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  26 <div class="titlepage"><div><div><h3 class="title">
  27 <a name="math_toolkit.logs_and_tables.all_table"></a><a class="link" href="all_table.html" title="Tables of Error Rates for all Functions">Tables of Error
  28       Rates for all Functions</a>
  29 </h3></div></div></div>
  30 <div class="table">
  31 <a name="math_toolkit.logs_and_tables.all_table.table_beta"></a><p class="title"><b>Table&#160;22.3.&#160;Error rates for beta</b></p>
  32 <div class="table-contents"><table class="table" summary="Error rates for beta">
  33 <colgroup>
  34 <col>
  35 <col>
  36 <col>
  37 <col>
  38 <col>
  39 </colgroup>
  40 <thead><tr>
  41 <th>
  42               </th>
  43 <th>
  44                 <p>
  45                   GNU C++ version 7.1.0<br> linux<br> double
  46                 </p>
  47               </th>
  48 <th>
  49                 <p>
  50                   GNU C++ version 7.1.0<br> linux<br> long double
  51                 </p>
  52               </th>
  53 <th>
  54                 <p>
  55                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
  56                 </p>
  57               </th>
  58 <th>
  59                 <p>
  60                   Microsoft Visual C++ version 14.1<br> Win32<br> double
  61                 </p>
  62               </th>
  63 </tr></thead>
  64 <tbody>
  65 <tr>
  66 <td>
  67                 <p>
  68                   Beta Function: Small Values
  69                 </p>
  70               </td>
  71 <td>
  72                 <p>
  73                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
  74                   2.1:</em></span> <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_beta_GSL_2_1_Beta_Function_Small_Values">And
  75                   other failures.</a>)</span><br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
  76                   Max = 1.14&#949; (Mean = 0.574&#949;))
  77                 </p>
  78               </td>
  79 <td>
  80                 <p>
  81                   <span class="blue">Max = 2.86&#949; (Mean = 1.22&#949;)</span><br> <br>
  82                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 364&#949; (Mean = 76.2&#949;))
  83                 </p>
  84               </td>
  85 <td>
  86                 <p>
  87                   <span class="blue">Max = 2.86&#949; (Mean = 1.22&#949;)</span>
  88                 </p>
  89               </td>
  90 <td>
  91                 <p>
  92                   <span class="blue">Max = 2.23&#949; (Mean = 1.14&#949;)</span>
  93                 </p>
  94               </td>
  95 </tr>
  96 <tr>
  97 <td>
  98                 <p>
  99                   Beta Function: Medium Values
 100                 </p>
 101               </td>
 102 <td>
 103                 <p>
 104                   <span class="blue">Max = 0.978&#949; (Mean = 0.0595&#949;)</span><br>
 105                   <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.18e+03&#949; (Mean = 238&#949;))<br>
 106                   (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.09e+03&#949; (Mean = 265&#949;))
 107                 </p>
 108               </td>
 109 <td>
 110                 <p>
 111                   <span class="blue">Max = 61.4&#949; (Mean = 19.4&#949;)</span><br> <br>
 112                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.07e+03&#949; (Mean = 264&#949;))
 113                 </p>
 114               </td>
 115 <td>
 116                 <p>
 117                   <span class="blue">Max = 107&#949; (Mean = 24.5&#949;)</span>
 118                 </p>
 119               </td>
 120 <td>
 121                 <p>
 122                   <span class="blue">Max = 96.5&#949; (Mean = 22.4&#949;)</span>
 123                 </p>
 124               </td>
 125 </tr>
 126 <tr>
 127 <td>
 128                 <p>
 129                   Beta Function: Divergent Values
 130                 </p>
 131               </td>
 132 <td>
 133                 <p>
 134                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
 135                   2.1:</em></span> Max = 12.1&#949; (Mean = 1.99&#949;))<br> (<span class="emphasis"><em>Rmath
 136                   3.2.3:</em></span> Max = 176&#949; (Mean = 28&#949;))
 137                 </p>
 138               </td>
 139 <td>
 140                 <p>
 141                   <span class="blue">Max = 8.99&#949; (Mean = 2.44&#949;)</span><br> <br>
 142                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 128&#949; (Mean = 23.8&#949;))
 143                 </p>
 144               </td>
 145 <td>
 146                 <p>
 147                   <span class="blue">Max = 18.8&#949; (Mean = 2.71&#949;)</span>
 148                 </p>
 149               </td>
 150 <td>
 151                 <p>
 152                   <span class="blue">Max = 11.4&#949; (Mean = 2.19&#949;)</span>
 153                 </p>
 154               </td>
 155 </tr>
 156 </tbody>
 157 </table></div>
 158 </div>
 159 <br class="table-break"><div class="table">
 160 <a name="math_toolkit.logs_and_tables.all_table.table_beta_incomplete_"></a><p class="title"><b>Table&#160;22.4.&#160;Error rates for beta (incomplete)</b></p>
 161 <div class="table-contents"><table class="table" summary="Error rates for beta (incomplete)">
 162 <colgroup>
 163 <col>
 164 <col>
 165 <col>
 166 <col>
 167 <col>
 168 </colgroup>
 169 <thead><tr>
 170 <th>
 171               </th>
 172 <th>
 173                 <p>
 174                   GNU C++ version 7.1.0<br> linux<br> double
 175                 </p>
 176               </th>
 177 <th>
 178                 <p>
 179                   GNU C++ version 7.1.0<br> linux<br> long double
 180                 </p>
 181               </th>
 182 <th>
 183                 <p>
 184                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
 185                 </p>
 186               </th>
 187 <th>
 188                 <p>
 189                   Microsoft Visual C++ version 14.1<br> Win32<br> double
 190                 </p>
 191               </th>
 192 </tr></thead>
 193 <tbody>
 194 <tr>
 195 <td>
 196                 <p>
 197                   Incomplete Beta Function: Small Values
 198                 </p>
 199               </td>
 200 <td>
 201                 <p>
 202                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
 203                 </p>
 204               </td>
 205 <td>
 206                 <p>
 207                   <span class="blue">Max = 11.1&#949; (Mean = 2.32&#949;)</span>
 208                 </p>
 209               </td>
 210 <td>
 211                 <p>
 212                   <span class="blue">Max = 18.7&#949; (Mean = 3.19&#949;)</span>
 213                 </p>
 214               </td>
 215 <td>
 216                 <p>
 217                   <span class="blue">Max = 9.94&#949; (Mean = 2.17&#949;)</span>
 218                 </p>
 219               </td>
 220 </tr>
 221 <tr>
 222 <td>
 223                 <p>
 224                   Incomplete Beta Function: Medium Values
 225                 </p>
 226               </td>
 227 <td>
 228                 <p>
 229                   <span class="blue">Max = 0.568&#949; (Mean = 0.0254&#949;)</span>
 230                 </p>
 231               </td>
 232 <td>
 233                 <p>
 234                   <span class="blue">Max = 69.2&#949; (Mean = 13.4&#949;)</span>
 235                 </p>
 236               </td>
 237 <td>
 238                 <p>
 239                   <span class="blue">Max = 174&#949; (Mean = 25&#949;)</span>
 240                 </p>
 241               </td>
 242 <td>
 243                 <p>
 244                   <span class="blue">Max = 90&#949; (Mean = 12.7&#949;)</span>
 245                 </p>
 246               </td>
 247 </tr>
 248 <tr>
 249 <td>
 250                 <p>
 251                   Incomplete Beta Function: Large and Diverse Values
 252                 </p>
 253               </td>
 254 <td>
 255                 <p>
 256                   <span class="blue">Max = 0.999&#949; (Mean = 0.0325&#949;)</span>
 257                 </p>
 258               </td>
 259 <td>
 260                 <p>
 261                   <span class="blue">Max = 6.84e+04&#949; (Mean = 2.76e+03&#949;)</span>
 262                 </p>
 263               </td>
 264 <td>
 265                 <p>
 266                   <span class="blue">Max = 6.86e+04&#949; (Mean = 2.79e+03&#949;)</span>
 267                 </p>
 268               </td>
 269 <td>
 270                 <p>
 271                   <span class="blue">Max = 633&#949; (Mean = 29.7&#949;)</span>
 272                 </p>
 273               </td>
 274 </tr>
 275 <tr>
 276 <td>
 277                 <p>
 278                   Incomplete Beta Function: Small Integer Values
 279                 </p>
 280               </td>
 281 <td>
 282                 <p>
 283                   <span class="blue">Max = 0.786&#949; (Mean = 0.0323&#949;)</span>
 284                 </p>
 285               </td>
 286 <td>
 287                 <p>
 288                   <span class="blue">Max = 11.6&#949; (Mean = 3.6&#949;)</span>
 289                 </p>
 290               </td>
 291 <td>
 292                 <p>
