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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.
  34     </p>
  35 <div class="caution"><table border="0" summary="Caution">
  36 <tr>
  37 <td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../../doc/src/images/caution.png"></td>
  38 <th align="left">Caution</th>
  39 </tr>
  40 <tr><td align="left" valign="top"><p>
  41         You should exercise extreme caution when interpreting these results, relative
  42         performance may vary by platform, the tests use data that gives good code
  43         coverage of <span class="emphasis"><em>our</em></span> code, but which may skew the results
  44         towards the corner cases. Finally, remember that different libraries make
  45         different choices with regard to performance verses numerical stability.
  46       </p></td></tr>
  47 </table></div>
  48 <h4>
  49 <a name="math_toolkit.comparisons.h0"></a>
  50       <span class="phrase"><a name="math_toolkit.comparisons.comparison_to_gsl_1_13_and_cephe"></a></span><a class="link" href="comparisons.html#math_toolkit.comparisons.comparison_to_gsl_1_13_and_cephe">Comparison
  51       to GSL-1.13 and Cephes</a>
  52     </h4>
  53 <p>
  54       All the results were measured on a 2.0GHz Intel T5800 Core 2 Duo, 4Gb RAM,
  55       Windows Vista machine, with the test program compiled with Microsoft Visual
  56       C++ 2009 using the /Ox option.
  57     </p>
  58 <div class="informaltable"><table class="table">
  59 <colgroup>
  60 <col>
  61 <col>
  62 <col>
  63 <col>
  64 </colgroup>
  65 <thead><tr>
  66 <th>
  67               <p>
  68                 Function
  69               </p>
  70             </th>
  71 <th>
  72               <p>
  73                 Boost
  74               </p>
  75             </th>
  76 <th>
  77               <p>
  78                 GSL-1.9
  79               </p>
  80             </th>
  81 <th>
  82               <p>
  83                 Cephes
  84               </p>
  85             </th>
  86 </tr></thead>
  87 <tbody>
  88 <tr>
  89 <td>
  90               <p>
  91                 <a class="link" href="powers/cbrt.html" title="cbrt">cbrt</a>
  92               </p>
  93             </td>
  94 <td>
  95               <p>
  96                 </p>
  97 <p><span class="bold"><strong>1.00</strong></span></p>
  98 <p> </p>
  99 <p>(4.873e-007s)</p>
 100 <p>
 101               </p>
 102             </td>
 103 <td>
 104               <p>
 105                 N/A
 106               </p>
 107             </td>
 108 <td>
 109               <p>
 110                 </p>
 111 <p><span class="bold"><strong>1.00</strong></span></p>
 112 <p> </p>
 113 <p>(6.699e-007s)</p>
 114 <p>
 115               </p>
 116             </td>
 117 </tr>
 118 <tr>
 119 <td>
 120               <p>
 121                 <a class="link" href="powers/log1p.html" title="log1p">log1p</a>
 122               </p>
 123             </td>
 124 <td>
 125               <p>
 126                 </p>
 127 <p><span class="bold"><strong>1.00</strong></span></p>
 128 <p> </p>
 129 <p>(1.664e-007s)</p>
 130 <p>
 131               </p>
 132             </td>
 133 <td>
 134               <p>
 135                 </p>
 136 <p><span class="bold"><strong>1.00</strong></span></p>
 137 <p> </p>
 138 <p>(2.677e-007s)</p>
 139 <p>
 140               </p>
 141             </td>
 142 <td>
 143               <p>
 144                 </p>
 145 <p><span class="bold"><strong>1.00</strong></span></p>
 146 <p> </p>
 147 <p>(1.189e-007s)</p>
 148 <p>
 149               </p>
 150             </td>
 151 </tr>
 152 <tr>
 153 <td>
 154               <p>
 155                 <a class="link" href="powers/expm1.html" title="expm1">expm1</a>
 156               </p>
 157             </td>
 158 <td>
 159               <p>
 160                 </p>
 161 <p><span class="bold"><strong>1.00</strong></span></p>
 162 <p> </p>
 163 <p>(8.760e-008s)</p>
 164 <p>
 165               </p>
 166             </td>
 167 <td>
 168               <p>
 169                 </p>
 170 <p><span class="bold"><strong>1.00</strong></span></p>
 171 <p> </p>
 172 <p>(1.248e-007s)</p>
 173 <p>
 174               </p>
 175             </td>
 176 <td>
 177               <p>
 178                 </p>
 179 <p><span class="bold"><strong>1.00</strong></span></p>
 180 <p> </p>
 181 <p>(8.169e-008s)</p>
 182 <p>
 183               </p>
 184             </td>
 185 </tr>
 186 <tr>
 187 <td>
 188               <p>
 189                 <a class="link" href="sf_gamma/tgamma.html" title="Gamma">tgamma</a>
 190               </p>
 191             </td>
 192 <td>
 193               <p>
 194                 </p>
 195 <p>1.80</p>
 196 <p> </p>
 197 <p>(2.997e-007s)</p>
 198 <p>
 199               </p>
 200             </td>
 201 <td>
 202               <p>
 203                 </p>
 204 <p>1.54</p>
 205 <p> </p>
 206 <p>(2.569e-007s)</p>
 207 <p>
 208               </p>
 209             </td>
 210 <td>
 211               <p>
 212                 </p>
 213 <p><span class="bold"><strong>1.00</strong></span></p>
 214 <p> </p>
 215 <p>(1.666e-007s)</p>
 216 <p>
 217               </p>
 218             </td>
 219 </tr>
 220 <tr>
 221 <td>
 222               <p>
 223                 <a class="link" href="sf_gamma/lgamma.html" title="Log Gamma">lgamma</a>
 224               </p>
 225             </td>
 226 <td>
 227               <p>
 228                 </p>
 229 <p>2.20</p>
 230 <p> </p>
 231 <p>(3.045e-007s)</p>
 232 <p>
 233               </p>
 234             </td>
 235 <td>
 236               <p>
 237                 </p>
 238 <p>4.14</p>
 239 <p> </p>
 240 <p>(5.713e-007s)</p>
 241 <p>
 242               </p>
 243             </td>
 244 <td>
 245               <p>
 246                 </p>
 247 <p><span class="bold"><strong>1.00</strong></span></p>
 248 <p> </p>
 249 <p>(1.381e-007s)</p>
 250 <p>
 251               </p>
 252             </td>
 253 </tr>
 254 <tr>
 255 <td>
 256               <p>
 257                 <a class="link" href="sf_erf/error_function.html" title="Error Functions">erf</a> and
 258                 <a class="link" href="sf_erf/error_function.html" title="Error Functions">erfc</a>
 259               </p>
 260             </td>
 261 <td>
 262               <p>
 263                 </p>
 264 <p><span class="bold"><strong>1.00</strong></span></p>
 265 <p> </p>
 266 <p>(1.483e-007s)</p>
 267 <p>
 268               </p>
 269             </td>
 270 <td>
 271               <p>
 272                 </p>
 273 <p><span class="bold"><strong>1.00</strong></span></p>
 274 <p> </p>
 275 <p>(7.052e-007s)</p>
 276 <p>
 277               </p>
 278             </td>
 279 <td>
 280               <p>
 281                 </p>
 282 <p><span class="bold"><strong>1.00</strong></span></p>
 283 <p> </p>
 284 <p>(1.722e-007s)</p>
 285 <p>
 286               </p>
 287             </td>
 288 </tr>
 289 <tr>
 290 <td>
 291               <p>
 292                 <a class="link" href="sf_gamma/igamma.html" title="Incomplete Gamma Functions">gamma_p</a> and
 293                 <a class="link" href="sf_gamma/igamma.html" title="Incomplete Gamma Functions">gamma_q</a>
 294               </p>
 295             </td>
 296 <td>
 297               <p>
 298                 </p>
 299 <p><span class="bold"><strong>1.00</strong></span></p>
 300 <p> </p>
 301 <p>(6.182e-007s)</p>
 302 <p>
 303               </p>
 304             </td>
 305 <td>
 306               <p>
 307                 </p>
 308 <p>3.57</p>
 309 <p> </p>
 310 <p>(2.209e-006s)</p>
 311 <p>
 312               </p>
 313             </td>
 314 <td>
 315               <p>
 316                 </p>
 317 <p>4.29</p>
 318 <p> </p>
 319 <p>(2.651e-006s)</p>
 320 <p>
 321               </p>
 322             </td>
 323 </tr>
 324 <tr>
 325 <td>
 326               <p>
 327                 <a class="link" href="sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_p_inv</a>
 328                 and <a class="link" href="sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_q_inv</a>
 329               </p>
 330             </td>
 331 <td>
 332               <p>
 333                 </p>
 334 <p><span class="bold"><strong>1.00</strong></span></p>
 335 <p> </p>
 336 <p>(1.943e-006s)</p>
 337 <p>
 338               </p>
 339             </td>
 340 <td>
 341               <p>
 342                 N/A
 343               </p>
 344             </td>
 345 <td>
 346               <p>
 347                 +INF <a href="#ftn.math_toolkit.comparisons.f0" class="footnote" name="math_toolkit.comparisons.f0"><sup class="footnote">[1]</sup></a>
 348               </p>
 349             </td>
 350 </tr>
 351 <tr>
 352 <td>
 353               <p>
 354                 <a class="link" href="sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibeta</a>
 355                 and <a class="link" href="sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibetac</a>
 356               </p>
 357             </td>
 358 <td>
 359               <p>
 360                 </p>
 361 <p><span class="bold"><strong>1.00</strong></span></p>
 362 <p> </p>
 363 <p>(1.670e-006s)</p>
 364 <p>
 365               </p>
 366             </td>
 367 <td>
 368               <p>
 369                 </p>
 370 <p>1.16</p>
 371 <p> </p>
 372 <p>(1.935e-006s)</p>
 373 <p>
 374               </p>
 375             </td>
 376 <td>
 377               <p>
 378                 </p>
 379 <p>1.16</p>
 380 <p> </p>
 381 <p>(1.935e-006s)</p>
 382 <p>
 383               </p>
 384             </td>
 385 </tr>
 386 <tr>
 387 <td>
 388               <p>
