 </p> 4741 </td> 4742<td> 4743 <p> 4744 <span class="blue">Max = 1.97ε (Mean = 0.629ε)</span> 4745 </p> 4746 </td> 4747<td> 4748 <p> 4749 <span class="blue">Max = 1.71ε (Mean = 0.553ε)</span> 4750 </p> 4751 </td> 4752</tr> 4753</tbody> 4754</table></div> 4755</div> 4756<br class="table-break"><div class="table"> 4757<a name="math_toolkit.logs_and_tables.all_table.table_ellint_3"></a><p class="title"><b>Table 23.31. Error rates for ellint_3</b></p> 4758<div class="table-contents"><table class="table" summary="Error rates for ellint_3"> 4759<colgroup> 4760<col> 4761<col> 4762<col> 4763<col> 4764<col> 4765</colgroup> 4766<thead><tr> 4767<th> 4768 </th> 4769<th> 4770 <p> 4771 GNU C++ version 7.1.0<br> linux<br> long double 4772 </p> 4773 </th> 4774<th> 4775 <p> 4776 GNU C++ version 7.1.0<br> linux<br> double 4777 </p> 4778 </th> 4779<th> 4780 <p> 4781 Sun compiler version 0x5150<br> Sun Solaris<br> long double 4782 </p> 4783 </th> 4784<th> 4785 <p> 4786 Microsoft Visual C++ version 14.1<br> Win32<br> double 4787 </p> 4788 </th> 4789</tr></thead> 4790<tbody> 4791<tr> 4792<td> 4793 <p> 4794 Elliptic Integral PI: Mathworld Data 4795 </p> 4796 </td> 4797<td> 4798 <p> 4799 <span class="blue">Max = 475ε (Mean = 86.3ε)</span><br> <br> 4800 (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = +INFε (Mean 4801 = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Mathworld_Data">And 4802 other failures.</a>)</span> 4803 </p> 4804 </td> 4805<td> 4806 <p> 4807 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 4808 2.1:</em></span> Max = 1.48e+05ε (Mean = 2.54e+04ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_ellint_3_GSL_2_1_Elliptic_Integral_PI_Mathworld_Data">And 4809 other failures.</a>) 4810 </p> 4811 </td> 4812<td> 4813 <p> 4814 <span class="blue">Max = 475ε (Mean = 86.3ε)</span> 4815 </p> 4816 </td> 4817<td> 4818 <p> 4819 <span class="blue">Max = 565ε (Mean = 102ε)</span> 4820 </p> 4821 </td> 4822</tr> 4823<tr> 4824<td> 4825 <p> 4826 Elliptic Integral PI: Random Data 4827 </p> 4828 </td> 4829<td> 4830 <p> 4831 <span class="blue">Max = 4.54ε (Mean = 0.895ε)</span><br> <br> 4832 (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 3.37e+20ε (Mean 4833 = 3.47e+19ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Random_Data">And 4834 other failures.</a>)</span> 4835 </p> 4836 </td> 4837<td> 4838 <p> 4839 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 4840 2.1:</em></span> Max = 633ε (Mean = 50.1ε)) 4841 </p> 4842 </td> 4843<td> 4844 <p> 4845 <span class="blue">Max = 4.49ε (Mean = 0.885ε)</span> 4846 </p> 4847 </td> 4848<td> 4849 <p> 4850 <span class="blue">Max = 8.33ε (Mean = 0.971ε)</span> 4851 </p> 4852 </td> 4853</tr> 4854<tr> 4855<td> 4856 <p> 4857 Elliptic Integral PI: Large Random Data 4858 </p> 4859 </td> 4860<td> 4861 <p> 4862 <span class="blue">Max = 3.7ε (Mean = 0.893ε)</span><br> <br> 4863 (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 2.52e+18ε (Mean 4864 = 4.83e+17ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Large_Random_Data">And 4865 other failures.</a>)</span> 4866 </p> 4867 </td> 4868<td> 4869 <p> 4870 <span class="blue">Max = 0.557ε (Mean = 0.0389ε)</span><br> 4871 <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 40.1ε (Mean = 7.77ε)) 4872 </p> 4873 </td> 4874<td> 4875 <p> 4876 <span class="blue">Max = 3.7ε (Mean = 0.892ε)</span> 4877 </p> 4878 </td> 4879<td> 4880 <p> 4881 <span class="blue">Max = 2.86ε (Mean = 0.944ε)</span> 4882 </p> 4883 </td> 4884</tr> 4885</tbody> 4886</table></div> 4887</div> 4888<br class="table-break"><div class="table"> 4889<a name="math_toolkit.logs_and_tables.all_table.table_ellint_3_complete_"></a><p class="title"><b>Table 23.32. Error rates for ellint_3 (complete)</b></p> 4890<div class="table-contents"><table class="table" summary="Error rates for ellint_3 (complete)"> 4891<colgroup> 4892<col> 4893<col> 4894<col> 4895<col> 4896<col> 4897</colgroup> 4898<thead><tr> 4899<th> 4900 </th> 4901<th> 4902 <p> 4903 GNU C++ version 7.1.0<br> linux<br> long double 4904 </p> 4905 </th> 4906<th> 4907 <p> 4908 GNU C++ version 7.1.0<br> linux<br> double 4909 </p> 4910 </th> 4911<th> 4912 <p> 4913 Sun compiler version 0x5150<br> Sun Solaris<br> long double 4914 </p> 4915 </th> 4916<th> 4917 <p> 4918 Microsoft Visual C++ version 14.1<br> Win32<br> double 4919 </p> 4920 </th> 4921</tr></thead> 4922<tbody> 4923<tr> 4924<td> 4925 <p> 4926 Complete Elliptic Integral PI: Mathworld Data 4927 </p> 4928 </td> 4929<td> 4930 <p> 4931 <span class="blue">Max = 1.4ε (Mean = 0.575ε)</span><br> <br> 4932 (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 6.31e+20ε (Mean 4933 = 1.53e+20ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3_complete___cmath__Complete_Elliptic_Integral_PI_Mathworld_Data">And 4934 other failures.</a>)</span> 4935 </p> 4936 </td> 4937<td> 4938 <p> 4939 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 4940 2.1:</em></span> Max = 6.33e+04ε (Mean = 1.54e+04ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_ellint_3_complete__GSL_2_1_Complete_Elliptic_Integral_PI_Mathworld_Data">And 4941 other failures.</a>) 4942 </p> 4943 </td> 4944<td> 4945 <p> 4946 <span class="blue">Max = 1.4ε (Mean = 0.575ε)</span> 4947 </p> 4948 </td> 4949<td> 4950 <p> 4951 <span class="blue">Max = 0.971ε (Mean = 0.464ε)</span> 4952 </p> 4953 </td> 4954</tr> 4955<tr> 4956<td> 4957 <p> 4958 Complete Elliptic Integral PI: Random Data 4959 </p> 4960 </td> 4961<td> 4962 <p> 4963 <span class="blue">Max = 2.45ε (Mean = 0.696ε)</span><br> <br> 4964 (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 8.78e+20ε (Mean 4965 = 1.02e+20ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3_complete___cmath__Complete_Elliptic_Integral_PI_Random_Data">And 4966 other failures.</a>)</span> 4967 </p> 4968 </td> 4969<td> 4970 <p> 4971 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 4972 2.1:</em></span> Max = 24ε (Mean = 2.99ε)) 4973 </p> 4974 </td> 4975<td> 4976 <p> 4977 <span class="blue">Max = 2.4ε (Mean = 0.677ε)</span> 4978 </p> 4979 </td> 4980<td> 4981 <p> 4982 <span class="blue">Max = 2.46ε (Mean = 0.657ε)</span> 4983 </p> 4984 </td> 4985</tr> 4986</tbody> 4987</table></div> 4988</div> 4989<br class="table-break"><div class="table"> 4990<a name="math_toolkit.logs_and_tables.all_table.table_ellint_d"></a><p class="title"><b>Table 23.33. Error rates for ellint_d</b></p> 4991<div class="table-contents"><table class="table" summary="Error rates for ellint_d"> 4992<colgroup> 4993<col> 4994<col> 4995<col> 4996<col> 4997<col> 4998</colgroup> 4999<thead><tr> 5000<th> 5001 </th> 5002<th> 5003 <p> 5004 GNU C++ version 7.1.0<br> linux<br> double 5005 </p> 5006 </th> 5007<th> 5008 <p> 5009 GNU C++ version 7.1.0<br> linux<br> long double 5010 </p> 5011 </th> 5012<th> 5013 <p> 5014 Sun compiler version 0x5150<br> Sun Solaris<br> long double 5015 </p> 5016 </th> 5017<th> 5018 <p> 5019 Microsoft Visual C++ version 14.1<br> Win32<br> double 5020 </p> 5021 </th> 5022</tr></thead> 5023<tbody> 5024<tr> 5025<td> 5026 <p> 5027 Elliptic Integral E: Mathworld Data 5028 </p> 5029 </td> 5030<td> 5031 <p> 5032 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 5033 2.1:</em></span> Max = 0.862ε (Mean = 0.568ε)) 5034 </p> 5035 </td> 5036<td> 5037 <p> 5038 <span class="blue">Max = 1.3ε (Mean = 0.813ε)</span> 5039 </p> 5040 </td> 5041<td> 5042 <p> 5043 <span class="blue">Max = 1.3ε (Mean = 0.813ε)</span> 5044 </p> 5045 </td> 5046<td> 5047 <p> 5048 <span class="blue">Max = 0.862ε (Mean = 0.457ε)</span> 5049 </p> 5050 </td> 5051</tr> 5052<tr> 5053<td> 5054 <p> 5055 Elliptic Integral D: Random Data 5056 </p> 5057 </td> 5058<td> 5059 <p> 5060 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 5061 2.1:</em></span> Max = 3.01ε (Mean = 0.928ε)) 5062 </p> 5063 </td> 5064<td> 5065 <p> 5066 <span class="blue">Max = 2.51ε (Mean = 0.883ε)</span> 5067 </p> 5068 </td> 5069<td> 5070 <p> 5071 <span class="blue">Max = 2.51ε (Mean = 0.883ε)</span> 5072 </p> 5073 </td> 5074<td> 5075 <p> 5076 <span class="blue">Max = 2.87ε (Mean = 0.805ε)</span> 5077 </p> 5078 </td> 5079</tr> 5080</tbody> 5081</table></div> 5082</div> 5083<br class="table-break"><div class="table"> 5084<a name="math_toolkit.logs_and_tables.all_table.table_ellint_d_complete_"></a><p class="title"><b>Table 23.34. Error rates for ellint_d (complete)</b></p> 5085<div class="table-contents"><table class="table" summary="Error rates for ellint_d (complete)"> 5086<colgroup> 5087<col> 5088<col> 5089<col> 5090<col> 5091<col> 5092</colgroup> 5093<thead><tr> 5094<th> 5095 </th> 5096<th> 5097 <p> 5098 GNU C++ version 7.1.0<br> linux<br> double 5099 </p> 5100 </th> 5101<th> 5102 <p> 5103 GNU C++ version 7.1.0<br> linux<br> long double 5104 </p> 5105 </th> 5106<th> 5107 <p> 5108 Sun compiler version 0x5150<br> Sun Solaris<br> long double 5109 </p> 5110 </th> 5111<th> 5112 <p> 5113 Microsoft Visual C++ version 14.1<br> Win32<br> double 5114 </p> 5115 </th> 5116</tr></thead> 5117<tbody> 5118<tr> 5119<td> 5120 <p> 5121 Elliptic Integral E: Mathworld Data 5122 </p> 5123 </td> 5124<td> 5125 <p> 5126 <span class="blue">Max = 0.637ε (Mean = 0.368ε)</span> 5127 </p> 5128 </td> 5129<td> 5130 <p> 5131 <span class="blue">Max = 1.27ε (Mean = 0.735ε)</span> 5132 </p> 5133 </td> 5134<td> 5135 <p> 5136 <span class="blue">Max = 1.27ε (Mean = 0.735ε)</span> 5137 </p> 5138 </td> 5139<td> 5140 <p> 5141 <span class="blue">Max = 0.637ε (Mean = 0.368ε)</span> 5142 </p> 5143 </td> 5144</tr> 5145<tr> 5146<td> 5147 <p> 5148 Elliptic Integral D: Random Data 5149 </p> 5150 </td> 5151<td> 5152 <p> 5153 <span class="blue">Max = 0ε (Mean = 0ε)</span> 5154 </p> 5155 </td> 5156<td> 5157 <p> 5158 <span class="blue">Max = 1.27ε (Mean = 0.334ε)</span> 5159 </p> 5160 </td> 5161<td> 5162 <p> 5163 <span class="blue">Max = 1.27ε (Mean = 0.334ε)</span> 5164 </p> 5165 </td> 5166<td> 5167 <p> 5168 <span class="blue">Max = 1.27ε (Mean = 0.355ε)</span> 5169 </p> 5170 </td> 5171</tr> 5172</tbody> 5173</table></div> 5174</div> 5175<br class="table-break"><div class="table"> 5176<a name="math_toolkit.logs_and_tables.all_table.table_ellint_rc"></a><p class="title"><b>Table 23.35. Error rates for ellint_rc</b></p> 5177<div class="table-contents"><table class="table" summary="Error rates for ellint_rc"> 5178<colgroup> 5179<col> 5180<col> 5181<col> 5182<col> 5183</colgroup> 5184<thead><tr> 5185<th> 5186 </th> 5187<th> 5188 <p> 5189 GNU C++ version 7.1.0<br> linux<br> double 5190 </p> 5191 </th> 5192<th> 5193 <p> 5194 GNU C++ version 7.1.0<br> linux<br> long double 5195 </p> 5196 </th> 5197<th> 5198 <p> 5199 Microsoft Visual C++ version 14.1<br> Win32<br> double 5200 </p> 5201 </th> 5202</tr></thead> 5203<tbody><tr> 5204<td> 5205 <p> 5206 RC: Random data 5207 </p> 5208 </td> 5209<td> 5210 <p> 5211 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 5212 2.1:</em></span> Max = 2.4ε (Mean = 0.624ε)) 5213 </p> 5214 </td> 5215<td> 5216 <p> 5217 <span class="blue">Max = 0.995ε (Mean = 0.433ε)</span> 5218 </p> 5219 </td> 5220<td> 5221 <p> 5222 <span class="blue">Max = 0.962ε (Mean = 0.407ε)</span> 5223 </p> 5224 </td> 5225</tr></tbody> 5226</table></div> 5227</div> 5228<br class="table-break"><div class="table"> 5229<a name="math_toolkit.logs_and_tables.all_table.table_ellint_rd"></a><p class="title"><b>Table 23.36. Error rates for ellint_rd</b></p> 5230<div class="table-contents"><table class="table" summary="Error rates for ellint_rd"> 5231<colgroup> 5232<col> 5233<col> 5234<col> 5235<col> 5236</colgroup> 5237<thead><tr> 5238<th> 5239 </th> 5240<th> 5241 <p> 5242 GNU C++ version 7.1.0<br> linux<br> double 5243 </p> 5244 </th> 5245<th> 5246 <p> 5247 GNU C++ version 7.1.0<br> linux<br> long double 5248 </p> 5249 </th> 5250<th> 5251 <p> 5252 Microsoft Visual C++ version 14.1<br> Win32<br> double 5253 </p> 5254 </th> 5255</tr></thead> 5256<tbody> 5257<tr> 5258<td> 5259 <p> 5260 RD: Random data 5261 </p> 5262 </td> 5263<td> 5264 <p> 5265 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 5266 2.1:</em></span> Max = 2.59ε (Mean = 0.878ε)) 5267 </p> 5268 </td> 5269<td> 5270 <p> 5271 <span class="blue">Max = 2.73ε (Mean = 0.831ε)</span> 5272 </p> 5273 </td> 5274<td> 5275 <p> 5276 <span class="blue">Max = 2.16ε (Mean = 0.803ε)</span> 5277 </p> 5278 </td> 5279</tr> 5280<tr> 5281<td> 5282 <p> 5283 RD: y = z 5284 </p> 5285 </td> 5286<td> 5287 <p> 5288 <span class="blue">Max = 0.896ε (Mean = 0.022ε)</span><br> <br> 5289 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.88ε (Mean = 0.839ε)) 5290 </p> 5291 </td> 5292<td> 5293 <p> 5294 <span class="blue">Max = 2.65ε (Mean = 0.82ε)</span> 5295 </p> 5296 </td> 5297<td> 5298 <p> 5299 <span class="blue">Max = 16.5ε (Mean = 0.843ε)</span> 5300 </p> 5301 </td> 5302</tr> 5303<tr> 5304<td> 5305 <p> 5306 RD: x = y 5307 </p> 5308 </td> 5309<td> 5310 <p> 5311 <span class="blue">Max = 0.824ε (Mean = 0.0272ε)</span><br> 5312 <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.74ε (Mean = 0.84ε)) 5313 </p> 5314 </td> 5315<td> 5316 <p> 5317 <span class="blue">Max = 2.85ε (Mean = 0.865ε)</span> 5318 </p> 5319 </td> 5320<td> 5321 <p> 5322 <span class="blue">Max = 3.51ε (Mean = 0.816ε)</span> 5323 </p> 5324 </td> 5325</tr> 5326<tr> 5327<td> 5328 <p> 5329 RD: x = 0, y = z 5330 </p> 5331 </td> 5332<td> 5333 <p> 5334 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 5335 2.1:</em></span> Max = 2ε (Mean = 0.656ε)) 5336 </p> 5337 </td> 5338<td> 5339 <p> 5340 <span class="blue">Max = 1.19ε (Mean = 0.522ε)</span> 5341 </p> 5342 </td> 5343<td> 5344 <p> 5345 <span class="blue">Max = 1.16ε (Mean = 0.497ε)</span> 5346 </p> 5347 </td> 5348</tr> 5349<tr> 5350<td> 5351 <p> 5352 RD: x = y = z 5353 </p> 5354 </td> 5355<td> 5356 <p> 5357 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 5358 2.1:</em></span> Max = 1.03ε (Mean = 0.418ε)) 5359 </p> 5360 </td> 5361<td> 5362 <p> 5363 <span class="blue">Max = 0.998ε (Mean = 0.387ε)</span> 5364 </p> 5365 </td> 5366<td> 5367 <p> 5368 <span class="blue">Max = 1.03ε (Mean = 0.418ε)</span> 5369 </p> 5370 </td> 5371</tr> 5372<tr> 5373<td> 5374 <p> 5375 RD: x = 0 5376 </p> 5377 </td> 5378<td> 5379 <p> 5380 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 5381 2.1:</em></span> Max = 2.85ε (Mean = 0.781ε)) 5382 </p> 5383 </td> 5384<td> 5385 <p> 5386 <span class="blue">Max = 2.79ε (Mean = 0.883ε)</span> 5387 </p> 5388 </td> 5389<td> 5390 <p> 5391 <span class="blue">Max = 2.64ε (Mean = 0.894ε)</span> 5392 </p> 5393 </td> 5394</tr> 5395</tbody> 5396</table></div> 5397</div> 5398<br class="table-break"><div class="table"> 5399<a name="math_toolkit.logs_and_tables.all_table.table_ellint_rf"></a><p class="title"><b>Table 23.37. Error rates for ellint_rf</b></p> 5400<div class="table-contents"><table class="table" summary="Error rates for ellint_rf"> 5401<colgroup> 5402<col> 5403<col> 5404<col> 5405<col> 5406</colgroup> 5407<thead><tr> 5408<th> 5409 </th> 5410<th> 5411 <p> 5412 GNU C++ version 7.1.0<br> linux<br> double 5413 </p> 5414 </th> 5415<th> 5416 <p> 5417 GNU C++ version 7.1.0<br> linux<br> long double 5418 </p> 5419 </th> 5420<th> 5421 <p> 5422 Microsoft Visual C++ version 14.1<br> Win32<br> double 5423 </p> 5424 </th> 5425</tr></thead> 5426<tbody> 5427<tr> 5428<td> 5429 <p> 5430 RF: Random data 5431 </p> 5432 </td> 5433<td> 5434 <p> 5435 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 5436 2.1:</em></span> Max = 2.73ε (Mean = 0.804ε)) 5437 </p> 5438 </td> 5439<td> 5440 <p> 5441 <span class="blue">Max = 2.54ε (Mean = 0.674ε)</span> 5442 </p> 5443 </td> 5444<td> 5445 <p> 5446 <span class="blue">Max = 2.02ε (Mean = 0.677ε)</span> 5447 </p> 5448 </td> 5449</tr> 5450<tr> 5451<td> 5452 <p> 5453 RF: x = y = z 5454 </p> 5455 </td> 5456<td> 5457 <p> 5458 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 5459 2.1:</em></span> Max = 0.999ε (Mean = 0.34ε)) 5460 </p> 5461 </td> 5462<td> 5463 <p> 5464 <span class="blue">Max = 0.991ε (Mean = 0.345ε)</span> 5465 </p> 5466 </td> 5467<td> 5468 <p> 5469 <span class="blue">Max = 0.999ε (Mean = 0.34ε)</span> 5470 </p> 5471 </td> 5472</tr> 5473<tr> 5474<td> 5475 <p> 5476 RF: x = y or y = z or x = z 5477 </p> 5478 </td> 5479<td> 5480 <p> 5481 <span class="blue">Max = 0.536ε (Mean = 0.00658ε)</span><br> 5482 <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.89ε (Mean = 0.749ε)) 5483 </p> 5484 </td> 5485<td> 5486 <p> 5487 <span class="blue">Max = 1.95ε (Mean = 0.418ε)</span> 5488 </p> 5489 </td> 5490<td> 5491 <p> 5492 <span class="blue">Max = 1.21ε (Mean = 0.394ε)</span> 5493 </p> 5494 </td> 5495</tr> 5496<tr> 5497<td> 5498 <p> 5499 RF: x = 0, y = z 5500 </p> 5501 </td> 5502<td> 5503 <p> 5504 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 5505 2.1:</em></span> Max = 1.29ε (Mean = 0.527ε)) 5506 </p> 5507 </td> 5508<td> 5509 <p> 5510 <span class="blue">Max = 0.894ε (Mean = 0.338ε)</span> 5511 </p> 5512 </td> 5513<td> 5514 <p> 5515 <span class="blue">Max = 0.999ε (Mean = 0.407ε)</span> 5516 </p> 5517 </td> 5518</tr> 5519<tr> 5520<td> 5521 <p> 5522 RF: z = 0 5523 </p> 5524 </td> 5525<td> 5526 <p> 5527 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 5528 2.1:</em></span> Max = 2.54ε (Mean = 0.781ε)) 5529 </p> 5530 </td> 5531<td> 5532 <p> 5533 <span class="blue">Max = 1.7ε (Mean = 0.539ε)</span> 5534 </p> 5535 </td> 5536<td> 5537 <p> 5538 <span class="blue">Max = 1.89ε (Mean = 0.587ε)</span> 5539 </p> 5540 </td> 5541</tr> 5542</tbody> 5543</table></div> 5544</div> 5545<br class="table-break"><div class="table"> 5546<a name="math_toolkit.logs_and_tables.all_table.table_ellint_rg"></a><p class="title"><b>Table 23.38. Error rates for ellint_rg</b></p> 5547<div class="table-contents"><table class="table" summary="Error rates for ellint_rg"> 5548<colgroup> 5549<col> 5550<col> 5551<col> 5552<col> 5553</colgroup> 5554<thead><tr> 5555<th> 5556 </th> 5557<th> 5558 <p> 5559 GNU C++ version 7.1.0<br> linux<br> double 5560 </p> 5561 </th> 5562<th> 5563 <p> 5564 GNU C++ version 7.1.0<br> linux<br> long double 5565 </p> 5566 </th> 5567<th> 5568 <p> 5569 Microsoft Visual C++ version 14.1<br> Win32<br> double 5570 </p> 5571 </th> 5572</tr></thead> 5573<tbody> 5574<tr> 5575<td> 5576 <p> 5577 RG: Random Data 5578 </p> 5579 </td> 5580<td> 5581 <p> 5582 <span class="blue">Max = 0.983ε (Mean = 0.0172ε)</span><br> 5583 <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.983ε (Mean = 0.0172ε)) 5584 </p> 5585 </td> 5586<td> 5587 <p> 5588 <span class="blue">Max = 3.95ε (Mean = 0.951ε)</span> 5589 </p> 5590 </td> 5591<td> 5592 <p> 5593 <span class="blue">Max = 3.65ε (Mean = 0.929ε)</span> 5594 </p> 5595 </td> 5596</tr> 5597<tr> 5598<td> 5599 <p> 5600 RG: two values 0 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 = 0ε (Mean = 0ε)) 5607 </p> 5608 </td> 5609<td> 5610 <p> 5611 <span class="blue">Max = 0ε (Mean = 0ε)</span> 5612 </p> 5613 </td> 5614<td> 5615 <p> 5616 <span class="blue">Max = 0ε (Mean = 0ε)</span> 5617 </p> 5618 </td> 5619</tr> 5620<tr> 5621<td> 5622 <p> 5623 RG: All values the same or zero 5624 </p> 5625 </td> 5626<td> 5627 <p> 5628 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 5629 2.1:</em></span> Max = 0ε (Mean = 0ε)) 5630 </p> 5631 </td> 5632<td> 5633 <p> 5634 <span class="blue">Max = 0.992ε (Mean = 0.288ε)</span> 5635 </p> 5636 </td> 5637<td> 5638 <p> 5639 <span class="blue">Max = 1.06ε (Mean = 0.348ε)</span> 5640 </p> 5641 </td> 5642</tr> 5643<tr> 5644<td> 5645 <p> 5646 RG: two values the same 5647 </p> 5648 </td> 5649<td> 5650 <p> 5651 <span class="blue">Max = 0.594ε (Mean = 0.0103ε)</span><br> 5652 <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.594ε (Mean = 0.0103ε)) 5653 </p> 5654 </td> 5655<td> 5656 <p> 5657 <span class="blue">Max = 1.51ε (Mean = 0.404ε)</span> 5658 </p> 5659 </td> 5660<td> 5661 <p> 5662 <span class="blue">Max = 1.96ε (Mean = 0.374ε)</span> 5663 </p> 5664 </td> 5665</tr> 5666<tr> 5667<td> 5668 <p> 5669 RG: one value zero 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 = 0ε (Mean = 0ε)) 5676 </p> 5677 </td> 5678<td> 5679 <p> 5680 <span class="blue">Max = 2.14ε (Mean = 0.722ε)</span> 5681 </p> 5682 </td> 5683<td> 5684 <p> 5685 <span class="blue">Max = 1.96ε (Mean = 0.674ε)</span> 5686 </p> 5687 </td> 5688</tr> 5689</tbody> 5690</table></div> 5691</div> 5692<br class="table-break"><div class="table"> 5693<a name="math_toolkit.logs_and_tables.all_table.table_ellint_rj"></a><p class="title"><b>Table 23.39. Error rates for ellint_rj</b></p> 5694<div class="table-contents"><table class="table" summary="Error rates for ellint_rj"> 5695<colgroup> 5696<col> 5697<col> 5698<col> 5699<col> 5700</colgroup> 5701<thead><tr> 5702<th> 5703 </th> 5704<th> 5705 <p> 5706 GNU C++ version 7.1.0<br> linux<br> double 5707 </p> 5708 </th> 5709<th> 5710 <p> 5711 GNU C++ version 7.1.0<br> linux<br> long double 5712 </p> 5713 </th> 5714<th> 5715 <p> 5716 Microsoft Visual C++ version 14.1<br> Win32<br> double 5717 </p> 5718 </th> 5719</tr></thead> 5720<tbody> 5721<tr> 5722<td> 5723 <p> 5724 RJ: Random data 5725 </p> 5726 </td> 5727<td> 5728 <p> 5729 <span class="blue">Max = 0.52ε (Mean = 0.0184ε)</span><br> <br> 5730 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.57ε (Mean = 0.704ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_ellint_rj_GSL_2_1_RJ_Random_data">And 5731 other failures.