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  26 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
  27 <a name="math_toolkit.comparisons"></a><a class="link" href="comparisons.html" title="Comparisons to Other Open Source Libraries">Comparisons to Other Open Source
  28     Libraries</a>
  29 </h2></div></div></div>
  30 <p>
  31       We've run our performance tests both for our own code, and against other open
  32       source implementations of the same functions. The results are presented below
  33       to give you a rough idea of how they all compare. In order to give a more-or-less
  34       level playing field our test data was screened against all the libraries being
  35       tested, and any unsupported domains removed, likewise for any test cases that
  36       gave large errors or unexpected non-finite values.
  37     </p>
  38 <div class="caution"><table border="0" summary="Caution">
  39 <tr>
  40 <td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../../doc/src/images/caution.png"></td>
  41 <th align="left">Caution</th>
  42 </tr>
  43 <tr><td align="left" valign="top"><p>
  44         You should exercise extreme caution when interpreting these results, relative
  45         performance may vary by platform, by compiler options settings, the tests
  46         use data that gives good code coverage of <span class="emphasis"><em>our</em></span> code,
  47         but which may skew the results towards the corner cases. Finally, remember
  48         that different libraries make different choices with regard to performance
  49         verses numerical stability.
  50       </p></td></tr>
  51 </table></div>
  52 <p>
  53       The first results compare standard library functions to Boost equivalents with
  54       MSVC-14.0:
  55     </p>
  56 <div class="table">
  57 <a name="math_toolkit.comparisons.table_Library_Comparison_with_Microsoft_Visual_C_version_14_0_on_Windows_x64"></a><p class="title"><b>Table&#160;21.7.&#160;Library Comparison with Microsoft Visual C++ version 14.0 on Windows
  58       x64</b></p>
  59 <div class="table-contents"><table class="table" summary="Library Comparison with Microsoft Visual C++ version 14.0 on Windows
  60       x64">
  61 <colgroup>
  62 <col>
  63 <col>
  64 <col>
  65 </colgroup>
  66 <thead><tr>
  67 <th>
  68               <p>
  69                 Function
  70               </p>
  71             </th>
  72 <th>
  73               <p>
  74                 boost 1.61
  75               </p>
  76             </th>
  77 <th>
  78               <p>
  79                 math.h
  80               </p>
  81             </th>
  82 </tr></thead>
  83 <tbody>
  84 <tr>
  85 <td>
  86               <p>
  87                 cbrt<br> (85/85 tests selected)
  88               </p>
  89             </td>
  90 <td>
  91               <p>
  92                 <span class="green">1.00<br> (45ns)</span>
  93               </p>
  94             </td>
  95 <td>
  96               <p>
  97                 <span class="blue">1.44<br> (65ns)</span>
  98               </p>
  99             </td>
 100 </tr>
 101 <tr>
 102 <td>
 103               <p>
 104                 cyl_bessel_j (integer order)<br> (267/268 tests selected)
 105               </p>
 106             </td>
 107 <td>
 108               <p>
 109                 <span class="green">1.00<br> (103ns)</span>
 110               </p>
 111             </td>
 112 <td>
 113               <p>
 114                 <span class="red">2.11<br> (217ns)</span>
 115               </p>
 116             </td>
 117 </tr>
 118 <tr>
 119 <td>
 120               <p>
 121                 cyl_neumann (integer order)<br> (428/428 tests selected)
 122               </p>
 123             </td>
 124 <td>
 125               <p>
 126                 <span class="blue">1.57<br> (225ns)</span>
 127               </p>
 128             </td>
 129 <td>
 130               <p>
 131                 <span class="green">1.00<br> (143ns)</span>
 132               </p>
 133             </td>
 134 </tr>
 135 <tr>
 136 <td>
 137               <p>
 138                 erf<br> (950/950 tests selected)
 139               </p>
 140             </td>
 141 <td>
 142               <p>
 143                 <span class="green">1.10<br> (23ns)</span>
 144               </p>
 145             </td>
 146 <td>
 147               <p>
 148                 <span class="green">1.00<br> (21ns)</span>
 149               </p>
 150             </td>
 151 </tr>
 152 <tr>
 153 <td>
 154               <p>
 155                 erfc<br> (950/950 tests selected)
 156               </p>
 157             </td>
 158 <td>
 159               <p>
 160                 <span class="green">1.00<br> (22ns)</span>
 161               </p>
 162             </td>
 163 <td>
 164               <p>
 165                 <span class="red">3.36<br> (74ns)</span>
 166               </p>
 167             </td>
 168 </tr>
 169 <tr>
 170 <td>
 171               <p>
 172                 expm1<br> (80/80 tests selected)
 173               </p>
 174             </td>
 175 <td>
 176               <p>
 177                 <span class="green">1.00<br> (10ns)</span>
 178               </p>
 179             </td>
 180 <td>
 181               <p>
 182                 <span class="green">1.10<br> (11ns)</span>
 183               </p>
 184             </td>
 185 </tr>
 186 <tr>
 187 <td>
 188               <p>
 189                 lgamma<br> (400/400 tests selected)
 190               </p>
 191             </td>
 192 <td>
 193               <p>
 194                 <span class="green">1.00<br> (73ns)</span>
 195               </p>
 196             </td>
 197 <td>
 198               <p>
 199                 <span class="blue">1.74<br> (127ns)</span>
 200               </p>
 201             </td>
 202 </tr>
 203 <tr>
 204 <td>
 205               <p>
 206                 log1p<br> (80/80 tests selected)
 207               </p>
 208             </td>
 209 <td>
 210               <p>
 211                 <span class="green">1.08<br> (14ns)</span>
 212               </p>
 213             </td>
 214 <td>
 215               <p>
 216                 <span class="green">1.00<br> (13ns)</span>
 217               </p>
 218             </td>
 219 </tr>
 220 <tr>
 221 <td>
 222               <p>
 223                 tgamma<br> (400/400 tests selected)
 224               </p>
 225             </td>
 226 <td>
 227               <p>
 228                 <span class="green">1.00<br> (77ns)</span>
 229               </p>
 230             </td>
 231 <td>
 232               <p>
 233                 <span class="red">12.12<br> (933ns)</span>
 234               </p>
 235             </td>
 236 </tr>
 237 </tbody>
 238 </table></div>
 239 </div>
 240 <br class="table-break"><p>
 241       On Linux with GCC, we can also compare to the TR1 functions, and to GSL and
 242       RMath:
 243     </p>
 244 <div class="table">
 245 <a name="math_toolkit.comparisons.table_Library_Comparison_with_GNU_C_version_5_3_0_on_linux"></a><p class="title"><b>Table&#160;21.8.&#160;Library Comparison with GNU C++ version 5.3.0 on linux</b></p>
 246 <div class="table-contents"><table class="table" summary="Library Comparison with GNU C++ version 5.3.0 on linux">
 247 <colgroup>
 248 <col>
 249 <col>
 250 <col>
 251 <col>
 252 <col>
 253 <col>
 254 <col>
 255 </colgroup>
 256 <thead><tr>
 257 <th>
 258               <p>
 259                 Function
 260               </p>
 261             </th>
 262 <th>
 263               <p>
 264                 boost 1.61
 265               </p>
 266             </th>
 267 <th>
 268               <p>
 269                 boost 1.61<br> promote_double&lt;false&gt;
 270               </p>
 271             </th>
 272 <th>
 273               <p>
 274                 tr1/cmath
 275               </p>
 276             </th>
 277 <th>
 278               <p>
 279                 GSL 1.16
 280               </p>
 281             </th>
 282 <th>
 283               <p>
 284                 Rmath 3.0.2
 285               </p>
 286             </th>
 287 <th>
 288               <p>
 289                 math.h
 290               </p>
 291             </th>
 292 </tr></thead>
 293 <tbody>
 294 <tr>
 295 <td>
 296               <p>
 297                 assoc_laguerre<br> (2240/2240 tests selected)
 298               </p>
 299             </td>
 300 <td>
 301               <p>
 302                 <span class="blue">1.36<br> (263ns)</span>
 303               </p>
 304             </td>
 305 <td>
 306               <p>
 307                 <span class="green">1.00<br> (194ns)</span>
 308               </p>
 309             </td>
 310 <td>
 311               <p>
 312                 <span class="green">1.20<br> (232ns)</span>
 313               </p>
 314             </td>
 315 <td>
 316               <p>
 317                 <span class="green">1.12<br> (218ns)</span>
 318               </p>
 319             </td>
 320 <td>
 321               <p>
 322                 <span class="grey">-</span>
 323               </p>
 324             </td>
 325 <td>
 326               <p>
 327                 <span class="grey">-</span>
 328               </p>
 329             </td>
 330 </tr>
 331 <tr>
 332 <td>
 333               <p>
 334                 assoc_legendre<br> (205/400 tests selected)
 335               </p>
 336             </td>
 337 <td>
 338               <p>
 339                 <span class="red">4.16<br> (258ns)</span>
 340               </p>
 341             </td>
 342 <td>
 343               <p>
 344                 <span class="blue">1.63<br> (101ns)</span>
 345               </p>
 346             </td>
 347 <td>
 348               <p>
 349                 <span class="green">1.00<br> (62ns)</span>
 350               </p>
 351             </td>
 352 <td>
 353               <p>
 354                 <span class="red">2.53<br> (157ns)</span>
 355               </p>
 356             </td>
 357 <td>
 358               <p>
 359                 <span class="grey">-</span>
 360               </p>
 361             </td>
 362 <td>
 363               <p>
 364                 <span class="grey">-</span>
 365               </p>
 366             </td>
 367 </tr>
 368 <tr>
 369 <td>
 370               <p>
 371                 beta (incomplete)<br> (2682/3210 tests selected)
 372               </p>
 373             </td>
 374 <td>
 375               <p>
 376                 <span class="red">3.12<br> (1796ns)</span>
 377               </p>
 378             </td>
 379 <td>
 380               <p>
 381                 <span class="green">1.00<br> (575ns)</span>
 382               </p>
 383             </td>
 384 <td>
 385               <p>
 386                 <span class="grey">-</span>
 387               </p>
 388             </td>
 389 <td>
 390               <p>
 391                 <span class="blue">1.36<br> (780ns)</span>
 392               </p>
 393             </td>
 394 <td>
 395               <p>
 396                 <span class="grey">-</span>
 397               </p>
 398             </td>
 399 <td>
 400               <p>
 401                 <span class="grey">-</span>
 402               </p>
 403             </td>
 404 </tr>
 405 <tr>
 406 <td>
 407               <p>
 408                 beta<br> (2203/2204 tests selected)
 409               </p>
 410             </td>
 411 <td>
 412               <p>
 413                 <span class="red">4.74<br> (734ns)</span>
 414               </p>
 415             </td>
 416 <td>
 417               <p>
 418                 <span class="green">1.01<br> (156ns)</span>
 419               </p>
 420             </td>
 421 <td>
 422               <p>
 423                 <span class="green">1.00<br> (155ns)</span>
 424               </p>
 425             </td>
 426 <td>
 427               <p>
 428                 <span class="red">2.57<br> (398ns)</span>
 429               </p>
 430             </td>
 431 <td>
 432               <p>
 433                 <span class="blue">1.65<br> (255ns)</span>
 434               </p>
 435             </td>
 436 <td>
 437               <p>
 438                 <span class="grey">-</span>
 439               </p>
 440             </td>
 441 </tr>
 442 <tr>
 443 <td>
 444               <p>
 445                 cbrt<br> (85/85 tests selected)
 446               </p>
 447             </td>
 448 <td>
 449               <p>
 450                 <span class="red">2.53<br> (43ns)</span>
 451               </p>
 452             </td>
 453 <td>
 454               <p>
 455                 <span class="green">1.00<br> (17ns)</span>
 456               </p>
 457             </td>
 458 <td>
 459               <p>
 460                 <span class="blue">1.24<br> (21ns)</span>
 461               </p>
 462             </td>
 463 <td>
 464               <p>
 465                 <span class="grey">-</span>
 466               </p>
 467             </td>
 468 <td>
 469               <p>
 470                 <span class="grey">-</span>
 471               </p>
 472             </td>
 473 <td>
 474               <p>
 475                 <span class="blue">1.24<br> (21ns)</span>
 476               </p>
 477             </td>
 478 </tr>
 479 <tr>
 480 <td>
 481               <p>
 482                 cyl_bessel_i (integer order)<br> (494/526 tests selected)
 483               </p>
 484             </td>
 485 <td>
 486               <p>
 487                 <span class="red">3.66<br> (893ns)</span>
 488               </p>
 489             </td>
 490 <td>
 491               <p>
 492                 <span class="green">1.08<br> (264ns)</span>
 493               </p>
 494             </td>
 495 <td>
 496               <p>
 497                 <span class="green">1.00<br> (244ns)</span>
 498               </p>
 499             </td>
 500 <td>
 501               <p>
 502                 <span class="blue">1.98<br> (482ns)</span>
 503               </p>
 504             </td>
 505 <td>
 506               <p>
 507                 <span class="red">4.69<br> (1145ns)</span>
 508               </p>
 509             </td>
 510 <td>
 511             </td>
 512 </tr>
 513 <tr>
 514 <td>
 515               <p>
 516                 cyl_bessel_i<br> (177/240 tests selected)
 517               </p>
 518             </td>
 519 <td>
 520               <p>
 521                 <span class="red">6.78<br> (1410ns)</span>
 522               </p>
 523             </td>
 524 <td>
 525               <p>
 526                 <span class="blue">1.95<br> (406ns)</span>
 527               </p>
 528             </td>
 529 <td>
 530               <p>
 531                 <span class="green">1.00<br> (208ns)</span>
 532               </p>
 533             </td>
 534 <td>
 535               <p>
 536                 <span class="red">4.47<br> (929ns)</span>
 537               </p>
 538             </td>
 539 <td>
 540               <p>
 541                 <span class="red">8.16<br> (1698ns)</span>
 542               </p>
 543             </td>
 544 <td>
 545               <p>
 546                 <span class="grey">-</span>
 547               </p>
 548             </td>
 549 </tr>
 550 <tr>
 551 <td>
 552               <p>
 553                 cyl_bessel_j (integer order)<br> (250/268 tests selected)
 554               </p>
 555             </td>
 556 <td>
 557               <p>
 558                 <span class="red">2.59<br> (275ns)</span>
 559               </p>
 560             </td>
 561 <td>