 293                   <span class="blue">Max = 51.8&#949; (Mean = 11&#949;)</span>
 294                 </p>
 295               </td>
 296 <td>
 297                 <p>
 298                   <span class="blue">Max = 26&#949; (Mean = 6.28&#949;)</span>
 299                 </p>
 300               </td>
 301 </tr>
 302 </tbody>
 303 </table></div>
 304 </div>
 305 <br class="table-break"><div class="table">
 306 <a name="math_toolkit.logs_and_tables.all_table.table_betac"></a><p class="title"><b>Table&#160;22.5.&#160;Error rates for betac</b></p>
 307 <div class="table-contents"><table class="table" summary="Error rates for betac">
 308 <colgroup>
 309 <col>
 310 <col>
 311 <col>
 312 <col>
 313 <col>
 314 </colgroup>
 315 <thead><tr>
 316 <th>
 317               </th>
 318 <th>
 319                 <p>
 320                   GNU C++ version 7.1.0<br> linux<br> double
 321                 </p>
 322               </th>
 323 <th>
 324                 <p>
 325                   GNU C++ version 7.1.0<br> linux<br> long double
 326                 </p>
 327               </th>
 328 <th>
 329                 <p>
 330                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
 331                 </p>
 332               </th>
 333 <th>
 334                 <p>
 335                   Microsoft Visual C++ version 14.1<br> Win32<br> double
 336                 </p>
 337               </th>
 338 </tr></thead>
 339 <tbody>
 340 <tr>
 341 <td>
 342                 <p>
 343                   Incomplete Beta Function: Small Values
 344                 </p>
 345               </td>
 346 <td>
 347                 <p>
 348                   <span class="blue">Max = 0.676&#949; (Mean = 0.0302&#949;)</span>
 349                 </p>
 350               </td>
 351 <td>
 352                 <p>
 353                   <span class="blue">Max = 9.92&#949; (Mean = 2.3&#949;)</span>
 354                 </p>
 355               </td>
 356 <td>
 357                 <p>
 358                   <span class="blue">Max = 11.2&#949; (Mean = 2.94&#949;)</span>
 359                 </p>
 360               </td>
 361 <td>
 362                 <p>
 363                   <span class="blue">Max = 8.94&#949; (Mean = 2.06&#949;)</span>
 364                 </p>
 365               </td>
 366 </tr>
 367 <tr>
 368 <td>
 369                 <p>
 370                   Incomplete Beta Function: Medium Values
 371                 </p>
 372               </td>
 373 <td>
 374                 <p>
 375                   <span class="blue">Max = 0.949&#949; (Mean = 0.098&#949;)</span>
 376                 </p>
 377               </td>
 378 <td>
 379                 <p>
 380                   <span class="blue">Max = 63.5&#949; (Mean = 13.5&#949;)</span>
 381                 </p>
 382               </td>
 383 <td>
 384                 <p>
 385                   <span class="blue">Max = 97.6&#949; (Mean = 24.3&#949;)</span>
 386                 </p>
 387               </td>
 388 <td>
 389                 <p>
 390                   <span class="blue">Max = 90.6&#949; (Mean = 14.8&#949;)</span>
 391                 </p>
 392               </td>
 393 </tr>
 394 <tr>
 395 <td>
 396                 <p>
 397                   Incomplete Beta Function: Large and Diverse Values
 398                 </p>
 399               </td>
 400 <td>
 401                 <p>
 402                   <span class="blue">Max = 1.12&#949; (Mean = 0.0458&#949;)</span>
 403                 </p>
 404               </td>
 405 <td>
 406                 <p>
 407                   <span class="blue">Max = 1.05e+05&#949; (Mean = 5.45e+03&#949;)</span>
 408                 </p>
 409               </td>
 410 <td>
 411                 <p>
 412                   <span class="blue">Max = 1.04e+05&#949; (Mean = 5.46e+03&#949;)</span>
 413                 </p>
 414               </td>
 415 <td>
 416                 <p>
 417                   <span class="blue">Max = 3.72e+03&#949; (Mean = 113&#949;)</span>
 418                 </p>
 419               </td>
 420 </tr>
 421 <tr>
 422 <td>
 423                 <p>
 424                   Incomplete Beta Function: Small Integer Values
 425                 </p>
 426               </td>
 427 <td>
 428                 <p>
 429                   <span class="blue">Max = 0.586&#949; (Mean = 0.0314&#949;)</span>
 430                 </p>
 431               </td>
 432 <td>
 433                 <p>
 434                   <span class="blue">Max = 11.1&#949; (Mean = 3.65&#949;)</span>
 435                 </p>
 436               </td>
 437 <td>
 438                 <p>
 439                   <span class="blue">Max = 103&#949; (Mean = 17.4&#949;)</span>
 440                 </p>
 441               </td>
 442 <td>
 443                 <p>
 444                   <span class="blue">Max = 26.2&#949; (Mean = 6.36&#949;)</span>
 445                 </p>
 446               </td>
 447 </tr>
 448 </tbody>
 449 </table></div>
 450 </div>
 451 <br class="table-break"><div class="table">
 452 <a name="math_toolkit.logs_and_tables.all_table.table_binomial_coefficient"></a><p class="title"><b>Table&#160;22.6.&#160;Error rates for binomial_coefficient</b></p>
 453 <div class="table-contents"><table class="table" summary="Error rates for binomial_coefficient">
 454 <colgroup>
 455 <col>
 456 <col>
 457 <col>
 458 <col>
 459 <col>
 460 </colgroup>
 461 <thead><tr>
 462 <th>
 463               </th>
 464 <th>
 465                 <p>
 466                   GNU C++ version 7.1.0<br> linux<br> double
 467                 </p>
 468               </th>
 469 <th>
 470                 <p>
 471                   GNU C++ version 7.1.0<br> linux<br> long double
 472                 </p>
 473               </th>
 474 <th>
 475                 <p>
 476                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
 477                 </p>
 478               </th>
 479 <th>
 480                 <p>
 481                   Microsoft Visual C++ version 14.1<br> Win32<br> double
 482                 </p>
 483               </th>
 484 </tr></thead>
 485 <tbody>
 486 <tr>
 487 <td>
 488                 <p>
 489                   Binomials: small arguments
 490                 </p>
 491               </td>
 492 <td>
 493                 <p>
 494                   <span class="blue">Max = 1&#949; (Mean = 0.369&#949;)</span>
 495                 </p>
 496               </td>
 497 <td>
 498                 <p>
 499                   <span class="blue">Max = 1.5&#949; (Mean = 0.339&#949;)</span>
 500                 </p>
 501               </td>
 502 <td>
 503                 <p>
 504                   <span class="blue">Max = 1.5&#949; (Mean = 0.339&#949;)</span>
 505                 </p>
 506               </td>
 507 <td>
 508                 <p>
 509                   <span class="blue">Max = 1&#949; (Mean = 0.369&#949;)</span>
 510                 </p>
 511               </td>
 512 </tr>
 513 <tr>
 514 <td>
 515                 <p>
 516                   Binomials: large arguments
 517                 </p>
 518               </td>
 519 <td>
 520                 <p>
 521                   <span class="blue">Max = 0.939&#949; (Mean = 0.314&#949;)</span>
 522                 </p>
 523               </td>
 524 <td>
 525                 <p>
 526                   <span class="blue">Max = 26.6&#949; (Mean = 6.13&#949;)</span>
 527                 </p>
 528               </td>
 529 <td>
 530                 <p>
 531                   <span class="blue">Max = 53.2&#949; (Mean = 10.8&#949;)</span>
 532                 </p>
 533               </td>
 534 <td>
 535                 <p>
 536                   <span class="blue">Max = 37.2&#949; (Mean = 7.4&#949;)</span>
 537                 </p>
 538               </td>
 539 </tr>
 540 </tbody>
 541 </table></div>
 542 </div>
 543 <br class="table-break"><div class="table">
 544 <a name="math_toolkit.logs_and_tables.all_table.table_boost_math_powm1"></a><p class="title"><b>Table&#160;22.7.&#160;Error rates for boost::math::powm1</b></p>
 545 <div class="table-contents"><table class="table" summary="Error rates for boost::math::powm1">
 546 <colgroup>
 547 <col>
 548 <col>
 549 <col>
 550 <col>
 551 <col>
 552 </colgroup>
 553 <thead><tr>
 554 <th>
 555               </th>
 556 <th>
 557                 <p>
 558                   GNU C++ version 7.1.0<br> linux<br> long double
 559                 </p>
 560               </th>
 561 <th>
 562                 <p>
 563                   GNU C++ version 7.1.0<br> linux<br> double
 564                 </p>
 565               </th>
 566 <th>
 567                 <p>
 568                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
 569                 </p>
 570               </th>
 571 <th>
 572                 <p>
 573                   Microsoft Visual C++ version 14.1<br> Win32<br> double
 574                 </p>
 575               </th>
 576 </tr></thead>
 577 <tbody><tr>
 578 <td>
 579                 <p>
 580                   powm1
 581                 </p>
 582               </td>
 583 <td>
 584                 <p>
 585                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 2.04&#949; (Mean = 0.493&#949;))<br>
 586                   <br> <span class="blue">Max = 2.04&#949; (Mean = 0.493&#949;)</span><br>
