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  26 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
  27 <a name="math_toolkit.comp_compilers"></a><a class="link" href="comp_compilers.html" title="Comparing Different Compilers">Comparing Different Compilers</a>
  28 </h2></div></div></div>
  29 <p>
  30       By running our performance test suite multiple times, we can compare the effect
  31       of different compilers: as might be expected, the differences are generally
  32       small compared to say disabling internal use of <code class="computeroutput"><span class="keyword">long</span>
  33       <span class="keyword">double</span></code>. However, there are still gains
  34       to be main, particularly from some of the commercial offerings:
  35     </p>
  36 <div class="table">
  37 <a name="math_toolkit.comp_compilers.table_Compiler_Comparison_on_Windows_x64"></a><p class="title"><b>Table&#160;21.5.&#160;Compiler Comparison on Windows x64</b></p>
  38 <div class="table-contents"><table class="table" summary="Compiler Comparison on Windows x64">
  39 <colgroup>
  40 <col>
  41 <col>
  42 <col>
  43 <col>
  44 <col>
  45 </colgroup>
  46 <thead><tr>
  47 <th>
  48               <p>
  49                 Function
  50               </p>
  51             </th>
  52 <th>
  53               <p>
  54                 Microsoft Visual C++ version 14.0<br> boost 1.61
  55               </p>
  56             </th>
  57 <th>
  58               <p>
  59                 GNU C++ version 5.3.0<br> boost 1.61
  60               </p>
  61             </th>
  62 <th>
  63               <p>
  64                 GNU C++ version 5.3.0<br> boost 1.61<br> promote_double&lt;false&gt;
  65               </p>
  66             </th>
  67 <th>
  68               <p>
  69                 Intel C++ C++0x mode version 1600<br> boost 1.61
  70               </p>
  71             </th>
  72 </tr></thead>
  73 <tbody>
  74 <tr>
  75 <td>
  76               <p>
  77                 assoc_laguerre
  78               </p>
  79             </td>
  80 <td>
  81               <p>
  82                 <span class="green">1.16<br> (208ns)</span>
  83               </p>
  84             </td>
  85 <td>
  86               <p>
  87                 <span class="blue">1.21<br> (217ns)</span>
  88               </p>
  89             </td>
  90 <td>
  91               <p>
  92                 <span class="green">1.06<br> (190ns)</span>
  93               </p>
  94             </td>
  95 <td>
  96               <p>
  97                 <span class="green">1.00<br> (180ns)</span>
  98               </p>
  99             </td>
 100 </tr>
 101 <tr>
 102 <td>
 103               <p>
 104                 assoc_legendre
 105               </p>
 106             </td>
 107 <td>
 108               <p>
 109                 <span class="blue">1.57<br> (151ns)</span>
 110               </p>
 111             </td>
 112 <td>
 113               <p>
 114                 <span class="blue">1.80<br> (173ns)</span>
 115               </p>
 116             </td>
 117 <td>
 118               <p>
 119                 <span class="green">1.16<br> (111ns)</span>
 120               </p>
 121             </td>
 122 <td>
 123               <p>
 124                 <span class="green">1.00<br> (96ns)</span>
 125               </p>
 126             </td>
 127 </tr>
 128 <tr>
 129 <td>
 130               <p>
 131                 beta
 132               </p>
 133             </td>
 134 <td>
 135               <p>
 136                 <span class="blue">1.74<br> (176ns)</span>
 137               </p>
 138             </td>
 139 <td>
 140               <p>
 141                 <span class="red">3.78<br> (382ns)</span>
 142               </p>
 143             </td>
 144 <td>
 145               <p>
 146                 <span class="red">2.17<br> (219ns)</span>
 147               </p>
 148             </td>
 149 <td>
 150               <p>
 151                 <span class="green">1.00<br> (101ns)</span>
 152               </p>
 153             </td>
 154 </tr>
 155 <tr>
 156 <td>
 157               <p>
 158                 beta (incomplete)
 159               </p>
 160             </td>
 161 <td>
 162               <p>
 163                 <span class="blue">1.44<br> (520ns)</span>
 164               </p>
 165             </td>
 166 <td>
 167               <p>
 168                 <span class="red">3.03<br> (1096ns)</span>
 169               </p>
 170             </td>
 171 <td>
 172               <p>
 173                 <span class="blue">1.84<br> (666ns)</span>
 174               </p>
 175             </td>
 176 <td>
 177               <p>
 178                 <span class="green">1.00<br> (362ns)</span>
 179               </p>
 180             </td>
 181 </tr>
 182 <tr>
 183 <td>
 184               <p>
 185                 cbrt
 186               </p>
 187             </td>
 188 <td>
 189               <p>
 190                 <span class="red">3.21<br> (45ns)</span>
 191               </p>
 192             </td>
 193 <td>
 194               <p>
 195                 <span class="red">3.43<br> (48ns)</span>
 196               </p>
 197             </td>
 198 <td>
 199               <p>
 200                 <span class="red">3.07<br> (43ns)</span>
 201               </p>
 202             </td>
 203 <td>
 204               <p>
 205                 <span class="green">1.00<br> (14ns)</span>
 206               </p>
 207             </td>
 208 </tr>
 209 <tr>
 210 <td>
 211               <p>
 212                 cyl_bessel_i
 213               </p>
 214             </td>
 215 <td>
 216               <p>
 217                 <span class="green">1.11<br> (404ns)</span>
 218               </p>
 219             </td>
 220 <td>
 221               <p>
 222                 <span class="red">2.78<br> (1016ns)</span>
 223               </p>
 224             </td>
 225 <td>
 226               <p>
 227                 <span class="blue">1.21<br> (442ns)</span>
 228               </p>
 229             </td>
 230 <td>
 231               <p>
 232                 <span class="green">1.00<br> (365ns)</span>
 233               </p>
 234             </td>
 235 </tr>
 236 <tr>
 237 <td>
 238               <p>
 239                 cyl_bessel_i (integer order)
 240               </p>
 241             </td>
 242 <td>
 243               <p>
 244                 <span class="blue">1.29<br> (261ns)</span>
 245               </p>
 246             </td>
 247 <td>
 248               <p>
 249                 <span class="red">3.16<br> (638ns)</span>
 250               </p>
 251             </td>
 252 <td>
 253               <p>
 254                 <span class="blue">1.22<br> (247ns)</span>
 255               </p>
 256             </td>
 257 <td>
 258               <p>
 259                 <span class="green">1.00<br> (202ns)</span>
 260               </p>
 261             </td>
 262 </tr>
 263 <tr>
 264 <td>
 265               <p>
 266                 cyl_bessel_j
 267               </p>
 268             </td>
 269 <td>
 270               <p>
 271                 <span class="green">1.19<br> (488ns)</span>
 272               </p>
 273             </td>
 274 <td>
 275               <p>
 276                 <span class="red">2.06<br> (841ns)</span>
 277               </p>
 278             </td>
 279 <td>
 280               <p>
 281                 <span class="blue">1.25<br> (513ns)</span>
 282               </p>
 283             </td>
 284 <td>
 285               <p>
 286                 <span class="green">1.00<br> (409ns)</span>
 287               </p>
 288             </td>
 289 </tr>
 290 <tr>
 291 <td>
 292               <p>
 293                 cyl_bessel_j (integer order)
 294               </p>
 295             </td>
 296 <td>
 297               <p>