 389                 <a class="link" href="sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_inv</a>
 390                 and <a class="link" href="sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibetac_inv</a>
 391               </p>
 392             </td>
 393 <td>
 394               <p>
 395                 </p>
 396 <p><span class="bold"><strong>1.00</strong></span></p>
 397 <p> </p>
 398 <p>(6.075e-006s)</p>
 399 <p>
 400               </p>
 401             </td>
 402 <td>
 403               <p>
 404                 N/A
 405               </p>
 406             </td>
 407 <td>
 408               <p>
 409                 </p>
 410 <p>2.45</p>
 411 <p> </p>
 412 <p>(1.489e-005s)</p>
 413 <p>
 414               </p>
 415             </td>
 416 </tr>
 417 <tr>
 418 <td>
 419               <p>
 420                 <a class="link" href="bessel/bessel_first.html" title="Bessel Functions of the First and Second Kinds">cyl_bessel_j</a>
 421               </p>
 422             </td>
 423 <td>
 424               <p>
 425                 </p>
 426 <p>17.89<a href="#ftn.math_toolkit.comparisons.f1" class="footnote" name="math_toolkit.comparisons.f1"><sup class="footnote">[2]</sup></a></p>
 427 <p> </p>
 428 <p>(4.248e-005s)</p>
 429 <p>
 430               </p>
 431             </td>
 432 <td>
 433               <p>
 434                 </p>
 435 <p><span class="bold"><strong>1.00</strong></span></p>
 436 <p> </p>
 437 <p>(5.214e-006s)</p>
 438 <p>
 439               </p>
 440             </td>
 441 <td>
 442               <p>
 443                 </p>
 444 <p><span class="bold"><strong>1.00</strong></span></p>
 445 <p> </p>
 446 <p>(2.374e-006s)</p>
 447 <p>
 448               </p>
 449             </td>
 450 </tr>
 451 <tr>
 452 <td>
 453               <p>
 454                 <a class="link" href="bessel/mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">cyl_bessel_i</a>
 455               </p>
 456             </td>
 457 <td>
 458               <p>
 459                 </p>
 460 <p><span class="bold"><strong>1.00</strong></span></p>
 461 <p> </p>
 462 <p>(5.924e-006s)</p>
 463 <p>
 464               </p>
 465             </td>
 466 <td>
 467               <p>
 468                 </p>
 469 <p><span class="bold"><strong>1.00</strong></span></p>
 470 <p> </p>
 471 <p>(4.487e-006s)</p>
 472 <p>
 473               </p>
 474             </td>
 475 <td>
 476               <p>
 477                 </p>
 478 <p><span class="bold"><strong>1.00</strong></span></p>
 479 <p> </p>
 480 <p>(4.823e-006s)</p>
 481 <p>
 482               </p>
 483             </td>
 484 </tr>
 485 <tr>
 486 <td>
 487               <p>
 488                 <a class="link" href="bessel/mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">cyl_bessel_k</a>
 489               </p>
 490             </td>
 491 <td>
 492               <p>
 493                 </p>
 494 <p><span class="bold"><strong>1.00</strong></span></p>
 495 <p> </p>
 496 <p>(2.783e-006s)</p>
 497 <p>
 498               </p>
 499             </td>
 500 <td>
 501               <p>
 502                 </p>
 503 <p><span class="bold"><strong>1.00</strong></span></p>
 504 <p> </p>
 505 <p>(3.927e-006s)</p>
 506 <p>
 507               </p>
 508             </td>
 509 <td>
 510               <p>
 511                 N/A
 512               </p>
 513             </td>
 514 </tr>
 515 <tr>
 516 <td>
 517               <p>
 518                 <a class="link" href="bessel/bessel_first.html" title="Bessel Functions of the First and Second Kinds">cyl_neumann</a>
 519               </p>
 520             </td>
 521 <td>
 522               <p>
 523                 </p>
 524 <p><span class="bold"><strong>1.00</strong></span></p>
 525 <p> </p>
 526 <p>(4.465e-006s)</p>
 527 <p>
 528               </p>
 529             </td>
 530 <td>
 531               <p>
 532                 </p>
 533 <p><span class="bold"><strong>1.00</strong></span></p>
 534 <p> </p>
 535 <p>(1.230e-005s)</p>
 536 <p>
 537               </p>
 538             </td>
 539 <td>
 540               <p>
 541                 </p>
 542 <p><span class="bold"><strong>1.00</strong></span></p>
 543 <p> </p>
 544 <p>(4.977e-006s)</p>
 545 <p>
 546               </p>
 547             </td>
 548 </tr>
 549 </tbody>
 550 <tbody class="footnotes"><tr><td colspan="4">
 551 <div id="ftn.math_toolkit.comparisons.f0" class="footnote"><p><a href="#math_toolkit.comparisons.f0" class="para"><sup class="para">[1] </sup></a>
 552                   Cephes gets stuck in an infinite loop while trying to execute our
 553                   test cases.
 554                 </p></div>
 555 <div id="ftn.math_toolkit.comparisons.f1" class="footnote"><p><a href="#math_toolkit.comparisons.f1" class="para"><sup class="para">[2] </sup></a>
 556                   The performance here is dominated by a few cases where the parameters
 557                   grow very large: faster asymptotic expansions are available, but
 558                   are of limited (or even frankly terrible) precision. The same issue
 559                   effects all of our Bessel function implementations, but doesn't
 560                   necessarily show in the current performance data. More investigation
 561                   is needed here.
 562                 </p></div>
 563 </td></tr></tbody>
 564 </table></div>
 565 <h4>
 566 <a name="math_toolkit.comparisons.h1"></a>
 567       <span class="phrase"><a name="math_toolkit.comparisons.comparison_to_the_r_and_dcdflib_"></a></span><a class="link" href="comparisons.html#math_toolkit.comparisons.comparison_to_the_r_and_dcdflib_">Comparison
 568       to the R and DCDFLIB Statistical Libraries on Windows</a>
 569     </h4>
 570 <p>
 571       All the results were measured on a 2.0GHz Intel T5800 Core 2 Duo, 4Gb RAM,
 572       Windows Vista machine, with the test program compiled with Microsoft Visual
 573       C++ 2009, and R-2.9.2 compiled in "standalone mode" with MinGW-4.3
 574       (R-2.9.2 appears not to be buildable with Visual C++).
 575     </p>
 576 <div class="table">
 577 <a name="math_toolkit.comparisons.a_comparison_to_the_r_statistica"></a><p class="title"><b>Table&#160;15.5.&#160;A Comparison to the R Statistical Library on Windows XP</b></p>
 578 <div class="table-contents"><table class="table" summary="A Comparison to the R Statistical Library on Windows XP">
 579 <colgroup>
 580 <col>
 581 <col>
 582 <col>
 583 <col>
 584 </colgroup>
 585 <thead><tr>
 586 <th>
 587               <p>
 588                 Statistical Function
 589               </p>
 590             </th>
 591 <th>
 592               <p>
 593                 Boost
 594               </p>
 595             </th>
 596 <th>
 597               <p>
 598                 R
 599               </p>
 600             </th>
 601 <th>
 602               <p>
 603                 DCDFLIB
 604               </p>
 605             </th>
 606 </tr></thead>
 607 <tbody>
 608 <tr>
 609 <td>
 610               <p>
 611                 <a class="link" href="dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a>
 612                 CDF
 613               </p>
 614             </td>
 615 <td>
 616               <p>
 617                 </p>
 618 <p>1.08</p>
 619 <p> </p>
 620 <p>(1.385e-006s)</p>
 621 <p>
 622               </p>
 623             </td>
 624 <td>
 625               <p>
 626                 </p>
 627 <p><span class="bold"><strong>1.00</strong></span></p>
 628 <p> </p>
 629 <p>(1.278e-006s)</p>
 630 <p>
 631               </p>
 632             </td>
 633 <td>
 634               <p>
 635                 </p>
 636 <p>1.06</p>
 637 <p> </p>
 638 <p>(1.349e-006s)</p>
 639 <p>
 640               </p>
 641             </td>
 642 </tr>
 643 <tr>
 644 <td>
 645               <p>
 646                 <a class="link" href="dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a>
 647                 Quantile
 648               </p>
 649             </td>
 650 <td>
 651               <p>
 652                 </p>
 653 <p><span class="bold"><strong>1.00</strong></span></p>
 654 <p> </p>
 655 <p>(4.975e-006s)</p>
 656 <p>
 657               </p>
 658             </td>
 659 <td>
 660               <p>
 661                 </p>
 662 <p>67.66<a href="#ftn.math_toolkit.comparisons.f2" class="footnote" name="math_toolkit.comparisons.f2"><sup class="footnote">[1]</sup></a></p>
 663 <p> </p>
 664 <p>(3.366e-004s)</p>
 665 <p>
 666               </p>
 667             </td>
 668 <td>
 669               <p>
 670                 </p>
 671 <p>4.23</p>
 672 <p> </p>
 673 <p>(2.103e-005s)</p>
 674 <p>
 675               </p>
 676             </td>
 677 </tr>
 678 <tr>
 679 <td>
 680               <p>
 681                 <a class="link" href="dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial
 682                 Distribution</a> CDF
 683               </p>
 684             </td>
 685 <td>
 686               <p>
 687                 </p>
 688 <p>1.06</p>
 689 <p> </p>
 690 <p>(4.503e-007s)</p>
 691 <p>
 692               </p>
 693             </td>
 694 <td>
 695               <p>
 696                 </p>
 697 <p>1.81</p>
 698 <p> </p>
 699 <p>(7.680e-007s)</p>
 700 <p>
 701               </p>
 702             </td>
 703 <td>
 704               <p>
 705                 </p>
 706 <p><span class="bold"><strong>1.00</strong></span></p>
 707 <p> </p>
 708 <p>(4.239e-007s)</p>
 709 <p>
 710               </p>
 711             </td>
 712 </tr>
 713 <tr>
 714 <td>
 715               <p>
 716                 <a class="link" href="dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial
 717                 Distribution</a> Quantile
 718               </p>