 587                   <br> (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 2.04&#949; (Mean = 0.493&#949;))
 588                 </p>
 589               </td>
 590 <td>
 591                 <p>
 592                   (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.06&#949; (Mean = 0.425&#949;))<br>
 593                   <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.06&#949; (Mean = 0.425&#949;))<br>
 594                   <br> <span class="blue">Max = 1.06&#949; (Mean = 0.425&#949;)</span>
 595                 </p>
 596               </td>
 597 <td>
 598                 <p>
 599                   <span class="blue">Max = 1.88&#949; (Mean = 0.49&#949;)</span><br> <br>
 600                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.88&#949; (Mean = 0.49&#949;))
 601                 </p>
 602               </td>
 603 <td>
 604                 <p>
 605                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.84&#949; (Mean = 0.486&#949;))<br>
 606                   <br> <span class="blue">Max = 1.84&#949; (Mean = 0.486&#949;)</span>
 607                 </p>
 608               </td>
 609 </tr></tbody>
 610 </table></div>
 611 </div>
 612 <br class="table-break"><div class="table">
 613 <a name="math_toolkit.logs_and_tables.all_table.table_cbrt"></a><p class="title"><b>Table&#160;22.8.&#160;Error rates for cbrt</b></p>
 614 <div class="table-contents"><table class="table" summary="Error rates for cbrt">
 615 <colgroup>
 616 <col>
 617 <col>
 618 <col>
 619 <col>
 620 <col>
 621 </colgroup>
 622 <thead><tr>
 623 <th>
 624               </th>
 625 <th>
 626                 <p>
 627                   GNU C++ version 7.1.0<br> linux<br> double
 628                 </p>
 629               </th>
 630 <th>
 631                 <p>
 632                   GNU C++ version 7.1.0<br> linux<br> long double
 633                 </p>
 634               </th>
 635 <th>
 636                 <p>
 637                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
 638                 </p>
 639               </th>
 640 <th>
 641                 <p>
 642                   Microsoft Visual C++ version 14.1<br> Win32<br> double
 643                 </p>
 644               </th>
 645 </tr></thead>
 646 <tbody><tr>
 647 <td>
 648                 <p>
 649                   cbrt Function
 650                 </p>
 651               </td>
 652 <td>
 653                 <p>
 654                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
 655                 </p>
 656               </td>
 657 <td>
 658                 <p>
 659                   <span class="blue">Max = 1.34&#949; (Mean = 0.471&#949;)</span><br> <br>
 660                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.34&#949; (Mean = 0.471&#949;))<br>
 661                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.34&#949; (Mean = 0.471&#949;))
 662                 </p>
 663               </td>
 664 <td>
 665                 <p>
 666                   <span class="blue">Max = 1.34&#949; (Mean = 0.471&#949;)</span><br> <br>
 667                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.34&#949; (Mean = 0.471&#949;))
 668                 </p>
 669               </td>
 670 <td>
 671                 <p>
 672                   <span class="blue">Max = 1.7&#949; (Mean = 0.565&#949;)</span><br> <br>
 673                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.7&#949; (Mean = 0.565&#949;))
 674                 </p>
 675               </td>
 676 </tr></tbody>
 677 </table></div>
 678 </div>
 679 <br class="table-break"><div class="table">
 680 <a name="math_toolkit.logs_and_tables.all_table.table_cos_pi"></a><p class="title"><b>Table&#160;22.9.&#160;Error rates for cos_pi</b></p>
 681 <div class="table-contents"><table class="table" summary="Error rates for cos_pi">
 682 <colgroup>
 683 <col>
 684 <col>
 685 <col>
 686 <col>
 687 <col>
 688 </colgroup>
 689 <thead><tr>
 690 <th>
 691               </th>
 692 <th>
 693                 <p>
 694                   GNU C++ version 7.1.0<br> linux<br> double
 695                 </p>
 696               </th>
 697 <th>
 698                 <p>
 699                   GNU C++ version 7.1.0<br> linux<br> long double
 700                 </p>
 701               </th>
 702 <th>
 703                 <p>
 704                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
 705                 </p>
 706               </th>
 707 <th>
 708                 <p>
 709                   Microsoft Visual C++ version 14.1<br> Win32<br> double
 710                 </p>
 711               </th>
 712 </tr></thead>
 713 <tbody>
 714 <tr>
 715 <td>
 716                 <p>
 717                   sin_pi and cos_pi
 718                 </p>
 719               </td>
 720 <td>
 721                 <p>
 722                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
 723                 </p>
 724               </td>
 725 <td>
 726                 <p>
 727                   <span class="blue">Max = 0.991&#949; (Mean = 0.302&#949;)</span>
 728                 </p>
 729               </td>
 730 <td>
 731                 <p>
 732                   <span class="blue">Max = 0.991&#949; (Mean = 0.302&#949;)</span>
 733                 </p>
 734               </td>
 735 <td>
 736                 <p>
 737                   <span class="blue">Max = 0.996&#949; (Mean = 0.284&#949;)</span>
 738                 </p>
 739               </td>
 740 </tr>
 741 <tr>
 742 <td>
 743                 <p>
 744                   sin_pi and cos_pi near integers and half integers
 745                 </p>
 746               </td>
 747 <td>
 748                 <p>
 749                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
 750                 </p>
 751               </td>
 752 <td>
 753                 <p>
 754                   <span class="blue">Max = 0.976&#949; (Mean = 0.28&#949;)</span>
 755                 </p>
 756               </td>
 757 <td>
 758                 <p>
 759                   <span class="blue">Max = 0.976&#949; (Mean = 0.28&#949;)</span>
 760                 </p>
 761               </td>
 762 <td>
 763                 <p>
 764                   <span class="blue">Max = 0.996&#949; (Mean = 0.298&#949;)</span>
 765                 </p>
 766               </td>
 767 </tr>
 768 </tbody>
 769 </table></div>
 770 </div>
 771 <br class="table-break"><div class="table">
 772 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_i"></a><p class="title"><b>Table&#160;22.10.&#160;Error rates for cyl_bessel_i</b></p>
 773 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i">
 774 <colgroup>
 775 <col>
 776 <col>
 777 <col>
 778 <col>
 779 <col>
 780 </colgroup>
 781 <thead><tr>
 782 <th>
 783               </th>
 784 <th>
 785                 <p>
 786                   GNU C++ version 7.1.0<br> linux<br> double
 787                 </p>
 788               </th>
 789 <th>
 790                 <p>
 791                   GNU C++ version 7.1.0<br> linux<br> long double
 792                 </p>
 793               </th>
 794 <th>
 795                 <p>
 796                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
 797                 </p>
 798               </th>
 799 <th>
 800                 <p>
 801                   Microsoft Visual C++ version 14.1<br> Win32<br> double
 802                 </p>
 803               </th>
 804 </tr></thead>
 805 <tbody>
 806 <tr>
 807 <td>
 808                 <p>
 809                   Bessel I0: Mathworld Data
 810                 </p>
 811               </td>
 812 <td>
 813                 <p>
 814                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
 815                   2.1:</em></span> Max = 270&#949; (Mean = 91.6&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_I0_Mathworld_Data">And
 816                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
 817                   Max = 1.52&#949; (Mean = 0.622&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_I0_Mathworld_Data">And
 818                   other failures.</a>)
 819                 </p>
 820               </td>
 821 <td>
 822                 <p>
 823                   <span class="blue">Max = 1.95&#949; (Mean = 0.738&#949;)</span><br> <br>
 824                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 8.49&#949; (Mean = 3.46&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_I0_Mathworld_Data">And
 825                   other failures.</a>)
 826                 </p>
 827               </td>
 828 <td>
 829                 <p>
 830                   <span class="blue">Max = 1.95&#949; (Mean = 0.661&#949;)</span>
 831                 </p>
 832               </td>
 833 <td>
 834                 <p>
 835                   <span class="blue">Max = 0.762&#949; (Mean = 0.329&#949;)</span>
 836                 </p>
 837               </td>
 838 </tr>
 839 <tr>
 840 <td>
 841                 <p>
 842                   Bessel I1: Mathworld Data
 843                 </p>
 844               </td>
 845 <td>
 846                 <p>
 847                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
 848                   2.1:</em></span> Max = 128&#949; (Mean = 41&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_I1_Mathworld_Data">And