</a>) 5732 </p> 5733 </td> 5734<td> 5735 <p> 5736 <span class="blue">Max = 186ε (Mean = 6.67ε)</span> 5737 </p> 5738 </td> 5739<td> 5740 <p> 5741 <span class="blue">Max = 215ε (Mean = 7.66ε)</span> 5742 </p> 5743 </td> 5744</tr> 5745<tr> 5746<td> 5747 <p> 5748 RJ: 4 Equal Values 5749 </p> 5750 </td> 5751<td> 5752 <p> 5753 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 5754 2.1:</em></span> Max = 1.03ε (Mean = 0.418ε)) 5755 </p> 5756 </td> 5757<td> 5758 <p> 5759 <span class="blue">Max = 0.998ε (Mean = 0.387ε)</span> 5760 </p> 5761 </td> 5762<td> 5763 <p> 5764 <span class="blue">Max = 1.03ε (Mean = 0.418ε)</span> 5765 </p> 5766 </td> 5767</tr> 5768<tr> 5769<td> 5770 <p> 5771 RJ: 3 Equal Values 5772 </p> 5773 </td> 5774<td> 5775 <p> 5776 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 5777 2.1:</em></span> Max = 3.96ε (Mean = 1.06ε)) 5778 </p> 5779 </td> 5780<td> 5781 <p> 5782 <span class="blue">Max = 20.8ε (Mean = 0.986ε)</span> 5783 </p> 5784 </td> 5785<td> 5786 <p> 5787 <span class="blue">Max = 39.9ε (Mean = 1.17ε)</span> 5788 </p> 5789 </td> 5790</tr> 5791<tr> 5792<td> 5793 <p> 5794 RJ: 2 Equal Values 5795 </p> 5796 </td> 5797<td> 5798 <p> 5799 <span class="blue">Max = 0.6ε (Mean = 0.0228ε)</span><br> <br> 5800 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.57ε (Mean = 0.754ε)) 5801 </p> 5802 </td> 5803<td> 5804 <p> 5805 <span class="blue">Max = 220ε (Mean = 6.64ε)</span> 5806 </p> 5807 </td> 5808<td> 5809 <p> 5810 <span class="blue">Max = 214ε (Mean = 5.28ε)</span> 5811 </p> 5812 </td> 5813</tr> 5814<tr> 5815<td> 5816 <p> 5817 RJ: Equal z and p 5818 </p> 5819 </td> 5820<td> 5821 <p> 5822 <span class="blue">Max = 0.742ε (Mean = 0.0166ε)</span><br> 5823 <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.62ε (Mean = 0.699ε)) 5824 </p> 5825 </td> 5826<td> 5827 <p> 5828 <span class="blue">Max = 17.2ε (Mean = 1.16ε)</span> 5829 </p> 5830 </td> 5831<td> 5832 <p> 5833 <span class="blue">Max = 16.1ε (Mean = 1.14ε)</span> 5834 </p> 5835 </td> 5836</tr> 5837</tbody> 5838</table></div> 5839</div> 5840<br class="table-break"><div class="table"> 5841<a name="math_toolkit.logs_and_tables.all_table.table_erf"></a><p class="title"><b>Table 23.40. Error rates for erf</b></p> 5842<div class="table-contents"><table class="table" summary="Error rates for erf"> 5843<colgroup> 5844<col> 5845<col> 5846<col> 5847<col> 5848<col> 5849</colgroup> 5850<thead><tr> 5851<th> 5852 </th> 5853<th> 5854 <p> 5855 GNU C++ version 7.1.0<br> linux<br> long double 5856 </p> 5857 </th> 5858<th> 5859 <p> 5860 GNU C++ version 7.1.0<br> linux<br> double 5861 </p> 5862 </th> 5863<th> 5864 <p> 5865 Sun compiler version 0x5150<br> Sun Solaris<br> long double 5866 </p> 5867 </th> 5868<th> 5869 <p> 5870 Microsoft Visual C++ version 14.1<br> Win32<br> double 5871 </p> 5872 </th> 5873</tr></thead> 5874<tbody> 5875<tr> 5876<td> 5877 <p> 5878 Erf Function: Small Values 5879 </p> 5880 </td> 5881<td> 5882 <p> 5883 <span class="blue">Max = 0.925ε (Mean = 0.193ε)</span><br> <br> 5884 (<span class="emphasis"><em><cmath>:</em></span> Max = 0.944ε (Mean = 0.191ε))<br> 5885 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.944ε (Mean = 0.191ε)) 5886 </p> 5887 </td> 5888<td> 5889 <p> 5890 <span class="blue">Max = 0.841ε (Mean = 0.0687ε)</span><br> 5891 <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.06ε (Mean = 0.319ε)) 5892 </p> 5893 </td> 5894<td> 5895 <p> 5896 <span class="blue">Max = 0.925ε (Mean = 0.193ε)</span><br> <br> 5897 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.944ε (Mean = 0.194ε)) 5898 </p> 5899 </td> 5900<td> 5901 <p> 5902 <span class="blue">Max = 0.996ε (Mean = 0.182ε)</span><br> <br> 5903 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.57ε (Mean = 0.317ε)) 5904 </p> 5905 </td> 5906</tr> 5907<tr> 5908<td> 5909 <p> 5910 Erf Function: Medium Values 5911 </p> 5912 </td> 5913<td> 5914 <p> 5915 <span class="blue">Max = 1.5ε (Mean = 0.193ε)</span><br> <br> 5916 (<span class="emphasis"><em><cmath>:</em></span> Max = 0.921ε (Mean = 0.0723ε))<br> 5917 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.921ε (Mean = 0.0723ε)) 5918 </p> 5919 </td> 5920<td> 5921 <p> 5922 <span class="blue">Max = 1ε (Mean = 0.119ε)</span><br> <br> 5923 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.31ε (Mean = 0.368ε)) 5924 </p> 5925 </td> 5926<td> 5927 <p> 5928 <span class="blue">Max = 1.5ε (Mean = 0.197ε)</span><br> <br> 5929 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.921ε (Mean = 0.071ε)) 5930 </p> 5931 </td> 5932<td> 5933 <p> 5934 <span class="blue">Max = 1ε (Mean = 0.171ε)</span><br> <br> 5935 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.19ε (Mean = 0.244ε)) 5936 </p> 5937 </td> 5938</tr> 5939<tr> 5940<td> 5941 <p> 5942 Erf Function: Large Values 5943 </p> 5944 </td> 5945<td> 5946 <p> 5947 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span> 5948 Max = 0ε (Mean = 0ε))<br> (<span class="emphasis"><em><math.h>:</em></span> 5949 Max = 0ε (Mean = 0ε)) 5950 </p> 5951 </td> 5952<td> 5953 <p> 5954 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 5955 2.1:</em></span> Max = 0ε (Mean = 0ε)) 5956 </p> 5957 </td> 5958<td> 5959 <p> 5960 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span> 5961 Max = 0ε (Mean = 0ε)) 5962 </p> 5963 </td> 5964<td> 5965 <p> 5966 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span> 5967 Max = 0ε (Mean = 0ε)) 5968 </p> 5969 </td> 5970</tr> 5971</tbody> 5972</table></div> 5973</div> 5974<br class="table-break"><div class="table"> 5975<a name="math_toolkit.logs_and_tables.all_table.table_erf_inv"></a><p class="title"><b>Table 23.41. Error rates for erf_inv</b></p> 5976<div class="table-contents"><table class="table" summary="Error rates for erf_inv"> 5977<colgroup> 5978<col> 5979<col> 5980<col> 5981<col> 5982<col> 5983</colgroup> 5984<thead><tr> 5985<th> 5986 </th> 5987<th> 5988 <p> 5989 GNU C++ version 7.1.0<br> linux<br> double 5990 </p> 5991 </th> 5992<th> 5993 <p> 5994 GNU C++ version 7.1.0<br> linux<br> long double 5995 </p> 5996 </th> 5997<th> 5998 <p> 5999 Sun compiler version 0x5150<br> Sun Solaris<br> long double 6000 </p> 6001 </th> 6002<th> 6003 <p> 6004 Microsoft Visual C++ version 14.1<br> Win32<br> double 6005 </p> 6006 </th> 6007</tr></thead> 6008<tbody><tr> 6009<td> 6010 <p> 6011 Inverse Erf Function 6012 </p> 6013 </td> 6014<td> 6015 <p> 6016 <span class="blue">Max = 0ε (Mean = 0ε)</span> 6017 </p> 6018 </td> 6019<td> 6020 <p> 6021 <span class="blue">Max = 0.996ε (Mean = 0.389ε)</span> 6022 </p> 6023 </td> 6024<td> 6025 <p> 6026 <span class="blue">Max = 1.08ε (Mean = 0.395ε)</span> 6027 </p> 6028 </td> 6029<td> 6030 <p> 6031 <span class="blue">Max = 1.09ε (Mean = 0.502ε)</span> 6032 </p> 6033 </td> 6034</tr></tbody> 6035</table></div> 6036</div> 6037<br class="table-break"><div class="table"> 6038<a name="math_toolkit.logs_and_tables.all_table.table_erfc"></a><p class="title"><b>Table 23.42. Error rates for erfc</b></p> 6039<div class="table-contents"><table class="table" summary="Error rates for erfc"> 6040<colgroup> 6041<col> 6042<col> 6043<col> 6044<col> 6045<col> 6046</colgroup> 6047<thead><tr> 6048<th> 6049 </th> 6050<th> 6051 <p> 6052 GNU C++ version 7.1.0<br> linux<br> long double 6053 </p> 6054 </th> 6055<th> 6056 <p> 6057 GNU C++ version 7.1.0<br> linux<br> double 6058 </p> 6059 </th> 6060<th> 6061 <p> 6062 Sun compiler version 0x5150<br> Sun Solaris<br> long double 6063 </p> 6064 </th> 6065<th> 6066 <p> 6067 Microsoft Visual C++ version 14.1<br> Win32<br> double 6068 </p> 6069 </th> 6070</tr></thead> 6071<tbody> 6072<tr> 6073<td> 6074 <p> 6075 Erf Function: Small Values 6076 </p> 6077 </td> 6078<td> 6079 <p> 6080 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span> 6081 Max = 0ε (Mean = 0ε))<br> (<span class="emphasis"><em><math.h>:</em></span> 6082 Max = 0ε (Mean = 0ε)) 6083 </p> 6084 </td> 6085<td> 6086 <p> 6087 <span class="blue">Max = 0.658ε (Mean = 0.0537ε)</span><br> 6088 <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.01ε (Mean = 0.485ε)) 6089 </p> 6090 </td> 6091<td> 6092 <p> 6093 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span> 6094 Max = 0ε (Mean = 0ε)) 6095 </p> 6096 </td> 6097<td> 6098 <p> 6099 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span> 6100 Max = 0ε (Mean = 0ε)) 6101 </p> 6102 </td> 6103</tr> 6104<tr> 6105<td> 6106 <p> 6107 Erf Function: Medium Values 6108 </p> 6109 </td> 6110<td> 6111 <p> 6112 <span class="blue">Max = 1.76ε (Mean = 0.365ε)</span><br> <br> 6113 (<span class="emphasis"><em><cmath>:</em></span> Max = 1.35ε (Mean = 0.307ε))<br> 6114 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.35ε (Mean = 0.307ε)) 6115 </p> 6116 </td> 6117<td> 6118 <p> 6119 <span class="blue">Max = 0.983ε (Mean = 0.213ε)</span><br> <br> 6120 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.64ε (Mean = 0.662ε)) 6121 </p> 6122 </td> 6123<td> 6124 <p> 6125 <span class="blue">Max = 1.76ε (Mean = 0.38ε)</span><br> <br> 6126 (<span class="emphasis"><em><math.h>:</em></span> Max = 2.81ε (Mean = 0.739ε)) 6127 </p> 6128 </td> 6129<td> 6130 <p> 6131 <span class="blue">Max = 1.65ε (Mean = 0.373ε)</span><br> <br> 6132 (<span class="emphasis"><em><math.h>:</em></span> Max = 2.36ε (Mean = 0.539ε)) 6133 </p> 6134 </td> 6135</tr> 6136<tr> 6137<td> 6138 <p> 6139 Erf Function: Large Values 6140 </p> 6141 </td> 6142<td> 6143 <p> 6144 <span class="blue">Max = 1.57ε (Mean = 0.542ε)</span><br> <br> 6145 (<span class="emphasis"><em><cmath>:</em></span> Max = 1.26ε (Mean = 0.441ε))<br> 6146 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.26ε (Mean = 0.441ε)) 6147 </p> 6148 </td> 6149<td> 6150 <p> 6151 <span class="blue">Max = 0.868ε (Mean = 0.147ε)</span><br> <br> 6152 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.9ε (Mean = 0.472ε)) 6153 </p> 6154 </td> 6155<td> 6156 <p> 6157 <span class="blue">Max = 1.57ε (Mean = 0.564ε)</span><br> <br> 6158 (<span class="emphasis"><em><math.h>:</em></span> Max = 4.91ε (Mean = 1.54ε)) 6159 </p> 6160 </td> 6161<td> 6162 <p> 6163 <span class="blue">Max = 1.14ε (Mean = 0.248ε)</span><br> <br> 6164 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.84ε (Mean = 0.331ε)) 6165 </p> 6166 </td> 6167</tr> 6168</tbody> 6169</table></div> 6170</div> 6171<br class="table-break"><div class="table"> 6172<a name="math_toolkit.logs_and_tables.all_table.table_erfc_inv"></a><p class="title"><b>Table 23.43. Error rates for erfc_inv</b></p> 6173<div class="table-contents"><table class="table" summary="Error rates for erfc_inv"> 6174<colgroup> 6175<col> 6176<col> 6177<col> 6178<col> 6179<col> 6180</colgroup> 6181<thead><tr> 6182<th> 6183 </th> 6184<th> 6185 <p> 6186 GNU C++ version 7.1.0<br> linux<br> double 6187 </p> 6188 </th> 6189<th> 6190 <p> 6191 GNU C++ version 7.1.0<br> linux<br> long double 6192 </p> 6193 </th> 6194<th> 6195 <p> 6196 Sun compiler version 0x5150<br> Sun Solaris<br> long double 6197 </p> 6198 </th> 6199<th> 6200 <p> 6201 Microsoft Visual C++ version 14.1<br> Win32<br> double 6202 </p> 6203 </th> 6204</tr></thead> 6205<tbody> 6206<tr> 6207<td> 6208 <p> 6209 Inverse Erfc Function 6210 </p> 6211 </td> 6212<td> 6213 <p> 6214 <span class="blue">Max = 0ε (Mean = 0ε)</span> 6215 </p> 6216 </td> 6217<td> 6218 <p> 6219 <span class="blue">Max = 0.996ε (Mean = 0.397ε)</span> 6220 </p> 6221 </td> 6222<td> 6223 <p> 6224 <span class="blue">Max = 1.08ε (Mean = 0.403ε)</span> 6225 </p> 6226 </td> 6227<td> 6228 <p> 6229 <span class="blue">Max = 1ε (Mean = 0.491ε)</span> 6230 </p> 6231 </td> 6232</tr> 6233<tr> 6234<td> 6235 <p> 6236 Inverse Erfc Function: extreme values 6237 </p> 6238 </td> 6239<td> 6240 </td> 6241<td> 6242 <p> 6243 <span class="blue">Max = 1.62ε (Mean = 0.383ε)</span> 6244 </p> 6245 </td> 6246<td> 6247 <p> 6248 <span class="blue">Max = 1.62ε (Mean = 0.383ε)</span> 6249 </p> 6250 </td> 6251<td> 6252 </td> 6253</tr> 6254</tbody> 6255</table></div> 6256</div> 6257<br class="table-break"><div class="table"> 6258<a name="math_toolkit.logs_and_tables.all_table.table_expint_Ei_"></a><p class="title"><b>Table 23.44. Error rates for expint (Ei)</b></p> 6259<div class="table-contents"><table class="table" summary="Error rates for expint (Ei)"> 6260<colgroup> 6261<col> 6262<col> 6263<col> 6264<col> 6265<col> 6266</colgroup> 6267<thead><tr> 6268<th> 6269 </th> 6270<th> 6271 <p> 6272 GNU C++ version 7.1.0<br> linux<br> long double 6273 </p> 6274 </th> 6275<th> 6276 <p> 6277 GNU C++ version 7.1.0<br> linux<br> double 6278 </p> 6279 </th> 6280<th> 6281 <p> 6282 Sun compiler version 0x5150<br> Sun Solaris<br> long double 6283 </p> 6284 </th> 6285<th> 6286 <p> 6287 Microsoft Visual C++ version 14.1<br> Win32<br> double 6288 </p> 6289 </th> 6290</tr></thead> 6291<tbody> 6292<tr> 6293<td> 6294 <p> 6295 Exponential Integral Ei 6296 </p> 6297 </td> 6298<td> 6299 <p> 6300 <span class="blue">Max = 5.05ε (Mean = 0.821ε)</span><br> <br> 6301 (<span class="emphasis"><em><cmath>:</em></span> Max = 14.1ε (Mean = 2.43ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_expint_Ei___cmath__Exponential_Integral_Ei">And 6302 other failures.</a>) 6303 </p> 6304 </td> 6305<td> 6306 <p> 6307 <span class="blue">Max = 0.994ε (Mean = 0.142ε)</span><br> <br> 6308 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.96ε (Mean = 0.703ε)) 6309 </p> 6310 </td> 6311<td> 6312 <p> 6313 <span class="blue">Max = 5.05ε (Mean = 0.835ε)</span> 6314 </p> 6315 </td> 6316<td> 6317 <p> 6318 <span class="blue">Max = 1.43ε (Mean = 0.54ε)</span> 6319 </p> 6320 </td> 6321</tr> 6322<tr> 6323<td> 6324 <p> 6325 Exponential Integral Ei: double exponent range 6326 </p> 6327 </td> 6328<td> 6329 <p> 6330 <span class="blue">Max = 1.72ε (Mean = 0.593ε)</span><br> <br> 6331 (<span class="emphasis"><em><cmath>:</em></span> Max = 3.11ε (Mean = 1.13ε)) 6332 </p> 6333 </td> 6334<td> 6335 <p> 6336 <span class="blue">Max = 0.998ε (Mean = 0.156ε)</span><br> <br> 6337 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.5ε (Mean = 0.612ε)) 6338 </p> 6339 </td> 6340<td> 6341 <p> 6342 <span class="blue">Max = 1.72ε (Mean = 0.607ε)</span> 6343 </p> 6344 </td> 6345<td> 6346 <p> 6347 <span class="blue">Max = 1.7ε (Mean = 0.66ε)</span> 6348 </p> 6349 </td> 6350</tr> 6351<tr> 6352<td> 6353 <p> 6354 Exponential Integral Ei: long exponent range 6355 </p> 6356 </td> 6357<td> 6358 <p> 6359 <span class="blue">Max = 1.98ε (Mean = 0.595ε)</span><br> <br> 6360 (<span class="emphasis"><em><cmath>:</em></span> Max = 1.93ε (Mean = 0.855ε)) 6361 </p> 6362 </td> 6363<td> 6364 </td> 6365<td> 6366 <p> 6367 <span class="blue">Max = 1.98ε (Mean = 0.575ε)</span> 6368 </p> 6369 </td> 6370<td> 6371 </td> 6372</tr> 6373</tbody> 6374</table></div> 6375</div> 6376<br class="table-break"><div class="table"> 6377<a name="math_toolkit.logs_and_tables.all_table.table_expint_En_"></a><p class="title"><b>Table 23.45. Error rates for expint (En)</b></p> 6378<div class="table-contents"><table class="table" summary="Error rates for expint (En)"> 6379<colgroup> 6380<col> 6381<col> 6382<col> 6383<col> 6384<col> 6385</colgroup> 6386<thead><tr> 6387<th> 6388 </th> 6389<th> 6390 <p> 6391 GNU C++ version 7.1.0<br> linux<br> double 6392 </p> 6393 </th> 6394<th> 6395 <p> 6396 GNU C++ version 7.1.0<br> linux<br> long double 6397 </p> 6398 </th> 6399<th> 6400 <p> 6401 Sun compiler version 0x5150<br> Sun Solaris<br> long double 6402 </p> 6403 </th> 6404<th> 6405 <p> 6406 Microsoft Visual C++ version 14.1<br> Win32<br> double 6407 </p> 6408 </th> 6409</tr></thead> 6410<tbody> 6411<tr> 6412<td> 6413 <p> 6414 Exponential Integral En 6415 </p> 6416 </td> 6417<td> 6418 <p> 6419 <span class="blue">Max = 0.589ε (Mean = 0.0331ε)</span><br> 6420 <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 58.5ε (Mean = 17.1ε)) 6421 </p> 6422 </td> 6423<td> 6424 <p> 6425 <span class="blue">Max = 9.97ε (Mean = 2.13ε)</span> 6426 </p> 6427 </td> 6428<td> 6429 <p> 6430 <span class="blue">Max = 9.97ε (Mean = 2.13ε)</span> 6431 </p> 6432 </td> 6433<td> 6434 <p> 6435 <span class="blue">Max = 7.16ε (Mean = 1.85ε)</span> 6436 </p> 6437 </td> 6438</tr> 6439<tr> 6440<td> 6441 <p> 6442 Exponential Integral En: small z values 6443 </p> 6444 </td> 6445<td> 6446 <p> 6447 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 6448 2.1:</em></span> Max = 115ε (Mean = 23.6ε)) 6449 </p> 6450 </td> 6451<td> 6452 <p> 6453 <span class="blue">Max = 1.99ε (Mean = 0.559ε)</span> 6454 </p> 6455 </td> 6456<td> 6457 <p> 6458 <span class="blue">Max = 1.99ε (Mean = 0.559ε)</span> 6459 </p> 6460 </td> 6461<td> 6462 <p> 6463 <span class="blue">Max = 2.62ε (Mean = 0.531ε)</span> 6464 </p> 6465 </td> 6466</tr> 6467<tr> 6468<td> 6469 <p> 6470 Exponential Integral E1 6471 </p> 6472 </td> 6473<td> 6474 <p> 6475 <span class="blue">Max = 0.556ε (Mean = 0.0625ε)</span><br> 6476 <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.988ε (Mean = 0.469ε)) 6477 </p> 6478 </td> 6479<td> 6480 <p> 6481 <span class="blue">Max = 0.965ε (Mean = 0.414ε)</span> 6482 </p> 6483 </td> 6484<td> 6485 <p> 6486 <span class="blue">Max = 0.965ε (Mean = 0.408ε)</span> 6487 </p> 6488 </td> 6489<td> 6490 <p> 6491 <span class="blue">Max = 0.988ε (Mean = 0.486ε)</span> 6492 </p> 6493 </td> 6494</tr> 6495</tbody> 6496</table></div> 6497</div> 6498<br class="table-break"><div class="table"> 6499<a name="math_toolkit.logs_and_tables.all_table.table_expm1"></a><p class="title"><b>Table 23.46. Error rates for expm1</b></p> 6500<div class="table-contents"><table class="table" summary="Error rates for expm1"> 6501<colgroup> 6502<col> 6503<col> 6504<col> 6505<col> 6506<col> 6507</colgroup> 6508<thead><tr> 6509<th> 6510 </th> 6511<th> 6512 <p> 6513 GNU C++ version 7.1.0<br> linux<br> long double 6514 </p> 6515 </th> 6516<th> 6517 <p> 6518 GNU C++ version 7.1.0<br> linux<br> double 6519 </p> 6520 </th> 6521<th> 6522 <p> 6523 Sun compiler version 0x5150<br> Sun Solaris<br> long double 6524 </p> 6525 </th> 6526<th> 6527 <p> 6528 Microsoft Visual C++ version 14.1<br> Win32<br> double 6529 </p> 6530 </th> 6531</tr></thead> 6532<tbody><tr> 6533<td> 6534 <p> 6535 Random test data 6536 </p> 6537 </td> 6538<td> 6539 <p> 6540 <span class="blue">Max = 0.992ε (Mean = 0.402ε)</span><br> <br> 6541 (<span class="emphasis"><em><cmath>:</em></span> Max = 0.992ε (Mean = 0.402ε))<br> 6542 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.992ε (Mean = 0.402ε)) 6543 </p> 6544 </td> 6545<td> 6546 <p> 6547 <span class="blue">Max = 0.793ε (Mean = 0.126ε)</span><br> <br> 6548 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 0.793ε (Mean = 0.126ε)) 6549 </p> 6550 </td> 6551<td> 6552 <p> 6553 <span class="blue">Max = 1.31ε (Mean = 0.428ε)</span><br> <br> 6554 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.996ε (Mean = 0.426ε)) 6555 </p> 6556 </td> 6557<td> 6558 <p> 6559 <span class="blue">Max = 1.31ε (Mean = 0.496ε)</span><br> <br> 6560 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.31ε (Mean = 0.496ε)) 6561 </p> 6562 </td> 6563</tr></tbody> 6564</table></div> 6565</div> 6566<br class="table-break"><div class="table"> 6567<a name="math_toolkit.logs_and_tables.all_table.table_gamma_p"></a><p class="title"><b>Table 23.47. Error rates for gamma_p</b></p> 6568<div class="table-contents"><table class="table" summary="Error rates for gamma_p"> 6569<colgroup> 6570<col> 6571<col> 6572<col> 6573<col> 6574<col> 6575</colgroup> 6576<thead><tr> 6577<th> 6578 </th> 6579<th> 6580 <p> 6581 GNU C++ version 7.1.0<br> linux<br> double 6582 </p> 6583 </th> 6584<th> 6585 <p> 6586 GNU C++ version 7.1.0<br> linux<br> long double 6587 </p> 6588 </th> 6589<th> 6590 <p> 6591 Sun compiler version 0x5150<br> Sun Solaris<br> long double 6592 </p> 6593 </th> 6594<th> 6595 <p> 6596 Microsoft Visual C++ version 14.1<br> Win32<br> double 6597 </p> 6598 </th> 6599</tr></thead> 6600<tbody> 6601<tr> 6602<td> 6603 <p> 6604 tgamma(a, z) medium values 6605 </p> 6606 </td> 6607<td> 6608 <p> 6609 <span class="blue">Max = 0.955ε (Mean = 0.05ε)</span><br> <br> 6610 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 342ε (Mean = 45.8ε))<br> (<span class="emphasis"><em>Rmath 6611 3.2.3:</em></span> Max = 389ε (Mean = 44ε)) 6612 </p> 6613 </td> 6614<td> 6615 <p> 6616 <span class="blue">Max = 41.6ε (Mean = 8.09ε)</span> 6617 </p> 6618 </td> 6619<td> 6620 <p> 6621 <span class="blue">Max = 239ε (Mean = 30.2ε)</span> 6622 </p> 6623 </td> 6624<td> 6625 <p> 6626 <span class="blue">Max = 35.1ε (Mean = 6.98ε)</span> 6627 </p> 6628 </td> 6629</tr> 6630<tr> 6631<td> 6632 <p> 6633 tgamma(a, z) small values 6634 </p> 6635 </td> 6636<td> 6637 <p> 6638 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 6639 2.1:</em></span> Max = 4.82ε (Mean = 0.758ε))<br> (<span class="emphasis"><em>Rmath 6640 3.2.3:</em></span> Max = 1.01ε (Mean = 0.306ε)) 6641 </p> 6642 </td> 6643<td> 6644 <p> 6645 <span class="blue">Max = 2ε (Mean = 0.464ε)</span> 6646 </p> 6647 </td> 6648<td> 6649 <p> 6650 <span class="blue">Max = 2ε (Mean = 0.461ε)</span> 6651 </p> 6652 </td> 6653<td> 6654 <p> 6655 <span class="blue">Max = 1.54ε (Mean = 0.439ε)</span> 6656 </p> 6657 </td> 6658</tr> 6659<tr> 6660<td> 6661 <p> 6662 tgamma(a, z) large values 6663 </p> 6664 </td> 6665<td> 6666 <p> 6667 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 6668 2.1:</em></span> Max = 1.02e+03ε (Mean = 105ε))<br> (<span class="emphasis"><em>Rmath 6669 3.2.3:</em></span> Max = 1.11e+03ε (Mean = 67.5ε)) 6670 </p> 6671 </td> 6672<td> 6673 <p> 6674 <span class="blue">Max = 3.08e+04ε (Mean = 1.86e+03ε)</span> 6675 </p> 6676 </td> 6677<td> 6678 <p> 6679 <span class="blue">Max = 3.02e+04ε (Mean = 1.91e+03ε)</span> 6680 </p> 6681 </td> 6682<td> 6683 <p> 6684 <span class="blue">Max = 243ε (Mean = 20.2ε)</span> 6685 </p> 6686 </td> 6687</tr> 6688<tr> 6689<td> 6690 <p> 6691 tgamma(a, z) integer and half integer values 6692 </p> 6693 </td> 6694<td> 6695 <p> 6696 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 6697 2.1:</em></span> Max = 128ε (Mean = 22.6ε))<br> (<span class="emphasis"><em>Rmath 6698 3.2.3:</em></span> Max = 66.2ε (Mean = 12.2ε)) 6699 </p> 6700 </td> 6701<td> 6702 <p> 6703 <span class="blue">Max = 11.8ε (Mean = 2.66ε)</span> 6704 </p> 6705 </td> 6706<td> 6707 <p> 6708 <span class="blue">Max = 71.6ε (Mean = 9.47ε)</span> 6709 </p> 6710 </td> 6711<td> 6712 <p> 6713 <span class="blue">Max = 13ε (Mean = 2.97ε)</span> 6714 </p> 6715 </td> 6716</tr> 6717</tbody> 6718</table></div> 6719</div> 6720<br class="table-break"><div class="table"> 6721<a name="math_toolkit.logs_and_tables.all_table.table_gamma_p_inv"></a><p class="title"><b>Table 23.48. Error rates for gamma_p_inv</b></p> 6722<div class="table-contents"><table class="table" summary="Error rates for gamma_p_inv"> 6723<colgroup> 6724<col> 6725<col> 6726<col> 6727<col> 6728<col> 6729</colgroup> 6730<thead><tr> 6731<th> 6732 </th> 6733<th> 6734 <p> 6735 GNU C++ version 7.1.0<br> linux<br> double 6736 </p> 6737 </th> 6738<th> 6739 <p> 6740 GNU C++ version 7.1.0<br> linux<br> long double 6741 </p> 6742 </th> 6743<th> 6744 <p> 6745 Sun compiler version 0x5150<br> Sun Solaris<br> long double 6746 </p> 6747 </th> 6748<th> 6749 <p> 6750 Microsoft Visual C++ version 14.1<br> Win32<br> double 6751 </p> 6752 </th> 6753</tr></thead> 6754<tbody> 6755<tr> 6756<td> 6757 <p> 6758 incomplete gamma inverse(a, z) medium values 6759 </p> 6760 </td> 6761<td> 6762 <p> 6763 <span class="blue">Max = 0.993ε (Mean = 0.15ε)</span><br> <br> 6764 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 4.88ε (Mean = 0.868ε)) 6765 </p> 6766 </td> 6767<td> 6768 <p> 6769 <span class="blue">Max = 1.8ε (Mean = 0.406ε)</span> 6770 </p> 6771 </td> 6772<td> 6773 <p> 6774 <span class="blue">Max = 1.89ε (Mean = 0.466ε)</span> 6775 </p> 6776 </td> 6777<td> 6778 <p> 6779 <span class="blue">Max = 1.71ε (Mean = 0.34ε)</span> 6780 </p> 6781 </td> 6782</tr> 6783<tr> 6784<td> 6785 <p> 6786 incomplete gamma inverse(a, z) large values 6787 </p> 6788 </td> 6789<td> 6790 <p> 6791 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath 6792 3.2.3:</em></span> Max = 0.816ε (Mean = 0.0874ε)) 6793 </p> 6794 </td> 6795<td> 6796 <p> 6797 <span class="blue">Max = 0.509ε (Mean = 0.0447ε)</span> 6798 </p> 6799 </td> 6800<td> 6801 <p> 6802 <span class="blue">Max = 0.509ε (Mean = 0.0447ε)</span> 6803 </p> 6804 </td> 6805<td> 6806 <p> 6807 <span class="blue">Max = 0.924ε (Mean = 0.108ε)</span> 6808 </p> 6809 </td> 6810</tr> 6811<tr> 6812<td> 6813 <p> 6814 incomplete gamma inverse(a, z) small values 6815 </p> 6816 </td> 6817<td> 6818 <p> 6819 <span class="blue">Max = 441ε (Mean = 53.9ε)</span><br> <br> 6820 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 547ε (Mean = 61.6ε)) 6821 </p> 6822 </td> 6823<td> 6824 <p> 6825 <span class="blue">Max = 9.17e+03ε (Mean = 1.45e+03ε)</span> 6826 </p> 6827 </td> 6828<td> 6829 <p> 6830 <span class="blue">Max = 1.09e+04ε (Mean = 1.3e+03ε)</span> 6831 </p> 6832 </td> 6833<td> 6834 <p> 6835 <span class="blue">Max = 1.1e+03ε (Mean = 131ε)</span> 6836 </p> 6837 </td> 6838</tr> 6839</tbody> 6840</table></div> 6841</div> 6842<br class="table-break"><div class="table"> 6843<a name="math_toolkit.logs_and_tables.all_table.table_gamma_p_inva"></a><p class="title"><b>Table 23.49. Error rates for gamma_p_inva</b></p> 6844<div class="table-contents"><table class="table" summary="Error rates for gamma_p_inva"> 6845<colgroup> 6846<col> 6847<col> 6848<col> 6849<col> 6850<col> 6851</colgroup> 6852<thead><tr> 6853<th> 6854 </th> 6855<th> 6856 <p> 6857 GNU C++ version 7.1.0<br> linux<br> double 6858 </p> 6859 </th> 6860<th> 6861 <p> 6862 GNU C++ version 7.1.0<br> linux<br> long double 6863 </p> 6864 </th> 6865<th> 6866 <p> 6867 Sun compiler version 0x5150<br> Sun Solaris<br> long double 6868 </p> 6869 </th> 6870<th> 6871 <p> 6872 Microsoft Visual C++ version 14.1<br> Win32<br> double 6873 </p> 6874 </th> 6875</tr></thead> 6876<tbody><tr> 6877<td> 6878 <p> 6879 Incomplete gamma inverses. 6880 </p> 6881 </td> 6882<td> 6883 <p> 6884 <span class="blue">Max = 0ε (Mean = 0ε)</span> 6885 </p> 6886 </td> 6887<td> 6888 <p> 6889 <span class="blue">Max = 7.87ε (Mean = 1.15ε)</span> 6890 </p> 6891 </td> 6892<td> 6893 <p> 6894 <span class="blue">Max = 4.08ε (Mean = 1.12ε)</span> 6895 </p> 6896 </td> 6897<td> 6898 <p> 6899 <span class="blue">Max = 4.92ε (Mean = 1.03ε)</span> 6900 </p> 6901 </td> 6902</tr></tbody> 6903</table></div> 6904</div> 6905<br class="table-break"><div class="table"> 6906<a name="math_toolkit.logs_and_tables.all_table.table_gamma_q"></a><p class="title"><b>Table 23.50. Error rates for gamma_q</b></p> 6907<div class="table-contents"><table class="table" summary="Error rates for gamma_q"> 6908<colgroup> 6909<col> 6910<col> 6911<col> 6912<col> 6913<col> 6914</colgroup> 6915<thead><tr> 6916<th> 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 GNU C++ version 7.1.0<br> linux<br> long double 6926 </p> 6927 </th> 6928<th> 6929 <p> 6930 Sun compiler version 0x5150<br> Sun Solaris<br> long double 6931 </p> 6932 </th> 6933<th> 6934 <p> 6935 Microsoft Visual C++ version 14.1<br> Win32<br> double 6936 </p> 6937 </th> 6938</tr></thead> 6939<tbody> 6940<tr> 6941<td> 6942 <p> 6943 tgamma(a, z) medium values 6944 </p> 6945 </td> 6946<td> 6947 <p> 6948 <span class="blue">Max = 0.927ε (Mean = 0.035ε)</span><br> <br> 6949 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 201ε (Mean = 13.5ε))<br> (<span class="emphasis"><em>Rmath 6950 3.2.3:</em></span> Max = 131ε (Mean = 12.7ε)) 6951 </p> 6952 </td> 6953<td> 6954 <p> 6955 <span class="blue">Max = 32.3ε (Mean = 6.61ε)</span> 6956 </p> 6957 </td> 6958<td> 6959 <p> 6960 <span class="blue">Max = 199ε (Mean = 26.6ε)</span> 6961 </p> 6962 </td> 6963<td> 6964 <p> 6965 <span class="blue">Max = 23.7ε (Mean = 4ε)</span> 6966 </p> 6967 </td> 6968</tr> 6969<tr> 6970<td> 6971 <p> 6972 tgamma(a, z) small values 6973 </p> 6974 </td> 6975<td> 6976 <p> 6977 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 6978 2.1:</em></span> <span class="red">Max = 1.38e+10ε (Mean = 1.05e+09ε))</span><br> 6979 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 65.6ε (Mean = 11ε)) 6980 </p> 6981 </td> 6982<td> 6983 <p> 6984 <span class="blue">Max = 2.45ε (Mean = 0.885ε)</span> 6985 </p> 6986 </td> 6987<td> 6988 <p> 6989 <span class="blue">Max = 2.45ε (Mean = 0.819ε)</span> 6990 </p> 6991 </td> 6992<td> 6993 <p> 6994 <span class="blue">Max = 2.26ε (Mean = 0.74ε)</span> 6995 </p> 6996 </td> 6997</tr> 6998<tr> 6999<td> 7000 <p> 7001 tgamma(a, z) large values 7002 </p> 7003 </td> 7004<td> 7005 <p> 7006 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 7007 2.1:</em></span> Max = 2.71e+04ε (Mean = 2.16e+03ε))<br> (<span class="emphasis"><em>Rmath 7008 3.2.3:</em></span> Max = 1.02e+03ε (Mean = 62.7ε)) 7009 </p> 7010 </td> 7011<td> 7012 <p> 7013 <span class="blue">Max = 6.82e+03ε (Mean = 414ε)</span> 7014 </p> 7015 </td> 7016<td> 7017 <p> 7018 <span class="blue">Max = 1.15e+04ε (Mean = 733ε)</span> 7019 </p> 7020 </td> 7021<td> 7022 <p> 7023 <span class="blue">Max = 469ε (Mean = 31.5ε)</span> 7024 </p> 7025 </td> 7026</tr> 7027<tr> 7028<td> 7029 <p> 7030 tgamma(a, z) integer and half integer values 7031 </p> 7032 </td> 7033<td> 7034 <p> 7035 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 7036 2.1:</em></span> Max = 118ε (Mean = 12.5ε))<br> (<span class="emphasis"><em>Rmath 7037 3.2.3:</em></span> Max = 138ε (Mean = 16.9ε)) 7038 </p> 7039 </td> 7040<td> 7041 <p> 7042 <span class="blue">Max = 11.1ε (Mean = 2.07ε)</span> 7043 </p> 7044 </td> 7045<td> 7046 <p> 7047 <span class="blue">Max = 54.7ε (Mean = 6.16ε)</span> 7048 </p> 7049 </td> 7050<td> 7051 <p> 7052 <span class="blue">Max = 8.72ε (Mean = 1.48ε)</span> 7053 </p> 7054 </td> 7055</tr> 7056</tbody> 7057</table></div> 7058</div> 7059<br class="table-break"><div class="table"> 7060<a name="math_toolkit.logs_and_tables.all_table.table_gamma_q_inv"></a><p class="title"><b>Table 23.51. Error rates for gamma_q_inv</b></p> 7061<div class="table-contents"><table class="table" summary="Error rates for gamma_q_inv"> 7062<colgroup> 7063<col> 7064<col> 7065<col> 7066<col> 7067<col> 7068</colgroup> 7069<thead><tr> 7070<th> 7071 </th> 7072<th> 7073 <p> 7074 GNU C++ version 7.1.0<br> linux<br> double 7075 </p> 7076 </th> 7077<th> 7078 <p> 7079 GNU C++ version 7.1.0<br> linux<br> long double 7080 </p> 7081 </th> 7082<th> 7083 <p> 7084 Sun compiler version 0x5150<br> Sun Solaris<br> long double 7085 </p> 7086 </th> 7087<th> 7088 <p> 7089 Microsoft Visual C++ version 14.1<br> Win32<br> double 7090 </p> 7091 </th> 7092</tr></thead> 7093<tbody> 7094<tr> 7095<td> 7096 <p> 7097 incomplete gamma inverse(a, z) medium values 7098 </p> 7099 </td> 7100<td> 7101 <p> 7102 <span class="blue">Max = 0.912ε (Mean = 0.154ε)</span><br> <br> 7103 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 4.66ε (Mean = 0.792ε)) 7104 </p> 7105 </td> 7106<td> 7107 <p> 7108 <span class="blue">Max = 6.2ε (Mean = 0.627ε)</span> 7109 </p> 7110 </td> 7111<td> 7112 <p> 7113 <span class="blue">Max = 6.2ε (Mean = 0.683ε)</span> 7114 </p> 7115 </td> 7116<td> 7117 <p> 7118 <span class="blue">Max = 2.88ε (Mean = 0.469ε)</span> 7119 </p> 7120 </td> 7121</tr> 7122<tr> 7123<td> 7124 <p> 7125 incomplete gamma inverse(a, z) large values 7126 </p> 7127 </td> 7128<td> 7129 <p> 7130 <span class="blue">Max = 0.894ε (Mean = 0.0915ε)</span><br> 7131 <br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 0.894ε (Mean = 0.106ε)) 7132 </p> 7133 </td> 7134<td> 7135 <p> 7136 <span class="blue">Max = 0ε (Mean = 0ε)</span> 7137 </p> 7138 </td> 7139<td> 7140 <p> 7141 <span class="blue">Max = 0ε (Mean = 0ε)</span> 7142 </p> 7143 </td> 7144<td> 7145 <p> 7146 <span class="blue">Max = 0.814ε (Mean = 0.0856ε)</span> 7147 </p> 7148 </td> 7149</tr> 7150<tr> 7151<td> 7152 <p> 7153 incomplete gamma inverse(a, z) small values 7154 </p> 7155 </td> 7156<td> 7157 <p> 7158 <span class="blue">Max = 292ε (Mean = 36.4ε)</span><br> <br> 7159 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 415ε (Mean = 48.7ε)) 7160 </p> 7161 </td> 7162<td> 7163 <p> 7164 <span class="blue">Max = 8.28e+03ε (Mean = 1.09e+03ε)</span> 7165 </p> 7166 </td> 7167<td> 7168 <p> 7169 <span class="blue">Max = 8.98e+03ε (Mean = 877ε)</span> 7170 </p> 7171 </td> 7172<td> 7173 <p> 7174 <span class="blue">Max = 451ε (Mean = 64.7ε)</span> 7175 </p> 7176 </td> 7177</tr> 7178</tbody> 7179</table></div> 7180</div> 7181<br class="table-break"><div class="table"> 7182<a name="math_toolkit.logs_and_tables.all_table.table_gamma_q_inva"></a><p class="title"><b>Table 23.52. Error rates for gamma_q_inva</b></p> 7183<div class="table-contents"><table class="table" summary="Error rates for gamma_q_inva"> 7184<colgroup> 7185<col> 7186<col> 7187<col> 7188<col> 7189<col> 7190</colgroup> 7191<thead><tr> 7192<th> 7193 </th> 7194<th> 7195 <p> 7196 GNU C++ version 7.1.0<br> linux<br> double 7197 </p> 7198 </th> 7199<th> 7200 <p> 7201 GNU C++ version 7.1.0<br> linux<br> long double 7202 </p> 7203 </th> 7204<th> 7205 <p> 7206 Sun compiler version 0x5150<br> Sun Solaris<br> long double 7207 </p> 7208 </th> 7209<th> 7210 <p> 7211 Microsoft Visual C++ version 14.1<br> Win32<br> double 7212 </p> 7213 </th> 7214</tr></thead> 7215<tbody><tr> 7216<td> 7217 <p> 7218 Incomplete gamma inverses. 7219 </p> 7220 </td> 7221<td> 7222 <p> 7223 <span class="blue">Max = 0ε (Mean = 0ε)</span> 7224 </p> 7225 </td> 7226<td> 7227 <p> 7228 <span class="blue">Max = 8.42ε (Mean = 1.3ε)</span> 7229 </p> 7230 </td> 7231<td> 7232 <p> 7233 <span class="blue">Max = 7.86ε (Mean = 1.24ε)</span> 7234 </p> 7235 </td> 7236<td> 7237 <p> 7238 <span class="blue">Max = 5.05ε (Mean = 1.08ε)</span> 7239 </p> 7240 </td> 7241</tr></tbody> 7242</table></div> 7243</div> 7244<br class="table-break"><div class="table"> 7245<a name="math_toolkit.logs_and_tables.all_table.table_hermite"></a><p class="title"><b>Table 23.53. Error rates for hermite</b></p> 7246<div class="table-contents"><table class="table" summary="Error rates for hermite"> 7247<colgroup> 7248<col> 7249<col> 7250<col> 7251<col> 7252<col> 7253</colgroup> 7254<thead><tr> 7255<th> 7256 </th> 7257<th> 7258 <p> 7259 GNU C++ version 7.1.0<br> linux<br> double 7260 </p> 7261 </th> 7262<th> 7263 <p> 7264 GNU C++ version 7.1.0<br> linux<br> long double 7265 </p> 7266 </th> 7267<th> 7268 <p> 7269 Sun compiler version 0x5150<br> Sun Solaris<br> long double 7270 </p> 7271 </th> 7272<th> 7273 <p> 7274 Microsoft Visual C++ version 14.1<br> Win32<br> double 7275 </p> 7276 </th> 7277</tr></thead> 7278<tbody><tr> 7279<td> 7280 <p> 7281 Hermite Polynomials 7282 </p> 7283 </td> 7284<td> 7285 <p> 7286 <span class="blue">Max = 0ε (Mean = 0ε)</span> 7287 </p> 7288 </td> 7289<td> 7290 <p> 7291 <span class="blue">Max = 6.24ε (Mean = 2.07ε)</span> 7292 </p> 7293 </td> 7294<td> 7295 <p> 7296 <span class="blue">Max = 6.24ε (Mean = 2.07ε)</span> 7297 </p> 7298 </td> 7299<td> 7300 <p> 7301 <span class="blue">Max = 4.46ε (Mean = 1.41ε)</span> 7302 </p> 7303 </td> 7304</tr></tbody> 7305</table></div> 7306</div> 7307<br class="table-break"><div class="table"> 7308<a name="math_toolkit.logs_and_tables.all_table.table_heuman_lambda"></a><p class="title"><b>Table 23.54. Error rates for heuman_lambda</b></p> 7309<div class="table-contents"><table class="table" summary="Error rates for heuman_lambda"> 7310<colgroup> 7311<col> 7312<col> 7313<col> 7314<col> 7315<col> 7316</colgroup> 7317<thead><tr> 7318<th> 7319 </th> 7320<th> 7321 <p> 7322 GNU C++ version 7.1.0<br> linux<br> double 7323 </p> 7324 </th> 7325<th> 7326 <p> 7327 GNU C++ version 7.1.0<br> linux<br> long double 7328 </p> 7329 </th> 7330<th> 7331 <p> 7332 Sun compiler version 0x5150<br> Sun Solaris<br> long double 7333 </p> 7334 </th> 7335<th> 7336 <p> 7337 Microsoft Visual C++ version 14.1<br> Win32<br> double 7338 </p> 7339 </th> 7340</tr></thead> 7341<tbody> 7342<tr> 7343<td> 7344 <p> 7345 Elliptic Integral Jacobi Zeta: Mathworld Data 7346 </p> 7347 </td> 7348<td> 7349 <p> 7350 <span class="blue">Max = 0ε (Mean = 0ε)</span> 7351 </p> 7352 </td> 7353<td> 7354 <p> 7355 <span class="blue">Max = 1.89ε (Mean = 0.887ε)</span> 7356 </p> 7357 </td> 7358<td> 7359 <p> 7360 <span class="blue">Max = 1.89ε (Mean = 0.887ε)</span> 7361 </p> 7362 </td> 7363<td> 7364 <p> 7365 <span class="blue">Max = 1.08ε (Mean = 0.734ε)</span> 7366 </p> 7367 </td> 7368</tr> 7369<tr> 7370<td> 7371 <p> 7372 Elliptic Integral Heuman Lambda: Random Data 7373 </p> 7374 </td> 7375<td> 7376 <p> 7377 <span class="blue">Max = 0ε (Mean = 0ε)</span> 7378 </p> 7379 </td> 7380<td> 7381 <p> 7382 <span class="blue">Max = 3.82ε (Mean = 0.609ε)</span> 7383 </p> 7384 </td> 7385<td> 7386 <p> 7387 <span class="blue">Max = 3.82ε (Mean = 0.608ε)</span> 7388 </p> 7389 </td> 7390<td> 7391 <p> 7392 <span class="blue">Max = 2.12ε (Mean = 0.588ε)</span> 7393 </p> 7394 </td> 7395</tr> 7396</tbody> 7397</table></div> 7398</div> 7399<br class="table-break"><div class="table"> 7400<a name="math_toolkit.logs_and_tables.all_table.table_ibeta"></a><p class="title"><b>Table 23.55. Error rates for ibeta</b></p> 7401<div class="table-contents"><table class="table" summary="Error rates for ibeta"> 7402<colgroup> 7403<col> 7404<col> 7405<col> 7406<col> 7407<col> 7408</colgroup> 7409<thead><tr> 7410<th> 7411 </th> 7412<th> 7413 <p> 7414 GNU C++ version 7.1.0<br> linux<br> double 7415 </p> 7416 </th> 7417<th> 7418 <p> 7419 GNU C++ version 7.1.0<br> linux<br> long double 7420 </p> 7421 </th> 7422<th> 7423 <p> 7424 Sun compiler version 0x5150<br> Sun Solaris<br> long double 7425 </p> 7426 </th> 7427<th> 7428 <p> 7429 Microsoft Visual C++ version 14.1<br> Win32<br> double 7430 </p> 7431 </th> 7432</tr></thead> 7433<tbody> 7434<tr> 7435<td> 7436 <p> 7437 Incomplete Beta Function: Small Values 7438 </p> 7439 </td> 7440<td> 7441 <p> 7442 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 7443 2.1:</em></span> Max = 682ε (Mean = 32.6ε))<br> (<span class="emphasis"><em>Rmath 7444 3.2.3:</em></span> Max = 22.9ε (Mean = 3.35ε)) 7445 </p> 7446 </td> 7447<td> 7448 <p> 7449 <span class="blue">Max = 8.97ε (Mean = 2.09ε)</span> 7450 </p> 7451 </td> 7452<td> 7453 <p> 7454 <span class="blue">Max = 21.3ε (Mean = 2.75ε)</span> 7455 </p> 7456 </td> 7457<td> 7458 <p> 7459 <span class="blue">Max = 8.4ε (Mean = 1.93ε)</span> 7460 </p> 7461 </td> 7462</tr> 7463<tr> 7464<td> 7465 <p> 7466 Incomplete Beta Function: Medium Values 7467 </p> 7468 </td> 7469<td> 7470 <p> 7471 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 7472 2.1:</em></span> Max = 690ε (Mean = 151ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 7473 Max = 232ε (Mean = 27.9ε)) 7474 </p> 7475 </td> 7476<td> 7477 <p> 7478 <span class="blue">Max = 50ε (Mean = 12.1ε)</span> 7479 </p> 7480 </td> 7481<td> 7482 <p> 7483 <span class="blue">Max = 124ε (Mean = 18.4ε)</span> 7484 </p> 7485 </td> 7486<td> 7487 <p> 7488 <span class="blue">Max = 106ε (Mean = 16.3ε)</span> 7489 </p> 7490 </td> 7491</tr> 7492<tr> 7493<td> 7494 <p> 7495 Incomplete Beta Function: Large and Diverse Values 7496 </p> 7497 </td> 7498<td> 7499 <p> 7500 <span class="blue">Max = 1.26ε (Mean = 0.063ε)</span><br> <br> 7501 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.9e+05ε (Mean = 1.82e+04ε) 7502 <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_ibeta_GSL_2_1_Incomplete_Beta_Function_Large_and_Diverse_Values">And 7503 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 7504 Max = 574ε (Mean = 49.4ε)) 7505 </p> 7506 </td> 7507<td> 7508 <p> 7509 <span class="blue">Max = 1.96e+04ε (Mean = 997ε)</span> 7510 </p> 7511 </td> 7512<td> 7513 <p> 7514 <span class="blue">Max = 4.98e+04ε (Mean = 2.07e+03ε)</span> 7515 </p> 7516 </td> 7517<td> 7518 <p> 7519 <span class="blue">Max = 1.32e+03ε (Mean = 68.5ε)</span> 7520 </p> 7521 </td> 7522</tr> 7523<tr> 7524<td> 7525 <p> 7526 Incomplete Beta Function: Small Integer Values 7527 </p> 7528 </td> 7529<td> 7530 <p> 7531 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 7532 2.1:</em></span> Max = 254ε (Mean = 50.9ε))<br> (<span class="emphasis"><em>Rmath 7533 3.2.3:</em></span> Max = 62.2ε (Mean = 8.95ε)) 7534 </p> 7535 </td> 7536<td> 7537 <p> 7538 <span class="blue">Max = 4.45ε (Mean = 0.814ε)</span> 7539 </p> 7540 </td> 7541<td> 7542 <p> 7543 <span class="blue">Max = 44.5ε (Mean = 10.1ε)</span> 7544 </p> 7545 </td> 7546<td> 7547 <p> 7548 <span class="blue">Max = 3.85ε (Mean = 0.791ε)</span> 7549 </p> 7550 </td> 7551</tr> 7552</tbody> 7553</table></div> 7554</div> 7555<br class="table-break"><div class="table"> 7556<a name="math_toolkit.logs_and_tables.all_table.table_ibeta_inv"></a><p class="title"><b>Table 23.56. Error rates for ibeta_inv</b></p> 7557<div class="table-contents"><table class="table" summary="Error rates for ibeta_inv"> 7558<colgroup> 7559<col> 7560<col> 7561<col> 7562<col> 7563<col> 7564</colgroup> 7565<thead><tr> 7566<th> 7567 </th> 7568<th> 7569 <p> 7570 GNU C++ version 7.1.0<br> linux<br> double 7571 </p> 7572 </th> 7573<th> 7574 <p> 7575 GNU C++ version 7.1.0<br> linux<br> long double 7576 </p> 7577 </th> 7578<th> 7579 <p> 7580 Sun compiler version 0x5150<br> Sun Solaris<br> long double 7581 </p> 7582 </th> 7583<th> 7584 <p> 7585 Microsoft Visual C++ version 14.1<br> Win32<br> double 7586 </p> 7587 </th> 7588</tr></thead> 7589<tbody><tr> 7590<td> 7591 <p> 7592 Inverse incomplete beta 7593 </p> 7594 </td> 7595<td> 7596 <p> 7597 <span class="blue">Max = 11ε (Mean = 0.345ε)</span><br> <br> 7598 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 1.14e+121ε (Mean 7599 = 3.28e+119ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_ibeta_inv_Rmath_3_2_3_Inverse_incomplete_beta">And 7600 other failures.