 298                 <span class="blue">1.36<br> (103ns)</span>
 299               </p>
 300             </td>
 301 <td>
 302               <p>
 303                 <span class="red">2.39<br> (182ns)</span>
 304               </p>
 305             </td>
 306 <td>
 307               <p>
 308                 <span class="blue">1.47<br> (112ns)</span>
 309               </p>
 310             </td>
 311 <td>
 312               <p>
 313                 <span class="green">1.00<br> (76ns)</span>
 314               </p>
 315             </td>
 316 </tr>
 317 <tr>
 318 <td>
 319               <p>
 320                 cyl_bessel_k
 321               </p>
 322             </td>
 323 <td>
 324               <p>
 325                 <span class="green">1.04<br> (747ns)</span>
 326               </p>
 327             </td>
 328 <td>
 329               <p>
 330                 <span class="red">9.43<br> (6743ns)</span>
 331               </p>
 332             </td>
 333 <td>
 334               <p>
 335                 <span class="green">1.03<br> (734ns)</span>
 336               </p>
 337             </td>
 338 <td>
 339               <p>
 340                 <span class="green">1.00<br> (715ns)</span>
 341               </p>
 342             </td>
 343 </tr>
 344 <tr>
 345 <td>
 346               <p>
 347                 cyl_bessel_k (integer order)
 348               </p>
 349             </td>
 350 <td>
 351               <p>
 352                 <span class="blue">1.26<br> (419ns)</span>
 353               </p>
 354             </td>
 355 <td>
 356               <p>
 357                 <span class="red">10.49<br> (3494ns)</span>
 358               </p>
 359             </td>
 360 <td>
 361               <p>
 362                 <span class="green">1.10<br> (367ns)</span>
 363               </p>
 364             </td>
 365 <td>
 366               <p>
 367                 <span class="green">1.00<br> (333ns)</span>
 368               </p>
 369             </td>
 370 </tr>
 371 <tr>
 372 <td>
 373               <p>
 374                 cyl_neumann
 375               </p>
 376             </td>
 377 <td>
 378               <p>
 379                 <span class="red">16.76<br> (11212ns)</span>
 380               </p>
 381             </td>
 382 <td>
 383               <p>
 384                 <span class="red">2.01<br> (1346ns)</span>
 385               </p>
 386             </td>
 387 <td>
 388               <p>
 389                 <span class="green">1.00<br> (669ns)</span>
 390               </p>
 391             </td>
 392 <td>
 393               <p>
 394                 <span class="red">15.35<br> (10266ns)</span>
 395               </p>
 396             </td>
 397 </tr>
 398 <tr>
 399 <td>
 400               <p>
 401                 cyl_neumann (integer order)
 402               </p>
 403             </td>
 404 <td>
 405               <p>
 406                 <span class="green">1.00<br> (225ns)</span>
 407               </p>
 408             </td>
 409 <td>
 410               <p>
 411                 <span class="blue">1.79<br> (403ns)</span>
 412               </p>
 413             </td>
 414 <td>
 415               <p>
 416                 <span class="blue">1.24<br> (279ns)</span>
 417               </p>
 418             </td>
 419 <td>
 420               <p>
 421                 <span class="green">1.02<br> (229ns)</span>
 422               </p>
 423             </td>
 424 </tr>
 425 <tr>
 426 <td>
 427               <p>
 428                 digamma
 429               </p>
 430             </td>
 431 <td>
 432               <p>
 433                 <span class="green">1.20<br> (24ns)</span>
 434               </p>
 435             </td>
 436 <td>
 437               <p>
 438                 <span class="red">3.75<br> (75ns)</span>
 439               </p>
 440             </td>
 441 <td>
 442               <p>
 443                 <span class="red">2.15<br> (43ns)</span>
 444               </p>
 445             </td>
 446 <td>
 447               <p>
 448                 <span class="green">1.00<br> (20ns)</span>
 449               </p>
 450             </td>
 451 </tr>
 452 <tr>
 453 <td>
 454               <p>
 455                 ellint_1
 456               </p>
 457             </td>
 458 <td>
 459               <p>
 460                 <span class="blue">1.87<br> (329ns)</span>
 461               </p>
 462             </td>
 463 <td>
 464               <p>
 465                 <span class="blue">1.99<br> (350ns)</span>
 466               </p>
 467             </td>
 468 <td>
 469               <p>
 470                 <span class="blue">1.32<br> (232ns)</span>
 471               </p>
 472             </td>
 473 <td>
 474               <p>
 475                 <span class="green">1.00<br> (176ns)</span>
 476               </p>
 477             </td>
 478 </tr>
 479 <tr>
 480 <td>
 481               <p>
 482                 ellint_1 (complete)
 483               </p>
 484             </td>
 485 <td>
 486               <p>
 487                 <span class="red">2.18<br> (61ns)</span>
 488               </p>
 489             </td>
 490 <td>
 491               <p>
 492                 <span class="red">2.57<br> (72ns)</span>
 493               </p>
 494             </td>
 495 <td>
 496               <p>
 497                 <span class="blue">1.57<br> (44ns)</span>
 498               </p>
 499             </td>
 500 <td>
 501               <p>
 502                 <span class="green">1.00<br> (28ns)</span>
 503               </p>
 504             </td>
 505 </tr>
 506 <tr>
 507 <td>
 508               <p>
 509                 ellint_2
 510               </p>
 511             </td>
 512 <td>
 513               <p>
 514                 <span class="blue">1.78<br> (525ns)</span>
 515               </p>
 516             </td>
 517 <td>
 518               <p>
 519                 <span class="red">2.17<br> (640ns)</span>
 520               </p>
 521             </td>
 522 <td>
 523               <p>
 524                 <span class="blue">1.52<br> (449ns)</span>
 525               </p>
 526             </td>
 527 <td>
 528               <p>
 529                 <span class="green">1.00<br> (295ns)</span>
 530               </p>
 531             </td>
 532 </tr>
 533 <tr>
 534 <td>
 535               <p>
 536                 ellint_2 (complete)
 537               </p>
 538             </td>
 539 <td>
 540               <p>
 541                 <span class="red">2.14<br> (62ns)</span>
 542               </p>
 543             </td>
 544 <td>
 545               <p>
 546                 <span class="red">2.07<br> (60ns)</span>
 547               </p>
 548             </td>
 549 <td>
 550               <p>
 551                 <span class="blue">1.24<br> (36ns)</span>
 552               </p>
 553             </td>
 554 <td>
 555               <p>
 556                 <span class="green">1.00<br> (29ns)</span>
 557               </p>
 558             </td>
 559 </tr>
 560 <tr>
 561 <td>
 562               <p>
 563                 ellint_3
 564               </p>
 565             </td>
 566 <td>
 567               <p>
 568                 <span class="blue">1.94<br> (1155ns)</span>
 569               </p>
 570             </td>
 571 <td>
 572               <p>
 573                 <span class="red">2.91<br> (1733ns)</span>
 574               </p>
 575             </td>
 576 <td>
 577               <p>
 578                 <span class="blue">1.65<br> (986ns)</span>
 579               </p>
 580             </td>
 581 <td>
 582               <p>
 583                 <span class="green">1.00<br> (596ns)</span>
 584               </p>
 585             </td>
 586 </tr>
 587 <tr>
 588 <td>
 589               <p>
 590                 ellint_3 (complete)
 591               </p>
