1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> 4<title>Performance Tuning Macros</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="../perf.html" title="Chapter 22. Performance"> 9<link rel="prev" href="multiprecision.html" title="Cost of High-Precision Non-built-in Floating-point"> 10<link rel="next" href="comp_compilers.html" title="Comparing Different Compilers"> 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="multiprecision.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../perf.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="comp_compilers.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a> 24</div> 25<div class="section"> 26<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 27<a name="math_toolkit.tuning"></a><a class="link" href="tuning.html" title="Performance Tuning Macros">Performance Tuning Macros</a> 28</h2></div></div></div> 29<p> 30 There are a small number of performance tuning options that are determined 31 by configuration macros. These should be set in boost/math/tools/user.hpp; 32 or else reported to the Boost-development mailing list so that the appropriate 33 option for a given compiler and OS platform can be set automatically in our 34 configuration setup. 35 </p> 36<div class="informaltable"><table class="table"> 37<colgroup> 38<col> 39<col> 40</colgroup> 41<thead><tr> 42<th> 43 <p> 44 Macro 45 </p> 46 </th> 47<th> 48 <p> 49 Meaning 50 </p> 51 </th> 52</tr></thead> 53<tbody> 54<tr> 55<td> 56 <p> 57 BOOST_MATH_POLY_METHOD 58 </p> 59 </td> 60<td> 61 <p> 62 Determines how polynomials and most rational functions are evaluated. 63 Define to one of the values 0, 1, 2 or 3: see below for the meaning 64 of these values. 65 </p> 66 </td> 67</tr> 68<tr> 69<td> 70 <p> 71 BOOST_MATH_RATIONAL_METHOD 72 </p> 73 </td> 74<td> 75 <p> 76 Determines how symmetrical rational functions are evaluated: mostly 77 this only effects how the Lanczos approximation is evaluated, and 78 how the <code class="computeroutput"><span class="identifier">evaluate_rational</span></code> 79 function behaves. Define to one of the values 0, 1, 2 or 3: see below 80 for the meaning of these values. 81 </p> 82 </td> 83</tr> 84<tr> 85<td> 86 <p> 87 BOOST_MATH_MAX_POLY_ORDER 88 </p> 89 </td> 90<td> 91 <p> 92 The maximum order of polynomial or rational function that will be 93 evaluated by a method other than 0 (a simple "for" loop). 94 </p> 95 </td> 96</tr> 97<tr> 98<td> 99 <p> 100 BOOST_MATH_INT_TABLE_TYPE(RT, IT) 101 </p> 102 </td> 103<td> 104 <p> 105 Many of the coefficients to the polynomials and rational functions 106 used by this library are integers. Normally these are stored as tables 107 as integers, but if mixed integer / floating point arithmetic is 108 much slower than regular floating point arithmetic then they can 109 be stored as tables of floating point values instead. If mixed arithmetic 110 is slow then add: 111 </p> 112 <div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem"> 113 define BOOST_MATH_INT_TABLE_TYPE(RT, IT) RT 114 </li></ol></div> 115 <p> 116 to boost/math/tools/user.hpp, otherwise the default of: 117 </p> 118 <div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem"> 119 define BOOST_MATH_INT_TABLE_TYPE(RT, IT) IT 120 </li></ol></div> 121 <p> 122 Set in boost/math/config.hpp is fine, and may well result in smaller 123 code. 124 </p> 125 </td> 126</tr> 127</tbody> 128</table></div> 129<p> 130 The values to which <code class="computeroutput"><span class="identifier">BOOST_MATH_POLY_METHOD</span></code> 131 and <code class="computeroutput"><span class="identifier">BOOST_MATH_RATIONAL_METHOD</span></code> 132 may be set are as follows: 133 </p> 134<div class="informaltable"><table class="table"> 135<colgroup> 136<col> 137<col> 138</colgroup> 139<thead><tr> 140<th> 141 <p> 142 Value 143 </p> 144 </th> 145<th> 146 <p> 147 Effect 148 </p> 149 </th> 150</tr></thead> 151<tbody> 152<tr> 153<td> 154 <p> 155 0 156 </p> 157 </td> 158<td> 159 <p> 160 The polynomial or rational function is evaluated using Horner's method, 161 and a simple for-loop. 162 </p> 163 <p> 164 Note that if the order of the polynomial or rational function is 165 a runtime parameter, or the order is greater than the value of <code class="computeroutput"><span class="identifier">BOOST_MATH_MAX_POLY_ORDER</span></code>, then 166 this method is always used, irrespective of the value of <code class="computeroutput"><span class="identifier">BOOST_MATH_POLY_METHOD</span></code> or <code class="computeroutput"><span class="identifier">BOOST_MATH_RATIONAL_METHOD</span></code>. 167 </p> 168 </td> 169</tr> 170<tr> 171<td> 172 <p> 173 1 174 </p> 175 </td> 176<td> 177 <p> 178 The polynomial or rational function is evaluated without the use 179 of a loop, and using Horner's method. This only occurs if the order 180 of the polynomial is known at compile time and is less than or equal 181 to <code class="computeroutput"><span class="identifier">BOOST_MATH_MAX_POLY_ORDER</span></code>. 182 </p> 183 </td> 184</tr> 185<tr> 186<td> 187 <p> 188 2 189 </p> 190 </td> 191<td> 192 <p> 193 The polynomial or rational function is evaluated without the use 194 of a loop, and using a second order Horner's method. In theory this 195 permits two operations to occur in parallel for polynomials, and 196 four in parallel for rational functions. This only occurs if the 197 order of the polynomial is known at compile time and is less than 198 or equal to <code class="computeroutput"><span class="identifier">BOOST_MATH_MAX_POLY_ORDER</span></code>. 199 </p> 200 </td> 201</tr> 202<tr> 203<td> 204 <p> 205 3 206 </p> 207 </td> 208<td> 209 <p> 210 The polynomial or rational function is evaluated without the use 211 of a loop, and using a second order Horner's method. In theory this 212 permits two operations to occur in parallel for polynomials, and 213 four in parallel for rational functions. This differs from method 214 "2" in that the code is carefully ordered to make the parallelisation 215 more obvious to the compiler: rather than relying on the compiler's 216 optimiser to spot the parallelisation opportunities. This only occurs 217 if the order of the polynomial is known at compile time and is less 218 than or equal to <code class="computeroutput"><span class="identifier">BOOST_MATH_MAX_POLY_ORDER</span></code>. 219 </p> 220 </td> 221</tr> 222</tbody> 223</table></div> 224<p> 225 The performance test suite generates a report for your particular compiler 226 showing which method is likely to work best, the following tables show the 227 results for MSVC-14.0 and GCC-5.1.0 (Linux). There's not much to choose between 228 the various methods, but generally loop-unrolled methods perform better. Interestingly, 229 ordering the code to try and "second guess" possible optimizations 230 seems not to be such a good idea (method 3 below). 231 </p> 232<div class="table"> 233<a name="math_toolkit.tuning.table_Polynomial_Method_Comparison_with_Microsoft_Visual_C_version_14_2_on_Windows_x64"></a><p class="title"><b>Table 22.4. Polynomial Method Comparison with Microsoft Visual C++ version 14.2 234 on Windows x64</b></p> 235<div class="table-contents"><table class="table" summary="Polynomial Method Comparison with Microsoft Visual C++ version 14.2 236 on Windows x64"> 237<colgroup> 238<col> 239<col> 240<col> 241<col> 242<col> 243<col> 244<col> 245<col> 246<col> 247</colgroup> 248<thead><tr> 249<th> 250 <p> 251 Function 252 </p> 253 </th> 254<th> 255 <p> 256 Method 0<br> (Double Coefficients) 257 </p> 258 </th> 259<th> 260 <p> 261 Method 0<br> (Integer Coefficients) 262 </p> 263 </th> 264<th> 265 <p> 266 Method 1<br> (Double Coefficients) 267 </p> 268 </th> 269<th> 270 <p> 271 Method 1<br> (Integer Coefficients) 272 </p> 273 </th> 274<th> 275 <p> 276 Method 2<br> (Double Coefficients) 277 </p> 278 </th> 279<th> 280 <p> 281 Method 2<br> (Integer Coefficients) 282 </p> 283 </th> 284<th> 285 <p> 286 Method 3<br> (Double Coefficients) 287 </p> 288 </th> 289<th> 290 <p> 291 Method 3<br> (Integer Coefficients) 292 </p> 293 </th> 294</tr></thead> 295<tbody> 296<tr> 297<td> 298 <p> 299 Order 2 300 </p> 301 </td> 302<td> 303 <p> 304 <span class="grey">-</span> 305 </p> 306 </td> 307<td> 308 <p> 309 <span class="grey">-</span> 310 </p> 311 </td> 312<td> 313 <p> 314 <span class="green">1.00<br> (6ns)</span> 315 </p> 316 </td> 317<td> 318 <p> 319 <span class="green">1.00<br> (6ns)</span> 320 </p> 321 </td> 322<td> 323 <p> 324 <span class="green">1.00<br> (6ns)</span> 325 </p> 326 </td> 327<td> 328 <p> 329 <span class="green">1.00<br> (6ns)</span> 330 </p> 331 </td> 332<td> 333 <p> 334 <span class="green">1.00<br> (6ns)</span> 335 </p> 336 </td> 337<td> 338 <p> 339 <span class="green">1.00<br> (6ns)</span> 340 </p> 341 </td> 342</tr> 343<tr> 344<td> 345 <p> 346 Order 3 347 </p> 348 </td> 349<td> 350 <p> 351 <span class="red">2.33<br> (21ns)</span> 352 </p> 353 </td> 354<td> 355 <p> 356 <span class="red">3.33<br> (30ns)</span> 357 </p> 358 </td> 359<td> 360 <p> 361 <span class="green">1.00<br> (9ns)</span> 362 </p> 363 </td> 364<td> 365 <p> 366 <span class="green">1.00<br> (9ns)</span> 367 </p> 368 </td> 369<td> 370 <p> 371 <span class="green">1.00<br> (9ns)</span> 372 </p> 373 </td> 374<td> 375 <p> 376 <span class="green">1.00<br> (9ns)</span> 377 </p> 378 </td> 379<td> 380 <p> 381 <span class="green">1.00<br> (9ns)</span> 382 </p> 383 </td> 384<td> 385 <p> 386 <span class="green">1.00<br> (9ns)</span> 387 </p> 388 </td> 389</tr> 390<tr> 391<td> 392 <p> 393 Order 4 394 </p> 395 </td> 396<td> 397 <p> 398 <span class="blue">2.00<br> (24ns)</span> 399 </p> 400 </td> 401<td> 402 <p> 403 <span class="red">3.00<br> (36ns)</span> 404 </p> 405 </td> 406<td> 407 <p> 408 <span class="green">1.00<br> (12ns)</span> 409 </p> 410 </td> 411<td> 412 <p> 413 <span class="green">1.00<br> (12ns)</span> 414 </p> 415 </td> 416<td> 417 <p> 418 <span class="green">1.00<br> (12ns)</span> 419 </p> 420 </td> 421<td> 422 <p> 423 <span class="green">1.00<br> (12ns)</span> 424 </p> 425 </td> 426<td> 427 <p> 428 <span class="green">1.08<br> (13ns)</span> 429 </p> 430 </td> 431<td> 432 <p> 433 <span class="green">1.08<br> (13ns)</span> 434 </p> 435 </td> 436</tr> 437<tr> 438<td> 439 <p> 440 Order 5 441 </p> 442 </td> 443<td> 444 <p> 445 <span class="blue">1.56<br> (25ns)</span> 446 </p> 447 </td> 448<td> 449 <p> 450 <span class="red">2.31<br> (37ns)</span> 451 </p> 452 </td> 453<td> 454 <p> 455 <span class="green">1.00<br> (16ns)</span> 456 </p> 457 </td> 458<td> 459 <p> 460 <span class="green">1.00<br> (16ns)</span> 461 </p> 462 </td> 463<td> 464 <p> 465 <span class="green">1.13<br> (18ns)</span> 466 </p> 467 </td> 468<td> 469 <p> 470 <span class="green">1.13<br> (18ns)</span> 471 </p> 472 </td> 473<td> 474 <p> 475 <span class="blue">1.56<br> (25ns)</span> 476 </p> 477 </td> 478<td> 479 <p> 480 <span class="blue">1.56<br> (25ns)</span> 481 </p> 482 </td> 483</tr> 484<tr> 485<td> 486 <p> 487 Order 6 488 </p> 489 </td> 490<td> 491 <p> 492 <span class="blue">1.48<br> (31ns)</span> 493 </p> 494 </td> 495<td> 496 <p> 497 <span class="red">2.19<br> (46ns)</span> 498 </p> 499 </td> 500<td> 501 <p> 502 <span class="green">1.05<br> (22ns)</span> 503 </p> 504 </td> 505<td> 506 <p> 507 <span class="green">1.00<br> (21ns)</span> 508 </p> 509 </td> 510<td> 511 <p> 512 <span class="green">1.00<br> (21ns)</span> 513 </p> 514 </td> 515<td> 516 <p> 517 <span class="green">1.00<br> (21ns)</span> 518 </p> 519 </td> 520<td> 521 <p> 522 <span class="blue">1.29<br> (27ns)</span> 523 </p> 524 </td> 525<td> 526 <p> 527 <span class="blue">1.29<br> (27ns)</span> 528 </p> 529 </td> 530</tr> 531<tr> 532<td> 533 <p> 534 Order 7 535 </p> 536 </td> 537<td> 538 <p> 539 <span class="blue">1.54<br> (37ns)</span> 540 </p> 541 </td> 542<td> 543 <p> 544 <span class="red">2.33<br> (56ns)</span> 545 </p> 546 </td> 547<td> 548 <p> 549 <span class="green">1.08<br> (26ns)</span> 550 </p> 551 </td> 552<td> 553 <p> 554 <span class="green">1.08<br> (26ns)</span> 555 </p> 556 </td> 557<td> 558 <p> 559 <span class="green">1.04<br> (25ns)</span> 560 </p> 561 </td> 562<td> 563 <p> 564 <span class="green">1.00<br> (24ns)</span> 565 </p> 566 </td> 567<td> 568 <p> 569 <span class="green">1.13<br> (27ns)</span> 570 </p> 571 </td> 572<td> 573 <p> 574 <span class="green">1.17<br> (28ns)</span> 575 </p> 576 </td> 577</tr> 578<tr> 579<td> 580 <p> 581 Order 8 582 </p> 583 </td> 584<td> 585 <p> 586 <span class="blue">1.53<br> (46ns)</span> 587 </p> 588 </td> 589<td> 590 <p> 591 <span class="red">2.23<br> (67ns)</span> 592 </p> 593 </td> 594<td> 595 <p> 596 <span class="green">1.07<br> (32ns)</span> 597 </p> 598 </td> 599<td> 600 <p> 601 <span class="green">1.07<br> (32ns)</span> 602 </p> 603 </td> 604<td> 605 <p> 606 <span class="green">1.00<br> (30ns)</span> 607 </p> 608 </td> 609<td> 610 <p> 611 <span class="green">1.00<br> (30ns)</span> 612 </p> 613 </td> 614<td> 615 <p> 616 <span class="green">1.03<br> (31ns)</span> 617 </p> 618 </td> 619<td> 620 <p> 621 <span class="green">1.03<br> (31ns)</span> 622 </p> 623 </td> 624</tr> 625<tr> 626<td> 627 <p> 628 Order 9 629 </p> 630 </td> 631<td> 632 <p> 633 <span class="blue">1.35<br> (46ns)</span> 634 </p> 635 </td> 636<td> 637 <p> 638 <span class="red">2.06<br> (70ns)</span> 639 </p> 640 </td> 641<td> 642 <p> 643 <span class="green">1.18<br> (40ns)</span> 644 </p> 645 </td> 646<td> 647 <p> 648 <span class="blue">1.32<br> (45ns)</span> 649 </p> 650 </td> 651<td> 652 <p> 653 <span class="green">1.00<br> (34ns)</span> 654 </p> 655 </td> 656<td> 657 <p> 658 <span class="green">1.00<br> (34ns)</span> 659 </p> 660 </td> 661<td> 662 <p> 663 <span class="green">1.09<br> (37ns)</span> 664 </p> 665 </td> 666<td> 667 <p> 668 <span class="green">1.06<br> (36ns)</span> 669 </p> 670 </td> 671</tr> 672<tr> 673<td> 674 <p> 675 Order 10 676 </p> 677 </td> 678<td> 679 <p> 680 <span class="blue">1.38<br> (54ns)</span> 681 </p> 682 </td> 683<td> 684 <p> 685 <span class="red">2.13<br> (83ns)</span> 686 </p> 687 </td> 688<td> 689 <p> 690 <span class="blue">1.21<br> (47ns)</span> 691 </p> 692 </td> 693<td> 694 <p> 695 <span class="green">1.15<br> (45ns)</span> 696 </p> 697 </td> 698<td> 699 <p> 700 <span class="green">1.00<br> (39ns)</span> 701 </p> 702 </td> 703<td> 704 <p> 705 <span class="green">1.00<br> (39ns)</span> 706 </p> 707 </td> 708<td> 709 <p> 710 <span class="green">1.03<br> (40ns)</span> 711 </p> 712 </td> 713<td> 714 <p> 715 <span class="green">1.03<br> (40ns)</span> 716 </p> 717 </td> 718</tr> 719<tr> 720<td> 721 <p> 722 Order 11 723 </p> 724 </td> 725<td> 726 <p> 727 <span class="blue">1.48<br> (62ns)</span> 728 </p> 729 </td> 730<td> 731 <p> 732 <span class="red">2.24<br> (94ns)</span> 733 </p> 734 </td> 735<td> 736 <p> 737 <span class="blue">1.24<br> (52ns)</span> 738 </p> 739 </td> 740<td> 741 <p> 742 <span class="blue">1.26<br> (53ns)</span> 743 </p> 744 </td> 745<td> 746 <p> 747 <span class="green">1.07<br> (45ns)</span> 748 </p> 749 </td> 750<td> 751 <p> 752 <span class="green">1.00<br> (42ns)</span> 753 </p> 754 </td> 755<td> 756 <p> 757 <span class="green">1.10<br> (46ns)</span> 758 </p> 759 </td> 760<td> 761 <p> 762 <span class="green">1.02<br> (43ns)</span> 763 </p> 764 </td> 765</tr> 766<tr> 767<td> 768 <p> 769 Order 12 770 </p> 771 </td> 772<td> 773 <p> 774 <span class="blue">1.48<br> (71ns)</span> 775 </p> 776 </td> 777<td> 778 <p> 779 <span class="red">2.27<br> (109ns)</span> 780 </p> 781 </td> 782<td> 783 <p> 784 <span class="blue">1.25<br> (60ns)</span> 785 </p> 786 </td> 787<td> 788 <p> 789 <span class="blue">1.27<br> (61ns)</span> 790 </p> 791 </td> 792<td> 793 <p> 794 <span class="green">1.04<br> (50ns)</span> 795 </p> 796 </td> 797<td> 798 <p> 799 <span class="green">1.00<br> (48ns)</span> 800 </p> 801 </td> 802<td> 803 <p> 804 <span class="green">1.00<br> (48ns)</span> 805 </p> 806 </td> 807<td> 808 <p> 809 <span class="green">1.00<br> (48ns)</span> 810 </p> 811 </td> 812</tr> 813<tr> 814<td> 815 <p> 816 Order 13 817 </p> 818 </td> 819<td> 820 <p> 821 <span class="blue">1.55<br> (76ns)</span> 822 </p> 823 </td> 824<td> 825 <p> 826 <span class="red">2.33<br> (114ns)</span> 827 </p> 828 </td> 829<td> 830 <p> 831 <span class="blue">1.31<br> (64ns)</span> 832 </p> 833 </td> 834<td> 835 <p> 836 <span class="blue">1.31<br> (64ns)</span> 837 </p> 838 </td> 839<td> 840 <p> 841 <span class="green">1.04<br> (51ns)</span> 842 </p> 843 </td> 844<td> 845 <p> 846 <span class="green">1.04<br> (51ns)</span> 847 </p> 848 </td> 849<td> 850 <p> 851 <span class="green">1.02<br> (50ns)</span> 852 </p> 853 </td> 854<td> 855 <p> 856 <span class="green">1.00<br> (49ns)</span> 857 </p> 858 </td> 859</tr> 860<tr> 861<td> 862 <p> 863 Order 14 864 </p> 865 </td> 866<td> 867 <p> 868 <span class="blue">1.53<br> (84ns)</span> 