</a>)</span> 7601 </p> 7602 </td> 7603<td> 7604 <p> 7605 <span class="blue">Max = 3.8e+04ε (Mean = 2.66e+03ε)</span> 7606 </p> 7607 </td> 7608<td> 7609 <p> 7610 <span class="blue">Max = 4.07e+04ε (Mean = 2.86e+03ε)</span> 7611 </p> 7612 </td> 7613<td> 7614 <p> 7615 <span class="blue">Max = 8.59e+03ε (Mean = 277ε)</span> 7616 </p> 7617 </td> 7618</tr></tbody> 7619</table></div> 7620</div> 7621<br class="table-break"><div class="table"> 7622<a name="math_toolkit.logs_and_tables.all_table.table_ibeta_inva"></a><p class="title"><b>Table 23.57. Error rates for ibeta_inva</b></p> 7623<div class="table-contents"><table class="table" summary="Error rates for ibeta_inva"> 7624<colgroup> 7625<col> 7626<col> 7627<col> 7628<col> 7629<col> 7630</colgroup> 7631<thead><tr> 7632<th> 7633 </th> 7634<th> 7635 <p> 7636 GNU C++ version 7.1.0<br> linux<br> double 7637 </p> 7638 </th> 7639<th> 7640 <p> 7641 GNU C++ version 7.1.0<br> linux<br> long double 7642 </p> 7643 </th> 7644<th> 7645 <p> 7646 Sun compiler version 0x5150<br> Sun Solaris<br> long double 7647 </p> 7648 </th> 7649<th> 7650 <p> 7651 Microsoft Visual C++ version 14.1<br> Win32<br> double 7652 </p> 7653 </th> 7654</tr></thead> 7655<tbody><tr> 7656<td> 7657 <p> 7658 Inverse incomplete beta 7659 </p> 7660 </td> 7661<td> 7662 <p> 7663 <span class="blue">Max = 0.602ε (Mean = 0.0239ε)</span> 7664 </p> 7665 </td> 7666<td> 7667 <p> 7668 <span class="blue">Max = 377ε (Mean = 24.4ε)</span> 7669 </p> 7670 </td> 7671<td> 7672 <p> 7673 <span class="blue">Max = 438ε (Mean = 31.3ε)</span> 7674 </p> 7675 </td> 7676<td> 7677 <p> 7678 <span class="blue">Max = 242ε (Mean = 22.9ε)</span> 7679 </p> 7680 </td> 7681</tr></tbody> 7682</table></div> 7683</div> 7684<br class="table-break"><div class="table"> 7685<a name="math_toolkit.logs_and_tables.all_table.table_ibeta_invb"></a><p class="title"><b>Table 23.58. Error rates for ibeta_invb</b></p> 7686<div class="table-contents"><table class="table" summary="Error rates for ibeta_invb"> 7687<colgroup> 7688<col> 7689<col> 7690<col> 7691<col> 7692<col> 7693</colgroup> 7694<thead><tr> 7695<th> 7696 </th> 7697<th> 7698 <p> 7699 GNU C++ version 7.1.0<br> linux<br> double 7700 </p> 7701 </th> 7702<th> 7703 <p> 7704 GNU C++ version 7.1.0<br> linux<br> long double 7705 </p> 7706 </th> 7707<th> 7708 <p> 7709 Sun compiler version 0x5150<br> Sun Solaris<br> long double 7710 </p> 7711 </th> 7712<th> 7713 <p> 7714 Microsoft Visual C++ version 14.1<br> Win32<br> double 7715 </p> 7716 </th> 7717</tr></thead> 7718<tbody><tr> 7719<td> 7720 <p> 7721 Inverse incomplete beta 7722 </p> 7723 </td> 7724<td> 7725 <p> 7726 <span class="blue">Max = 0.765ε (Mean = 0.0422ε)</span> 7727 </p> 7728 </td> 7729<td> 7730 <p> 7731 <span class="blue">Max = 407ε (Mean = 27.2ε)</span> 7732 </p> 7733 </td> 7734<td> 7735 <p> 7736 <span class="blue">Max = 407ε (Mean = 24.4ε)</span> 7737 </p> 7738 </td> 7739<td> 7740 <p> 7741 <span class="blue">Max = 409ε (Mean = 19.3ε)</span> 7742 </p> 7743 </td> 7744</tr></tbody> 7745</table></div> 7746</div> 7747<br class="table-break"><div class="table"> 7748<a name="math_toolkit.logs_and_tables.all_table.table_ibetac"></a><p class="title"><b>Table 23.59. Error rates for ibetac</b></p> 7749<div class="table-contents"><table class="table" summary="Error rates for ibetac"> 7750<colgroup> 7751<col> 7752<col> 7753<col> 7754<col> 7755<col> 7756</colgroup> 7757<thead><tr> 7758<th> 7759 </th> 7760<th> 7761 <p> 7762 GNU C++ version 7.1.0<br> linux<br> double 7763 </p> 7764 </th> 7765<th> 7766 <p> 7767 GNU C++ version 7.1.0<br> linux<br> long double 7768 </p> 7769 </th> 7770<th> 7771 <p> 7772 Sun compiler version 0x5150<br> Sun Solaris<br> long double 7773 </p> 7774 </th> 7775<th> 7776 <p> 7777 Microsoft Visual C++ version 14.1<br> Win32<br> double 7778 </p> 7779 </th> 7780</tr></thead> 7781<tbody> 7782<tr> 7783<td> 7784 <p> 7785 Incomplete Beta Function: Small Values 7786 </p> 7787 </td> 7788<td> 7789 <p> 7790 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath 7791 3.2.3:</em></span> Max = 22.4ε (Mean = 3.67ε)) 7792 </p> 7793 </td> 7794<td> 7795 <p> 7796 <span class="blue">Max = 10.6ε (Mean = 2.22ε)</span> 7797 </p> 7798 </td> 7799<td> 7800 <p> 7801 <span class="blue">Max = 13.8ε (Mean = 2.68ε)</span> 7802 </p> 7803 </td> 7804<td> 7805 <p> 7806 <span class="blue">Max = 6.94ε (Mean = 1.71ε)</span> 7807 </p> 7808 </td> 7809</tr> 7810<tr> 7811<td> 7812 <p> 7813 Incomplete Beta Function: Medium Values 7814 </p> 7815 </td> 7816<td> 7817 <p> 7818 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath 7819 3.2.3:</em></span> Max = 204ε (Mean = 25.8ε)) 7820 </p> 7821 </td> 7822<td> 7823 <p> 7824 <span class="blue">Max = 73.9ε (Mean = 11.2ε)</span> 7825 </p> 7826 </td> 7827<td> 7828 <p> 7829 <span class="blue">Max = 132ε (Mean = 19.8ε)</span> 7830 </p> 7831 </td> 7832<td> 7833 <p> 7834 <span class="blue">Max = 56.7ε (Mean = 14.3ε)</span> 7835 </p> 7836 </td> 7837</tr> 7838<tr> 7839<td> 7840 <p> 7841 Incomplete Beta Function: Large and Diverse Values 7842 </p> 7843 </td> 7844<td> 7845 <p> 7846 <span class="blue">Max = 0.981ε (Mean = 0.0573ε)</span><br> 7847 <br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 889ε (Mean = 68.4ε)) 7848 </p> 7849 </td> 7850<td> 7851 <p> 7852 <span class="blue">Max = 3.45e+04ε (Mean = 1.32e+03ε)</span> 7853 </p> 7854 </td> 7855<td> 7856 <p> 7857 <span class="blue">Max = 6.31e+04ε (Mean = 2.04e+03ε)</span> 7858 </p> 7859 </td> 7860<td> 7861 <p> 7862 <span class="blue">Max = 1.88e+03ε (Mean = 82.7ε)</span> 7863 </p> 7864 </td> 7865</tr> 7866<tr> 7867<td> 7868 <p> 7869 Incomplete Beta Function: Small Integer Values 7870 </p> 7871 </td> 7872<td> 7873 <p> 7874 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath 7875 3.2.3:</em></span> Max = 84.6ε (Mean = 18ε)) 7876 </p> 7877 </td> 7878<td> 7879 <p> 7880 <span class="blue">Max = 5.34ε (Mean = 1.11ε)</span> 7881 </p> 7882 </td> 7883<td> 7884 <p> 7885 <span class="blue">Max = 107ε (Mean = 17.1ε)</span> 7886 </p> 7887 </td> 7888<td> 7889 <p> 7890 <span class="blue">Max = 6.37ε (Mean = 1.03ε)</span> 7891 </p> 7892 </td> 7893</tr> 7894</tbody> 7895</table></div> 7896</div> 7897<br class="table-break"><div class="table"> 7898<a name="math_toolkit.logs_and_tables.all_table.table_ibetac_inv"></a><p class="title"><b>Table 23.60. Error rates for ibetac_inv</b></p> 7899<div class="table-contents"><table class="table" summary="Error rates for ibetac_inv"> 7900<colgroup> 7901<col> 7902<col> 7903<col> 7904<col> 7905<col> 7906</colgroup> 7907<thead><tr> 7908<th> 7909 </th> 7910<th> 7911 <p> 7912 GNU C++ version 7.1.0<br> linux<br> double 7913 </p> 7914 </th> 7915<th> 7916 <p> 7917 GNU C++ version 7.1.0<br> linux<br> long double 7918 </p> 7919 </th> 7920<th> 7921 <p> 7922 Sun compiler version 0x5150<br> Sun Solaris<br> long double 7923 </p> 7924 </th> 7925<th> 7926 <p> 7927 Microsoft Visual C++ version 14.1<br> Win32<br> double 7928 </p> 7929 </th> 7930</tr></thead> 7931<tbody><tr> 7932<td> 7933 <p> 7934 Inverse incomplete beta 7935 </p> 7936 </td> 7937<td> 7938 <p> 7939 <span class="blue">Max = 0.977ε (Mean = 0.0976ε)</span><br> 7940 <br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max 7941 = 3.01e+132ε (Mean = 8.65e+130ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_ibetac_inv_Rmath_3_2_3_Inverse_incomplete_beta">And 7942 other failures.</a>)</span> 7943 </p> 7944 </td> 7945<td> 7946 <p> 7947 <span class="blue">Max = 4.88e+04ε (Mean = 3.16e+03ε)</span> 7948 </p> 7949 </td> 7950<td> 7951 <p> 7952 <span class="blue">Max = 5.05e+04ε (Mean = 3.33e+03ε)</span> 7953 </p> 7954 </td> 7955<td> 7956 <p> 7957 <span class="blue">Max = 2.93e+03ε (Mean = 198ε)</span> 7958 </p> 7959 </td> 7960</tr></tbody> 7961</table></div> 7962</div> 7963<br class="table-break"><div class="table"> 7964<a name="math_toolkit.logs_and_tables.all_table.table_ibetac_inva"></a><p class="title"><b>Table 23.61. Error rates for ibetac_inva</b></p> 7965<div class="table-contents"><table class="table" summary="Error rates for ibetac_inva"> 7966<colgroup> 7967<col> 7968<col> 7969<col> 7970<col> 7971<col> 7972</colgroup> 7973<thead><tr> 7974<th> 7975 </th> 7976<th> 7977 <p> 7978 GNU C++ version 7.1.0<br> linux<br> double 7979 </p> 7980 </th> 7981<th> 7982 <p> 7983 GNU C++ version 7.1.0<br> linux<br> long double 7984 </p> 7985 </th> 7986<th> 7987 <p> 7988 Sun compiler version 0x5150<br> Sun Solaris<br> long double 7989 </p> 7990 </th> 7991<th> 7992 <p> 7993 Microsoft Visual C++ version 14.1<br> Win32<br> double 7994 </p> 7995 </th> 7996</tr></thead> 7997<tbody><tr> 7998<td> 7999 <p> 8000 Inverse incomplete beta 8001 </p> 8002 </td> 8003<td> 8004 <p> 8005 <span class="blue">Max = 0.683ε (Mean = 0.0314ε)</span> 8006 </p> 8007 </td> 8008<td> 8009 <p> 8010 <span class="blue">Max = 382ε (Mean = 22.2ε)</span> 8011 </p> 8012 </td> 8013<td> 8014 <p> 8015 <span class="blue">Max = 315ε (Mean = 23.7ε)</span> 8016 </p> 8017 </td> 8018<td> 8019 <p> 8020 <span class="blue">Max = 408ε (Mean = 26.7ε)</span> 8021 </p> 8022 </td> 8023</tr></tbody> 8024</table></div> 8025</div> 8026<br class="table-break"><div class="table"> 8027<a name="math_toolkit.logs_and_tables.all_table.table_ibetac_invb"></a><p class="title"><b>Table 23.62. Error rates for ibetac_invb</b></p> 8028<div class="table-contents"><table class="table" summary="Error rates for ibetac_invb"> 8029<colgroup> 8030<col> 8031<col> 8032<col> 8033<col> 8034<col> 8035</colgroup> 8036<thead><tr> 8037<th> 8038 </th> 8039<th> 8040 <p> 8041 GNU C++ version 7.1.0<br> linux<br> double 8042 </p> 8043 </th> 8044<th> 8045 <p> 8046 GNU C++ version 7.1.0<br> linux<br> long double 8047 </p> 8048 </th> 8049<th> 8050 <p> 8051 Sun compiler version 0x5150<br> Sun Solaris<br> long double 8052 </p> 8053 </th> 8054<th> 8055 <p> 8056 Microsoft Visual C++ version 14.1<br> Win32<br> double 8057 </p> 8058 </th> 8059</tr></thead> 8060<tbody><tr> 8061<td> 8062 <p> 8063 Inverse incomplete beta 8064 </p> 8065 </td> 8066<td> 8067 <p> 8068 <span class="blue">Max = 0.724ε (Mean = 0.0303ε)</span> 8069 </p> 8070 </td> 8071<td> 8072 <p> 8073 <span class="blue">Max = 317ε (Mean = 19.8ε)</span> 8074 </p> 8075 </td> 8076<td> 8077 <p> 8078 <span class="blue">Max = 369ε (Mean = 22.6ε)</span> 8079 </p> 8080 </td> 8081<td> 8082 <p> 8083 <span class="blue">Max = 271ε (Mean = 16.4ε)</span> 8084 </p> 8085 </td> 8086</tr></tbody> 8087</table></div> 8088</div> 8089<br class="table-break"><div class="table"> 8090<a name="math_toolkit.logs_and_tables.all_table.table_jacobi_cn"></a><p class="title"><b>Table 23.63. Error rates for jacobi_cn</b></p> 8091<div class="table-contents"><table class="table" summary="Error rates for jacobi_cn"> 8092<colgroup> 8093<col> 8094<col> 8095<col> 8096<col> 8097<col> 8098</colgroup> 8099<thead><tr> 8100<th> 8101 </th> 8102<th> 8103 <p> 8104 GNU C++ version 7.1.0<br> linux<br> double 8105 </p> 8106 </th> 8107<th> 8108 <p> 8109 GNU C++ version 7.1.0<br> linux<br> long double 8110 </p> 8111 </th> 8112<th> 8113 <p> 8114 Sun compiler version 0x5150<br> Sun Solaris<br> long double 8115 </p> 8116 </th> 8117<th> 8118 <p> 8119 Microsoft Visual C++ version 14.1<br> Win32<br> double 8120 </p> 8121 </th> 8122</tr></thead> 8123<tbody> 8124<tr> 8125<td> 8126 <p> 8127 Jacobi Elliptic: Mathworld Data 8128 </p> 8129 </td> 8130<td> 8131 <p> 8132 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 8133 2.1:</em></span> Max = 17.3ε (Mean = 4.29ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data">And 8134 other failures.</a>) 8135 </p> 8136 </td> 8137<td> 8138 <p> 8139 <span class="blue">Max = 71.6ε (Mean = 19.3ε)</span> 8140 </p> 8141 </td> 8142<td> 8143 <p> 8144 <span class="blue">Max = 71.6ε (Mean = 19.4ε)</span> 8145 </p> 8146 </td> 8147<td> 8148 <p> 8149 <span class="blue">Max = 45.8ε (Mean = 11.4ε)</span> 8150 </p> 8151 </td> 8152</tr> 8153<tr> 8154<td> 8155 <p> 8156 Jacobi Elliptic: Random Data 8157 </p> 8158 </td> 8159<td> 8160 <p> 8161 <span class="blue">Max = 0.816ε (Mean = 0.0563ε)</span><br> 8162 <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.43ε (Mean = 0.803ε)) 8163 </p> 8164 </td> 8165<td> 8166 <p> 8167 <span class="blue">Max = 1.68ε (Mean = 0.443ε)</span> 8168 </p> 8169 </td> 8170<td> 8171 <p> 8172 <span class="blue">Max = 1.68ε (Mean = 0.454ε)</span> 8173 </p> 8174 </td> 8175<td> 8176 <p> 8177 <span class="blue">Max = 1.83ε (Mean = 0.455ε)</span> 8178 </p> 8179 </td> 8180</tr> 8181<tr> 8182<td> 8183 <p> 8184 Jacobi Elliptic: Random Small Values 8185 </p> 8186 </td> 8187<td> 8188 <p> 8189 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 8190 2.1:</em></span> Max = 55.2ε (Mean = 1.64ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values">And 8191 other failures.</a>) 8192 </p> 8193 </td> 8194<td> 8195 <p> 8196 <span class="blue">Max = 10.4ε (Mean = 0.594ε)</span> 8197 </p> 8198 </td> 8199<td> 8200 <p> 8201 <span class="blue">Max = 10.4ε (Mean = 0.602ε)</span> 8202 </p> 8203 </td> 8204<td> 8205 <p> 8206 <span class="blue">Max = 26.2ε (Mean = 1.17ε)</span> 8207 </p> 8208 </td> 8209</tr> 8210<tr> 8211<td> 8212 <p> 8213 Jacobi Elliptic: Modulus near 1 8214 </p> 8215 </td> 8216<td> 8217 <p> 8218 <span class="blue">Max = 0.919ε (Mean = 0.127ε)</span><br> <br> 8219 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0ε (Mean = 0ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1">And 8220 other failures.</a>) 8221 </p> 8222 </td> 8223<td> 8224 <p> 8225 <span class="blue">Max = 675ε (Mean = 87.1ε)</span> 8226 </p> 8227 </td> 8228<td> 8229 <p> 8230 <span class="blue">Max = 675ε (Mean = 86.8ε)</span> 8231 </p> 8232 </td> 8233<td> 8234 <p> 8235 <span class="blue">Max = 513ε (Mean = 126ε)</span> 8236 </p> 8237 </td> 8238</tr> 8239<tr> 8240<td> 8241 <p> 8242 Jacobi Elliptic: Large Phi 8243 </p> 8244 </td> 8245<td> 8246 <p> 8247 <span class="blue">Max = 14.2ε (Mean = 0.927ε)</span><br> <br> 8248 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 5.92e+03ε (Mean = 477ε)) 8249 </p> 8250 </td> 8251<td> 8252 <p> 8253 <span class="blue">Max = 2.97e+04ε (Mean = 1.9e+03ε)</span> 8254 </p> 8255 </td> 8256<td> 8257 <p> 8258 <span class="blue">Max = 2.97e+04ε (Mean = 1.9e+03ε)</span> 8259 </p> 8260 </td> 8261<td> 8262 <p> 8263 <span class="blue">Max = 3.27e+04ε (Mean = 1.93e+03ε)</span> 8264 </p> 8265 </td> 8266</tr> 8267</tbody> 8268</table></div> 8269</div> 8270<br class="table-break"><div class="table"> 8271<a name="math_toolkit.logs_and_tables.all_table.table_jacobi_dn"></a><p class="title"><b>Table 23.64. Error rates for jacobi_dn</b></p> 8272<div class="table-contents"><table class="table" summary="Error rates for jacobi_dn"> 8273<colgroup> 8274<col> 8275<col> 8276<col> 8277<col> 8278<col> 8279</colgroup> 8280<thead><tr> 8281<th> 8282 </th> 8283<th> 8284 <p> 8285 GNU C++ version 7.1.0<br> linux<br> double 8286 </p> 8287 </th> 8288<th> 8289 <p> 8290 GNU C++ version 7.1.0<br> linux<br> long double 8291 </p> 8292 </th> 8293<th> 8294 <p> 8295 Sun compiler version 0x5150<br> Sun Solaris<br> long double 8296 </p> 8297 </th> 8298<th> 8299 <p> 8300 Microsoft Visual C++ version 14.1<br> Win32<br> double 8301 </p> 8302 </th> 8303</tr></thead> 8304<tbody> 8305<tr> 8306<td> 8307 <p> 8308 Jacobi Elliptic: Mathworld Data 8309 </p> 8310 </td> 8311<td> 8312 <p> 8313 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 8314 2.1:</em></span> Max = 2.82ε (Mean = 1.18ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data">And 8315 other failures.</a>) 8316 </p> 8317 </td> 8318<td> 8319 <p> 8320 <span class="blue">Max = 49ε (Mean = 14ε)</span> 8321 </p> 8322 </td> 8323<td> 8324 <p> 8325 <span class="blue">Max = 49ε (Mean = 14ε)</span> 8326 </p> 8327 </td> 8328<td> 8329 <p> 8330 <span class="blue">Max = 34.3ε (Mean = 8.71ε)</span> 8331 </p> 8332 </td> 8333</tr> 8334<tr> 8335<td> 8336 <p> 8337 Jacobi Elliptic: Random Data 8338 </p> 8339 </td> 8340<td> 8341 <p> 8342 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 8343 2.1:</em></span> Max = 3ε (Mean = 0.61ε)) 8344 </p> 8345 </td> 8346<td> 8347 <p> 8348 <span class="blue">Max = 1.53ε (Mean = 0.473ε)</span> 8349 </p> 8350 </td> 8351<td> 8352 <p> 8353 <span class="blue">Max = 1.53ε (Mean = 0.481ε)</span> 8354 </p> 8355 </td> 8356<td> 8357 <p> 8358 <span class="blue">Max = 1.52ε (Mean = 0.466ε)</span> 8359 </p> 8360 </td> 8361</tr> 8362<tr> 8363<td> 8364 <p> 8365 Jacobi Elliptic: Random Small Values 8366 </p> 8367 </td> 8368<td> 8369 <p> 8370 <span class="blue">Max = 0.5ε (Mean = 0.0122ε)</span><br> <br> 8371 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.5ε (Mean = 0.391ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values">And 8372 other failures.</a>) 8373 </p> 8374 </td> 8375<td> 8376 <p> 8377 <span class="blue">Max = 22.4ε (Mean = 0.777ε)</span> 8378 </p> 8379 </td> 8380<td> 8381 <p> 8382 <span class="blue">Max = 22.4ε (Mean = 0.763ε)</span> 8383 </p> 8384 </td> 8385<td> 8386 <p> 8387 <span class="blue">Max = 16.1ε (Mean = 0.685ε)</span> 8388 </p> 8389 </td> 8390</tr> 8391<tr> 8392<td> 8393 <p> 8394 Jacobi Elliptic: Modulus near 1 8395 </p> 8396 </td> 8397<td> 8398 <p> 8399 <span class="blue">Max = 2.28ε (Mean = 0.194ε)</span><br> <br> 8400 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0ε (Mean = 0ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1">And 8401 other failures.</a>) 8402 </p> 8403 </td> 8404<td> 8405 <p> 8406 <span class="blue">Max = 3.75e+03ε (Mean = 293ε)</span> 8407 </p> 8408 </td> 8409<td> 8410 <p> 8411 <span class="blue">Max = 3.75e+03ε (Mean = 293ε)</span> 8412 </p> 8413 </td> 8414<td> 8415 <p> 8416 <span class="blue">Max = 6.24e+03ε (Mean = 482ε)</span> 8417 </p> 8418 </td> 8419</tr> 8420<tr> 8421<td> 8422 <p> 8423 Jacobi Elliptic: Large Phi 8424 </p> 8425 </td> 8426<td> 8427 <p> 8428 <span class="blue">Max = 14.1ε (Mean = 0.897ε)</span><br> <br> 8429 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 121ε (Mean = 22ε)) 8430 </p> 8431 </td> 8432<td> 8433 <p> 8434 <span class="blue">Max = 2.82e+04ε (Mean = 1.79e+03ε)</span> 8435 </p> 8436 </td> 8437<td> 8438 <p> 8439 <span class="blue">Max = 2.82e+04ε (Mean = 1.79e+03ε)</span> 8440 </p> 8441 </td> 8442<td> 8443 <p> 8444 <span class="blue">Max = 1.67e+04ε (Mean = 1e+03ε)</span> 8445 </p> 8446 </td> 8447</tr> 8448</tbody> 8449</table></div> 8450</div> 8451<br class="table-break"><div class="table"> 8452<a name="math_toolkit.logs_and_tables.all_table.table_jacobi_sn"></a><p class="title"><b>Table 23.65. Error rates for jacobi_sn</b></p> 8453<div class="table-contents"><table class="table" summary="Error rates for jacobi_sn"> 8454<colgroup> 8455<col> 8456<col> 8457<col> 8458<col> 8459<col> 8460</colgroup> 8461<thead><tr> 8462<th> 8463 </th> 8464<th> 8465 <p> 8466 GNU C++ version 7.1.0<br> linux<br> double 8467 </p> 8468 </th> 8469<th> 8470 <p> 8471 GNU C++ version 7.1.0<br> linux<br> long double 8472 </p> 8473 </th> 8474<th> 8475 <p> 8476 Sun compiler version 0x5150<br> Sun Solaris<br> long double 8477 </p> 8478 </th> 8479<th> 8480 <p> 8481 Microsoft Visual C++ version 14.1<br> Win32<br> double 8482 </p> 8483 </th> 8484</tr></thead> 8485<tbody> 8486<tr> 8487<td> 8488 <p> 8489 Jacobi Elliptic: Mathworld Data 8490 </p> 8491 </td> 8492<td> 8493 <p> 8494 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 8495 2.1:</em></span> Max = 588ε (Mean = 146ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data">And 8496 other failures.</a>) 8497 </p> 8498 </td> 8499<td> 8500 <p> 8501 <span class="blue">Max = 341ε (Mean = 80.7ε)</span> 8502 </p> 8503 </td> 8504<td> 8505 <p> 8506 <span class="blue">Max = 341ε (Mean = 80.7ε)</span> 8507 </p> 8508 </td> 8509<td> 8510 <p> 8511 <span class="blue">Max = 481ε (Mean = 113ε)</span> 8512 </p> 8513 </td> 8514</tr> 8515<tr> 8516<td> 8517 <p> 8518 Jacobi Elliptic: Random Data 8519 </p> 8520 </td> 8521<td> 8522 <p> 8523 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 8524 2.1:</em></span> Max = 4.02ε (Mean = 1.07ε)) 8525 </p> 8526 </td> 8527<td> 8528 <p> 8529 <span class="blue">Max = 2.01ε (Mean = 0.584ε)</span> 8530 </p> 8531 </td> 8532<td> 8533 <p> 8534 <span class="blue">Max = 2.01ε (Mean = 0.593ε)</span> 8535 </p> 8536 </td> 8537<td> 8538 <p> 8539 <span class="blue">Max = 1.92ε (Mean = 0.567ε)</span> 8540 </p> 8541 </td> 8542</tr> 8543<tr> 8544<td> 8545 <p> 8546 Jacobi Elliptic: Random Small Values 8547 </p> 8548 </td> 8549<td> 8550 <p> 8551 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 8552 2.1:</em></span> Max = 11.7ε (Mean = 1.65ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values">And 8553 other failures.