 719             </td>
 720 <td>
 721               <p>
 722                 </p>
 723 <p><span class="bold"><strong>1.00</strong></span></p>
 724 <p> </p>
 725 <p>(3.254e-006s)</p>
 726 <p>
 727               </p>
 728             </td>
 729 <td>
 730               <p>
 731                 </p>
 732 <p>1.15</p>
 733 <p> </p>
 734 <p>(3.746e-006s)</p>
 735 <p>
 736               </p>
 737             </td>
 738 <td>
 739               <p>
 740                 </p>
 741 <p>7.25</p>
 742 <p> </p>
 743 <p>(2.358e-005s)</p>
 744 <p>
 745               </p>
 746             </td>
 747 </tr>
 748 <tr>
 749 <td>
 750               <p>
 751                 <a class="link" href="dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy Distribution</a>
 752                 CDF
 753               </p>
 754             </td>
 755 <td>
 756               <p>
 757                 </p>
 758 <p><span class="bold"><strong>1.00</strong></span></p>
 759 <p> </p>
 760 <p>(1.134e-007s)</p>
 761 <p>
 762               </p>
 763             </td>
 764 <td>
 765               <p>
 766                 </p>
 767 <p>1.08</p>
 768 <p> </p>
 769 <p>(1.227e-007s)</p>
 770 <p>
 771               </p>
 772             </td>
 773 <td>
 774               <p>
 775                 NA
 776               </p>
 777             </td>
 778 </tr>
 779 <tr>
 780 <td>
 781               <p>
 782                 <a class="link" href="dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy Distribution</a>
 783                 Quantile
 784               </p>
 785             </td>
 786 <td>
 787               <p>
 788                 </p>
 789 <p><span class="bold"><strong>1.00</strong></span></p>
 790 <p> </p>
 791 <p>(1.203e-007s)</p>
 792 <p>
 793               </p>
 794             </td>
 795 <td>
 796               <p>
 797                 </p>
 798 <p><span class="bold"><strong>1.00</strong></span></p>
 799 <p> </p>
 800 <p>(1.203e-007s)</p>
 801 <p>
 802               </p>
 803             </td>
 804 <td>
 805               <p>
 806                 NA
 807               </p>
 808             </td>
 809 </tr>
 810 <tr>
 811 <td>
 812               <p>
 813                 <a class="link" href="dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi
 814                 Squared Distribution</a> CDF
 815               </p>
 816             </td>
 817 <td>
 818               <p>
 819                 </p>
 820 <p>1.21</p>
 821 <p> </p>
 822 <p>(5.021e-007s)</p>
 823 <p>
 824               </p>
 825             </td>
 826 <td>
 827               <p>
 828                 </p>
 829 <p>2.83</p>
 830 <p> </p>
 831 <p>(1.176e-006s)</p>
 832 <p>
 833               </p>
 834             </td>
 835 <td>
 836               <p>
 837                 </p>
 838 <p><span class="bold"><strong>1.00</strong></span></p>
 839 <p> </p>
 840 <p>(4.155e-007s)</p>
 841 <p>
 842               </p>
 843             </td>
 844 </tr>
 845 <tr>
 846 <td>
 847               <p>
 848                 <a class="link" href="dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi
 849                 Squared Distribution</a> Quantile
 850               </p>
 851             </td>
 852 <td>
 853               <p>
 854                 </p>
 855 <p><span class="bold"><strong>1.00</strong></span></p>
 856 <p> </p>
 857 <p>(1.930e-006s)</p>
 858 <p>
 859               </p>
 860             </td>
 861 <td>
 862               <p>
 863                 </p>
 864 <p>2.72</p>
 865 <p> </p>
 866 <p>(5.243e-006s)</p>
 867 <p>
 868               </p>
 869             </td>
 870 <td>
 871               <p>
 872                 </p>
 873 <p>5.73</p>
 874 <p> </p>
 875 <p>(1.106e-005s)</p>
 876 <p>
 877               </p>
 878             </td>
 879 </tr>
 880 <tr>
 881 <td>
 882               <p>
 883                 <a class="link" href="dist_ref/dists/exp_dist.html" title="Exponential Distribution">Exponential
 884                 Distribution</a> CDF
 885               </p>
 886             </td>
 887 <td>
 888               <p>
 889                 </p>
 890 <p><span class="bold"><strong>1.00</strong></span></p>
 891 <p> </p>
 892 <p>(3.798e-008s)</p>
 893 <p>
 894               </p>
 895             </td>
 896 <td>
 897               <p>
 898                 </p>
 899 <p>5.89</p>
 900 <p> </p>
 901 <p>(2.236e-007s)</p>
 902 <p>
 903               </p>
 904             </td>
 905 <td>
 906               <p>
 907                 NA
 908               </p>
 909             </td>
 910 </tr>
 911 <tr>
 912 <td>
 913               <p>
 914                 <a class="link" href="dist_ref/dists/exp_dist.html" title="Exponential Distribution">Exponential
 915                 Distribution</a> Quantile
 916               </p>
 917             </td>
 918 <td>
 919               <p>
 920                 </p>
 921 <p>1.41</p>
 922 <p> </p>
 923 <p>(9.006e-008s)</p>
 924 <p>
 925               </p>
 926             </td>
 927 <td>
 928               <p>
 929                 </p>
 930 <p><span class="bold"><strong>1.00</strong></span></p>
 931 <p> </p>
 932 <p>(6.380e-008s)</p>
 933 <p>
 934               </p>
 935             </td>
 936 <td>
 937               <p>
 938                 NA
 939               </p>
 940             </td>
 941 </tr>
 942 <tr>
 943 <td>
 944               <p>
 945                 <a class="link" href="dist_ref/dists/f_dist.html" title="F Distribution">Fisher F Distribution</a>
 946                 CDF
 947               </p>
 948             </td>
 949 <td>
 950               <p>
 951                 </p>
 952 <p><span class="bold"><strong>1.00</strong></span></p>
 953 <p> </p>
 954 <p>(9.556e-007s)</p>
 955 <p>
 956               </p>
 957             </td>
 958 <td>
 959               <p>
 960                 </p>
 961 <p>1.34</p>
 962 <p> </p>
 963 <p>(1.283e-006s)</p>
 964 <p>
 965               </p>
 966             </td>
 967 <td>
 968               <p>
 969                 </p>
 970 <p>1.24</p>
 971 <p> </p>
 972 <p>(1.183e-006s)</p>
 973 <p>
 974               </p>
 975             </td>
 976 </tr>
 977 <tr>
 978 <td>
 979               <p>
 980                 <a class="link" href="dist_ref/dists/f_dist.html" title="F Distribution">Fisher F Distribution</a>
 981                 Quantile
 982               </p>
 983             </td>
 984 <td>
 985               <p>
 986                 </p>
 987 <p><span class="bold"><strong>1.00</strong></span></p>
 988 <p> </p>
 989 <p>(6.987e-006s)</p>
 990 <p>
 991               </p>
 992             </td>
 993 <td>
 994               <p>
 995                 </p>
 996 <p>1.33</p>
 997 <p> </p>
 998 <p>(9.325e-006s)</p>
 999 <p>
1000               </p>
1001             </td>
1002 <td>
1003               <p>
1004                 </p>
1005 <p>3.16</p>
1006 <p> </p>
1007 <p>(2.205e-005s)</p>
1008 <p>
1009               </p>
1010             </td>
1011 </tr>
1012 <tr>
1013 <td>
1014               <p>
1015                 <a class="link" href="dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma Distribution</a>
1016                 CDF
1017               </p>
1018             </td>
1019 <td>
1020               <p>
1021                 </p>
1022 <p>1.52</p>
1023 <p> </p>
1024 <p>(6.240e-007s)</p>
1025 <p>
1026               </p>
1027             </td>
1028 <td>
1029               <p>
1030                 </p>
1031 <p>3.11</p>
1032 <p> </p>
1033 <p>(1.279e-006s)</p>
1034 <p>
1035               </p>
1036             </td>
1037 <td>
1038               <p>
1039                 </p>
1040 <p><span class="bold"><strong>1.00</strong></span></p>
1041 <p> </p>
1042 <p>(4.111e-007s)</p>
1043 <p>
1044               </p>
1045             </td>
1046 </tr>
1047 <tr>
1048 <td>
1049               <p>
1050                 <a class="link" href="dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma Distribution</a>
1051                 Quantile
1052               </p>
1053             </td>
1054 <td>
1055               <p>
1056                 </p>
1057 <p>1.24</p>
1058 <p> </p>
1059 <p>(2.179e-006s)</p>
1060 <p>
1061               </p>
1062             </td>
1063 <td>
1064               <p>
1065                 </p>
1066 <p>6.25</p>
1067 <p> </p>
1068 <p>(1.102e-005s)</p>
1069 <p>
1070               </p>
1071             </td>
1072 <td>
1073               <p>
1074                 </p>
1075 <p><span class="bold"><strong>1.00</strong></span></p>
1076 <p> </p>
1077 <p>(1.764e-006s)</p>
1078 <p>
1079               </p>
1080             </td>
1081 </tr>
1082 <tr>
1083 <td>
1084               <p>
1085                 <a class="link" href="dist_ref/dists/hypergeometric_dist.html" title="Hypergeometric Distribution">hypergeometric
1086                 Distribution</a> CDF
1087               </p>
1088             </td>
1089 <td>
1090               <p>
1091                 </p>
1092 <p>3.60<a href="#ftn.math_toolkit.comparisons.f3" class="footnote" name="math_toolkit.comparisons.f3"><sup class="footnote">[2]</sup></a></p>
1093 <p> </p>
1094 <p>(5.987e-007s)</p>
1095 <p>
1096               </p>
1097             </td>
1098 <td>
1099               <p>
1100                 </p>
1101 <p><span class="bold"><strong>1.00</strong></span></p>
1102 <p> </p>
1103 <p>(1.665e-007s)</p>
1104 <p>
1105               </p>
1106             </td>
1107 <td>
1108               <p>
1109                 NA
1110               </p>
1111             </td>
1112 </tr>
1113 <tr>
1114 <td>
1115               <p>
1116                 <a class="link" href="dist_ref/dists/hypergeometric_dist.html" title="Hypergeometric Distribution">hypergeometric
1117                 Distribution</a> Quantile
1118               </p>
1119             </td>
1120 <td>