869 </p> 870 </td> 871<td> 872 <p> 873 <span class="red">2.40<br> (132ns)</span> 874 </p> 875 </td> 876<td> 877 <p> 878 <span class="blue">1.44<br> (79ns)</span> 879 </p> 880 </td> 881<td> 882 <p> 883 <span class="blue">1.40<br> (77ns)</span> 884 </p> 885 </td> 886<td> 887 <p> 888 <span class="green">1.04<br> (57ns)</span> 889 </p> 890 </td> 891<td> 892 <p> 893 <span class="green">1.02<br> (56ns)</span> 894 </p> 895 </td> 896<td> 897 <p> 898 <span class="green">1.00<br> (55ns)</span> 899 </p> 900 </td> 901<td> 902 <p> 903 <span class="green">1.00<br> (55ns)</span> 904 </p> 905 </td> 906</tr> 907<tr> 908<td> 909 <p> 910 Order 15 911 </p> 912 </td> 913<td> 914 <p> 915 <span class="blue">1.51<br> (95ns)</span> 916 </p> 917 </td> 918<td> 919 <p> 920 <span class="red">2.33<br> (147ns)</span> 921 </p> 922 </td> 923<td> 924 <p> 925 <span class="blue">1.37<br> (86ns)</span> 926 </p> 927 </td> 928<td> 929 <p> 930 <span class="blue">1.38<br> (87ns)</span> 931 </p> 932 </td> 933<td> 934 <p> 935 <span class="green">1.05<br> (66ns)</span> 936 </p> 937 </td> 938<td> 939 <p> 940 <span class="green">1.06<br> (67ns)</span> 941 </p> 942 </td> 943<td> 944 <p> 945 <span class="green">1.00<br> (63ns)</span> 946 </p> 947 </td> 948<td> 949 <p> 950 <span class="green">1.00<br> (63ns)</span> 951 </p> 952 </td> 953</tr> 954<tr> 955<td> 956 <p> 957 Order 16 958 </p> 959 </td> 960<td> 961 <p> 962 <span class="blue">1.47<br> (106ns)</span> 963 </p> 964 </td> 965<td> 966 <p> 967 <span class="red">2.18<br> (157ns)</span> 968 </p> 969 </td> 970<td> 971 <p> 972 <span class="blue">1.40<br> (101ns)</span> 973 </p> 974 </td> 975<td> 976 <p> 977 <span class="blue">1.33<br> (96ns)</span> 978 </p> 979 </td> 980<td> 981 <p> 982 <span class="green">1.01<br> (73ns)</span> 983 </p> 984 </td> 985<td> 986 <p> 987 <span class="green">1.03<br> (74ns)</span> 988 </p> 989 </td> 990<td> 991 <p> 992 <span class="green">1.00<br> (72ns)</span> 993 </p> 994 </td> 995<td> 996 <p> 997 <span class="green">1.04<br> (75ns)</span> 998 </p> 999 </td> 1000</tr> 1001<tr> 1002<td> 1003 <p> 1004 Order 17 1005 </p> 1006 </td> 1007<td> 1008 <p> 1009 <span class="blue">1.46<br> (114ns)</span> 1010 </p> 1011 </td> 1012<td> 1013 <p> 1014 <span class="red">2.08<br> (162ns)</span> 1015 </p> 1016 </td> 1017<td> 1018 <p> 1019 <span class="blue">1.44<br> (112ns)</span> 1020 </p> 1021 </td> 1022<td> 1023 <p> 1024 <span class="blue">1.44<br> (112ns)</span> 1025 </p> 1026 </td> 1027<td> 1028 <p> 1029 <span class="green">1.00<br> (78ns)</span> 1030 </p> 1031 </td> 1032<td> 1033 <p> 1034 <span class="green">1.01<br> (79ns)</span> 1035 </p> 1036 </td> 1037<td> 1038 <p> 1039 <span class="green">1.05<br> (82ns)</span> 1040 </p> 1041 </td> 1042<td> 1043 <p> 1044 <span class="green">1.03<br> (80ns)</span> 1045 </p> 1046 </td> 1047</tr> 1048<tr> 1049<td> 1050 <p> 1051 Order 18 1052 </p> 1053 </td> 1054<td> 1055 <p> 1056 <span class="blue">1.48<br> (126ns)</span> 1057 </p> 1058 </td> 1059<td> 1060 <p> 1061 <span class="red">2.08<br> (177ns)</span> 1062 </p> 1063 </td> 1064<td> 1065 <p> 1066 <span class="blue">1.44<br> (122ns)</span> 1067 </p> 1068 </td> 1069<td> 1070 <p> 1071 <span class="blue">1.46<br> (124ns)</span> 1072 </p> 1073 </td> 1074<td> 1075 <p> 1076 <span class="green">1.02<br> (87ns)</span> 1077 </p> 1078 </td> 1079<td> 1080 <p> 1081 <span class="green">1.04<br> (88ns)</span> 1082 </p> 1083 </td> 1084<td> 1085 <p> 1086 <span class="green">1.01<br> (86ns)</span> 1087 </p> 1088 </td> 1089<td> 1090 <p> 1091 <span class="green">1.00<br> (85ns)</span> 1092 </p> 1093 </td> 1094</tr> 1095<tr> 1096<td> 1097 <p> 1098 Order 19 1099 </p> 1100 </td> 1101<td> 1102 <p> 1103 <span class="blue">1.49<br> (136ns)</span> 1104 </p> 1105 </td> 1106<td> 1107 <p> 1108 <span class="red">2.07<br> (188ns)</span> 1109 </p> 1110 </td> 1111<td> 1112 <p> 1113 <span class="blue">1.47<br> (134ns)</span> 1114 </p> 1115 </td> 1116<td> 1117 <p> 1118 <span class="blue">1.47<br> (134ns)</span> 1119 </p> 1120 </td> 1121<td> 1122 <p> 1123 <span class="green">1.00<br> (91ns)</span> 1124 </p> 1125 </td> 1126<td> 1127 <p> 1128 <span class="green">1.01<br> (92ns)</span> 1129 </p> 1130 </td> 1131<td> 1132 <p> 1133 <span class="green">1.05<br> (96ns)</span> 1134 </p> 1135 </td> 1136<td> 1137 <p> 1138 <span class="green">1.03<br> (94ns)</span> 1139 </p> 1140 </td> 1141</tr> 1142<tr> 1143<td> 1144 <p> 1145 Order 20 1146 </p> 1147 </td> 1148<td> 1149 <p> 1150 <span class="blue">1.52<br> (150ns)</span> 1151 </p> 1152 </td> 1153<td> 1154 <p> 1155 <span class="red">2.05<br> (203ns)</span> 1156 </p> 1157 </td> 1158<td> 1159 <p> 1160 <span class="blue">1.45<br> (144ns)</span> 1161 </p> 1162 </td> 1163<td> 1164 <p> 1165 <span class="blue">1.46<br> (145ns)</span> 1166 </p> 1167 </td> 1168<td> 1169 <p> 1170 <span class="green">1.00<br> (99ns)</span> 1171 </p> 1172 </td> 1173<td> 1174 <p> 1175 <span class="green">1.02<br> (101ns)</span> 1176 </p> 1177 </td> 1178<td> 1179 <p> 1180 <span class="green">1.02<br> (101ns)</span> 1181 </p> 1182 </td> 1183<td> 1184 <p> 1185 <span class="green">1.02<br> (101ns)</span> 1186 </p> 1187 </td> 1188</tr> 1189</tbody> 1190</table></div> 1191</div> 1192<br class="table-break"><div class="table"> 1193<a name="math_toolkit.tuning.table_Rational_Method_Comparison_with_Microsoft_Visual_C_version_14_2_on_Windows_x64"></a><p class="title"><b>Table 22.5. Rational Method Comparison with Microsoft Visual C++ version 14.2 on 1194 Windows x64</b></p> 1195<div class="table-contents"><table class="table" summary="Rational Method Comparison with Microsoft Visual C++ version 14.2 on 1196 Windows x64"> 1197<colgroup> 1198<col> 1199<col> 1200<col> 1201<col> 1202<col> 1203<col> 1204<col> 1205<col> 1206<col> 1207</colgroup> 1208<thead><tr> 1209<th> 1210 <p> 1211 Function 1212 </p> 1213 </th> 1214<th> 1215 <p> 1216 Method 0<br> (Double Coefficients) 1217 </p> 1218 </th> 1219<th> 1220 <p> 1221 Method 0<br> (Integer Coefficients) 1222 </p> 1223 </th> 1224<th> 1225 <p> 1226 Method 1<br> (Double Coefficients) 1227 </p> 1228 </th> 1229<th> 1230 <p> 1231 Method 1<br> (Integer Coefficients) 1232 </p> 1233 </th> 1234<th> 1235 <p> 1236 Method 2<br> (Double Coefficients) 1237 </p> 1238 </th> 1239<th> 1240 <p> 1241 Method 2<br> (Integer Coefficients) 1242 </p> 1243 </th> 1244<th> 1245 <p> 1246 Method 3<br> (Double Coefficients) 1247 </p> 1248 </th> 1249<th> 1250 <p> 1251 Method 3<br> (Integer Coefficients) 1252 </p> 1253 </th> 1254</tr></thead> 1255<tbody> 1256<tr> 1257<td> 1258 <p> 1259 Order 2 1260 </p> 1261 </td> 1262<td> 1263 <p> 1264 <span class="grey">-</span> 1265 </p> 1266 </td> 1267<td> 1268 <p> 1269 <span class="grey">-</span> 1270 </p> 1271 </td> 1272<td> 1273 <p> 1274 <span class="blue">1.92<br> (23ns)</span> 1275 </p> 1276 </td> 1277<td> 1278 <p> 1279 <span class="blue">1.92<br> (23ns)</span> 1280 </p> 1281 </td> 1282<td> 1283 <p> 1284 <span class="green">1.00<br> (12ns)</span> 1285 </p> 1286 </td> 1287<td> 1288 <p> 1289 <span class="green">1.17<br> (14ns)</span> 1290 </p> 1291 </td> 1292<td> 1293 <p> 1294 <span class="green">1.00<br> (12ns)</span> 1295 </p> 1296 </td> 1297<td> 1298 <p> 1299 <span class="green">1.00<br> (12ns)</span> 1300 </p> 1301 </td> 1302</tr> 1303<tr> 1304<td> 1305 <p> 1306 Order 3 1307 </p> 1308 </td> 1309<td> 1310 <p> 1311 <span class="blue">1.89<br> (34ns)</span> 1312 </p> 1313 </td> 1314<td> 1315 <p> 1316 <span class="red">2.28<br> (41ns)</span> 1317 </p> 1318 </td> 1319<td> 1320 <p> 1321 <span class="blue">1.67<br> (30ns)</span> 1322 </p> 1323 </td> 1324<td> 1325 <p> 1326 <span class="blue">1.61<br> (29ns)</span> 1327 </p> 1328 </td> 1329<td> 1330 <p> 1331 <span class="green">1.06<br> (19ns)</span> 1332 </p> 1333 </td> 1334<td> 1335 <p> 1336 <span class="green">1.00<br> (18ns)</span> 1337 </p> 1338 </td> 1339<td> 1340 <p> 1341 <span class="green">1.00<br> (18ns)</span> 1342 </p> 1343 </td> 1344<td> 1345 <p> 1346 <span class="green">1.00<br> (18ns)</span> 1347 </p> 1348 </td> 1349</tr> 1350<tr> 1351<td> 1352 <p> 1353 Order 4 1354 </p> 1355 </td> 1356<td> 1357 <p> 1358 <span class="blue">1.72<br> (43ns)</span> 1359 </p> 1360 </td> 1361<td> 1362 <p> 1363 <span class="red">2.16<br> (54ns)</span> 1364 </p> 1365 </td> 1366<td> 1367 <p> 1368 <span class="blue">1.64<br> (41ns)</span> 1369 </p> 1370 </td> 1371<td> 1372 <p> 1373 <span class="blue">1.60<br> (40ns)</span> 1374 </p> 1375 </td> 1376<td> 1377 <p> 1378 <span class="green">1.00<br> (25ns)</span> 1379 </p> 1380 </td> 1381<td> 1382 <p> 1383 <span class="green">1.00<br> (25ns)</span> 1384 </p> 1385 </td> 1386<td> 1387 <p> 1388 <span class="green">1.00<br> (25ns)</span> 1389 </p> 1390 </td> 1391<td> 1392 <p> 1393 <span class="green">1.04<br> (26ns)</span> 1394 </p> 1395 </td> 1396</tr> 1397<tr> 1398<td> 1399 <p> 1400 Order 5 1401 </p> 1402 </td> 1403<td> 1404 <p> 1405 <span class="green">1.08<br> (53ns)</span> 1406 </p> 1407 </td> 1408<td> 1409 <p> 1410 <span class="blue">1.41<br> (69ns)</span> 1411 </p> 1412 </td> 1413<td> 1414 <p> 1415 <span class="green">1.00<br> (49ns)</span> 1416 </p> 1417 </td> 1418<td> 1419 <p> 1420 <span class="green">1.00<br> (49ns)</span> 1421 </p> 1422 </td> 1423<td> 1424 <p> 1425 <span class="green">1.08<br> (53ns)</span> 1426 </p> 1427 </td> 1428<td> 1429 <p> 1430 <span class="green">1.08<br> (53ns)</span> 1431 </p> 1432 </td> 1433<td> 1434 <p> 1435 <span class="green">1.00<br> (49ns)</span> 1436 </p> 1437 </td> 1438<td> 1439 <p> 1440 <span class="green">1.10<br> (54ns)</span> 1441 </p> 1442 </td> 1443</tr> 1444<tr> 1445<td> 1446 <p> 1447 Order 6 1448 </p> 1449 </td> 1450<td> 1451 <p> 1452 <span class="green">1.08<br> (65ns)</span> 1453 </p> 1454 </td> 1455<td> 1456 <p> 1457 <span class="blue">1.42<br> (85ns)</span> 1458 </p> 1459 </td> 1460<td> 1461 <p> 1462 <span class="green">1.02<br> (61ns)</span> 1463 </p> 1464 </td> 1465<td> 1466 <p> 1467 <span class="green">1.00<br> (60ns)</span> 1468 </p> 1469 </td> 1470<td> 1471 <p> 1472 <span class="green">1.05<br> (63ns)</span> 1473 </p> 1474 </td> 1475<td> 1476 <p> 1477 <span class="blue">1.23<br> (74ns)</span> 1478 </p> 1479 </td> 1480<td> 1481 <p> 1482 <span class="blue">1.25<br> (75ns)</span> 1483 </p> 1484 </td> 1485<td> 1486 <p> 1487 <span class="blue">1.40<br> (84ns)</span> 1488 </p> 1489 </td> 1490</tr> 1491<tr> 1492<td> 1493 <p> 1494 Order 7 1495 </p> 1496 </td> 1497<td> 1498 <p> 1499 <span class="green">1.06<br> (75ns)</span> 1500 </p> 1501 </td> 1502<td> 1503 <p> 1504 <span class="blue">1.37<br> (97ns)</span> 1505 </p> 1506 </td> 1507<td> 1508 <p> 1509 <span class="green">1.01<br> (72ns)</span> 1510 </p> 1511 </td> 1512<td> 1513 <p> 1514 <span class="green">1.00<br> (71ns)</span> 1515 </p> 1516 </td> 1517<td> 1518 <p> 1519 <span class="green">1.14<br> (81ns)</span> 1520 </p> 1521 </td> 1522<td> 1523 <p> 1524 <span class="green">1.01<br> (72ns)</span> 1525 </p> 1526 </td> 1527<td> 1528 <p> 1529 <span class="green">1.20<br> (85ns)</span> 1530 </p> 1531 </td> 1532<td> 1533 <p> 1534 <span class="blue">1.35<br> (96ns)</span> 1535 </p> 1536 </td> 1537</tr> 1538<tr> 1539<td> 1540 <p> 1541 Order 8 1542 </p> 1543 </td> 1544<td> 1545 <p> 1546 <span class="green">1.07<br> (87ns)</span> 1547 </p> 1548 </td> 1549<td> 1550 <p> 1551 <span class="blue">1.38<br> (112ns)</span> 1552 </p> 1553 </td> 1554<td> 1555 <p> 1556 <span class="green">1.04<br> (84ns)</span> 1557 </p> 1558 </td> 1559<td> 1560 <p> 1561 <span class="green">1.02<br> (83ns)</span> 1562 </p> 1563 </td> 1564<td> 1565 <p> 1566 <span class="green">1.01<br> (82ns)</span> 1567 </p> 1568 </td> 1569<td> 1570 <p> 1571 <span class="green">1.00<br> (81ns)</span> 1572 </p> 1573 </td> 1574<td> 1575 <p> 1576 <span class="red">2.49<br> (202ns)</span> 1577 </p> 1578 </td> 1579<td> 1580 <p> 1581 <span class="red">2.60<br> (211ns)</span> 1582 </p> 1583 </td> 1584</tr> 1585<tr> 1586<td> 1587 <p> 1588 Order 9 1589 </p> 1590 </td> 1591<td> 1592 <p> 1593 <span class="green">1.16<br> (103ns)</span> 1594 </p> 1595 </td> 1596<td> 1597 <p> 1598 <span class="blue">1.61<br> (143ns)</span> 1599 </p> 1600 </td> 1601<td> 1602 <p> 1603 <span class="green">1.18<br> (105ns)</span> 1604 </p> 1605 </td> 1606<td> 1607 <p> 1608 <span class="blue">1.27<br> (113ns)</span> 1609 </p> 1610 </td> 1611<td> 1612 <p> 1613 <span class="green">1.01<br> (90ns)</span> 1614 </p> 1615 </td> 1616<td> 1617 <p> 1618 <span class="green">1.02<br> (91ns)</span> 1619 </p> 1620 </td> 1621<td> 1622 <p> 1623 <span class="green">1.02<br> (91ns)</span> 1624 </p> 1625 </td> 1626<td> 1627 <p> 1628 <span class="green">1.00<br> (89ns)</span> 1629 </p> 1630 </td> 1631</tr> 1632<tr> 1633<td> 1634 <p> 1635 Order 10 1636 </p> 1637 </td> 1638<td> 1639 <p> 1640 <span class="green">1.15<br> (115ns)</span> 1641 </p> 1642 </td> 1643<td> 1644 <p> 1645 <span class="blue">1.46<br> (146ns)</span> 1646 </p> 1647 </td> 1648<td> 1649 <p> 1650 <span class="green">1.14<br> (114ns)</span> 1651 </p> 1652 </td> 1653<td> 1654 <p> 1655 <span class="green">1.12<br> (112ns)</span> 1656 </p> 1657 </td> 1658<td> 1659 <p> 1660 <span class="green">1.01<br> (101ns)</span> 1661 </p> 1662 </td> 1663<td> 1664 <p> 1665 <span class="green">1.02<br> (102ns)</span> 1666 </p> 1667 </td> 1668<td> 1669 <p> 1670 <span class="green">1.01<br> (101ns)</span> 1671 </p> 1672 </td> 1673<td> 1674 <p> 1675 <span class="green">1.00<br> (100ns)</span> 1676 </p> 1677 </td> 1678</tr> 1679<tr> 1680<td> 1681 <p> 1682 Order 11 1683 </p> 1684 </td> 1685<td> 1686 <p> 1687 <span class="blue">1.21<br> (131ns)</span> 1688 </p> 1689 </td> 1690<td> 1691 <p> 1692 <span class="blue">1.48<br> (160ns)</span> 1693 </p> 1694 </td> 1695<td> 1696 <p> 1697 <span class="green">1.17<br> (126ns)</span> 1698 </p> 1699 </td> 1700<td> 1701 <p> 1702 <span class="green">1.16<br> (125ns)</span> 1703 </p> 1704 </td> 1705<td> 1706 <p> 1707 <span class="green">1.00<br> (108ns)</span> 1708 </p> 1709 </td> 1710<td> 1711 <p> 1712 <span class="blue">1.27<br> (137ns)</span> 1713 </p> 1714 </td> 1715<td> 1716 <p> 1717 <span class="green">1.00<br> (108ns)</span> 1718 </p> 1719 </td> 1720<td> 1721 <p> 1722 <span class="green">1.01<br> (109ns)</span> 1723 </p> 1724 </td> 1725</tr> 1726<tr> 1727<td> 1728 <p> 1729 Order 12 1730 </p> 1731 </td> 1732<td> 1733 <p> 1734 <span class="blue">1.26<br> (148ns)</span> 1735 </p> 1736 </td> 1737<td> 1738 <p> 1739 <span class="blue">1.53<br> (179ns)</span> 1740 </p> 1741 </td> 1742<td> 1743 <p> 1744 <span class="green">1.19<br> (139ns)</span> 1745 </p> 1746 </td> 1747<td> 1748 <p> 1749 <span class="green">1.19<br> (139ns)</span> 1750 </p> 1751 </td> 1752<td> 1753 <p> 1754 <span class="green">1.02<br> (119ns)</span> 1755 </p> 1756 </td> 1757<td> 1758 <p> 1759 <span class="blue">1.24<br> (145ns)</span> 1760 </p> 1761 </td> 1762<td> 1763 <p> 1764 <span class="green">1.00<br> (117ns)</span> 1765 </p> 1766 </td> 1767<td> 1768 <p> 1769 <span class="green">1.00<br> (117ns)</span> 1770 </p> 1771 </td> 1772</tr> 1773<tr> 1774<td> 1775 <p> 1776 Order 13 1777 </p> 1778 </td> 1779<td> 1780 <p> 1781 <span class="blue">1.31<br> (163ns)</span> 1782 </p> 1783 </td> 1784<td> 1785 <p> 1786 <span class="blue">1.71<br> (212ns)</span> 1787 </p> 1788 </td> 1789<td> 1790 <p> 1791 <span class="blue">1.23<br> (153ns)</span> 1792 </p> 1793 </td> 1794<td> 1795 <p> 1796 <span class="blue">1.52<br> (189ns)</span> 1797 </p> 1798 </td> 1799<td> 1800 <p> 1801 <span class="green">1.01<br> (125ns)</span> 1802 </p> 1803 </td> 1804<td> 1805 <p> 1806 <span class="blue">1.29<br> (160ns)</span> 1807 </p> 1808 </td> 1809<td> 1810 <p> 1811 <span class="green">1.01<br> (125ns)</span> 1812 </p> 1813 </td> 1814<td> 1815 <p> 1816 <span class="green">1.00<br> (124ns)</span> 1817 </p> 1818 </td> 1819</tr> 1820<tr> 1821<td> 1822 <p> 1823 Order 14 1824 </p> 1825 </td> 1826<td> 1827 <p> 1828 <span class="blue">1.42<br> (190ns)</span> 1829 </p> 1830 </td> 1831<td> 1832 <p> 1833 <span class="blue">1.56<br> (209ns)</span> 1834 </p> 1835 </td> 1836<td> 1837 <p> 1838 <span class="blue">1.32<br> (177ns)</span> 1839 </p> 1840 </td> 1841<td> 1842 <p> 1843 <span class="blue">1.47<br> (197ns)</span> 1844 </p> 1845 </td> 1846<td> 1847 <p> 1848 <span class="green">1.02<br> (137ns)</span> 1849 </p> 1850 </td> 1851<td> 1852 <p> 1853 <span class="blue">1.31<br> (175ns)</span> 1854 </p> 1855 </td> 1856<td> 1857 <p> 1858 <span class="green">1.00<br> (134ns)</span> 1859 </p> 1860 </td> 1861<td> 1862 <p> 1863 <span class="green">1.01<br> (136ns)</span> 1864 </p> 1865 </td> 1866</tr> 1867<tr> 1868<td> 1869 <p> 1870 Order 15 1871 </p> 1872 </td> 1873<td> 1874 <p> 1875 <span class="blue">1.34<br> (194ns)</span> 1876 </p> 1877 </td> 1878<td> 1879 <p> 1880 <span class="blue">1.51<br> (219ns)</span> 1881 </p> 1882 </td> 1883<td> 1884 <p> 1885 <span class="blue">1.36<br> (197ns)</span> 1886 </p> 1887 </td> 1888<td> 1889 <p> 1890 <span class="blue">1.46<br> (212ns)</span> 1891 </p> 1892 </td> 1893<td> 1894 <p> 1895 <span class="green">1.02<br> (148ns)</span> 1896 </p> 1897 </td> 1898<td> 1899 <p> 1900 <span class="blue">1.30<br> (188ns)</span> 1901 </p> 1902 </td> 1903<td> 1904 <p> 1905 <span class="green">1.00<br> (145ns)</span> 1906 </p> 1907 </td> 1908<td> 1909 <p> 1910 <span class="red">2.23<br> (323ns)</span> 1911 </p> 1912 </td> 1913</tr> 1914<tr> 1915<td> 1916 <p> 1917 Order 16 1918 </p> 1919 </td> 1920<td> 1921 <p> 1922 <span class="blue">1.38<br> (216ns)</span> 1923 </p> 1924 </td> 1925<td> 1926 <p> 1927 <span class="blue">1.56<br> (244ns)</span> 1928 </p> 1929 </td> 1930<td> 1931 <p> 1932 <span class="blue">1.36<br> (212ns)</span> 1933 </p> 1934 </td> 1935<td> 1936 <p> 1937 <span class="blue">1.31<br> (204ns)</span> 1938 </p> 1939 </td> 1940<td> 1941 <p> 1942 <span class="green">1.15<br> (179ns)</span> 1943 </p> 1944 </td> 1945<td> 1946 <p> 1947 <span class="blue">1.34<br> (209ns)</span> 1948 </p> 1949 </td> 1950<td> 1951 <p> 1952 <span class="green">1.00<br> (156ns)</span> 1953 </p> 1954 </td> 1955<td> 1956 <p> 1957 <span class="red">2.10<br> (328ns)</span> 1958 </p> 1959 </td> 1960</tr> 1961<tr> 1962<td> 1963 <p> 1964 Order 17 1965 </p> 1966 </td> 1967<td> 1968 <p> 1969 <span class="blue">1.39<br> (227ns)</span> 1970 </p> 1971 </td> 1972<td> 1973 <p> 1974 <span class="blue">1.67<br> (273ns)</span> 1975 </p> 1976 </td> 1977<td> 1978 <p> 1979 <span class="blue">1.34<br> (218ns)</span> 1980 </p> 1981 </td> 1982<td> 1983 <p> 1984 <span class="blue">1.69<br> (275ns)</span> 1985 </p> 1986 </td> 1987<td> 1988 <p> 1989 <span class="green">1.00<br> (163ns)</span> 1990 </p> 1991 </td> 1992<td> 1993 <p> 1994 <span class="blue">1.32<br> (215ns)</span> 1995 </p> 1996 </td> 1997<td> 1998 <p> 1999 <span class="green">1.02<br> (167ns)</span> 2000 </p> 2001 </td> 2002<td> 2003 <p> 2004 <span class="red">2.53<br> (412ns)</span> 2005 </p> 2006 </td> 2007</tr> 2008<tr> 2009<td> 2010 <p> 2011 Order 18 2012 </p> 2013 </td> 2014<td> 2015 <p> 2016 <span class="blue">1.37<br> (242ns)</span> 2017 </p> 2018 </td> 2019<td> 2020 <p> 2021 <span class="blue">1.73<br> (306ns)</span> 2022 </p> 2023 </td> 2024<td> 2025 <p> 2026 <span class="blue">1.40<br> (248ns)</span> 2027 </p> 2028 </td> 2029<td> 2030 <p> 2031 <span class="blue">1.56<br> (276ns)</span> 2032 </p> 2033 </td> 2034<td> 2035 <p> 2036 <span class="green">1.06<br> (187ns)</span> 2037 </p> 2038 </td> 2039<td> 2040 <p> 2041 <span class="blue">1.32<br> (233ns)</span> 2042 </p> 2043 </td> 2044<td> 2045 <p> 2046 <span class="green">1.00<br> (177ns)</span> 2047 </p> 2048 </td> 2049<td> 2050 <p> 2051 <span class="red">2.15<br> (380ns)</span> 2052 </p> 2053 </td> 2054</tr> 2055<tr> 2056<td> 2057 <p> 2058 Order 19 2059 </p> 2060 </td> 2061<td> 2062 <p> 2063 <span class="blue">1.28<br> (254ns)</span> 2064 </p> 2065 </td> 2066<td> 2067 <p> 2068 <span class="blue">1.60<br> (319ns)</span> 2069 </p> 2070 </td> 2071<td> 2072 <p> 2073 <span class="blue">1.27<br> (253ns)</span> 2074 </p> 2075 </td> 2076<td> 2077 <p> 2078 <span class="blue">1.51<br> (300ns)</span> 2079 </p> 2080 </td> 2081<td> 2082 <p> 2083 <span class="green">1.00<br> (199ns)</span> 2084 </p> 2085 </td> 2086<td> 2087 <p> 2088 <span class="blue">1.22<br> (243ns)</span> 2089 </p> 2090 </td> 2091<td> 2092 <p> 2093 <span class="blue">1.80<br> (359ns)</span> 2094 </p> 2095 </td> 2096<td> 2097 <p> 2098 <span class="blue">1.92<br> (382ns)</span> 2099 </p> 2100 </td> 2101</tr> 2102<tr> 2103<td> 2104 <p> 2105 Order 20 2106 </p> 2107 </td> 2108<td> 2109 <p> 2110 <span class="blue">1.28<br> (268ns)</span> 2111 </p> 2112 </td> 2113<td> 2114 <p> 2115 <span class="blue">1.62<br> (338ns)</span> 2116 </p> 2117 </td> 2118<td> 2119 <p> 2120 <span class="blue">1.27<br> (265ns)</span> 2121 </p> 2122 </td> 2123<td> 2124 <p> 2125 <span class="blue">1.56<br> (325ns)</span> 2126 </p> 2127 </td> 2128<td> 2129 <p> 2130 <span class="green">1.00<br> (209ns)</span> 2131 </p> 2132 </td> 2133<td> 2134 <p> 2135 <span class="blue">1.24<br> (259ns)</span> 2136 </p> 2137 </td> 2138<td> 2139 <p> 2140 <span class="blue">1.87<br> (391ns)</span> 2141 </p> 2142 </td> 2143<td> 2144 <p> 2145 <span class="red">2.04<br> (427ns)</span> 2146 </p> 2147 </td> 2148</tr> 2149</tbody> 2150</table></div> 2151</div> 2152<br class="table-break"><div class="table"> 2153<a name="math_toolkit.tuning.table_Polynomial_Method_Comparison_with_GNU_C_version_9_2_1_20191008_on_linux"></a><p class="title"><b>Table 22.6. Polynomial Method Comparison with GNU C++ version 9.2.1 20191008 on 2154 linux</b></p> 2155<div class="table-contents"><table class="table" summary="Polynomial Method Comparison with GNU C++ version 9.2.1 20191008 on 2156 linux"> 2157<colgroup> 2158<col> 2159<col> 2160<col> 2161<col> 2162<col> 2163<col> 2164<col> 2165<col> 2166<col> 2167</colgroup> 2168<thead><tr> 2169<th> 2170 <p> 2171 Function 2172 </p> 2173 </th> 2174<th> 2175 <p> 2176 Method 0<br> (Double Coefficients) 2177 </p> 2178 </th> 2179<th> 2180 <p> 2181 Method 0<br> (Integer Coefficients) 2182 </p> 2183 </th> 2184<th> 2185 <p> 2186 Method 1<br> (Double Coefficients) 2187 </p> 2188 </th> 2189<th> 2190 <p> 2191 Method 1<br> (Integer Coefficients) 2192 </p> 2193 </th> 2194<th> 2195 <p> 2196 Method 2<br> (Double Coefficients) 2197 </p> 2198 </th> 2199<th> 2200 <p> 2201 Method 2<br> (Integer Coefficients) 2202 </p> 2203 </th> 2204<th> 2205 <p> 2206 Method 3<br> (Double Coefficients) 2207 </p> 2208 </th> 2209<th> 2210 <p> 2211 Method 3<br> (Integer Coefficients) 2212 </p> 2213 </th> 2214</tr></thead> 2215<tbody> 2216<tr> 2217<td> 2218 <p> 2219 Order 2 2220 </p> 2221 </td> 2222<td> 2223 <p> 2224 <span class="grey">-</span> 2225 </p> 2226 </td> 2227<td> 2228 <p> 2229 <span class="grey">-</span> 2230 </p> 2231 </td> 2232<td> 2233 <p> 2234 <span class="green">1.00<br> (6ns)</span> 2235 </p> 2236 </td> 2237<td> 2238 <p> 2239 <span class="green">1.00<br> (6ns)</span> 2240 </p> 2241 </td> 2242<td> 2243 <p> 2244 <span class="green">1.00<br> (6ns)</span> 2245 </p> 2246 </td> 2247<td> 2248 <p> 2249 <span class="green">1.00<br> (6ns)</span> 2250 </p> 2251 </td> 2252<td> 2253 <p> 2254 <span class="green">1.00<br> (6ns)</span> 2255 </p> 2256 </td> 2257<td> 2258 <p> 2259 <span class="green">1.00<br> (6ns)</span> 2260 </p> 2261 </td> 2262</tr> 2263<tr> 2264<td> 2265 <p> 2266 Order 3 2267 </p> 2268 </td> 2269<td> 2270 <p> 2271 <span class="blue">1.70<br> (17ns)</span> 2272 </p> 2273 </td> 2274<td> 2275 <p> 2276 <span class="red">2.40<br> (24ns)</span> 2277 </p> 2278 </td> 2279<td> 2280 <p> 2281 <span class="green">1.00<br> (10ns)</span> 2282 </p> 2283 </td> 2284<td> 2285 <p> 2286 <span class="green">1.00<br> (10ns)</span> 2287 </p> 2288 </td> 2289<td> 2290 <p> 2291 <span class="green">1.00<br> (10ns)</span> 2292 </p> 2293 </td> 2294<td> 2295 <p> 2296 <span class="green">1.00<br> (10ns)</span> 2297 </p> 2298 </td> 2299<td> 2300 <p> 2301 <span class="green">1.00<br> (10ns)</span> 2302 </p> 2303 </td> 2304<td> 2305 <p> 2306 <span class="green">1.00<br> (10ns)</span> 2307 </p> 2308 </td> 2309</tr> 2310<tr> 2311<td> 2312 <p> 2313 Order 4 2314 </p> 2315 </td> 2316<td> 2317 <p> 2318 <span class="blue">1.85<br> (24ns)</span> 2319 </p> 2320 </td> 2321<td> 2322 <p> 2323 <span class="red">2.31<br> (30ns)</span> 2324 </p> 2325 </td> 2326<td> 2327 <p> 2328 <span class="green">1.08<br> (14ns)</span> 2329 </p> 2330 </td> 2331<td> 2332 <p> 2333 <span class="green">1.08<br> (14ns)</span> 2334 </p> 2335 </td> 2336<td> 2337 <p> 2338 <span class="green">1.08<br> (14ns)</span> 2339 </p> 2340 </td> 2341<td> 2342 <p> 2343 <span class="green">1.15<br> (15ns)</span> 2344 </p> 2345 </td> 2346<td> 2347 <p> 2348 <span class="green">1.00<br> (13ns)</span> 2349 </p> 2350 </td> 2351<td> 2352 <p> 2353 <span class="green">1.08<br> (14ns)</span> 2354 </p> 2355 </td> 2356</tr> 2357<tr> 2358<td> 2359 <p> 2360 Order 5 2361 </p> 2362 </td> 2363<td> 2364 <p> 2365 <span class="red">2.18<br> (37ns)</span> 2366 </p> 2367 </td> 2368<td> 2369 <p> 2370 <span class="red">2.41<br> (41ns)</span> 2371 </p> 2372 </td> 2373<td> 2374 <p> 2375 <span class="green">1.06<br> (18ns)</span> 2376 </p> 2377 </td> 2378<td> 2379 <p> 2380 <span class="green">1.00<br> (17ns)</span> 2381 </p> 2382 </td> 2383<td> 2384 <p> 2385 <span class="blue">1.29<br> (22ns)</span> 2386 </p> 2387 </td> 2388<td> 2389 <p> 2390 <span class="green">1.18<br> (20ns)</span> 2391 </p> 2392 </td> 2393<td> 2394 <p> 2395 <span class="green">1.12<br> (19ns)</span> 2396 </p> 2397 </td> 2398<td> 2399 <p> 2400 <span class="green">1.12<br> (19ns)</span> 2401 </p> 2402 </td> 2403</tr> 2404<tr> 2405<td> 2406 <p> 2407 Order 6 2408 </p> 2409 </td> 2410<td> 2411 <p> 2412 <span class="blue">1.68<br> (37ns)</span> 2413 </p> 2414 </td> 2415<td> 2416 <p> 2417 <span class="red">2.18<br> (48ns)</span> 2418 </p> 2419 </td> 2420<td> 2421 <p> 2422 <span class="green">1.00<br> (22ns)</span> 2423 </p> 2424 </td> 2425<td> 2426 <p> 2427 <span class="green">1.00<br> (22ns)</span> 2428 </p> 2429 </td> 2430<td> 2431 <p> 2432 <span class="green">1.09<br> (24ns)</span> 2433 </p> 2434 </td> 2435<td> 2436 <p> 2437 <span class="green">1.05<br> (23ns)</span> 2438 </p> 2439 </td> 2440<td> 2441 <p> 2442 <span class="green">1.05<br> (23ns)</span> 2443 </p> 2444 </td> 2445<td> 2446 <p> 2447 <span class="green">1.05<br> (23ns)</span> 2448 </p> 2449 </td> 2450</tr> 2451<tr> 2452<td> 2453 <p> 2454 Order 7 2455 </p> 2456 </td> 2457<td> 2458 <p> 2459 <span class="red">2.12<br> (55ns)</span> 2460 </p> 2461 </td> 2462<td> 2463 <p> 2464 <span class="red">2.35<br> (61ns)</span> 2465 </p> 2466 </td> 2467<td> 2468 <p> 2469 <span class="green">1.08<br> (28ns)</span> 2470 </p> 2471 </td> 2472<td> 2473 <p> 2474 <span class="green">1.12<br> (29ns)</span> 2475 </p> 2476 </td> 2477<td> 2478 <p> 2479 <span class="green">1.04<br> (27ns)</span> 2480 </p> 2481 </td> 2482<td> 2483 <p> 2484 <span class="green">1.08<br> (28ns)</span> 2485 </p> 2486 </td> 2487<td> 2488 <p> 2489 <span class="green">1.04<br> (27ns)</span> 2490 </p> 2491 </td> 2492<td> 2493 <p> 2494 <span class="green">1.00<br> (26ns)</span> 2495 </p> 2496 </td> 2497</tr> 2498<tr> 2499<td> 2500 <p> 2501 Order 8 2502 </p> 2503 </td> 2504<td> 2505 <p> 2506 <span class="blue">1.81<br> (56ns)</span> 2507 </p> 2508 </td> 2509<td> 2510 <p> 2511 <span class="red">2.42<br> (75ns)</span> 2512 </p> 2513 </td> 2514<td> 2515 <p> 2516 <span class="green">1.10<br> (34ns)</span> 2517 </p> 2518 </td> 2519<td> 2520 <p> 2521 <span class="green">1.06<br> (33ns)</span> 2522 </p> 2523 </td> 2524<td> 2525 <p> 2526 <span class="green">1.10<br> (34ns)</span> 2527 </p> 2528 </td> 2529<td> 2530 <p> 2531 <span class="green">1.00<br> (31ns)</span> 2532 </p> 2533 </td> 2534<td> 2535 <p> 2536 <span class="green">1.00<br> (31ns)</span> 2537 </p> 2538 </td> 2539<td> 2540 <p> 2541 <span class="green">1.00<br> (31ns)</span> 2542 </p> 2543 </td> 2544</tr> 2545<tr> 2546<td> 2547 <p> 2548 Order 9 2549 </p> 2550 </td> 2551<td> 2552 <p> 2553 <span class="blue">1.88<br> (64ns)</span> 2554 </p> 2555 </td> 2556<td> 2557 <p> 2558 <span class="red">2.56<br> (87ns)</span> 2559 </p> 2560 </td> 2561<td> 2562 <p> 2563 <span class="blue">1.24<br> (42ns)</span> 2564 </p> 2565 </td> 2566<td> 2567 <p> 2568 <span class="green">1.18<br> (40ns)</span> 2569 </p> 2570 </td> 2571<td> 2572 <p> 2573 <span class="green">1.00<br> (34ns)</span> 2574 </p> 2575 </td> 2576<td> 2577 <p> 2578 <span class="green">1.09<br> (37ns)</span> 2579 </p> 2580 </td> 2581<td> 2582 <p> 2583 <span class="green">1.03<br> (35ns)</span> 2584 </p> 2585 </td> 2586<td> 2587 <p> 2588 <span class="green">1.06<br> (36ns)</span> 2589 </p> 2590 </td> 2591</tr> 2592<tr> 2593<td> 2594 <p> 2595 Order 10 2596 </p> 2597 </td> 2598<td> 2599 <p> 2600 <span class="blue">1.70<br> (68ns)</span> 2601 </p> 2602 </td> 2603<td> 2604 <p> 2605 <span class="red">2.65<br> (106ns)</span> 2606 </p> 2607 </td> 2608<td> 2609 <p> 2610 <span class="green">1.20<br> (48ns)</span> 2611 </p> 2612 </td> 2613<td> 2614 <p> 2615 <span class="green">1.20<br> (48ns)</span> 2616 </p> 2617 </td> 2618<td> 2619 <p> 2620 <span class="green">1.02<br> (41ns)</span> 2621 </p> 2622 </td> 2623<td> 2624 <p> 2625 <span class="green">1.00<br> (40ns)</span> 2626 </p> 2627 </td> 2628<td> 2629 <p> 2630 <span class="green">1.02<br> (41ns)</span> 2631 </p> 2632 </td> 2633<td> 2634 <p> 2635 <span class="green">1.00<br> (40ns)</span> 2636 </p> 2637 </td> 2638</tr> 2639<tr> 2640<td> 2641 <p> 2642 Order 11 2643 </p> 2644 </td> 2645<td> 2646 <p> 2647 <span class="blue">1.91<br> (84ns)</span> 2648 </p> 2649 </td> 2650<td> 2651 <p> 2652 <span class="red">2.45<br> (108ns)</span> 2653 </p> 2654 </td> 2655<td> 2656 <p> 2657 <span class="blue">1.25<br> (55ns)</span> 2658 </p> 2659 </td> 2660<td> 2661 <p> 2662 <span class="blue">1.25<br> (55ns)</span> 2663 </p> 2664 </td> 2665<td> 2666 <p> 2667 <span class="green">1.02<br> (45ns)</span> 2668 </p> 2669 </td> 2670<td> 2671 <p> 2672 <span class="green">1.05<br> (46ns)</span> 2673 </p> 2674 </td> 2675<td> 2676 <p> 2677 <span class="green">1.00<br> (44ns)</span> 2678 </p> 2679 </td> 2680<td> 2681 <p> 2682 <span class="green">1.02<br> (45ns)</span> 2683 </p> 2684 </td> 2685</tr> 2686<tr> 2687<td> 2688 <p> 2689 Order 12 2690 </p> 2691 </td> 2692<td> 2693 <p> 2694 <span class="blue">1.84<br> (92ns)</span> 2695 </p> 2696 </td> 2697<td> 2698 <p> 2699 <span class="red">2.56<br> (128ns)</span> 2700 </p> 2701 </td> 2702<td> 2703 <p> 2704 <span class="blue">1.34<br> (67ns)</span> 2705 </p> 2706 </td> 2707<td> 2708 <p> 2709 <span class="blue">1.26<br> (63ns)</span> 2710 </p> 2711 </td> 2712<td> 2713 <p> 2714 <span class="green">1.00<br> (50ns)</span> 2715 </p> 2716 </td> 2717<td> 2718 <p> 2719 <span class="green">1.06<br> (53ns)</span> 2720 </p> 2721 </td> 2722<td> 2723 <p> 2724 <span class="green">1.02<br> (51ns)</span> 2725 </p> 2726 </td> 2727<td> 2728 <p> 2729 <span class="green">1.00<br> (50ns)</span> 2730 </p> 2731 </td> 2732</tr> 2733<tr> 2734<td> 2735 <p> 2736 Order 13 2737 </p> 2738 </td> 2739<td> 2740 <p> 2741 <span class="red">2.02<br> (103ns)</span> 2742 </p> 2743 </td> 2744<td> 2745 <p> 2746 <span class="red">2.73<br> (139ns)</span> 2747 </p> 2748 </td> 2749<td> 2750 <p> 2751 <span class="blue">1.37<br> (70ns)</span> 2752 </p> 2753 </td> 2754<td> 2755 <p> 2756 <span class="blue">1.31<br> (67ns)</span> 2757 </p> 2758 </td> 2759<td> 2760 <p> 2761 <span class="green">1.08<br> (55ns)</span> 2762 </p> 2763 </td> 2764<td> 2765 <p> 2766 <span class="green">1.04<br> (53ns)</span> 2767 </p> 2768 </td> 2769<td> 2770 <p> 2771 <span class="green">1.02<br> (52ns)</span> 2772 </p> 2773 </td> 2774<td> 2775 <p> 2776 <span class="green">1.00<br> (51ns)</span> 2777 </p> 2778 </td> 2779</tr> 2780<tr> 2781<td> 2782 <p> 2783 Order 14 2784 </p> 2785 </td> 2786<td> 2787 <p> 2788 <span class="red">2.02<br> (115ns)</span> 2789 </p> 2790 </td> 2791<td> 2792 <p> 2793 <span class="red">2.74<br> (156ns)</span> 2794 </p> 2795 </td> 2796<td> 2797 <p> 2798 <span class="blue">1.49<br> (85ns)</span> 2799 </p> 2800 </td> 2801<td> 2802 <p> 2803 <span class="blue">1.44<br> (82ns)</span> 2804 </p> 2805 </td> 2806<td> 2807 <p> 2808 <span class="green">1.04<br> (59ns)</span> 2809 </p> 2810 </td> 2811<td> 2812 <p> 2813 <span class="green">1.02<br> (58ns)</span> 2814 </p> 2815 </td> 2816<td> 2817 <p> 2818 <span class="green">1.00<br> (57ns)</span> 2819 </p> 2820 </td> 2821<td> 2822 <p> 2823 <span class="green">1.00<br> (57ns)</span> 2824 </p> 2825 </td> 2826</tr> 2827<tr> 2828<td> 2829 <p> 2830 Order 15 2831 </p> 2832 </td> 2833<td> 2834 <p> 2835 <span class="blue">1.89<br> (125ns)</span> 2836 </p> 2837 </td> 2838<td> 2839 <p> 2840 <span class="red">2.55<br> (168ns)</span> 2841 </p> 2842 </td> 2843<td> 2844 <p> 2845 <span class="blue">1.41<br> (93ns)</span> 2846 </p> 2847 </td> 2848<td> 2849 <p> 2850 <span class="blue">1.38<br> (91ns)</span> 2851 </p> 2852 </td> 2853<td> 2854 <p> 2855 <span class="green">1.00<br> (66ns)</span> 2856 </p> 2857 </td> 2858<td> 2859 <p> 2860 <span class="green">1.00<br> (66ns)</span> 2861 </p> 2862 </td> 2863<td> 2864 <p> 2865 <span class="green">1.02<br> (67ns)</span> 2866 </p> 2867 </td> 2868<td> 2869 <p> 2870 <span class="green">1.03<br> (68ns)</span> 2871 </p> 2872 </td> 2873</tr> 2874<tr> 2875<td> 2876 <p> 2877 Order 16 2878 </p> 2879 </td> 2880<td> 2881 <p> 2882 <span class="blue">1.77<br> (136ns)</span> 2883 </p> 2884 </td> 2885<td> 2886 <p> 2887 <span class="red">2.40<br> (185ns)</span> 2888 </p> 2889 </td> 2890<td> 2891 <p> 2892 <span class="blue">1.34<br> (103ns)</span> 2893 </p> 2894 </td> 2895<td> 2896 <p> 2897 <span class="blue">1.40<br> (108ns)</span> 2898 </p> 2899 </td> 2900<td> 2901 <p> 2902 <span class="green">1.10<br> (85ns)</span> 2903 </p> 2904 </td> 2905<td> 2906 <p> 2907 <span class="green">1.06<br> (82ns)</span> 2908 </p> 2909 </td> 2910<td> 2911 <p> 2912 <span class="green">1.00<br> (77ns)</span> 2913 </p> 2914 </td> 2915<td> 2916 <p> 2917 <span class="green">1.00<br> (77ns)</span> 2918 </p> 2919 </td> 2920</tr> 2921<tr> 2922<td> 2923 <p> 2924 Order 17 2925 </p> 2926 </td> 2927<td> 2928 <p> 2929 <span class="blue">1.77<br> (143ns)</span> 2930 </p> 2931 </td> 2932<td> 2933 <p> 2934 <span class="red">2.60<br> (211ns)</span> 2935 </p> 2936 </td> 2937<td> 2938 <p> 2939 <span class="blue">1.43<br> (116ns)</span> 2940 </p> 2941 </td> 2942<td> 2943 <p> 2944 <span class="blue">1.44<br> (117ns)</span> 2945 </p> 2946 </td> 2947<td> 2948 <p> 2949 <span class="green">1.04<br> (84ns)</span> 2950 </p> 2951 </td> 2952<td> 2953 <p> 2954 <span class="green">1.00<br> (81ns)</span> 2955 </p> 2956 </td> 2957<td> 2958 <p> 2959 <span class="green">1.02<br> (83ns)</span> 2960 </p> 2961 </td> 2962<td> 2963 <p> 2964 <span class="green">1.16<br> (94ns)</span> 2965 </p> 2966 </td> 2967</tr> 2968<tr> 2969<td> 2970 <p> 2971 Order 18 2972 </p> 2973 </td> 2974<td> 2975 <p> 2976 <span class="blue">1.85<br> (163ns)</span> 2977 </p> 2978 </td> 2979<td> 2980 <p> 2981 <span class="red">2.39<br> (210ns)</span> 2982 </p> 2983 </td> 2984<td> 2985 <p> 2986 <span class="blue">1.47<br> (129ns)</span> 2987 </p> 2988 </td> 2989<td> 2990 <p> 2991 <span class="blue">1.53<br> (135ns)</span> 2992 </p> 2993 </td> 2994<td> 2995 <p> 2996 <span class="green">1.00<br> (88ns)</span> 2997 </p> 2998 </td> 2999<td> 3000 <p> 3001 <span class="green">1.01<br> (89ns)</span> 3002 </p> 3003 </td> 3004<td> 3005 <p> 3006 <span class="green">1.00<br> (88ns)</span> 3007 </p> 3008 </td> 3009<td> 3010 <p> 3011 <span class="green">1.00<br> (88ns)</span> 3012 </p> 3013 </td> 3014</tr> 3015<tr> 3016<td> 3017 <p> 3018 Order 19 3019 </p> 3020 </td> 3021<td> 3022 <p> 3023 <span class="red">2.01<br> (183ns)</span> 3024 </p> 3025 </td> 3026<td> 3027 <p> 3028 <span class="red">2.55<br> (232ns)</span> 3029 </p> 3030 </td> 3031<td> 3032 <p> 3033 <span class="blue">1.53<br> (139ns)</span> 3034 </p> 3035 </td> 3036<td> 3037 <p> 3038 <span class="blue">1.53<br> (139ns)</span> 3039 </p> 3040 </td> 3041<td> 3042 <p> 3043 <span class="green">1.04<br> (95ns)</span> 3044 </p> 3045 </td> 3046<td> 3047 <p> 3048 <span class="green">1.05<br> (96ns)</span> 3049 </p> 3050 </td> 3051<td> 3052 <p> 3053 <span class="green">1.00<br> (91ns)</span> 3054 </p> 3055 </td> 3056<td> 3057 <p> 3058 <span class="green">1.05<br> (96ns)</span> 3059 </p> 3060 </td> 3061</tr> 3062<tr> 3063<td> 3064 <p> 3065 Order 20 3066 </p> 3067 </td> 3068<td> 3069 <p> 3070 <span class="blue">1.94<br> (194ns)</span> 3071 </p> 3072 </td> 3073<td> 3074 <p> 3075 <span class="red">2.55<br> (255ns)</span> 3076 </p> 3077 </td> 3078<td> 3079 <p> 3080 <span class="blue">1.48<br> (148ns)</span> 3081 </p> 3082 </td> 3083<td> 3084 <p> 3085 <span class="blue">1.51<br> (151ns)</span> 3086 </p> 3087 </td> 3088<td> 3089 <p> 3090 <span class="green">1.00<br> (100ns)</span> 3091 </p> 3092 </td> 3093<td> 3094 <p> 3095 <span class="green">1.00<br> (100ns)</span> 3096 </p> 3097 </td> 3098<td> 3099 <p> 3100 <span class="green">1.18<br> (118ns)</span> 3101 </p> 3102 </td> 3103<td> 3104 <p> 3105 <span class="green">1.03<br> (103ns)</span> 3106 </p> 3107 </td> 3108</tr> 3109</tbody> 3110</table></div> 3111</div> 3112<br class="table-break"><div class="table"> 3113<a name="math_toolkit.tuning.table_Rational_Method_Comparison_with_GNU_C_version_9_2_1_20191008_on_linux"></a><p class="title"><b>Table 22.7. Rational Method Comparison with GNU C++ version 9.2.1 20191008 on linux</b></p> 3114<div class="table-contents"><table class="table" summary="Rational Method Comparison with GNU C++ version 9.2.1 20191008 on linux"> 3115<colgroup> 3116<col> 3117<col> 3118<col> 3119<col> 3120<col> 3121<col> 3122<col> 3123<col> 3124<col> 3125</colgroup> 3126<thead><tr> 3127<th> 3128 <p> 3129 Function 3130 </p> 3131 </th> 3132<th> 3133 <p> 3134 Method 0<br> (Double Coefficients) 3135 </p> 3136 </th> 3137<th> 3138 <p> 3139 Method 0<br> (Integer Coefficients) 3140 </p> 3141 </th> 3142<th> 3143 <p> 3144 Method 1<br> (Double Coefficients) 3145 </p> 3146 </th> 3147<th> 3148 <p> 3149 Method 1<br> (Integer Coefficients) 3150 </p> 3151 </th> 3152<th> 3153 <p> 3154 Method 2<br> (Double Coefficients) 3155 </p> 3156 </th> 3157<th> 3158 <p> 3159 Method 2<br> (Integer Coefficients) 3160 </p> 3161 </th> 3162<th> 3163 <p> 3164 Method 3<br> (Double Coefficients) 3165 </p> 3166 </th> 3167<th> 3168 <p> 3169 Method 3<br> (Integer Coefficients) 3170 </p> 3171 </th> 3172</tr></thead> 3173<tbody> 3174<tr> 3175<td> 3176 <p> 3177 Order 2 3178 </p> 3179 </td> 3180<td> 3181 <p> 3182 <span class="grey">-</span> 3183 </p> 3184 </td> 3185<td> 3186 <p> 3187 <span class="grey">-</span> 3188 </p> 3189 </td> 3190<td> 3191 <p> 3192 <span class="blue">1.92<br> (23ns)</span> 3193 </p> 3194 </td> 3195<td> 3196 <p> 3197 <span class="blue">1.92<br> (23ns)</span> 3198 </p> 3199 </td> 3200<td> 3201 <p> 3202 <span class="blue">1.25<br> (15ns)</span> 3203 </p> 3204 </td> 3205<td> 3206 <p> 3207 <span class="green">1.08<br> (13ns)</span> 3208 </p> 3209 </td> 3210<td> 3211 <p> 3212 <span class="green">1.00<br> (12ns)</span> 3213 </p> 3214 </td> 3215<td> 3216 <p> 3217 <span class="green">1.08<br> (13ns)</span> 3218 </p> 3219 </td> 3220</tr> 3221<tr> 3222<td> 3223 <p> 3224 Order 3 3225 </p> 3226 </td> 3227<td> 3228 <p> 3229 <span class="blue">1.89<br> (36ns)</span> 3230 </p> 3231 </td> 3232<td> 3233 <p> 3234 <span class="red">2.21<br> (42ns)</span> 3235 </p> 3236 </td> 3237<td> 3238 <p> 3239 <span class="blue">1.63<br> (31ns)</span> 3240 </p> 3241 </td> 3242<td> 3243 <p> 3244 <span class="blue">1.47<br> (28ns)</span> 3245 </p> 3246 </td> 3247<td> 3248 <p> 3249 <span class="green">1.00<br> (19ns)</span> 3250 </p> 3251 </td> 3252<td> 3253 <p> 3254 <span class="green">1.00<br> (19ns)</span> 3255 </p> 3256 </td> 3257<td> 3258 <p> 3259 <span class="green">1.11<br> (21ns)</span> 3260 </p> 3261 </td> 3262<td> 3263 <p> 3264 <span class="green">1.16<br> (22ns)</span> 3265 </p> 3266 </td> 3267</tr> 3268<tr> 3269<td> 3270 <p> 3271 Order 4 3272 </p> 3273 </td> 3274<td> 3275 <p> 3276 <span class="blue">1.85<br> (48ns)</span> 3277 </p> 3278 </td> 3279<td> 3280 <p> 3281 <span class="red">2.42<br> (63ns)</span> 3282 </p> 3283 </td> 3284<td> 3285 <p> 3286 <span class="blue">1.54<br> (40ns)</span> 3287 </p> 3288 </td> 3289<td> 3290 <p> 3291 <span class="blue">1.54<br> (40ns)</span> 3292 </p> 3293 </td> 3294<td> 3295 <p> 3296 <span class="green">1.00<br> (26ns)</span> 3297 </p> 3298 </td> 3299<td> 3300 <p> 3301 <span class="green">1.00<br> (26ns)</span> 3302 </p> 3303 </td> 3304<td> 3305 <p> 3306 <span class="green">1.04<br> (27ns)</span> 3307 </p> 3308 </td> 3309<td> 3310 <p> 3311 <span class="green">1.00<br> (26ns)</span> 3312 </p> 3313 </td> 3314</tr> 3315<tr> 3316<td> 3317 <p> 3318 Order 5 3319 </p> 3320 </td> 3321<td> 3322 <p> 3323 <span class="green">1.18<br> (59ns)</span> 3324 </p> 3325 </td> 3326<td> 3327 <p> 3328 <span class="blue">1.42<br> (71ns)</span> 3329 </p> 3330 </td> 3331<td> 3332 <p> 3333 <span class="green">1.00<br> (50ns)</span> 3334 </p> 3335 </td> 3336<td> 3337 <p> 3338 <span class="green">1.00<br> (50ns)</span> 3339 </p> 3340 </td> 3341<td> 3342 <p> 3343 <span class="green">1.10<br> (55ns)</span> 3344 </p> 3345 </td> 3346<td> 3347 <p> 3348 <span class="green">1.10<br> (55ns)</span> 3349 </p> 3350 </td> 3351<td> 3352 <p> 3353 <span class="green">1.12<br> (56ns)</span> 3354 </p> 3355 </td> 3356<td> 3357 <p> 3358 <span class="green">1.10<br> (55ns)</span> 3359 </p> 3360 </td> 3361</tr> 3362<tr> 3363<td> 3364 <p> 3365 Order 6 3366 </p> 3367 </td> 3368<td> 3369 <p> 3370 <span class="green">1.11<br> (69ns)</span> 3371 </p> 3372 </td> 3373<td> 3374 <p> 3375 <span class="blue">1.37<br> (85ns)</span> 3376 </p> 3377 </td> 3378<td> 3379 <p> 3380 <span class="green">1.06<br> (66ns)</span> 3381 </p> 3382 </td> 3383<td> 3384 <p> 3385 <span class="green">1.00<br> (62ns)</span> 3386 </p> 3387 </td> 3388<td> 3389 <p> 3390 <span class="green">1.02<br> (63ns)</span> 3391 </p> 3392 </td> 3393<td> 3394 <p> 3395 <span class="green">1.02<br> (63ns)</span> 3396 </p> 3397 </td> 3398<td> 3399 <p> 3400 <span class="green">1.05<br> (65ns)</span> 3401 </p> 3402 </td> 3403<td> 3404 <p> 3405 <span class="green">1.18<br> (73ns)</span> 3406 </p> 3407 </td> 3408</tr> 3409<tr> 3410<td> 3411 <p> 3412 Order 7 3413 </p> 3414 </td> 3415<td> 3416 <p> 3417 <span class="green">1.09<br> (81ns)</span> 3418 </p> 3419 </td> 3420<td> 3421 <p> 3422 <span class="blue">1.35<br> (100ns)</span> 3423 </p> 3424 </td> 3425<td> 3426 <p> 3427 <span class="green">1.00<br> (74ns)</span> 3428 </p> 3429 </td> 3430<td> 3431 <p> 3432 <span class="green">1.00<br> (74ns)</span> 3433 </p> 3434 </td> 3435<td> 3436 <p> 3437 <span class="green">1.00<br> (74ns)</span> 3438 </p> 3439 </td> 3440<td> 3441 <p> 3442 <span class="green">1.01<br> (75ns)</span> 3443 </p> 3444 </td> 3445<td> 3446 <p> 3447 <span class="green">1.03<br> (76ns)</span> 3448 </p> 3449 </td> 3450<td> 3451 <p> 3452 <span class="green">1.03<br> (76ns)</span> 3453 </p> 3454 </td> 3455</tr> 3456<tr> 3457<td> 3458 <p> 3459 Order 8 3460 </p> 3461 </td> 3462<td> 3463 <p> 3464 <span class="green">1.13<br> (96ns)</span> 3465 </p> 3466 </td> 3467<td> 3468 <p> 3469 <span class="blue">1.33<br> (113ns)</span> 3470 </p> 3471 </td> 3472<td> 3473 <p> 3474 <span class="green">1.01<br> (86ns)</span> 3475 </p> 3476 </td> 3477<td> 3478 <p> 3479 <span class="green">1.00<br> (85ns)</span> 3480 </p> 3481 </td> 3482<td> 3483 <p> 3484 <span class="green">1.00<br> (85ns)</span> 3485 </p> 3486 </td> 3487<td> 3488 <p> 3489 <span class="green">1.01<br> (86ns)</span> 3490 </p> 3491 </td> 3492<td> 3493 <p> 3494 <span class="green">1.01<br> (86ns)</span> 3495 </p> 3496 </td> 3497<td> 3498 <p> 3499 <span class="green">1.04<br> (88ns)</span> 3500 </p> 3501 </td> 3502</tr> 3503<tr> 3504<td> 3505 <p> 3506 Order 9 3507 </p> 3508 </td> 3509<td> 3510 <p> 3511 <span class="green">1.15<br> (108ns)</span> 3512 </p> 3513 </td> 3514<td> 3515 <p> 3516 <span class="blue">1.34<br> (126ns)</span> 3517 </p> 3518 </td> 3519<td> 3520 <p> 3521 <span class="green">1.05<br> (99ns)</span> 3522 </p> 3523 </td> 3524<td> 3525 <p> 3526 <span class="green">1.05<br> (99ns)</span> 3527 </p> 3528 </td> 3529<td> 3530 <p> 3531 <span class="green">1.01<br> (95ns)</span> 3532 </p> 3533 </td> 3534<td> 3535 <p> 3536 <span class="green">1.00<br> (94ns)</span> 3537 </p> 3538 </td> 3539<td> 3540 <p> 3541 <span class="green">1.02<br> (96ns)</span> 3542 </p> 3543 </td> 3544<td> 3545 <p> 3546 <span class="green">1.12<br> (105ns)</span> 3547 </p> 3548 </td> 3549</tr> 3550<tr> 3551<td> 3552 <p> 3553 Order 10 3554 </p> 3555 </td> 3556<td> 3557 <p> 3558 <span class="green">1.17<br> (123ns)</span> 3559 </p> 3560 </td> 3561<td> 3562 <p> 3563 <span class="blue">1.36<br> (143ns)</span> 3564 </p> 3565 </td> 3566<td> 3567 <p> 3568 <span class="green">1.10<br> (115ns)</span> 3569 </p> 3570 </td> 3571<td> 3572 <p> 3573 <span class="green">1.10<br> (115ns)</span> 3574 </p> 3575 </td> 3576<td> 3577 <p> 3578 <span class="green">1.02<br> (107ns)</span> 3579 </p> 3580 </td> 3581<td> 3582 <p> 3583 <span class="green">1.05<br> (110ns)</span> 3584 </p> 3585 </td> 3586<td> 3587 <p> 3588 <span class="green">1.01<br> (106ns)</span> 3589 </p> 3590 </td> 3591<td> 3592 <p> 3593 <span class="green">1.00<br> (105ns)</span> 3594 </p> 3595 </td> 3596</tr> 3597<tr> 3598<td> 3599 <p> 3600 Order 11 3601 </p> 3602 </td> 3603<td> 3604 <p> 3605 <span class="green">1.15<br> (135ns)</span> 3606 </p> 3607 </td> 3608<td> 3609 <p> 3610 <span class="blue">1.34<br> (157ns)</span> 3611 </p> 3612 </td> 3613<td> 3614 <p> 3615 <span class="green">1.15<br> (134ns)</span> 3616 </p> 3617 </td> 3618<td> 3619 <p> 3620 <span class="green">1.09<br> (128ns)</span> 3621 </p> 3622 </td> 3623<td> 3624 <p> 3625 <span class="green">1.01<br> (118ns)</span> 3626 </p> 3627 </td> 3628<td> 3629 <p> 3630 <span class="green">1.01<br> (118ns)</span> 3631 </p> 3632 </td> 3633<td> 3634 <p> 3635 <span class="green">1.00<br> (117ns)</span> 3636 </p> 3637 </td> 3638<td> 3639 <p> 3640 <span class="green">1.02<br> (119ns)</span> 3641 </p> 3642 </td> 3643</tr> 3644<tr> 3645<td> 3646 <p> 3647 Order 12 3648 </p> 3649 </td> 3650<td> 3651 <p> 3652 <span class="green">1.19<br> (150ns)</span> 3653 </p> 3654 </td> 3655<td> 3656 <p> 3657 <span class="blue">1.34<br> (169ns)</span> 3658 </p> 3659 </td> 3660<td> 3661 <p> 3662 <span class="green">1.17<br> (148ns)</span> 3663 </p> 3664 </td> 3665<td> 3666 <p> 3667 <span class="blue">1.28<br> (161ns)</span> 3668 </p> 3669 </td> 3670<td> 3671 <p> 3672 <span class="green">1.01<br> (127ns)</span> 3673 </p> 3674 </td> 3675<td> 3676 <p> 3677 <span class="green">1.00<br> (126ns)</span> 3678 </p> 3679 </td> 3680<td> 3681 <p> 3682 <span class="green">1.00<br> (126ns)</span> 3683 </p> 3684 </td> 3685<td> 3686 <p> 3687 <span class="green">1.00<br> (126ns)</span> 3688 </p> 3689 </td> 3690</tr> 3691<tr> 3692<td> 3693 <p> 3694 Order 13 3695 </p> 3696 </td> 3697<td> 3698 <p> 3699 <span class="blue">1.28<br> (171ns)</span> 3700 </p> 3701 </td> 3702<td> 3703 <p> 3704 <span class="blue">1.40<br> (187ns)</span> 3705 </p> 3706 </td> 3707<td> 3708 <p> 3709 <span class="blue">1.34<br> (180ns)</span> 3710 </p> 3711 </td> 3712<td> 3713 <p> 3714 <span class="blue">1.28<br> (172ns)</span> 3715 </p> 3716 </td> 3717<td> 3718 <p> 3719 <span class="green">1.01<br> (136ns)</span> 3720 </p> 3721 </td> 3722<td> 3723 <p> 3724 <span class="green">1.00<br> (134ns)</span> 3725 </p> 3726 </td> 3727<td> 3728 <p> 3729 <span class="green">1.01<br> (136ns)</span> 3730 </p> 3731 </td> 3732<td> 3733 <p> 3734 <span class="green">1.06<br> (142ns)</span> 3735 </p> 3736 </td> 3737</tr> 3738<tr> 3739<td> 3740 <p> 3741 Order 14 3742 </p> 3743 </td> 3744<td> 3745 <p> 3746 <span class="blue">1.34<br> (191ns)</span> 3747 </p> 3748 </td> 3749<td> 3750 <p> 3751 <span class="blue">1.43<br> (204ns)</span> 3752 </p> 3753 </td> 3754<td> 3755 <p> 3756 <span class="blue">1.27<br> (181ns)</span> 3757 </p> 3758 </td> 3759<td> 3760 <p> 3761 <span class="blue">1.31<br> (188ns)</span> 3762 </p> 3763 </td> 3764<td> 3765 <p> 3766 <span class="green">1.01<br> (144ns)</span> 3767 </p> 3768 </td> 3769<td> 3770 <p> 3771 <span class="green">1.03<br> (148ns)</span> 3772 </p> 3773 </td> 3774<td> 3775 <p> 3776 <span class="green">1.00<br> (143ns)</span> 3777 </p> 3778 </td> 3779<td> 3780 <p> 3781 <span class="green">1.07<br> (153ns)</span> 3782 </p> 3783 </td> 3784</tr> 3785<tr> 3786<td> 3787 <p> 3788 Order 15 3789 </p> 3790 </td> 3791<td> 3792 <p> 3793 <span class="blue">1.41<br> (206ns)</span> 3794 </p> 3795 </td> 3796<td> 3797 <p> 3798 <span class="blue">1.50<br> (219ns)</span> 3799 </p> 3800 </td> 3801<td> 3802 <p> 3803 <span class="blue">1.36<br> (199ns)</span> 3804 </p> 3805 </td> 3806<td> 3807 <p> 3808 <span class="blue">1.31<br> (191ns)</span> 3809 </p> 3810 </td> 3811<td> 3812 <p> 3813 <span class="green">1.16<br> (169ns)</span> 3814 </p> 3815 </td> 3816<td> 3817 <p> 3818 <span class="blue">1.30<br> (190ns)</span> 3819 </p> 3820 </td> 3821<td> 3822 <p> 3823 <span class="green">1.02<br> (149ns)</span> 3824 </p> 3825 </td> 3826<td> 3827 <p> 3828 <span class="green">1.00<br> (146ns)</span> 3829 </p> 3830 </td> 3831</tr> 3832<tr> 3833<td> 3834 <p> 3835 Order 16 3836 </p> 3837 </td> 3838<td> 3839 <p> 3840 <span class="blue">1.37<br> (217ns)</span> 3841 </p> 3842 </td> 3843<td> 3844 <p> 3845 <span class="blue">1.48<br> (234ns)</span> 3846 </p> 3847 </td> 3848<td> 3849 <p> 3850 <span class="blue">1.32<br> (209ns)</span> 3851 </p> 3852 </td> 3853<td> 3854 <p> 3855 <span class="blue">1.35<br> (213ns)</span> 3856 </p> 3857 </td> 3858<td> 3859 <p> 3860 <span class="blue">1.32<br> (209ns)</span> 3861 </p> 3862 </td> 3863<td> 3864 <p> 3865 <span class="green">1.19<br> (188ns)</span> 3866 </p> 3867 </td> 3868<td> 3869 <p> 3870 <span class="green">1.00<br> (158ns)</span> 3871 </p> 3872 </td> 3873<td> 3874 <p> 3875 <span class="green">1.03<br> (163ns)</span> 3876 </p> 3877 </td> 3878</tr> 3879<tr> 3880<td> 3881 <p> 3882 Order 17 3883 </p> 3884 </td> 3885<td> 3886 <p> 3887 <span class="blue">1.36<br> (234ns)</span> 3888 </p> 3889 </td> 3890<td> 3891 <p> 3892 <span class="blue">1.48<br> (254ns)</span> 3893 </p> 3894 </td> 3895<td> 3896 <p> 3897 <span class="blue">1.32<br> (227ns)</span> 3898 </p> 3899 </td> 3900<td> 3901 <p> 3902 <span class="blue">1.30<br> (224ns)</span> 3903 </p> 3904 </td> 3905<td> 3906 <p> 3907 <span class="green">1.13<br> (194ns)</span> 3908 </p> 3909 </td> 3910<td> 3911 <p> 3912 <span class="green">1.05<br> (180ns)</span> 3913 </p> 3914 </td> 3915<td> 3916 <p> 3917 <span class="green">1.00<br> (172ns)</span> 3918 </p> 3919 </td> 3920<td> 3921 <p> 3922 <span class="green">1.02<br> (176ns)</span> 3923 </p> 3924 </td> 3925</tr> 3926<tr> 3927<td> 3928 <p> 3929 Order 18 3930 </p> 3931 </td> 3932<td> 3933 <p> 3934 <span class="blue">1.37<br> (248ns)</span> 3935 </p> 3936 </td> 3937<td> 3938 <p> 3939 <span class="blue">1.57<br> (284ns)</span> 3940 </p> 3941 </td> 3942<td> 3943 <p> 3944 <span class="blue">1.35<br> (244ns)</span> 3945 </p> 3946 </td> 3947<td> 3948 <p> 3949 <span class="blue">1.39<br> (252ns)</span> 3950 </p> 3951 </td> 3952<td> 3953 <p> 3954 <span class="green">1.08<br> (195ns)</span> 3955 </p> 3956 </td> 3957<td> 3958 <p> 3959 <span class="green">1.07<br> (193ns)</span> 3960 </p> 3961 </td> 3962<td> 3963 <p> 3964 <span class="green">1.02<br> (185ns)</span> 3965 </p> 3966 </td> 3967<td> 3968 <p> 3969 <span class="green">1.00<br> (181ns)</span> 3970 </p> 3971 </td> 3972</tr> 3973<tr> 3974<td> 3975 <p> 3976 Order 19 3977 </p> 3978 </td> 3979<td> 3980 <p> 3981 <span class="blue">1.40<br> (268ns)</span> 3982 </p> 3983 </td> 3984<td> 3985 <p> 3986 <span class="blue">1.77<br> (338ns)</span> 3987 </p> 3988 </td> 3989<td> 3990 <p> 3991 <span class="blue">1.38<br> (264ns)</span> 3992 </p> 3993 </td> 3994<td> 3995 <p> 3996 <span class="blue">1.40<br> (267ns)</span> 3997 </p> 3998 </td> 3999<td> 4000 <p> 4001 <span class="green">1.01<br> (193ns)</span> 4002 </p> 4003 </td> 4004<td> 4005 <p> 4006 <span class="green">1.00<br> (191ns)</span> 4007 </p> 4008 </td> 4009<td> 4010 <p> 4011 <span class="green">1.02<br> (195ns)</span> 4012 </p> 4013 </td> 4014<td> 4015 <p> 4016 <span class="green">1.04<br> (198ns)</span> 4017 </p> 4018 </td> 4019</tr> 4020<tr> 4021<td> 4022 <p> 4023 Order 20 4024 </p> 4025 </td> 4026<td> 4027 <p> 4028 <span class="blue">1.39<br> (286ns)</span> 4029 </p> 4030 </td> 4031<td> 4032 <p> 4033 <span class="blue">1.63<br> (336ns)</span> 4034 </p> 4035 </td> 4036<td> 4037 <p> 4038 <span class="blue">1.41<br> (291ns)</span> 4039 </p> 4040 </td> 4041<td> 4042 <p> 4043 <span class="blue">1.45<br> (298ns)</span> 4044 </p> 4045 </td> 4046<td> 4047 <p> 4048 <span class="green">1.00<br> (206ns)</span> 4049 </p> 4050 </td> 4051<td> 4052 <p> 4053 <span class="green">1.01<br> (208ns)</span> 4054 </p> 4055 </td> 4056<td> 4057 <p> 4058 <span class="green">1.03<br> (213ns)</span> 4059 </p> 4060 </td> 4061<td> 4062 <p> 4063 <span class="green">1.01<br> (209ns)</span> 4064 </p> 4065 </td> 4066</tr> 4067</tbody> 4068</table></div> 4069</div> 4070<br class="table-break"><div class="table"> 4071<a name="math_toolkit.tuning.table_Polynomial_Method_Comparison_with_Clang_version_9_0_0_tags_RELEASE_900_final_on_linux"></a><p class="title"><b>Table 22.8. Polynomial Method Comparison with Clang version 9.0.0 (tags/RELEASE_900/final) 4072 on linux</b></p> 4073<div class="table-contents"><table class="table" summary="Polynomial Method Comparison with Clang version 9.0.0 (tags/RELEASE_900/final) 4074 on linux"> 4075<colgroup> 4076<col> 4077<col> 4078<col> 4079<col> 4080<col> 4081<col> 4082<col> 4083<col> 4084<col> 4085</colgroup> 4086<thead><tr> 4087<th> 4088 <p> 4089 Function 4090 </p> 4091 </th> 4092<th> 4093 <p> 4094 Method 0<br> (Double Coefficients) 4095 </p> 4096 </th> 4097<th> 4098 <p> 4099 Method 0<br> (Integer Coefficients) 4100 </p> 4101 </th> 4102<th> 4103 <p> 4104 Method 1<br> (Double Coefficients) 4105 </p> 4106 </th> 4107<th> 4108 <p> 4109 Method 1<br> (Integer Coefficients) 4110 </p> 4111 </th> 4112<th> 4113 <p> 4114 Method 2<br> (Double Coefficients) 4115 </p> 4116 </th> 4117<th> 4118 <p> 4119 Method 2<br> (Integer Coefficients) 4120 </p> 4121 </th> 4122<th> 4123 <p> 4124 Method 3<br> (Double Coefficients) 4125 </p> 4126 </th> 4127<th> 4128 <p> 4129 Method 3<br> (Integer Coefficients) 4130 </p> 4131 </th> 4132</tr></thead> 4133<tbody> 4134<tr> 4135<td> 4136 <p> 4137 Order 2 4138 </p> 4139 </td> 4140<td> 4141 <p> 4142 <span class="grey">-</span> 4143 </p> 4144 </td> 4145<td> 4146 <p> 4147 <span class="grey">-</span> 4148 </p> 4149 </td> 4150<td> 4151 <p> 4152 <span class="green">1.20<br> (6ns)</span> 4153 </p> 4154 </td> 4155<td> 4156 <p> 4157 <span class="green">1.20<br> (6ns)</span> 4158 </p> 4159 </td> 4160<td> 4161 <p> 4162 <span class="green">1.20<br> (6ns)</span> 4163 </p> 4164 </td> 4165<td> 4166 <p> 4167 <span class="green">1.20<br> (6ns)</span> 4168 </p> 4169 </td> 4170<td> 4171 <p> 4172 <span class="green">1.00<br> (5ns)</span> 4173 </p> 4174 </td> 4175<td> 4176 <p> 4177 <span class="green">1.00<br> (5ns)</span> 4178 </p> 4179 </td> 4180</tr> 4181<tr> 4182<td> 4183 <p> 4184 Order 3 4185 </p> 4186 </td> 4187<td> 4188 <p> 4189 <span class="blue">2.00<br> (16ns)</span> 4190 </p> 4191 </td> 4192<td> 4193 <p> 4194 <span class="red">3.00<br> (24ns)</span> 4195 </p> 4196 </td> 4197<td> 4198 <p> 4199 <span class="green">1.12<br> (9ns)</span> 4200 </p> 4201 </td> 4202<td> 4203 <p> 4204 <span class="green">1.12<br> (9ns)</span> 4205 </p> 4206 </td> 4207<td> 4208 <p> 4209 <span class="green">1.12<br> (9ns)</span> 4210 </p> 4211 </td> 4212<td> 4213 <p> 4214 <span class="blue">1.25<br> (10ns)</span> 4215 </p> 4216 </td> 4217<td> 4218 <p> 4219 <span class="green">1.00<br> (8ns)</span> 4220 </p> 4221 </td> 4222<td> 4223 <p> 4224 <span class="green">1.00<br> (8ns)</span> 4225 </p> 4226 </td> 4227</tr> 4228<tr> 4229<td> 4230 <p> 4231 Order 4 4232 </p> 4233 </td> 4234<td> 4235 <p> 4236 <span class="blue">1.83<br> (22ns)</span> 4237 </p> 4238 </td> 4239<td> 4240 <p> 4241 <span class="red">2.67<br> (32ns)</span> 4242 </p> 4243 </td> 4244<td> 4245 <p> 4246 <span class="green">1.00<br> (12ns)</span> 4247 </p> 4248 </td> 4249<td> 4250 <p> 4251 <span class="green">1.00<br> (12ns)</span> 4252 </p> 4253 </td> 4254<td> 4255 <p> 4256 <span class="green">1.08<br> (13ns)</span> 4257 </p> 4258 </td> 4259<td> 4260 <p> 4261 <span class="green">1.08<br> (13ns)</span> 4262 </p> 4263 </td> 4264<td> 4265 <p> 4266 <span class="green">1.00<br> (12ns)</span> 4267 </p> 4268 </td> 4269<td> 4270 <p> 4271 <span class="green">1.00<br> (12ns)</span> 4272 </p> 4273 </td> 4274</tr> 4275<tr> 4276<td> 4277 <p> 4278 Order 5 4279 </p> 4280 </td> 4281<td> 4282 <p> 4283 <span class="green">1.12<br> (19ns)</span> 4284 </p> 4285 </td> 4286<td> 4287 <p> 4288 <span class="blue">1.71<br> (29ns)</span> 4289 </p> 4290 </td> 4291<td> 4292 <p> 4293 <span class="green">1.00<br> (17ns)</span> 4294 </p> 4295 </td> 4296<td> 4297 <p> 4298 <span class="green">1.00<br> (17ns)</span> 4299 </p> 4300 </td> 4301<td> 4302 <p> 4303 <span class="green">1.06<br> (18ns)</span> 4304 </p> 4305 </td> 4306<td> 4307 <p> 4308 <span class="green">1.12<br> (19ns)</span> 4309 </p> 4310 </td> 4311<td> 4312 <p> 4313 <span class="green">1.00<br> (17ns)</span> 4314 </p> 4315 </td> 4316<td> 4317 <p> 4318 <span class="green">1.00<br> (17ns)</span> 4319 </p> 4320 </td> 4321</tr> 4322<tr> 4323<td> 4324 <p> 4325 Order 6 4326 </p> 4327 </td> 4328<td> 4329 <p> 4330 <span class="blue">1.45<br> (29ns)</span> 4331 </p> 4332 </td> 4333<td> 4334 <p> 4335 <span class="red">2.05<br> (41ns)</span> 4336 </p> 4337 </td> 4338<td> 4339 <p> 4340 <span class="blue">1.30<br> (26ns)</span> 4341 </p> 4342 </td> 4343<td> 4344 <p> 4345 <span class="blue">1.30<br> (26ns)</span> 4346 </p> 4347 </td> 4348<td> 4349 <p> 4350 <span class="green">1.10<br> (22ns)</span> 4351 </p> 4352 </td> 4353<td> 4354 <p> 4355 <span class="green">1.10<br> (22ns)</span> 4356 </p> 4357 </td> 4358<td> 4359 <p> 4360 <span class="green">1.00<br> (20ns)</span> 4361 </p> 4362 </td> 4363<td> 4364 <p> 4365 <span class="green">1.05<br> (21ns)</span> 4366 </p> 4367 </td> 4368</tr> 4369<tr> 4370<td> 4371 <p> 4372 Order 7 4373 </p> 4374 </td> 4375<td> 4376 <p> 4377 <span class="green">1.15<br> (31ns)</span> 4378 </p> 4379 </td> 4380<td> 4381 <p> 4382 <span class="red">2.22<br> (60ns)</span> 4383 </p> 4384 </td> 4385<td> 4386 <p> 4387 <span class="blue">1.22<br> (33ns)</span> 4388 </p> 4389 </td> 4390<td> 4391 <p> 4392 <span class="blue">1.22<br> (33ns)</span> 4393 </p> 4394 </td> 4395<td> 4396 <p> 4397 <span class="green">1.07<br> (29ns)</span> 4398 </p> 4399 </td> 4400<td> 4401 <p> 4402 <span class="green">1.07<br> (29ns)</span> 4403 </p> 4404 </td> 4405<td> 4406 <p> 4407 <span class="green">1.00<br> (27ns)</span> 4408 </p> 4409 </td> 4410<td> 4411 <p> 4412 <span class="green">1.00<br> (27ns)</span> 4413 </p> 4414 </td> 4415</tr> 4416<tr> 4417<td> 4418 <p> 4419 Order 8 4420 </p> 4421 </td> 4422<td> 4423 <p> 4424 <span class="blue">1.32<br> (37ns)</span> 4425 </p> 4426 </td> 4427<td> 4428 <p> 4429 <span class="red">2.18<br> (61ns)</span> 4430 </p> 4431 </td> 4432<td> 4433 <p> 4434 <span class="blue">1.43<br> (40ns)</span> 4435 </p> 4436 </td> 4437<td> 4438 <p> 4439 <span class="blue">1.36<br> (38ns)</span> 4440 </p> 4441 </td> 4442<td> 4443 <p> 4444 <span class="green">1.07<br> (30ns)</span> 4445 </p> 4446 </td> 4447<td> 4448 <p> 4449 <span class="green">1.07<br> (30ns)</span> 4450 </p> 4451 </td> 4452<td> 4453 <p> 4454 <span class="green">1.00<br> (28ns)</span> 4455 </p> 4456 </td> 4457<td> 4458 <p> 4459 <span class="green">1.04<br> (29ns)</span> 4460 </p> 4461 </td> 4462</tr> 4463<tr> 4464<td> 4465 <p> 4466 Order 9 4467 </p> 4468 </td> 4469<td> 4470 <p> 4471 <span class="green">1.17<br> (42ns)</span> 4472 </p> 4473 </td> 4474<td> 4475 <p> 4476 <span class="blue">1.72<br> (62ns)</span> 4477 </p> 4478 </td> 4479<td> 4480 <p> 4481 <span class="blue">1.36<br> (49ns)</span> 4482 </p> 4483 </td> 4484<td> 4485 <p> 4486 <span class="blue">1.36<br> (49ns)</span> 4487 </p> 4488 </td> 4489<td> 4490 <p> 4491 <span class="green">1.06<br> (38ns)</span> 4492 </p> 4493 </td> 4494<td> 4495 <p> 4496 <span class="green">1.14<br> (41ns)</span> 4497 </p> 4498 </td> 4499<td> 4500 <p> 4501 <span class="green">1.00<br> (36ns)</span> 4502 </p> 4503 </td> 4504<td> 4505 <p> 4506 <span class="green">1.00<br> (36ns)</span> 4507 </p> 4508 </td> 4509</tr> 4510<tr> 4511<td> 4512 <p> 4513 Order 10 4514 </p> 4515 </td> 4516<td> 4517 <p> 4518 <span class="blue">1.33<br> (48ns)</span> 4519 </p> 4520 </td> 4521<td> 4522 <p> 4523 <span class="red">2.19<br> (79ns)</span> 4524 </p> 4525 </td> 4526<td> 4527 <p> 4528 <span class="blue">1.64<br> (59ns)</span> 4529 </p> 4530 </td> 4531<td> 4532 <p> 4533 <span class="blue">1.64<br> (59ns)</span> 4534 </p> 4535 </td> 4536<td> 4537 <p> 4538 <span class="green">1.11<br> (40ns)</span> 4539 </p> 4540 </td> 4541<td> 4542 <p> 4543 <span class="green">1.08<br> (39ns)</span> 4544 </p> 4545 </td> 4546<td> 4547 <p> 4548 <span class="green">1.00<br> (36ns)</span> 4549 </p> 4550 </td> 4551<td> 4552 <p> 4553 <span class="green">1.00<br> (36ns)</span> 4554 </p> 4555 </td> 4556</tr> 4557<tr> 4558<td> 4559 <p> 4560 Order 11 4561 </p> 4562 </td> 4563<td> 4564 <p> 4565 <span class="blue">1.32<br> (58ns)</span> 4566 </p> 4567 </td> 4568<td> 4569 <p> 4570 <span class="red">2.02<br> (89ns)</span> 4571 </p> 4572 </td> 4573<td> 4574 <p> 4575 <span class="blue">1.66<br> (73ns)</span> 4576 </p> 4577 </td> 4578<td> 4579 <p> 4580 <span class="blue">1.68<br> (74ns)</span> 4581 </p> 4582 </td> 4583<td> 4584 <p> 4585 <span class="green">1.09<br> (48ns)</span> 4586 </p> 4587 </td> 4588<td> 4589 <p> 4590 <span class="green">1.05<br> (46ns)</span> 4591 </p> 4592 </td> 4593<td> 4594 <p> 4595 <span class="green">1.05<br> (46ns)</span> 4596 </p> 4597 </td> 4598<td> 4599 <p> 4600 <span class="green">1.00<br> (44ns)</span> 4601 </p> 4602 </td> 4603</tr> 4604<tr> 4605<td> 4606 <p> 4607 Order 12 4608 </p> 4609 </td> 4610<td> 4611 <p> 4612 <span class="blue">1.42<br> (64ns)</span> 4613 </p> 4614 </td> 4615<td> 4616 <p> 4617 <span class="red">2.38<br> (107ns)</span> 4618 </p> 4619 </td> 4620<td> 4621 <p> 4622 <span class="blue">1.89<br> (85ns)</span> 4623 </p> 4624 </td> 4625<td> 4626 <p> 4627 <span class="blue">1.84<br> (83ns)</span> 4628 </p> 4629 </td> 4630<td> 4631 <p> 4632 <span class="green">1.04<br> (47ns)</span> 4633 </p> 4634 </td> 4635<td> 4636 <p> 4637 <span class="green">1.04<br> (47ns)</span> 4638 </p> 4639 </td> 4640<td> 4641 <p> 4642 <span class="green">1.00<br> (45ns)</span> 4643 </p> 4644 </td> 4645<td> 4646 <p> 4647 <span class="green">1.00<br> (45ns)</span> 4648 </p> 4649 </td> 4650</tr> 4651<tr> 4652<td> 4653 <p> 4654 Order 13 4655 </p> 4656 </td> 4657<td> 4658 <p> 4659 <span class="blue">1.51<br> (71ns)</span> 4660 </p> 4661 </td> 4662<td> 4663 <p> 4664 <span class="red">2.21<br> (104ns)</span> 4665 </p> 4666 </td> 4667<td> 4668 <p> 4669 <span class="blue">1.79<br> (84ns)</span> 4670 </p> 4671 </td> 4672<td> 4673 <p> 4674 <span class="blue">1.83<br> (86ns)</span> 4675 </p> 4676 </td> 4677<td> 4678 <p> 4679 <span class="green">1.06<br> (50ns)</span> 4680 </p> 4681 </td> 4682<td> 4683 <p> 4684 <span class="green">1.11<br> (52ns)</span> 4685 </p> 4686 </td> 4687<td> 4688 <p> 4689 <span class="green">1.00<br> (47ns)</span> 4690 </p> 4691 </td> 4692<td> 4693 <p> 4694 <span class="green">1.00<br> (47ns)</span> 4695 </p> 4696 </td> 4697</tr> 4698<tr> 4699<td> 4700 <p> 4701 Order 14 4702 </p> 4703 </td> 4704<td> 4705 <p> 4706 <span class="blue">1.52<br> (79ns)</span> 4707 </p> 4708 </td> 4709<td> 4710 <p> 4711 <span class="red">2.38<br> (124ns)</span> 4712 </p> 4713 </td> 4714<td> 4715 <p> 4716 <span class="red">2.02<br> (105ns)</span> 4717 </p> 4718 </td> 4719<td> 4720 <p> 4721 <span class="blue">1.96<br> (102ns)</span> 4722 </p> 4723 </td> 4724<td> 4725 <p> 4726 <span class="green">1.08<br> (56ns)</span> 4727 </p> 4728 </td> 4729<td> 4730 <p> 4731 <span class="green">1.08<br> (56ns)</span> 4732 </p> 4733 </td> 4734<td> 4735 <p> 4736 <span class="green">1.00<br> (52ns)</span> 4737 </p> 4738 </td> 4739<td> 4740 <p> 4741 <span class="green">1.00<br> (52ns)</span> 4742 </p> 4743 </td> 4744</tr> 4745<tr> 4746<td> 4747 <p> 4748 Order 15 4749 </p> 4750 </td> 4751<td> 4752 <p> 4753 <span class="blue">1.25<br> (91ns)</span> 4754 </p> 4755 </td> 4756<td> 4757 <p> 4758 <span class="blue">1.92<br> (140ns)</span> 4759 </p> 4760 </td> 4761<td> 4762 <p> 4763 <span class="blue">1.56<br> (114ns)</span> 4764 </p> 4765 </td> 4766<td> 4767 <p> 4768 <span class="blue">1.60<br> (117ns)</span> 4769 </p> 4770 </td> 4771<td> 4772 <p> 4773 <span class="green">1.07<br> (78ns)</span> 4774 </p> 4775 </td> 4776<td> 4777 <p> 4778 <span class="green">1.11<br> (81ns)</span> 4779 </p> 4780 </td> 4781<td> 4782 <p> 4783 <span class="green">1.01<br> (74ns)</span> 4784 </p> 4785 </td> 4786<td> 4787 <p> 4788 <span class="green">1.00<br> (73ns)</span> 4789 </p> 4790 </td> 4791</tr> 4792<tr> 4793<td> 4794 <p> 4795 Order 16 4796 </p> 4797 </td> 4798<td> 4799 <p> 4800 <span class="blue">1.59<br> (100ns)</span> 4801 </p> 4802 </td> 4803<td> 4804 <p> 4805 <span class="red">2.51<br> (158ns)</span> 4806 </p> 4807 </td> 4808<td> 4809 <p> 4810 <span class="blue">1.97<br> (124ns)</span> 4811 </p> 4812 </td> 4813<td> 4814 <p> 4815 <span class="blue">1.98<br> (125ns)</span> 4816 </p> 4817 </td> 4818<td> 4819 <p> 4820 <span class="green">1.05<br> (66ns)</span> 4821 </p> 4822 </td> 4823<td> 4824 <p> 4825 <span class="green">1.06<br> (67ns)</span> 4826 </p> 4827 </td> 4828<td> 4829 <p> 4830 <span class="green">1.00<br> (63ns)</span> 4831 </p> 4832 </td> 4833<td> 4834 <p> 4835 <span class="green">1.00<br> (63ns)</span> 4836 </p> 4837 </td> 4838</tr> 4839<tr> 4840<td> 4841 <p> 4842 Order 17 4843 </p> 4844 </td> 4845<td> 4846 <p> 4847 <span class="blue">1.29<br> (108ns)</span> 4848 </p> 4849 </td> 4850<td> 4851 <p> 4852 <span class="blue">1.90<br> (160ns)</span> 4853 </p> 4854 </td> 4855<td> 4856 <p> 4857 <span class="blue">1.36<br> (114ns)</span> 4858 </p> 4859 </td> 4860<td> 4861 <p> 4862 <span class="red">4.58<br> (385ns)</span> 4863 </p> 4864 </td> 4865<td> 4866 <p> 4867 <span class="green">1.15<br> (97ns)</span> 4868 </p> 4869 </td> 4870<td> 4871 <p> 4872 <span class="red">2.05<br> (172ns)</span> 4873 </p> 4874 </td> 4875<td> 4876 <p> 4877 <span class="green">1.00<br> (84ns)</span> 4878 </p> 4879 </td> 4880<td> 4881 <p> 4882 <span class="blue">1.63<br> (137ns)</span> 4883 </p> 4884 </td> 4885</tr> 4886<tr> 4887<td> 4888 <p> 4889 Order 18 4890 </p> 4891 </td> 4892<td> 4893 <p> 4894 <span class="red">2.22<br> (120ns)</span> 4895 </p> 4896 </td> 4897<td> 4898 <p> 4899 <span class="red">3.22<br> (174ns)</span> 4900 </p> 4901 </td> 4902<td> 4903 <p> 4904 <span class="red">2.28<br> (123ns)</span> 4905 </p> 4906 </td> 4907<td> 4908 <p> 4909 <span class="red">7.74<br> (418ns)</span> 4910 </p> 4911 </td> 4912<td> 4913 <p> 4914 <span class="green">1.06<br> (57ns)</span> 4915 </p> 4916 </td> 4917<td> 4918 <p> 4919 <span class="red">2.85<br> (154ns)</span> 4920 </p> 4921 </td> 4922<td> 4923 <p> 