 849                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
 850                   Max = 1.53&#949; (Mean = 0.483&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_I1_Mathworld_Data">And
 851                   other failures.</a>)
 852                 </p>
 853               </td>
 854 <td>
 855                 <p>
 856                   <span class="blue">Max = 0.64&#949; (Mean = 0.202&#949;)</span><br> <br>
 857                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 5&#949; (Mean = 2.15&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_I1_Mathworld_Data">And
 858                   other failures.</a>)
 859                 </p>
 860               </td>
 861 <td>
 862                 <p>
 863                   <span class="blue">Max = 0.64&#949; (Mean = 0.202&#949;)</span>
 864                 </p>
 865               </td>
 866 <td>
 867                 <p>
 868                   <span class="blue">Max = 0.767&#949; (Mean = 0.398&#949;)</span>
 869                 </p>
 870               </td>
 871 </tr>
 872 <tr>
 873 <td>
 874                 <p>
 875                   Bessel In: Mathworld Data
 876                 </p>
 877               </td>
 878 <td>
 879                 <p>
 880                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
 881                   2.1:</em></span> Max = 2.31&#949; (Mean = 0.838&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_In_Mathworld_Data">And
 882                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
 883                   Max = 1.73&#949; (Mean = 0.601&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_In_Mathworld_Data">And
 884                   other failures.</a>)
 885                 </p>
 886               </td>
 887 <td>
 888                 <p>
 889                   <span class="blue">Max = 1.8&#949; (Mean = 1.33&#949;)</span><br> <br>
 890                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 430&#949; (Mean = 163&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_In_Mathworld_Data">And
 891                   other failures.</a>)
 892                 </p>
 893               </td>
 894 <td>
 895                 <p>
 896                   <span class="blue">Max = 463&#949; (Mean = 140&#949;)</span>
 897                 </p>
 898               </td>
 899 <td>
 900                 <p>
 901                   <span class="blue">Max = 3.46&#949; (Mean = 1.32&#949;)</span>
 902                 </p>
 903               </td>
 904 </tr>
 905 <tr>
 906 <td>
 907                 <p>
 908                   Bessel Iv: Mathworld Data
 909                 </p>
 910               </td>
 911 <td>
 912                 <p>
 913                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
 914                   2.1:</em></span> Max = 5.95&#949; (Mean = 2.08&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Mathworld_Data">And
 915                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
 916                   Max = 3.53&#949; (Mean = 1.39&#949;))
 917                 </p>
 918               </td>
 919 <td>
 920                 <p>
 921                   <span class="blue">Max = 4.12&#949; (Mean = 1.85&#949;)</span><br> <br>
 922                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 616&#949; (Mean = 221&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Mathworld_Data">And
 923                   other failures.</a>)
 924                 </p>
 925               </td>
 926 <td>
 927                 <p>
 928                   <span class="blue">Max = 4.12&#949; (Mean = 1.95&#949;)</span>
 929                 </p>
 930               </td>
 931 <td>
 932                 <p>
 933                   <span class="blue">Max = 2.97&#949; (Mean = 1.24&#949;)</span>
 934                 </p>
 935               </td>
 936 </tr>
 937 <tr>
 938 <td>
 939                 <p>
 940                   Bessel In: Random Data
 941                 </p>
 942               </td>
 943 <td>
 944                 <p>
 945                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
 946                   2.1:</em></span> Max = 261&#949; (Mean = 53.2&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_In_Random_Data">And
 947                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
 948                   Max = 7.37&#949; (Mean = 2.4&#949;))
 949                 </p>
 950               </td>
 951 <td>
 952                 <p>
 953                   <span class="blue">Max = 4.62&#949; (Mean = 1.06&#949;)</span><br> <br>
 954                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 645&#949; (Mean = 132&#949;))
 955                 </p>
 956               </td>
 957 <td>
 958                 <p>
 959                   <span class="blue">Max = 176&#949; (Mean = 39.1&#949;)</span>
 960                 </p>
 961               </td>
 962 <td>
 963                 <p>
 964                   <span class="blue">Max = 9.67&#949; (Mean = 1.88&#949;)</span>
 965                 </p>
 966               </td>
 967 </tr>
 968 <tr>
 969 <td>
 970                 <p>
 971                   Bessel Iv: Random Data
 972                 </p>
 973               </td>
 974 <td>
 975                 <p>
 976                   <span class="blue">Max = 0.661&#949; (Mean = 0.0441&#949;)</span><br>
 977                   <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 6.18e+03&#949; (Mean = 1.55e+03&#949;)
 978                   <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Random_Data">And
 979                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
 980                   <span class="red">Max = 4.28e+08&#949; (Mean = 2.85e+07&#949;))</span>
 981                 </p>
 982               </td>
 983 <td>
 984                 <p>
 985                   <span class="blue">Max = 8.35&#949; (Mean = 1.62&#949;)</span><br> <br>
 986                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.05e+03&#949; (Mean = 224&#949;)
 987                   <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Random_Data">And
 988                   other failures.</a>)
 989                 </p>
 990               </td>
 991 <td>
 992                 <p>
 993                   <span class="blue">Max = 283&#949; (Mean = 88.4&#949;)</span>
 994                 </p>
 995               </td>
 996 <td>
 997                 <p>
 998                   <span class="blue">Max = 7.46&#949; (Mean = 1.71&#949;)</span>
 999                 </p>
1000               </td>
1001 </tr>
1002 <tr>
1003 <td>
1004                 <p>
1005                   Bessel Iv: Mathworld Data (large values)
1006                 </p>
1007               </td>
1008 <td>
1009                 <p>
1010                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
1011                   2.1:</em></span> Max = 37&#949; (Mean = 18&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Mathworld_Data_large_values_">And
1012                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
1013                   <span class="red">Max = 3.77e+168&#949; (Mean = 2.39e+168&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_Iv_Mathworld_Data_large_values_">And
1014                   other failures.</a>)</span>
1015                 </p>
1016               </td>
1017 <td>
1018                 <p>
1019                   <span class="blue">Max = 14.7&#949; (Mean = 6.66&#949;)</span><br> <br>
1020                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 118&#949; (Mean = 57.2&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Mathworld_Data_large_values_">And
1021                   other failures.</a>)
1022                 </p>
1023               </td>
1024 <td>
1025                 <p>
1026                   <span class="blue">Max = 14.7&#949; (Mean = 6.59&#949;)</span>
1027                 </p>
1028               </td>
1029 <td>
1030                 <p>
1031                   <span class="blue">Max = 3.67&#949; (Mean = 1.64&#949;)</span>
1032                 </p>
1033               </td>
1034 </tr>
1035 </tbody>
1036 </table></div>
1037 </div>
1038 <br class="table-break"><div class="table">
1039 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_i_integer_orders_"></a><p class="title"><b>Table&#160;22.11.&#160;Error rates for cyl_bessel_i (integer orders)</b></p>
1040 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i (integer orders)">
1041 <colgroup>
1042 <col>
1043 <col>
1044 <col>
1045 <col>
1046 <col>
1047 </colgroup>
1048 <thead><tr>
1049 <th>
1050               </th>
1051 <th>
1052                 <p>
1053                   GNU C++ version 7.1.0<br> linux<br> double
1054                 </p>
1055               </th>
1056 <th>
1057                 <p>
1058                   GNU C++ version 7.1.0<br> linux<br> long double
1059                 </p>
1060               </th>
1061 <th>
1062                 <p>
1063                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
1064                 </p>
1065               </th>
1066 <th>
1067                 <p>
1068                   Microsoft Visual C++ version 14.1<br> Win32<br> double
1069                 </p>
1070               </th>
1071 </tr></thead>
1072 <tbody>
1073 <tr>
1074 <td>
1075                 <p>
1076                   Bessel I0: Mathworld Data (Integer Version)