1121               <p>
1122                 </p>
1123 <p><span class="bold"><strong>1.00</strong></span></p>
1124 <p> </p>
1125 <p>(5.684e-007s)</p>
1126 <p>
1127               </p>
1128             </td>
1129 <td>
1130               <p>
1131                 </p>
1132 <p>3.53</p>
1133 <p> </p>
1134 <p>(2.004e-006s)</p>
1135 <p>
1136               </p>
1137             </td>
1138 <td>
1139               <p>
1140                 NA
1141               </p>
1142             </td>
1143 </tr>
1144 <tr>
1145 <td>
1146               <p>
1147                 <a class="link" href="dist_ref/dists/logistic_dist.html" title="Logistic Distribution">Logistic
1148                 Distribution</a> CDF
1149               </p>
1150             </td>
1151 <td>
1152               <p>
1153                 </p>
1154 <p><span class="bold"><strong>1.00</strong></span></p>
1155 <p> </p>
1156 <p>(1.714e-007s)</p>
1157 <p>
1158               </p>
1159             </td>
1160 <td>
1161               <p>
1162                 </p>
1163 <p>5.24</p>
1164 <p> </p>
1165 <p>(8.984e-007s)</p>
1166 <p>
1167               </p>
1168             </td>
1169 <td>
1170               <p>
1171                 NA
1172               </p>
1173             </td>
1174 </tr>
1175 <tr>
1176 <td>
1177               <p>
1178                 <a class="link" href="dist_ref/dists/logistic_dist.html" title="Logistic Distribution">Logistic
1179                 Distribution</a> Quantile
1180               </p>
1181             </td>
1182 <td>
1183               <p>
1184                 </p>
1185 <p>1.02</p>
1186 <p> </p>
1187 <p>(2.084e-007s)</p>
1188 <p>
1189               </p>
1190             </td>
1191 <td>
1192               <p>
1193                 </p>
1194 <p><span class="bold"><strong>1.00</strong></span></p>
1195 <p> </p>
1196 <p>(2.043e-007s)</p>
1197 <p>
1198               </p>
1199             </td>
1200 <td>
1201               <p>
1202                 NA
1203               </p>
1204             </td>
1205 </tr>
1206 <tr>
1207 <td>
1208               <p>
1209                 <a class="link" href="dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">Log-normal
1210                 Distribution</a> CDF
1211               </p>
1212             </td>
1213 <td>
1214               <p>
1215                 </p>
1216 <p><span class="bold"><strong>1.00</strong></span></p>
1217 <p> </p>
1218 <p>(3.579e-007s)</p>
1219 <p>
1220               </p>
1221             </td>
1222 <td>
1223               <p>
1224                 </p>
1225 <p>1.49</p>
1226 <p> </p>
1227 <p>(5.332e-007s)</p>
1228 <p>
1229               </p>
1230             </td>
1231 <td>
1232               <p>
1233                 NA
1234               </p>
1235             </td>
1236 </tr>
1237 <tr>
1238 <td>
1239               <p>
1240                 <a class="link" href="dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">Log-normal
1241                 Distribution</a> Quantile
1242               </p>
1243             </td>
1244 <td>
1245               <p>
1246                 </p>
1247 <p><span class="bold"><strong>1.00</strong></span></p>
1248 <p> </p>
1249 <p>(9.622e-007s)</p>
1250 <p>
1251               </p>
1252             </td>
1253 <td>
1254               <p>
1255                 </p>
1256 <p>1.57</p>
1257 <p> </p>
1258 <p>(1.507e-006s)</p>
1259 <p>
1260               </p>
1261             </td>
1262 <td>
1263               <p>
1264                 NA
1265               </p>
1266             </td>
1267 </tr>
1268 <tr>
1269 <td>
1270               <p>
1271                 <a class="link" href="dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative
1272                 Binomial Distribution</a> CDF
1273               </p>
1274             </td>
1275 <td>
1276               <p>
1277                 </p>
1278 <p><span class="bold"><strong>1.00</strong></span></p>
1279 <p> </p>
1280 <p>(6.227e-007s)</p>
1281 <p>
1282               </p>
1283             </td>
1284 <td>
1285               <p>
1286                 </p>
1287 <p>2.25</p>
1288 <p> </p>
1289 <p>(1.403e-006s)</p>
1290 <p>
1291               </p>
1292             </td>
1293 <td>
1294               <p>
1295                 </p>
1296 <p>2.21</p>
1297 <p> </p>
1298 <p>(1.378e-006s)</p>
1299 <p>
1300               </p>
1301             </td>
1302 </tr>
1303 <tr>
1304 <td>
1305               <p>
1306                 <a class="link" href="dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative
1307                 Binomial Distribution</a> Quantile
1308               </p>
1309             </td>
1310 <td>
1311               <p>
1312                 </p>
1313 <p><span class="bold"><strong>1.00</strong></span></p>
1314 <p> </p>
1315 <p>(8.594e-006s)</p>
1316 <p>
1317               </p>
1318             </td>
1319 <td>
1320               <p>
1321                 </p>
1322 <p>43.43<a href="#ftn.math_toolkit.comparisons.f4" class="footnote" name="math_toolkit.comparisons.f4"><sup class="footnote">[3]</sup></a></p>
1323 <p> </p>
1324 <p>(3.732e-004s)</p>
1325 <p>
1326               </p>
1327             </td>
1328 <td>
1329               <p>
1330                 </p>
1331 <p>3.48</p>
1332 <p> </p>
1333 <p>(2.994e-005s)</p>
1334 <p>
1335               </p>
1336             </td>
1337 </tr>
1338 <tr>
1339 <td>
1340               <p>
1341                 <a class="link" href="dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral
1342                 Chi Squared Distribution</a> CDF
1343               </p>
1344             </td>
1345 <td>
1346               <p>
1347                 </p>
1348 <p>2.16</p>
1349 <p> </p>
1350 <p>(3.926e-006s)</p>
1351 <p>
1352               </p>
1353             </td>
1354 <td>
1355               <p>
1356                 </p>
1357 <p>79.93</p>
1358 <p> </p>
1359 <p>(1.450e-004s)</p>
1360 <p>
1361               </p>
1362             </td>
1363 <td>
1364               <p>
1365                 </p>
1366 <p><span class="bold"><strong>1.00</strong></span></p>
1367 <p> </p>
1368 <p>(1.814e-006s)</p>
1369 <p>
1370               </p>
1371             </td>
1372 </tr>
1373 <tr>
1374 <td>
1375               <p>
1376                 <a class="link" href="dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral
1377                 Chi Squared Distribution</a> Quantile
1378               </p>
1379             </td>
1380 <td>
1381               <p>
1382                 </p>
1383 <p>5.00</p>
1384 <p> </p>
1385 <p>(3.393e-004s)</p>
1386 <p>
1387               </p>
1388             </td>
1389 <td>
1390               <p>
1391                 </p>
1392 <p>393.90<a href="#ftn.math_toolkit.comparisons.f5" class="footnote" name="math_toolkit.comparisons.f5"><sup class="footnote">[4]</sup></a></p>
1393 <p> </p>
1394 <p>(2.673e-002s)</p>
1395 <p>
1396               </p>
1397             </td>
1398 <td>
1399               <p>
1400                 </p>
1401 <p><span class="bold"><strong>1.00</strong></span></p>
1402 <p> </p>
1403 <p>(6.786e-005s)</p>
1404 <p>
1405               </p>
1406             </td>
1407 </tr>
1408 <tr>
1409 <td>
1410               <p>
1411                 <a class="link" href="dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">Noncentral
1412                 F Distribution</a> CDF
1413               </p>
1414             </td>
1415 <td>
1416               <p>
1417                 </p>
1418 <p>1.59</p>
1419 <p> </p>
1420 <p>(1.128e-005s)</p>
1421 <p>
1422               </p>
1423             </td>
1424 <td>
1425               <p>
1426                 </p>
1427 <p><span class="bold"><strong>1.00</strong></span></p>
1428 <p> </p>
1429 <p>(7.087e-006s)</p>
1430 <p>
1431               </p>
1432             </td>
1433 <td>
1434               <p>
1435                 </p>
1436 <p><span class="bold"><strong>1.00</strong></span></p>
1437 <p> </p>
1438 <p>(4.274e-006s)</p>
1439 <p>
1440               </p>
1441             </td>
1442 </tr>
1443 <tr>
1444 <td>
1445               <p>
1446                 <a class="link" href="dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">Noncentral
1447                 F Distribution</a> Quantile
1448               </p>
1449             </td>
1450 <td>
1451               <p>
1452                 </p>
1453 <p><span class="bold"><strong>1.00</strong></span></p>
1454 <p> </p>
1455 <p>(4.750e-004s)</p>
1456 <p>
1457               </p>
1458             </td>
1459 <td>
1460               <p>
1461                 </p>
1462 <p>1.62</p>
1463 <p> </p>
1464 <p>(7.681e-004s)</p>
1465 <p>
1466               </p>
1467             </td>
1468 <td>
1469               <p>
1470                 </p>
1471 <p><span class="bold"><strong>1.00</strong></span></p>
1472 <p> </p>
1473 <p>(4.274e-006s)</p>
1474 <p>
1475               </p>
1476             </td>
1477 </tr>
1478 <tr>
1479 <td>
1480               <p>
1481                 <a class="link" href="dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">noncentral
1482                 T distribution</a> CDF
1483               </p>
1484             </td>
1485 <td>
1486               <p>
1487                 </p>
1488 <p>3.41</p>
1489 <p> </p>
1490 <p>(1.852e-005s)</p>
1491 <p>
1492               </p>
1493             </td>
1494 <td>
1495               <p>
1496                 </p>
1497 <p><span class="bold"><strong>1.00</strong></span></p>
1498 <p> </p>
1499 <p>(5.436e-006s)</p>
1500 <p>
1501               </p>
1502             </td>
1503 <td>
1504               <p>
1505                 NA
1506               </p>
1507             </td>
1508 </tr>
1509 <tr>
1510 <td>
1511               <p>
1512                 <a class="link" href="dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">noncentral