 562               <p>
 563                 <span class="green">1.00<br> (106ns)</span>
 564               </p>
 565             </td>
 566 <td>
 567               <p>
 568                 <span class="red">2.50<br> (265ns)</span>
 569               </p>
 570             </td>
 571 <td>
 572               <p>
 573                 <span class="red">2.52<br> (267ns)</span>
 574               </p>
 575             </td>
 576 <td>
 577               <p>
 578                 <span class="red">4.22<br> (447ns)</span>
 579               </p>
 580             </td>
 581 <td>
 582               <p>
 583                 <span class="blue">1.94<br> (206ns)</span>
 584               </p>
 585             </td>
 586 </tr>
 587 <tr>
 588 <td>
 589               <p>
 590                 cyl_bessel_j<br> (423/451 tests selected)
 591               </p>
 592             </td>
 593 <td>
 594               <p>
 595                 <span class="red">2.83<br> (1071ns)</span>
 596               </p>
 597             </td>
 598 <td>
 599               <p>
 600                 <span class="green">1.05<br> (398ns)</span>
 601               </p>
 602             </td>
 603 <td>
 604               <p>
 605                 <span class="green">1.00<br> (379ns)</span>
 606               </p>
 607             </td>
 608 <td>
 609               <p>
 610                 <span class="red">2.28<br> (865ns)</span>
 611               </p>
 612             </td>
 613 <td>
 614               <p>
 615                 <span class="blue">1.20<br> (456ns)</span>
 616               </p>
 617             </td>
 618 <td>
 619               <p>
 620                 <span class="grey">-</span>
 621               </p>
 622             </td>
 623 </tr>
 624 <tr>
 625 <td>
 626               <p>
 627                 cyl_bessel_k (integer order)<br> (505/508 tests selected)
 628               </p>
 629             </td>
 630 <td>
 631               <p>
 632                 <span class="red">13.91<br> (3673ns)</span>
 633               </p>
 634             </td>
 635 <td>
 636               <p>
 637                 <span class="blue">1.37<br> (361ns)</span>
 638               </p>
 639             </td>
 640 <td>
 641               <p>
 642                 <span class="red">10.34<br> (2729ns)</span>
 643               </p>
 644             </td>
 645 <td>
 646               <p>
 647                 <span class="green">1.00<br> (264ns)</span>
 648               </p>
 649             </td>
 650 <td>
 651               <p>
 652                 <span class="blue">1.34<br> (355ns)</span>
 653               </p>
 654             </td>
 655 <td>
 656               <p>
 657                 <span class="grey">-</span>
 658               </p>
 659             </td>
 660 </tr>
 661 <tr>
 662 <td>
 663               <p>
 664                 cyl_bessel_k<br> (96/279 tests selected)
 665               </p>
 666             </td>
 667 <td>
 668               <p>
 669                 <span class="red">6.86<br> (4589ns)</span>
 670               </p>
 671             </td>
 672 <td>
 673               <p>
 674                 <span class="green">1.00<br> (669ns)</span>
 675               </p>
 676             </td>
 677 <td>
 678               <p>
 679                 <span class="blue">1.20<br> (803ns)</span>
 680               </p>
 681             </td>
 682 <td>
 683               <p>
 684                 <span class="blue">1.31<br> (877ns)</span>
 685               </p>
 686             </td>
 687 <td>
 688               <p>
 689                 <span class="blue">1.27<br> (851ns)</span>
 690               </p>
 691             </td>
 692 <td>
 693               <p>
 694                 <span class="grey">-</span>
 695               </p>
 696             </td>
 697 </tr>
 698 <tr>
 699 <td>
 700               <p>
 701                 cyl_neumann (integer order)<br> (423/428 tests selected)
 702               </p>
 703             </td>
 704 <td>
 705               <p>
 706                 <span class="red">2.20<br> (484ns)</span>
 707               </p>
 708             </td>
 709 <td>
 710               <p>
 711                 <span class="green">1.00<br> (220ns)</span>
 712               </p>
 713             </td>
 714 <td>
 715               <p>
 716                 <span class="red">3.26<br> (718ns)</span>
 717               </p>
 718             </td>
 719 <td>
 720               <p>
 721                 <span class="red">2.42<br> (533ns)</span>
 722               </p>
 723             </td>
 724 <td>
 725               <p>
 726                 <span class="red">4.95<br> (1089ns)</span>
 727               </p>
 728             </td>
 729 <td>
 730               <p>
 731                 <span class="blue">1.78<br> (392ns)</span>
 732               </p>
 733             </td>
 734 </tr>
 735 <tr>
 736 <td>
 737               <p>
 738                 cyl_neumann<br> (400/450 tests selected)
 739               </p>
 740             </td>
 741 <td>
 742               <p>
 743                 <span class="red">2.48<br> (1478ns)</span>
 744               </p>
 745             </td>
 746 <td>
 747               <p>
 748                 <span class="green">1.00<br> (597ns)</span>
 749               </p>
 750             </td>
 751 <td>
 752               <p>
 753                 <span class="blue">1.26<br> (754ns)</span>
 754               </p>
 755             </td>
 756 <td>
 757               <p>
 758                 <span class="red">2.42<br> (1444ns)</span>
 759               </p>
 760             </td>
 761 <td>
 762               <p>
 763                 <span class="green">1.07<br> (637ns)</span>
 764               </p>
 765             </td>
 766 <td>
 767               <p>
 768                 <span class="grey">-</span>
 769               </p>
 770             </td>
 771 </tr>
 772 <tr>
 773 <td>
 774               <p>
 775                 digamma<br> (1019/1019 tests selected)
 776               </p>
 777             </td>
 778 <td>
 779               <p>
 780                 <span class="blue">1.92<br> (75ns)</span>
 781               </p>
 782             </td>
 783 <td>
 784               <p>
 785                 <span class="green">1.00<br> (39ns)</span>
 786               </p>
 787             </td>
 788 <td>
 789               <p>
 790                 <span class="grey">-</span>
 791               </p>
 792             </td>
 793 <td>
 794               <p>
 795                 <span class="red">2.69<br> (105ns)</span>
 796               </p>
 797             </td>
 798 <td>
 799               <p>
 800                 <span class="red">4.31<br> (168ns)</span>
 801               </p>
 802             </td>
 803 <td>
 804               <p>
 805                 <span class="grey">-</span>
 806               </p>
 807             </td>
 808 </tr>
 809 <tr>
 810 <td>
 811               <p>
 812                 ellint_1 (complete)<br> (109/109 tests selected)
 813               </p>
 814             </td>
 815 <td>
 816               <p>
 817                 <span class="blue">1.86<br> (52ns)</span>
 818               </p>
 819             </td>
 820 <td>
 821               <p>
 822                 <span class="green">1.00<br> (28ns)</span>
 823               </p>
 824             </td>
 825 <td>
 826               <p>
 827                 <span class="red">8.89<br> (249ns)</span>
 828               </p>
 829             </td>
 830 <td>
 831               <p>
 832                 <span class="red">10.54<br> (295ns)</span>
 833               </p>
 834             </td>
 835 <td>
 836               <p>
 837                 <span class="grey">-</span>
 838               </p>
 839             </td>
 840 <td>
 841             </td>
 842 </tr>
 843 <tr>
 844 <td>
 845               <p>
 846                 ellint_1<br> (627/629 tests selected)
 847               </p>
 848             </td>
 849 <td>
 850               <p>
 851                 <span class="blue">1.94<br> (358ns)</span>
 852               </p>
 853             </td>
 854 <td>
 855               <p>
 856                 <span class="green">1.00<br> (185ns)</span>
 857               </p>
 858             </td>
 859 <td>
 860               <p>
 861                 <span class="red">2.31<br> (428ns)</span>
 862               </p>
 863             </td>
 864 <td>
 865               <p>
 866                 <span class="red">2.51<br> (464ns)</span>
 867               </p>
 868             </td>
 869 <td>
 870               <p>
 871                 <span class="grey">-</span>
 872               </p>
 873             </td>
 874 <td>
 875               <p>
 876                 <span class="grey">-</span>
 877               </p>
 878             </td>
 879 </tr>
 880 <tr>
 881 <td>
 882               <p>
 883                 ellint_2 (complete)<br> (109/110 tests selected)
 884               </p>
 885             </td>
 886 <td>
 887               <p>
 888                 <span class="blue">1.71<br> (60ns)</span>
 889               </p>
 890             </td>
 891 <td>
 892               <p>
 893                 <span class="green">1.00<br> (35ns)</span>
 894               </p>
 895             </td>
 896 <td>
 897               <p>
 898                 <span class="red">15.23<br> (533ns)</span>
 899               </p>
 900             </td>
 901 <td>
 902               <p>
 903                 <span class="red">17.31<br> (606ns)</span>
 904               </p>
 905             </td>
 906 <td>
 907               <p>
 908                 <span class="grey">-</span>
 909               </p>
 910             </td>
 911 <td>
 912               <p>
 913                 <span class="grey">-</span>
 914               </p>
 915             </td>
 916 </tr>
 917 <tr>
 918 <td>
 919               <p>
 920                 ellint_2<br> (527/530 tests selected)
 921               </p>
 922             </td>
 923 <td>
 924               <p>
 925                 <span class="red">2.32<br> (805ns)</span>
 926               </p>
 927             </td>
 928 <td>
 929               <p>
 930                 <span class="green">1.00<br> (347ns)</span>
 931               </p>
 932             </td>
 933 <td>
 934               <p>
 935                 <span class="blue">1.90<br> (658ns)</span>
 936               </p>
 937             </td>
 938 <td>
 939               <p>
 940                 <span class="red">2.17<br> (754ns)</span>
 941               </p>
 942             </td>
 943 <td>
 944               <p>
 945                 <span class="grey">-</span>
 946               </p>
 947             </td>
 948 <td>
 949               <p>
 950                 <span class="grey">-</span>
 951               </p>
 952             </td>
 953 </tr>
 954 <tr>
 955 <td>
 956               <p>
 957                 ellint_3 (complete)<br> (500/500 tests selected)
 958               </p>
 959             </td>
 960 <td>
 961               <p>
 962                 <span class="red">2.23<br> (1172ns)</span>
 963               </p>
 964             </td>
 965 <td>
 966               <p>
 967                 <span class="green">1.00<br> (525ns)</span>
 968               </p>
 969             </td>
 970 <td>
 971               <p>
 972                 <span class="blue">1.66<br> (873ns)</span>
 973               </p>
 974             </td>
 975 <td>
 976               <p>
 977                 <span class="blue">1.98<br> (1037ns)</span>
 978               </p>
 979             </td>
 980 <td>
 981             </td>
 982 <td>
 983             </td>
 984 </tr>
 985 <tr>
 986 <td>
 987               <p>
 988                 ellint_3<br> (831/845 tests selected)
 989               </p>
 990             </td>
 991 <td>
 992               <p>
 993                 <span class="red">2.75<br> (2154ns)</span>
 994               </p>
 995             </td>
 996 <td>
 997               <p>
 998                 <span class="green">1.00<br> (783ns)</span>
 999               </p>
1000             </td>
1001 <td>
1002               <p>
1003                 <span class="blue">1.59<br> (1243ns)</span>
1004               </p>
1005             </td>
1006 <td>
1007               <p>
1008                 <span class="blue">1.77<br> (1383ns)</span>
1009               </p>
1010             </td>
1011 <td>
1012               <p>
1013                 <span class="grey">-</span>
1014               </p>
1015             </td>
1016 <td>
1017               <p>
1018                 <span class="grey">-</span>
1019               </p>
1020             </td>
1021 </tr>
1022 <tr>
1023 <td>
1024               <p>
1025                 ellint_rc<br> (201/201 tests selected)
1026               </p>
1027             </td>
1028 <td>
1029               <p>
1030                 <span class="blue">1.57<br> (77ns)</span>
1031               </p>
1032             </td>
1033 <td>
1034               <p>
1035                 <span class="green">1.00<br> (49ns)</span>
1036               </p>
1037             </td>
1038 <td>
1039               <p>
1040                 <span class="grey">-</span>
1041               </p>
1042             </td>
1043 <td>
1044               <p>
1045                 <span class="red">4.41<br> (216ns)</span>
1046               </p>
1047             </td>
1048 <td>
1049               <p>
1050                 <span class="grey">-</span>
1051               </p>
1052             </td>
1053 <td>
1054               <p>
1055                 <span class="grey">-</span>
1056               </p>
1057             </td>
1058 </tr>
1059 <tr>
1060 <td>
1061               <p>
1062                 ellint_rd<br> (7588/7588 tests selected)
1063               </p>
1064             </td>
1065 <td>
1066               <p>
1067                 <span class="red">2.23<br> (520ns)</span>
1068               </p>
1069             </td>
1070 <td>
1071               <p>
1072                 <span class="green">1.00<br> (233ns)</span>
1073               </p>
1074             </td>
1075 <td>
1076               <p>
1077                 <span class="grey">-</span>
1078               </p>
1079             </td>
1080 <td>
1081               <p>
1082                 <span class="blue">1.64<br> (381ns)</span>
1083               </p>
1084             </td>
1085 <td>
1086               <p>
1087                 <span class="grey">-</span>
1088               </p>
1089             </td>
1090 <td>
1091               <p>
1092                 <span class="grey">-</span>
1093               </p>
1094             </td>
1095 </tr>
1096 <tr>
1097 <td>
1098               <p>
1099                 ellint_rf<br> (7788/7788 tests selected)
1100               </p>
1101             </td>
1102 <td>
1103               <p>
1104                 <span class="blue">1.51<br> (95ns)</span>
1105               </p>
1106             </td>
1107 <td>
1108               <p>
1109                 <span class="green">1.00<br> (63ns)</span>
1110               </p>
1111             </td>
1112 <td>
1113               <p>
1114                 <span class="grey">-</span>
1115               </p>
1116             </td>
1117 <td>
1118               <p>
1119                 <span class="red">5.54<br> (349ns)</span>
1120               </p>
1121             </td>
1122 <td>
1123               <p>
1124                 <span class="grey">-</span>
1125               </p>
1126             </td>
1127 <td>
1128               <p>
1129                 <span class="grey">-</span>
1130               </p>
1131             </td>
1132 </tr>
1133 <tr>
1134 <td>
1135               <p>