1077                 </p>
1078               </td>
1079 <td>
1080                 <p>
1081                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
1082                   2.1:</em></span> Max = 0.79&#949; (Mean = 0.482&#949;))<br> (<span class="emphasis"><em>Rmath
1083                   3.2.3:</em></span> Max = 1.52&#949; (Mean = 0.622&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_I0_Mathworld_Data_Integer_Version_">And
1084                   other failures.</a>)
1085                 </p>
1086               </td>
1087 <td>
1088                 <p>
1089                   <span class="blue">Max = 1.95&#949; (Mean = 0.738&#949;)</span><br> <br>
1090                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 8.49&#949; (Mean = 3.46&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_I0_Mathworld_Data_Integer_Version_">And
1091                   other failures.</a>)
1092                 </p>
1093               </td>
1094 <td>
1095                 <p>
1096                   <span class="blue">Max = 1.95&#949; (Mean = 0.661&#949;)</span>
1097                 </p>
1098               </td>
1099 <td>
1100                 <p>
1101                   <span class="blue">Max = 0.762&#949; (Mean = 0.329&#949;)</span>
1102                 </p>
1103               </td>
1104 </tr>
1105 <tr>
1106 <td>
1107                 <p>
1108                   Bessel I1: Mathworld Data (Integer Version)
1109                 </p>
1110               </td>
1111 <td>
1112                 <p>
1113                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
1114                   2.1:</em></span> Max = 0.82&#949; (Mean = 0.456&#949;))<br> (<span class="emphasis"><em>Rmath
1115                   3.2.3:</em></span> Max = 1.53&#949; (Mean = 0.483&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_I1_Mathworld_Data_Integer_Version_">And
1116                   other failures.</a>)
1117                 </p>
1118               </td>
1119 <td>
1120                 <p>
1121                   <span class="blue">Max = 0.64&#949; (Mean = 0.202&#949;)</span><br> <br>
1122                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 5&#949; (Mean = 2.15&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_I1_Mathworld_Data_Integer_Version_">And
1123                   other failures.</a>)
1124                 </p>
1125               </td>
1126 <td>
1127                 <p>
1128                   <span class="blue">Max = 0.64&#949; (Mean = 0.202&#949;)</span>
1129                 </p>
1130               </td>
1131 <td>
1132                 <p>
1133                   <span class="blue">Max = 0.767&#949; (Mean = 0.398&#949;)</span>
1134                 </p>
1135               </td>
1136 </tr>
1137 <tr>
1138 <td>
1139                 <p>
1140                   Bessel In: Mathworld Data (Integer Version)
1141                 </p>
1142               </td>
1143 <td>
1144                 <p>
1145                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
1146                   2.1:</em></span> Max = 5.15&#949; (Mean = 2.13&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__GSL_2_1_Bessel_In_Mathworld_Data_Integer_Version_">And
1147                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
1148                   Max = 1.73&#949; (Mean = 0.601&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_In_Mathworld_Data_Integer_Version_">And
1149                   other failures.</a>)
1150                 </p>
1151               </td>
1152 <td>
1153                 <p>
1154                   <span class="blue">Max = 1.8&#949; (Mean = 1.33&#949;)</span><br> <br>
1155                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 430&#949; (Mean = 163&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_In_Mathworld_Data_Integer_Version_">And
1156                   other failures.</a>)
1157                 </p>
1158               </td>
1159 <td>
1160                 <p>
1161                   <span class="blue">Max = 463&#949; (Mean = 140&#949;)</span>
1162                 </p>
1163               </td>
1164 <td>
1165                 <p>
1166                   <span class="blue">Max = 3.46&#949; (Mean = 1.32&#949;)</span>
1167                 </p>
1168               </td>
1169 </tr>
1170 </tbody>
1171 </table></div>
1172 </div>
1173 <br class="table-break"><div class="table">
1174 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_i_prime"></a><p class="title"><b>Table&#160;22.12.&#160;Error rates for cyl_bessel_i_prime</b></p>
1175 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i_prime">
1176 <colgroup>
1177 <col>
1178 <col>
1179 <col>
1180 <col>
1181 <col>
1182 </colgroup>
1183 <thead><tr>
1184 <th>
1185               </th>
1186 <th>
1187                 <p>
1188                   GNU C++ version 7.1.0<br> linux<br> double
1189                 </p>
1190               </th>
1191 <th>
1192                 <p>
1193                   GNU C++ version 7.1.0<br> linux<br> long double
1194                 </p>
1195               </th>
1196 <th>
1197                 <p>
1198                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
1199                 </p>
1200               </th>
1201 <th>
1202                 <p>
1203                   Microsoft Visual C++ version 14.1<br> Win32<br> double
1204                 </p>
1205               </th>
1206 </tr></thead>
1207 <tbody>
1208 <tr>
1209 <td>
1210                 <p>
1211                   Bessel I'0: Mathworld Data
1212                 </p>
1213               </td>
1214 <td>
1215                 <p>
1216                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
1217                 </p>
1218               </td>
1219 <td>
1220                 <p>
1221                   <span class="blue">Max = 0.82&#949; (Mean = 0.259&#949;)</span>
1222                 </p>
1223               </td>
1224 <td>
1225                 <p>
1226                   <span class="blue">Max = 0.82&#949; (Mean = 0.259&#949;)</span>
1227                 </p>
1228               </td>
1229 <td>
1230                 <p>
1231                   <span class="blue">Max = 0.82&#949; (Mean = 0.354&#949;)</span>
1232                 </p>
1233               </td>
1234 </tr>
1235 <tr>
1236 <td>
1237                 <p>
1238                   Bessel I'1: Mathworld Data
1239                 </p>
1240               </td>
1241 <td>
1242                 <p>
1243                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
1244                 </p>
1245               </td>
1246 <td>
1247                 <p>
1248                   <span class="blue">Max = 1.97&#949; (Mean = 0.757&#949;)</span>
1249                 </p>
1250               </td>
1251 <td>
1252                 <p>
1253                   <span class="blue">Max = 1.97&#949; (Mean = 0.757&#949;)</span>
1254                 </p>
1255               </td>
1256 <td>
1257                 <p>
1258                   <span class="blue">Max = 1.36&#949; (Mean = 0.782&#949;)</span>
1259                 </p>
1260               </td>
1261 </tr>
1262 <tr>
1263 <td>
1264                 <p>
1265                   Bessel I'n: Mathworld Data
1266                 </p>
1267               </td>
1268 <td>
1269                 <p>
1270                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
1271                 </p>
1272               </td>
1273 <td>
1274                 <p>
1275                   <span class="blue">Max = 2.31&#949; (Mean = 1.41&#949;)</span>
1276                 </p>
1277               </td>
1278 <td>
1279                 <p>
1280                   <span class="blue">Max = 701&#949; (Mean = 212&#949;)</span>
1281                 </p>
1282               </td>
1283 <td>
1284                 <p>
1285                   <span class="blue">Max = 3.61&#949; (Mean = 1.22&#949;)</span>
1286                 </p>
1287               </td>
1288 </tr>
1289 <tr>
1290 <td>
1291                 <p>
1292                   Bessel I'v: Mathworld Data
1293                 </p>
1294               </td>
1295 <td>
1296                 <p>
1297                   <span class="blue">Max = 1.62&#949; (Mean = 0.512&#949;)</span>
1298                 </p>
1299               </td>
1300 <td>
1301                 <p>
1302                   <span class="blue">Max = 2.89e+03&#949; (Mean = 914&#949;)</span>
1303                 </p>
1304               </td>
1305 <td>
1306                 <p>
1307                   <span class="blue">Max = 2.89e+03&#949; (Mean = 914&#949;)</span>
1308                 </p>
1309               </td>
1310 <td>
1311                 <p>
1312                   <span class="blue">Max = 3.76e+03&#949; (Mean = 1.19e+03&#949;)</span>
1313                 </p>
1314               </td>
1315 </tr>
1316 <tr>
1317 <td>
1318                 <p>
1319                   Bessel I'n: Random Data
1320                 </p>
1321               </td>
1322 <td>
1323                 <p>
1324                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
1325                 </p>
1326               </td>
1327 <td>
1328                 <p>
1329                   <span class="blue">Max = 3.95&#949; (Mean = 1.06&#949;)</span>
1330                 </p>
1331               </td>
1332 <td>
1333                 <p>