4924 <span class="green">1.00<br> (54ns)</span> 4925 </p> 4926 </td> 4927<td> 4928 <p> 4929 <span class="red">3.78<br> (204ns)</span> 4930 </p> 4931 </td> 4932</tr> 4933<tr> 4934<td> 4935 <p> 4936 Order 19 4937 </p> 4938 </td> 4939<td> 4940 <p> 4941 <span class="red">2.28<br> (130ns)</span> 4942 </p> 4943 </td> 4944<td> 4945 <p> 4946 <span class="red">3.28<br> (187ns)</span> 4947 </p> 4948 </td> 4949<td> 4950 <p> 4951 <span class="red">2.42<br> (138ns)</span> 4952 </p> 4953 </td> 4954<td> 4955 <p> 4956 <span class="red">7.74<br> (441ns)</span> 4957 </p> 4958 </td> 4959<td> 4960 <p> 4961 <span class="green">1.07<br> (61ns)</span> 4962 </p> 4963 </td> 4964<td> 4965 <p> 4966 <span class="red">3.58<br> (204ns)</span> 4967 </p> 4968 </td> 4969<td> 4970 <p> 4971 <span class="green">1.00<br> (57ns)</span> 4972 </p> 4973 </td> 4974<td> 4975 <p> 4976 <span class="red">2.67<br> (152ns)</span> 4977 </p> 4978 </td> 4979</tr> 4980<tr> 4981<td> 4982 <p> 4983 Order 20 4984 </p> 4985 </td> 4986<td> 4987 <p> 4988 <span class="red">2.43<br> (146ns)</span> 4989 </p> 4990 </td> 4991<td> 4992 <p> 4993 <span class="red">3.35<br> (201ns)</span> 4994 </p> 4995 </td> 4996<td> 4997 <p> 4998 <span class="red">2.53<br> (152ns)</span> 4999 </p> 5000 </td> 5001<td> 5002 <p> 5003 <span class="red">8.17<br> (490ns)</span> 5004 </p> 5005 </td> 5006<td> 5007 <p> 5008 <span class="green">1.07<br> (64ns)</span> 5009 </p> 5010 </td> 5011<td> 5012 <p> 5013 <span class="red">4.12<br> (247ns)</span> 5014 </p> 5015 </td> 5016<td> 5017 <p> 5018 <span class="green">1.00<br> (60ns)</span> 5019 </p> 5020 </td> 5021<td> 5022 <p> 5023 <span class="red">2.90<br> (174ns)</span> 5024 </p> 5025 </td> 5026</tr> 5027</tbody> 5028</table></div> 5029</div> 5030<br class="table-break"><div class="table"> 5031<a name="math_toolkit.tuning.table_Rational_Method_Comparison_with_Clang_version_9_0_0_tags_RELEASE_900_final_on_linux"></a><p class="title"><b>Table 22.9. Rational Method Comparison with Clang version 9.0.0 (tags/RELEASE_900/final) 5032 on linux</b></p> 5033<div class="table-contents"><table class="table" summary="Rational Method Comparison with Clang version 9.0.0 (tags/RELEASE_900/final) 5034 on linux"> 5035<colgroup> 5036<col> 5037<col> 5038<col> 5039<col> 5040<col> 5041<col> 5042<col> 5043<col> 5044<col> 5045</colgroup> 5046<thead><tr> 5047<th> 5048 <p> 5049 Function 5050 </p> 5051 </th> 5052<th> 5053 <p> 5054 Method 0<br> (Double Coefficients) 5055 </p> 5056 </th> 5057<th> 5058 <p> 5059 Method 0<br> (Integer Coefficients) 5060 </p> 5061 </th> 5062<th> 5063 <p> 5064 Method 1<br> (Double Coefficients) 5065 </p> 5066 </th> 5067<th> 5068 <p> 5069 Method 1<br> (Integer Coefficients) 5070 </p> 5071 </th> 5072<th> 5073 <p> 5074 Method 2<br> (Double Coefficients) 5075 </p> 5076 </th> 5077<th> 5078 <p> 5079 Method 2<br> (Integer Coefficients) 5080 </p> 5081 </th> 5082<th> 5083 <p> 5084 Method 3<br> (Double Coefficients) 5085 </p> 5086 </th> 5087<th> 5088 <p> 5089 Method 3<br> (Integer Coefficients) 5090 </p> 5091 </th> 5092</tr></thead> 5093<tbody> 5094<tr> 5095<td> 5096 <p> 5097 Order 2 5098 </p> 5099 </td> 5100<td> 5101 <p> 5102 <span class="grey">-</span> 5103 </p> 5104 </td> 5105<td> 5106 <p> 5107 <span class="grey">-</span> 5108 </p> 5109 </td> 5110<td> 5111 <p> 5112 <span class="blue">2.00<br> (24ns)</span> 5113 </p> 5114 </td> 5115<td> 5116 <p> 5117 <span class="red">2.08<br> (25ns)</span> 5118 </p> 5119 </td> 5120<td> 5121 <p> 5122 <span class="green">1.00<br> (12ns)</span> 5123 </p> 5124 </td> 5125<td> 5126 <p> 5127 <span class="green">1.00<br> (12ns)</span> 5128 </p> 5129 </td> 5130<td> 5131 <p> 5132 <span class="green">1.00<br> (12ns)</span> 5133 </p> 5134 </td> 5135<td> 5136 <p> 5137 <span class="green">1.00<br> (12ns)</span> 5138 </p> 5139 </td> 5140</tr> 5141<tr> 5142<td> 5143 <p> 5144 Order 3 5145 </p> 5146 </td> 5147<td> 5148 <p> 5149 <span class="blue">1.58<br> (30ns)</span> 5150 </p> 5151 </td> 5152<td> 5153 <p> 5154 <span class="blue">1.89<br> (36ns)</span> 5155 </p> 5156 </td> 5157<td> 5158 <p> 5159 <span class="blue">1.47<br> (28ns)</span> 5160 </p> 5161 </td> 5162<td> 5163 <p> 5164 <span class="blue">1.53<br> (29ns)</span> 5165 </p> 5166 </td> 5167<td> 5168 <p> 5169 <span class="green">1.00<br> (19ns)</span> 5170 </p> 5171 </td> 5172<td> 5173 <p> 5174 <span class="green">1.00<br> (19ns)</span> 5175 </p> 5176 </td> 5177<td> 5178 <p> 5179 <span class="green">1.00<br> (19ns)</span> 5180 </p> 5181 </td> 5182<td> 5183 <p> 5184 <span class="blue">1.58<br> (30ns)</span> 5185 </p> 5186 </td> 5187</tr> 5188<tr> 5189<td> 5190 <p> 5191 Order 4 5192 </p> 5193 </td> 5194<td> 5195 <p> 5196 <span class="blue">1.48<br> (37ns)</span> 5197 </p> 5198 </td> 5199<td> 5200 <p> 5201 <span class="blue">1.88<br> (47ns)</span> 5202 </p> 5203 </td> 5204<td> 5205 <p> 5206 <span class="blue">1.44<br> (36ns)</span> 5207 </p> 5208 </td> 5209<td> 5210 <p> 5211 <span class="blue">1.52<br> (38ns)</span> 5212 </p> 5213 </td> 5214<td> 5215 <p> 5216 <span class="green">1.04<br> (26ns)</span> 5217 </p> 5218 </td> 5219<td> 5220 <p> 5221 <span class="green">1.00<br> (25ns)</span> 5222 </p> 5223 </td> 5224<td> 5225 <p> 5226 <span class="blue">1.24<br> (31ns)</span> 5227 </p> 5228 </td> 5229<td> 5230 <p> 5231 <span class="green">1.04<br> (26ns)</span> 5232 </p> 5233 </td> 5234</tr> 5235<tr> 5236<td> 5237 <p> 5238 Order 5 5239 </p> 5240 </td> 5241<td> 5242 <p> 5243 <span class="green">1.00<br> (44ns)</span> 5244 </p> 5245 </td> 5246<td> 5247 <p> 5248 <span class="blue">1.32<br> (58ns)</span> 5249 </p> 5250 </td> 5251<td> 5252 <p> 5253 <span class="green">1.11<br> (49ns)</span> 5254 </p> 5255 </td> 5256<td> 5257 <p> 5258 <span class="red">2.16<br> (95ns)</span> 5259 </p> 5260 </td> 5261<td> 5262 <p> 5263 <span class="green">1.18<br> (52ns)</span> 5264 </p> 5265 </td> 5266<td> 5267 <p> 5268 <span class="blue">1.98<br> (87ns)</span> 5269 </p> 5270 </td> 5271<td> 5272 <p> 5273 <span class="blue">1.25<br> (55ns)</span> 5274 </p> 5275 </td> 5276<td> 5277 <p> 5278 <span class="blue">2.00<br> (88ns)</span> 5279 </p> 5280 </td> 5281</tr> 5282<tr> 5283<td> 5284 <p> 5285 Order 6 5286 </p> 5287 </td> 5288<td> 5289 <p> 5290 <span class="green">1.00<br> (53ns)</span> 5291 </p> 5292 </td> 5293<td> 5294 <p> 5295 <span class="blue">1.30<br> (69ns)</span> 5296 </p> 5297 </td> 5298<td> 5299 <p> 5300 <span class="blue">1.45<br> (77ns)</span> 5301 </p> 5302 </td> 5303<td> 5304 <p> 5305 <span class="red">2.21<br> (117ns)</span> 5306 </p> 5307 </td> 5308<td> 5309 <p> 5310 <span class="blue">1.45<br> (77ns)</span> 5311 </p> 5312 </td> 5313<td> 5314 <p> 5315 <span class="blue">1.64<br> (87ns)</span> 5316 </p> 5317 </td> 5318<td> 5319 <p> 5320 <span class="blue">1.51<br> (80ns)</span> 5321 </p> 5322 </td> 5323<td> 5324 <p> 5325 <span class="blue">1.72<br> (91ns)</span> 5326 </p> 5327 </td> 5328</tr> 5329<tr> 5330<td> 5331 <p> 5332 Order 7 5333 </p> 5334 </td> 5335<td> 5336 <p> 5337 <span class="green">1.00<br> (81ns)</span> 5338 </p> 5339 </td> 5340<td> 5341 <p> 5342 <span class="blue">1.36<br> (110ns)</span> 5343 </p> 5344 </td> 5345<td> 5346 <p> 5347 <span class="green">1.10<br> (89ns)</span> 5348 </p> 5349 </td> 5350<td> 5351 <p> 5352 <span class="blue">1.78<br> (144ns)</span> 5353 </p> 5354 </td> 5355<td> 5356 <p> 5357 <span class="green">1.09<br> (88ns)</span> 5358 </p> 5359 </td> 5360<td> 5361 <p> 5362 <span class="blue">1.26<br> (102ns)</span> 5363 </p> 5364 </td> 5365<td> 5366 <p> 5367 <span class="green">1.04<br> (84ns)</span> 5368 </p> 5369 </td> 5370<td> 5371 <p> 5372 <span class="blue">1.25<br> (101ns)</span> 5373 </p> 5374 </td> 5375</tr> 5376<tr> 5377<td> 5378 <p> 5379 Order 8 5380 </p> 5381 </td> 5382<td> 5383 <p> 5384 <span class="green">1.01<br> (88ns)</span> 5385 </p> 5386 </td> 5387<td> 5388 <p> 5389 <span class="blue">1.32<br> (115ns)</span> 5390 </p> 5391 </td> 5392<td> 5393 <p> 5394 <span class="green">1.15<br> (100ns)</span> 5395 </p> 5396 </td> 5397<td> 5398 <p> 5399 <span class="blue">1.90<br> (165ns)</span> 5400 </p> 5401 </td> 5402<td> 5403 <p> 5404 <span class="green">1.11<br> (97ns)</span> 5405 </p> 5406 </td> 5407<td> 5408 <p> 5409 <span class="blue">1.25<br> (109ns)</span> 5410 </p> 5411 </td> 5412<td> 5413 <p> 5414 <span class="green">1.00<br> (87ns)</span> 5415 </p> 5416 </td> 5417<td> 5418 <p> 5419 <span class="blue">1.22<br> (106ns)</span> 5420 </p> 5421 </td> 5422</tr> 5423<tr> 5424<td> 5425 <p> 5426 Order 9 5427 </p> 5428 </td> 5429<td> 5430 <p> 5431 <span class="green">1.00<br> (91ns)</span> 5432 </p> 5433 </td> 5434<td> 5435 <p> 5436 <span class="blue">1.37<br> (125ns)</span> 5437 </p> 5438 </td> 5439<td> 5440 <p> 5441 <span class="blue">1.30<br> (118ns)</span> 5442 </p> 5443 </td> 5444<td> 5445 <p> 5446 <span class="red">2.08<br> (189ns)</span> 5447 </p> 5448 </td> 5449<td> 5450 <p> 5451 <span class="green">1.15<br> (105ns)</span> 5452 </p> 5453 </td> 5454<td> 5455 <p> 5456 <span class="blue">1.31<br> (119ns)</span> 5457 </p> 5458 </td> 5459<td> 5460 <p> 5461 <span class="green">1.01<br> (92ns)</span> 5462 </p> 5463 </td> 5464<td> 5465 <p> 5466 <span class="blue">1.21<br> (110ns)</span> 5467 </p> 5468 </td> 5469</tr> 5470<tr> 5471<td> 5472 <p> 5473 Order 10 5474 </p> 5475 </td> 5476<td> 5477 <p> 5478 <span class="green">1.00<br> (94ns)</span> 5479 </p> 5480 </td> 5481<td> 5482 <p> 5483 <span class="blue">1.30<br> (122ns)</span> 5484 </p> 5485 </td> 5486<td> 5487 <p> 5488 <span class="blue">1.39<br> (131ns)</span> 5489 </p> 5490 </td> 5491<td> 5492 <p> 5493 <span class="red">2.29<br> (215ns)</span> 5494 </p> 5495 </td> 5496<td> 5497 <p> 5498 <span class="blue">1.20<br> (113ns)</span> 5499 </p> 5500 </td> 5501<td> 5502 <p> 5503 <span class="blue">1.44<br> (135ns)</span> 5504 </p> 5505 </td> 5506<td> 5507 <p> 5508 <span class="green">1.05<br> (99ns)</span> 5509 </p> 5510 </td> 5511<td> 5512 <p> 5513 <span class="blue">1.23<br> (116ns)</span> 5514 </p> 5515 </td> 5516</tr> 5517<tr> 5518<td> 5519 <p> 5520 Order 11 5521 </p> 5522 </td> 5523<td> 5524 <p> 5525 <span class="green">1.03<br> (108ns)</span> 5526 </p> 5527 </td> 5528<td> 5529 <p> 5530 <span class="blue">1.35<br> (142ns)</span> 5531 </p> 5532 </td> 5533<td> 5534 <p> 5535 <span class="blue">1.44<br> (151ns)</span> 5536 </p> 5537 </td> 5538<td> 5539 <p> 5540 <span class="red">2.25<br> (236ns)</span> 5541 </p> 5542 </td> 5543<td> 5544 <p> 5545 <span class="blue">1.23<br> (129ns)</span> 5546 </p> 5547 </td> 5548<td> 5549 <p> 5550 <span class="blue">1.40<br> (147ns)</span> 5551 </p> 5552 </td> 5553<td> 5554 <p> 5555 <span class="green">1.00<br> (105ns)</span> 5556 </p> 5557 </td> 5558<td> 5559 <p> 5560 <span class="blue">1.24<br> (130ns)</span> 5561 </p> 5562 </td> 5563</tr> 5564<tr> 5565<td> 5566 <p> 5567 Order 12 5568 </p> 5569 </td> 5570<td> 5571 <p> 5572 <span class="green">1.03<br> (120ns)</span> 5573 </p> 5574 </td> 5575<td> 5576 <p> 5577 <span class="blue">1.33<br> (154ns)</span> 5578 </p> 5579 </td> 5580<td> 5581 <p> 5582 <span class="blue">1.46<br> (169ns)</span> 5583 </p> 5584 </td> 5585<td> 5586 <p> 5587 <span class="red">2.27<br> (263ns)</span> 5588 </p> 5589 </td> 5590<td> 5591 <p> 5592 <span class="green">1.16<br> (134ns)</span> 5593 </p> 5594 </td> 5595<td> 5596 <p> 5597 <span class="blue">1.39<br> (161ns)</span> 5598 </p> 5599 </td> 5600<td> 5601 <p> 5602 <span class="green">1.00<br> (116ns)</span> 5603 </p> 5604 </td> 5605<td> 5606 <p> 5607 <span class="blue">1.27<br> (147ns)</span> 5608 </p> 5609 </td> 5610</tr> 5611<tr> 5612<td> 5613 <p> 5614 Order 13 5615 </p> 5616 </td> 5617<td> 5618 <p> 5619 <span class="green">1.07<br> (129ns)</span> 5620 </p> 5621 </td> 5622<td> 5623 <p> 5624 <span class="blue">1.54<br> (186ns)</span> 5625 </p> 5626 </td> 5627<td> 5628 <p> 5629 <span class="blue">1.49<br> (180ns)</span> 5630 </p> 5631 </td> 5632<td> 5633 <p> 5634 <span class="red">2.41<br> (292ns)</span> 5635 </p> 5636 </td> 5637<td> 5638 <p> 5639 <span class="blue">1.24<br> (150ns)</span> 5640 </p> 5641 </td> 5642<td> 5643 <p> 5644 <span class="blue">1.45<br> (176ns)</span> 5645 </p> 5646 </td> 5647<td> 5648 <p> 5649 <span class="green">1.00<br> (121ns)</span> 5650 </p> 5651 </td> 5652<td> 5653 <p> 5654 <span class="blue">1.40<br> (170ns)</span> 5655 </p> 5656 </td> 5657</tr> 5658<tr> 5659<td> 5660 <p> 5661 Order 14 5662 </p> 5663 </td> 5664<td> 5665 <p> 5666 <span class="green">1.00<br> (139ns)</span> 5667 </p> 5668 </td> 5669<td> 5670 <p> 5671 <span class="blue">1.32<br> (183ns)</span> 5672 </p> 5673 </td> 5674<td> 5675 <p> 5676 <span class="blue">1.48<br> (206ns)</span> 5677 </p> 5678 </td> 5679<td> 5680 <p> 5681 <span class="red">2.22<br> (308ns)</span> 5682 </p> 5683 </td> 5684<td> 5685 <p> 5686 <span class="blue">1.26<br> (175ns)</span> 5687 </p> 5688 </td> 5689<td> 5690 <p> 5691 <span class="blue">1.37<br> (191ns)</span> 5692 </p> 5693 </td> 5694<td> 5695 <p> 5696 <span class="green">1.01<br> (140ns)</span> 5697 </p> 5698 </td> 5699<td> 5700 <p> 5701 <span class="green">1.16<br> (161ns)</span> 5702 </p> 5703 </td> 5704</tr> 5705<tr> 5706<td> 5707 <p> 5708 Order 15 5709 </p> 5710 </td> 5711<td> 5712 <p> 5713 <span class="green">1.04<br> (147ns)</span> 5714 </p> 5715 </td> 5716<td> 5717 <p> 5718 <span class="blue">1.45<br> (206ns)</span> 5719 </p> 5720 </td> 5721<td> 5722 <p> 5723 <span class="blue">1.61<br> (229ns)</span> 5724 </p> 5725 </td> 5726<td> 5727 <p> 5728 <span class="red">2.39<br> (340ns)</span> 5729 </p> 5730 </td> 5731<td> 5732 <p> 5733 <span class="blue">1.20<br> (171ns)</span> 5734 </p> 5735 </td> 5736<td> 5737 <p> 5738 <span class="blue">1.41<br> (200ns)</span> 5739 </p> 5740 </td> 5741<td> 5742 <p> 5743 <span class="green">1.00<br> (142ns)</span> 5744 </p> 5745 </td> 5746<td> 5747 <p> 5748 <span class="green">1.18<br> (167ns)</span> 5749 </p> 5750 </td> 5751</tr> 5752<tr> 5753<td> 5754 <p> 5755 Order 16 5756 </p> 5757 </td> 5758<td> 5759 <p> 5760 <span class="green">1.03<br> (157ns)</span> 5761 </p> 5762 </td> 5763<td> 5764 <p> 5765 <span class="blue">1.40<br> (214ns)</span> 5766 </p> 5767 </td> 5768<td> 5769 <p> 5770 <span class="blue">1.52<br> (233ns)</span> 5771 </p> 5772 </td> 5773<td> 5774 <p> 5775 <span class="red">2.33<br> (357ns)</span> 5776 </p> 5777 </td> 5778<td> 5779 <p> 5780 <span class="blue">1.21<br> (185ns)</span> 5781 </p> 5782 </td> 5783<td> 5784 <p> 5785 <span class="blue">1.49<br> (228ns)</span> 5786 </p> 5787 </td> 5788<td> 5789 <p> 5790 <span class="green">1.00<br> (153ns)</span> 5791 </p> 5792 </td> 5793<td> 5794 <p> 5795 <span class="green">1.18<br> (180ns)</span> 5796 </p> 5797 </td> 5798</tr> 5799<tr> 5800<td> 5801 <p> 5802 Order 17 5803 </p> 5804 </td> 5805<td> 5806 <p> 5807 <span class="green">1.02<br> (179ns)</span> 5808 </p> 5809 </td> 5810<td> 5811 <p> 5812 <span class="blue">1.25<br> (218ns)</span> 5813 </p> 5814 </td> 5815<td> 5816 <p> 5817 <span class="blue">1.45<br> (253ns)</span> 5818 </p> 5819 </td> 5820<td> 5821 <p> 5822 <span class="red">2.17<br> (380ns)</span> 5823 </p> 5824 </td> 5825<td> 5826 <p> 5827 <span class="green">1.16<br> (203ns)</span> 5828 </p> 5829 </td> 5830<td> 5831 <p> 5832 <span class="blue">1.36<br> (238ns)</span> 5833 </p> 5834 </td> 5835<td> 5836 <p> 5837 <span class="green">1.00<br> (175ns)</span> 5838 </p> 5839 </td> 5840<td> 5841 <p> 5842 <span class="green">1.10<br> (192ns)</span> 5843 </p> 5844 </td> 5845</tr> 5846<tr> 5847<td> 5848 <p> 5849 Order 18 5850 </p> 5851 </td> 5852<td> 5853 <p> 5854 <span class="blue">1.21<br> (201ns)</span> 5855 </p> 5856 </td> 5857<td> 5858 <p> 5859 <span class="blue">1.40<br> (232ns)</span> 5860 </p> 5861 </td> 5862<td> 5863 <p> 5864 <span class="blue">1.64<br> (272ns)</span> 5865 </p> 5866 </td> 5867<td> 5868 <p> 5869 <span class="red">2.42<br> (402ns)</span> 5870 </p> 5871 </td> 5872<td> 5873 <p> 5874 <span class="blue">1.24<br> (206ns)</span> 5875 </p> 5876 </td> 5877<td> 5878 <p> 5879 <span class="blue">1.60<br> (266ns)</span> 5880 </p> 5881 </td> 5882<td> 5883 <p> 5884 <span class="green">1.00<br> (166ns)</span> 5885 </p> 5886 </td> 5887<td> 5888 <p> 5889 <span class="blue">1.20<br> (200ns)</span> 5890 </p> 5891 </td> 5892</tr> 5893<tr> 5894<td> 5895 <p> 5896 Order 19 5897 </p> 5898 </td> 5899<td> 5900 <p> 5901 <span class="blue">1.24<br> (211ns)</span> 5902 </p> 5903 </td> 5904<td> 5905 <p> 5906 <span class="blue">1.48<br> (252ns)</span> 5907 </p> 5908 </td> 5909<td> 5910 <p> 5911 <span class="blue">1.74<br> (295ns)</span> 5912 </p> 5913 </td> 5914<td> 5915 <p> 5916 <span class="red">2.49<br> (423ns)</span> 5917 </p> 5918 </td> 5919<td> 5920 <p> 5921 <span class="blue">1.41<br> (240ns)</span> 5922 </p> 5923 </td> 5924<td> 5925 <p> 5926 <span class="blue">1.59<br> (271ns)</span> 5927 </p> 5928 </td> 5929<td> 5930 <p> 5931 <span class="green">1.00<br> (170ns)</span> 5932 </p> 5933 </td> 