1136                 ellint_rj<br> (7642/8032 tests selected)
1137               </p>
1138             </td>
1139 <td>
1140               <p>
1141                 <span class="red">2.33<br> (481ns)</span>
1142               </p>
1143             </td>
1144 <td>
1145               <p>
1146                 <span class="green">1.00<br> (206ns)</span>
1147               </p>
1148             </td>
1149 <td>
1150               <p>
1151                 <span class="grey">-</span>
1152               </p>
1153             </td>
1154 <td>
1155               <p>
1156                 <span class="red">11.31<br> (2329ns)</span>
1157               </p>
1158             </td>
1159 <td>
1160               <p>
1161                 <span class="grey">-</span>
1162               </p>
1163             </td>
1164 <td>
1165               <p>
1166                 <span class="grey">-</span>
1167               </p>
1168             </td>
1169 </tr>
1170 <tr>
1171 <td>
1172               <p>
1173                 erf<br> (950/950 tests selected)
1174               </p>
1175             </td>
1176 <td>
1177               <p>
1178                 <span class="green">1.00<br> (15ns)</span>
1179               </p>
1180             </td>
1181 <td>
1182               <p>
1183                 <span class="grey">-</span>
1184               </p>
1185             </td>
1186 <td>
1187               <p>
1188                 <span class="green">1.20<br> (18ns)</span>
1189               </p>
1190             </td>
1191 <td>
1192               <p>
1193                 <span class="red">10.27<br> (154ns)</span>
1194               </p>
1195             </td>
1196 <td>
1197               <p>
1198                 <span class="grey">-</span>
1199               </p>
1200             </td>
1201 <td>
1202               <p>
1203                 <span class="green">1.20<br> (18ns)</span>
1204               </p>
1205             </td>
1206 </tr>
1207 <tr>
1208 <td>
1209               <p>
1210                 erfc<br> (950/950 tests selected)
1211               </p>
1212             </td>
1213 <td>
1214               <p>
1215                 <span class="red">2.68<br> (59ns)</span>
1216               </p>
1217             </td>
1218 <td>
1219               <p>
1220                 <span class="green">1.00<br> (22ns)</span>
1221               </p>
1222             </td>
1223 <td>
1224               <p>
1225                 <span class="green">1.18<br> (26ns)</span>
1226               </p>
1227             </td>
1228 <td>
1229               <p>
1230                 <span class="red">3.50<br> (77ns)</span>
1231               </p>
1232             </td>
1233 <td>
1234               <p>
1235                 <span class="grey">-</span>
1236               </p>
1237             </td>
1238 <td>
1239               <p>
1240                 <span class="green">1.14<br> (25ns)</span>
1241               </p>
1242             </td>
1243 </tr>
1244 <tr>
1245 <td>
1246               <p>
1247                 expint (En)<br> (1059/1059 tests selected)
1248               </p>
1249             </td>
1250 <td>
1251               <p>
1252                 <span class="blue">1.86<br> (273ns)</span>
1253               </p>
1254             </td>
1255 <td>
1256               <p>
1257                 <span class="green">1.00<br> (147ns)</span>
1258               </p>
1259             </td>
1260 <td>
1261               <p>
1262                 <span class="grey">-</span>
1263               </p>
1264             </td>
1265 <td>
1266               <p>
1267                 <span class="red">4.87<br> (716ns)</span>
1268               </p>
1269             </td>
1270 <td>
1271               <p>
1272                 <span class="grey">-</span>
1273               </p>
1274             </td>
1275 <td>
1276               <p>
1277                 <span class="grey">-</span>
1278               </p>
1279             </td>
1280 </tr>
1281 <tr>
1282 <td>
1283               <p>
1284                 expint<br> (436/436 tests selected)
1285               </p>
1286             </td>
1287 <td>
1288               <p>
1289                 <span class="red">2.47<br> (94ns)</span>
1290               </p>
1291             </td>
1292 <td>
1293               <p>
1294                 <span class="green">1.00<br> (38ns)</span>
1295               </p>
1296             </td>
1297 <td>
1298               <p>
1299                 <span class="red">5.34<br> (203ns)</span>
1300               </p>
1301             </td>
1302 <td>
1303               <p>
1304                 <span class="red">3.76<br> (143ns)</span>
1305               </p>
1306             </td>
1307 <td>
1308               <p>
1309                 <span class="grey">-</span>
1310               </p>
1311             </td>
1312 <td>
1313               <p>
1314                 <span class="grey">-</span>
1315               </p>
1316             </td>
1317 </tr>
1318 <tr>
1319 <td>
1320               <p>
1321                 expm1<br> (80/80 tests selected)
1322               </p>
1323             </td>
1324 <td>
1325               <p>
1326                 <span class="green">1.00<br> (10ns)</span>
1327               </p>
1328             </td>
1329 <td>
1330               <p>
1331                 <span class="green">1.10<br> (11ns)</span>
1332               </p>
1333             </td>
1334 <td>
1335               <p>
1336                 <span class="green">1.00<br> (10ns)</span>
1337               </p>
1338             </td>
1339 <td>
1340               <p>
1341                 <span class="grey">-</span>
1342               </p>
1343             </td>
1344 <td>
1345               <p>
1346                 <span class="grey">-</span>
1347               </p>
1348             </td>
1349 <td>
1350               <p>
1351                 <span class="green">1.00<br> (10ns)</span>
1352               </p>
1353             </td>
1354 </tr>
1355 <tr>
1356 <td>
1357               <p>
1358                 gamma_p<br> (1379/1379 tests selected)
1359               </p>
1360             </td>
1361 <td>
1362               <p>
1363                 <span class="red">2.42<br> (492ns)</span>
1364               </p>
1365             </td>
1366 <td>
1367               <p>
1368                 <span class="green">1.00<br> (203ns)</span>
1369               </p>
1370             </td>
1371 <td>
1372               <p>
1373                 <span class="grey">-</span>
1374               </p>
1375             </td>
1376 <td>
1377               <p>
1378                 <span class="red">4.77<br> (968ns)</span>
1379               </p>
1380             </td>
1381 <td>
1382               <p>
1383                 <span class="blue">1.61<br> (326ns)</span>
1384               </p>
1385             </td>
1386 <td>
1387               <p>
1388                 <span class="grey">-</span>
1389               </p>
1390             </td>
1391 </tr>
1392 <tr>
1393 <td>
1394               <p>
1395                 gamma_p_inv<br> (559/559 tests selected)
1396               </p>
1397             </td>
1398 <td>
1399               <p>
1400                 <span class="red">2.24<br> (1577ns)</span>
1401               </p>
1402             </td>
1403 <td>
1404               <p>
1405                 <span class="green">1.00<br> (704ns)</span>
1406               </p>
1407             </td>
1408 <td>
1409               <p>
1410                 <span class="grey">-</span>
1411               </p>
1412             </td>
1413 <td>
1414               <p>
1415                 <span class="grey">-</span>
1416               </p>
1417             </td>
1418 <td>
1419               <p>
1420                 <span class="red">2.22<br> (1560ns)</span>
1421               </p>
1422             </td>
1423 <td>
1424               <p>
1425                 <span class="grey">-</span>
1426               </p>
1427             </td>
1428 </tr>
1429 <tr>
1430 <td>
1431               <p>
1432                 gamma_q<br> (1371/1379 tests selected)
1433               </p>
1434             </td>
1435 <td>
1436               <p>
1437                 <span class="red">2.53<br> (508ns)</span>
1438               </p>
1439             </td>
1440 <td>
1441               <p>
1442                 <span class="green">1.00<br> (201ns)</span>
1443               </p>
1444             </td>
1445 <td>
1446               <p>
1447                 <span class="grey">-</span>
1448               </p>
1449             </td>
1450 <td>
1451               <p>
1452                 <span class="red">5.70<br> (1146ns)</span>
1453               </p>
1454             </td>
1455 <td>
1456               <p>
1457                 <span class="blue">1.78<br> (358ns)</span>
1458               </p>
1459             </td>
1460 <td>
1461               <p>
1462                 <span class="grey">-</span>
1463               </p>
1464             </td>
1465 </tr>
1466 <tr>
1467 <td>
1468               <p>
1469                 gamma_q_inv<br> (78/559 tests selected)
1470               </p>
1471             </td>
1472 <td>
1473               <p>
1474                 <span class="red">2.45<br> (1841ns)</span>
1475               </p>
1476             </td>
1477 <td>
1478               <p>
1479                 <span class="green">1.00<br> (751ns)</span>
1480               </p>
1481             </td>
1482 <td>
1483               <p>
1484                 <span class="grey">-</span>
1485               </p>
1486             </td>
1487 <td>
1488               <p>
1489                 <span class="grey">-</span>
1490               </p>
1491             </td>
1492 <td>
1493               <p>
1494                 <span class="green">1.09<br> (822ns)</span>
1495               </p>
1496             </td>
1497 <td>
1498               <p>
1499                 <span class="grey">-</span>
1500               </p>
1501             </td>
1502 </tr>
1503 <tr>
1504 <td>
1505               <p>
1506                 ibeta<br> (3210/3210 tests selected)
1507               </p>
1508             </td>
1509 <td>
1510               <p>
1511                 <span class="red">3.47<br> (1715ns)</span>
1512               </p>
1513             </td>
1514 <td>
1515               <p>
1516                 <span class="blue">1.28<br> (634ns)</span>
1517               </p>
1518             </td>
1519 <td>
1520               <p>
1521                 <span class="grey">-</span>
1522               </p>
1523             </td>
1524 <td>
1525               <p>
1526                 <span class="grey">-</span>
1527               </p>
1528             </td>
1529 <td>
1530               <p>
1531                 <span class="green">1.00<br> (494ns)</span>
1532               </p>
1533             </td>
1534 <td>
1535               <p>
1536                 <span class="grey">-</span>
1537               </p>
1538             </td>
1539 </tr>
1540 <tr>
1541 <td>
1542               <p>
1543                 ibeta_inv<br> (952/1210 tests selected)
1544               </p>
1545             </td>
1546 <td>
1547               <p>
1548                 <span class="red">2.58<br> (5742ns)</span>
1549               </p>
1550             </td>
1551 <td>
1552               <p>
1553                 <span class="green">1.00<br> (2224ns)</span>
1554               </p>
1555             </td>
1556 <td>
1557               <p>
1558                 <span class="grey">-</span>
1559               </p>
1560             </td>
1561 <td>
1562               <p>
1563                 <span class="grey">-</span>
1564               </p>
1565             </td>
1566 <td>
1567               <p>
1568                 <span class="red">26.72<br> (59415ns)</span>
1569               </p>
1570             </td>
1571 <td>
1572               <p>
1573                 <span class="grey">-</span>
1574               </p>
1575             </td>
1576 </tr>
1577 <tr>
1578 <td>
1579               <p>
1580                 ibetac<br> (3210/3210 tests selected)
1581               </p>
1582             </td>
1583 <td>
1584               <p>
1585                 <span class="red">3.51<br> (1736ns)</span>
1586               </p>
1587             </td>
1588 <td>
1589               <p>
1590                 <span class="blue">1.32<br> (653ns)</span>
1591               </p>
1592             </td>
1593 <td>
1594               <p>
1595                 <span class="grey">-</span>
1596               </p>
1597             </td>
1598 <td>
1599               <p>
1600                 <span class="grey">-</span>
1601               </p>
1602             </td>
1603 <td>
1604               <p>
1605                 <span class="green">1.00<br> (495ns)</span>
1606               </p>
1607             </td>
1608 <td>
1609               <p>
1610                 <span class="grey">-</span>
1611               </p>
1612             </td>
1613 </tr>
1614 <tr>
1615 <td>
1616               <p>
1617                 ibetac_inv<br> (945/1210 tests selected)
1618               </p>
1619             </td>
1620 <td>
1621               <p>
1622                 <span class="red">2.44<br> (5451ns)</span>
1623               </p>
1624             </td>
1625 <td>
1626               <p>
1627                 <span class="green">1.00<br> (2237ns)</span>
1628               </p>
1629             </td>
1630 <td>
1631               <p>
1632                 <span class="grey">-</span>
1633               </p>
1634             </td>
1635 <td>
1636               <p>
1637                 <span class="grey">-</span>
1638               </p>
1639             </td>
1640 <td>
1641               <p>
1642                 <span class="red">19.20<br> (42953ns)</span>
1643               </p>
1644             </td>
1645 <td>
1646               <p>
1647                 <span class="grey">-</span>
1648               </p>
1649             </td>
1650 </tr>
1651 <tr>
1652 <td>
1653               <p>
1654                 jacobi_cn<br> (2368/2757 tests selected)
1655               </p>
1656             </td>
1657 <td>
1658               <p>
1659                 <span class="red">5.01<br> (476ns)</span>
1660               </p>
1661             </td>
1662 <td>
1663               <p>
1664                 <span class="blue">1.81<br> (172ns)</span>
1665               </p>
1666             </td>
1667 <td>
1668               <p>
1669                 <span class="grey">-</span>
1670               </p>
1671             </td>
1672 <td>
1673               <p>
1674                 <span class="green">1.00<br> (95ns)</span>
1675               </p>
1676             </td>
1677 <td>
1678               <p>
1679                 <span class="grey">-</span>
1680               </p>
1681             </td>
1682 <td>
1683               <p>
1684                 <span class="grey">-</span>
1685               </p>
1686             </td>
1687 </tr>
1688 <tr>
1689 <td>
1690               <p>
1691                 jacobi_dn<br> (2368/2757 tests selected)
1692               </p>
1693             </td>
1694 <td>
1695               <p>
1696                 <span class="red">5.12<br> (481ns)</span>
1697               </p>
1698             </td>
1699 <td>
1700               <p>
1701                 <span class="blue">1.83<br> (172ns)</span>
1702               </p>
1703             </td>
1704 <td>
1705               <p>
1706                 <span class="grey">-</span>
1707               </p>
1708             </td>
1709 <td>
1710               <p>
1711                 <span class="green">1.00<br> (94ns)</span>
1712               </p>
1713             </td>
1714 <td>
1715               <p>