1334                   <span class="blue">Max = 195&#949; (Mean = 37.1&#949;)</span>
1335                 </p>
1336               </td>
1337 <td>
1338                 <p>
1339                   <span class="blue">Max = 9.85&#949; (Mean = 1.82&#949;)</span>
1340                 </p>
1341               </td>
1342 </tr>
1343 <tr>
1344 <td>
1345                 <p>
1346                   Bessel I'v: Random Data
1347                 </p>
1348               </td>
1349 <td>
1350                 <p>
1351                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
1352                 </p>
1353               </td>
1354 <td>
1355                 <p>
1356                   <span class="blue">Max = 14.1&#949; (Mean = 2.93&#949;)</span>
1357                 </p>
1358               </td>
1359 <td>
1360                 <p>
1361                   <span class="blue">Max = 336&#949; (Mean = 68.5&#949;)</span>
1362                 </p>
1363               </td>
1364 <td>
1365                 <p>
1366                   <span class="blue">Max = 14&#949; (Mean = 2.5&#949;)</span>
1367                 </p>
1368               </td>
1369 </tr>
1370 <tr>
1371 <td>
1372                 <p>
1373                   Bessel I'v: Mathworld Data (large values)
1374                 </p>
1375               </td>
1376 <td>
1377                 <p>
1378                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
1379                 </p>
1380               </td>
1381 <td>
1382                 <p>
1383                   <span class="blue">Max = 42.6&#949; (Mean = 20.2&#949;)</span>
1384                 </p>
1385               </td>
1386 <td>
1387                 <p>
1388                   <span class="blue">Max = 42.6&#949; (Mean = 20.2&#949;)</span>
1389                 </p>
1390               </td>
1391 <td>
1392                 <p>
1393                   <span class="blue">Max = 59.5&#949; (Mean = 26.6&#949;)</span>
1394                 </p>
1395               </td>
1396 </tr>
1397 </tbody>
1398 </table></div>
1399 </div>
1400 <br class="table-break"><div class="table">
1401 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_i_prime_integer_orders_"></a><p class="title"><b>Table&#160;22.13.&#160;Error rates for cyl_bessel_i_prime (integer orders)</b></p>
1402 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i_prime (integer orders)">
1403 <colgroup>
1404 <col>
1405 <col>
1406 <col>
1407 <col>
1408 <col>
1409 </colgroup>
1410 <thead><tr>
1411 <th>
1412               </th>
1413 <th>
1414                 <p>
1415                   GNU C++ version 7.1.0<br> linux<br> double
1416                 </p>
1417               </th>
1418 <th>
1419                 <p>
1420                   GNU C++ version 7.1.0<br> linux<br> long double
1421                 </p>
1422               </th>
1423 <th>
1424                 <p>
1425                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
1426                 </p>
1427               </th>
1428 <th>
1429                 <p>
1430                   Microsoft Visual C++ version 14.1<br> Win32<br> double
1431                 </p>
1432               </th>
1433 </tr></thead>
1434 <tbody>
1435 <tr>
1436 <td>
1437                 <p>
1438                   Bessel I'0: Mathworld Data (Integer Version)
1439                 </p>
1440               </td>
1441 <td>
1442                 <p>
1443                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
1444                 </p>
1445               </td>
1446 <td>
1447                 <p>
1448                   <span class="blue">Max = 0.82&#949; (Mean = 0.259&#949;)</span>
1449                 </p>
1450               </td>
1451 <td>
1452                 <p>
1453                   <span class="blue">Max = 0.82&#949; (Mean = 0.259&#949;)</span>
1454                 </p>
1455               </td>
1456 <td>
1457                 <p>
1458                   <span class="blue">Max = 0.82&#949; (Mean = 0.354&#949;)</span>
1459                 </p>
1460               </td>
1461 </tr>
1462 <tr>
1463 <td>
1464                 <p>
1465                   Bessel I'1: Mathworld Data (Integer Version)
1466                 </p>
1467               </td>
1468 <td>
1469                 <p>
1470                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
1471                 </p>
1472               </td>
1473 <td>
1474                 <p>
1475                   <span class="blue">Max = 1.97&#949; (Mean = 0.757&#949;)</span>
1476                 </p>
1477               </td>
1478 <td>
1479                 <p>
1480                   <span class="blue">Max = 1.97&#949; (Mean = 0.757&#949;)</span>
1481                 </p>
1482               </td>
1483 <td>
1484                 <p>
1485                   <span class="blue">Max = 1.36&#949; (Mean = 0.782&#949;)</span>
1486                 </p>
1487               </td>
1488 </tr>
1489 <tr>
1490 <td>
1491                 <p>
1492                   Bessel I'n: Mathworld Data (Integer Version)
1493                 </p>
1494               </td>
1495 <td>
1496                 <p>
1497                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
1498                 </p>
1499               </td>
1500 <td>
1501                 <p>
1502                   <span class="blue">Max = 2.31&#949; (Mean = 1.41&#949;)</span>
1503                 </p>
1504               </td>
1505 <td>
1506                 <p>
1507                   <span class="blue">Max = 701&#949; (Mean = 212&#949;)</span>
1508                 </p>
1509               </td>
1510 <td>
1511                 <p>
1512                   <span class="blue">Max = 3.61&#949; (Mean = 1.22&#949;)</span>
1513                 </p>
1514               </td>
1515 </tr>
1516 </tbody>
1517 </table></div>
1518 </div>
1519 <br class="table-break"><div class="table">
1520 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_j"></a><p class="title"><b>Table&#160;22.14.&#160;Error rates for cyl_bessel_j</b></p>
1521 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j">
1522 <colgroup>
1523 <col>
1524 <col>
1525 <col>
1526 <col>
1527 <col>
1528 </colgroup>
1529 <thead><tr>
1530 <th>
1531               </th>
1532 <th>
1533                 <p>
1534                   GNU C++ version 7.1.0<br> linux<br> long double
1535                 </p>
1536               </th>
1537 <th>
1538                 <p>
1539                   GNU C++ version 7.1.0<br> linux<br> double
1540                 </p>
1541               </th>
1542 <th>
1543                 <p>
1544                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
1545                 </p>
1546               </th>
1547 <th>
1548                 <p>
1549                   Microsoft Visual C++ version 14.1<br> Win32<br> double
1550                 </p>
1551               </th>
1552 </tr></thead>
1553 <tbody>
1554 <tr>
1555 <td>
1556                 <p>
1557                   Bessel J0: Mathworld Data
1558                 </p>
1559               </td>
1560 <td>
1561                 <p>
1562                   <span class="blue">Max = 6.55&#949; (Mean = 2.86&#949;)</span><br> <br>
1563                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 5.04&#949; (Mean = 1.78&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J0_Mathworld_Data">And
1564                   other failures.</a>)
1565                 </p>
1566               </td>
1567 <td>
1568                 <p>
1569                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
1570                   2.1:</em></span> Max = 0.629&#949; (Mean = 0.223&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J0_Mathworld_Data">And
1571                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
1572                   Max = 0.629&#949; (Mean = 0.223&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J0_Mathworld_Data">And
1573                   other failures.</a>)
1574                 </p>
1575               </td>
1576 <td>
1577                 <p>
1578                   <span class="blue">Max = 6.55&#949; (Mean = 2.86&#949;)</span>
1579                 </p>
1580               </td>
1581 <td>
1582                 <p>
1583                   <span class="blue">Max = 2.52&#949; (Mean = 1.2&#949;)</span>
1584                 </p>
1585               </td>
1586 </tr>
1587 <tr>
1588 <td>
1589                 <p>
1590                   Bessel J0: Mathworld Data (Tricky cases)
1591                 </p>
1592               </td>
1593 <td>
1594                 <p>
1595                   <span class="blue">Max = 1.64e+08&#949; (Mean = 6.69e+07&#949;)</span><br>
1596                   <br> (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 4.79e+08&#949; (Mean
1597                   = 1.96e+08&#949;))
1598                 </p>
1599               </td>
1600 <td>
1601                 <p>
1602                   <span class="blue">Max = 8e+04&#949; (Mean = 3.27e+04&#949;)</span><br>
1603                   <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 6.5e+07&#949; (Mean = 2.66e+07&#949;))<br>
1604                   (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.04e+07&#949; (Mean = 4.29e+06&#949;))
1605                 </p>
1606               </td>
1607 <td>
1608                 <p>
1609                   <span class="blue">Max = 1.64e+08&#949; (Mean = 6.69e+07&#949;)</span>
1610                 </p>