 592             </td>
 593 <td>
 594               <p>
 595                 <span class="red">2.05<br> (721ns)</span>
 596               </p>
 597             </td>
 598 <td>
 599               <p>
 600                 <span class="red">3.07<br> (1079ns)</span>
 601               </p>
 602             </td>
 603 <td>
 604               <p>
 605                 <span class="blue">1.46<br> (514ns)</span>
 606               </p>
 607             </td>
 608 <td>
 609               <p>
 610                 <span class="green">1.00<br> (352ns)</span>
 611               </p>
 612             </td>
 613 </tr>
 614 <tr>
 615 <td>
 616               <p>
 617                 ellint_rc
 618               </p>
 619             </td>
 620 <td>
 621               <p>
 622                 <span class="blue">1.58<br> (49ns)</span>
 623               </p>
 624             </td>
 625 <td>
 626               <p>
 627                 <span class="red">2.68<br> (83ns)</span>
 628               </p>
 629             </td>
 630 <td>
 631               <p>
 632                 <span class="blue">1.55<br> (48ns)</span>
 633               </p>
 634             </td>
 635 <td>
 636               <p>
 637                 <span class="green">1.00<br> (31ns)</span>
 638               </p>
 639             </td>
 640 </tr>
 641 <tr>
 642 <td>
 643               <p>
 644                 ellint_rd
 645               </p>
 646             </td>
 647 <td>
 648               <p>
 649                 <span class="blue">1.75<br> (332ns)</span>
 650               </p>
 651             </td>
 652 <td>
 653               <p>
 654                 <span class="blue">1.83<br> (348ns)</span>
 655               </p>
 656             </td>
 657 <td>
 658               <p>
 659                 <span class="blue">1.40<br> (266ns)</span>
 660               </p>
 661             </td>
 662 <td>
 663               <p>
 664                 <span class="green">1.00<br> (190ns)</span>
 665               </p>
 666             </td>
 667 </tr>
 668 <tr>
 669 <td>
 670               <p>
 671                 ellint_rf
 672               </p>
 673             </td>
 674 <td>
 675               <p>
 676                 <span class="blue">1.69<br> (71ns)</span>
 677               </p>
 678             </td>
 679 <td>
 680               <p>
 681                 <span class="red">2.40<br> (101ns)</span>
 682               </p>
 683             </td>
 684 <td>
 685               <p>
 686                 <span class="blue">1.57<br> (66ns)</span>
 687               </p>
 688             </td>
 689 <td>
 690               <p>
 691                 <span class="green">1.00<br> (42ns)</span>
 692               </p>
 693             </td>
 694 </tr>
 695 <tr>
 696 <td>
 697               <p>
 698                 ellint_rj
 699               </p>
 700             </td>
 701 <td>
 702               <p>
 703                 <span class="blue">1.91<br> (344ns)</span>
 704               </p>
 705             </td>
 706 <td>
 707               <p>
 708                 <span class="red">2.96<br> (532ns)</span>
 709               </p>
 710             </td>
 711 <td>
 712               <p>
 713                 <span class="blue">1.43<br> (257ns)</span>
 714               </p>
 715             </td>
 716 <td>
 717               <p>
 718                 <span class="green">1.00<br> (180ns)</span>
 719               </p>
 720             </td>
 721 </tr>
 722 <tr>
 723 <td>
 724               <p>
 725                 erf
 726               </p>
 727             </td>
 728 <td>
 729               <p>
 730                 <span class="blue">1.77<br> (23ns)</span>
 731               </p>
 732             </td>
 733 <td>
 734               <p>
 735                 <span class="red">2.92<br> (38ns)</span>
 736               </p>
 737             </td>
 738 <td>
 739               <p>
 740                 <span class="blue">1.92<br> (25ns)</span>
 741               </p>
 742             </td>
 743 <td>
 744               <p>
 745                 <span class="green">1.00<br> (13ns)</span>
 746               </p>
 747             </td>
 748 </tr>
 749 <tr>
 750 <td>
 751               <p>
 752                 erfc
 753               </p>
 754             </td>
 755 <td>
 756               <p>
 757                 <span class="blue">1.29<br> (22ns)</span>
 758               </p>
 759             </td>
 760 <td>
 761               <p>
 762                 <span class="red">3.41<br> (58ns)</span>
 763               </p>
 764             </td>
 765 <td>
 766               <p>
 767                 <span class="red">2.06<br> (35ns)</span>
 768               </p>
 769             </td>
 770 <td>
 771               <p>
 772                 <span class="green">1.00<br> (17ns)</span>
 773               </p>
 774             </td>
 775 </tr>
 776 <tr>
 777 <td>
 778               <p>
 779                 expint
 780               </p>
 781             </td>
 782 <td>
 783               <p>
 784                 <span class="blue">1.39<br> (39ns)</span>
 785               </p>
 786             </td>
 787 <td>
 788               <p>
 789                 <span class="red">3.07<br> (86ns)</span>
 790               </p>
 791             </td>
 792 <td>
 793               <p>
 794                 <span class="red">2.14<br> (60ns)</span>
 795               </p>
 796             </td>
 797 <td>
 798               <p>
 799                 <span class="green">1.00<br> (28ns)</span>
 800               </p>
 801             </td>
 802 </tr>
 803 <tr>
 804 <td>
 805               <p>
 806                 expint (En)
 807               </p>
 808             </td>
 809 <td>
 810               <p>
 811                 <span class="green">1.10<br> (117ns)</span>
 812               </p>
 813             </td>
 814 <td>
 815               <p>
 816                 <span class="red">2.19<br> (232ns)</span>
 817               </p>
 818             </td>
 819 <td>
 820               <p>
 821                 <span class="blue">1.38<br> (146ns)</span>
 822               </p>
 823             </td>
 824 <td>
 825               <p>
 826                 <span class="green">1.00<br> (106ns)</span>
 827               </p>
 828             </td>
 829 </tr>
 830 <tr>
 831 <td>
 832               <p>
 833                 expm1
 834               </p>
 835             </td>
 836 <td>
 837               <p>
 838                 <span class="green">1.00<br> (10ns)</span>
 839               </p>
 840             </td>
 841 <td>
 842               <p>
 843                 <span class="red">3.10<br> (31ns)</span>
 844               </p>
 845             </td>
 846 <td>
 847               <p>
 848                 <span class="red">2.40<br> (24ns)</span>
 849               </p>
 850             </td>
 851 <td>
 852               <p>
 853                 <span class="green">1.10<br> (11ns)</span>
 854               </p>
 855             </td>
 856 </tr>
 857 <tr>
 858 <td>
 859               <p>
 860                 gamma_p
 861               </p>
 862             </td>
 863 <td>
 864               <p>
 865                 <span class="blue">1.29<br> (192ns)</span>
 866               </p>
 867             </td>
 868 <td>
 869               <p>
 870                 <span class="red">2.64<br> (393ns)</span>
 871               </p>
 872             </td>
 873 <td>
 874               <p>
 875                 <span class="blue">1.71<br> (255ns)</span>
 876               </p>
 877             </td>
 878 <td>
 879               <p>
 880                 <span class="green">1.00<br> (149ns)</span>
 881               </p>
 882             </td>
 883 </tr>
 884 <tr>
 885 <td>
 886               <p>
 887                 gamma_p_inv
 888               </p>
 889             </td>
 890 <td>
 891               <p>