1716                 <span class="grey">-</span>
1717               </p>
1718             </td>
1719 <td>
1720               <p>
1721                 <span class="grey">-</span>
1722               </p>
1723             </td>
1724 </tr>
1725 <tr>
1726 <td>
1727               <p>
1728                 jacobi_sn<br> (2368/2757 tests selected)
1729               </p>
1730             </td>
1731 <td>
1732               <p>
1733                 <span class="red">5.23<br> (492ns)</span>
1734               </p>
1735             </td>
1736 <td>
1737               <p>
1738                 <span class="blue">1.83<br> (172ns)</span>
1739               </p>
1740             </td>
1741 <td>
1742               <p>
1743                 <span class="grey">-</span>
1744               </p>
1745             </td>
1746 <td>
1747               <p>
1748                 <span class="green">1.00<br> (94ns)</span>
1749               </p>
1750             </td>
1751 <td>
1752               <p>
1753                 <span class="grey">-</span>
1754               </p>
1755             </td>
1756 <td>
1757               <p>
1758                 <span class="grey">-</span>
1759               </p>
1760             </td>
1761 </tr>
1762 <tr>
1763 <td>
1764               <p>
1765                 laguerre<br> (280/280 tests selected)
1766               </p>
1767             </td>
1768 <td>
1769               <p>
1770                 <span class="green">1.09<br> (139ns)</span>
1771               </p>
1772             </td>
1773 <td>
1774               <p>
1775                 <span class="green">1.00<br> (128ns)</span>
1776               </p>
1777             </td>
1778 <td>
1779               <p>
1780                 <span class="blue">1.25<br> (160ns)</span>
1781               </p>
1782             </td>
1783 <td>
1784               <p>
1785                 <span class="green">1.18<br> (151ns)</span>
1786               </p>
1787             </td>
1788 <td>
1789               <p>
1790                 <span class="grey">-</span>
1791               </p>
1792             </td>
1793 <td>
1794               <p>
1795                 <span class="grey">-</span>
1796               </p>
1797             </td>
1798 </tr>
1799 <tr>
1800 <td>
1801               <p>
1802                 legendre Q<br> (300/300 tests selected)
1803               </p>
1804             </td>
1805 <td>
1806               <p>
1807                 <span class="green">1.18<br> (496ns)</span>
1808               </p>
1809             </td>
1810 <td>
1811               <p>
1812                 <span class="green">1.00<br> (422ns)</span>
1813               </p>
1814             </td>
1815 <td>
1816               <p>
1817                 <span class="grey">-</span>
1818               </p>
1819             </td>
1820 <td>
1821               <p>
1822                 <span class="green">1.09<br> (461ns)</span>
1823               </p>
1824             </td>
1825 <td>
1826               <p>
1827                 <span class="grey">-</span>
1828               </p>
1829             </td>
1830 <td>
1831               <p>
1832                 <span class="grey">-</span>
1833               </p>
1834             </td>
1835 </tr>
1836 <tr>
1837 <td>
1838               <p>
1839                 legendre<br> (300/300 tests selected)
1840               </p>
1841             </td>
1842 <td>
1843               <p>
1844                 <span class="green">1.16<br> (399ns)</span>
1845               </p>
1846             </td>
1847 <td>
1848               <p>
1849                 <span class="green">1.00<br> (345ns)</span>
1850               </p>
1851             </td>
1852 <td>
1853               <p>
1854                 <span class="green">1.10<br> (380ns)</span>
1855               </p>
1856             </td>
1857 <td>
1858               <p>
1859                 <span class="red">2.10<br> (726ns)</span>
1860               </p>
1861             </td>
1862 <td>
1863               <p>
1864                 <span class="grey">-</span>
1865               </p>
1866             </td>
1867 <td>
1868               <p>
1869                 <span class="grey">-</span>
1870               </p>
1871             </td>
1872 </tr>
1873 <tr>
1874 <td>
1875               <p>
1876                 lgamma<br> (400/400 tests selected)
1877               </p>
1878             </td>
1879 <td>
1880               <p>
1881                 <span class="red">5.35<br> (257ns)</span>
1882               </p>
1883             </td>
1884 <td>
1885               <p>
1886                 <span class="red">2.44<br> (117ns)</span>
1887               </p>
1888             </td>
1889 <td>
1890               <p>
1891                 <span class="green">1.00<br> (48ns)</span>
1892               </p>
1893             </td>
1894 <td>
1895               <p>
1896                 <span class="red">5.92<br> (284ns)</span>
1897               </p>
1898             </td>
1899 <td>
1900               <p>
1901                 <span class="blue">1.96<br> (94ns)</span>
1902               </p>
1903             </td>
1904 <td>
1905               <p>
1906                 <span class="green">1.00<br> (48ns)</span>
1907               </p>
1908             </td>
1909 </tr>
1910 <tr>
1911 <td>
1912               <p>
1913                 log1p<br> (80/80 tests selected)
1914               </p>
1915             </td>
1916 <td>
1917               <p>
1918                 <span class="green">1.09<br> (12ns)</span>
1919               </p>
1920             </td>
1921 <td>
1922               <p>
1923                 <span class="green">1.09<br> (12ns)</span>
1924               </p>
1925             </td>
1926 <td>
1927               <p>
1928                 <span class="green">1.00<br> (11ns)</span>
1929               </p>
1930             </td>
1931 <td>
1932               <p>
1933                 <span class="grey">-</span>
1934               </p>
1935             </td>
1936 <td>
1937               <p>
1938                 <span class="grey">-</span>
1939               </p>
1940             </td>
1941 <td>
1942               <p>
1943                 <span class="green">1.00<br> (11ns)</span>
1944               </p>
1945             </td>
1946 </tr>
1947 <tr>
1948 <td>
1949               <p>
1950                 polygamma<br> (823/1535 tests selected)
1951               </p>
1952             </td>
1953 <td>
1954               <p>
1955                 <span class="red">8.69<br> (2885ns)</span>
1956               </p>
1957             </td>
1958 <td>
1959               <p>
1960                 <span class="red">2.21<br> (734ns)</span>
1961               </p>
1962             </td>
1963 <td>
1964               <p>
1965                 <span class="grey">-</span>
1966               </p>
1967             </td>
1968 <td>
1969               <p>
1970                 <span class="red">7.47<br> (2480ns)</span>
1971               </p>
1972             </td>
1973 <td>
1974               <p>
1975                 <span class="green">1.00<br> (332ns)</span>
1976               </p>
1977             </td>
1978 <td>
1979               <p>
1980                 <span class="grey">-</span>
1981               </p>
1982             </td>
1983 </tr>
1984 <tr>
1985 <td>
1986               <p>
1987                 sph_bessel<br> (483/483 tests selected)
1988               </p>
1989             </td>
1990 <td>
1991               <p>
1992                 <span class="blue">1.71<br> (1563ns)</span>
1993               </p>
1994             </td>
1995 <td>
1996               <p>
1997                 <span class="green">1.00<br> (915ns)</span>
1998               </p>
1999             </td>
2000 <td>
2001               <p>
2002                 <span class="red">2.11<br> (1935ns)</span>
2003               </p>
2004             </td>
2005 <td>
2006               <p>
2007                 <span class="red">2.68<br> (2452ns)</span>
2008               </p>
2009             </td>
2010 <td>
2011               <p>
2012                 <span class="grey">-</span>
2013               </p>
2014             </td>
2015 <td>
2016               <p>
2017                 <span class="grey">-</span>
2018               </p>
2019             </td>
2020 </tr>
2021 <tr>
2022 <td>
2023               <p>
2024                 sph_neumann<br> (284/284 tests selected)
2025               </p>
2026             </td>
2027 <td>
2028               <p>
2029                 <span class="red">8.32<br> (3745ns)</span>
2030               </p>
2031             </td>
2032 <td>
2033               <p>
2034                 <span class="red">3.88<br> (1744ns)</span>
2035               </p>
2036             </td>
2037 <td>
2038               <p>
2039                 <span class="red">6.46<br> (2906ns)</span>
2040               </p>
2041             </td>
2042 <td>
2043               <p>
2044                 <span class="green">1.00<br> (450ns)</span>
2045               </p>
2046             </td>
2047 <td>
2048               <p>
2049                 <span class="grey">-</span>
2050               </p>
2051             </td>
2052 <td>
2053               <p>
2054                 <span class="grey">-</span>
2055               </p>
2056             </td>
2057 </tr>
2058 <tr>
2059 <td>
2060               <p>
2061                 tgamma (incomplete)<br> (1266/1379 tests selected)
2062               </p>
2063             </td>
2064 <td>
2065               <p>
2066                 <span class="red">2.35<br> (744ns)</span>
2067               </p>
2068             </td>
2069 <td>
2070               <p>
2071                 <span class="green">1.00<br> (316ns)</span>
2072               </p>
2073             </td>
2074 <td>
2075               <p>
2076                 <span class="grey">-</span>
2077               </p>
2078             </td>
2079 <td>
2080               <p>
2081                 <span class="red">2.93<br> (927ns)</span>
2082               </p>
2083             </td>
2084 <td>
2085               <p>
2086                 <span class="grey">-</span>
2087               </p>
2088             </td>
2089 <td>
2090               <p>
2091                 <span class="grey">-</span>
2092               </p>
2093             </td>
2094 </tr>
2095 <tr>
2096 <td>
2097               <p>
2098                 tgamma<br> (400/400 tests selected)
2099               </p>
2100             </td>
2101 <td>
2102               <p>
2103                 <span class="red">4.54<br> (354ns)</span>
2104               </p>
2105             </td>
2106 <td>
2107               <p>
2108                 <span class="blue">1.23<br> (96ns)</span>
2109               </p>
2110             </td>
2111 <td>
2112               <p>
2113                 <span class="red">2.05<br> (160ns)</span>
2114               </p>
2115             </td>
2116 <td>
2117               <p>
2118                 <span class="blue">1.21<br> (94ns)</span>
2119               </p>
2120             </td>
2121 <td>
2122               <p>
2123                 <span class="green">1.00<br> (78ns)</span>
2124               </p>
2125             </td>
2126 <td>
2127               <p>
2128                 <span class="red">2.06<br> (161ns)</span>
2129               </p>
2130             </td>
2131 </tr>
2132 <tr>
2133 <td>
2134               <p>
2135                 trigamma<br> (659/659 tests selected)
2136               </p>
2137             </td>
2138 <td>
2139               <p>
2140                 <span class="blue">1.64<br> (36ns)</span>
2141               </p>
2142             </td>
2143 <td>
2144               <p>
2145                 <span class="green">1.00<br> (22ns)</span>
2146               </p>
2147             </td>
2148 <td>
2149               <p>
2150                 <span class="grey">-</span>
2151               </p>
2152             </td>
2153 <td>
2154               <p>
2155                 <span class="red">39.41<br> (867ns)</span>
2156               </p>
2157             </td>
2158 <td>
2159               <p>
2160                 <span class="red">12.09<br> (266ns)</span>
2161               </p>
2162             </td>
2163 <td>
2164               <p>
2165                 <span class="grey">-</span>
2166               </p>
2167             </td>
2168 </tr>
2169 <tr>
2170 <td>
2171               <p>
2172                 zeta<br> (448/448 tests selected)
2173               </p>
2174             </td>
2175 <td>
2176               <p>
2177                 <span class="red">2.71<br> (509ns)</span>
2178               </p>
2179             </td>
2180 <td>
2181               <p>
2182                 <span class="green">1.00<br> (188ns)</span>
2183               </p>
2184             </td>
2185 <td>
2186               <p>
2187                 <span class="red">752.52<br> (141474ns)</span>
2188               </p>
2189             </td>
2190 <td>
2191               <p>
2192                 <span class="blue">1.52<br> (285ns)</span>
2193               </p>
2194             </td>
2195 <td>
2196               <p>
2197                 <span class="grey">-</span>
2198               </p>
2199             </td>
2200 <td>
2201               <p>
2202                 <span class="grey">-</span>
2203               </p>
2204             </td>
2205 </tr>
2206 </tbody>
2207 </table></div>
2208 </div>
2209 <br class="table-break"><p>
2210       And finally we can compare the statistical distributions to GSL, RMath and
2211       DCDFLIB:
2212     </p>
2213 <div class="table">
2214 <a name="math_toolkit.comparisons.table_Distribution_performance_comparison_with_GNU_C_version_5_3_0_on_linux"></a><p class="title"><b>Table&#160;21.9.&#160;Distribution performance comparison with GNU C++ version 5.3.0 on linux</b></p>
2215 <div class="table-contents"><table class="table" summary="Distribution performance comparison with GNU C++ version 5.3.0 on linux">
2216 <colgroup>
2217 <col>
2218 <col>
2219 <col>
2220 <col>
2221 <col>
2222 <col>
2223 </colgroup>
2224 <thead><tr>
2225 <th>
2226               <p>
2227                 Function
2228               </p>
2229             </th>
2230 <th>
2231               <p>
2232                 boost 1.61
2233               </p>
2234             </th>
2235 <th>
2236               <p>
2237                 Boost<br> promote_double&lt;false&gt;
2238               </p>
2239             </th>
2240 <th>
2241               <p>
2242                 GSL
2243               </p>
2244             </th>
2245 <th>
2246               <p>
2247                 Rmath 3.0.2
2248               </p>
2249             </th>
2250 <th>
2251               <p>
2252                 DCDFLIB
2253               </p>
2254             </th>
2255 </tr></thead>
2256 <tbody>
2257 <tr>
2258 <td>
2259               <p>
2260                 ArcSine (CDF)
2261               </p>
2262             </td>
2263 <td>
2264               <p>
2265                 <span class="green">1.00<br> (33ns)</span>
2266               </p>
2267             </td>
2268 <td>
2269               <p>
2270                 <span class="green">1.03<br> (34ns)</span>
2271               </p>
2272             </td>
2273 <td>
2274             </td>
2275 <td>
2276             </td>
2277 <td>
2278             </td>
2279 </tr>
2280 <tr>
2281 <td>
2282               <p>
2283                 ArcSine (PDF)
2284               </p>
2285             </td>
2286 <td>
2287               <p>
2288                 <span class="green">1.00<br> (9ns)</span>
2289               </p>
2290             </td>
2291 <td>
2292               <p>
2293                 <span class="green">1.00<br> (9ns)</span>