</a>) 8554 </p> 8555 </td> 8556<td> 8557 <p> 8558 <span class="blue">Max = 1.99ε (Mean = 0.347ε)</span> 8559 </p> 8560 </td> 8561<td> 8562 <p> 8563 <span class="blue">Max = 1.99ε (Mean = 0.347ε)</span> 8564 </p> 8565 </td> 8566<td> 8567 <p> 8568 <span class="blue">Max = 2.11ε (Mean = 0.385ε)</span> 8569 </p> 8570 </td> 8571</tr> 8572<tr> 8573<td> 8574 <p> 8575 Jacobi Elliptic: Modulus near 1 8576 </p> 8577 </td> 8578<td> 8579 <p> 8580 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 8581 2.1:</em></span> Max = 0ε (Mean = 0ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1">And 8582 other failures.</a>) 8583 </p> 8584 </td> 8585<td> 8586 <p> 8587 <span class="blue">Max = 109ε (Mean = 7.35ε)</span> 8588 </p> 8589 </td> 8590<td> 8591 <p> 8592 <span class="blue">Max = 109ε (Mean = 7.38ε)</span> 8593 </p> 8594 </td> 8595<td> 8596 <p> 8597 <span class="blue">Max = 23.2ε (Mean = 1.85ε)</span> 8598 </p> 8599 </td> 8600</tr> 8601<tr> 8602<td> 8603 <p> 8604 Jacobi Elliptic: Large Phi 8605 </p> 8606 </td> 8607<td> 8608 <p> 8609 <span class="blue">Max = 12ε (Mean = 0.771ε)</span><br> <br> 8610 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 4.54e+04ε (Mean = 2.63e+03ε)) 8611 </p> 8612 </td> 8613<td> 8614 <p> 8615 <span class="blue">Max = 2.45e+04ε (Mean = 1.51e+03ε)</span> 8616 </p> 8617 </td> 8618<td> 8619 <p> 8620 <span class="blue">Max = 2.45e+04ε (Mean = 1.51e+03ε)</span> 8621 </p> 8622 </td> 8623<td> 8624 <p> 8625 <span class="blue">Max = 4.36e+04ε (Mean = 2.54e+03ε)</span> 8626 </p> 8627 </td> 8628</tr> 8629</tbody> 8630</table></div> 8631</div> 8632<br class="table-break"><div class="table"> 8633<a name="math_toolkit.logs_and_tables.all_table.table_jacobi_zeta"></a><p class="title"><b>Table 23.66. Error rates for jacobi_zeta</b></p> 8634<div class="table-contents"><table class="table" summary="Error rates for jacobi_zeta"> 8635<colgroup> 8636<col> 8637<col> 8638<col> 8639<col> 8640<col> 8641</colgroup> 8642<thead><tr> 8643<th> 8644 </th> 8645<th> 8646 <p> 8647 GNU C++ version 7.1.0<br> linux<br> double 8648 </p> 8649 </th> 8650<th> 8651 <p> 8652 GNU C++ version 7.1.0<br> linux<br> long double 8653 </p> 8654 </th> 8655<th> 8656 <p> 8657 Sun compiler version 0x5150<br> Sun Solaris<br> long double 8658 </p> 8659 </th> 8660<th> 8661 <p> 8662 Microsoft Visual C++ version 14.1<br> Win32<br> double 8663 </p> 8664 </th> 8665</tr></thead> 8666<tbody> 8667<tr> 8668<td> 8669 <p> 8670 Elliptic Integral Jacobi Zeta: Mathworld Data 8671 </p> 8672 </td> 8673<td> 8674 <p> 8675 <span class="blue">Max = 0ε (Mean = 0ε)</span> 8676 </p> 8677 </td> 8678<td> 8679 <p> 8680 <span class="blue">Max = 1.66ε (Mean = 0.48ε)</span> 8681 </p> 8682 </td> 8683<td> 8684 <p> 8685 <span class="blue">Max = 1.66ε (Mean = 0.48ε)</span> 8686 </p> 8687 </td> 8688<td> 8689 <p> 8690 <span class="blue">Max = 1.52ε (Mean = 0.357ε)</span> 8691 </p> 8692 </td> 8693</tr> 8694<tr> 8695<td> 8696 <p> 8697 Elliptic Integral Jacobi Zeta: Random Data 8698 </p> 8699 </td> 8700<td> 8701 <p> 8702 <span class="blue">Max = 0ε (Mean = 0ε)</span> 8703 </p> 8704 </td> 8705<td> 8706 <p> 8707 <span class="blue">Max = 2.99ε (Mean = 0.824ε)</span> 8708 </p> 8709 </td> 8710<td> 8711 <p> 8712 <span class="blue">Max = 3.96ε (Mean = 1.06ε)</span> 8713 </p> 8714 </td> 8715<td> 8716 <p> 8717 <span class="blue">Max = 3.89ε (Mean = 0.824ε)</span> 8718 </p> 8719 </td> 8720</tr> 8721<tr> 8722<td> 8723 <p> 8724 Elliptic Integral Jacobi Zeta: Large Phi Values 8725 </p> 8726 </td> 8727<td> 8728 <p> 8729 <span class="blue">Max = 0ε (Mean = 0ε)</span> 8730 </p> 8731 </td> 8732<td> 8733 <p> 8734 <span class="blue">Max = 2.92ε (Mean = 0.951ε)</span> 8735 </p> 8736 </td> 8737<td> 8738 <p> 8739 <span class="blue">Max = 3.05ε (Mean = 1.13ε)</span> 8740 </p> 8741 </td> 8742<td> 8743 <p> 8744 <span class="blue">Max = 2.52ε (Mean = 0.977ε)</span> 8745 </p> 8746 </td> 8747</tr> 8748</tbody> 8749</table></div> 8750</div> 8751<br class="table-break"><div class="table"> 8752<a name="math_toolkit.logs_and_tables.all_table.table_laguerre_n_m_x_"></a><p class="title"><b>Table 23.67. Error rates for laguerre(n, m, x)</b></p> 8753<div class="table-contents"><table class="table" summary="Error rates for laguerre(n, m, x)"> 8754<colgroup> 8755<col> 8756<col> 8757<col> 8758<col> 8759<col> 8760</colgroup> 8761<thead><tr> 8762<th> 8763 </th> 8764<th> 8765 <p> 8766 GNU C++ version 7.1.0<br> linux<br> double 8767 </p> 8768 </th> 8769<th> 8770 <p> 8771 GNU C++ version 7.1.0<br> linux<br> long double 8772 </p> 8773 </th> 8774<th> 8775 <p> 8776 Sun compiler version 0x5150<br> Sun Solaris<br> long double 8777 </p> 8778 </th> 8779<th> 8780 <p> 8781 Microsoft Visual C++ version 14.1<br> Win32<br> double 8782 </p> 8783 </th> 8784</tr></thead> 8785<tbody><tr> 8786<td> 8787 <p> 8788 Associated Laguerre Polynomials 8789 </p> 8790 </td> 8791<td> 8792 <p> 8793 <span class="blue">Max = 0.84ε (Mean = 0.0358ε)</span><br> <br> 8794 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 434ε (Mean = 10.7ε)) 8795 </p> 8796 </td> 8797<td> 8798 <p> 8799 <span class="blue">Max = 167ε (Mean = 6.38ε)</span><br> <br> 8800 (<span class="emphasis"><em><cmath>:</em></span> Max = 206ε (Mean = 6.86ε)) 8801 </p> 8802 </td> 8803<td> 8804 <p> 8805 <span class="blue">Max = 167ε (Mean = 6.38ε)</span> 8806 </p> 8807 </td> 8808<td> 8809 <p> 8810 <span class="blue">Max = 434ε (Mean = 11.1ε)</span> 8811 </p> 8812 </td> 8813</tr></tbody> 8814</table></div> 8815</div> 8816<br class="table-break"><div class="table"> 8817<a name="math_toolkit.logs_and_tables.all_table.table_laguerre_n_x_"></a><p class="title"><b>Table 23.68. Error rates for laguerre(n, x)</b></p> 8818<div class="table-contents"><table class="table" summary="Error rates for laguerre(n, x)"> 8819<colgroup> 8820<col> 8821<col> 8822<col> 8823<col> 8824<col> 8825</colgroup> 8826<thead><tr> 8827<th> 8828 </th> 8829<th> 8830 <p> 8831 GNU C++ version 7.1.0<br> linux<br> double 8832 </p> 8833 </th> 8834<th> 8835 <p> 8836 GNU C++ version 7.1.0<br> linux<br> long double 8837 </p> 8838 </th> 8839<th> 8840 <p> 8841 Sun compiler version 0x5150<br> Sun Solaris<br> long double 8842 </p> 8843 </th> 8844<th> 8845 <p> 8846 Microsoft Visual C++ version 14.1<br> Win32<br> double 8847 </p> 8848 </th> 8849</tr></thead> 8850<tbody><tr> 8851<td> 8852 <p> 8853 Laguerre Polynomials 8854 </p> 8855 </td> 8856<td> 8857 <p> 8858 <span class="blue">Max = 6.82ε (Mean = 0.408ε)</span><br> <br> 8859 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.1e+03ε (Mean = 185ε)) 8860 </p> 8861 </td> 8862<td> 8863 <p> 8864 <span class="blue">Max = 1.39e+04ε (Mean = 828ε)</span><br> 8865 <br> (<span class="emphasis"><em><cmath>:</em></span> Max = 4.2e+03ε (Mean 8866 = 251ε)) 8867 </p> 8868 </td> 8869<td> 8870 <p> 8871 <span class="blue">Max = 1.39e+04ε (Mean = 828ε)</span> 8872 </p> 8873 </td> 8874<td> 8875 <p> 8876 <span class="blue">Max = 3.1e+03ε (Mean = 185ε)</span> 8877 </p> 8878 </td> 8879</tr></tbody> 8880</table></div> 8881</div> 8882<br class="table-break"><div class="table"> 8883<a name="math_toolkit.logs_and_tables.all_table.table_legendre_p"></a><p class="title"><b>Table 23.69. Error rates for legendre_p</b></p> 8884<div class="table-contents"><table class="table" summary="Error rates for legendre_p"> 8885<colgroup> 8886<col> 8887<col> 8888<col> 8889<col> 8890<col> 8891</colgroup> 8892<thead><tr> 8893<th> 8894 </th> 8895<th> 8896 <p> 8897 GNU C++ version 7.1.0<br> linux<br> double 8898 </p> 8899 </th> 8900<th> 8901 <p> 8902 GNU C++ version 7.1.0<br> linux<br> long double 8903 </p> 8904 </th> 8905<th> 8906 <p> 8907 Sun compiler version 0x5150<br> Sun Solaris<br> long double 8908 </p> 8909 </th> 8910<th> 8911 <p> 8912 Microsoft Visual C++ version 14.1<br> Win32<br> double 8913 </p> 8914 </th> 8915</tr></thead> 8916<tbody> 8917<tr> 8918<td> 8919 <p> 8920 Legendre Polynomials: Small Values 8921 </p> 8922 </td> 8923<td> 8924 <p> 8925 <span class="blue">Max = 0.732ε (Mean = 0.0619ε)</span><br> 8926 <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 211ε (Mean = 20.4ε)) 8927 </p> 8928 </td> 8929<td> 8930 <p> 8931 <span class="blue">Max = 69.2ε (Mean = 9.58ε)</span><br> <br> 8932 (<span class="emphasis"><em><cmath>:</em></span> Max = 124ε (Mean = 13.2ε)) 8933 </p> 8934 </td> 8935<td> 8936 <p> 8937 <span class="blue">Max = 69.2ε (Mean = 9.58ε)</span> 8938 </p> 8939 </td> 8940<td> 8941 <p> 8942 <span class="blue">Max = 211ε (Mean = 20.4ε)</span> 8943 </p> 8944 </td> 8945</tr> 8946<tr> 8947<td> 8948 <p> 8949 Legendre Polynomials: Large Values 8950 </p> 8951 </td> 8952<td> 8953 <p> 8954 <span class="blue">Max = 0.632ε (Mean = 0.0693ε)</span><br> 8955 <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 300ε (Mean = 33.2ε)) 8956 </p> 8957 </td> 8958<td> 8959 <p> 8960 <span class="blue">Max = 699ε (Mean = 59.6ε)</span><br> <br> 8961 (<span class="emphasis"><em><cmath>:</em></span> Max = 343ε (Mean = 32.1ε)) 8962 </p> 8963 </td> 8964<td> 8965 <p> 8966 <span class="blue">Max = 699ε (Mean = 59.6ε)</span> 8967 </p> 8968 </td> 8969<td> 8970 <p> 8971 <span class="blue">Max = 300ε (Mean = 33.2ε)</span> 8972 </p> 8973 </td> 8974</tr> 8975</tbody> 8976</table></div> 8977</div> 8978<br class="table-break"><div class="table"> 8979<a name="math_toolkit.logs_and_tables.all_table.table_legendre_p_associated_"></a><p class="title"><b>Table 23.70. Error rates for legendre_p (associated)</b></p> 8980<div class="table-contents"><table class="table" summary="Error rates for legendre_p (associated)"> 8981<colgroup> 8982<col> 8983<col> 8984<col> 8985<col> 8986<col> 8987</colgroup> 8988<thead><tr> 8989<th> 8990 </th> 8991<th> 8992 <p> 8993 GNU C++ version 7.1.0<br> linux<br> double 8994 </p> 8995 </th> 8996<th> 8997 <p> 8998 GNU C++ version 7.1.0<br> linux<br> long double 8999 </p> 9000 </th> 9001<th> 9002 <p> 9003 Sun compiler version 0x5150<br> Sun Solaris<br> long double 9004 </p> 9005 </th> 9006<th> 9007 <p> 9008 Microsoft Visual C++ version 14.1<br> Win32<br> double 9009 </p> 9010 </th> 9011</tr></thead> 9012<tbody><tr> 9013<td> 9014 <p> 9015 Associated Legendre Polynomials: Small Values 9016 </p> 9017 </td> 9018<td> 9019 <p> 9020 <span class="blue">Max = 0.999ε (Mean = 0.05ε)</span><br> <br> 9021 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 121ε (Mean = 6.75ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_legendre_p_associated__GSL_2_1_Associated_Legendre_Polynomials_Small_Values">And 9022 other failures.</a>) 9023 </p> 9024 </td> 9025<td> 9026 <p> 9027 <span class="blue">Max = 175ε (Mean = 9.88ε)</span><br> <br> 9028 (<span class="emphasis"><em><cmath>:</em></span> Max = 175ε (Mean = 9.36ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_legendre_p_associated___cmath__Associated_Legendre_Polynomials_Small_Values">And 9029 other failures.</a>) 9030 </p> 9031 </td> 9032<td> 9033 <p> 9034 <span class="blue">Max = 77.7ε (Mean = 5.59ε)</span> 9035 </p> 9036 </td> 9037<td> 9038 <p> 9039 <span class="blue">Max = 121ε (Mean = 7.14ε)</span> 9040 </p> 9041 </td> 9042</tr></tbody> 9043</table></div> 9044</div> 9045<br class="table-break"><div class="table"> 9046<a name="math_toolkit.logs_and_tables.all_table.table_legendre_q"></a><p class="title"><b>Table 23.71. Error rates for legendre_q</b></p> 9047<div class="table-contents"><table class="table" summary="Error rates for legendre_q"> 9048<colgroup> 9049<col> 9050<col> 9051<col> 9052<col> 9053<col> 9054</colgroup> 9055<thead><tr> 9056<th> 9057 </th> 9058<th> 9059 <p> 9060 GNU C++ version 7.1.0<br> linux<br> double 9061 </p> 9062 </th> 9063<th> 9064 <p> 9065 GNU C++ version 7.1.0<br> linux<br> long double 9066 </p> 9067 </th> 9068<th> 9069 <p> 9070 Sun compiler version 0x5150<br> Sun Solaris<br> long double 9071 </p> 9072 </th> 9073<th> 9074 <p> 9075 Microsoft Visual C++ version 14.1<br> Win32<br> double 9076 </p> 9077 </th> 9078</tr></thead> 9079<tbody> 9080<tr> 9081<td> 9082 <p> 9083 Legendre Polynomials: Small Values 9084 </p> 9085 </td> 9086<td> 9087 <p> 9088 <span class="blue">Max = 0.612ε (Mean = 0.0517ε)</span><br> 9089 <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 46.4ε (Mean = 7.46ε)) 9090 </p> 9091 </td> 9092<td> 9093 <p> 9094 <span class="blue">Max = 50.9ε (Mean = 9ε)</span> 9095 </p> 9096 </td> 9097<td> 9098 <p> 9099 <span class="blue">Max = 50.9ε (Mean = 8.98ε)</span> 9100 </p> 9101 </td> 9102<td> 9103 <p> 9104 <span class="blue">Max = 46.4ε (Mean = 7.32ε)</span> 9105 </p> 9106 </td> 9107</tr> 9108<tr> 9109<td> 9110 <p> 9111 Legendre Polynomials: Large Values 9112 </p> 9113 </td> 9114<td> 9115 <p> 9116 <span class="blue">Max = 2.49ε (Mean = 0.202ε)</span><br> <br> 9117 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 4.6e+03ε (Mean = 366ε)) 9118 </p> 9119 </td> 9120<td> 9121 <p> 9122 <span class="blue">Max = 5.98e+03ε (Mean = 478ε)</span> 9123 </p> 9124 </td> 9125<td> 9126 <p> 9127 <span class="blue">Max = 5.98e+03ε (Mean = 478ε)</span> 9128 </p> 9129 </td> 9130<td> 9131 <p> 9132 <span class="blue">Max = 4.6e+03ε (Mean = 366ε)</span> 9133 </p> 9134 </td> 9135</tr> 9136</tbody> 9137</table></div> 9138</div> 9139<br class="table-break"><div class="table"> 9140<a name="math_toolkit.logs_and_tables.all_table.table_lgamma"></a><p class="title"><b>Table 23.72. Error rates for lgamma</b></p> 9141<div class="table-contents"><table class="table" summary="Error rates for lgamma"> 9142<colgroup> 9143<col> 9144<col> 9145<col> 9146<col> 9147<col> 9148</colgroup> 9149<thead><tr> 9150<th> 9151 </th> 9152<th> 9153 <p> 9154 GNU C++ version 7.1.0<br> linux<br> double 9155 </p> 9156 </th> 9157<th> 9158 <p> 9159 GNU C++ version 7.1.0<br> linux<br> long double 9160 </p> 9161 </th> 9162<th> 9163 <p> 9164 Sun compiler version 0x5150<br> Sun Solaris<br> long double 9165 </p> 9166 </th> 9167<th> 9168 <p> 9169 Microsoft Visual C++ version 14.1<br> Win32<br> double 9170 </p> 9171 </th> 9172</tr></thead> 9173<tbody> 9174<tr> 9175<td> 9176 <p> 9177 factorials 9178 </p> 9179 </td> 9180<td> 9181 <p> 9182 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 9183 2.1:</em></span> Max = 33.6ε (Mean = 2.78ε))<br> (<span class="emphasis"><em>Rmath 9184 3.2.3:</em></span> Max = 1.55ε (Mean = 0.592ε)) 9185 </p> 9186 </td> 9187<td> 9188 <p> 9189 <span class="blue">Max = 0.991ε (Mean = 0.308ε)</span><br> <br> 9190 (<span class="emphasis"><em><cmath>:</em></span> Max = 1.67ε (Mean = 0.487ε))<br> 9191 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.67ε (Mean = 0.487ε)) 9192 </p> 9193 </td> 9194<td> 9195 <p> 9196 <span class="blue">Max = 0.991ε (Mean = 0.383ε)</span><br> <br> 9197 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.36ε (Mean = 0.476ε)) 9198 </p> 9199 </td> 9200<td> 9201 <p> 9202 <span class="blue">Max = 0.914ε (Mean = 0.175ε)</span><br> <br> 9203 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.958ε (Mean = 0.38ε)) 9204 </p> 9205 </td> 9206</tr> 9207<tr> 9208<td> 9209 <p> 9210 near 0 9211 </p> 9212 </td> 9213<td> 9214 <p> 9215 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 9216 2.1:</em></span> Max = 5.21ε (Mean = 1.57ε))<br> (<span class="emphasis"><em>Rmath 9217 3.2.3:</em></span> Max = 0ε (Mean = 0ε)) 9218 </p> 9219 </td> 9220<td> 9221 <p> 9222 <span class="blue">Max = 1.42ε (Mean = 0.566ε)</span><br> <br> 9223 (<span class="emphasis"><em><cmath>:</em></span> Max = 0.964ε (Mean = 0.543ε))<br> 9224 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.964ε (Mean = 0.543ε)) 9225 </p> 9226 </td> 9227<td> 9228 <p> 9229 <span class="blue">Max = 1.42ε (Mean = 0.566ε)</span><br> <br> 9230 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.964ε (Mean = 0.543ε)) 9231 </p> 9232 </td> 9233<td> 9234 <p> 9235 <span class="blue">Max = 0.964ε (Mean = 0.462ε)</span><br> <br> 9236 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.962ε (Mean = 0.372ε)) 9237 </p> 9238 </td> 9239</tr> 9240<tr> 9241<td> 9242 <p> 9243 near 1 9244 </p> 9245 </td> 9246<td> 9247 <p> 9248 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 9249 2.1:</em></span> Max = 442ε (Mean = 88.8ε))<br> (<span class="emphasis"><em>Rmath 9250 3.2.3:</em></span> Max = 7.99e+04ε (Mean = 1.68e+04ε)) 9251 </p> 9252 </td> 9253<td> 9254 <p> 9255 <span class="blue">Max = 0.948ε (Mean = 0.36ε)</span><br> <br> 9256 (<span class="emphasis"><em><cmath>:</em></span> Max = 0.615ε (Mean = 0.096ε))<br> 9257 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.615ε (Mean = 0.096ε)) 9258 </p> 9259 </td> 9260<td> 9261 <p> 9262 <span class="blue">Max = 0.948ε (Mean = 0.36ε)</span><br> <br> 9263 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.71ε (Mean = 0.581ε)) 9264 </p> 9265 </td> 9266<td> 9267 <p> 9268 <span class="blue">Max = 0.867ε (Mean = 0.468ε)</span><br> <br> 9269 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.906ε (Mean = 0.565ε)) 9270 </p> 9271 </td> 9272</tr> 9273<tr> 9274<td> 9275 <p> 9276 near 2 9277 </p> 9278 </td> 9279<td> 9280 <p> 9281 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 9282 2.1:</em></span> Max = 1.17e+03ε (Mean = 274ε))<br> (<span class="emphasis"><em>Rmath 9283 3.2.3:</em></span> Max = 2.63e+05ε (Mean = 5.84e+04ε)) 9284 </p> 9285 </td> 9286<td> 9287 <p> 9288 <span class="blue">Max = 0.878ε (Mean = 0.242ε)</span><br> <br> 9289 (<span class="emphasis"><em><cmath>:</em></span> Max = 0.741ε (Mean = 0.263ε))<br> 9290 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.741ε (Mean = 0.263ε)) 9291 </p> 9292 </td> 9293<td> 9294 <p> 9295 <span class="blue">Max = 0.878ε (Mean = 0.242ε)</span><br> <br> 9296 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.598ε (Mean = 0.235ε)) 9297 </p> 9298 </td> 9299<td> 9300 <p> 9301 <span class="blue">Max = 0.591ε (Mean = 0.159ε)</span><br> <br> 9302 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.741ε (Mean = 0.473ε)) 9303 </p> 9304 </td> 9305</tr> 9306<tr> 9307<td> 9308 <p> 9309 near -10 9310 </p> 9311 </td> 9312<td> 9313 <p> 9314 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 9315 2.1:</em></span> Max = 24.9ε (Mean = 4.6ε))<br> (<span class="emphasis"><em>Rmath 9316 3.2.3:</em></span> Max = 4.22ε (Mean = 1.26ε)) 9317 </p> 9318 </td> 9319<td> 9320 <p> 9321 <span class="blue">Max = 3.81ε (Mean = 1.01ε)</span><br> <br> 9322 (<span class="emphasis"><em><cmath>:</em></span> Max = 0.997ε (Mean = 0.412ε))<br> 9323 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.997ε (Mean = 0.412ε)) 9324 </p> 9325 </td> 9326<td> 9327 <p> 9328 <span class="blue">Max = 3.81ε (Mean = 1.01ε)</span><br> <br> 9329 (<span class="emphasis"><em><math.h>:</em></span> Max = 3.04ε (Mean = 1.01ε)) 9330 </p> 9331 </td> 9332<td> 9333 <p> 9334 <span class="blue">Max = 4.22ε (Mean = 1.33ε)</span><br> <br> 9335 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.997ε (Mean = 0.444ε)) 9336 </p> 9337 </td> 9338</tr> 9339<tr> 9340<td> 9341 <p> 9342 near -55 9343 </p> 9344 </td> 9345<td> 9346 <p> 9347 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 9348 2.1:</em></span> Max = 7.02ε (Mean = 1.47ε))<br> (<span class="emphasis"><em>Rmath 9349 3.2.3:</em></span> Max = 250ε (Mean = 60.9ε)) 9350 </p> 9351 </td> 9352<td> 9353 <p> 9354 <span class="blue">Max = 0.821ε (Mean = 0.513ε)</span><br> <br> 9355 (<span class="emphasis"><em><cmath>:</em></span> Max = 1.58ε (Mean = 0.672ε))<br> 9356 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.58ε (Mean = 0.672ε)) 9357 </p> 9358 </td> 9359<td> 9360 <p> 9361 <span class="blue">Max = 1.59ε (Mean = 0.587ε)</span><br> <br> 9362 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.821ε (Mean = 0.674ε)) 9363 </p> 9364 </td> 9365<td> 9366 <p> 9367 <span class="blue">Max = 0.821ε (Mean = 0.419ε)</span><br> <br> 9368 (<span class="emphasis"><em><math.h>:</em></span> Max = 249ε (Mean = 43.1ε)) 9369 </p> 9370 </td> 9371</tr> 9372</tbody> 9373</table></div> 9374</div> 9375<br class="table-break"><div class="table"> 9376<a name="math_toolkit.logs_and_tables.all_table.table_log1p"></a><p class="title"><b>Table 23.73. Error rates for log1p</b></p> 9377<div class="table-contents"><table class="table" summary="Error rates for log1p"> 9378<colgroup> 9379<col> 9380<col> 9381<col> 9382<col> 9383<col> 9384</colgroup> 9385<thead><tr> 9386<th> 9387 </th> 9388<th> 9389 <p> 9390 GNU C++ version 7.1.0<br> linux<br> long double 9391 </p> 9392 </th> 9393<th> 9394 <p> 9395 GNU C++ version 7.1.0<br> linux<br> double 9396 </p> 9397 </th> 9398<th> 9399 <p> 9400 Sun compiler version 0x5150<br> Sun Solaris<br> long double 9401 </p> 9402 </th> 9403<th> 9404 <p> 9405 Microsoft Visual C++ version 14.1<br> Win32<br> double 9406 </p> 9407 </th> 9408</tr></thead> 9409<tbody><tr> 9410<td> 9411 <p> 9412 Random test data 9413 </p> 9414 </td> 9415<td> 9416 <p> 9417 <span class="blue">Max = 0.818ε (Mean = 0.227ε)</span><br> <br> 9418 (<span class="emphasis"><em><cmath>:</em></span> Max = 0.818ε (Mean = 0.227ε))<br> 9419 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.818ε (Mean = 0.227ε)) 9420 </p> 9421 </td> 9422<td> 9423 <p> 9424 <span class="blue">Max = 0.846ε (Mean = 0.153ε)</span><br> <br> 9425 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 0.846ε (Mean = 0.153ε)) 9426 </p> 9427 </td> 9428<td> 9429 <p> 9430 <span class="blue">Max = 2.3ε (Mean = 0.66ε)</span><br> <br> 9431 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.818ε (Mean = 0.249ε)) 9432 </p> 9433 </td> 9434<td> 9435 <p> 9436 <span class="blue">Max = 0.509ε (Mean = 0.057ε)</span><br> <br> 9437 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.509ε (Mean = 0.057ε)) 9438 </p> 9439 </td> 9440</tr></tbody> 9441</table></div> 9442</div> 9443<br class="table-break"><div class="table"> 9444<a name="math_toolkit.logs_and_tables.all_table.table_non_central_beta_CDF"></a><p class="title"><b>Table 23.74. Error rates for non central beta CDF</b></p> 9445<div class="table-contents"><table class="table" summary="Error rates for non central beta CDF"> 9446<colgroup> 9447<col> 9448<col> 9449<col> 9450<col> 9451<col> 9452</colgroup> 9453<thead><tr> 9454<th> 9455 </th> 9456<th> 9457 <p> 9458 GNU C++ version 7.1.0<br> linux<br> double 9459 </p> 9460 </th> 9461<th> 9462 <p> 9463 GNU C++ version 7.1.0<br> linux<br> long double 9464 </p> 9465 </th> 9466<th> 9467 <p> 9468 Sun compiler version 0x5150<br> Sun Solaris<br> long double 9469 </p> 9470 </th> 9471<th> 9472 <p> 9473 Microsoft Visual C++ version 14.1<br> Win32<br> double 9474 </p> 9475 </th> 9476</tr></thead> 9477<tbody> 9478<tr> 9479<td> 9480 <p> 9481 Non Central Beta, medium parameters 9482 </p> 9483 </td> 9484<td> 9485 <p> 9486 <span class="blue">Max = 0.998ε (Mean = 0.0649ε)</span><br> 9487 <br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max 9488 = 1.46e+26ε (Mean = 3.5e+24ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_Rmath_3_2_3_Non_Central_Beta_medium_parameters">And 9489 other failures.