1513                 T distribution</a> Quantile
1514               </p>
1515             </td>
1516 <td>
1517               <p>
1518                 </p>
1519 <p>1.31</p>
1520 <p> </p>
1521 <p>(5.768e-004s)</p>
1522 <p>
1523               </p>
1524             </td>
1525 <td>
1526               <p>
1527                 </p>
1528 <p><span class="bold"><strong>1.00</strong></span><a href="#ftn.math_toolkit.comparisons.f6" class="footnote" name="math_toolkit.comparisons.f6"><sup class="footnote">[5]</sup></a></p>
1529 <p> </p>
1530 <p>(4.411e-004s)</p>
1531 <p>
1532               </p>
1533             </td>
1534 <td>
1535               <p>
1536                 NA
1537               </p>
1538             </td>
1539 </tr>
1540 <tr>
1541 <td>
1542               <p>
1543                 <a class="link" href="dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal Distribution</a>
1544                 CDF
1545               </p>
1546             </td>
1547 <td>
1548               <p>
1549                 </p>
1550 <p><span class="bold"><strong>1.00</strong></span></p>
1551 <p> </p>
1552 <p>(8.373e-008s)</p>
1553 <p>
1554               </p>
1555             </td>
1556 <td>
1557               <p>
1558                 </p>
1559 <p>1.68</p>
1560 <p> </p>
1561 <p>(1.409e-007s)</p>
1562 <p>
1563               </p>
1564             </td>
1565 <td>
1566               <p>
1567                 </p>
1568 <p>6.01</p>
1569 <p> </p>
1570 <p>(5.029e-007s)</p>
1571 <p>
1572               </p>
1573             </td>
1574 </tr>
1575 <tr>
1576 <td>
1577               <p>
1578                 <a class="link" href="dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal Distribution</a>
1579                 Quantile
1580               </p>
1581             </td>
1582 <td>
1583               <p>
1584                 </p>
1585 <p>1.29</p>
1586 <p> </p>
1587 <p>(1.521e-007s)</p>
1588 <p>
1589               </p>
1590             </td>
1591 <td>
1592               <p>
1593                 </p>
1594 <p><span class="bold"><strong>1.00</strong></span></p>
1595 <p> </p>
1596 <p>(1.182e-007s)</p>
1597 <p>
1598               </p>
1599             </td>
1600 <td>
1601               <p>
1602                 </p>
1603 <p>10.85</p>
1604 <p> </p>
1605 <p>(1.283e-006s)</p>
1606 <p>
1607               </p>
1608             </td>
1609 </tr>
1610 <tr>
1611 <td>
1612               <p>
1613                 <a class="link" href="dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson
1614                 Distribution</a> CDF
1615               </p>
1616             </td>
1617 <td>
1618               <p>
1619                 </p>
1620 <p>1.18</p>
1621 <p> </p>
1622 <p>(5.193e-007s)</p>
1623 <p>
1624               </p>
1625             </td>
1626 <td>
1627               <p>
1628                 </p>
1629 <p>2.98</p>
1630 <p> </p>
1631 <p>(1.314e-006s)</p>
1632 <p>
1633               </p>
1634             </td>
1635 <td>
1636               <p>
1637                 </p>
1638 <p><span class="bold"><strong>1.00</strong></span></p>
1639 <p> </p>
1640 <p>(4.410e-007s)</p>
1641 <p>
1642               </p>
1643             </td>
1644 </tr>
1645 <tr>
1646 <td>
1647               <p>
1648                 <a class="link" href="dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson
1649                 Distribution</a>
1650               </p>
1651             </td>
1652 <td>
1653               <p>
1654                 </p>
1655 <p><span class="bold"><strong>1.00</strong></span></p>
1656 <p> </p>
1657 <p>(1.203e-006s)</p>
1658 <p>
1659               </p>
1660             </td>
1661 <td>
1662               <p>
1663                 </p>
1664 <p>2.20</p>
1665 <p> </p>
1666 <p>(2.642e-006s)</p>
1667 <p>
1668               </p>
1669             </td>
1670 <td>
1671               <p>
1672                 </p>
1673 <p>7.86</p>
1674 <p> </p>
1675 <p>(9.457e-006s)</p>
1676 <p>
1677               </p>
1678             </td>
1679 </tr>
1680 <tr>
1681 <td>
1682               <p>
1683                 <a class="link" href="dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students
1684                 t Distribution</a> CDF
1685               </p>
1686             </td>
1687 <td>
1688               <p>
1689                 </p>
1690 <p><span class="bold"><strong>1.00</strong></span></p>
1691 <p> </p>
1692 <p>(8.655e-007s)</p>
1693 <p>
1694               </p>
1695             </td>
1696 <td>
1697               <p>
1698                 </p>
1699 <p>1.06</p>
1700 <p> </p>
1701 <p>(9.166e-007s)</p>
1702 <p>
1703               </p>
1704             </td>
1705 <td>
1706               <p>
1707                 </p>
1708 <p>1.04</p>
1709 <p> </p>
1710 <p>(8.999e-007s)</p>
1711 <p>
1712               </p>
1713             </td>
1714 </tr>
1715 <tr>
1716 <td>
1717               <p>
1718                 <a class="link" href="dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students
1719                 t Distribution</a> Quantile
1720               </p>
1721             </td>
1722 <td>
1723               <p>
1724                 </p>
1725 <p><span class="bold"><strong>1.00</strong></span></p>
1726 <p> </p>
1727 <p>(2.294e-006s)</p>
1728 <p>
1729               </p>
1730             </td>
1731 <td>
1732               <p>
1733                 </p>
1734 <p>1.36</p>
1735 <p> </p>
1736 <p>(3.131e-006s)</p>
1737 <p>
1738               </p>
1739             </td>
1740 <td>
1741               <p>
1742                 </p>
1743 <p>4.82</p>
1744 <p> </p>
1745 <p>(1.106e-005s)</p>
1746 <p>
1747               </p>
1748             </td>
1749 </tr>
1750 <tr>
1751 <td>
1752               <p>
1753                 <a class="link" href="dist_ref/dists/weibull_dist.html" title="Weibull Distribution">Weibull
1754                 Distribution</a> CDF
1755               </p>
1756             </td>
1757 <td>
1758               <p>
1759                 </p>
1760 <p><span class="bold"><strong>1.00</strong></span></p>
1761 <p> </p>
1762 <p>(1.865e-007s)</p>
1763 <p>
1764               </p>
1765             </td>
1766 <td>
1767               <p>
1768                 </p>
1769 <p>2.33</p>
1770 <p> </p>
1771 <p>(4.341e-007s)</p>
1772 <p>
1773               </p>
1774             </td>
1775 <td>
1776               <p>
1777                 NA
1778               </p>
1779             </td>
1780 </tr>
1781 <tr>
1782 <td>
1783               <p>
1784                 <a class="link" href="dist_ref/dists/weibull_dist.html" title="Weibull Distribution">Weibull
1785                 Distribution</a> Quantile
1786               </p>
1787             </td>
1788 <td>
1789               <p>
1790                 </p>
1791 <p><span class="bold"><strong>1.00</strong></span></p>
1792 <p> </p>
1793 <p>(3.608e-007s)</p>
1794 <p>
1795               </p>
1796             </td>
1797 <td>
1798               <p>
1799                 </p>
1800 <p>1.22</p>
1801 <p> </p>
1802 <p>(4.410e-007s)</p>
1803 <p>
1804               </p>
1805             </td>
1806 <td>
1807               <p>
1808                 NA
1809               </p>
1810             </td>
1811 </tr>
1812 </tbody>
1813 <tbody class="footnotes"><tr><td colspan="4">
1814 <div id="ftn.math_toolkit.comparisons.f2" class="footnote"><p><a href="#math_toolkit.comparisons.f2" class="para"><sup class="para">[1] </sup></a>
1815                   There are a small number of our test cases where the R library
1816                   fails to converge on a result: these tend to dominate the performance
1817                   result.
1818                 </p></div>
1819 <div id="ftn.math_toolkit.comparisons.f3" class="footnote"><p><a href="#math_toolkit.comparisons.f3" class="para"><sup class="para">[2] </sup></a>
1820                   This result is somewhat misleading: for small values of the parameters
1821                   there is virtually no difference between the two libraries, but
1822                   for large values the Boost implementation is <span class="emphasis"><em>much</em></span>
1823                   slower, albeit with much improved precision.
1824                 </p></div>
1825 <div id="ftn.math_toolkit.comparisons.f4" class="footnote"><p><a href="#math_toolkit.comparisons.f4" class="para"><sup class="para">[3] </sup></a>
1826                   The R library appears to use a linear-search strategy, that can
1827                   perform very badly in a small number of pathological cases, but
1828                   may or may not be more efficient in "typical" cases
1829                 </p></div>
1830 <div id="ftn.math_toolkit.comparisons.f5" class="footnote"><p><a href="#math_toolkit.comparisons.f5" class="para"><sup class="para">[4] </sup></a>
1831                   There are a small number of our test cases where the R library
1832                   fails to converge on a result: these tend to dominate the performance
1833                   result.
1834                 </p></div>
1835 <div id="ftn.math_toolkit.comparisons.f6" class="footnote"><p><a href="#math_toolkit.comparisons.f6" class="para"><sup class="para">[5] </sup></a>
1836                   There are a small number of our test cases where the R library
1837                   fails to converge on a result: these tend to dominate the performance
1838                   result.
1839                 </p></div>
1840 </td></tr></tbody>
1841 </table></div>
1842 </div>
1843 <br class="table-break"><h4>
1844 <a name="math_toolkit.comparisons.h2"></a>
1845       <span class="phrase"><a name="math_toolkit.comparisons.comparison_to_the_r_statistical_"></a></span><a class="link" href="comparisons.html#math_toolkit.comparisons.comparison_to_the_r_statistical_">Comparison