 892                 <span class="blue">1.36<br> (706ns)</span>
 893               </p>
 894             </td>
 895 <td>
 896               <p>
 897                 <span class="red">2.47<br> (1288ns)</span>
 898               </p>
 899             </td>
 900 <td>
 901               <p>
 902                 <span class="blue">1.91<br> (997ns)</span>
 903               </p>
 904             </td>
 905 <td>
 906               <p>
 907                 <span class="green">1.00<br> (521ns)</span>
 908               </p>
 909             </td>
 910 </tr>
 911 <tr>
 912 <td>
 913               <p>
 914                 gamma_q
 915               </p>
 916             </td>
 917 <td>
 918               <p>
 919                 <span class="green">1.16<br> (179ns)</span>
 920               </p>
 921             </td>
 922 <td>
 923               <p>
 924                 <span class="red">2.79<br> (429ns)</span>
 925               </p>
 926             </td>
 927 <td>
 928               <p>
 929                 <span class="blue">1.61<br> (248ns)</span>
 930               </p>
 931             </td>
 932 <td>
 933               <p>
 934                 <span class="green">1.00<br> (154ns)</span>
 935               </p>
 936             </td>
 937 </tr>
 938 <tr>
 939 <td>
 940               <p>
 941                 gamma_q_inv
 942               </p>
 943             </td>
 944 <td>
 945               <p>
 946                 <span class="blue">1.37<br> (703ns)</span>
 947               </p>
 948             </td>
 949 <td>
 950               <p>
 951                 <span class="red">2.38<br> (1225ns)</span>
 952               </p>
 953             </td>
 954 <td>
 955               <p>
 956                 <span class="blue">1.89<br> (971ns)</span>
 957               </p>
 958             </td>
 959 <td>
 960               <p>
 961                 <span class="green">1.00<br> (515ns)</span>
 962               </p>
 963             </td>
 964 </tr>
 965 <tr>
 966 <td>
 967               <p>
 968                 ibeta
 969               </p>
 970             </td>
 971 <td>
 972               <p>
 973                 <span class="blue">1.34<br> (520ns)</span>
 974               </p>
 975             </td>
 976 <td>
 977               <p>
 978                 <span class="red">3.13<br> (1218ns)</span>
 979               </p>
 980             </td>
 981 <td>
 982               <p>
 983                 <span class="blue">1.83<br> (711ns)</span>
 984               </p>
 985             </td>
 986 <td>
 987               <p>
 988                 <span class="green">1.00<br> (389ns)</span>
 989               </p>
 990             </td>
 991 </tr>
 992 <tr>
 993 <td>
 994               <p>
 995                 ibeta_inv
 996               </p>
 997             </td>
 998 <td>
 999               <p>
1000                 <span class="blue">1.51<br> (2193ns)</span>
1001               </p>
1002             </td>
1003 <td>
1004               <p>
1005                 <span class="red">2.81<br> (4085ns)</span>
1006               </p>
1007             </td>
1008 <td>
1009               <p>
1010                 <span class="red">2.27<br> (3303ns)</span>
1011               </p>
1012             </td>
1013 <td>
1014               <p>
1015                 <span class="green">1.00<br> (1452ns)</span>
1016               </p>
1017             </td>
1018 </tr>
1019 <tr>
1020 <td>
1021               <p>
1022                 ibetac
1023               </p>
1024             </td>
1025 <td>
1026               <p>
1027                 <span class="blue">1.29<br> (518ns)</span>
1028               </p>
1029             </td>
1030 <td>
1031               <p>
1032                 <span class="red">2.94<br> (1179ns)</span>
1033               </p>
1034             </td>
1035 <td>
1036               <p>
1037                 <span class="blue">1.73<br> (694ns)</span>
1038               </p>
1039             </td>
1040 <td>
1041               <p>
1042                 <span class="green">1.00<br> (401ns)</span>
1043               </p>
1044             </td>
1045 </tr>
1046 <tr>
1047 <td>
1048               <p>
1049                 ibetac_inv
1050               </p>
1051             </td>
1052 <td>
1053               <p>
1054                 <span class="blue">1.41<br> (2045ns)</span>
1055               </p>
1056             </td>
1057 <td>
1058               <p>
1059                 <span class="red">2.80<br> (4058ns)</span>
1060               </p>
1061             </td>
1062 <td>
1063               <p>
1064                 <span class="blue">1.78<br> (2572ns)</span>
1065               </p>
1066             </td>
1067 <td>
1068               <p>
1069                 <span class="green">1.00<br> (1447ns)</span>
1070               </p>
1071             </td>
1072 </tr>
1073 <tr>
1074 <td>
1075               <p>
1076                 jacobi_cn
1077               </p>
1078             </td>
1079 <td>
1080               <p>
1081                 <span class="blue">1.36<br> (182ns)</span>
1082               </p>
1083             </td>
1084 <td>
1085               <p>
1086                 <span class="red">3.72<br> (499ns)</span>
1087               </p>
1088             </td>
1089 <td>
1090               <p>
1091                 <span class="red">2.28<br> (306ns)</span>
1092               </p>
1093             </td>
1094 <td>
1095               <p>
1096                 <span class="green">1.00<br> (134ns)</span>
1097               </p>
1098             </td>
1099 </tr>
1100 <tr>
1101 <td>
1102               <p>
1103                 jacobi_dn
1104               </p>
1105             </td>
1106 <td>
1107               <p>
1108                 <span class="blue">1.82<br> (262ns)</span>
1109               </p>
1110             </td>
1111 <td>
1112               <p>
1113                 <span class="red">3.68<br> (530ns)</span>
1114               </p>
1115             </td>
1116 <td>
1117               <p>
1118                 <span class="red">2.27<br> (327ns)</span>
1119               </p>
1120             </td>
1121 <td>
1122               <p>
1123                 <span class="green">1.00<br> (144ns)</span>
1124               </p>
1125             </td>
1126 </tr>
1127 <tr>
1128 <td>
1129               <p>
1130                 jacobi_sn
1131               </p>
1132             </td>
1133 <td>
1134               <p>
1135                 <span class="blue">1.31<br> (179ns)</span>
1136               </p>
1137             </td>
1138 <td>
1139               <p>
1140                 <span class="red">3.73<br> (511ns)</span>
1141               </p>
1142             </td>
1143 <td>
1144               <p>
1145                 <span class="red">2.43<br> (333ns)</span>
1146               </p>
1147             </td>
1148 <td>
1149               <p>
1150                 <span class="green">1.00<br> (137ns)</span>
1151               </p>
1152             </td>
1153 </tr>
1154 <tr>
1155 <td>
1156               <p>
1157                 laguerre
1158               </p>
1159             </td>
1160 <td>
1161               <p>
1162                 <span class="green">1.00<br> (121ns)</span>
1163               </p>
1164             </td>
1165 <td>
1166               <p>
1167                 <span class="green">1.15<br> (139ns)</span>
1168               </p>
1169             </td>
1170 <td>
1171               <p>
1172                 <span class="green">1.04<br> (126ns)</span>
1173               </p>
1174             </td>
1175 <td>
1176               <p>
1177                 <span class="green">1.10<br> (133ns)</span>
1178               </p>
1179             </td>
1180 </tr>
1181 <tr>
1182 <td>
1183               <p>
1184                 legendre
1185               </p>
1186             </td>
1187 <td>
1188               <p>