2294               </p>
2295             </td>
2296 <td>
2297             </td>
2298 <td>
2299             </td>
2300 <td>
2301             </td>
2302 </tr>
2303 <tr>
2304 <td>
2305               <p>
2306                 ArcSine (quantile)
2307               </p>
2308             </td>
2309 <td>
2310               <p>
2311                 <span class="green">1.00<br> (21ns)</span>
2312               </p>
2313             </td>
2314 <td>
2315               <p>
2316                 <span class="green">1.05<br> (22ns)</span>
2317               </p>
2318             </td>
2319 <td>
2320             </td>
2321 <td>
2322             </td>
2323 <td>
2324             </td>
2325 </tr>
2326 <tr>
2327 <td>
2328               <p>
2329                 Beta (CDF)
2330               </p>
2331             </td>
2332 <td>
2333               <p>
2334                 <span class="red">2.40<br> (452ns)</span>
2335               </p>
2336             </td>
2337 <td>
2338               <p>
2339                 <span class="green">1.00<br> (188ns)</span>
2340               </p>
2341             </td>
2342 <td>
2343               <p>
2344                 <span class="red">2.66<br> (500ns)</span>
2345               </p>
2346             </td>
2347 <td>
2348               <p>
2349                 <span class="blue">1.64<br> (308ns)</span>
2350               </p>
2351             </td>
2352 <td>
2353               <p>
2354                 <span class="red">2.39<br> (449ns)</span>
2355               </p>
2356             </td>
2357 </tr>
2358 <tr>
2359 <td>
2360               <p>
2361                 Beta (PDF)
2362               </p>
2363             </td>
2364 <td>
2365               <p>
2366                 <span class="red">2.52<br> (355ns)</span>
2367               </p>
2368             </td>
2369 <td>
2370               <p>
2371                 <span class="green">1.00<br> (141ns)</span>
2372               </p>
2373             </td>
2374 <td>
2375               <p>
2376                 <span class="grey">-</span>
2377               </p>
2378             </td>
2379 <td>
2380               <p>
2381                 <span class="blue">1.71<br> (241ns)</span>
2382               </p>
2383             </td>
2384 <td>
2385             </td>
2386 </tr>
2387 <tr>
2388 <td>
2389               <p>
2390                 Beta (quantile)
2391               </p>
2392             </td>
2393 <td>
2394               <p>
2395                 <span class="red">2.40<br> (2863ns)</span>
2396               </p>
2397             </td>
2398 <td>
2399               <p>
2400                 <span class="green">1.00<br> (1192ns)</span>
2401               </p>
2402             </td>
2403 <td>
2404               <p>
2405                 <span class="red">13.48<br> (16063ns)</span>
2406               </p>
2407             </td>
2408 <td>
2409               <p>
2410                 <span class="red">15.15<br> (18064ns)</span>
2411               </p>
2412             </td>
2413 <td>
2414               <p>
2415                 <span class="red">7.43<br> (8852ns)</span>
2416               </p>
2417             </td>
2418 </tr>
2419 <tr>
2420 <td>
2421               <p>
2422                 Binomial (CDF)
2423               </p>
2424             </td>
2425 <td>
2426               <p>
2427                 <span class="blue">1.72<br> (1133ns)</span>
2428               </p>
2429             </td>
2430 <td>
2431               <p>
2432                 <span class="green">1.00<br> (657ns)</span>
2433               </p>
2434             </td>
2435 <td>
2436               <p>
2437                 <span class="blue">1.40<br> (920ns)</span>
2438               </p>
2439             </td>
2440 <td>
2441               <p>
2442                 <span class="green">1.17<br> (768ns)</span>
2443               </p>
2444             </td>
2445 <td>
2446               <p>
2447                 <span class="blue">1.23<br> (807ns)</span>
2448               </p>
2449             </td>
2450 </tr>
2451 <tr>
2452 <td>
2453               <p>
2454                 Binomial (PDF)
2455               </p>
2456             </td>
2457 <td>
2458               <p>
2459                 <span class="red">2.25<br> (376ns)</span>
2460               </p>
2461             </td>
2462 <td>
2463               <p>
2464                 <span class="green">1.00<br> (167ns)</span>
2465               </p>
2466             </td>
2467 <td>
2468               <p>
2469                 <span class="grey">-</span>
2470               </p>
2471             </td>
2472 <td>
2473               <p>
2474                 <span class="green">1.07<br> (179ns)</span>
2475               </p>
2476             </td>
2477 <td>
2478             </td>
2479 </tr>
2480 <tr>
2481 <td>
2482               <p>
2483                 Binomial (quantile)
2484               </p>
2485             </td>
2486 <td>
2487               <p>
2488                 <span class="red">2.47<br> (5047ns)</span>
2489               </p>
2490             </td>
2491 <td>
2492               <p>
2493                 <span class="blue">1.48<br> (3017ns)</span>
2494               </p>
2495             </td>
2496 <td>
2497               <p>
2498                 <span class="grey">-</span>
2499               </p>
2500             </td>
2501 <td>
2502               <p>
2503                 <span class="green">1.00<br> (2040ns)</span>
2504               </p>
2505             </td>
2506 <td>
2507               <p>
2508                 <span class="red">6.21<br> (12659ns)</span>
2509               </p>
2510             </td>
2511 </tr>
2512 <tr>
2513 <td>
2514               <p>
2515                 Cauchy (CDF)
2516               </p>
2517             </td>
2518 <td>
2519               <p>
2520                 <span class="blue">1.38<br> (29ns)</span>
2521               </p>
2522             </td>
2523 <td>
2524               <p>
2525                 <span class="blue">1.33<br> (28ns)</span>
2526               </p>
2527             </td>
2528 <td>
2529               <p>
2530                 <span class="green">1.00<br> (21ns)</span>
2531               </p>
2532             </td>
2533 <td>
2534               <p>
2535                 <span class="blue">1.81<br> (38ns)</span>
2536               </p>
2537             </td>
2538 <td>
2539             </td>
2540 </tr>
2541 <tr>
2542 <td>
2543               <p>
2544                 Cauchy (PDF)
2545               </p>
2546             </td>
2547 <td>
2548               <p>
2549                 <span class="green">1.12<br> (9ns)</span>
2550               </p>
2551             </td>
2552 <td>
2553               <p>
2554                 <span class="green">1.00<br> (8ns)</span>
2555               </p>
2556             </td>
2557 <td>
2558               <p>
2559                 <span class="grey">-</span>
2560               </p>
2561             </td>
2562 <td>
2563               <p>
2564                 <span class="blue">1.50<br> (12ns)</span>
2565               </p>
2566             </td>
2567 <td>
2568             </td>
2569 </tr>
2570 <tr>
2571 <td>
2572               <p>
2573                 Cauchy (quantile)
2574               </p>
2575             </td>
2576 <td>
2577               <p>
2578                 <span class="green">1.00<br> (43ns)</span>
2579               </p>
2580             </td>
2581 <td>
2582               <p>
2583                 <span class="green">1.00<br> (43ns)</span>
2584               </p>
2585             </td>
2586 <td>
2587               <p>
2588                 <span class="red">59.65<br> (2565ns)</span>
2589               </p>
2590             </td>
2591 <td>
2592               <p>
2593                 <span class="red">59.21<br> (2546ns)</span>
2594               </p>
2595             </td>
2596 <td>
2597             </td>
2598 </tr>
2599 <tr>
2600 <td>
2601               <p>
2602                 ChiSquared (CDF)
2603               </p>
2604             </td>
2605 <td>
2606               <p>
2607                 <span class="red">2.28<br> (545ns)</span>
2608               </p>
2609             </td>
2610 <td>
2611               <p>
2612                 <span class="green">1.06<br> (253ns)</span>
2613               </p>
2614             </td>
2615 <td>
2616               <p>
2617                 <span class="red">16.73<br> (3999ns)</span>
2618               </p>
2619             </td>
2620 <td>
2621               <p>
2622                 <span class="blue">1.23<br> (293ns)</span>
2623               </p>
2624             </td>
2625 <td>
2626               <p>
2627                 <span class="green">1.00<br> (239ns)</span>
2628               </p>
2629             </td>
2630 </tr>
2631 <tr>
2632 <td>
2633               <p>
2634                 ChiSquared (PDF)
2635               </p>
2636             </td>
2637 <td>
2638               <p>
2639                 <span class="red">3.20<br> (362ns)</span>
2640               </p>
2641             </td>
2642 <td>
2643               <p>
2644                 <span class="blue">1.24<br> (140ns)</span>
2645               </p>
2646             </td>
2647 <td>
2648               <p>
2649                 <span class="grey">-</span>
2650               </p>
2651             </td>
2652 <td>
2653               <p>
2654                 <span class="green">1.00<br> (113ns)</span>
2655               </p>
2656             </td>
2657 <td>
2658             </td>
2659 </tr>
2660 <tr>
2661 <td>
2662               <p>
2663                 ChiSquared (quantile)
2664               </p>
2665             </td>
2666 <td>
2667               <p>
2668                 <span class="blue">1.94<br> (1416ns)</span>
2669               </p>
2670             </td>
2671 <td>
2672               <p>
2673                 <span class="green">1.00<br> (729ns)</span>
2674               </p>
2675             </td>
2676 <td>
2677               <p>
2678                 <span class="red">51.52<br> (37557ns)</span>
2679               </p>
2680             </td>
2681 <td>
2682               <p>
2683                 <span class="red">2.26<br> (1644ns)</span>
2684               </p>
2685             </td>
2686 <td>
2687               <p>
2688                 <span class="red">7.71<br> (5623ns)</span>
2689               </p>
2690             </td>
2691 </tr>
2692 <tr>
2693 <td>
2694               <p>
2695                 Exponential (CDF)
2696               </p>
2697             </td>
2698 <td>
2699               <p>
2700                 <span class="green">1.05<br> (20ns)</span>
2701               </p>
2702             </td>
2703 <td>
2704               <p>
2705                 <span class="green">1.00<br> (19ns)</span>
2706               </p>
2707             </td>
2708 <td>
2709               <p>
2710                 <span class="blue">1.21<br> (23ns)</span>
2711               </p>
2712             </td>
2713 <td>
2714               <p>
2715                 <span class="blue">1.53<br> (29ns)</span>
2716               </p>
2717             </td>
2718 <td>
2719             </td>
2720 </tr>
2721 <tr>
2722 <td>
2723               <p>
2724                 Exponential (PDF)
2725               </p>
2726             </td>
2727 <td>
2728               <p>
2729                 <span class="green">1.00<br> (26ns)</span>
2730               </p>
2731             </td>
2732 <td>
2733               <p>
2734                 <span class="green">1.00<br> (26ns)</span>
2735               </p>
2736             </td>
2737 <td>
2738               <p>
2739                 <span class="grey">-</span>
2740               </p>
2741             </td>
2742 <td>
2743               <p>
2744                 <span class="blue">1.27<br> (33ns)</span>
2745               </p>
2746             </td>
2747 <td>
2748             </td>
2749 </tr>
2750 <tr>
2751 <td>
2752               <p>
2753                 Exponential (quantile)
2754               </p>
2755             </td>
2756 <td>
2757               <p>
2758                 <span class="blue">1.56<br> (25ns)</span>
2759               </p>
2760             </td>
2761 <td>
2762               <p>
2763                 <span class="blue">1.44<br> (23ns)</span>
2764               </p>
2765             </td>
2766 <td>
2767               <p>
2768                 <span class="green">1.00<br> (16ns)</span>
2769               </p>
2770             </td>
2771 <td>
2772               <p>
2773                 <span class="blue">1.44<br> (23ns)</span>
2774               </p>
2775             </td>
2776 <td>
2777             </td>
2778 </tr>
2779 <tr>
2780 <td>
2781               <p>
2782                 ExtremeValue (CDF)
2783               </p>
2784             </td>
2785 <td>
2786               <p>
2787                 <span class="green">1.00<br> (48ns)</span>
2788               </p>
2789             </td>
2790 <td>
2791               <p>
2792                 <span class="green">1.00<br> (48ns)</span>
2793               </p>
2794             </td>
2795 <td>
2796             </td>
2797 <td>
2798             </td>
2799 <td>
2800             </td>
2801 </tr>
2802 <tr>
2803 <td>
2804               <p>
2805                 ExtremeValue (PDF)
2806               </p>
2807             </td>
2808 <td>
2809               <p>
2810                 <span class="green">1.01<br> (68ns)</span>
2811               </p>
2812             </td>
2813 <td>
2814               <p>
2815                 <span class="green">1.00<br> (67ns)</span>
2816               </p>
2817             </td>
2818 <td>
2819             </td>
2820 <td>
2821             </td>
2822 <td>
2823             </td>
2824 </tr>
2825 <tr>
2826 <td>
2827               <p>
2828                 ExtremeValue (quantile)
2829               </p>
2830             </td>
2831 <td>
2832               <p>
2833                 <span class="green">1.05<br> (68ns)</span>
2834               </p>
2835             </td>
2836 <td>
2837               <p>
2838                 <span class="green">1.00<br> (65ns)</span>
2839               </p>
2840             </td>
2841 <td>
2842             </td>
2843 <td>
2844             </td>
2845 <td>
2846             </td>
2847 </tr>
2848 <tr>
2849 <td>
2850               <p>
2851                 F (CDF)
2852               </p>
2853             </td>
2854 <td>
2855               <p>
2856                 <span class="blue">1.77<br> (1028ns)</span>
2857               </p>
2858             </td>
2859 <td>
2860               <p>
2861                 <span class="green">1.00<br> (580ns)</span>
2862               </p>
2863             </td>
2864 <td>
2865               <p>
2866                 <span class="blue">1.59<br> (921ns)</span>
2867               </p>
2868             </td>
2869 <td>
2870               <p>
2871                 <span class="green">1.13<br> (653ns)</span>
2872               </p>
2873             </td>
2874 <td>
2875               <p>
2876                 <span class="green">1.10<br> (637ns)</span>
2877               </p>
2878             </td>
2879 </tr>
2880 <tr>
2881 <td>
2882               <p>
2883                 F (PDF)
2884               </p>
2885             </td>
2886 <td>
2887               <p>
2888                 <span class="red">2.39<br> (409ns)</span>
2889               </p>
2890             </td>
2891 <td>
2892               <p>
2893                 <span class="green">1.00<br> (171ns)</span>
2894               </p>
2895             </td>
2896 <td>
2897               <p>
2898                 <span class="grey">-</span>
2899               </p>
2900             </td>
2901 <td>
2902               <p>