5934<td> 5935 <p> 5936 <span class="blue">1.21<br> (205ns)</span> 5937 </p> 5938 </td> 5939</tr> 5940<tr> 5941<td> 5942 <p> 5943 Order 20 5944 </p> 5945 </td> 5946<td> 5947 <p> 5948 <span class="blue">1.27<br> (223ns)</span> 5949 </p> 5950 </td> 5951<td> 5952 <p> 5953 <span class="blue">1.67<br> (294ns)</span> 5954 </p> 5955 </td> 5956<td> 5957 <p> 5958 <span class="blue">1.86<br> (327ns)</span> 5959 </p> 5960 </td> 5961<td> 5962 <p> 5963 <span class="red">2.70<br> (475ns)</span> 5964 </p> 5965 </td> 5966<td> 5967 <p> 5968 <span class="blue">1.34<br> (235ns)</span> 5969 </p> 5970 </td> 5971<td> 5972 <p> 5973 <span class="blue">1.56<br> (274ns)</span> 5974 </p> 5975 </td> 5976<td> 5977 <p> 5978 <span class="green">1.00<br> (176ns)</span> 5979 </p> 5980 </td> 5981<td> 5982 <p> 5983 <span class="blue">1.21<br> (213ns)</span> 5984 </p> 5985 </td> 5986</tr> 5987</tbody> 5988</table></div> 5989</div> 5990<br class="table-break"><div class="table"> 5991<a name="math_toolkit.tuning.table_Polynomial_Method_Comparison_with_Intel_C_C_0x_mode_version_1910_on_linux"></a><p class="title"><b>Table 22.10. Polynomial Method Comparison with Intel C++ C++0x mode version 1910 5992 on linux</b></p> 5993<div class="table-contents"><table class="table" summary="Polynomial Method Comparison with Intel C++ C++0x mode version 1910 5994 on linux"> 5995<colgroup> 5996<col> 5997<col> 5998<col> 5999<col> 6000<col> 6001<col> 6002<col> 6003<col> 6004<col> 6005</colgroup> 6006<thead><tr> 6007<th> 6008 <p> 6009 Function 6010 </p> 6011 </th> 6012<th> 6013 <p> 6014 Method 0<br> (Double Coefficients) 6015 </p> 6016 </th> 6017<th> 6018 <p> 6019 Method 0<br> (Integer Coefficients) 6020 </p> 6021 </th> 6022<th> 6023 <p> 6024 Method 1<br> (Double Coefficients) 6025 </p> 6026 </th> 6027<th> 6028 <p> 6029 Method 1<br> (Integer Coefficients) 6030 </p> 6031 </th> 6032<th> 6033 <p> 6034 Method 2<br> (Double Coefficients) 6035 </p> 6036 </th> 6037<th> 6038 <p> 6039 Method 2<br> (Integer Coefficients) 6040 </p> 6041 </th> 6042<th> 6043 <p> 6044 Method 3<br> (Double Coefficients) 6045 </p> 6046 </th> 6047<th> 6048 <p> 6049 Method 3<br> (Integer Coefficients) 6050 </p> 6051 </th> 6052</tr></thead> 6053<tbody> 6054<tr> 6055<td> 6056 <p> 6057 Order 2 6058 </p> 6059 </td> 6060<td> 6061 <p> 6062 <span class="grey">-</span> 6063 </p> 6064 </td> 6065<td> 6066 <p> 6067 <span class="grey">-</span> 6068 </p> 6069 </td> 6070<td> 6071 <p> 6072 <span class="green">1.00<br> (3ns)</span> 6073 </p> 6074 </td> 6075<td> 6076 <p> 6077 <span class="green">1.00<br> (3ns)</span> 6078 </p> 6079 </td> 6080<td> 6081 <p> 6082 <span class="blue">1.33<br> (4ns)</span> 6083 </p> 6084 </td> 6085<td> 6086 <p> 6087 <span class="blue">1.33<br> (4ns)</span> 6088 </p> 6089 </td> 6090<td> 6091 <p> 6092 <span class="blue">1.33<br> (4ns)</span> 6093 </p> 6094 </td> 6095<td> 6096 <p> 6097 <span class="green">1.00<br> (3ns)</span> 6098 </p> 6099 </td> 6100</tr> 6101<tr> 6102<td> 6103 <p> 6104 Order 3 6105 </p> 6106 </td> 6107<td> 6108 <p> 6109 <span class="blue">1.75<br> (14ns)</span> 6110 </p> 6111 </td> 6112<td> 6113 <p> 6114 <span class="red">2.12<br> (17ns)</span> 6115 </p> 6116 </td> 6117<td> 6118 <p> 6119 <span class="green">1.00<br> (8ns)</span> 6120 </p> 6121 </td> 6122<td> 6123 <p> 6124 <span class="green">1.00<br> (8ns)</span> 6125 </p> 6126 </td> 6127<td> 6128 <p> 6129 <span class="green">1.00<br> (8ns)</span> 6130 </p> 6131 </td> 6132<td> 6133 <p> 6134 <span class="green">1.00<br> (8ns)</span> 6135 </p> 6136 </td> 6137<td> 6138 <p> 6139 <span class="green">1.00<br> (8ns)</span> 6140 </p> 6141 </td> 6142<td> 6143 <p> 6144 <span class="green">1.00<br> (8ns)</span> 6145 </p> 6146 </td> 6147</tr> 6148<tr> 6149<td> 6150 <p> 6151 Order 4 6152 </p> 6153 </td> 6154<td> 6155 <p> 6156 <span class="blue">1.64<br> (18ns)</span> 6157 </p> 6158 </td> 6159<td> 6160 <p> 6161 <span class="red">2.18<br> (24ns)</span> 6162 </p> 6163 </td> 6164<td> 6165 <p> 6166 <span class="green">1.09<br> (12ns)</span> 6167 </p> 6168 </td> 6169<td> 6170 <p> 6171 <span class="green">1.18<br> (13ns)</span> 6172 </p> 6173 </td> 6174<td> 6175 <p> 6176 <span class="green">1.00<br> (11ns)</span> 6177 </p> 6178 </td> 6179<td> 6180 <p> 6181 <span class="green">1.00<br> (11ns)</span> 6182 </p> 6183 </td> 6184<td> 6185 <p> 6186 <span class="green">1.00<br> (11ns)</span> 6187 </p> 6188 </td> 6189<td> 6190 <p> 6191 <span class="green">1.00<br> (11ns)</span> 6192 </p> 6193 </td> 6194</tr> 6195<tr> 6196<td> 6197 <p> 6198 Order 5 6199 </p> 6200 </td> 6201<td> 6202 <p> 6203 <span class="blue">1.60<br> (24ns)</span> 6204 </p> 6205 </td> 6206<td> 6207 <p> 6208 <span class="red">2.13<br> (32ns)</span> 6209 </p> 6210 </td> 6211<td> 6212 <p> 6213 <span class="green">1.00<br> (15ns)</span> 6214 </p> 6215 </td> 6216<td> 6217 <p> 6218 <span class="green">1.00<br> (15ns)</span> 6219 </p> 6220 </td> 6221<td> 6222 <p> 6223 <span class="green">1.07<br> (16ns)</span> 6224 </p> 6225 </td> 6226<td> 6227 <p> 6228 <span class="blue">1.27<br> (19ns)</span> 6229 </p> 6230 </td> 6231<td> 6232 <p> 6233 <span class="green">1.00<br> (15ns)</span> 6234 </p> 6235 </td> 6236<td> 6237 <p> 6238 <span class="green">1.07<br> (16ns)</span> 6239 </p> 6240 </td> 6241</tr> 6242<tr> 6243<td> 6244 <p> 6245 Order 6 6246 </p> 6247 </td> 6248<td> 6249 <p> 6250 <span class="blue">1.88<br> (30ns)</span> 6251 </p> 6252 </td> 6253<td> 6254 <p> 6255 <span class="red">2.56<br> (41ns)</span> 6256 </p> 6257 </td> 6258<td> 6259 <p> 6260 <span class="green">1.00<br> (16ns)</span> 6261 </p> 6262 </td> 6263<td> 6264 <p> 6265 <span class="green">1.00<br> (16ns)</span> 6266 </p> 6267 </td> 6268<td> 6269 <p> 6270 <span class="blue">1.44<br> (23ns)</span> 6271 </p> 6272 </td> 6273<td> 6274 <p> 6275 <span class="blue">1.31<br> (21ns)</span> 6276 </p> 6277 </td> 6278<td> 6279 <p> 6280 <span class="blue">1.25<br> (20ns)</span> 6281 </p> 6282 </td> 6283<td> 6284 <p> 6285 <span class="blue">1.25<br> (20ns)</span> 6286 </p> 6287 </td> 6288</tr> 6289<tr> 6290<td> 6291 <p> 6292 Order 7 6293 </p> 6294 </td> 6295<td> 6296 <p> 6297 <span class="blue">2.00<br> (36ns)</span> 6298 </p> 6299 </td> 6300<td> 6301 <p> 6302 <span class="red">2.67<br> (48ns)</span> 6303 </p> 6304 </td> 6305<td> 6306 <p> 6307 <span class="green">1.06<br> (19ns)</span> 6308 </p> 6309 </td> 6310<td> 6311 <p> 6312 <span class="green">1.00<br> (18ns)</span> 6313 </p> 6314 </td> 6315<td> 6316 <p> 6317 <span class="blue">1.33<br> (24ns)</span> 6318 </p> 6319 </td> 6320<td> 6321 <p> 6322 <span class="blue">1.44<br> (26ns)</span> 6323 </p> 6324 </td> 6325<td> 6326 <p> 6327 <span class="blue">1.28<br> (23ns)</span> 6328 </p> 6329 </td> 6330<td> 6331 <p> 6332 <span class="blue">1.28<br> (23ns)</span> 6333 </p> 6334 </td> 6335</tr> 6336<tr> 6337<td> 6338 <p> 6339 Order 8 6340 </p> 6341 </td> 6342<td> 6343 <p> 6344 <span class="blue">1.86<br> (41ns)</span> 6345 </p> 6346 </td> 6347<td> 6348 <p> 6349 <span class="red">2.55<br> (56ns)</span> 6350 </p> 6351 </td> 6352<td> 6353 <p> 6354 <span class="green">1.00<br> (22ns)</span> 6355 </p> 6356 </td> 6357<td> 6358 <p> 6359 <span class="green">1.00<br> (22ns)</span> 6360 </p> 6361 </td> 6362<td> 6363 <p> 6364 <span class="blue">1.32<br> (29ns)</span> 6365 </p> 6366 </td> 6367<td> 6368 <p> 6369 <span class="blue">1.27<br> (28ns)</span> 6370 </p> 6371 </td> 6372<td> 6373 <p> 6374 <span class="green">1.18<br> (26ns)</span> 6375 </p> 6376 </td> 6377<td> 6378 <p> 6379 <span class="green">1.18<br> (26ns)</span> 6380 </p> 6381 </td> 6382</tr> 6383<tr> 6384<td> 6385 <p> 6386 Order 9 6387 </p> 6388 </td> 6389<td> 6390 <p> 6391 <span class="blue">1.85<br> (48ns)</span> 6392 </p> 6393 </td> 6394<td> 6395 <p> 6396 <span class="red">2.46<br> (64ns)</span> 6397 </p> 6398 </td> 6399<td> 6400 <p> 6401 <span class="green">1.00<br> (26ns)</span> 6402 </p> 6403 </td> 6404<td> 6405 <p> 6406 <span class="green">1.00<br> (26ns)</span> 6407 </p> 6408 </td> 6409<td> 6410 <p> 6411 <span class="blue">1.27<br> (33ns)</span> 6412 </p> 6413 </td> 6414<td> 6415 <p> 6416 <span class="blue">1.31<br> (34ns)</span> 6417 </p> 6418 </td> 6419<td> 6420 <p> 6421 <span class="green">1.15<br> (30ns)</span> 6422 </p> 6423 </td> 6424<td> 6425 <p> 6426 <span class="green">1.15<br> (30ns)</span> 6427 </p> 6428 </td> 6429</tr> 6430<tr> 6431<td> 6432 <p> 6433 Order 10 6434 </p> 6435 </td> 6436<td> 6437 <p> 6438 <span class="blue">1.69<br> (54ns)</span> 6439 </p> 6440 </td> 6441<td> 6442 <p> 6443 <span class="red">2.28<br> (73ns)</span> 6444 </p> 6445 </td> 6446<td> 6447 <p> 6448 <span class="green">1.00<br> (32ns)</span> 6449 </p> 6450 </td> 6451<td> 6452 <p> 6453 <span class="green">1.00<br> (32ns)</span> 6454 </p> 6455 </td> 6456<td> 6457 <p> 6458 <span class="blue">1.22<br> (39ns)</span> 6459 </p> 6460 </td> 6461<td> 6462 <p> 6463 <span class="green">1.19<br> (38ns)</span> 6464 </p> 6465 </td> 6466<td> 6467 <p> 6468 <span class="green">1.06<br> (34ns)</span> 6469 </p> 6470 </td> 6471<td> 6472 <p> 6473 <span class="green">1.09<br> (35ns)</span> 6474 </p> 6475 </td> 6476</tr> 6477<tr> 6478<td> 6479 <p> 6480 Order 11 6481 </p> 6482 </td> 6483<td> 6484 <p> 6485 <span class="blue">1.77<br> (62ns)</span> 6486 </p> 6487 </td> 6488<td> 6489 <p> 6490 <span class="red">2.29<br> (80ns)</span> 6491 </p> 6492 </td> 6493<td> 6494 <p> 6495 <span class="green">1.00<br> (35ns)</span> 6496 </p> 6497 </td> 6498<td> 6499 <p> 6500 <span class="green">1.00<br> (35ns)</span> 6501 </p> 6502 </td> 6503<td> 6504 <p> 6505 <span class="blue">1.26<br> (44ns)</span> 6506 </p> 6507 </td> 6508<td> 6509 <p> 6510 <span class="blue">1.49<br> (52ns)</span> 6511 </p> 6512 </td> 6513<td> 6514 <p> 6515 <span class="green">1.06<br> (37ns)</span> 6516 </p> 6517 </td> 6518<td> 6519 <p> 6520 <span class="green">1.09<br> (38ns)</span> 6521 </p> 6522 </td> 6523</tr> 6524<tr> 6525<td> 6526 <p> 6527 Order 12 6528 </p> 6529 </td> 6530<td> 6531 <p> 6532 <span class="blue">1.77<br> (71ns)</span> 6533 </p> 6534 </td> 6535<td> 6536 <p> 6537 <span class="red">2.20<br> (88ns)</span> 6538 </p> 6539 </td> 6540<td> 6541 <p> 6542 <span class="green">1.05<br> (42ns)</span> 6543 </p> 6544 </td> 6545<td> 6546 <p> 6547 <span class="green">1.00<br> (40ns)</span> 6548 </p> 6549 </td> 6550<td> 6551 <p> 6552 <span class="blue">1.35<br> (54ns)</span> 6553 </p> 6554 </td> 6555<td> 6556 <p> 6557 <span class="blue">1.32<br> (53ns)</span> 6558 </p> 6559 </td> 6560<td> 6561 <p> 6562 <span class="blue">1.35<br> (54ns)</span> 6563 </p> 6564 </td> 6565<td> 6566 <p> 6567 <span class="blue">1.48<br> (59ns)</span> 6568 </p> 6569 </td> 6570</tr> 6571<tr> 6572<td> 6573 <p> 6574 Order 13 6575 </p> 6576 </td> 6577<td> 6578 <p> 6579 <span class="blue">1.81<br> (76ns)</span> 6580 </p> 6581 </td> 6582<td> 6583 <p> 6584 <span class="red">2.33<br> (98ns)</span> 6585 </p> 6586 </td> 6587<td> 6588 <p> 6589 <span class="green">1.02<br> (43ns)</span> 6590 </p> 6591 </td> 6592<td> 6593 <p> 6594 <span class="green">1.00<br> (42ns)</span> 6595 </p> 6596 </td> 6597<td> 6598 <p> 6599 <span class="blue">1.36<br> (57ns)</span> 6600 </p> 6601 </td> 6602<td> 6603 <p> 6604 <span class="blue">1.24<br> (52ns)</span> 6605 </p> 6606 </td> 6607<td> 6608 <p> 6609 <span class="blue">1.57<br> (66ns)</span> 6610 </p> 6611 </td> 6612<td> 6613 <p> 6614 <span class="blue">1.36<br> (57ns)</span> 6615 </p> 6616 </td> 6617</tr> 6618<tr> 6619<td> 6620 <p> 6621 Order 14 6622 </p> 6623 </td> 6624<td> 6625 <p> 6626 <span class="blue">1.98<br> (85ns)</span> 6627 </p> 6628 </td> 6629<td> 6630 <p> 6631 <span class="red">2.47<br> (106ns)</span> 6632 </p> 6633 </td> 6634<td> 6635 <p> 6636 <span class="green">1.00<br> (43ns)</span> 6637 </p> 6638 </td> 6639<td> 6640 <p> 6641 <span class="green">1.00<br> (43ns)</span> 6642 </p> 6643 </td> 6644<td> 6645 <p> 6646 <span class="blue">1.33<br> (57ns)</span> 6647 </p> 6648 </td> 6649<td> 6650 <p> 6651 <span class="blue">1.30<br> (56ns)</span> 6652 </p> 6653 </td> 6654<td> 6655 <p> 6656 <span class="blue">1.35<br> (58ns)</span> 6657 </p> 6658 </td> 6659<td> 6660 <p> 6661 <span class="green">1.16<br> (50ns)</span> 6662 </p> 6663 </td> 6664</tr> 6665<tr> 6666<td> 6667 <p> 6668 Order 15 6669 </p> 6670 </td> 6671<td> 6672 <p> 6673 <span class="red">2.26<br> (95ns)</span> 6674 </p> 6675 </td> 6676<td> 6677 <p> 6678 <span class="red">2.67<br> (112ns)</span> 6679 </p> 6680 </td> 6681<td> 6682 <p> 6683 <span class="green">1.05<br> (44ns)</span> 6684 </p> 6685 </td> 6686<td> 6687 <p> 6688 <span class="green">1.00<br> (42ns)</span> 6689 </p> 6690 </td> 6691<td> 6692 <p> 6693 <span class="green">1.14<br> (48ns)</span> 6694 </p> 6695 </td> 6696<td> 6697 <p> 6698 <span class="green">1.17<br> (49ns)</span> 6699 </p> 6700 </td> 6701<td> 6702 <p> 6703 <span class="green">1.19<br> (50ns)</span> 6704 </p> 6705 </td> 6706<td> 6707 <p> 6708 <span class="green">1.12<br> (47ns)</span> 6709 </p> 6710 </td> 6711</tr> 6712<tr> 6713<td> 6714 <p> 6715 Order 16 6716 </p> 6717 </td> 6718<td> 6719 <p> 6720 <span class="red">2.31<br> (97ns)</span> 6721 </p> 6722 </td> 6723<td> 6724 <p> 6725 <span class="red">2.86<br> (120ns)</span> 6726 </p> 6727 </td> 6728<td> 6729 <p> 6730 <span class="green">1.00<br> (42ns)</span> 6731 </p> 6732 </td> 6733<td> 6734 <p> 6735 <span class="green">1.02<br> (43ns)</span> 6736 </p> 6737 </td> 6738<td> 6739 <p> 6740 <span class="green">1.12<br> (47ns)</span> 6741 </p> 6742 </td> 6743<td> 6744 <p> 6745 <span class="green">1.12<br> (47ns)</span> 6746 </p> 6747 </td> 6748<td> 6749 <p> 6750 <span class="blue">1.33<br> (56ns)</span> 6751 </p> 6752 </td> 6753<td> 6754 <p> 6755 <span class="blue">1.69<br> (71ns)</span> 6756 </p> 6757 </td> 6758</tr> 6759<tr> 6760<td> 6761 <p> 6762 Order 17 6763 </p> 6764 </td> 6765<td> 6766 <p> 6767 <span class="red">2.39<br> (105ns)</span> 6768 </p> 6769 </td> 6770<td> 6771 <p> 6772 <span class="red">2.93<br> (129ns)</span> 6773 </p> 6774 </td> 6775<td> 6776 <p> 6777 <span class="green">1.00<br> (44ns)</span> 6778 </p> 6779 </td> 6780<td> 6781 <p> 6782 <span class="green">1.02<br> (45ns)</span> 6783 </p> 6784 </td> 6785<td> 6786 <p> 6787 <span class="blue">1.34<br> (59ns)</span> 6788 </p> 6789 </td> 6790<td> 6791 <p> 6792 <span class="green">1.11<br> (49ns)</span> 6793 </p> 6794 </td> 6795<td> 6796 <p> 6797 <span class="blue">1.23<br> (54ns)</span> 6798 </p> 6799 </td> 6800<td> 6801 <p> 6802 <span class="green">1.02<br> (45ns)</span> 6803 </p> 6804 </td> 6805</tr> 6806<tr> 6807<td> 6808 <p> 6809 Order 18 6810 </p> 6811 </td> 6812<td> 6813 <p> 6814 <span class="red">2.63<br> (113ns)</span> 6815 </p> 6816 </td> 6817<td> 6818 <p> 6819 <span class="red">3.19<br> (137ns)</span> 6820 </p> 6821 </td> 6822<td> 6823 <p> 6824 <span class="green">1.00<br> (43ns)</span> 6825 </p> 6826 </td> 6827<td> 6828 <p> 6829 <span class="green">1.00<br> (43ns)</span> 6830 </p> 6831 </td> 6832<td> 6833 <p> 6834 <span class="green">1.14<br> (49ns)</span> 6835 </p> 6836 </td> 6837<td> 6838 <p> 6839 <span class="green">1.14<br> (49ns)</span> 6840 </p> 6841 </td> 6842<td> 6843 <p> 6844 <span class="blue">1.37<br> (59ns)</span> 6845 </p> 6846 </td> 6847<td> 6848 <p> 6849 <span class="green">1.14<br> (49ns)</span> 6850 </p> 6851 </td> 6852</tr> 6853<tr> 6854<td> 6855 <p> 6856 Order 19 6857 </p> 6858 </td> 6859<td> 6860 <p> 6861 <span class="red">2.93<br> (123ns)</span> 6862 </p> 6863 </td> 6864<td> 6865 <p> 6866 <span class="red">3.50<br> (147ns)</span> 6867 </p> 6868 </td> 6869<td> 6870 <p> 6871 <span class="green">1.02<br> (43ns)</span> 6872 </p> 6873 </td> 6874<td> 6875 <p> 6876 <span class="green">1.00<br> (42ns)</span> 6877 </p> 6878 </td> 6879<td> 6880 <p> 6881 <span class="green">1.12<br> (47ns)</span> 6882 </p> 6883 </td> 6884<td> 6885 <p> 6886 <span class="green">1.10<br> (46ns)</span> 6887 </p> 6888 </td> 6889<td> 6890 <p> 6891 <span class="green">1.10<br> (46ns)</span> 6892 </p> 6893 </td> 6894<td> 6895 <p> 6896 <span class="green">1.10<br> (46ns)</span> 6897 </p> 6898 </td> 6899</tr> 6900<tr> 6901<td> 6902 <p> 6903 Order 20 6904 </p> 6905 </td> 6906<td> 6907 <p> 6908 <span class="red">3.28<br> (141ns)</span> 6909 </p> 6910 </td> 6911<td> 6912 <p> 6913 <span class="red">3.60<br> (155ns)</span> 6914 </p> 6915 </td> 6916<td> 6917 <p> 6918 <span class="green">1.00<br> (43ns)</span> 6919 </p> 6920 </td> 6921<td> 6922 <p> 6923 <span class="green">1.02<br> (44ns)</span> 6924 </p> 6925 </td> 6926<td> 6927 <p> 6928 <span class="green">1.09<br> (47ns)</span> 6929 </p> 6930 </td> 6931<td> 6932 <p> 6933 <span class="green">1.14<br> (49ns)</span> 6934 </p> 6935 </td> 6936<td> 6937 <p> 6938 <span class="green">1.07<br> (46ns)</span> 6939 </p> 6940 </td> 6941<td> 6942 <p> 6943 <span class="green">1.05<br> (45ns)</span> 6944 </p> 6945 </td> 6946</tr> 6947</tbody> 6948</table></div> 6949</div> 6950<br class="table-break"><div