1189                 <span class="green">1.07<br> (364ns)</span>
1190               </p>
1191             </td>
1192 <td>
1193               <p>
1194                 <span class="green">1.16<br> (396ns)</span>
1195               </p>
1196             </td>
1197 <td>
1198               <p>
1199                 <span class="green">1.00<br> (340ns)</span>
1200               </p>
1201             </td>
1202 <td>
1203               <p>
1204                 <span class="green">1.13<br> (383ns)</span>
1205               </p>
1206             </td>
1207 </tr>
1208 <tr>
1209 <td>
1210               <p>
1211                 legendre Q
1212               </p>
1213             </td>
1214 <td>
1215               <p>
1216                 <span class="green">1.00<br> (427ns)</span>
1217               </p>
1218             </td>
1219 <td>
1220               <p>
1221                 <span class="green">1.20<br> (512ns)</span>
1222               </p>
1223             </td>
1224 <td>
1225               <p>
1226                 <span class="green">1.01<br> (430ns)</span>
1227               </p>
1228             </td>
1229 <td>
1230               <p>
1231                 <span class="green">1.07<br> (455ns)</span>
1232               </p>
1233             </td>
1234 </tr>
1235 <tr>
1236 <td>
1237               <p>
1238                 lgamma
1239               </p>
1240             </td>
1241 <td>
1242               <p>
1243                 <span class="green">1.00<br> (73ns)</span>
1244               </p>
1245             </td>
1246 <td>
1247               <p>
1248                 <span class="red">3.07<br> (224ns)</span>
1249               </p>
1250             </td>
1251 <td>
1252               <p>
1253                 <span class="blue">1.82<br> (133ns)</span>
1254               </p>
1255             </td>
1256 <td>
1257               <p>
1258                 <span class="green">1.05<br> (77ns)</span>
1259               </p>
1260             </td>
1261 </tr>
1262 <tr>
1263 <td>
1264               <p>
1265                 log1p
1266               </p>
1267             </td>
1268 <td>
1269               <p>
1270                 <span class="green">1.00<br> (14ns)</span>
1271               </p>
1272             </td>
1273 <td>
1274               <p>
1275                 <span class="blue">2.00<br> (28ns)</span>
1276               </p>
1277             </td>
1278 <td>
1279               <p>
1280                 <span class="green">1.14<br> (16ns)</span>
1281               </p>
1282             </td>
1283 <td>
1284               <p>
1285                 <span class="green">1.00<br> (14ns)</span>
1286               </p>
1287             </td>
1288 </tr>
1289 <tr>
1290 <td>
1291               <p>
1292                 polygamma
1293               </p>
1294             </td>
1295 <td>
1296               <p>
1297                 <span class="green">1.16<br> (3773ns)</span>
1298               </p>
1299             </td>
1300 <td>
1301               <p>
1302                 <span class="green">1.02<br> (3320ns)</span>
1303               </p>
1304             </td>
1305 <td>
1306               <p>
1307                 <span class="red">2.24<br> (7270ns)</span>
1308               </p>
1309             </td>
1310 <td>
1311               <p>
1312                 <span class="green">1.00<br> (3246ns)</span>
1313               </p>
1314             </td>
1315 </tr>
1316 <tr>
1317 <td>
1318               <p>
1319                 sph_bessel
1320               </p>
1321             </td>
1322 <td>
1323               <p>
1324                 <span class="green">1.17<br> (1005ns)</span>
1325               </p>
1326             </td>
1327 <td>
1328               <p>
1329                 <span class="blue">1.55<br> (1325ns)</span>
1330               </p>
1331             </td>
1332 <td>
1333               <p>
1334                 <span class="green">1.09<br> (931ns)</span>
1335               </p>
1336             </td>
1337 <td>
1338               <p>
1339                 <span class="green">1.00<br> (857ns)</span>
1340               </p>
1341             </td>
1342 </tr>
1343 <tr>
1344 <td>
1345               <p>
1346                 sph_neumann
1347               </p>
1348             </td>
1349 <td>
1350               <p>
1351                 <span class="green">1.08<br> (1827ns)</span>
1352               </p>
1353             </td>
1354 <td>
1355               <p>
1356                 <span class="red">2.07<br> (3483ns)</span>
1357               </p>
1358             </td>
1359 <td>
1360               <p>
1361                 <span class="green">1.00<br> (1685ns)</span>
1362               </p>
1363             </td>
1364 <td>
1365               <p>
1366                 <span class="green">1.01<br> (1702ns)</span>
1367               </p>
1368             </td>
1369 </tr>
1370 <tr>
1371 <td>
1372               <p>
1373                 tgamma
1374               </p>
1375             </td>
1376 <td>
1377               <p>
1378                 <span class="blue">1.31<br> (77ns)</span>
1379               </p>
1380             </td>
1381 <td>
1382               <p>
1383                 <span class="red">4.03<br> (238ns)</span>
1384               </p>
1385             </td>
1386 <td>
1387               <p>
1388                 <span class="red">2.49<br> (147ns)</span>
1389               </p>
1390             </td>
1391 <td>
1392               <p>
1393                 <span class="green">1.00<br> (59ns)</span>
1394               </p>
1395             </td>
1396 </tr>
1397 <tr>
1398 <td>
1399               <p>
1400                 tgamma (incomplete)
1401               </p>
1402             </td>
1403 <td>
1404               <p>
1405                 <span class="blue">1.26<br> (276ns)</span>
1406               </p>
1407             </td>
1408 <td>
1409               <p>
1410                 <span class="red">2.52<br> (552ns)</span>
1411               </p>
1412             </td>
1413 <td>
1414               <p>
1415                 <span class="blue">1.73<br> (379ns)</span>
1416               </p>
1417             </td>
1418 <td>
1419               <p>
1420                 <span class="green">1.00<br> (219ns)</span>
1421               </p>
1422             </td>
1423 </tr>
1424 <tr>
1425 <td>
1426               <p>
1427                 trigamma
1428               </p>
1429             </td>
1430 <td>
1431               <p>
1432                 <span class="blue">1.35<br> (23ns)</span>
1433               </p>
1434             </td>
1435 <td>
1436               <p>
1437                 <span class="red">2.88<br> (49ns)</span>
1438               </p>
1439             </td>
1440 <td>
1441               <p>
1442                 <span class="blue">1.41<br> (24ns)</span>
1443               </p>
1444             </td>
1445 <td>
1446               <p>
1447                 <span class="green">1.00<br> (17ns)</span>
1448               </p>
1449             </td>
1450 </tr>
1451 <tr>
1452 <td>
1453               <p>
1454                 zeta
1455               </p>
1456             </td>
1457 <td>
1458               <p>
1459                 <span class="blue">1.34<br> (121ns)</span>
1460               </p>
1461             </td>
1462 <td>
1463               <p>
1464                 <span class="red">3.83<br> (345ns)</span>
1465               </p>
1466             </td>
1467 <td>
1468               <p>
1469                 <span class="red">2.52<br> (227ns)</span>
1470               </p>
1471             </td>
1472 <td>
1473               <p>
1474                 <span class="green">1.00<br> (90ns)</span>
1475               </p>
1476             </td>
1477 </tr>
1478 </tbody>
1479 </table></div>
1480 </div>
1481 <br class="table-break"><div class="table">
1482 <a name="math_toolkit.comp_compilers.table_Compiler_Comparison_on_linux"></a><p class="title"><b>Table&#160;21.6.&#160;Compiler Comparison on linux</b></p>