2903                 <span class="green">1.12<br> (192ns)</span>
2904               </p>
2905             </td>
2906 <td>
2907             </td>
2908 </tr>
2909 <tr>
2910 <td>
2911               <p>
2912                 F (quantile)
2913               </p>
2914             </td>
2915 <td>
2916               <p>
2917                 <span class="blue">1.86<br> (2899ns)</span>
2918               </p>
2919             </td>
2920 <td>
2921               <p>
2922                 <span class="green">1.00<br> (1556ns)</span>
2923               </p>
2924             </td>
2925 <td>
2926               <p>
2927                 <span class="red">9.67<br> (15050ns)</span>
2928               </p>
2929             </td>
2930 <td>
2931               <p>
2932                 <span class="blue">1.98<br> (3083ns)</span>
2933               </p>
2934             </td>
2935 <td>
2936               <p>
2937                 <span class="red">5.85<br> (9110ns)</span>
2938               </p>
2939             </td>
2940 </tr>
2941 <tr>
2942 <td>
2943               <p>
2944                 Gamma (CDF)
2945               </p>
2946             </td>
2947 <td>
2948               <p>
2949                 <span class="red">2.48<br> (619ns)</span>
2950               </p>
2951             </td>
2952 <td>
2953               <p>
2954                 <span class="green">1.01<br> (253ns)</span>
2955               </p>
2956             </td>
2957 <td>
2958               <p>
2959                 <span class="red">6.12<br> (1529ns)</span>
2960               </p>
2961             </td>
2962 <td>
2963               <p>
2964                 <span class="blue">1.40<br> (349ns)</span>
2965               </p>
2966             </td>
2967 <td>
2968               <p>
2969                 <span class="green">1.00<br> (250ns)</span>
2970               </p>
2971             </td>
2972 </tr>
2973 <tr>
2974 <td>
2975               <p>
2976                 Gamma (PDF)
2977               </p>
2978             </td>
2979 <td>
2980               <p>
2981                 <span class="red">2.91<br> (480ns)</span>
2982               </p>
2983             </td>
2984 <td>
2985               <p>
2986                 <span class="green">1.02<br> (169ns)</span>
2987               </p>
2988             </td>
2989 <td>
2990               <p>
2991                 <span class="grey">-</span>
2992               </p>
2993             </td>
2994 <td>
2995               <p>
2996                 <span class="green">1.00<br> (165ns)</span>
2997               </p>
2998             </td>
2999 <td>
3000             </td>
3001 </tr>
3002 <tr>
3003 <td>
3004               <p>
3005                 Gamma (quantile)
3006               </p>
3007             </td>
3008 <td>
3009               <p>
3010                 <span class="red">2.29<br> (1971ns)</span>
3011               </p>
3012             </td>
3013 <td>
3014               <p>
3015                 <span class="green">1.00<br> (860ns)</span>
3016               </p>
3017             </td>
3018 <td>
3019               <p>
3020                 <span class="red">13.93<br> (11979ns)</span>
3021               </p>
3022             </td>
3023 <td>
3024               <p>
3025                 <span class="red">2.13<br> (1829ns)</span>
3026               </p>
3027             </td>
3028 <td>
3029               <p>
3030                 <span class="green">1.03<br> (886ns)</span>
3031               </p>
3032             </td>
3033 </tr>
3034 <tr>
3035 <td>
3036               <p>
3037                 Geometric (CDF)
3038               </p>
3039             </td>
3040 <td>
3041               <p>
3042                 <span class="green">1.00<br> (26ns)</span>
3043               </p>
3044             </td>
3045 <td>
3046               <p>
3047                 <span class="green">1.08<br> (28ns)</span>
3048               </p>
3049             </td>
3050 <td>
3051               <p>
3052                 <span class="green">1.00<br> (26ns)</span>
3053               </p>
3054             </td>
3055 <td>
3056               <p>
3057                 <span class="red">2.08<br> (54ns)</span>
3058               </p>
3059             </td>
3060 <td>
3061             </td>
3062 </tr>
3063 <tr>
3064 <td>
3065               <p>
3066                 Geometric (PDF)
3067               </p>
3068             </td>
3069 <td>
3070               <p>
3071                 <span class="green">1.00<br> (33ns)</span>
3072               </p>
3073             </td>
3074 <td>
3075               <p>
3076                 <span class="green">1.06<br> (35ns)</span>
3077               </p>
3078             </td>
3079 <td>
3080               <p>
3081                 <span class="grey">-</span>
3082               </p>
3083             </td>
3084 <td>
3085               <p>
3086                 <span class="red">7.15<br> (236ns)</span>
3087               </p>
3088             </td>
3089 <td>
3090             </td>
3091 </tr>
3092 <tr>
3093 <td>
3094               <p>
3095                 Geometric (quantile)
3096               </p>
3097             </td>
3098 <td>
3099               <p>
3100                 <span class="green">1.00<br> (22ns)</span>
3101               </p>
3102             </td>
3103 <td>
3104               <p>
3105                 <span class="green">1.00<br> (22ns)</span>
3106               </p>
3107             </td>
3108 <td>
3109               <p>
3110                 <span class="grey">-</span>
3111               </p>
3112             </td>
3113 <td>
3114               <p>
3115                 <span class="red">2.18<br> (48ns)</span>
3116               </p>
3117             </td>
3118 <td>
3119             </td>
3120 </tr>
3121 <tr>
3122 <td>
3123               <p>
3124                 Hypergeometric (CDF)
3125               </p>
3126             </td>
3127 <td>
3128               <p>
3129                 <span class="red">12.07<br> (11779ns)</span>
3130               </p>
3131             </td>
3132 <td>
3133               <p>
3134                 <span class="red">6.58<br> (6423ns)</span>
3135               </p>
3136             </td>
3137 <td>
3138               <p>
3139                 <span class="blue">1.61<br> (1568ns)</span>
3140               </p>
3141             </td>
3142 <td>
3143               <p>
3144                 <span class="green">1.00<br> (976ns)</span>
3145               </p>
3146             </td>
3147 <td>
3148             </td>
3149 </tr>
3150 <tr>
3151 <td>
3152               <p>
3153                 Hypergeometric (PDF)
3154               </p>
3155             </td>
3156 <td>
3157               <p>
3158                 <span class="red">25.41<br> (11384ns)</span>
3159               </p>
3160             </td>
3161 <td>
3162               <p>
3163                 <span class="red">13.51<br> (6054ns)</span>
3164               </p>
3165             </td>
3166 <td>
3167               <p>
3168                 <span class="grey">-</span>
3169               </p>
3170             </td>
3171 <td>
3172               <p>
3173                 <span class="green">1.00<br> (448ns)</span>
3174               </p>
3175             </td>
3176 <td>
3177             </td>
3178 </tr>
3179 <tr>
3180 <td>
3181               <p>
3182                 Hypergeometric (quantile)
3183               </p>
3184             </td>
3185 <td>
3186               <p>
3187                 <span class="green">1.00<br> (57820ns)</span>
3188               </p>
3189             </td>
3190 <td>
3191               <p>
3192                 <span class="blue">1.54<br> (89233ns)</span>
3193               </p>
3194             </td>
3195 <td>
3196               <p>
3197                 <span class="grey">-</span>
3198               </p>
3199             </td>
3200 <td>
3201               <p>
3202                 <span class="blue">1.60<br> (92679ns)</span>
3203               </p>
3204             </td>
3205 <td>
3206             </td>
3207 </tr>
3208 <tr>
3209 <td>
3210               <p>
3211                 InverseChiSquared (CDF)
3212               </p>
3213             </td>
3214 <td>
3215               <p>
3216                 <span class="red">2.23<br> (546ns)</span>
3217               </p>
3218             </td>
3219 <td>
3220               <p>
3221                 <span class="green">1.00<br> (245ns)</span>
3222               </p>
3223             </td>
3224 <td>
3225             </td>
3226 <td>
3227             </td>
3228 <td>
3229             </td>
3230 </tr>
3231 <tr>
3232 <td>
3233               <p>
3234                 InverseChiSquared (PDF)
3235               </p>
3236             </td>
3237 <td>
3238               <p>
3239                 <span class="red">2.28<br> (342ns)</span>
3240               </p>
3241             </td>
3242 <td>
3243               <p>
3244                 <span class="green">1.00<br> (150ns)</span>
3245               </p>
3246             </td>
3247 <td>
3248             </td>
3249 <td>
3250             </td>
3251 <td>
3252             </td>
3253 </tr>
3254 <tr>
3255 <td>
3256               <p>
3257                 InverseChiSquared (quantile)
3258               </p>
3259             </td>
3260 <td>
3261               <p>
3262                 <span class="blue">1.86<br> (1378ns)</span>
3263               </p>
3264             </td>
3265 <td>
3266               <p>
3267                 <span class="green">1.00<br> (740ns)</span>
3268               </p>
3269             </td>
3270 <td>
3271             </td>
3272 <td>
3273             </td>
3274 <td>
3275             </td>
3276 </tr>
3277 <tr>
3278 <td>
3279               <p>
3280                 InverseGamma (CDF)
3281               </p>
3282             </td>
3283 <td>
3284               <p>
3285                 <span class="red">2.50<br> (610ns)</span>
3286               </p>
3287             </td>
3288 <td>
3289               <p>
3290                 <span class="green">1.00<br> (244ns)</span>
3291               </p>
3292             </td>
3293 <td>
3294             </td>
3295 <td>
3296             </td>
3297 <td>
3298             </td>
3299 </tr>
3300 <tr>
3301 <td>
3302               <p>
3303                 InverseGamma (PDF)
3304               </p>
3305             </td>
3306 <td>
3307               <p>
3308                 <span class="red">2.76<br> (477ns)</span>
3309               </p>
3310             </td>
3311 <td>
3312               <p>
3313                 <span class="green">1.00<br> (173ns)</span>
3314               </p>
3315             </td>
3316 <td>
3317             </td>
3318 <td>
3319             </td>
3320 <td>
3321             </td>
3322 </tr>
3323 <tr>
3324 <td>
3325               <p>
3326                 InverseGamma (quantile)
3327               </p>
3328             </td>
3329 <td>
3330               <p>
3331                 <span class="red">2.23<br> (1870ns)</span>
3332               </p>
3333             </td>
3334 <td>
3335               <p>
3336                 <span class="green">1.00<br> (838ns)</span>
3337               </p>
3338             </td>
3339 <td>
3340             </td>
3341 <td>
3342             </td>
3343 <td>
3344             </td>
3345 </tr>
3346 <tr>
3347 <td>
3348               <p>
3349                 InverseGaussian (CDF)
3350               </p>
3351             </td>
3352 <td>
3353               <p>
3354                 <span class="green">1.00<br> (108ns)</span>
3355               </p>
3356             </td>
3357 <td>
3358               <p>
3359                 <span class="green">1.00<br> (108ns)</span>
3360               </p>
3361             </td>
3362 <td>
3363             </td>
3364 <td>
3365             </td>
3366 <td>
3367             </td>
3368 </tr>
3369 <tr>
3370 <td>
3371               <p>
3372                 InverseGaussian (PDF)
3373               </p>
3374             </td>
3375 <td>
3376               <p>
3377                 <span class="green">1.00<br> (19ns)</span>
3378               </p>
3379             </td>
3380 <td>
3381               <p>
3382                 <span class="green">1.00<br> (19ns)</span>
3383               </p>
3384             </td>
3385 <td>
3386             </td>
3387 <td>
3388             </td>
3389 <td>
3390             </td>
3391 </tr>
3392 <tr>
3393 <td>
3394               <p>
3395                 InverseGaussian (quantile)
3396               </p>
3397             </td>
3398 <td>
3399               <p>
3400                 <span class="green">1.01<br> (2105ns)</span>
3401               </p>
3402             </td>
3403 <td>
3404               <p>
3405                 <span class="green">1.00<br> (2074ns)</span>
3406               </p>
3407             </td>
3408 <td>
3409             </td>
3410 <td>
3411             </td>
3412 <td>
3413             </td>
3414 </tr>
3415 <tr>
3416 <td>
3417               <p>
3418                 Laplace (CDF)
3419               </p>
3420             </td>
3421 <td>
3422               <p>
3423                 <span class="blue">1.35<br> (27ns)</span>
3424               </p>
3425             </td>
3426 <td>
3427               <p>
3428                 <span class="blue">1.35<br> (27ns)</span>
3429               </p>
3430             </td>
3431 <td>
3432               <p>
3433                 <span class="green">1.00<br> (20ns)</span>
3434               </p>
3435             </td>
3436 <td>
3437             </td>
3438 <td>
3439             </td>
3440 </tr>
3441 <tr>
3442 <td>
3443               <p>
3444                 Laplace (PDF)
3445               </p>
3446             </td>
3447 <td>
3448               <p>
3449                 <span class="green">1.00<br> (28ns)</span>
3450               </p>
3451             </td>
3452 <td>
3453               <p>
3454                 <span class="green">1.00<br> (28ns)</span>
3455               </p>
3456             </td>
3457 <td>
3458             </td>
3459 <td>
3460             </td>
3461 <td>
3462             </td>
3463 </tr>
3464 <tr>
3465 <td>
3466               <p>
3467                 Laplace (quantile)
3468               </p>
3469             </td>
3470 <td>
3471               <p>
3472                 <span class="green">1.14<br> (32ns)</span>
3473               </p>
3474             </td>
3475 <td>
3476               <p>
3477                 <span class="green">1.18<br> (33ns)</span>
3478               </p>
3479             </td>
3480 <td>
3481               <p>
3482                 <span class="green">1.00<br> (28ns)</span>
3483               </p>
3484             </td>
3485 <td>
3486             </td>
3487 <td>
3488             </td>
3489 </tr>
3490 <tr>
3491 <td>
3492               <p>
3493                 LogNormal (CDF)
3494               </p>
3495             </td>
3496 <td>
3497               <p>
3498                 <span class="blue">1.67<br> (115ns)</span>
3499               </p>
3500             </td>
3501 <td>
3502               <p>
3503                 <span class="green">1.00<br> (69ns)</span>
3504               </p>
3505             </td>
3506 <td>
3507               <p>
3508                 <span class="green">1.13<br> (78ns)</span>
3509               </p>
3510             </td>
3511 <td>
3512               <p>
3513                 <span class="blue">1.46<br> (101ns)</span>
3514               </p>
3515             </td>
3516 <td>
3517             </td>
3518 </tr>
3519 <tr>
3520 <td>
3521               <p>
3522                 LogNormal (PDF)
3523               </p>
3524             </td>
3525 <td>
3526               <p>
3527                 <span class="green">1.00<br> (66ns)</span>