1846       to the R Statistical Library on Linux</a>
1847     </h4>
1848 <p>
1849       All the results were measured on a 2.0GHz Intel T5800 Core 2 Duo, 4Gb RAM,
1850       Ubuntu Linux 9 machine, with the test program and R-2.9.2 compiled with GNU
1851       G++ 4.3.3 using -O3 -DNDEBUG=1.
1852     </p>
1853 <div class="table">
1854 <a name="math_toolkit.comparisons.a_comparison_to_the_r_statistic0"></a><p class="title"><b>Table&#160;15.6.&#160;A Comparison to the R Statistical Library on Linux</b></p>
1855 <div class="table-contents"><table class="table" summary="A Comparison to the R Statistical Library on Linux">
1856 <colgroup>
1857 <col>
1858 <col>
1859 <col>
1860 <col>
1861 </colgroup>
1862 <thead><tr>
1863 <th>
1864               <p>
1865                 Statistical Function
1866               </p>
1867             </th>
1868 <th>
1869               <p>
1870                 Boost
1871               </p>
1872             </th>
1873 <th>
1874               <p>
1875                 R
1876               </p>
1877             </th>
1878 <th>
1879               <p>
1880                 DCDFLIB
1881               </p>
1882             </th>
1883 </tr></thead>
1884 <tbody>
1885 <tr>
1886 <td>
1887               <p>
1888                 <a class="link" href="dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a>
1889                 CDF
1890               </p>
1891             </td>
1892 <td>
1893               <p>
1894                 </p>
1895 <p>2.09</p>
1896 <p> </p>
1897 <p>(3.189e-006s)</p>
1898 <p>
1899               </p>
1900             </td>
1901 <td>
1902               <p>
1903                 </p>
1904 <p><span class="bold"><strong>1.00</strong></span></p>
1905 <p> </p>
1906 <p>(1.526e-006s)</p>
1907 <p>
1908               </p>
1909             </td>
1910 <td>
1911               <p>
1912                 </p>
1913 <p>1.19</p>
1914 <p> </p>
1915 <p>(1.822e-006s)</p>
1916 <p>
1917               </p>
1918             </td>
1919 </tr>
1920 <tr>
1921 <td>
1922               <p>
1923                 <a class="link" href="dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a>
1924                 Quantile
1925               </p>
1926             </td>
1927 <td>
1928               <p>
1929                 </p>
1930 <p><span class="bold"><strong>1.00</strong></span></p>
1931 <p> </p>
1932 <p>(1.185e-005s)</p>
1933 <p>
1934               </p>
1935             </td>
1936 <td>
1937               <p>
1938                 </p>
1939 <p>30.51<a href="#ftn.math_toolkit.comparisons.f7" class="footnote" name="math_toolkit.comparisons.f7"><sup class="footnote">[1]</sup></a></p>
1940 <p> </p>
1941 <p>(3.616e-004s)</p>
1942 <p>
1943               </p>
1944             </td>
1945 <td>
1946               <p>
1947                 </p>
1948 <p>2.52</p>
1949 <p> </p>
1950 <p>(2.989e-005s)</p>
1951 <p>
1952               </p>
1953             </td>
1954 </tr>
1955 <tr>
1956 <td>
1957               <p>
1958                 <a class="link" href="dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial
1959                 Distribution</a> CDF
1960               </p>
1961             </td>
1962 <td>
1963               <p>
1964                 </p>
1965 <p>4.41</p>
1966 <p> </p>
1967 <p>(9.175e-007s)</p>
1968 <p>
1969               </p>
1970             </td>
1971 <td>
1972               <p>
1973                 </p>
1974 <p>3.59</p>
1975 <p> </p>
1976 <p>(7.476e-007s)</p>
1977 <p>
1978               </p>
1979             </td>
1980 <td>
1981               <p>
1982                 </p>
1983 <p><span class="bold"><strong>1.00</strong></span></p>
1984 <p> </p>
1985 <p>(2.081e-007s)</p>
1986 <p>
1987               </p>
1988             </td>
1989 </tr>
1990 <tr>
1991 <td>
1992               <p>
1993                 <a class="link" href="dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial
1994                 Distribution</a> Quantile
1995               </p>
1996             </td>
1997 <td>
1998               <p>
1999                 </p>
2000 <p>1.57</p>
2001 <p> </p>
2002 <p>(6.925e-006s)</p>
2003 <p>
2004               </p>
2005             </td>
2006 <td>
2007               <p>
2008                 </p>
2009 <p><span class="bold"><strong>1.00</strong></span></p>
2010 <p> </p>
2011 <p>(4.407e-006s)</p>
2012 <p>
2013               </p>
2014             </td>
2015 <td>
2016               <p>
2017                 </p>
2018 <p>7.43</p>
2019 <p> </p>
2020 <p>(3.274e-005s)</p>
2021 <p>
2022               </p>
2023             </td>
2024 </tr>
2025 <tr>
2026 <td>
2027               <p>
2028                 <a class="link" href="dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy Distribution</a>
2029                 CDF
2030               </p>
2031             </td>
2032 <td>
2033               <p>
2034                 </p>
2035 <p><span class="bold"><strong>1.00</strong></span></p>
2036 <p> </p>
2037 <p>(1.594e-007s)</p>
2038 <p>
2039               </p>
2040             </td>
2041 <td>
2042               <p>
2043                 </p>
2044 <p>1.04</p>
2045 <p> </p>
2046 <p>(1.654e-007s)</p>
2047 <p>
2048               </p>
2049             </td>
2050 <td>
2051               <p>
2052                 NA
2053               </p>
2054             </td>
2055 </tr>
2056 <tr>
2057 <td>
2058               <p>
2059                 <a class="link" href="dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy Distribution</a>
2060                 Quantile
2061               </p>
2062             </td>
2063 <td>
2064               <p>
2065                 </p>
2066 <p>1.21</p>
2067 <p> </p>
2068 <p>(1.752e-007s)</p>
2069 <p>
2070               </p>
2071             </td>
2072 <td>
2073               <p>
2074                 </p>
2075 <p><span class="bold"><strong>1.00</strong></span></p>
2076 <p> </p>
2077 <p>(1.448e-007s)</p>
2078 <p>
2079               </p>
2080             </td>
2081 <td>
2082               <p>
2083                 NA
2084               </p>
2085             </td>
2086 </tr>
2087 <tr>
2088 <td>
2089               <p>
2090                 <a class="link" href="dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi
2091                 Squared Distribution</a> CDF
2092               </p>
2093             </td>
2094 <td>
2095               <p>
2096                 </p>
2097 <p>2.61</p>
2098 <p> </p>
2099 <p>(1.376e-006s)</p>
2100 <p>
2101               </p>
2102             </td>
2103 <td>
2104               <p>
2105                 </p>
2106 <p>2.36</p>
2107 <p> </p>
2108 <p>(1.243e-006s)</p>
2109 <p>
2110               </p>
2111             </td>
2112 <td>
2113               <p>
2114                 </p>
2115 <p><span class="bold"><strong>1.00</strong></span></p>
2116 <p> </p>
2117 <p>(5.270e-007s)</p>
2118 <p>
2119               </p>
2120             </td>
2121 </tr>
2122 <tr>
2123 <td>
2124               <p>
2125                 <a class="link" href="dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi
2126                 Squared Distribution</a> Quantile
2127               </p>
2128             </td>
2129 <td>
2130               <p>
2131                 </p>
2132 <p><span class="bold"><strong>1.00</strong></span></p>
2133 <p> </p>
2134 <p>(4.252e-006s)</p>
2135 <p>
2136               </p>
2137             </td>
2138 <td>
2139               <p>
2140                 </p>
2141 <p>1.34</p>
2142 <p> </p>
2143 <p>(5.700e-006s)</p>
2144 <p>
2145               </p>
2146             </td>
2147 <td>
2148               <p>
2149                 </p>
2150 <p>3.47</p>
2151 <p> </p>
2152 <p>(1.477e-005s)</p>
2153 <p>
2154               </p>
2155             </td>
2156 </tr>
2157 <tr>
2158 <td>
2159               <p>
2160                 <a class="link" href="dist_ref/dists/exp_dist.html" title="Exponential Distribution">Exponential
2161                 Distribution</a> CDF
2162               </p>
2163             </td>
2164 <td>
2165               <p>
2166                 </p>
2167 <p><span class="bold"><strong>1.00</strong></span></p>
2168 <p> </p>
2169 <p>(1.342e-007s)</p>
2170 <p>
2171               </p>
2172             </td>
2173 <td>
2174               <p>
2175                 </p>
2176 <p>1.25</p>
2177 <p> </p>
2178 <p>(1.677e-007s)</p>
2179 <p>
2180               </p>
2181             </td>
2182 <td>
2183               <p>
2184                 NA
2185               </p>
2186             </td>
2187 </tr>
2188 <tr>
2189 <td>
2190               <p>
2191                 <a class="link" href="dist_ref/dists/exp_dist.html" title="Exponential Distribution">Exponential
2192                 Distribution</a> Quantile
2193               </p>
2194             </td>
2195 <td>
2196               <p>
2197                 </p>
2198 <p><span class="bold"><strong>1.00</strong></span></p>
2199 <p> </p>
2200 <p>(8.827e-008s)</p>
2201 <p>
2202               </p>
2203             </td>
2204 <td>
2205               <p>
2206                 </p>
2207 <p>1.07</p>
2208 <p> </p>
2209 <p>(9.470e-008s)</p>
2210 <p>
2211               </p>
2212             </td>
2213 <td>
2214               <p>
2215                 NA
2216               </p>
2217             </td>
2218 </tr>
2219 <tr>
2220 <td>
2221               <p>
2222                 <a class="link" href="dist_ref/dists/f_dist.html" title="F Distribution">Fisher F Distribution</a>
2223                 CDF
2224               </p>
2225             </td>
2226 <td>
2227               <p>
2228                 </p>
2229 <p>1.62</p>
2230 <p> </p>
2231 <p>(2.324e-006s)</p>
2232 <p>
2233               </p>
2234             </td>
2235 <td>
2236               <p>
2237                 </p>
2238 <p>1.19</p>
2239 <p> </p>
2240 <p>(1.711e-006s)</p>
2241 <p>
2242               </p>
2243             </td>
2244 <td>
2245               <p>
2246                 </p>
2247 <p><span class="bold"><strong>1.00</strong></span></p>
2248 <p> </p>
2249 <p>(1.437e-006s)</p>
2250 <p>
2251               </p>
2252             </td>
2253 </tr>
2254 <tr>
2255 <td>
2256               <p>
2257                 <a class="link" href="dist_ref/dists/f_dist.html" title="F Distribution">Fisher F Distribution</a>
2258                 Quantile
2259               </p>
2260             </td>
2261 <td>
2262               <p>
2263                 </p>
2264 <p>1.53</p>
2265 <p> </p>
2266 <p>(1.577e-005s)</p>
2267 <p>
2268               </p>
2269             </td>
2270 <td>
2271               <p>
2272                 </p>
2273 <p><span class="bold"><strong>1.00</strong></span></p>
2274 <p> </p>
2275 <p>(1.033e-005s)</p>
2276 <p>
2277               </p>
2278             </td>
2279 <td>
2280               <p>
2281                 </p>
2282 <p>2.63</p>
2283 <p> </p>
2284 <p>(2.719e-005s)</p>
2285 <p>
2286               </p>
2287             </td>
2288 </tr>
2289 <tr>
2290 <td>
2291               <p>
2292                 <a class="link" href="dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma Distribution</a>
2293                 CDF
2294               </p>
2295             </td>
2296 <td>
2297               <p>
2298                 </p>
2299 <p>3.18</p>
2300 <p> </p>