1483 <div class="table-contents"><table class="table" summary="Compiler Comparison on linux">
1484 <colgroup>
1485 <col>
1486 <col>
1487 <col>
1488 </colgroup>
1489 <thead><tr>
1490 <th>
1491               <p>
1492                 Function
1493               </p>
1494             </th>
1495 <th>
1496               <p>
1497                 GNU C++ version 5.3.0<br> boost 1.61
1498               </p>
1499             </th>
1500 <th>
1501               <p>
1502                 GNU C++ version 5.3.0<br> boost 1.61<br> promote_double&lt;false&gt;
1503               </p>
1504             </th>
1505 </tr></thead>
1506 <tbody>
1507 <tr>
1508 <td>
1509               <p>
1510                 assoc_laguerre
1511               </p>
1512             </td>
1513 <td>
1514               <p>
1515                 <span class="blue">1.36<br> (263ns)</span>
1516               </p>
1517             </td>
1518 <td>
1519               <p>
1520                 <span class="green">1.00<br> (194ns)</span>
1521               </p>
1522             </td>
1523 </tr>
1524 <tr>
1525 <td>
1526               <p>
1527                 assoc_legendre
1528               </p>
1529             </td>
1530 <td>
1531               <p>
1532                 <span class="red">2.55<br> (258ns)</span>
1533               </p>
1534             </td>
1535 <td>
1536               <p>
1537                 <span class="green">1.00<br> (101ns)</span>
1538               </p>
1539             </td>
1540 </tr>
1541 <tr>
1542 <td>
1543               <p>
1544                 beta
1545               </p>
1546             </td>
1547 <td>
1548               <p>
1549                 <span class="red">4.71<br> (734ns)</span>
1550               </p>
1551             </td>
1552 <td>
1553               <p>
1554                 <span class="green">1.00<br> (156ns)</span>
1555               </p>
1556             </td>
1557 </tr>
1558 <tr>
1559 <td>
1560               <p>
1561                 beta (incomplete)
1562               </p>
1563             </td>
1564 <td>
1565               <p>
1566                 <span class="red">3.12<br> (1796ns)</span>
1567               </p>
1568             </td>
1569 <td>
1570               <p>
1571                 <span class="green">1.00<br> (575ns)</span>
1572               </p>
1573             </td>
1574 </tr>
1575 <tr>
1576 <td>
1577               <p>
1578                 cbrt
1579               </p>
1580             </td>
1581 <td>
1582               <p>
1583                 <span class="red">2.53<br> (43ns)</span>
1584               </p>
1585             </td>
1586 <td>
1587               <p>
1588                 <span class="green">1.00<br> (17ns)</span>
1589               </p>
1590             </td>
1591 </tr>
1592 <tr>
1593 <td>
1594               <p>
1595                 cyl_bessel_i
1596               </p>
1597             </td>
1598 <td>
1599               <p>
1600                 <span class="red">3.47<br> (1410ns)</span>
1601               </p>
1602             </td>
1603 <td>
1604               <p>
1605                 <span class="green">1.00<br> (406ns)</span>
1606               </p>
1607             </td>
1608 </tr>
1609 <tr>
1610 <td>
1611               <p>
1612                 cyl_bessel_i (integer order)
1613               </p>
1614             </td>
1615 <td>
1616               <p>
1617                 <span class="red">3.38<br> (893ns)</span>
1618               </p>
1619             </td>
1620 <td>
1621               <p>
1622                 <span class="green">1.00<br> (264ns)</span>
1623               </p>
1624             </td>
1625 </tr>
1626 <tr>
1627 <td>
1628               <p>
1629                 cyl_bessel_j
1630               </p>
1631             </td>
1632 <td>
1633               <p>
1634                 <span class="red">2.69<br> (1071ns)</span>
1635               </p>
1636             </td>
1637 <td>
1638               <p>
1639                 <span class="green">1.00<br> (398ns)</span>
1640               </p>
1641             </td>
1642 </tr>
1643 <tr>
1644 <td>
1645               <p>
1646                 cyl_bessel_j (integer order)
1647               </p>
1648             </td>
1649 <td>
1650               <p>
1651                 <span class="red">2.59<br> (275ns)</span>
1652               </p>
1653             </td>
1654 <td>
1655               <p>
1656                 <span class="green">1.00<br> (106ns)</span>
1657               </p>
1658             </td>
1659 </tr>
1660 <tr>
1661 <td>
1662               <p>
1663                 cyl_bessel_k
1664               </p>
1665             </td>
1666 <td>
1667               <p>
1668                 <span class="red">6.86<br> (4589ns)</span>
1669               </p>
1670             </td>
1671 <td>
1672               <p>
1673                 <span class="green">1.00<br> (669ns)</span>
1674               </p>
1675             </td>
1676 </tr>
1677 <tr>
1678 <td>
1679               <p>
1680                 cyl_bessel_k (integer order)
1681               </p>
1682             </td>
1683 <td>
1684               <p>
1685                 <span class="red">10.17<br> (3673ns)</span>
1686               </p>
1687             </td>
1688 <td>
1689               <p>
1690                 <span class="green">1.00<br> (361ns)</span>
1691               </p>
1692             </td>
1693 </tr>
1694 <tr>
1695 <td>
1696               <p>
1697                 cyl_neumann
1698               </p>
1699             </td>
1700 <td>
1701               <p>
1702                 <span class="red">2.48<br> (1478ns)</span>
1703               </p>
1704             </td>
1705 <td>
1706               <p>
1707                 <span class="green">1.00<br> (597ns)</span>
1708               </p>
1709             </td>
1710 </tr>
1711 <tr>
1712 <td>
1713               <p>
1714                 cyl_neumann (integer order)
1715               </p>
1716             </td>
1717 <td>
1718               <p>
1719                 <span class="red">2.20<br> (484ns)</span>
1720               </p>
1721             </td>
1722 <td>
1723               <p>
1724                 <span class="green">1.00<br> (220ns)</span>
1725               </p>
1726             </td>
1727 </tr>
1728 <tr>
1729 <td>
1730               <p>
1731                 digamma
1732               </p>
1733             </td>
1734 <td>
1735               <p>
1736                 <span class="blue">1.92<br> (75ns)</span>
1737               </p>
1738             </td>
1739 <td>
1740               <p>
1741                 <span class="green">1.00<br> (39ns)</span>
1742               </p>
1743             </td>
1744 </tr>
1745 <tr>
1746 <td>
1747               <p>
1748                 ellint_1
1749               </p>
1750             </td>
1751 <td>
1752               <p>
1753                 <span class="blue">1.94<br> (358ns)</span>
1754               </p>
1755             </td>
1756 <td>
1757               <p>
1758                 <span class="green">1.00<br> (185ns)</span>
1759               </p>
1760             </td>
1761 </tr>
1762 <tr>
1763 <td>
1764               <p>
1765                 ellint_1 (complete)
1766               </p>
1767             </td>
1768 <td>
1769               <p>
1770                 <span class="blue">1.86<br> (52ns)</span>
1771               </p>
1772             </td>
1773 <td>
1774               <p>
1775                 <span class="green">1.00<br> (28ns)</span>
1776               </p>
1777             </td>
1778 </tr>
1779 <tr>
1780 <td>
1781               <p>
1782                 ellint_2
1783               </p>
1784             </td>
1785 <td>
1786               <p>
1787                 <span class="red">2.32<br> (805ns)</span>
1788               </p>
1789             </td>
1790 <td>
1791               <p>