3528               </p>
3529             </td>
3530 <td>
3531               <p>
3532                 <span class="green">1.02<br> (67ns)</span>
3533               </p>
3534             </td>
3535 <td>
3536               <p>
3537                 <span class="grey">-</span>
3538               </p>
3539             </td>
3540 <td>
3541               <p>
3542                 <span class="green">1.08<br> (71ns)</span>
3543               </p>
3544             </td>
3545 <td>
3546             </td>
3547 </tr>
3548 <tr>
3549 <td>
3550               <p>
3551                 LogNormal (quantile)
3552               </p>
3553             </td>
3554 <td>
3555               <p>
3556                 <span class="blue">1.45<br> (103ns)</span>
3557               </p>
3558             </td>
3559 <td>
3560               <p>
3561                 <span class="blue">1.32<br> (94ns)</span>
3562               </p>
3563             </td>
3564 <td>
3565               <p>
3566                 <span class="green">1.00<br> (71ns)</span>
3567               </p>
3568             </td>
3569 <td>
3570               <p>
3571                 <span class="blue">1.32<br> (94ns)</span>
3572               </p>
3573             </td>
3574 <td>
3575             </td>
3576 </tr>
3577 <tr>
3578 <td>
3579               <p>
3580                 Logistic (CDF)
3581               </p>
3582             </td>
3583 <td>
3584               <p>
3585                 <span class="green">1.00<br> (28ns)</span>
3586               </p>
3587             </td>
3588 <td>
3589               <p>
3590                 <span class="green">1.04<br> (29ns)</span>
3591               </p>
3592             </td>
3593 <td>
3594               <p>
3595                 <span class="green">1.04<br> (29ns)</span>
3596               </p>
3597             </td>
3598 <td>
3599               <p>
3600                 <span class="blue">1.25<br> (35ns)</span>
3601               </p>
3602             </td>
3603 <td>
3604             </td>
3605 </tr>
3606 <tr>
3607 <td>
3608               <p>
3609                 Logistic (PDF)
3610               </p>
3611             </td>
3612 <td>
3613               <p>
3614                 <span class="green">1.00<br> (31ns)</span>
3615               </p>
3616             </td>
3617 <td>
3618               <p>
3619                 <span class="green">1.03<br> (32ns)</span>
3620               </p>
3621             </td>
3622 <td>
3623               <p>
3624                 <span class="grey">-</span>
3625               </p>
3626             </td>
3627 <td>
3628               <p>
3629                 <span class="green">1.03<br> (32ns)</span>
3630               </p>
3631             </td>
3632 <td>
3633             </td>
3634 </tr>
3635 <tr>
3636 <td>
3637               <p>
3638                 Logistic (quantile)
3639               </p>
3640             </td>
3641 <td>
3642               <p>
3643                 <span class="green">1.09<br> (36ns)</span>
3644               </p>
3645             </td>
3646 <td>
3647               <p>
3648                 <span class="green">1.12<br> (37ns)</span>
3649               </p>
3650             </td>
3651 <td>
3652               <p>
3653                 <span class="green">1.00<br> (33ns)</span>
3654               </p>
3655             </td>
3656 <td>
3657               <p>
3658                 <span class="blue">1.27<br> (42ns)</span>
3659               </p>
3660             </td>
3661 <td>
3662             </td>
3663 </tr>
3664 <tr>
3665 <td>
3666               <p>
3667                 NegativeBinomial (CDF)
3668               </p>
3669             </td>
3670 <td>
3671               <p>
3672                 <span class="red">2.08<br> (1733ns)</span>
3673               </p>
3674             </td>
3675 <td>
3676               <p>
3677                 <span class="blue">1.23<br> (1028ns)</span>
3678               </p>
3679             </td>
3680 <td>
3681               <p>
3682                 <span class="blue">1.58<br> (1317ns)</span>
3683               </p>
3684             </td>
3685 <td>
3686               <p>
3687                 <span class="green">1.10<br> (916ns)</span>
3688               </p>
3689             </td>
3690 <td>
3691               <p>
3692                 <span class="green">1.00<br> (833ns)</span>
3693               </p>
3694             </td>
3695 </tr>
3696 <tr>
3697 <td>
3698               <p>
3699                 NegativeBinomial (PDF)
3700               </p>
3701             </td>
3702 <td>
3703               <p>
3704                 <span class="red">2.19<br> (384ns)</span>
3705               </p>
3706             </td>
3707 <td>
3708               <p>
3709                 <span class="green">1.00<br> (175ns)</span>
3710               </p>
3711             </td>
3712 <td>
3713               <p>
3714                 <span class="grey">-</span>
3715               </p>
3716             </td>
3717 <td>
3718               <p>
3719                 <span class="green">1.12<br> (196ns)</span>
3720               </p>
3721             </td>
3722 <td>
3723             </td>
3724 </tr>
3725 <tr>
3726 <td>
3727               <p>
3728                 NegativeBinomial (quantile)
3729               </p>
3730             </td>
3731 <td>
3732               <p>
3733                 <span class="blue">1.74<br> (9167ns)</span>
3734               </p>
3735             </td>
3736 <td>
3737               <p>
3738                 <span class="green">1.00<br> (5278ns)</span>
3739               </p>
3740             </td>
3741 <td>
3742               <p>
3743                 <span class="grey">-</span>
3744               </p>
3745             </td>
3746 <td>
3747               <p>
3748                 <span class="red">3.35<br> (17681ns)</span>
3749               </p>
3750             </td>
3751 <td>
3752               <p>
3753                 <span class="red">3.01<br> (15887ns)</span>
3754               </p>
3755             </td>
3756 </tr>
3757 <tr>
3758 <td>
3759               <p>
3760                 NonCentralBeta (CDF)
3761               </p>
3762             </td>
3763 <td>
3764               <p>
3765                 <span class="red">2.25<br> (2715ns)</span>
3766               </p>
3767             </td>
3768 <td>
3769               <p>
3770                 <span class="green">1.18<br> (1421ns)</span>
3771               </p>
3772             </td>
3773 <td>
3774               <p>
3775                 <span class="grey">-</span>
3776               </p>
3777             </td>
3778 <td>
3779               <p>
3780                 <span class="green">1.00<br> (1205ns)</span>
3781               </p>
3782             </td>
3783 <td>
3784             </td>
3785 </tr>
3786 <tr>
3787 <td>
3788               <p>
3789                 NonCentralBeta (PDF)
3790               </p>
3791             </td>
3792 <td>
3793               <p>
3794                 <span class="red">2.13<br> (2036ns)</span>
3795               </p>
3796             </td>
3797 <td>
3798               <p>
3799                 <span class="blue">1.23<br> (1179ns)</span>
3800               </p>
3801             </td>
3802 <td>
3803               <p>
3804                 <span class="grey">-</span>
3805               </p>
3806             </td>
3807 <td>
3808               <p>
3809                 <span class="green">1.00<br> (956ns)</span>
3810               </p>
3811             </td>
3812 <td>
3813             </td>
3814 </tr>
3815 <tr>
3816 <td>
3817               <p>
3818                 NonCentralBeta (quantile)
3819               </p>
3820             </td>
3821 <td>
3822               <p>
3823                 <span class="red">2.15<br> (63495ns)</span>
3824               </p>
3825             </td>
3826 <td>
3827               <p>
3828                 <span class="green">1.00<br> (29566ns)</span>
3829               </p>
3830             </td>
3831 <td>
3832               <p>
3833                 <span class="grey">-</span>
3834               </p>
3835             </td>
3836 <td>
3837               <p>
3838                 <span class="red">2.89<br> (85371ns)</span>
3839               </p>
3840             </td>
3841 <td>
3842             </td>
3843 </tr>
3844 <tr>
3845 <td>
3846               <p>
3847                 NonCentralChiSquared (CDF)
3848               </p>
3849             </td>
3850 <td>
3851               <p>
3852                 <span class="red">10.17<br> (7258ns)</span>
3853               </p>
3854             </td>
3855 <td>
3856               <p>
3857                 <span class="red">6.32<br> (4515ns)</span>
3858               </p>
3859             </td>
3860 <td>
3861               <p>
3862                 <span class="grey">-</span>
3863               </p>
3864             </td>
3865 <td>
3866               <p>
3867                 <span class="red">15.17<br> (10828ns)</span>
3868               </p>
3869             </td>
3870 <td>
3871               <p>
3872                 <span class="green">1.00<br> (714ns)</span>
3873               </p>
3874             </td>
3875 </tr>
3876 <tr>
3877 <td>
3878               <p>
3879                 NonCentralChiSquared (PDF)
3880               </p>
3881             </td>
3882 <td>
3883               <p>
3884                 <span class="red">2.81<br> (1275ns)</span>
3885               </p>
3886             </td>
3887 <td>
3888               <p>
3889                 <span class="blue">1.55<br> (705ns)</span>
3890               </p>
3891             </td>
3892 <td>
3893               <p>
3894                 <span class="grey">-</span>
3895               </p>
3896             </td>
3897 <td>
3898               <p>
3899                 <span class="green">1.00<br> (454ns)</span>
3900               </p>
3901             </td>
3902 <td>
3903             </td>
3904 </tr>
3905 <tr>
3906 <td>
3907               <p>
3908                 NonCentralChiSquared (quantile)
3909               </p>
3910             </td>
3911 <td>
3912               <p>
3913                 <span class="red">3.29<br> (51391ns)</span>
3914               </p>
3915             </td>
3916 <td>
3917               <p>
3918                 <span class="blue">1.72<br> (26920ns)</span>
3919               </p>
3920             </td>
3921 <td>
3922               <p>
3923                 <span class="grey">-</span>
3924               </p>
3925             </td>
3926 <td>
3927               <p>
3928                 <span class="red">34.31<br> (536514ns)</span>
3929               </p>
3930             </td>
3931 <td>
3932               <p>
3933                 <span class="green">1.00<br> (15636ns)</span>
3934               </p>
3935             </td>
3936 </tr>
3937 <tr>
3938 <td>
3939               <p>
3940                 NonCentralF (CDF)
3941               </p>
3942             </td>
3943 <td>
3944               <p>
3945                 <span class="blue">1.96<br> (2583ns)</span>
3946               </p>
3947             </td>
3948 <td>
3949               <p>
3950                 <span class="green">1.04<br> (1364ns)</span>
3951               </p>
3952             </td>
3953 <td>
3954               <p>
3955                 <span class="grey">-</span>
3956               </p>
3957             </td>
3958 <td>
3959               <p>
3960                 <span class="green">1.00<br> (1316ns)</span>
3961               </p>
3962             </td>
3963 <td>
3964               <p>
3965                 <span class="green">1.15<br> (1512ns)</span>
3966               </p>
3967             </td>
3968 </tr>
3969 <tr>
3970 <td>
3971               <p>
3972                 NonCentralF (PDF)
3973               </p>
3974             </td>
3975 <td>
3976               <p>
3977                 <span class="red">2.39<br> (2102ns)</span>
3978               </p>
3979             </td>
3980 <td>
3981               <p>
3982                 <span class="blue">1.25<br> (1099ns)</span>
3983               </p>
3984             </td>
3985 <td>
3986               <p>
3987                 <span class="grey">-</span>
3988               </p>
3989             </td>
3990 <td>
3991               <p>
3992                 <span class="green">1.00<br> (878ns)</span>
3993               </p>
3994             </td>
3995 <td>
3996             </td>
3997 </tr>
3998 <tr>
3999 <td>
4000               <p>
4001                 NonCentralF (quantile)
4002               </p>
4003             </td>
4004 <td>
4005               <p>
4006                 <span class="red">2.30<br> (39838ns)</span>
4007               </p>
4008             </td>
4009 <td>
4010               <p>
4011                 <span class="green">1.15<br> (19939ns)</span>
4012               </p>
4013             </td>
4014 <td>
4015               <p>
4016                 <span class="grey">-</span>
4017               </p>
4018             </td>
4019 <td>
4020               <p>
4021                 <span class="red">4.06<br> (70302ns)</span>
4022               </p>
4023             </td>
4024 <td>
4025               <p>
4026                 <span class="green">1.00<br> (17331ns)</span>
4027               </p>
4028             </td>
4029 </tr>
4030 <tr>
4031 <td>
4032               <p>
4033                 NonCentralT (CDF)
4034               </p>
4035             </td>
4036 <td>
4037               <p>
4038                 <span class="red">5.04<br> (9817ns)</span>
4039               </p>
4040             </td>
4041 <td>
4042               <p>
4043                 <span class="red">3.10<br> (6036ns)</span>
4044               </p>
4045             </td>
4046 <td>
4047               <p>
4048                 <span class="grey">-</span>
4049               </p>
4050             </td>
4051 <td>
4052               <p>
4053                 <span class="green">1.00<br> (1949ns)</span>
4054               </p>
4055             </td>
4056 <td>
4057               <p>
4058                 <span class="blue">1.84<br> (3591ns)</span>
4059               </p>
4060             </td>
4061 </tr>
4062 <tr>
4063 <td>
4064               <p>
4065                 NonCentralT (PDF)
4066               </p>
4067             </td>
4068 <td>
4069               <p>
4070                 <span class="blue">1.82<br> (7422ns)</span>
4071               </p>
4072             </td>
4073 <td>
4074               <p>
4075                 <span class="green">1.19<br> (4838ns)</span>
4076               </p>
4077             </td>
4078 <td>
4079               <p>
4080                 <span class="grey">-</span>
4081               </p>
4082             </td>
4083 <td>
4084               <p>
4085                 <span class="green">1.00<br> (4078ns)</span>
4086               </p>
4087             </td>
4088 <td>
4089             </td>
4090 </tr>
4091 <tr>
4092 <td>
4093               <p>
4094                 NonCentralT (quantile)
4095               </p>
4096             </td>
4097 <td>
4098               <p>
4099                 <span class="blue">1.88<br> (100206ns)</span>
4100               </p>
4101             </td>
4102 <td>
4103               <p>
4104                 <span class="green">1.12<br> (59572ns)</span>
4105               </p>
4106             </td>
4107 <td>
4108               <p>
4109                 <span class="grey">-</span>
4110               </p>
4111             </td>
4112 <td>
4113               <p>
4114                 <span class="blue">1.70<br> (90848ns)</span>
4115               </p>
4116             </td>
4117 <td>
4118               <p>
4119                 <span class="green">1.00<br> (53399ns)</span>
4120               </p>