</a>)</span> 9490 </p> 9491 </td> 9492<td> 9493 <p> 9494 <span class="blue">Max = 824ε (Mean = 27.4ε)</span> 9495 </p> 9496 </td> 9497<td> 9498 <p> 9499 <span class="blue">Max = 832ε (Mean = 38.1ε)</span> 9500 </p> 9501 </td> 9502<td> 9503 <p> 9504 <span class="blue">Max = 242ε (Mean = 31ε)</span> 9505 </p> 9506 </td> 9507</tr> 9508<tr> 9509<td> 9510 <p> 9511 Non Central Beta, large parameters 9512 </p> 9513 </td> 9514<td> 9515 <p> 9516 <span class="blue">Max = 1.18ε (Mean = 0.175ε)</span><br> <br> 9517 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 1.01e+36ε (Mean 9518 = 1.19e+35ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_Rmath_3_2_3_Non_Central_Beta_large_parameters">And 9519 other failures.</a>)</span> 9520 </p> 9521 </td> 9522<td> 9523 <p> 9524 <span class="blue">Max = 2.5e+04ε (Mean = 3.78e+03ε)</span> 9525 </p> 9526 </td> 9527<td> 9528 <p> 9529 <span class="blue">Max = 2.57e+04ε (Mean = 4.45e+03ε)</span> 9530 </p> 9531 </td> 9532<td> 9533 <p> 9534 <span class="blue">Max = 3.66e+03ε (Mean = 500ε)</span> 9535 </p> 9536 </td> 9537</tr> 9538</tbody> 9539</table></div> 9540</div> 9541<br class="table-break"><div class="table"> 9542<a name="math_toolkit.logs_and_tables.all_table.table_non_central_beta_CDF_complement"></a><p class="title"><b>Table 23.75. Error rates for non central beta CDF complement</b></p> 9543<div class="table-contents"><table class="table" summary="Error rates for non central beta CDF complement"> 9544<colgroup> 9545<col> 9546<col> 9547<col> 9548<col> 9549<col> 9550</colgroup> 9551<thead><tr> 9552<th> 9553 </th> 9554<th> 9555 <p> 9556 GNU C++ version 7.1.0<br> linux<br> double 9557 </p> 9558 </th> 9559<th> 9560 <p> 9561 GNU C++ version 7.1.0<br> linux<br> long double 9562 </p> 9563 </th> 9564<th> 9565 <p> 9566 Sun compiler version 0x5150<br> Sun Solaris<br> long double 9567 </p> 9568 </th> 9569<th> 9570 <p> 9571 Microsoft Visual C++ version 14.1<br> Win32<br> double 9572 </p> 9573 </th> 9574</tr></thead> 9575<tbody> 9576<tr> 9577<td> 9578 <p> 9579 Non Central Beta, medium parameters 9580 </p> 9581 </td> 9582<td> 9583 <p> 9584 <span class="blue">Max = 0.998ε (Mean = 0.0936ε)</span><br> 9585 <br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max 9586 = 7.5e+97ε (Mean = 1.37e+96ε) <a class="link" href="logs.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 9587 other failures.</a>)</span> 9588 </p> 9589 </td> 9590<td> 9591 <p> 9592 <span class="blue">Max = 396ε (Mean = 50.7ε)</span> 9593 </p> 9594 </td> 9595<td> 9596 <p> 9597 <span class="blue">Max = 554ε (Mean = 57.2ε)</span> 9598 </p> 9599 </td> 9600<td> 9601 <p> 9602 <span class="blue">Max = 624ε (Mean = 62.7ε)</span> 9603 </p> 9604 </td> 9605</tr> 9606<tr> 9607<td> 9608 <p> 9609 Non Central Beta, large parameters 9610 </p> 9611 </td> 9612<td> 9613 <p> 9614 <span class="blue">Max = 0.986ε (Mean = 0.188ε)</span><br> <br> 9615 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = +INFε (Mean 9616 = +INFε) <a class="link" href="logs.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 9617 other failures.</a>)</span> 9618 </p> 9619 </td> 9620<td> 9621 <p> 9622 <span class="blue">Max = 6.83e+03ε (Mean = 993ε)</span> 9623 </p> 9624 </td> 9625<td> 9626 <p> 9627 <span class="blue">Max = 3.56e+03ε (Mean = 707ε)</span> 9628 </p> 9629 </td> 9630<td> 9631 <p> 9632 <span class="blue">Max = 1.25e+04ε (Mean = 1.49e+03ε)</span> 9633 </p> 9634 </td> 9635</tr> 9636</tbody> 9637</table></div> 9638</div> 9639<br class="table-break"><div class="table"> 9640<a name="math_toolkit.logs_and_tables.all_table.table_non_central_chi_squared_CDF"></a><p class="title"><b>Table 23.76. Error rates for non central chi squared CDF</b></p> 9641<div class="table-contents"><table class="table" summary="Error rates for non central chi squared CDF"> 9642<colgroup> 9643<col> 9644<col> 9645<col> 9646<col> 9647<col> 9648</colgroup> 9649<thead><tr> 9650<th> 9651 </th> 9652<th> 9653 <p> 9654 GNU C++ version 7.1.0<br> linux<br> double 9655 </p> 9656 </th> 9657<th> 9658 <p> 9659 GNU C++ version 7.1.0<br> linux<br> long double 9660 </p> 9661 </th> 9662<th> 9663 <p> 9664 Sun compiler version 0x5150<br> Sun Solaris<br> long double 9665 </p> 9666 </th> 9667<th> 9668 <p> 9669 Microsoft Visual C++ version 14.1<br> Win32<br> double 9670 </p> 9671 </th> 9672</tr></thead> 9673<tbody> 9674<tr> 9675<td> 9676 <p> 9677 Non Central Chi Squared, medium parameters 9678 </p> 9679 </td> 9680<td> 9681 <p> 9682 <span class="blue">Max = 0.99ε (Mean = 0.0544ε)</span><br> <br> 9683 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 727ε (Mean = 121ε)) 9684 </p> 9685 </td> 9686<td> 9687 <p> 9688 <span class="blue">Max = 46.5ε (Mean = 10.3ε)</span> 9689 </p> 9690 </td> 9691<td> 9692 <p> 9693 <span class="blue">Max = 115ε (Mean = 13.9ε)</span> 9694 </p> 9695 </td> 9696<td> 9697 <p> 9698 <span class="blue">Max = 48.9ε (Mean = 10ε)</span> 9699 </p> 9700 </td> 9701</tr> 9702<tr> 9703<td> 9704 <p> 9705 Non Central Chi Squared, large parameters 9706 </p> 9707 </td> 9708<td> 9709 <p> 9710 <span class="blue">Max = 1.07ε (Mean = 0.102ε)</span><br> <br> 9711 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 3.27e+08ε (Mean 9712 = 2.23e+07ε))</span> 9713 </p> 9714 </td> 9715<td> 9716 <p> 9717 <span class="blue">Max = 3.07e+03ε (Mean = 336ε)</span> 9718 </p> 9719 </td> 9720<td> 9721 <p> 9722 <span class="blue">Max = 6.17e+03ε (Mean = 677ε)</span> 9723 </p> 9724 </td> 9725<td> 9726 <p> 9727 <span class="blue">Max = 9.79e+03ε (Mean = 723ε)</span> 9728 </p> 9729 </td> 9730</tr> 9731</tbody> 9732</table></div> 9733</div> 9734<br class="table-break"><div class="table"> 9735<a name="math_toolkit.logs_and_tables.all_table.table_non_central_chi_squared_CDF_complement"></a><p class="title"><b>Table 23.77. Error rates for non central chi squared CDF complement</b></p> 9736<div class="table-contents"><table class="table" summary="Error rates for non central chi squared CDF complement"> 9737<colgroup> 9738<col> 9739<col> 9740<col> 9741<col> 9742<col> 9743</colgroup> 9744<thead><tr> 9745<th> 9746 </th> 9747<th> 9748 <p> 9749 GNU C++ version 7.1.0<br> linux<br> double 9750 </p> 9751 </th> 9752<th> 9753 <p> 9754 GNU C++ version 7.1.0<br> linux<br> long double 9755 </p> 9756 </th> 9757<th> 9758 <p> 9759 Sun compiler version 0x5150<br> Sun Solaris<br> long double 9760 </p> 9761 </th> 9762<th> 9763 <p> 9764 Microsoft Visual C++ version 14.1<br> Win32<br> double 9765 </p> 9766 </th> 9767</tr></thead> 9768<tbody> 9769<tr> 9770<td> 9771 <p> 9772 Non Central Chi Squared, medium parameters 9773 </p> 9774 </td> 9775<td> 9776 <p> 9777 <span class="blue">Max = 0.96ε (Mean = 0.0635ε)</span><br> <br> 9778 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = +INFε (Mean 9779 = +INFε) <a class="link" href="logs.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 9780 other failures.</a>)</span> 9781 </p> 9782 </td> 9783<td> 9784 <p> 9785 <span class="blue">Max = 107ε (Mean = 17.2ε)</span> 9786 </p> 9787 </td> 9788<td> 9789 <p> 9790 <span class="blue">Max = 171ε (Mean = 22.8ε)</span> 9791 </p> 9792 </td> 9793<td> 9794 <p> 9795 <span class="blue">Max = 98.6ε (Mean = 15.8ε)</span> 9796 </p> 9797 </td> 9798</tr> 9799<tr> 9800<td> 9801 <p> 9802 Non Central Chi Squared, large parameters 9803 </p> 9804 </td> 9805<td> 9806 <p> 9807 <span class="blue">Max = 2.11ε (Mean = 0.278ε)</span><br> <br> 9808 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = +INFε (Mean 9809 = +INFε) <a class="link" href="logs.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 9810 other failures.</a>)</span> 9811 </p> 9812 </td> 9813<td> 9814 <p> 9815 <span class="blue">Max = 5.02e+03ε (Mean = 630ε)</span> 9816 </p> 9817 </td> 9818<td> 9819 <p> 9820 <span class="blue">Max = 5.1e+03ε (Mean = 577ε)</span> 9821 </p> 9822 </td> 9823<td> 9824 <p> 9825 <span class="blue">Max = 5.43e+03ε (Mean = 705ε)</span> 9826 </p> 9827 </td> 9828</tr> 9829</tbody> 9830</table></div> 9831</div> 9832<br class="table-break"><div class="table"> 9833<a name="math_toolkit.logs_and_tables.all_table.table_non_central_t_CDF"></a><p class="title"><b>Table 23.78. Error rates for non central t CDF</b></p> 9834<div class="table-contents"><table class="table" summary="Error rates for non central t CDF"> 9835<colgroup> 9836<col> 9837<col> 9838<col> 9839<col> 9840<col> 9841</colgroup> 9842<thead><tr> 9843<th> 9844 </th> 9845<th> 9846 <p> 9847 GNU C++ version 7.1.0<br> linux<br> double 9848 </p> 9849 </th> 9850<th> 9851 <p> 9852 GNU C++ version 7.1.0<br> linux<br> long double 9853 </p> 9854 </th> 9855<th> 9856 <p> 9857 Sun compiler version 0x5150<br> Sun Solaris<br> long double 9858 </p> 9859 </th> 9860<th> 9861 <p> 9862 Microsoft Visual C++ version 14.1<br> Win32<br> double 9863 </p> 9864 </th> 9865</tr></thead> 9866<tbody> 9867<tr> 9868<td> 9869 <p> 9870 Non Central T 9871 </p> 9872 </td> 9873<td> 9874 <p> 9875 <span class="blue">Max = 0.796ε (Mean = 0.0691ε)</span><br> 9876 <br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max 9877 = 5.28e+15ε (Mean = 8.49e+14ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_non_central_t_CDF_Rmath_3_2_3_Non_Central_T">And 9878 other failures.</a>)</span> 9879 </p> 9880 </td> 9881<td> 9882 <p> 9883 <span class="blue">Max = 139ε (Mean = 31ε)</span> 9884 </p> 9885 </td> 9886<td> 9887 <p> 9888 <span class="blue">Max = 145ε (Mean = 30.9ε)</span> 9889 </p> 9890 </td> 9891<td> 9892 <p> 9893 <span class="blue">Max = 135ε (Mean = 32.1ε)</span> 9894 </p> 9895 </td> 9896</tr> 9897<tr> 9898<td> 9899 <p> 9900 Non Central T (small non-centrality) 9901 </p> 9902 </td> 9903<td> 9904 <p> 9905 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath 9906 3.2.3:</em></span> Max = 2.09e+03ε (Mean = 244ε)) 9907 </p> 9908 </td> 9909<td> 9910 <p> 9911 <span class="blue">Max = 3.86ε (Mean = 1.4ε)</span> 9912 </p> 9913 </td> 9914<td> 9915 <p> 9916 <span class="blue">Max = 9.15ε (Mean = 2.13ε)</span> 9917 </p> 9918 </td> 9919<td> 9920 <p> 9921 <span class="blue">Max = 6.17ε (Mean = 1.45ε)</span> 9922 </p> 9923 </td> 9924</tr> 9925<tr> 9926<td> 9927 <p> 9928 Non Central T (large parameters) 9929 </p> 9930 </td> 9931<td> 9932 <p> 9933 <span class="blue">Max = 257ε (Mean = 72.1ε)</span><br> <br> 9934 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.46ε (Mean = 0.657ε)) 9935 </p> 9936 </td> 9937<td> 9938 <p> 9939 <span class="blue">Max = 5.26e+05ε (Mean = 1.48e+05ε)</span> 9940 </p> 9941 </td> 9942<td> 9943 <p> 9944 <span class="blue">Max = 5.24e+05ε (Mean = 1.47e+05ε)</span> 9945 </p> 9946 </td> 9947<td> 9948 <p> 9949 <span class="blue">Max = 286ε (Mean = 62.8ε)</span> 9950 </p> 9951 </td> 9952</tr> 9953</tbody> 9954</table></div> 9955</div> 9956<br class="table-break"><div class="table"> 9957<a name="math_toolkit.logs_and_tables.all_table.table_non_central_t_CDF_complement"></a><p class="title"><b>Table 23.79. Error rates for non central t CDF complement</b></p> 9958<div class="table-contents"><table class="table" summary="Error rates for non central t CDF complement"> 9959<colgroup> 9960<col> 9961<col> 9962<col> 9963<col> 9964<col> 9965</colgroup> 9966<thead><tr> 9967<th> 9968 </th> 9969<th> 9970 <p> 9971 GNU C++ version 7.1.0<br> linux<br> double 9972 </p> 9973 </th> 9974<th> 9975 <p> 9976 GNU C++ version 7.1.0<br> linux<br> long double 9977 </p> 9978 </th> 9979<th> 9980 <p> 9981 Sun compiler version 0x5150<br> Sun Solaris<br> long double 9982 </p> 9983 </th> 9984<th> 9985 <p> 9986 Microsoft Visual C++ version 14.1<br> Win32<br> double 9987 </p> 9988 </th> 9989</tr></thead> 9990<tbody> 9991<tr> 9992<td> 9993 <p> 9994 Non Central T 9995 </p> 9996 </td> 9997<td> 9998 <p> 9999 <span class="blue">Max = 0.707ε (Mean = 0.0497ε)</span><br> 10000 <br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max 10001 = 6.19e+15ε (Mean = 6.72e+14ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_non_central_t_CDF_complement_Rmath_3_2_3_Non_Central_T">And 10002 other failures.</a>)</span> 10003 </p> 10004 </td> 10005<td> 10006 <p> 10007 <span class="blue">Max = 201ε (Mean = 31.7ε)</span> 10008 </p> 10009 </td> 10010<td> 10011 <p> 10012 <span class="blue">Max = 340ε (Mean = 43.2ε)</span> 10013 </p> 10014 </td> 10015<td> 10016 <p> 10017 <span class="blue">Max = 154ε (Mean = 32.1ε)</span> 10018 </p> 10019 </td> 10020</tr> 10021<tr> 10022<td> 10023 <p> 10024 Non Central T (small non-centrality) 10025 </p> 10026 </td> 10027<td> 10028 <p> 10029 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath 10030 3.2.3:</em></span> Max = 1.87e+03ε (Mean = 263ε)) 10031 </p> 10032 </td> 10033<td> 10034 <p> 10035 <span class="blue">Max = 10.5ε (Mean = 2.13ε)</span> 10036 </p> 10037 </td> 10038<td> 10039 <p> 10040 <span class="blue">Max = 10.5ε (Mean = 2.39ε)</span> 10041 </p> 10042 </td> 10043<td> 10044 <p> 10045 <span class="blue">Max = 4.6ε (Mean = 1.63ε)</span> 10046 </p> 10047 </td> 10048</tr> 10049<tr> 10050<td> 10051 <p> 10052 Non Central T (large parameters) 10053 </p> 10054 </td> 10055<td> 10056 <p> 10057 <span class="blue">Max = 478ε (Mean = 96.3ε)</span><br> <br> 10058 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.24ε (Mean = 0.945ε)) 10059 </p> 10060 </td> 10061<td> 10062 <p> 10063 <span class="blue">Max = 9.79e+05ε (Mean = 1.97e+05ε)</span> 10064 </p> 10065 </td> 10066<td> 10067 <p> 10068 <span class="blue">Max = 9.79e+05ε (Mean = 1.97e+05ε)</span> 10069 </p> 10070 </td> 10071<td> 10072 <p> 10073 <span class="blue">Max = 227ε (Mean = 50.4ε)</span> 10074 </p> 10075 </td> 10076</tr> 10077</tbody> 10078</table></div> 10079</div> 10080<br class="table-break"><div class="table"> 10081<a name="math_toolkit.logs_and_tables.all_table.table_owens_t"></a><p class="title"><b>Table 23.80. Error rates for owens_t</b></p> 10082<div class="table-contents"><table class="table" summary="Error rates for owens_t"> 10083<colgroup> 10084<col> 10085<col> 10086<col> 10087<col> 10088<col> 10089</colgroup> 10090<thead><tr> 10091<th> 10092 </th> 10093<th> 10094 <p> 10095 GNU C++ version 7.1.0<br> linux<br> double 10096 </p> 10097 </th> 10098<th> 10099 <p> 10100 GNU C++ version 7.1.0<br> linux<br> long double 10101 </p> 10102 </th> 10103<th> 10104 <p> 10105 Sun compiler version 0x5150<br> Sun Solaris<br> long double 10106 </p> 10107 </th> 10108<th> 10109 <p> 10110 Microsoft Visual C++ version 14.1<br> Win32<br> double 10111 </p> 10112 </th> 10113</tr></thead> 10114<tbody> 10115<tr> 10116<td> 10117 <p> 10118 Owens T (medium small values) 10119 </p> 10120 </td> 10121<td> 10122 <p> 10123 <span class="blue">Max = 0ε (Mean = 0ε)</span> 10124 </p> 10125 </td> 10126<td> 10127 <p> 10128 <span class="blue">Max = 3.34ε (Mean = 0.944ε)</span> 10129 </p> 10130 </td> 10131<td> 10132 <p> 10133 <span class="blue">Max = 3.34ε (Mean = 0.911ε)</span> 10134 </p> 10135 </td> 10136<td> 10137 <p> 10138 <span class="blue">Max = 4.37ε (Mean = 0.98ε)</span> 10139 </p> 10140 </td> 10141</tr> 10142<tr> 10143<td> 10144 <p> 10145 Owens T (large and diverse values) 10146 </p> 10147 </td> 10148<td> 10149 <p> 10150 <span class="blue">Max = 0ε (Mean = 0ε)</span> 10151 </p> 10152 </td> 10153<td> 10154 <p> 10155 <span class="blue">Max = 49ε (Mean = 2.16ε)</span> 10156 </p> 10157 </td> 10158<td> 10159 <p> 10160 <span class="blue">Max = 24.5ε (Mean = 1.39ε)</span> 10161 </p> 10162 </td> 10163<td> 10164 <p> 10165 <span class="blue">Max = 3.78ε (Mean = 0.621ε)</span> 10166 </p> 10167 </td> 10168</tr> 10169</tbody> 10170</table></div> 10171</div> 10172<br class="table-break"><div class="table"> 10173<a name="math_toolkit.logs_and_tables.all_table.table_polygamma"></a><p class="title"><b>Table 23.81. Error rates for polygamma</b></p> 10174<div class="table-contents"><table class="table" summary="Error rates for polygamma"> 10175<colgroup> 10176<col> 10177<col> 10178<col> 10179<col> 10180<col> 10181</colgroup> 10182<thead><tr> 10183<th> 10184 </th> 10185<th> 10186 <p> 10187 GNU C++ version 7.1.0<br> linux<br> double 10188 </p> 10189 </th> 10190<th> 10191 <p> 10192 GNU C++ version 7.1.0<br> linux<br> long double 10193 </p> 10194 </th> 10195<th> 10196 <p> 10197 Sun compiler version 0x5150<br> Sun Solaris<br> long double 10198 </p> 10199 </th> 10200<th> 10201 <p> 10202 Microsoft Visual C++ version 14.1<br> Win32<br> double 10203 </p> 10204 </th> 10205</tr></thead> 10206<tbody> 10207<tr> 10208<td> 10209 <p> 10210 Mathematica Data 10211 </p> 10212 </td> 10213<td> 10214 <p> 10215 <span class="blue">Max = 0.824ε (Mean = 0.0574ε)</span><br> 10216 <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 62.9ε (Mean = 12.8ε))<br> 10217 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 108ε (Mean = 15.2ε)) 10218 </p> 10219 </td> 10220<td> 10221 <p> 10222 <span class="blue">Max = 7.38ε (Mean = 1.84ε)</span> 10223 </p> 10224 </td> 10225<td> 10226 <p> 10227 <span class="blue">Max = 34.3ε (Mean = 7.65ε)</span> 10228 </p> 10229 </td> 10230<td> 10231 <p> 10232 <span class="blue">Max = 9.32ε (Mean = 1.95ε)</span> 10233 </p> 10234 </td> 10235</tr> 10236<tr> 10237<td> 10238 <p> 10239 Mathematica Data - large arguments 10240 </p> 10241 </td> 10242<td> 10243 <p> 10244 <span class="blue">Max = 0.998ε (Mean = 0.0592ε)</span><br> 10245 <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 244ε (Mean = 32.8ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_large_arguments">And 10246 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 10247 <span class="red">Max = 1.71e+56ε (Mean = 1.01e+55ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_large_arguments">And 10248 other failures.</a>)</span> 10249 </p> 10250 </td> 10251<td> 10252 <p> 10253 <span class="blue">Max = 2.23ε (Mean = 0.323ε)</span> 10254 </p> 10255 </td> 10256<td> 10257 <p> 10258 <span class="blue">Max = 11.1ε (Mean = 0.848ε)</span> 10259 </p> 10260 </td> 10261<td> 10262 <p> 10263 <span class="blue">Max = 150ε (Mean = 13.9ε)</span> 10264 </p> 10265 </td> 10266</tr> 10267<tr> 10268<td> 10269 <p> 10270 Mathematica Data - negative arguments 10271 </p> 10272 </td> 10273<td> 10274 <p> 10275 <span class="blue">Max = 0.516ε (Mean = 0.022ε)</span><br> <br> 10276 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 36.6ε (Mean = 3.04ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_negative_arguments">And 10277 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 10278 Max = 0ε (Mean = 0ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_negative_arguments">And 10279 other failures.