1792                 <span class="green">1.00<br> (347ns)</span>
1793               </p>
1794             </td>
1795 </tr>
1796 <tr>
1797 <td>
1798               <p>
1799                 ellint_2 (complete)
1800               </p>
1801             </td>
1802 <td>
1803               <p>
1804                 <span class="blue">1.71<br> (60ns)</span>
1805               </p>
1806             </td>
1807 <td>
1808               <p>
1809                 <span class="green">1.00<br> (35ns)</span>
1810               </p>
1811             </td>
1812 </tr>
1813 <tr>
1814 <td>
1815               <p>
1816                 ellint_3
1817               </p>
1818             </td>
1819 <td>
1820               <p>
1821                 <span class="red">2.75<br> (2154ns)</span>
1822               </p>
1823             </td>
1824 <td>
1825               <p>
1826                 <span class="green">1.00<br> (783ns)</span>
1827               </p>
1828             </td>
1829 </tr>
1830 <tr>
1831 <td>
1832               <p>
1833                 ellint_3 (complete)
1834               </p>
1835             </td>
1836 <td>
1837               <p>
1838                 <span class="red">2.23<br> (1172ns)</span>
1839               </p>
1840             </td>
1841 <td>
1842               <p>
1843                 <span class="green">1.00<br> (525ns)</span>
1844               </p>
1845             </td>
1846 </tr>
1847 <tr>
1848 <td>
1849               <p>
1850                 ellint_rc
1851               </p>
1852             </td>
1853 <td>
1854               <p>
1855                 <span class="blue">1.57<br> (77ns)</span>
1856               </p>
1857             </td>
1858 <td>
1859               <p>
1860                 <span class="green">1.00<br> (49ns)</span>
1861               </p>
1862             </td>
1863 </tr>
1864 <tr>
1865 <td>
1866               <p>
1867                 ellint_rd
1868               </p>
1869             </td>
1870 <td>
1871               <p>
1872                 <span class="red">2.23<br> (520ns)</span>
1873               </p>
1874             </td>
1875 <td>
1876               <p>
1877                 <span class="green">1.00<br> (233ns)</span>
1878               </p>
1879             </td>
1880 </tr>
1881 <tr>
1882 <td>
1883               <p>
1884                 ellint_rf
1885               </p>
1886             </td>
1887 <td>
1888               <p>
1889                 <span class="blue">1.51<br> (95ns)</span>
1890               </p>
1891             </td>
1892 <td>
1893               <p>
1894                 <span class="green">1.00<br> (63ns)</span>
1895               </p>
1896             </td>
1897 </tr>
1898 <tr>
1899 <td>
1900               <p>
1901                 ellint_rj
1902               </p>
1903             </td>
1904 <td>
1905               <p>
1906                 <span class="red">2.33<br> (481ns)</span>
1907               </p>
1908             </td>
1909 <td>
1910               <p>
1911                 <span class="green">1.00<br> (206ns)</span>
1912               </p>
1913             </td>
1914 </tr>
1915 <tr>
1916 <td>
1917               <p>
1918                 erf
1919               </p>
1920             </td>
1921 <td>
1922               <p>
1923                 <span class="red">2.60<br> (39ns)</span>
1924               </p>
1925             </td>
1926 <td>
1927               <p>
1928                 <span class="green">1.00<br> (15ns)</span>
1929               </p>
1930             </td>
1931 </tr>
1932 <tr>
1933 <td>
1934               <p>
1935                 erfc
1936               </p>
1937             </td>
1938 <td>
1939               <p>
1940                 <span class="red">2.68<br> (59ns)</span>
1941               </p>
1942             </td>
1943 <td>
1944               <p>
1945                 <span class="green">1.00<br> (22ns)</span>
1946               </p>
1947             </td>
1948 </tr>
1949 <tr>
1950 <td>
1951               <p>
1952                 expint
1953               </p>
1954             </td>
1955 <td>
1956               <p>
1957                 <span class="red">2.47<br> (94ns)</span>
1958               </p>
1959             </td>
1960 <td>
1961               <p>
1962                 <span class="green">1.00<br> (38ns)</span>
1963               </p>
1964             </td>
1965 </tr>
1966 <tr>
1967 <td>
1968               <p>
1969                 expint (En)
1970               </p>
1971             </td>
1972 <td>
1973               <p>
1974                 <span class="blue">1.86<br> (273ns)</span>
1975               </p>
1976             </td>
1977 <td>
1978               <p>
1979                 <span class="green">1.00<br> (147ns)</span>
1980               </p>
1981             </td>
1982 </tr>
1983 <tr>
1984 <td>
1985               <p>
1986                 expm1
1987               </p>
1988             </td>
1989 <td>
1990               <p>
1991                 <span class="green">1.00<br> (10ns)</span>
1992               </p>
1993             </td>
1994 <td>
1995               <p>
1996                 <span class="green">1.10<br> (11ns)</span>
1997               </p>
1998             </td>
1999 </tr>
2000 <tr>
2001 <td>
2002               <p>
2003                 gamma_p
2004               </p>
2005             </td>
2006 <td>
2007               <p>
2008                 <span class="red">2.42<br> (492ns)</span>
2009               </p>
2010             </td>
2011 <td>
2012               <p>
2013                 <span class="green">1.00<br> (203ns)</span>
2014               </p>
2015             </td>
2016 </tr>
2017 <tr>
2018 <td>
2019               <p>
2020                 gamma_p_inv
2021               </p>
2022             </td>
2023 <td>
2024               <p>
2025                 <span class="red">2.24<br> (1577ns)</span>
2026               </p>
2027             </td>
2028 <td>
2029               <p>
2030                 <span class="green">1.00<br> (704ns)</span>
2031               </p>
2032             </td>
2033 </tr>
2034 <tr>
2035 <td>
2036               <p>
2037                 gamma_q
2038               </p>
2039             </td>
2040 <td>
2041               <p>
2042                 <span class="red">2.53<br> (508ns)</span>
2043               </p>
2044             </td>
2045 <td>
2046               <p>
2047                 <span class="green">1.00<br> (201ns)</span>
2048               </p>
2049             </td>
2050 </tr>
2051 <tr>
2052 <td>
2053               <p>
2054                 gamma_q_inv
2055               </p>
2056             </td>
2057 <td>
2058               <p>
2059                 <span class="red">2.45<br> (1841ns)</span>
2060               </p>
2061             </td>
2062 <td>
2063               <p>
2064                 <span class="green">1.00<br> (751ns)</span>
2065               </p>
2066             </td>
2067 </tr>
2068 <tr>
2069 <td>
2070               <p>
2071                 ibeta
2072               </p>
2073             </td>
2074 <td>
2075               <p>
2076                 <span class="red">2.71<br> (1715ns)</span>
2077               </p>
2078             </td>
2079 <td>
2080               <p>
2081                 <span class="green">1.00<br> (634ns)</span>
2082               </p>
2083             </td>
2084 </tr>
2085 <tr>
2086 <td>
2087               <p>
2088                 ibeta_inv
2089               </p>
2090             </td>
2091 <td>
2092               <p>
2093                 <span class="red">2.58<br> (5742ns)</span>
2094               </p>
2095             </td>
2096 <td>
2097               <p>
2098                 <span class="green">1.00<br> (2224ns)</span>
2099               </p>
2100             </td>
2101 </tr>
2102 <tr>
2103 <td>
2104               <p>
2105                 ibetac
2106               </p>
2107             </td>