1611               </td>
1612 <td>
1613                 <p>
1614                   <span class="blue">Max = 1e+07&#949; (Mean = 4.09e+06&#949;)</span>
1615                 </p>
1616               </td>
1617 </tr>
1618 <tr>
1619 <td>
1620                 <p>
1621                   Bessel J1: Mathworld Data
1622                 </p>
1623               </td>
1624 <td>
1625                 <p>
1626                   <span class="blue">Max = 3.59&#949; (Mean = 1.33&#949;)</span><br> <br>
1627                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 6.1&#949; (Mean = 2.95&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J1_Mathworld_Data">And
1628                   other failures.</a>)
1629                 </p>
1630               </td>
1631 <td>
1632                 <p>
1633                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
1634                   2.1:</em></span> Max = 6.62&#949; (Mean = 2.35&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J1_Mathworld_Data">And
1635                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
1636                   Max = 0.946&#949; (Mean = 0.39&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J1_Mathworld_Data">And
1637                   other failures.</a>)
1638                 </p>
1639               </td>
1640 <td>
1641                 <p>
1642                   <span class="blue">Max = 1.44&#949; (Mean = 0.637&#949;)</span>
1643                 </p>
1644               </td>
1645 <td>
1646                 <p>
1647                   <span class="blue">Max = 1.73&#949; (Mean = 0.976&#949;)</span>
1648                 </p>
1649               </td>
1650 </tr>
1651 <tr>
1652 <td>
1653                 <p>
1654                   Bessel J1: Mathworld Data (tricky cases)
1655                 </p>
1656               </td>
1657 <td>
1658                 <p>
1659                   <span class="blue">Max = 2.18e+05&#949; (Mean = 9.76e+04&#949;)</span><br>
1660                   <br> (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 2.15e+06&#949; (Mean
1661                   = 1.58e+06&#949;))
1662                 </p>
1663               </td>
1664 <td>
1665                 <p>
1666                   <span class="blue">Max = 106&#949; (Mean = 47.5&#949;)</span><br> <br>
1667                   (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.75e+05&#949; (Mean = 5.32e+05&#949;))<br>
1668                   (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.93e+06&#949; (Mean = 1.7e+06&#949;))
1669                 </p>
1670               </td>
1671 <td>
1672                 <p>
1673                   <span class="blue">Max = 2.18e+05&#949; (Mean = 9.76e+04&#949;)</span>
1674                 </p>
1675               </td>
1676 <td>
1677                 <p>
1678                   <span class="blue">Max = 3.23e+04&#949; (Mean = 1.45e+04&#949;)</span>
1679                 </p>
1680               </td>
1681 </tr>
1682 <tr>
1683 <td>
1684                 <p>
1685                   Bessel JN: Mathworld Data
1686                 </p>
1687               </td>
1688 <td>
1689                 <p>
1690                   <span class="blue">Max = 6.85&#949; (Mean = 3.35&#949;)</span><br> <br>
1691                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = 2.13e+19&#949; (Mean
1692                   = 5.16e+18&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_JN_Mathworld_Data">And
1693                   other failures.</a>)</span>
1694                 </p>
1695               </td>
1696 <td>
1697                 <p>
1698                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
1699                   2.1:</em></span> Max = 6.9e+05&#949; (Mean = 2.15e+05&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_JN_Mathworld_Data">And
1700                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
1701                   <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_JN_Mathworld_Data">And
1702                   other failures.</a>)</span>
1703                 </p>
1704               </td>
1705 <td>
1706                 <p>
1707                   <span class="blue">Max = 463&#949; (Mean = 112&#949;)</span>
1708                 </p>
1709               </td>
1710 <td>
1711                 <p>
1712                   <span class="blue">Max = 14.7&#949; (Mean = 5.4&#949;)</span>
1713                 </p>
1714               </td>
1715 </tr>
1716 <tr>
1717 <td>
1718                 <p>
1719                   Bessel J: Mathworld Data
1720                 </p>
1721               </td>
1722 <td>
1723                 <p>
1724                   <span class="blue">Max = 14.7&#949; (Mean = 4.11&#949;)</span><br> <br>
1725                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 3.49e+05&#949; (Mean = 8.09e+04&#949;)
1726                   <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J_Mathworld_Data">And
1727                   other failures.</a>)
1728                 </p>
1729               </td>
1730 <td>
1731                 <p>
1732                   <span class="blue">Max = 10&#949; (Mean = 2.24&#949;)</span><br> <br>
1733                   (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.39e+05&#949; (Mean = 5.37e+04&#949;)
1734                   <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Mathworld_Data">And
1735                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
1736                   <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J_Mathworld_Data">And
1737                   other failures.</a>)</span>
1738                 </p>
1739               </td>
1740 <td>
1741                 <p>
1742                   <span class="blue">Max = 14.7&#949; (Mean = 4.22&#949;)</span>
1743                 </p>
1744               </td>
1745 <td>
1746                 <p>
1747                   <span class="blue">Max = 14.9&#949; (Mean = 3.89&#949;)</span>
1748                 </p>
1749               </td>
1750 </tr>
1751 <tr>
1752 <td>
1753                 <p>
1754                   Bessel J: Mathworld Data (large values)
1755                 </p>
1756               </td>
1757 <td>
1758                 <p>
1759                   <span class="blue">Max = 607&#949; (Mean = 305&#949;)</span><br> <br>
1760                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 34.9&#949; (Mean = 17.4&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J_Mathworld_Data_large_values_">And
1761                   other failures.</a>)
1762                 </p>
1763               </td>
1764 <td>
1765                 <p>
1766                   <span class="blue">Max = 0.536&#949; (Mean = 0.268&#949;)</span><br> <br>
1767                   (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 4.91e+03&#949; (Mean = 2.46e+03&#949;)
1768                   <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Mathworld_Data_large_values_">And
1769                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
1770                   Max = 5.9&#949; (Mean = 3.76&#949;))
1771                 </p>
1772               </td>
1773 <td>
1774                 <p>
1775                   <span class="blue">Max = 607&#949; (Mean = 305&#949;)</span>
1776                 </p>
1777               </td>
1778 <td>
1779                 <p>
1780                   <span class="blue">Max = 9.31&#949; (Mean = 5.52&#949;)</span>
1781                 </p>
1782               </td>
1783 </tr>
1784 <tr>
1785 <td>
1786                 <p>
1787                   Bessel JN: Random Data
1788                 </p>
1789               </td>
1790 <td>
1791                 <p>
1792                   <span class="blue">Max = 50.8&#949; (Mean = 3.69&#949;)</span><br> <br>
1793                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.12e+03&#949; (Mean = 88.7&#949;))
1794                 </p>
1795               </td>
1796 <td>
1797                 <p>
1798                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
1799                   2.1:</em></span> Max = 75.7&#949; (Mean = 5.36&#949;))<br> (<span class="emphasis"><em>Rmath
1800                   3.2.3:</em></span> Max = 3.93&#949; (Mean = 1.22&#949;))
1801                 </p>
1802               </td>
1803 <td>
1804                 <p>
1805                   <span class="blue">Max = 99.6&#949; (Mean = 22&#949;)</span>
1806                 </p>
1807               </td>
1808 <td>
1809                 <p>
1810                   <span class="blue">Max = 17.5&#949; (Mean = 1.46&#949;)</span>
1811                 </p>
1812               </td>
1813 </tr>
1814 <tr>
1815 <td>
1816                 <p>
1817                   Bessel J: Random Data
1818                 </p>
1819               </td>
1820 <td>
1821                 <p>
1822                   <span class="blue">Max = 11.4&#949; (Mean = 1.68&#949;)</span><br> <br>
1823                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 501&#949; (Mean = 52.3&#949;))
1824                 </p>
1825               </td>
1826 <td>
1827                 <p>
1828                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
1829                   2.1:</em></span> Max = 15.5&#949; (Mean = 3.33&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Random_Data">And
1830                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