</a>) 10280 </p> 10281 </td> 10282<td> 10283 <p> 10284 <span class="blue">Max = 269ε (Mean = 87.7ε)</span> 10285 </p> 10286 </td> 10287<td> 10288 <p> 10289 <span class="blue">Max = 269ε (Mean = 88.4ε)</span> 10290 </p> 10291 </td> 10292<td> 10293 <p> 10294 <span class="blue">Max = 497ε (Mean = 129ε)</span> 10295 </p> 10296 </td> 10297</tr> 10298<tr> 10299<td> 10300 <p> 10301 Mathematica Data - large negative arguments 10302 </p> 10303 </td> 10304<td> 10305 <p> 10306 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 10307 2.1:</em></span> Max = 1.79ε (Mean = 0.197ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_large_negative_arguments">And 10308 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 10309 Max = 0ε (Mean = 0ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_large_negative_arguments">And 10310 other failures.</a>) 10311 </p> 10312 </td> 10313<td> 10314 <p> 10315 <span class="blue">Max = 155ε (Mean = 96.4ε)</span> 10316 </p> 10317 </td> 10318<td> 10319 <p> 10320 <span class="blue">Max = 155ε (Mean = 96.4ε)</span> 10321 </p> 10322 </td> 10323<td> 10324 <p> 10325 <span class="blue">Max = 162ε (Mean = 101ε)</span> 10326 </p> 10327 </td> 10328</tr> 10329<tr> 10330<td> 10331 <p> 10332 Mathematica Data - small arguments 10333 </p> 10334 </td> 10335<td> 10336 <p> 10337 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 10338 2.1:</em></span> Max = 15.2ε (Mean = 5.03ε))<br> (<span class="emphasis"><em>Rmath 10339 3.2.3:</em></span> Max = 106ε (Mean = 20ε)) 10340 </p> 10341 </td> 10342<td> 10343 <p> 10344 <span class="blue">Max = 3.33ε (Mean = 0.75ε)</span> 10345 </p> 10346 </td> 10347<td> 10348 <p> 10349 <span class="blue">Max = 3.33ε (Mean = 0.75ε)</span> 10350 </p> 10351 </td> 10352<td> 10353 <p> 10354 <span class="blue">Max = 3ε (Mean = 0.496ε)</span> 10355 </p> 10356 </td> 10357</tr> 10358<tr> 10359<td> 10360 <p> 10361 Mathematica Data - Large orders and other bug cases 10362 </p> 10363 </td> 10364<td> 10365 <p> 10366 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 10367 2.1:</em></span> Max = 151ε (Mean = 39.3ε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_Large_orders_and_other_bug_cases">And 10368 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> 10369 <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_Large_orders_and_other_bug_cases">And 10370 other failures.</a>)</span> 10371 </p> 10372 </td> 10373<td> 10374 <p> 10375 <span class="blue">Max = 54.5ε (Mean = 13.3ε)</span> 10376 </p> 10377 </td> 10378<td> 10379 <p> 10380 <span class="blue">Max = 145ε (Mean = 55.9ε)</span> 10381 </p> 10382 </td> 10383<td> 10384 <p> 10385 <span class="blue">Max = 200ε (Mean = 57.2ε)</span> 10386 </p> 10387 </td> 10388</tr> 10389</tbody> 10390</table></div> 10391</div> 10392<br class="table-break"><div class="table"> 10393<a name="math_toolkit.logs_and_tables.all_table.table_powm1"></a><p class="title"><b>Table 23.82. Error rates for powm1</b></p> 10394<div class="table-contents"><table class="table" summary="Error rates for powm1"> 10395<colgroup> 10396<col> 10397<col> 10398<col> 10399<col> 10400<col> 10401</colgroup> 10402<thead><tr> 10403<th> 10404 </th> 10405<th> 10406 <p> 10407 GNU C++ version 7.1.0<br> linux<br> double 10408 </p> 10409 </th> 10410<th> 10411 <p> 10412 GNU C++ version 7.1.0<br> linux<br> long double 10413 </p> 10414 </th> 10415<th> 10416 <p> 10417 Sun compiler version 0x5150<br> Sun Solaris<br> long double 10418 </p> 10419 </th> 10420<th> 10421 <p> 10422 Microsoft Visual C++ version 14.1<br> Win32<br> double 10423 </p> 10424 </th> 10425</tr></thead> 10426<tbody><tr> 10427<td> 10428 <p> 10429 powm1 10430 </p> 10431 </td> 10432<td> 10433 <p> 10434 <span class="blue">Max = 1.06ε (Mean = 0.425ε)</span> 10435 </p> 10436 </td> 10437<td> 10438 <p> 10439 <span class="blue">Max = 2.04ε (Mean = 0.493ε)</span> 10440 </p> 10441 </td> 10442<td> 10443 <p> 10444 <span class="blue">Max = 1.88ε (Mean = 0.49ε)</span> 10445 </p> 10446 </td> 10447<td> 10448 <p> 10449 <span class="blue">Max = 1.84ε (Mean = 0.486ε)</span> 10450 </p> 10451 </td> 10452</tr></tbody> 10453</table></div> 10454</div> 10455<br class="table-break"><div class="table"> 10456<a name="math_toolkit.logs_and_tables.all_table.table_sin_pi"></a><p class="title"><b>Table 23.83. Error rates for sin_pi</b></p> 10457<div class="table-contents"><table class="table" summary="Error rates for sin_pi"> 10458<colgroup> 10459<col> 10460<col> 10461<col> 10462<col> 10463<col> 10464</colgroup> 10465<thead><tr> 10466<th> 10467 </th> 10468<th> 10469 <p> 10470 GNU C++ version 7.1.0<br> linux<br> double 10471 </p> 10472 </th> 10473<th> 10474 <p> 10475 GNU C++ version 7.1.0<br> linux<br> long double 10476 </p> 10477 </th> 10478<th> 10479 <p> 10480 Sun compiler version 0x5150<br> Sun Solaris<br> long double 10481 </p> 10482 </th> 10483<th> 10484 <p> 10485 Microsoft Visual C++ version 14.1<br> Win32<br> double 10486 </p> 10487 </th> 10488</tr></thead> 10489<tbody> 10490<tr> 10491<td> 10492 <p> 10493 sin_pi and cos_pi 10494 </p> 10495 </td> 10496<td> 10497 <p> 10498 <span class="blue">Max = 0ε (Mean = 0ε)</span> 10499 </p> 10500 </td> 10501<td> 10502 <p> 10503 <span class="blue">Max = 0.996ε (Mean = 0.335ε)</span> 10504 </p> 10505 </td> 10506<td> 10507 <p> 10508 <span class="blue">Max = 0.996ε (Mean = 0.336ε)</span> 10509 </p> 10510 </td> 10511<td> 10512 <p> 10513 <span class="blue">Max = 0.99ε (Mean = 0.328ε)</span> 10514 </p> 10515 </td> 10516</tr> 10517<tr> 10518<td> 10519 <p> 10520 sin_pi and cos_pi near integers and half integers 10521 </p> 10522 </td> 10523<td> 10524 <p> 10525 <span class="blue">Max = 0ε (Mean = 0ε)</span> 10526 </p> 10527 </td> 10528<td> 10529 <p> 10530 <span class="blue">Max = 0.976ε (Mean = 0.293ε)</span> 10531 </p> 10532 </td> 10533<td> 10534 <p> 10535 <span class="blue">Max = 0.976ε (Mean = 0.293ε)</span> 10536 </p> 10537 </td> 10538<td> 10539 <p> 10540 <span class="blue">Max = 0.996ε (Mean = 0.343ε)</span> 10541 </p> 10542 </td> 10543</tr> 10544</tbody> 10545</table></div> 10546</div> 10547<br class="table-break"><div class="table"> 10548<a name="math_toolkit.logs_and_tables.all_table.table_sph_bessel"></a><p class="title"><b>Table 23.84. Error rates for sph_bessel</b></p> 10549<div class="table-contents"><table class="table" summary="Error rates for sph_bessel"> 10550<colgroup> 10551<col> 10552<col> 10553<col> 10554<col> 10555<col> 10556</colgroup> 10557<thead><tr> 10558<th> 10559 </th> 10560<th> 10561 <p> 10562 GNU C++ version 7.1.0<br> linux<br> long double 10563 </p> 10564 </th> 10565<th> 10566 <p> 10567 GNU C++ version 7.1.0<br> linux<br> double 10568 </p> 10569 </th> 10570<th> 10571 <p> 10572 Sun compiler version 0x5150<br> Sun Solaris<br> long double 10573 </p> 10574 </th> 10575<th> 10576 <p> 10577 Microsoft Visual C++ version 14.1<br> Win32<br> double 10578 </p> 10579 </th> 10580</tr></thead> 10581<tbody><tr> 10582<td> 10583 <p> 10584 Bessel j: Random Data 10585 </p> 10586 </td> 10587<td> 10588 <p> 10589 <span class="blue">Max = 243ε (Mean = 13.3ε)</span><br> <br> 10590 (<span class="emphasis"><em><cmath>:</em></span> Max = 1.91e+06ε (Mean = 1.09e+05ε)) 10591 </p> 10592 </td> 10593<td> 10594 <p> 10595 <span class="blue">Max = 0.978ε (Mean = 0.0445ε)</span><br> 10596 <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.79e+03ε (Mean = 107ε)) 10597 </p> 10598 </td> 10599<td> 10600 <p> 10601 <span class="blue">Max = 243ε (Mean = 33.7ε)</span> 10602 </p> 10603 </td> 10604<td> 10605 <p> 10606 <span class="blue">Max = 245ε (Mean = 16.3ε)</span> 10607 </p> 10608 </td> 10609</tr></tbody> 10610</table></div> 10611</div> 10612<br class="table-break"><div class="table"> 10613<a name="math_toolkit.logs_and_tables.all_table.table_sph_bessel_prime"></a><p class="title"><b>Table 23.85. Error rates for sph_bessel_prime</b></p> 10614<div class="table-contents"><table class="table" summary="Error rates for sph_bessel_prime"> 10615<colgroup> 10616<col> 10617<col> 10618<col> 10619<col> 10620<col> 10621</colgroup> 10622<thead><tr> 10623<th> 10624 </th> 10625<th> 10626 <p> 10627 GNU C++ version 7.1.0<br> linux<br> double 10628 </p> 10629 </th> 10630<th> 10631 <p> 10632 GNU C++ version 7.1.0<br> linux<br> long double 10633 </p> 10634 </th> 10635<th> 10636 <p> 10637 Sun compiler version 0x5150<br> Sun Solaris<br> long double 10638 </p> 10639 </th> 10640<th> 10641 <p> 10642 Microsoft Visual C++ version 14.1<br> Win32<br> double 10643 </p> 10644 </th> 10645</tr></thead> 10646<tbody><tr> 10647<td> 10648 <p> 10649 Bessel j': Random Data 10650 </p> 10651 </td> 10652<td> 10653 <p> 10654 <span class="blue">Max = 0.753ε (Mean = 0.0343ε)</span> 10655 </p> 10656 </td> 10657<td> 10658 <p> 10659 <span class="blue">Max = 167ε (Mean = 12ε)</span> 10660 </p> 10661 </td> 10662<td> 10663 <p> 10664 <span class="blue">Max = 167ε (Mean = 33.2ε)</span> 10665 </p> 10666 </td> 10667<td> 10668 <p> 10669 <span class="blue">Max = 307ε (Mean = 25.2ε)</span> 10670 </p> 10671 </td> 10672</tr></tbody> 10673</table></div> 10674</div> 10675<br class="table-break"><div class="table"> 10676<a name="math_toolkit.logs_and_tables.all_table.table_sph_neumann"></a><p class="title"><b>Table 23.86. Error rates for sph_neumann</b></p> 10677<div class="table-contents"><table class="table" summary="Error rates for sph_neumann"> 10678<colgroup> 10679<col> 10680<col> 10681<col> 10682<col> 10683<col> 10684</colgroup> 10685<thead><tr> 10686<th> 10687 </th> 10688<th> 10689 <p> 10690 GNU C++ version 7.1.0<br> linux<br> long double 10691 </p> 10692 </th> 10693<th> 10694 <p> 10695 GNU C++ version 7.1.0<br> linux<br> double 10696 </p> 10697 </th> 10698<th> 10699 <p> 10700 Sun compiler version 0x5150<br> Sun Solaris<br> long double 10701 </p> 10702 </th> 10703<th> 10704 <p> 10705 Microsoft Visual C++ version 14.1<br> Win32<br> double 10706 </p> 10707 </th> 10708</tr></thead> 10709<tbody><tr> 10710<td> 10711 <p> 10712 y: Random Data 10713 </p> 10714 </td> 10715<td> 10716 <p> 10717 <span class="blue">Max = 234ε (Mean = 19.5ε)</span><br> <br> 10718 (<span class="emphasis"><em><cmath>:</em></span> Max = 1.6e+06ε (Mean = 1.4e+05ε)) 10719 </p> 10720 </td> 10721<td> 10722 <p> 10723 <span class="blue">Max = 0.995ε (Mean = 0.0665ε)</span><br> 10724 <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.5e+04ε (Mean = 5.33e+03ε)) 10725 </p> 10726 </td> 10727<td> 10728 <p> 10729 <span class="blue">Max = 234ε (Mean = 19.8ε)</span> 10730 </p> 10731 </td> 10732<td> 10733 <p> 10734 <span class="blue">Max = 281ε (Mean = 31.1ε)</span> 10735 </p> 10736 </td> 10737</tr></tbody> 10738</table></div> 10739</div> 10740<br class="table-break"><div class="table"> 10741<a name="math_toolkit.logs_and_tables.all_table.table_sph_neumann_prime"></a><p class="title"><b>Table 23.87. Error rates for sph_neumann_prime</b></p> 10742<div class="table-contents"><table class="table" summary="Error rates for sph_neumann_prime"> 10743<colgroup> 10744<col> 10745<col> 10746<col> 10747<col> 10748<col> 10749</colgroup> 10750<thead><tr> 10751<th> 10752 </th> 10753<th> 10754 <p> 10755 GNU C++ version 7.1.0<br> linux<br> double 10756 </p> 10757 </th> 10758<th> 10759 <p> 10760 GNU C++ version 7.1.0<br> linux<br> long double 10761 </p> 10762 </th> 10763<th> 10764 <p> 10765 Sun compiler version 0x5150<br> Sun Solaris<br> long double 10766 </p> 10767 </th> 10768<th> 10769 <p> 10770 Microsoft Visual C++ version 14.1<br> Win32<br> double 10771 </p> 10772 </th> 10773</tr></thead> 10774<tbody><tr> 10775<td> 10776 <p> 10777 y': Random Data 10778 </p> 10779 </td> 10780<td> 10781 <p> 10782 <span class="blue">Max = 0.988ε (Mean = 0.0869ε)</span> 10783 </p> 10784 </td> 10785<td> 10786 <p> 10787 <span class="blue">Max = 158ε (Mean = 18.8ε)</span> 10788 </p> 10789 </td> 10790<td> 10791 <p> 10792 <span class="blue">Max = 158ε (Mean = 20.2ε)</span> 10793 </p> 10794 </td> 10795<td> 10796 <p> 10797 <span class="blue">Max = 296ε (Mean = 25.6ε)</span> 10798 </p> 10799 </td> 10800</tr></tbody> 10801</table></div> 10802</div> 10803<br class="table-break"><div class="table"> 10804<a name="math_toolkit.logs_and_tables.all_table.table_spherical_harmonic_i"></a><p class="title"><b>Table 23.88. Error rates for spherical_harmonic_i</b></p> 10805<div class="table-contents"><table class="table" summary="Error rates for spherical_harmonic_i"> 10806<colgroup> 10807<col> 10808<col> 10809<col> 10810<col> 10811<col> 10812</colgroup> 10813<thead><tr> 10814<th> 10815 </th> 10816<th> 10817 <p> 10818 GNU C++ version 7.1.0<br> linux<br> double 10819 </p> 10820 </th> 10821<th> 10822 <p> 10823 GNU C++ version 7.1.0<br> linux<br> long double 10824 </p> 10825 </th> 10826<th> 10827 <p> 10828 Sun compiler version 0x5150<br> Sun Solaris<br> long double 10829 </p> 10830 </th> 10831<th> 10832 <p> 10833 Microsoft Visual C++ version 14.1<br> Win32<br> double 10834 </p> 10835 </th> 10836</tr></thead> 10837<tbody><tr> 10838<td> 10839 <p> 10840 Spherical Harmonics 10841 </p> 10842 </td> 10843<td> 10844 <p> 10845 <span class="blue">Max = 1.36ε (Mean = 0.0765ε)</span> 10846 </p> 10847 </td> 10848<td> 10849 <p> 10850 <span class="blue">Max = 2.89e+03ε (Mean = 108ε)</span> 10851 </p> 10852 </td> 10853<td> 10854 <p> 10855 <span class="blue">Max = 1.03e+04ε (Mean = 327ε)</span> 10856 </p> 10857 </td> 10858<td> 10859 <p> 10860 <span class="blue">Max = 2.27e+04ε (Mean = 725ε)</span> 10861 </p> 10862 </td> 10863</tr></tbody> 10864</table></div> 10865</div> 10866<br class="table-break"><div class="table"> 10867<a name="math_toolkit.logs_and_tables.all_table.table_spherical_harmonic_r"></a><p class="title"><b>Table 23.89. Error rates for spherical_harmonic_r</b></p> 10868<div class="table-contents"><table class="table" summary="Error rates for spherical_harmonic_r"> 10869<colgroup> 10870<col> 10871<col> 10872<col> 10873<col> 10874<col> 10875</colgroup> 10876<thead><tr> 10877<th> 10878 </th> 10879<th> 10880 <p> 10881 GNU C++ version 7.1.0<br> linux<br> double 10882 </p> 10883 </th> 10884<th> 10885 <p> 10886 GNU C++ version 7.1.0<br> linux<br> long double 10887 </p> 10888 </th> 10889<th> 10890 <p> 10891 Sun compiler version 0x5150<br> Sun Solaris<br> long double 10892 </p> 10893 </th> 10894<th> 10895 <p> 10896 Microsoft Visual C++ version 14.1<br> Win32<br> double 10897 </p> 10898 </th> 10899</tr></thead> 10900<tbody><tr> 10901<td> 10902 <p> 10903 Spherical Harmonics 10904 </p> 10905 </td> 10906<td> 10907 <p> 10908 <span class="blue">Max = 1.58ε (Mean = 0.0707ε)</span> 10909 </p> 10910 </td> 10911<td> 10912 <p> 10913 <span class="blue">Max = 2.89e+03ε (Mean = 108ε)</span> 10914 </p> 10915 </td> 10916<td> 10917 <p> 10918 <span class="blue">Max = 1.03e+04ε (Mean = 327ε)</span> 10919 </p> 10920 </td> 10921<td> 10922 <p> 10923 <span class="blue">Max = 2.27e+04ε (Mean = 725ε)</span> 10924 </p> 10925 </td> 10926</tr></tbody> 10927</table></div> 10928</div> 10929<br class="table-break"><div class="table"> 10930<a name="math_toolkit.logs_and_tables.all_table.table_sqrt1pm1"></a><p class="title"><b>Table 23.90. Error rates for sqrt1pm1</b></p> 10931<div class="table-contents"><table class="table" summary="Error rates for sqrt1pm1"> 10932<colgroup> 10933<col> 10934<col> 10935<col> 10936<col> 10937<col> 10938</colgroup> 10939<thead><tr> 10940<th> 10941 </th> 10942<th> 10943 <p> 10944 GNU C++ version 7.1.0<br> linux<br> double 10945 </p> 10946 </th> 10947<th> 10948 <p> 10949 GNU C++ version 7.1.0<br> linux<br> long double 10950 </p> 10951 </th> 10952<th> 10953 <p> 10954 Sun compiler version 0x5150<br> Sun Solaris<br> long double 10955 </p> 10956 </th> 10957<th> 10958 <p> 10959 Microsoft Visual C++ version 14.1<br> Win32<br> double 10960 </p> 10961 </th> 10962</tr></thead> 10963<tbody><tr> 10964<td> 10965 <p> 10966 sqrt1pm1 10967 </p> 10968 </td> 10969<td> 10970 <p> 10971 <span class="blue">Max = 1.3ε (Mean = 0.404ε)</span> 10972 </p> 10973 </td> 10974<td> 10975 <p> 10976 <span class="blue">Max = 1.33ε (Mean = 0.404ε)</span> 10977 </p> 10978 </td> 10979<td> 10980 <p> 10981 <span class="blue">Max = 1.54ε (Mean = 0.563ε)</span> 10982 </p> 10983 </td> 10984<td> 10985 <p> 10986 <span class="blue">Max = 1.35ε (Mean = 0.497ε)</span> 10987 </p> 10988 </td> 10989</tr></tbody> 10990</table></div> 10991</div> 10992<br class="table-break"><div class="table"> 10993<a name="math_toolkit.logs_and_tables.all_table.table_tgamma"></a><p class="title"><b>Table 23.91. Error rates for tgamma</b></p> 10994<div class="table-contents"><table class="table" summary="Error rates for tgamma"> 10995<colgroup> 10996<col> 10997<col> 10998<col> 10999<col> 11000<col> 11001</colgroup> 11002<thead><tr> 11003<th> 11004 </th> 11005<th> 11006 <p> 11007 GNU C++ version 7.1.0<br> linux<br> double 11008 </p> 11009 </th> 11010<th> 11011 <p> 11012 GNU C++ version 7.1.0<br> linux<br> long double 11013 </p> 11014 </th> 11015<th> 11016 <p> 11017 Sun compiler version 0x5150<br> Sun Solaris<br> long double 11018 </p> 11019 </th> 11020<th> 11021 <p> 11022 Microsoft Visual C++ version 14.1<br> Win32<br> double 11023 </p> 11024 </th> 11025</tr></thead> 11026<tbody> 11027<tr> 11028<td> 11029 <p> 11030 factorials 11031 </p> 11032 </td> 11033<td> 11034 <p> 11035 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 11036 2.1:</em></span> Max = 3.95ε (Mean = 0.783ε))<br> (<span class="emphasis"><em>Rmath 11037 3.2.3:</em></span> Max = 314ε (Mean = 93.4ε)) 11038 </p> 11039 </td> 11040<td> 11041 <p> 11042 <span class="blue">Max = 2.67ε (Mean = 0.617ε)</span><br> <br> 11043 (<span class="emphasis"><em><cmath>:</em></span> Max = 1.66ε (Mean = 0.584ε))<br> 11044 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.66ε (Mean = 0.584ε)) 11045 </p> 11046 </td> 11047<td> 11048 <p> 11049 <span class="blue">Max = 172ε (Mean = 41ε)</span><br> <br> 11050 (<span class="emphasis"><em><math.h>:</em></span> Max = 0ε (Mean = 0ε)) 11051 </p> 11052 </td> 11053<td> 11054 <p> 11055 <span class="blue">Max = 1.85ε (Mean = 0.566ε)</span><br> <br> 11056 (<span class="emphasis"><em><math.h>:</em></span> Max = 3.17ε (Mean = 0.928ε)) 11057 </p> 11058 </td> 11059</tr> 11060<tr> 11061<td> 11062 <p> 11063 near 0 11064 </p> 11065 </td> 11066<td> 11067 <p> 11068 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 11069 2.1:</em></span> Max = 4.51ε (Mean = 1.92ε))<br> (<span class="emphasis"><em>Rmath 11070 3.2.3:</em></span> Max = 1ε (Mean = 0.335ε)) 11071 </p> 11072 </td> 11073<td> 11074 <p> 11075 <span class="blue">Max = 2ε (Mean = 0.608ε)</span><br> <br> 11076 (<span class="emphasis"><em><cmath>:</em></span> Max = 1ε (Mean = 0.376ε))<br> 11077 (<span class="emphasis"><em><math.h>:</em></span> Max = 1ε (Mean = 0.376ε)) 11078 </p> 11079 </td> 11080<td> 11081 <p> 11082 <span class="blue">Max = 2ε (Mean = 0.647ε)</span><br> <br> 11083 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.5ε (Mean = 0.0791ε)) 11084 </p> 11085 </td> 11086<td> 11087 <p> 11088 <span class="blue">Max = 1.5ε (Mean = 0.635ε)</span><br> <br> 11089 (<span class="emphasis"><em><math.h>:</em></span> Max = 1ε (Mean = 0.405ε)) 11090 </p> 11091 </td> 11092</tr> 11093<tr> 11094<td> 11095 <p> 11096 near 1 11097 </p> 11098 </td> 11099<td> 11100 <p> 11101 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 11102 2.1:</em></span> Max = 4.41ε (Mean = 1.81ε))<br> (<span class="emphasis"><em>Rmath 11103 3.2.3:</em></span> Max = 1ε (Mean = 0.32ε)) 11104 </p> 11105 </td> 11106<td> 11107 <p> 11108 <span class="blue">Max = 2.51ε (Mean = 1.02ε)</span><br> <br> 11109 (<span class="emphasis"><em><cmath>:</em></span> Max = 0.918ε (Mean = 0.203ε))<br> 11110 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.918ε (Mean = 0.203ε)) 11111 </p> 11112 </td> 11113<td> 11114 <p> 11115 <span class="blue">Max = 3.01ε (Mean = 1.06ε)</span><br> <br> 11116 (<span class="emphasis"><em><math.h>:</em></span> Max = 1ε (Mean = 0.175ε)) 11117 </p> 11118 </td> 11119<td> 11120 <p> 11121 <span class="blue">Max = 1.1ε (Mean = 0.59ε)</span><br> <br> 11122 (<span class="emphasis"><em><math.h>:</em></span> Max = 1ε (Mean = 0.4ε)) 11123 </p> 11124 </td> 11125</tr> 11126<tr> 11127<td> 11128 <p> 11129 near 2 11130 </p> 11131 </td> 11132<td> 11133 <p> 11134 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 11135 2.1:</em></span> Max = 7.95ε (Mean = 3.12ε))<br> (<span class="emphasis"><em>Rmath 11136 3.2.3:</em></span> Max = 1ε (Mean = 0.191ε)) 11137 </p> 11138 </td> 11139<td> 11140 <p> 11141 <span class="blue">Max = 4.1ε (Mean = 1.55ε)</span><br> <br> 11142 (<span class="emphasis"><em><cmath>:</em></span> Max = 0.558ε (Mean = 0.298ε))<br> 11143 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.558ε (Mean = 0.298ε)) 11144 </p> 11145 </td> 11146<td> 11147 <p> 11148 <span class="blue">Max = 5.01ε (Mean = 1.89ε)</span><br> <br> 11149 (<span class="emphasis"><em><math.h>:</em></span> Max = 0ε (Mean = 0ε)) 11150 </p> 11151 </td> 11152<td> 11153 <p> 11154 <span class="blue">Max = 2ε (Mean = 0.733ε)</span><br> <br> 11155 (<span class="emphasis"><em><math.h>:</em></span> Max = 0ε (Mean = 0ε)) 11156 </p> 11157 </td> 11158</tr> 11159<tr> 11160<td> 11161 <p> 11162 near -10 11163 </p> 