4121             </td>
4122 </tr>
4123 <tr>
4124 <td>
4125               <p>
4126                 Normal (CDF)
4127               </p>
4128             </td>
4129 <td>
4130               <p>
4131                 <span class="red">2.55<br> (79ns)</span>
4132               </p>
4133             </td>
4134 <td>
4135               <p>
4136                 <span class="green">1.13<br> (35ns)</span>
4137               </p>
4138             </td>
4139 <td>
4140               <p>
4141                 <span class="green">1.00<br> (31ns)</span>
4142               </p>
4143             </td>
4144 <td>
4145               <p>
4146                 <span class="red">2.06<br> (64ns)</span>
4147               </p>
4148             </td>
4149 <td>
4150               <p>
4151                 <span class="red">6.61<br> (205ns)</span>
4152               </p>
4153             </td>
4154 </tr>
4155 <tr>
4156 <td>
4157               <p>
4158                 Normal (PDF)
4159               </p>
4160             </td>
4161 <td>
4162               <p>
4163                 <span class="green">1.03<br> (33ns)</span>
4164               </p>
4165             </td>
4166 <td>
4167               <p>
4168                 <span class="green">1.00<br> (32ns)</span>
4169               </p>
4170             </td>
4171 <td>
4172               <p>
4173                 <span class="grey">-</span>
4174               </p>
4175             </td>
4176 <td>
4177               <p>
4178                 <span class="blue">1.25<br> (40ns)</span>
4179               </p>
4180             </td>
4181 <td>
4182             </td>
4183 </tr>
4184 <tr>
4185 <td>
4186               <p>
4187                 Normal (quantile)
4188               </p>
4189             </td>
4190 <td>
4191               <p>
4192                 <span class="red">2.03<br> (67ns)</span>
4193               </p>
4194             </td>
4195 <td>
4196               <p>
4197                 <span class="blue">1.58<br> (52ns)</span>
4198               </p>
4199             </td>
4200 <td>
4201               <p>
4202                 <span class="green">1.00<br> (33ns)</span>
4203               </p>
4204             </td>
4205 <td>
4206               <p>
4207                 <span class="blue">1.36<br> (45ns)</span>
4208               </p>
4209             </td>
4210 <td>
4211               <p>
4212                 <span class="red">17.58<br> (580ns)</span>
4213               </p>
4214             </td>
4215 </tr>
4216 <tr>
4217 <td>
4218               <p>
4219                 Pareto (CDF)
4220               </p>
4221             </td>
4222 <td>
4223               <p>
4224                 <span class="green">1.00<br> (52ns)</span>
4225               </p>
4226             </td>
4227 <td>
4228               <p>
4229                 <span class="green">1.02<br> (53ns)</span>
4230               </p>
4231             </td>
4232 <td>
4233               <p>
4234                 <span class="blue">1.21<br> (63ns)</span>
4235               </p>
4236             </td>
4237 <td>
4238             </td>
4239 <td>
4240             </td>
4241 </tr>
4242 <tr>
4243 <td>
4244               <p>
4245                 Pareto (PDF)
4246               </p>
4247             </td>
4248 <td>
4249               <p>
4250                 <span class="green">1.01<br> (91ns)</span>
4251               </p>
4252             </td>
4253 <td>
4254               <p>
4255                 <span class="green">1.00<br> (90ns)</span>
4256               </p>
4257             </td>
4258 <td>
4259             </td>
4260 <td>
4261             </td>
4262 <td>
4263             </td>
4264 </tr>
4265 <tr>
4266 <td>
4267               <p>
4268                 Pareto (quantile)
4269               </p>
4270             </td>
4271 <td>
4272               <p>
4273                 <span class="green">1.04<br> (55ns)</span>
4274               </p>
4275             </td>
4276 <td>
4277               <p>
4278                 <span class="blue">1.25<br> (66ns)</span>
4279               </p>
4280             </td>
4281 <td>
4282               <p>
4283                 <span class="green">1.00<br> (53ns)</span>
4284               </p>
4285             </td>
4286 <td>
4287             </td>
4288 <td>
4289             </td>
4290 </tr>
4291 <tr>
4292 <td>
4293               <p>
4294                 Poisson (CDF)
4295               </p>
4296             </td>
4297 <td>
4298               <p>
4299                 <span class="red">2.01<br> (251ns)</span>
4300               </p>
4301             </td>
4302 <td>
4303               <p>
4304                 <span class="green">1.00<br> (125ns)</span>
4305               </p>
4306             </td>
4307 <td>
4308               <p>
4309                 <span class="red">5.84<br> (730ns)</span>
4310               </p>
4311             </td>
4312 <td>
4313               <p>
4314                 <span class="red">2.22<br> (278ns)</span>
4315               </p>
4316             </td>
4317 <td>
4318               <p>
4319                 <span class="blue">1.68<br> (210ns)</span>
4320               </p>
4321             </td>
4322 </tr>
4323 <tr>
4324 <td>
4325               <p>
4326                 Poisson (PDF)
4327               </p>
4328             </td>
4329 <td>
4330               <p>
4331                 <span class="red">2.09<br> (196ns)</span>
4332               </p>
4333             </td>
4334 <td>
4335               <p>
4336                 <span class="green">1.00<br> (94ns)</span>
4337               </p>
4338             </td>
4339 <td>
4340               <p>
4341                 <span class="grey">-</span>
4342               </p>
4343             </td>
4344 <td>
4345               <p>
4346                 <span class="green">1.01<br> (95ns)</span>
4347               </p>
4348             </td>
4349 <td>
4350             </td>
4351 </tr>
4352 <tr>
4353 <td>
4354               <p>
4355                 Poisson (quantile)
4356               </p>
4357             </td>
4358 <td>
4359               <p>
4360                 <span class="blue">1.99<br> (1120ns)</span>
4361               </p>
4362             </td>
4363 <td>
4364               <p>
4365                 <span class="green">1.00<br> (562ns)</span>
4366               </p>
4367             </td>
4368 <td>
4369               <p>
4370                 <span class="grey">-</span>
4371               </p>
4372             </td>
4373 <td>
4374               <p>
4375                 <span class="blue">1.21<br> (682ns)</span>
4376               </p>
4377             </td>
4378 <td>
4379               <p>
4380                 <span class="red">5.51<br> (3097ns)</span>
4381               </p>
4382             </td>
4383 </tr>
4384 <tr>
4385 <td>
4386               <p>
4387                 Rayleigh (CDF)
4388               </p>
4389             </td>
4390 <td>
4391               <p>
4392                 <span class="green">1.10<br> (23ns)</span>
4393               </p>
4394             </td>
4395 <td>
4396               <p>
4397                 <span class="green">1.05<br> (22ns)</span>
4398               </p>
4399             </td>
4400 <td>
4401               <p>
4402                 <span class="green">1.00<br> (21ns)</span>
4403               </p>
4404             </td>
4405 <td>
4406             </td>
4407 <td>
4408             </td>
4409 </tr>
4410 <tr>
4411 <td>
4412               <p>
4413                 Rayleigh (PDF)
4414               </p>
4415             </td>
4416 <td>
4417               <p>
4418                 <span class="green">1.15<br> (31ns)</span>
4419               </p>
4420             </td>
4421 <td>
4422               <p>
4423                 <span class="green">1.00<br> (27ns)</span>
4424               </p>
4425             </td>
4426 <td>
4427             </td>
4428 <td>
4429             </td>
4430 <td>
4431             </td>
4432 </tr>
4433 <tr>
4434 <td>
4435               <p>
4436                 Rayleigh (quantile)
4437               </p>
4438             </td>
4439 <td>
4440               <p>
4441                 <span class="blue">1.25<br> (25ns)</span>
4442               </p>
4443             </td>
4444 <td>
4445               <p>
4446                 <span class="green">1.20<br> (24ns)</span>
4447               </p>
4448             </td>
4449 <td>
4450               <p>
4451                 <span class="green">1.00<br> (20ns)</span>
4452               </p>
4453             </td>
4454 <td>
4455             </td>
4456 <td>
4457             </td>
4458 </tr>
4459 <tr>
4460 <td>
4461               <p>
4462                 SkewNormal (CDF)
4463               </p>
4464             </td>
4465 <td>
4466               <p>
4467                 <span class="green">1.09<br> (471ns)</span>
4468               </p>
4469             </td>
4470 <td>
4471               <p>
4472                 <span class="green">1.00<br> (433ns)</span>
4473               </p>
4474             </td>
4475 <td>
4476             </td>
4477 <td>
4478             </td>
4479 <td>
4480             </td>
4481 </tr>
4482 <tr>
4483 <td>
4484               <p>
4485                 SkewNormal (PDF)
4486               </p>
4487             </td>
4488 <td>
4489               <p>
4490                 <span class="blue">1.53<br> (90ns)</span>
4491               </p>
4492             </td>
4493 <td>
4494               <p>
4495                 <span class="green">1.00<br> (59ns)</span>
4496               </p>
4497             </td>
4498 <td>
4499             </td>
4500 <td>
4501             </td>
4502 <td>
4503             </td>
4504 </tr>
4505 <tr>
4506 <td>
4507               <p>
4508                 SkewNormal (quantile)
4509               </p>
4510             </td>
4511 <td>
4512               <p>
4513                 <span class="green">1.07<br> (3697ns)</span>
4514               </p>
4515             </td>
4516 <td>
4517               <p>
4518                 <span class="green">1.00<br> (3440ns)</span>
4519               </p>
4520             </td>
4521 <td>
4522             </td>
4523 <td>
4524             </td>
4525 <td>
4526             </td>
4527 </tr>
4528 <tr>
4529 <td>
4530               <p>
4531                 StudentsT (CDF)
4532               </p>
4533             </td>
4534 <td>
4535               <p>
4536                 <span class="red">5.72<br> (1517ns)</span>
4537               </p>
4538             </td>
4539 <td>
4540               <p>
4541                 <span class="blue">1.82<br> (481ns)</span>
4542               </p>
4543             </td>
4544 <td>
4545               <p>
4546                 <span class="green">1.00<br> (265ns)</span>
4547               </p>
4548             </td>
4549 <td>
4550               <p>
4551                 <span class="blue">1.42<br> (375ns)</span>
4552               </p>
4553             </td>
4554 <td>
4555               <p>
4556                 <span class="blue">1.68<br> (446ns)</span>
4557               </p>
4558             </td>
4559 </tr>
4560 <tr>
4561 <td>
4562               <p>
4563                 StudentsT (PDF)
4564               </p>
4565             </td>
4566 <td>
4567               <p>
4568                 <span class="red">5.23<br> (716ns)</span>
4569               </p>
4570             </td>
4571 <td>
4572               <p>
4573                 <span class="blue">1.45<br> (198ns)</span>
4574               </p>
4575             </td>
4576 <td>
4577               <p>
4578                 <span class="grey">-</span>
4579               </p>
4580             </td>
4581 <td>
4582               <p>
4583                 <span class="green">1.00<br> (137ns)</span>
4584               </p>
4585             </td>
4586 <td>
4587             </td>
4588 </tr>
4589 <tr>
4590 <td>
4591               <p>
4592                 StudentsT (quantile)
4593               </p>
4594             </td>
4595 <td>
4596               <p>
4597                 <span class="red">3.04<br> (2557ns)</span>
4598               </p>
4599             </td>
4600 <td>
4601               <p>
4602                 <span class="green">1.00<br> (841ns)</span>
4603               </p>
4604             </td>
4605 <td>
4606               <p>
4607                 <span class="blue">1.37<br> (1148ns)</span>
4608               </p>
4609             </td>
4610 <td>
4611               <p>
4612                 <span class="green">1.16<br> (977ns)</span>
4613               </p>
4614             </td>
4615 <td>
4616               <p>
4617                 <span class="red">4.48<br> (3770ns)</span>
4618               </p>
4619             </td>
4620 </tr>
4621 <tr>
4622 <td>
4623               <p>
4624                 Weibull (CDF)
4625               </p>
4626             </td>
4627 <td>
4628               <p>
4629                 <span class="green">1.07<br> (91ns)</span>
4630               </p>
4631             </td>
4632 <td>
4633               <p>
4634                 <span class="green">1.00<br> (85ns)</span>
4635               </p>
4636             </td>
4637 <td>
4638               <p>
4639                 <span class="green">1.00<br> (85ns)</span>
4640               </p>
4641             </td>
4642 <td>
4643               <p>
4644                 <span class="green">1.19<br> (101ns)</span>
4645               </p>
4646             </td>
4647 <td>
4648             </td>
4649 </tr>
4650 <tr>
4651 <td>
4652               <p>
4653                 Weibull (PDF)
4654               </p>
4655             </td>
4656 <td>
4657               <p>
4658                 <span class="blue">1.48<br> (155ns)</span>
4659               </p>
4660             </td>
4661 <td>
4662               <p>
4663                 <span class="blue">1.47<br> (154ns)</span>
4664               </p>
4665             </td>
4666 <td>
4667               <p>
4668                 <span class="grey">-</span>
4669               </p>
4670             </td>
4671 <td>
4672               <p>
4673                 <span class="green">1.00<br> (105ns)</span>
4674               </p>
4675             </td>
4676 <td>
4677             </td>
4678 </tr>
4679 <tr>
4680 <td>
4681               <p>
4682                 Weibull (quantile)
4683               </p>
4684             </td>
4685 <td>
4686               <p>
4687                 <span class="green">1.00<br> (89ns)</span>
4688               </p>
4689             </td>
4690 <td>
4691               <p>
4692                 <span class="green">1.00<br> (89ns)</span>
4693               </p>
4694             </td>
4695 <td>
4696               <p>
4697                 <span class="green">1.16<br> (103ns)</span>
4698               </p>
4699             </td>
4700 <td>
4701               <p>
4702                 <span class="green">1.08<br> (96ns)</span>
4703               </p>
4704             </td>
4705 <td>
4706             </td>
4707 </tr>
4708 </tbody>
4709 </table></div>
4710 </div>
4711 <br class="table-break">
4712 </div>
4713 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
4714 <td align="left"></td>
4715 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
4716       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
4717       Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
4718       R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
4719       Daryle Walker and Xiaogang Zhang<p>
4720         Distributed under the Boost Software License, Version 1.0. (See accompanying
4721         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>)
4722       </p>
4723 </div></td>
4724 </tr></table>
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