2301 <p>(1.582e-006s)</p>
2302 <p>
2303               </p>
2304             </td>
2305 <td>
2306               <p>
2307                 </p>
2308 <p>2.63</p>
2309 <p> </p>
2310 <p>(1.309e-006s)</p>
2311 <p>
2312               </p>
2313             </td>
2314 <td>
2315               <p>
2316                 </p>
2317 <p><span class="bold"><strong>1.00</strong></span></p>
2318 <p> </p>
2319 <p>(4.980e-007s)</p>
2320 <p>
2321               </p>
2322             </td>
2323 </tr>
2324 <tr>
2325 <td>
2326               <p>
2327                 <a class="link" href="dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma Distribution</a>
2328                 Quantile
2329               </p>
2330             </td>
2331 <td>
2332               <p>
2333                 </p>
2334 <p>2.19</p>
2335 <p> </p>
2336 <p>(4.770e-006s)</p>
2337 <p>
2338               </p>
2339             </td>
2340 <td>
2341               <p>
2342                 </p>
2343 <p>6.94</p>
2344 <p> </p>
2345 <p>(1.513e-005s)</p>
2346 <p>
2347               </p>
2348             </td>
2349 <td>
2350               <p>
2351                 </p>
2352 <p><span class="bold"><strong>1.00</strong></span></p>
2353 <p> </p>
2354 <p>(2.179e-006s)</p>
2355 <p>
2356               </p>
2357             </td>
2358 </tr>
2359 <tr>
2360 <td>
2361               <p>
2362                 <a class="link" href="dist_ref/dists/hypergeometric_dist.html" title="Hypergeometric Distribution">hypergeometric
2363                 Distribution</a> CDF
2364               </p>
2365             </td>
2366 <td>
2367               <p>
2368                 </p>
2369 <p>2.20<a href="#ftn.math_toolkit.comparisons.f8" class="footnote" name="math_toolkit.comparisons.f8"><sup class="footnote">[2]</sup></a></p>
2370 <p> </p>
2371 <p>(3.522e-007s)</p>
2372 <p>
2373               </p>
2374             </td>
2375 <td>
2376               <p>
2377                 </p>
2378 <p><span class="bold"><strong>1.00</strong></span></p>
2379 <p> </p>
2380 <p>(1.601e-007s)</p>
2381 <p>
2382               </p>
2383             </td>
2384 <td>
2385               <p>
2386                 NA
2387               </p>
2388             </td>
2389 </tr>
2390 <tr>
2391 <td>
2392               <p>
2393                 <a class="link" href="dist_ref/dists/hypergeometric_dist.html" title="Hypergeometric Distribution">hypergeometric
2394                 Distribution</a> Quantile
2395               </p>
2396             </td>
2397 <td>
2398               <p>
2399                 </p>
2400 <p><span class="bold"><strong>1.00</strong></span></p>
2401 <p> </p>
2402 <p>(8.279e-007s)</p>
2403 <p>
2404               </p>
2405             </td>
2406 <td>
2407               <p>
2408                 </p>
2409 <p>2.57</p>
2410 <p> </p>
2411 <p>(2.125e-006s)</p>
2412 <p>
2413               </p>
2414             </td>
2415 <td>
2416               <p>
2417                 NA
2418               </p>
2419             </td>
2420 </tr>
2421 <tr>
2422 <td>
2423               <p>
2424                 <a class="link" href="dist_ref/dists/logistic_dist.html" title="Logistic Distribution">Logistic
2425                 Distribution</a> CDF
2426               </p>
2427             </td>
2428 <td>
2429               <p>
2430                 </p>
2431 <p><span class="bold"><strong>1.00</strong></span></p>
2432 <p> </p>
2433 <p>(9.398e-008s)</p>
2434 <p>
2435               </p>
2436             </td>
2437 <td>
2438               <p>
2439                 </p>
2440 <p>2.75</p>
2441 <p> </p>
2442 <p>(2.588e-007s)</p>
2443 <p>
2444               </p>
2445             </td>
2446 <td>
2447               <p>
2448                 NA
2449               </p>
2450             </td>
2451 </tr>
2452 <tr>
2453 <td>
2454               <p>
2455                 <a class="link" href="dist_ref/dists/logistic_dist.html" title="Logistic Distribution">Logistic
2456                 Distribution</a> Quantile
2457               </p>
2458             </td>
2459 <td>
2460               <p>
2461                 </p>
2462 <p><span class="bold"><strong>1.00</strong></span></p>
2463 <p> </p>
2464 <p>(9.893e-008s)</p>
2465 <p>
2466               </p>
2467             </td>
2468 <td>
2469               <p>
2470                 </p>
2471 <p>1.30</p>
2472 <p> </p>
2473 <p>(1.285e-007s)</p>
2474 <p>
2475               </p>
2476             </td>
2477 <td>
2478               <p>
2479                 NA
2480               </p>
2481             </td>
2482 </tr>
2483 <tr>
2484 <td>
2485               <p>
2486                 <a class="link" href="dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">Log-normal
2487                 Distribution</a> CDF
2488               </p>
2489             </td>
2490 <td>
2491               <p>
2492                 </p>
2493 <p><span class="bold"><strong>1.00</strong></span></p>
2494 <p> </p>
2495 <p>(1.831e-007s)</p>
2496 <p>
2497               </p>
2498             </td>
2499 <td>
2500               <p>
2501                 </p>
2502 <p>1.39</p>
2503 <p> </p>
2504 <p>(2.539e-007s)</p>
2505 <p>
2506               </p>
2507             </td>
2508 <td>
2509               <p>
2510                 NA
2511               </p>
2512             </td>
2513 </tr>
2514 <tr>
2515 <td>
2516               <p>
2517                 <a class="link" href="dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">Log-normal
2518                 Distribution</a> Quantile
2519               </p>
2520             </td>
2521 <td>
2522               <p>
2523                 </p>
2524 <p>1.10</p>
2525 <p> </p>
2526 <p>(5.551e-007s)</p>
2527 <p>
2528               </p>
2529             </td>
2530 <td>
2531               <p>
2532                 </p>
2533 <p><span class="bold"><strong>1.00</strong></span></p>
2534 <p> </p>
2535 <p>(5.037e-007s)</p>
2536 <p>
2537               </p>
2538             </td>
2539 <td>
2540               <p>
2541                 NA
2542               </p>
2543             </td>
2544 </tr>
2545 <tr>
2546 <td>
2547               <p>
2548                 <a class="link" href="dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative
2549                 Binomial Distribution</a> CDF
2550               </p>
2551             </td>
2552 <td>
2553               <p>
2554                 </p>
2555 <p>1.08</p>
2556 <p> </p>
2557 <p>(1.563e-006s)</p>
2558 <p>
2559               </p>
2560             </td>
2561 <td>
2562               <p>
2563                 </p>
2564 <p><span class="bold"><strong>1.00</strong></span></p>
2565 <p> </p>
2566 <p>(1.444e-006s)</p>
2567 <p>
2568               </p>
2569             </td>
2570 <td>
2571               <p>
2572                 </p>
2573 <p><span class="bold"><strong>1.00</strong></span></p>
2574 <p> </p>
2575 <p>(1.444e-006s)</p>
2576 <p>
2577               </p>
2578             </td>
2579 </tr>
2580 <tr>
2581 <td>
2582               <p>
2583                 <a class="link" href="dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative
2584                 Binomial Distribution</a> Quantile
2585               </p>
2586             </td>
2587 <td>
2588               <p>
2589                 </p>
2590 <p><span class="bold"><strong>1.00</strong></span></p>
2591 <p> </p>
2592 <p>(1.700e-005s)</p>
2593 <p>
2594               </p>
2595             </td>
2596 <td>
2597               <p>
2598                 </p>
2599 <p>25.92<a href="#ftn.math_toolkit.comparisons.f9" class="footnote" name="math_toolkit.comparisons.f9"><sup class="footnote">[3]</sup></a></p>
2600 <p> </p>
2601 <p>(4.407e-004s)</p>
2602 <p>
2603               </p>
2604             </td>
2605 <td>
2606               <p>
2607                 </p>
2608 <p>1.93</p>
2609 <p> </p>
2610 <p>(3.274e-005s)</p>
2611 <p>
2612               </p>
2613             </td>
2614 </tr>
2615 <tr>
2616 <td>
2617               <p>
2618                 <a class="link" href="dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral
2619                 Chi Squared Distribution</a> CDF
2620               </p>
2621             </td>
2622 <td>
2623               <p>
2624                 </p>
2625 <p>5.06</p>
2626 <p> </p>
2627 <p>(2.841e-005s)</p>
2628 <p>
2629               </p>
2630             </td>
2631 <td>
2632               <p>
2633                 </p>
2634 <p>25.01</p>
2635 <p> </p>
2636 <p>(1.405e-004s)</p>
2637 <p>
2638               </p>
2639             </td>
2640 <td>
2641               <p>
2642                 </p>
2643 <p><span class="bold"><strong>1.00</strong></span></p>
2644 <p> </p>
2645 <p>(5.617e-006s)</p>
2646 <p>
2647               </p>
2648             </td>
2649 </tr>
2650 <tr>
2651 <td>
2652               <p>
2653                 <a class="link" href="dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral
2654                 Chi Squared Distribution</a> Quantile
2655               </p>
2656             </td>
2657 <td>
2658               <p>
2659                 </p>
2660 <p>8.47</p>
2661 <p> </p>
2662 <p>(1.879e-003s)</p>
2663 <p>
2664               </p>
2665             </td>
2666 <td>
2667               <p>
2668                 </p>
2669 <p>144.91<a href="#ftn.math_toolkit.comparisons.f10" class="footnote" name="math_toolkit.comparisons.f10"><sup class="footnote">[4]</sup></a></p>
2670 <p> </p>
2671 <p>(3.214e-002s)</p>
2672 <p>
2673               </p>
2674             </td>
2675 <td>
2676               <p>
2677                 </p>
2678 <p><span class="bold"><strong>1.00</strong></span></p>
2679 <p> </p>
2680 <p>(2.218e-004s)</p>
2681 <p>
2682               </p>
2683             </td>
2684 </tr>
2685 <tr>
2686 <td>
2687               <p>
2688                 <a class="link" href="dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">Noncentral
2689                 F Distribution</a> CDF
2690               </p>
2691             </td>
2692 <td>
2693               <p>
2694                 </p>
2695 <p>10.33</p>
2696 <p> </p>
2697 <p>(5.868e-005s)</p>
2698 <p>
2699               </p>
2700             </td>
2701 <td>
2702               <p>
2703                 </p>
2704 <p>1.42</p>
2705 <p> </p>
2706 <p>(8.058e-006s)</p>
2707 <p>
2708               </p>
2709             </td>
2710 <td>
2711               <p>
2712                 </p>
2713 <p><span class="bold"><strong>1.00</strong></span></p>
2714 <p> </p>
2715 <p>(5.682e-006s)</p>
2716 <p>
2717               </p>
2718             </td>
2719 </tr>
2720 <tr>
2721 <td>
2722               <p>
2723                 <a class="link" href="dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">Noncentral
2724                 F Distribution</a> Quantile
2725               </p>
2726             </td>
2727 <td>
2728               <p>
2729                 </p>
2730 <p>5.64</p>
2731 <p> </p>
2732 <p>(7.869e-004s)</p>
2733 <p>
2734               </p>
2735             </td>
2736 <td>
2737               <p>
2738                 </p>
2739 <p>6.63</p>
2740 <p> </p>
2741 <p>(9.256e-004s)</p>
2742 <p>
2743               </p>
2744             </td>
2745 <td>
2746               <p>
2747                 </p>
2748 <p><span class="bold"><strong>1.00</strong></span></p>