class="table"> 6951<a name="math_toolkit.tuning.table_Rational_Method_Comparison_with_Intel_C_C_0x_mode_version_1910_on_linux"></a><p class="title"><b>Table 22.11. Rational Method Comparison with Intel C++ C++0x mode version 1910 on 6952 linux</b></p> 6953<div class="table-contents"><table class="table" summary="Rational Method Comparison with Intel C++ C++0x mode version 1910 on 6954 linux"> 6955<colgroup> 6956<col> 6957<col> 6958<col> 6959<col> 6960<col> 6961<col> 6962<col> 6963<col> 6964<col> 6965</colgroup> 6966<thead><tr> 6967<th> 6968 <p> 6969 Function 6970 </p> 6971 </th> 6972<th> 6973 <p> 6974 Method 0<br> (Double Coefficients) 6975 </p> 6976 </th> 6977<th> 6978 <p> 6979 Method 0<br> (Integer Coefficients) 6980 </p> 6981 </th> 6982<th> 6983 <p> 6984 Method 1<br> (Double Coefficients) 6985 </p> 6986 </th> 6987<th> 6988 <p> 6989 Method 1<br> (Integer Coefficients) 6990 </p> 6991 </th> 6992<th> 6993 <p> 6994 Method 2<br> (Double Coefficients) 6995 </p> 6996 </th> 6997<th> 6998 <p> 6999 Method 2<br> (Integer Coefficients) 7000 </p> 7001 </th> 7002<th> 7003 <p> 7004 Method 3<br> (Double Coefficients) 7005 </p> 7006 </th> 7007<th> 7008 <p> 7009 Method 3<br> (Integer Coefficients) 7010 </p> 7011 </th> 7012</tr></thead> 7013<tbody> 7014<tr> 7015<td> 7016 <p> 7017 Order 2 7018 </p> 7019 </td> 7020<td> 7021 <p> 7022 <span class="grey">-</span> 7023 </p> 7024 </td> 7025<td> 7026 <p> 7027 <span class="grey">-</span> 7028 </p> 7029 </td> 7030<td> 7031 <p> 7032 <span class="red">2.17<br> (26ns)</span> 7033 </p> 7034 </td> 7035<td> 7036 <p> 7037 <span class="blue">2.00<br> (24ns)</span> 7038 </p> 7039 </td> 7040<td> 7041 <p> 7042 <span class="green">1.08<br> (13ns)</span> 7043 </p> 7044 </td> 7045<td> 7046 <p> 7047 <span class="green">1.08<br> (13ns)</span> 7048 </p> 7049 </td> 7050<td> 7051 <p> 7052 <span class="green">1.00<br> (12ns)</span> 7053 </p> 7054 </td> 7055<td> 7056 <p> 7057 <span class="green">1.00<br> (12ns)</span> 7058 </p> 7059 </td> 7060</tr> 7061<tr> 7062<td> 7063 <p> 7064 Order 3 7065 </p> 7066 </td> 7067<td> 7068 <p> 7069 <span class="red">2.88<br> (49ns)</span> 7070 </p> 7071 </td> 7072<td> 7073 <p> 7074 <span class="red">3.18<br> (54ns)</span> 7075 </p> 7076 </td> 7077<td> 7078 <p> 7079 <span class="blue">1.59<br> (27ns)</span> 7080 </p> 7081 </td> 7082<td> 7083 <p> 7084 <span class="blue">1.41<br> (24ns)</span> 7085 </p> 7086 </td> 7087<td> 7088 <p> 7089 <span class="green">1.00<br> (17ns)</span> 7090 </p> 7091 </td> 7092<td> 7093 <p> 7094 <span class="green">1.00<br> (17ns)</span> 7095 </p> 7096 </td> 7097<td> 7098 <p> 7099 <span class="green">1.00<br> (17ns)</span> 7100 </p> 7101 </td> 7102<td> 7103 <p> 7104 <span class="green">1.00<br> (17ns)</span> 7105 </p> 7106 </td> 7107</tr> 7108<tr> 7109<td> 7110 <p> 7111 Order 4 7112 </p> 7113 </td> 7114<td> 7115 <p> 7116 <span class="red">4.00<br> (68ns)</span> 7117 </p> 7118 </td> 7119<td> 7120 <p> 7121 <span class="red">4.35<br> (74ns)</span> 7122 </p> 7123 </td> 7124<td> 7125 <p> 7126 <span class="blue">1.88<br> (32ns)</span> 7127 </p> 7128 </td> 7129<td> 7130 <p> 7131 <span class="blue">1.88<br> (32ns)</span> 7132 </p> 7133 </td> 7134<td> 7135 <p> 7136 <span class="green">1.06<br> (18ns)</span> 7137 </p> 7138 </td> 7139<td> 7140 <p> 7141 <span class="green">1.06<br> (18ns)</span> 7142 </p> 7143 </td> 7144<td> 7145 <p> 7146 <span class="green">1.00<br> (17ns)</span> 7147 </p> 7148 </td> 7149<td> 7150 <p> 7151 <span class="green">1.00<br> (17ns)</span> 7152 </p> 7153 </td> 7154</tr> 7155<tr> 7156<td> 7157 <p> 7158 Order 5 7159 </p> 7160 </td> 7161<td> 7162 <p> 7163 <span class="red">2.15<br> (86ns)</span> 7164 </p> 7165 </td> 7166<td> 7167 <p> 7168 <span class="red">2.25<br> (90ns)</span> 7169 </p> 7170 </td> 7171<td> 7172 <p> 7173 <span class="green">1.00<br> (40ns)</span> 7174 </p> 7175 </td> 7176<td> 7177 <p> 7178 <span class="green">1.00<br> (40ns)</span> 7179 </p> 7180 </td> 7181<td> 7182 <p> 7183 <span class="green">1.20<br> (48ns)</span> 7184 </p> 7185 </td> 7186<td> 7187 <p> 7188 <span class="blue">1.23<br> (49ns)</span> 7189 </p> 7190 </td> 7191<td> 7192 <p> 7193 <span class="green">1.05<br> (42ns)</span> 7194 </p> 7195 </td> 7196<td> 7197 <p> 7198 <span class="green">1.07<br> (43ns)</span> 7199 </p> 7200 </td> 7201</tr> 7202<tr> 7203<td> 7204 <p> 7205 Order 6 7206 </p> 7207 </td> 7208<td> 7209 <p> 7210 <span class="red">2.16<br> (106ns)</span> 7211 </p> 7212 </td> 7213<td> 7214 <p> 7215 <span class="red">2.20<br> (108ns)</span> 7216 </p> 7217 </td> 7218<td> 7219 <p> 7220 <span class="green">1.04<br> (51ns)</span> 7221 </p> 7222 </td> 7223<td> 7224 <p> 7225 <span class="green">1.00<br> (49ns)</span> 7226 </p> 7227 </td> 7228<td> 7229 <p> 7230 <span class="green">1.08<br> (53ns)</span> 7231 </p> 7232 </td> 7233<td> 7234 <p> 7235 <span class="green">1.08<br> (53ns)</span> 7236 </p> 7237 </td> 7238<td> 7239 <p> 7240 <span class="green">1.06<br> (52ns)</span> 7241 </p> 7242 </td> 7243<td> 7244 <p> 7245 <span class="blue">1.24<br> (61ns)</span> 7246 </p> 7247 </td> 7248</tr> 7249<tr> 7250<td> 7251 <p> 7252 Order 7 7253 </p> 7254 </td> 7255<td> 7256 <p> 7257 <span class="red">2.14<br> (126ns)</span> 7258 </p> 7259 </td> 7260<td> 7261 <p> 7262 <span class="red">2.20<br> (130ns)</span> 7263 </p> 7264 </td> 7265<td> 7266 <p> 7267 <span class="green">1.02<br> (60ns)</span> 7268 </p> 7269 </td> 7270<td> 7271 <p> 7272 <span class="green">1.00<br> (59ns)</span> 7273 </p> 7274 </td> 7275<td> 7276 <p> 7277 <span class="green">1.02<br> (60ns)</span> 7278 </p> 7279 </td> 7280<td> 7281 <p> 7282 <span class="green">1.02<br> (60ns)</span> 7283 </p> 7284 </td> 7285<td> 7286 <p> 7287 <span class="green">1.07<br> (63ns)</span> 7288 </p> 7289 </td> 7290<td> 7291 <p> 7292 <span class="green">1.02<br> (60ns)</span> 7293 </p> 7294 </td> 7295</tr> 7296<tr> 7297<td> 7298 <p> 7299 Order 8 7300 </p> 7301 </td> 7302<td> 7303 <p> 7304 <span class="red">2.43<br> (170ns)</span> 7305 </p> 7306 </td> 7307<td> 7308 <p> 7309 <span class="red">2.11<br> (148ns)</span> 7310 </p> 7311 </td> 7312<td> 7313 <p> 7314 <span class="green">1.03<br> (72ns)</span> 7315 </p> 7316 </td> 7317<td> 7318 <p> 7319 <span class="green">1.01<br> (71ns)</span> 7320 </p> 7321 </td> 7322<td> 7323 <p> 7324 <span class="green">1.00<br> (70ns)</span> 7325 </p> 7326 </td> 7327<td> 7328 <p> 7329 <span class="green">1.00<br> (70ns)</span> 7330 </p> 7331 </td> 7332<td> 7333 <p> 7334 <span class="green">1.00<br> (70ns)</span> 7335 </p> 7336 </td> 7337<td> 7338 <p> 7339 <span class="blue">1.53<br> (107ns)</span> 7340 </p> 7341 </td> 7342</tr> 7343<tr> 7344<td> 7345 <p> 7346 Order 9 7347 </p> 7348 </td> 7349<td> 7350 <p> 7351 <span class="red">2.06<br> (165ns)</span> 7352 </p> 7353 </td> 7354<td> 7355 <p> 7356 <span class="red">2.12<br> (170ns)</span> 7357 </p> 7358 </td> 7359<td> 7360 <p> 7361 <span class="green">1.14<br> (91ns)</span> 7362 </p> 7363 </td> 7364<td> 7365 <p> 7366 <span class="green">1.15<br> (92ns)</span> 7367 </p> 7368 </td> 7369<td> 7370 <p> 7371 <span class="green">1.02<br> (82ns)</span> 7372 </p> 7373 </td> 7374<td> 7375 <p> 7376 <span class="green">1.00<br> (80ns)</span> 7377 </p> 7378 </td> 7379<td> 7380 <p> 7381 <span class="green">1.01<br> (81ns)</span> 7382 </p> 7383 </td> 7384<td> 7385 <p> 7386 <span class="blue">1.44<br> (115ns)</span> 7387 </p> 7388 </td> 7389</tr> 7390<tr> 7391<td> 7392 <p> 7393 Order 10 7394 </p> 7395 </td> 7396<td> 7397 <p> 7398 <span class="red">2.22<br> (189ns)</span> 7399 </p> 7400 </td> 7401<td> 7402 <p> 7403 <span class="red">2.26<br> (192ns)</span> 7404 </p> 7405 </td> 7406<td> 7407 <p> 7408 <span class="green">1.13<br> (96ns)</span> 7409 </p> 7410 </td> 7411<td> 7412 <p> 7413 <span class="green">1.12<br> (95ns)</span> 7414 </p> 7415 </td> 7416<td> 7417 <p> 7418 <span class="green">1.01<br> (86ns)</span> 7419 </p> 7420 </td> 7421<td> 7422 <p> 7423 <span class="green">1.04<br> (88ns)</span> 7424 </p> 7425 </td> 7426<td> 7427 <p> 7428 <span class="green">1.00<br> (85ns)</span> 7429 </p> 7430 </td> 7431<td> 7432 <p> 7433 <span class="blue">1.47<br> (125ns)</span> 7434 </p> 7435 </td> 7436</tr> 7437<tr> 7438<td> 7439 <p> 7440 Order 11 7441 </p> 7442 </td> 7443<td> 7444 <p> 7445 <span class="red">2.15<br> (209ns)</span> 7446 </p> 7447 </td> 7448<td> 7449 <p> 7450 <span class="red">2.15<br> (209ns)</span> 7451 </p> 7452 </td> 7453<td> 7454 <p> 7455 <span class="green">1.12<br> (109ns)</span> 7456 </p> 7457 </td> 7458<td> 7459 <p> 7460 <span class="green">1.20<br> (116ns)</span> 7461 </p> 7462 </td> 7463<td> 7464 <p> 7465 <span class="green">1.00<br> (97ns)</span> 7466 </p> 7467 </td> 7468<td> 7469 <p> 7470 <span class="green">1.01<br> (98ns)</span> 7471 </p> 7472 </td> 7473<td> 7474 <p> 7475 <span class="blue">1.46<br> (142ns)</span> 7476 </p> 7477 </td> 7478<td> 7479 <p> 7480 <span class="blue">1.42<br> (138ns)</span> 7481 </p> 7482 </td> 7483</tr> 7484<tr> 7485<td> 7486 <p> 7487 Order 12 7488 </p> 7489 </td> 7490<td> 7491 <p> 7492 <span class="red">2.10<br> (227ns)</span> 7493 </p> 7494 </td> 7495<td> 7496 <p> 7497 <span class="red">2.17<br> (234ns)</span> 7498 </p> 7499 </td> 7500<td> 7501 <p> 7502 <span class="green">1.19<br> (128ns)</span> 7503 </p> 7504 </td> 7505<td> 7506 <p> 7507 <span class="green">1.13<br> (122ns)</span> 7508 </p> 7509 </td> 7510<td> 7511 <p> 7512 <span class="green">1.01<br> (109ns)</span> 7513 </p> 7514 </td> 7515<td> 7516 <p> 7517 <span class="green">1.00<br> (108ns)</span> 7518 </p> 7519 </td> 7520<td> 7521 <p> 7522 <span class="blue">1.31<br> (141ns)</span> 7523 </p> 7524 </td> 7525<td> 7526 <p> 7527 <span class="blue">1.37<br> (148ns)</span> 7528 </p> 7529 </td> 7530</tr> 7531<tr> 7532<td> 7533 <p> 7534 Order 13 7535 </p> 7536 </td> 7537<td> 7538 <p> 7539 <span class="red">2.73<br> (246ns)</span> 7540 </p> 7541 </td> 7542<td> 7543 <p> 7544 <span class="red">2.78<br> (250ns)</span> 7545 </p> 7546 </td> 7547<td> 7548 <p> 7549 <span class="green">1.18<br> (106ns)</span> 7550 </p> 7551 </td> 7552<td> 7553 <p> 7554 <span class="green">1.17<br> (105ns)</span> 7555 </p> 7556 </td> 7557<td> 7558 <p> 7559 <span class="green">1.01<br> (91ns)</span> 7560 </p> 7561 </td> 7562<td> 7563 <p> 7564 <span class="green">1.00<br> (90ns)</span> 7565 </p> 7566 </td> 7567<td> 7568 <p> 7569 <span class="blue">1.66<br> (149ns)</span> 7570 </p> 7571 </td> 7572<td> 7573 <p> 7574 <span class="blue">1.80<br> (162ns)</span> 7575 </p> 7576 </td> 7577</tr> 7578<tr> 7579<td> 7580 <p> 7581 Order 14 7582 </p> 7583 </td> 7584<td> 7585 <p> 7586 <span class="red">2.92<br> (266ns)</span> 7587 </p> 7588 </td> 7589<td> 7590 <p> 7591 <span class="red">3.03<br> (276ns)</span> 7592 </p> 7593 </td> 7594<td> 7595 <p> 7596 <span class="green">1.18<br> (107ns)</span> 7597 </p> 7598 </td> 7599<td> 7600 <p> 7601 <span class="red">2.89<br> (263ns)</span> 7602 </p> 7603 </td> 7604<td> 7605 <p> 7606 <span class="green">1.00<br> (91ns)</span> 7607 </p> 7608 </td> 7609<td> 7610 <p> 7611 <span class="green">1.04<br> (95ns)</span> 7612 </p> 7613 </td> 7614<td> 7615 <p> 7616 <span class="blue">1.78<br> (162ns)</span> 7617 </p> 7618 </td> 7619<td> 7620 <p> 7621 <span class="red">2.15<br> (196ns)</span> 7622 </p> 7623 </td> 7624</tr> 7625<tr> 7626<td> 7627 <p> 7628 Order 15 7629 </p> 7630 </td> 7631<td> 7632 <p> 7633 <span class="red">2.97<br> (288ns)</span> 7634 </p> 7635 </td> 7636<td> 7637 <p> 7638 <span class="red">2.97<br> (288ns)</span> 7639 </p> 7640 </td> 7641<td> 7642 <p> 7643 <span class="green">1.11<br> (108ns)</span> 7644 </p> 7645 </td> 7646<td> 7647 <p> 7648 <span class="red">2.98<br> (289ns)</span> 7649 </p> 7650 </td> 7651<td> 7652 <p> 7653 <span class="green">1.00<br> (97ns)</span> 7654 </p> 7655 </td> 7656<td> 7657 <p> 7658 <span class="red">2.38<br> (231ns)</span> 7659 </p> 7660 </td> 7661<td> 7662 <p> 7663 <span class="blue">1.79<br> (174ns)</span> 7664 </p> 7665 </td> 7666<td> 7667 <p> 7668 <span class="blue">1.82<br> (177ns)</span> 7669 </p> 7670 </td> 7671</tr> 7672<tr> 7673<td> 7674 <p> 7675 Order 16 7676 </p> 7677 </td> 7678<td> 7679 <p> 7680 <span class="red">3.17<br> (314ns)</span> 7681 </p> 7682 </td> 7683<td> 7684 <p> 7685 <span class="red">3.15<br> (312ns)</span> 7686 </p> 7687 </td> 7688<td> 7689 <p> 7690 <span class="green">1.13<br> (112ns)</span> 7691 </p> 7692 </td> 7693<td> 7694 <p> 7695 <span class="red">3.35<br> (332ns)</span> 7696 </p> 7697 </td> 7698<td> 7699 <p> 7700 <span class="green">1.00<br> (99ns)</span> 7701 </p> 7702 </td> 7703<td> 7704 <p> 7705 <span class="red">2.53<br> (250ns)</span> 7706 </p> 7707 </td> 7708<td> 7709 <p> 7710 <span class="blue">1.89<br> (187ns)</span> 7711 </p> 7712 </td> 7713<td> 7714 <p> 7715 <span class="blue">1.94<br> (192ns)</span> 7716 </p> 7717 </td> 7718</tr> 7719<tr> 7720<td> 7721 <p> 7722 Order 17 7723 </p> 7724 </td> 7725<td> 7726 <p> 7727 <span class="red">2.99<br> (326ns)</span> 7728 </p> 7729 </td> 7730<td> 7731 <p> 7732 <span class="red">3.11<br> (339ns)</span> 7733 </p> 7734 </td> 7735<td> 7736 <p> 7737 <span class="green">1.11<br> (121ns)</span> 7738 </p> 7739 </td> 7740<td> 7741 <p> 7742 <span class="red">3.31<br> (361ns)</span> 7743 </p> 7744 </td> 7745<td> 7746 <p> 7747 <span class="green">1.00<br> (109ns)</span> 7748 </p> 7749 </td> 7750<td> 7751 <p> 7752 <span class="red">2.42<br> (264ns)</span> 7753 </p> 7754 </td> 7755<td> 7756 <p> 7757 <span class="blue">1.81<br> (197ns)</span> 7758 </p> 7759 </td> 7760<td> 7761 <p> 7762 <span class="blue">1.83<br> (200ns)</span> 7763 </p> 7764 </td> 7765</tr> 7766<tr> 7767<td> 7768 <p> 7769 Order 18 7770 </p> 7771 </td> 7772<td> 7773 <p> 7774 <span class="red">3.43<br> (350ns)</span> 7775 </p> 7776 </td> 7777<td> 7778 <p> 7779 <span class="red">3.52<br> (359ns)</span> 7780 </p> 7781 </td> 7782<td> 7783 <p> 7784 <span class="blue">1.21<br> (123ns)</span> 7785 </p> 7786 </td> 7787<td> 7788 <p> 7789 <span class="red">3.94<br> (402ns)</span> 7790 </p> 7791 </td> 7792<td> 7793 <p> 7794 <span class="green">1.00<br> (102ns)</span> 7795 </p> 7796 </td> 7797<td> 7798 <p> 7799 <span class="red">2.86<br> (292ns)</span> 7800 </p> 7801 </td> 7802<td> 7803 <p> 7804 <span class="blue">1.98<br> (202ns)</span> 7805 </p> 7806 </td> 7807<td> 7808 <p> 7809 <span class="red">2.08<br> (212ns)</span> 7810 </p> 7811 </td> 7812</tr> 7813<tr> 7814<td> 7815 <p> 7816 Order 19 7817 </p> 7818 </td> 7819<td> 7820 <p> 7821 <span class="red">3.51<br> (379ns)</span> 7822 </p> 7823 </td> 7824<td> 7825 <p> 7826 <span class="red">3.43<br> (370ns)</span> 7827 </p> 7828 </td> 7829<td> 7830 <p> 7831 <span class="green">1.16<br> (125ns)</span> 7832 </p> 7833 </td> 7834<td> 7835 <p> 7836 <span class="red">3.97<br> (429ns)</span> 7837 </p> 7838 </td> 7839<td> 7840 <p> 7841 <span class="green">1.00<br> (108ns)</span> 7842 </p> 7843 </td> 7844<td> 7845 <p> 7846 <span class="red">3.01<br> (325ns)</span> 7847 </p> 7848 </td> 7849<td> 7850 <p> 7851 <span class="blue">1.94<br> (209ns)</span> 7852 </p> 7853 </td> 7854<td> 7855 <p> 7856 <span class="red">2.17<br> (234ns)</span> 7857 </p> 7858 </td> 7859</tr> 7860<tr> 7861<td> 7862 <p> 7863 Order 20 7864 </p> 7865 </td> 7866<td> 7867 <p> 7868 <span class="red">3.69<br> (421ns)</span> 7869 </p> 7870 </td> 7871<td> 7872 <p> 7873 <span class="red">4.34<br> (495ns)</span> 7874 </p> 7875 </td> 7876<td> 7877 <p> 7878 <span class="green">1.18<br> (134ns)</span> 7879 </p> 7880 </td> 7881<td> 7882 <p> 7883 <span class="red">4.31<br> (491ns)</span> 7884 </p> 7885 </td> 7886<td> 7887 <p> 7888 <span class="green">1.00<br> (114ns)</span> 7889 </p> 7890 </td> 7891<td> 7892 <p> 7893 <span class="red">3.08<br> (351ns)</span> 7894 </p> 7895 </td> 7896<td> 7897 <p> 7898 <span class="blue">1.96<br> (224ns)</span> 7899 </p> 7900 </td> 7901<td> 7902 <p> 7903 <span class="red">2.06<br> (235ns)</span> 7904 </p> 7905 </td> 7906</tr> 7907</tbody> 7908</table></div> 7909</div> 7910<br class="table-break"> 7911</div> 7912<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> 7913<td align="left"></td> 7914<td align="right"><div class="copyright-footer">Copyright © 2006-2019 Nikhar 7915 Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, 7916 Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan 7917 Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, 7918 Daryle Walker and Xiaogang Zhang<p> 7919 Distributed under the Boost Software License, Version 1.0. (See accompanying 7920 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>) 7921 </p> 7922</div></td> 7923</tr></table> 7924<hr> 7925<div class="spirit-nav"> 7926<a accesskey="p" href="multiprecision.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../perf.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="comp_compilers.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a> 7927</div> 7928</body> 7929</html> 7930