11164 </td> 11165<td> 11166 <p> 11167 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 11168 2.1:</em></span> Max = 2.6ε (Mean = 1.05ε))<br> (<span class="emphasis"><em>Rmath 11169 3.2.3:</em></span> Max = 34.9ε (Mean = 9.2ε)) 11170 </p> 11171 </td> 11172<td> 11173 <p> 11174 <span class="blue">Max = 1.75ε (Mean = 0.895ε)</span><br> <br> 11175 (<span class="emphasis"><em><cmath>:</em></span> Max = 2.26ε (Mean = 1.08ε))<br> 11176 (<span class="emphasis"><em><math.h>:</em></span> Max = 2.26ε (Mean = 1.08ε)) 11177 </p> 11178 </td> 11179<td> 11180 <p> 11181 <span class="blue">Max = 1.75ε (Mean = 0.819ε)</span><br> <br> 11182 (<span class="emphasis"><em><math.h>:</em></span> Max = 0ε (Mean = 0ε)) 11183 </p> 11184 </td> 11185<td> 11186 <p> 11187 <span class="blue">Max = 1.86ε (Mean = 0.881ε)</span><br> <br> 11188 (<span class="emphasis"><em><math.h>:</em></span> Max = 0.866ε (Mean = 0.445ε)) 11189 </p> 11190 </td> 11191</tr> 11192<tr> 11193<td> 11194 <p> 11195 near -55 11196 </p> 11197 </td> 11198<td> 11199 <p> 11200 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 11201 2.1:</em></span> Max = 1.8ε (Mean = 0.782ε))<br> (<span class="emphasis"><em>Rmath 11202 3.2.3:</em></span> Max = 3.89e+04ε (Mean = 9.52e+03ε)) 11203 </p> 11204 </td> 11205<td> 11206 <p> 11207 <span class="blue">Max = 2.69ε (Mean = 1.09ε)</span><br> <br> 11208 (<span class="emphasis"><em><cmath>:</em></span> Max = 1.79ε (Mean = 0.75ε))<br> 11209 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.79ε (Mean = 0.75ε)) 11210 </p> 11211 </td> 11212<td> 11213 <p> 11214 <span class="blue">Max = 98.5ε (Mean = 53.4ε)</span><br> <br> 11215 (<span class="emphasis"><em><math.h>:</em></span> Max = 0ε (Mean = 0ε)) 11216 </p> 11217 </td> 11218<td> 11219 <p> 11220 <span class="blue">Max = 2.7ε (Mean = 1.35ε)</span><br> <br> 11221 (<span class="emphasis"><em><math.h>:</em></span> Max = 3.87e+04ε (Mean = 6.71e+03ε)) 11222 </p> 11223 </td> 11224</tr> 11225</tbody> 11226</table></div> 11227</div> 11228<br class="table-break"><div class="table"> 11229<a name="math_toolkit.logs_and_tables.all_table.table_tgamma1pm1"></a><p class="title"><b>Table 23.92. Error rates for tgamma1pm1</b></p> 11230<div class="table-contents"><table class="table" summary="Error rates for tgamma1pm1"> 11231<colgroup> 11232<col> 11233<col> 11234<col> 11235<col> 11236<col> 11237</colgroup> 11238<thead><tr> 11239<th> 11240 </th> 11241<th> 11242 <p> 11243 GNU C++ version 7.1.0<br> linux<br> double 11244 </p> 11245 </th> 11246<th> 11247 <p> 11248 GNU C++ version 7.1.0<br> linux<br> long double 11249 </p> 11250 </th> 11251<th> 11252 <p> 11253 Sun compiler version 0x5150<br> Sun Solaris<br> long double 11254 </p> 11255 </th> 11256<th> 11257 <p> 11258 Microsoft Visual C++ version 14.1<br> Win32<br> double 11259 </p> 11260 </th> 11261</tr></thead> 11262<tbody><tr> 11263<td> 11264 <p> 11265 tgamma1pm1(dz) 11266 </p> 11267 </td> 11268<td> 11269 <p> 11270 <span class="blue">Max = 0ε (Mean = 0ε)</span> 11271 </p> 11272 </td> 11273<td> 11274 <p> 11275 <span class="blue">Max = 1.12ε (Mean = 0.49ε)</span> 11276 </p> 11277 </td> 11278<td> 11279 <p> 11280 <span class="blue">Max = 6.61ε (Mean = 0.84ε)</span> 11281 </p> 11282 </td> 11283<td> 11284 <p> 11285 <span class="blue">Max = 3.31ε (Mean = 0.517ε)</span> 11286 </p> 11287 </td> 11288</tr></tbody> 11289</table></div> 11290</div> 11291<br class="table-break"><div class="table"> 11292<a name="math_toolkit.logs_and_tables.all_table.table_tgamma_delta_ratio"></a><p class="title"><b>Table 23.93. Error rates for tgamma_delta_ratio</b></p> 11293<div class="table-contents"><table class="table" summary="Error rates for tgamma_delta_ratio"> 11294<colgroup> 11295<col> 11296<col> 11297<col> 11298<col> 11299<col> 11300</colgroup> 11301<thead><tr> 11302<th> 11303 </th> 11304<th> 11305 <p> 11306 GNU C++ version 7.1.0<br> linux<br> double 11307 </p> 11308 </th> 11309<th> 11310 <p> 11311 GNU C++ version 7.1.0<br> linux<br> long double 11312 </p> 11313 </th> 11314<th> 11315 <p> 11316 Sun compiler version 0x5150<br> Sun Solaris<br> long double 11317 </p> 11318 </th> 11319<th> 11320 <p> 11321 Microsoft Visual C++ version 14.1<br> Win32<br> double 11322 </p> 11323 </th> 11324</tr></thead> 11325<tbody> 11326<tr> 11327<td> 11328 <p> 11329 tgamma + small delta ratios 11330 </p> 11331 </td> 11332<td> 11333 <p> 11334 <span class="blue">Max = 0ε (Mean = 0ε)</span> 11335 </p> 11336 </td> 11337<td> 11338 <p> 11339 <span class="blue">Max = 5.83ε (Mean = 1.3ε)</span> 11340 </p> 11341 </td> 11342<td> 11343 <p> 11344 <span class="blue">Max = 15.4ε (Mean = 2.09ε)</span> 11345 </p> 11346 </td> 11347<td> 11348 <p> 11349 <span class="blue">Max = 7.56ε (Mean = 1.31ε)</span> 11350 </p> 11351 </td> 11352</tr> 11353<tr> 11354<td> 11355 <p> 11356 tgamma + small delta ratios (negative delta) 11357 </p> 11358 </td> 11359<td> 11360 <p> 11361 <span class="blue">Max = 0ε (Mean = 0ε)</span> 11362 </p> 11363 </td> 11364<td> 11365 <p> 11366 <span class="blue">Max = 7.94ε (Mean = 1.4ε)</span> 11367 </p> 11368 </td> 11369<td> 11370 <p> 11371 <span class="blue">Max = 18.3ε (Mean = 2.03ε)</span> 11372 </p> 11373 </td> 11374<td> 11375 <p> 11376 <span class="blue">Max = 7.43ε (Mean = 1.42ε)</span> 11377 </p> 11378 </td> 11379</tr> 11380<tr> 11381<td> 11382 <p> 11383 tgamma + small integer ratios 11384 </p> 11385 </td> 11386<td> 11387 <p> 11388 <span class="blue">Max = 0ε (Mean = 0ε)</span> 11389 </p> 11390 </td> 11391<td> 11392 <p> 11393 <span class="blue">Max = 1.96ε (Mean = 0.677ε)</span> 11394 </p> 11395 </td> 11396<td> 11397 <p> 11398 <span class="blue">Max = 1.96ε (Mean = 0.677ε)</span> 11399 </p> 11400 </td> 11401<td> 11402 <p> 11403 <span class="blue">Max = 2.74ε (Mean = 0.736ε)</span> 11404 </p> 11405 </td> 11406</tr> 11407<tr> 11408<td> 11409 <p> 11410 tgamma + small integer ratios (negative delta) 11411 </p> 11412 </td> 11413<td> 11414 <p> 11415 <span class="blue">Max = 0ε (Mean = 0ε)</span> 11416 </p> 11417 </td> 11418<td> 11419 <p> 11420 <span class="blue">Max = 1.62ε (Mean = 0.451ε)</span> 11421 </p> 11422 </td> 11423<td> 11424 <p> 11425 <span class="blue">Max = 1.62ε (Mean = 0.451ε)</span> 11426 </p> 11427 </td> 11428<td> 11429 <p> 11430 <span class="blue">Max = 2.15ε (Mean = 0.685ε)</span> 11431 </p> 11432 </td> 11433</tr> 11434<tr> 11435<td> 11436 <p> 11437 integer tgamma ratios 11438 </p> 11439 </td> 11440<td> 11441 <p> 11442 <span class="blue">Max = 0ε (Mean = 0ε)</span> 11443 </p> 11444 </td> 11445<td> 11446 <p> 11447 <span class="blue">Max = 0.997ε (Mean = 0.4ε)</span> 11448 </p> 11449 </td> 11450<td> 11451 <p> 11452 <span class="blue">Max = 0.997ε (Mean = 0.4ε)</span> 11453 </p> 11454 </td> 11455<td> 11456 <p> 11457 <span class="blue">Max = 0.968ε (Mean = 0.386ε)</span> 11458 </p> 11459 </td> 11460</tr> 11461<tr> 11462<td> 11463 <p> 11464 integer tgamma ratios (negative delta) 11465 </p> 11466 </td> 11467<td> 11468 <p> 11469 <span class="blue">Max = 0ε (Mean = 0ε)</span> 11470 </p> 11471 </td> 11472<td> 11473 <p> 11474 <span class="blue">Max = 0.853ε (Mean = 0.176ε)</span> 11475 </p> 11476 </td> 11477<td> 11478 <p> 11479 <span class="blue">Max = 0.853ε (Mean = 0.176ε)</span> 11480 </p> 11481 </td> 11482<td> 11483 <p> 11484 <span class="blue">Max = 0.974ε (Mean = 0.175ε)</span> 11485 </p> 11486 </td> 11487</tr> 11488</tbody> 11489</table></div> 11490</div> 11491<br class="table-break"><div class="table"> 11492<a name="math_toolkit.logs_and_tables.all_table.table_tgamma_incomplete_"></a><p class="title"><b>Table 23.94. Error rates for tgamma (incomplete)</b></p> 11493<div class="table-contents"><table class="table" summary="Error rates for tgamma (incomplete)"> 11494<colgroup> 11495<col> 11496<col> 11497<col> 11498<col> 11499<col> 11500</colgroup> 11501<thead><tr> 11502<th> 11503 </th> 11504<th> 11505 <p> 11506 GNU C++ version 7.1.0<br> linux<br> double 11507 </p> 11508 </th> 11509<th> 11510 <p> 11511 GNU C++ version 7.1.0<br> linux<br> long double 11512 </p> 11513 </th> 11514<th> 11515 <p> 11516 Sun compiler version 0x5150<br> Sun Solaris<br> long double 11517 </p> 11518 </th> 11519<th> 11520 <p> 11521 Microsoft Visual C++ version 14.1<br> Win32<br> double 11522 </p> 11523 </th> 11524</tr></thead> 11525<tbody> 11526<tr> 11527<td> 11528 <p> 11529 tgamma(a, z) medium values 11530 </p> 11531 </td> 11532<td> 11533 <p> 11534 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 11535 2.1:</em></span> Max = 200ε (Mean = 13.3ε)) 11536 </p> 11537 </td> 11538<td> 11539 <p> 11540 <span class="blue">Max = 8.47ε (Mean = 1.9ε)</span> 11541 </p> 11542 </td> 11543<td> 11544 <p> 11545 <span class="blue">Max = 412ε (Mean = 95.5ε)</span> 11546 </p> 11547 </td> 11548<td> 11549 <p> 11550 <span class="blue">Max = 8.14ε (Mean = 1.76ε)</span> 11551 </p> 11552 </td> 11553</tr> 11554<tr> 11555<td> 11556 <p> 11557 tgamma(a, z) small values 11558 </p> 11559 </td> 11560<td> 11561 <p> 11562 <span class="blue">Max = 0.753ε (Mean = 0.0474ε)</span><br> 11563 <br> (<span class="emphasis"><em>GSL 2.1:</em></span> <span class="red">Max = 11564 1.38e+10ε (Mean = 1.05e+09ε))</span> 11565 </p> 11566 </td> 11567<td> 11568 <p> 11569 <span class="blue">Max = 2.31ε (Mean = 0.775ε)</span> 11570 </p> 11571 </td> 11572<td> 11573 <p> 11574 <span class="blue">Max = 2.13ε (Mean = 0.717ε)</span> 11575 </p> 11576 </td> 11577<td> 11578 <p> 11579 <span class="blue">Max = 2.53ε (Mean = 0.66ε)</span> 11580 </p> 11581 </td> 11582</tr> 11583<tr> 11584<td> 11585 <p> 11586 tgamma(a, z) integer and half integer values 11587 </p> 11588 </td> 11589<td> 11590 <p> 11591 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 11592 2.1:</em></span> Max = 117ε (Mean = 12.5ε)) 11593 </p> 11594 </td> 11595<td> 11596 <p> 11597 <span class="blue">Max = 5.52ε (Mean = 1.48ε)</span> 11598 </p> 11599 </td> 11600<td> 11601 <p> 11602 <span class="blue">Max = 79.6ε (Mean = 20.9ε)</span> 11603 </p> 11604 </td> 11605<td> 11606 <p> 11607 <span class="blue">Max = 5.16ε (Mean = 1.33ε)</span> 11608 </p> 11609 </td> 11610</tr> 11611</tbody> 11612</table></div> 11613</div> 11614<br class="table-break"><div class="table"> 11615<a name="math_toolkit.logs_and_tables.all_table.table_tgamma_lower"></a><p class="title"><b>Table 23.95. Error rates for tgamma_lower</b></p> 11616<div class="table-contents"><table class="table" summary="Error rates for tgamma_lower"> 11617<colgroup> 11618<col> 11619<col> 11620<col> 11621<col> 11622<col> 11623</colgroup> 11624<thead><tr> 11625<th> 11626 </th> 11627<th> 11628 <p> 11629 GNU C++ version 7.1.0<br> linux<br> double 11630 </p> 11631 </th> 11632<th> 11633 <p> 11634 GNU C++ version 7.1.0<br> linux<br> long double 11635 </p> 11636 </th> 11637<th> 11638 <p> 11639 Sun compiler version 0x5150<br> Sun Solaris<br> long double 11640 </p> 11641 </th> 11642<th> 11643 <p> 11644 Microsoft Visual C++ version 14.1<br> Win32<br> double 11645 </p> 11646 </th> 11647</tr></thead> 11648<tbody> 11649<tr> 11650<td> 11651 <p> 11652 tgamma(a, z) medium values 11653 </p> 11654 </td> 11655<td> 11656 <p> 11657 <span class="blue">Max = 0.833ε (Mean = 0.0315ε)</span><br> 11658 <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.833ε (Mean = 0.0315ε)) 11659 </p> 11660 </td> 11661<td> 11662 <p> 11663 <span class="blue">Max = 6.79ε (Mean = 1.46ε)</span> 11664 </p> 11665 </td> 11666<td> 11667 <p> 11668 <span class="blue">Max = 363ε (Mean = 63.8ε)</span> 11669 </p> 11670 </td> 11671<td> 11672 <p> 11673 <span class="blue">Max = 5.62ε (Mean = 1.49ε)</span> 11674 </p> 11675 </td> 11676</tr> 11677<tr> 11678<td> 11679 <p> 11680 tgamma(a, z) small values 11681 </p> 11682 </td> 11683<td> 11684 <p> 11685 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 11686 2.1:</em></span> Max = 0ε (Mean = 0ε)) 11687 </p> 11688 </td> 11689<td> 11690 <p> 11691 <span class="blue">Max = 1.97ε (Mean = 0.555ε)</span> 11692 </p> 11693 </td> 11694<td> 11695 <p> 11696 <span class="blue">Max = 1.97ε (Mean = 0.558ε)</span> 11697 </p> 11698 </td> 11699<td> 11700 <p> 11701 <span class="blue">Max = 1.57ε (Mean = 0.525ε)</span> 11702 </p> 11703 </td> 11704</tr> 11705<tr> 11706<td> 11707 <p> 11708 tgamma(a, z) integer and half integer values 11709 </p> 11710 </td> 11711<td> 11712 <p> 11713 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 11714 2.1:</em></span> Max = 0ε (Mean = 0ε)) 11715 </p> 11716 </td> 11717<td> 11718 <p> 11719 <span class="blue">Max = 4.83ε (Mean = 1.15ε)</span> 11720 </p> 11721 </td> 11722<td> 11723 <p> 11724 <span class="blue">Max = 84.7ε (Mean = 17.5ε)</span> 11725 </p> 11726 </td> 11727<td> 11728 <p> 11729 <span class="blue">Max = 2.69ε (Mean = 0.849ε)</span> 11730 </p> 11731 </td> 11732</tr> 11733</tbody> 11734</table></div> 11735</div> 11736<br class="table-break"><div class="table"> 11737<a name="math_toolkit.logs_and_tables.all_table.table_tgamma_ratio"></a><p class="title"><b>Table 23.96. Error rates for tgamma_ratio</b></p> 11738<div class="table-contents"><table class="table" summary="Error rates for tgamma_ratio"> 11739<colgroup> 11740<col> 11741<col> 11742<col> 11743<col> 11744<col> 11745</colgroup> 11746<thead><tr> 11747<th> 11748 </th> 11749<th> 11750 <p> 11751 GNU C++ version 7.1.0<br> linux<br> double 11752 </p> 11753 </th> 11754<th> 11755 <p> 11756 GNU C++ version 7.1.0<br> linux<br> long double 11757 </p> 11758 </th> 11759<th> 11760 <p> 11761 Sun compiler version 0x5150<br> Sun Solaris<br> long double 11762 </p> 11763 </th> 11764<th> 11765 <p> 11766 Microsoft Visual C++ version 14.1<br> Win32<br> double 11767 </p> 11768 </th> 11769</tr></thead> 11770<tbody><tr> 11771<td> 11772 <p> 11773 tgamma ratios 11774 </p> 11775 </td> 11776<td> 11777 <p> 11778 <span class="blue">Max = 0.694ε (Mean = 0.0347ε)</span> 11779 </p> 11780 </td> 11781<td> 11782 <p> 11783 <span class="blue">Max = 2.99ε (Mean = 1.15ε)</span> 11784 </p> 11785 </td> 11786<td> 11787 <p> 11788 <span class="blue">Max = 174ε (Mean = 61.2ε)</span> 11789 </p> 11790 </td> 11791<td> 11792 <p> 11793 <span class="blue">Max = 3.28ε (Mean = 1.12ε)</span> 11794 </p> 11795 </td> 11796</tr></tbody> 11797</table></div> 11798</div> 11799<br class="table-break"><div class="table"> 11800<a name="math_toolkit.logs_and_tables.all_table.table_trigamma"></a><p class="title"><b>Table 23.97. Error rates for trigamma</b></p> 11801<div class="table-contents"><table class="table" summary="Error rates for trigamma"> 11802<colgroup> 11803<col> 11804<col> 11805<col> 11806<col> 11807<col> 11808</colgroup> 11809<thead><tr> 11810<th> 11811 </th> 11812<th> 11813 <p> 11814 GNU C++ version 7.1.0<br> linux<br> double 11815 </p> 11816 </th> 11817<th> 11818 <p> 11819 GNU C++ version 7.1.0<br> linux<br> long double 11820 </p> 11821 </th> 11822<th> 11823 <p> 11824 Sun compiler version 0x5150<br> Sun Solaris<br> long double 11825 </p> 11826 </th> 11827<th> 11828 <p> 11829 Microsoft Visual C++ version 14.1<br> Win32<br> double 11830 </p> 11831 </th> 11832</tr></thead> 11833<tbody><tr> 11834<td> 11835 <p> 11836 Mathematica Data 11837 </p> 11838 </td> 11839<td> 11840 <p> 11841 <span class="blue">Max = 0.998ε (Mean = 0.105ε)</span><br> <br> 11842 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.34e+04ε (Mean = 1.49e+03ε))<br> 11843 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.34e+04ε (Mean = 1.51e+03ε)) 11844 </p> 11845 </td> 11846<td> 11847 <p> 11848 <span class="blue">Max = 1.28ε (Mean = 0.449ε)</span> 11849 </p> 11850 </td> 11851<td> 11852 <p> 11853 <span class="blue">Max = 1.28ε (Mean = 0.449ε)</span> 11854 </p> 11855 </td> 11856<td> 11857 <p> 11858 <span class="blue">Max = 1ε (Mean = 0.382ε)</span> 11859 </p> 11860 </td> 11861</tr></tbody> 11862</table></div> 11863</div> 11864<br class="table-break"><div class="table"> 11865<a name="math_toolkit.logs_and_tables.all_table.table_zeta"></a><p class="title"><b>Table 23.98. Error rates for zeta</b></p> 11866<div class="table-contents"><table class="table" summary="Error rates for zeta"> 11867<colgroup> 11868<col> 11869<col> 11870<col> 11871<col> 11872<col> 11873</colgroup> 11874<thead><tr> 11875<th> 11876 </th> 11877<th> 11878 <p> 11879 GNU C++ version 7.1.0<br> linux<br> long double 11880 </p> 11881 </th> 11882<th> 11883 <p> 11884 GNU C++ version 7.1.0<br> linux<br> double 11885 </p> 11886 </th> 11887<th> 11888 <p> 11889 Sun compiler version 0x5150<br> Sun Solaris<br> long double 11890 </p> 11891 </th> 11892<th> 11893 <p> 11894 Microsoft Visual C++ version 14.1<br> Win32<br> double 11895 </p> 11896 </th> 11897</tr></thead> 11898<tbody> 11899<tr> 11900<td> 11901 <p> 11902 Zeta: Random values greater than 1 11903 </p> 11904 </td> 11905<td> 11906 <p> 11907 <span class="blue">Max = 0.846ε (Mean = 0.0833ε)</span><br> 11908 <br> (<span class="emphasis"><em><cmath>:</em></span> Max = 5.45ε (Mean = 1ε)) 11909 </p> 11910 </td> 11911<td> 11912 <p> 11913 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 11914 2.1:</em></span> Max = 8.69ε (Mean = 1.03ε)) 11915 </p> 11916 </td> 11917<td> 11918 <p> 11919 <span class="blue">Max = 0.846ε (Mean = 0.0833ε)</span> 11920 </p> 11921 </td> 11922<td> 11923 <p> 11924 <span class="blue">Max = 0.836ε (Mean = 0.093ε)</span> 11925 </p> 11926 </td> 11927</tr> 11928<tr> 11929<td> 11930 <p> 11931 Zeta: Random values less than 1 11932 </p> 11933 </td> 11934<td> 11935 <p> 11936 <span class="blue">Max = 7.03ε (Mean = 2.93ε)</span><br> <br> 11937 (<span class="emphasis"><em><cmath>:</em></span> Max = 538ε (Mean = 59.3ε)) 11938 </p> 11939 </td> 11940<td> 11941 <p> 11942 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 11943 2.1:</em></span> Max = 137ε (Mean = 13.8ε)) 11944 </p> 11945 </td> 11946<td> 11947 <p> 11948 <span class="blue">Max = 70.1ε (Mean = 17.1ε)</span> 11949 </p> 11950 </td> 11951<td> 11952 <p> 11953 <span class="blue">Max = 6.84ε (Mean = 3.12ε)</span> 11954 </p> 11955 </td> 11956</tr> 11957<tr> 11958<td> 11959 <p> 11960 Zeta: Values close to and greater than 1 11961 </p> 11962 </td> 11963<td> 11964 <p> 11965 <span class="blue">Max = 0.995ε (Mean = 0.5ε)</span><br> <br> 11966 (<span class="emphasis"><em><cmath>:</em></span> Max = 1.9e+06ε (Mean = 5.11e+05ε)) 11967 </p> 11968 </td> 11969<td> 11970 <p> 11971 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 11972 2.1:</em></span> Max = 7.73ε (Mean = 4.07ε)) 11973 </p> 11974 </td> 11975<td> 11976 <p> 11977 <span class="blue">Max = 0.995ε (Mean = 0.5ε)</span> 11978 </p> 11979 </td> 11980<td> 11981 <p> 11982 <span class="blue">Max = 0.994ε (Mean = 0.421ε)</span> 11983 </p> 11984 </td> 11985</tr> 11986<tr> 11987<td> 11988 <p> 11989 Zeta: Values close to and less than 1 11990 </p> 11991 </td> 11992<td> 11993 <p> 11994 <span class="blue">Max = 0.998ε (Mean = 0.508ε)</span><br> <br> 11995 (<span class="emphasis"><em><cmath>:</em></span> Max = 8.53e+06ε (Mean = 1.87e+06ε)) 11996 </p> 11997 </td> 11998<td> 11999 <p> 12000 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 12001 2.1:</em></span> Max = 0.991ε (Mean = 0.28ε)) 12002 </p> 12003 </td> 12004<td> 12005 <p> 12006 <span class="blue">Max = 0.998ε (Mean = 0.508ε)</span> 12007 </p> 12008 </td> 12009<td> 12010 <p> 12011 <span class="blue">Max = 0.991ε (Mean = 0.375ε)</span> 12012 </p> 12013 </td> 12014</tr> 12015<tr> 12016<td> 12017 <p> 12018 Zeta: Integer arguments 12019 </p> 12020 </td> 12021<td> 12022 <p> 12023 <span class="blue">Max = 9ε (Mean = 3.06ε)</span><br> <br> 12024 (<span class="emphasis"><em><cmath>:</em></span> Max = 70.3ε (Mean = 17.4ε)) 12025 </p> 12026 </td> 12027<td> 12028 <p> 12029 <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL 12030 2.1:</em></span> Max = 3.75ε (Mean = 1.1ε)) 12031 </p> 12032 </td> 12033<td> 12034 <p> 12035 <span class="blue">Max = 28ε (Mean = 5.62ε)</span> 12036 </p> 12037 </td> 12038<td> 12039 <p> 12040 <span class="blue">Max = 9ε (Mean = 3ε)</span> 12041 </p> 12042 </td> 12043</tr> 12044</tbody> 12045</table></div> 12046</div> 12047<br class="table-break"> 12048</div> 12049<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> 12050<td align="left"></td> 12051<td align="right"><div class="copyright-footer">Copyright © 2006-2019 Nikhar 12052 Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, 12053 Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan 12054 Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, 12055 Daryle Walker and Xiaogang Zhang<p> 12056 Distributed under the Boost Software License, Version 1.0. (See accompanying 12057 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>) 12058 </p> 12059</div></td> 12060</tr></table> 12061<hr> 12062<div class="spirit-nav"> 12063<a accesskey="p" href="../logs_and_tables.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../logs_and_tables.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="logs.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> 12064</div> 12065</body> 12066</html> 12067