2749 <p> </p>
2750 <p>(1.396e-004s)</p>
2751 <p>
2752               </p>
2753             </td>
2754 </tr>
2755 <tr>
2756 <td>
2757               <p>
2758                 <a class="link" href="dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">noncentral
2759                 T distribution</a> CDF
2760               </p>
2761             </td>
2762 <td>
2763               <p>
2764                 </p>
2765 <p>4.91</p>
2766 <p> </p>
2767 <p>(3.357e-005s)</p>
2768 <p>
2769               </p>
2770             </td>
2771 <td>
2772               <p>
2773                 </p>
2774 <p><span class="bold"><strong>1.00</strong></span></p>
2775 <p> </p>
2776 <p>(6.844e-006s)</p>
2777 <p>
2778               </p>
2779             </td>
2780 <td>
2781               <p>
2782                 NA
2783               </p>
2784             </td>
2785 </tr>
2786 <tr>
2787 <td>
2788               <p>
2789                 <a class="link" href="dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">noncentral
2790                 T distribution</a> Quantile
2791               </p>
2792             </td>
2793 <td>
2794               <p>
2795                 </p>
2796 <p>1.57</p>
2797 <p> </p>
2798 <p>(9.265e-004s)</p>
2799 <p>
2800               </p>
2801             </td>
2802 <td>
2803               <p>
2804                 </p>
2805 <p><span class="bold"><strong>1.00</strong></span><a href="#ftn.math_toolkit.comparisons.f11" class="footnote" name="math_toolkit.comparisons.f11"><sup class="footnote">[5]</sup></a></p>
2806 <p> </p>
2807 <p>(5.916e-004s)</p>
2808 <p>
2809               </p>
2810             </td>
2811 <td>
2812               <p>
2813                 NA
2814               </p>
2815             </td>
2816 </tr>
2817 <tr>
2818 <td>
2819               <p>
2820                 <a class="link" href="dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal Distribution</a>
2821                 CDF
2822               </p>
2823             </td>
2824 <td>
2825               <p>
2826                 </p>
2827 <p><span class="bold"><strong>1.00</strong></span></p>
2828 <p> </p>
2829 <p>(1.074e-007s)</p>
2830 <p>
2831               </p>
2832             </td>
2833 <td>
2834               <p>
2835                 </p>
2836 <p>1.16</p>
2837 <p> </p>
2838 <p>(1.245e-007s)</p>
2839 <p>
2840               </p>
2841             </td>
2842 <td>
2843               <p>
2844                 </p>
2845 <p>5.36</p>
2846 <p> </p>
2847 <p>(5.762e-007s)</p>
2848 <p>
2849               </p>
2850             </td>
2851 </tr>
2852 <tr>
2853 <td>
2854               <p>
2855                 <a class="link" href="dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal Distribution</a>
2856                 Quantile
2857               </p>
2858             </td>
2859 <td>
2860               <p>
2861                 </p>
2862 <p>1.28</p>
2863 <p> </p>
2864 <p>(1.902e-007s)</p>
2865 <p>
2866               </p>
2867             </td>
2868 <td>
2869               <p>
2870                 </p>
2871 <p><span class="bold"><strong>1.00</strong></span></p>
2872 <p> </p>
2873 <p>(1.490e-007s)</p>
2874 <p>
2875               </p>
2876             </td>
2877 <td>
2878               <p>
2879                 </p>
2880 <p>10.35</p>
2881 <p> </p>
2882 <p>(1.542e-006s)</p>
2883 <p>
2884               </p>
2885             </td>
2886 </tr>
2887 <tr>
2888 <td>
2889               <p>
2890                 <a class="link" href="dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson
2891                 Distribution</a> CDF
2892               </p>
2893             </td>
2894 <td>
2895               <p>
2896                 </p>
2897 <p>2.43</p>
2898 <p> </p>
2899 <p>(1.198e-006s)</p>
2900 <p>
2901               </p>
2902             </td>
2903 <td>
2904               <p>
2905                 </p>
2906 <p>2.25</p>
2907 <p> </p>
2908 <p>(1.110e-006s)</p>
2909 <p>
2910               </p>
2911             </td>
2912 <td>
2913               <p>
2914                 </p>
2915 <p><span class="bold"><strong>1.00</strong></span></p>
2916 <p> </p>
2917 <p>(4.937e-007s)</p>
2918 <p>
2919               </p>
2920             </td>
2921 </tr>
2922 <tr>
2923 <td>
2924               <p>
2925                 <a class="link" href="dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson
2926                 Distribution</a>
2927               </p>
2928             </td>
2929 <td>
2930               <p>
2931                 </p>
2932 <p>1.11</p>
2933 <p> </p>
2934 <p>(3.032e-006s)</p>
2935 <p>
2936               </p>
2937             </td>
2938 <td>
2939               <p>
2940                 </p>
2941 <p><span class="bold"><strong>1.00</strong></span></p>
2942 <p> </p>
2943 <p>(2.724e-006s)</p>
2944 <p>
2945               </p>
2946             </td>
2947 <td>
2948               <p>
2949                 </p>
2950 <p>4.07</p>
2951 <p> </p>
2952 <p>(1.110e-005s)</p>
2953 <p>
2954               </p>
2955             </td>
2956 </tr>
2957 <tr>
2958 <td>
2959               <p>
2960                 <a class="link" href="dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students
2961                 t Distribution</a> CDF
2962               </p>
2963             </td>
2964 <td>
2965               <p>
2966                 </p>
2967 <p>2.17</p>
2968 <p> </p>
2969 <p>(2.020e-006s)</p>
2970 <p>
2971               </p>
2972             </td>
2973 <td>
2974               <p>
2975                 </p>
2976 <p><span class="bold"><strong>1.00</strong></span></p>
2977 <p> </p>
2978 <p>(9.321e-007s)</p>
2979 <p>
2980               </p>
2981             </td>
2982 <td>
2983               <p>
2984                 </p>
2985 <p>1.10</p>
2986 <p> </p>
2987 <p>(1.021e-006s)</p>
2988 <p>
2989               </p>
2990             </td>
2991 </tr>
2992 <tr>
2993 <td>
2994               <p>
2995                 <a class="link" href="dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students
2996                 t Distribution</a> Quantile
2997               </p>
2998             </td>
2999 <td>
3000               <p>
3001                 </p>
3002 <p>1.18</p>
3003 <p> </p>
3004 <p>(3.972e-006s)</p>
3005 <p>
3006               </p>
3007             </td>
3008 <td>
3009               <p>
3010                 </p>
3011 <p><span class="bold"><strong>1.00</strong></span></p>
3012 <p> </p>
3013 <p>(3.364e-006s)</p>
3014 <p>
3015               </p>
3016             </td>
3017 <td>
3018               <p>
3019                 </p>
3020 <p>3.89</p>
3021 <p> </p>
3022 <p>(1.308e-005s)</p>
3023 <p>
3024               </p>
3025             </td>
3026 </tr>
3027 <tr>
3028 <td>
3029               <p>
3030                 <a class="link" href="dist_ref/dists/weibull_dist.html" title="Weibull Distribution">Weibull
3031                 Distribution</a> CDF
3032               </p>
3033             </td>
3034 <td>
3035               <p>
3036                 </p>
3037 <p><span class="bold"><strong>1.00</strong></span></p>
3038 <p> </p>
3039 <p>(3.662e-007s)</p>
3040 <p>
3041               </p>
3042             </td>
3043 <td>
3044               <p>
3045                 </p>
3046 <p>1.04</p>
3047 <p> </p>
3048 <p>(3.808e-007s)</p>
3049 <p>
3050               </p>
3051             </td>
3052 <td>
3053               <p>
3054                 NA
3055               </p>
3056             </td>
3057 </tr>
3058 <tr>
3059 <td>
3060               <p>
3061                 <a class="link" href="dist_ref/dists/weibull_dist.html" title="Weibull Distribution">Weibull
3062                 Distribution</a> Quantile
3063               </p>
3064             </td>
3065 <td>
3066               <p>
3067                 </p>
3068 <p><span class="bold"><strong>1.00</strong></span></p>
3069 <p> </p>
3070 <p>(4.112e-007s)</p>
3071 <p>
3072               </p>
3073             </td>
3074 <td>
3075               <p>
3076                 </p>
3077 <p>1.05</p>
3078 <p> </p>
3079 <p>(4.317e-007s)</p>
3080 <p>
3081               </p>
3082             </td>
3083 <td>
3084               <p>
3085                 NA
3086               </p>
3087             </td>
3088 </tr>
3089 </tbody>
3090 <tbody class="footnotes"><tr><td colspan="4">
3091 <div id="ftn.math_toolkit.comparisons.f7" class="footnote"><p><a href="#math_toolkit.comparisons.f7" class="para"><sup class="para">[1] </sup></a>
3092                   There are a small number of our test cases where the R library
3093                   fails to converge on a result: these tend to dominate the performance
3094                   result.
3095                 </p></div>
3096 <div id="ftn.math_toolkit.comparisons.f8" class="footnote"><p><a href="#math_toolkit.comparisons.f8" class="para"><sup class="para">[2] </sup></a>
3097                   This result is somewhat misleading: for small values of the parameters
3098                   there is virtually no difference between the two libraries, but
3099                   for large values the Boost implementation is <span class="emphasis"><em>much</em></span>
3100                   slower, albeit with much improved precision.
3101                 </p></div>
3102 <div id="ftn.math_toolkit.comparisons.f9" class="footnote"><p><a href="#math_toolkit.comparisons.f9" class="para"><sup class="para">[3] </sup></a>
3103                   The R library appears to use a linear-search strategy, that can
3104                   perform very badly in a small number of pathological cases, but
3105                   may or may not be more efficient in "typical" cases
3106                 </p></div>
3107 <div id="ftn.math_toolkit.comparisons.f10" class="footnote"><p><a href="#math_toolkit.comparisons.f10" class="para"><sup class="para">[4] </sup></a>
3108                   There are a small number of our test cases where the R library
3109                   fails to converge on a result: these tend to dominate the performance
3110                   result.
3111                 </p></div>
3112 <div id="ftn.math_toolkit.comparisons.f11" class="footnote"><p><a href="#math_toolkit.comparisons.f11" class="para"><sup class="para">[5] </sup></a>
3113                   There are a small number of our test cases where the R library
3114                   fails to converge on a result: these tend to dominate the performance
3115                   result.
3116                 </p></div>
3117 </td></tr></tbody>
3118 </table></div>
3119 </div>
3120 <br class="table-break">
3121 </div>
3122 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
3123 <td align="left"></td>
3124 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014 Nikhar Agrawal,
3125       Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
3126       Holin, Bruno Lalande, John Maddock, Johan R&#229;de, Gautam Sewani, Benjamin Sobotta,
3127       Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
3128         Distributed under the Boost Software License, Version 1.0. (See accompanying
3129         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>)
3130       </p>
3131 </div></td>
3132 </tr></table>
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