2108 <td>
2109               <p>
2110                 <span class="red">2.66<br> (1736ns)</span>
2111               </p>
2112             </td>
2113 <td>
2114               <p>
2115                 <span class="green">1.00<br> (653ns)</span>
2116               </p>
2117             </td>
2118 </tr>
2119 <tr>
2120 <td>
2121               <p>
2122                 ibetac_inv
2123               </p>
2124             </td>
2125 <td>
2126               <p>
2127                 <span class="red">2.44<br> (5451ns)</span>
2128               </p>
2129             </td>
2130 <td>
2131               <p>
2132                 <span class="green">1.00<br> (2237ns)</span>
2133               </p>
2134             </td>
2135 </tr>
2136 <tr>
2137 <td>
2138               <p>
2139                 jacobi_cn
2140               </p>
2141             </td>
2142 <td>
2143               <p>
2144                 <span class="red">2.77<br> (476ns)</span>
2145               </p>
2146             </td>
2147 <td>
2148               <p>
2149                 <span class="green">1.00<br> (172ns)</span>
2150               </p>
2151             </td>
2152 </tr>
2153 <tr>
2154 <td>
2155               <p>
2156                 jacobi_dn
2157               </p>
2158             </td>
2159 <td>
2160               <p>
2161                 <span class="red">2.80<br> (481ns)</span>
2162               </p>
2163             </td>
2164 <td>
2165               <p>
2166                 <span class="green">1.00<br> (172ns)</span>
2167               </p>
2168             </td>
2169 </tr>
2170 <tr>
2171 <td>
2172               <p>
2173                 jacobi_sn
2174               </p>
2175             </td>
2176 <td>
2177               <p>
2178                 <span class="red">2.86<br> (492ns)</span>
2179               </p>
2180             </td>
2181 <td>
2182               <p>
2183                 <span class="green">1.00<br> (172ns)</span>
2184               </p>
2185             </td>
2186 </tr>
2187 <tr>
2188 <td>
2189               <p>
2190                 laguerre
2191               </p>
2192             </td>
2193 <td>
2194               <p>
2195                 <span class="green">1.09<br> (139ns)</span>
2196               </p>
2197             </td>
2198 <td>
2199               <p>
2200                 <span class="green">1.00<br> (128ns)</span>
2201               </p>
2202             </td>
2203 </tr>
2204 <tr>
2205 <td>
2206               <p>
2207                 legendre
2208               </p>
2209             </td>
2210 <td>
2211               <p>
2212                 <span class="green">1.16<br> (399ns)</span>
2213               </p>
2214             </td>
2215 <td>
2216               <p>
2217                 <span class="green">1.00<br> (345ns)</span>
2218               </p>
2219             </td>
2220 </tr>
2221 <tr>
2222 <td>
2223               <p>
2224                 legendre Q
2225               </p>
2226             </td>
2227 <td>
2228               <p>
2229                 <span class="green">1.18<br> (496ns)</span>
2230               </p>
2231             </td>
2232 <td>
2233               <p>
2234                 <span class="green">1.00<br> (422ns)</span>
2235               </p>
2236             </td>
2237 </tr>
2238 <tr>
2239 <td>
2240               <p>
2241                 lgamma
2242               </p>
2243             </td>
2244 <td>
2245               <p>
2246                 <span class="red">2.20<br> (257ns)</span>
2247               </p>
2248             </td>
2249 <td>
2250               <p>
2251                 <span class="green">1.00<br> (117ns)</span>
2252               </p>
2253             </td>
2254 </tr>
2255 <tr>
2256 <td>
2257               <p>
2258                 log1p
2259               </p>
2260             </td>
2261 <td>
2262               <p>
2263                 <span class="green">1.00<br> (12ns)</span>
2264               </p>
2265             </td>
2266 <td>
2267               <p>
2268                 <span class="green">1.00<br> (12ns)</span>
2269               </p>
2270             </td>
2271 </tr>
2272 <tr>
2273 <td>
2274               <p>
2275                 polygamma
2276               </p>
2277             </td>
2278 <td>
2279               <p>
2280                 <span class="red">3.93<br> (2885ns)</span>
2281               </p>
2282             </td>
2283 <td>
2284               <p>
2285                 <span class="green">1.00<br> (734ns)</span>
2286               </p>
2287             </td>
2288 </tr>
2289 <tr>
2290 <td>
2291               <p>
2292                 sph_bessel
2293               </p>
2294             </td>
2295 <td>
2296               <p>
2297                 <span class="blue">1.71<br> (1563ns)</span>
2298               </p>
2299             </td>
2300 <td>
2301               <p>
2302                 <span class="green">1.00<br> (915ns)</span>
2303               </p>
2304             </td>
2305 </tr>
2306 <tr>
2307 <td>
2308               <p>
2309                 sph_neumann
2310               </p>
2311             </td>
2312 <td>
2313               <p>
2314                 <span class="red">2.15<br> (3745ns)</span>
2315               </p>
2316             </td>
2317 <td>
2318               <p>
2319                 <span class="green">1.00<br> (1744ns)</span>
2320               </p>
2321             </td>
2322 </tr>
2323 <tr>
2324 <td>
2325               <p>
2326                 tgamma
2327               </p>
2328             </td>
2329 <td>
2330               <p>
2331                 <span class="red">3.69<br> (354ns)</span>
2332               </p>
2333             </td>
2334 <td>
2335               <p>
2336                 <span class="green">1.00<br> (96ns)</span>
2337               </p>
2338             </td>
2339 </tr>
2340 <tr>
2341 <td>
2342               <p>
2343                 tgamma (incomplete)
2344               </p>
2345             </td>
2346 <td>
2347               <p>
2348                 <span class="red">2.35<br> (744ns)</span>
2349               </p>
2350             </td>
2351 <td>
2352               <p>
2353                 <span class="green">1.00<br> (316ns)</span>
2354               </p>
2355             </td>
2356 </tr>
2357 <tr>
2358 <td>
2359               <p>
2360                 trigamma
2361               </p>
2362             </td>
2363 <td>
2364               <p>
2365                 <span class="blue">1.64<br> (36ns)</span>
2366               </p>
2367             </td>
2368 <td>
2369               <p>
2370                 <span class="green">1.00<br> (22ns)</span>
2371               </p>
2372             </td>
2373 </tr>
2374 <tr>
2375 <td>
2376               <p>
2377                 zeta
2378               </p>
2379             </td>
2380 <td>
2381               <p>
2382                 <span class="red">2.71<br> (509ns)</span>
2383               </p>
2384             </td>
2385 <td>
2386               <p>
2387                 <span class="green">1.00<br> (188ns)</span>
2388               </p>
2389             </td>
2390 </tr>
2391 </tbody>
2392 </table></div>
2393 </div>
2394 <br class="table-break">
2395 </div>
2396 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
2397 <td align="left"></td>
2398 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
2399       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
2400       Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
2401       R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
2402       Daryle Walker and Xiaogang Zhang<p>
2403         Distributed under the Boost Software License, Version 1.0. (See accompanying
2404         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>)
2405       </p>
2406 </div></td>
2407 </tr></table>
2408 <hr>
2409 <div class="spirit-nav">
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