1831                   Max = 6.74&#949; (Mean = 1.3&#949;))
1832                 </p>
1833               </td>
1834 <td>
1835                 <p>
1836                   <span class="blue">Max = 260&#949; (Mean = 34&#949;)</span>
1837                 </p>
1838               </td>
1839 <td>
1840                 <p>
1841                   <span class="blue">Max = 9.24&#949; (Mean = 1.17&#949;)</span>
1842                 </p>
1843               </td>
1844 </tr>
1845 <tr>
1846 <td>
1847                 <p>
1848                   Bessel J: Random Data (Tricky large values)
1849                 </p>
1850               </td>
1851 <td>
1852                 <p>
1853                   <span class="blue">Max = 785&#949; (Mean = 94.2&#949;)</span><br> <br>
1854                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = 5.01e+17&#949; (Mean
1855                   = 6.23e+16&#949;))</span>
1856                 </p>
1857               </td>
1858 <td>
1859                 <p>
1860                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
1861                   2.1:</em></span> Max = 2.48e+05&#949; (Mean = 5.11e+04&#949;))<br> (<span class="emphasis"><em>Rmath
1862                   3.2.3:</em></span> Max = 71.6&#949; (Mean = 11.7&#949;))
1863                 </p>
1864               </td>
1865 <td>
1866                 <p>
1867                   <span class="blue">Max = 785&#949; (Mean = 97.4&#949;)</span>
1868                 </p>
1869               </td>
1870 <td>
1871                 <p>
1872                   <span class="blue">Max = 59.2&#949; (Mean = 8.67&#949;)</span>
1873                 </p>
1874               </td>
1875 </tr>
1876 </tbody>
1877 </table></div>
1878 </div>
1879 <br class="table-break"><div class="table">
1880 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_j_integer_orders_"></a><p class="title"><b>Table&#160;22.15.&#160;Error rates for cyl_bessel_j (integer orders)</b></p>
1881 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j (integer orders)">
1882 <colgroup>
1883 <col>
1884 <col>
1885 <col>
1886 <col>
1887 <col>
1888 </colgroup>
1889 <thead><tr>
1890 <th>
1891               </th>
1892 <th>
1893                 <p>
1894                   GNU C++ version 7.1.0<br> linux<br> long double
1895                 </p>
1896               </th>
1897 <th>
1898                 <p>
1899                   GNU C++ version 7.1.0<br> linux<br> double
1900                 </p>
1901               </th>
1902 <th>
1903                 <p>
1904                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
1905                 </p>
1906               </th>
1907 <th>
1908                 <p>
1909                   Microsoft Visual C++ version 14.1<br> Win32<br> double
1910                 </p>
1911               </th>
1912 </tr></thead>
1913 <tbody>
1914 <tr>
1915 <td>
1916                 <p>
1917                   Bessel J0: Mathworld Data (Integer Version)
1918                 </p>
1919               </td>
1920 <td>
1921                 <p>
1922                   <span class="blue">Max = 6.55&#949; (Mean = 2.86&#949;)</span><br> <br>
1923                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 5.04&#949; (Mean = 1.78&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_J0_Mathworld_Data_Integer_Version_">And
1924                   other failures.</a>)
1925                 </p>
1926               </td>
1927 <td>
1928                 <p>
1929                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
1930                   2.1:</em></span> Max = 1.12&#949; (Mean = 0.488&#949;))<br> (<span class="emphasis"><em>Rmath
1931                   3.2.3:</em></span> Max = 0.629&#949; (Mean = 0.223&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_J0_Mathworld_Data_Integer_Version_">And
1932                   other failures.</a>)
1933                 </p>
1934               </td>
1935 <td>
1936                 <p>
1937                   <span class="blue">Max = 6.55&#949; (Mean = 2.86&#949;)</span>
1938                 </p>
1939               </td>
1940 <td>
1941                 <p>
1942                   <span class="blue">Max = 2.52&#949; (Mean = 1.2&#949;)</span><br> <br>
1943                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.89&#949; (Mean = 0.988&#949;))
1944                 </p>
1945               </td>
1946 </tr>
1947 <tr>
1948 <td>
1949                 <p>
1950                   Bessel J0: Mathworld Data (Tricky cases) (Integer Version)
1951                 </p>
1952               </td>
1953 <td>
1954                 <p>
1955                   <span class="blue">Max = 1.64e+08&#949; (Mean = 6.69e+07&#949;)</span><br>
1956                   <br> (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 4.79e+08&#949; (Mean
1957                   = 1.96e+08&#949;))
1958                 </p>
1959               </td>
1960 <td>
1961                 <p>
1962                   <span class="blue">Max = 8e+04&#949; (Mean = 3.27e+04&#949;)</span><br>
1963                   <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1e+07&#949; (Mean = 4.11e+06&#949;))<br>
1964                   (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.04e+07&#949; (Mean = 4.29e+06&#949;))
1965                 </p>
1966               </td>
1967 <td>
1968                 <p>
1969                   <span class="blue">Max = 1.64e+08&#949; (Mean = 6.69e+07&#949;)</span>
1970                 </p>
1971               </td>
1972 <td>
1973                 <p>
1974                   <span class="blue">Max = 1e+07&#949; (Mean = 4.09e+06&#949;)</span><br>
1975                   <br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> <span class="red">Max
1976                   = 2.54e+08&#949; (Mean = 1.04e+08&#949;))</span>
1977                 </p>
1978               </td>
1979 </tr>
1980 <tr>
1981 <td>
1982                 <p>
1983                   Bessel J1: Mathworld Data (Integer Version)
1984                 </p>
1985               </td>
1986 <td>
1987                 <p>
1988                   <span class="blue">Max = 3.59&#949; (Mean = 1.33&#949;)</span><br> <br>
1989                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 6.1&#949; (Mean = 2.95&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_J1_Mathworld_Data_Integer_Version_">And
1990                   other failures.</a>)
1991                 </p>
1992               </td>
1993 <td>
1994                 <p>
1995                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
1996                   2.1:</em></span> Max = 1.89&#949; (Mean = 0.721&#949;))<br> (<span class="emphasis"><em>Rmath
1997                   3.2.3:</em></span> Max = 0.946&#949; (Mean = 0.39&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_J1_Mathworld_Data_Integer_Version_">And
1998                   other failures.</a>)
1999                 </p>
2000               </td>
2001 <td>
2002                 <p>
2003                   <span class="blue">Max = 1.44&#949; (Mean = 0.637&#949;)</span>
2004                 </p>
2005               </td>
2006 <td>
2007                 <p>
2008                   <span class="blue">Max = 1.73&#949; (Mean = 0.976&#949;)</span><br> <br>
2009                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 11.4&#949; (Mean = 4.15&#949;))
2010                 </p>
2011               </td>
2012 </tr>
2013 <tr>
2014 <td>
2015                 <p>
2016                   Bessel J1: Mathworld Data (tricky cases) (Integer Version)
2017                 </p>
2018               </td>
2019 <td>
2020                 <p>
2021                   <span class="blue">Max = 2.18e+05&#949; (Mean = 9.76e+04&#949;)</span><br>
2022                   <br> (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 2.15e+06&#949; (Mean
2023                   = 1.58e+06&#949;))
2024                 </p>
2025               </td>
2026 <td>
2027                 <p>
2028                   <span class="blue">Max = 106&#949; (Mean = 47.5&#949;)</span><br> <br>
2029                   (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.26e+06&#949; (Mean = 6.28e+05&#949;))<br>
2030                   (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.93e+06&#949; (Mean = 1.7e+06&#949;))
2031                 </p>
2032               </td>
2033 <td>
2034                 <p>
2035                   <span class="blue">Max = 2.18e+05&#949; (Mean = 9.76e+04&#949;)</span>
2036                 </p>
2037               </td>
2038 <td>
2039                 <p>
2040                   <span class="blue">Max = 3.23e+04&#949; (Mean = 1.45e+04&#949;)</span><br>
2041                   <br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.44e+07&#949; (Mean
2042                   = 6.5e+06&#949;))
2043                 </p>
2044               </td>
2045 </tr>
2046 <tr>
2047 <td>
2048                 <p>
2049                   Bessel JN: Mathworld Data (Integer Version)
2050                 </p>
2051               </td>
2052 <td>
2053                 <p>
2054                   <span class="blue">Max = 6.85&#949; (Mean = 3.35&#949;)</span><br> <br>
2055                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = 2.13e+19&#949; (Mean
2056                   = 5.16e+18&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_JN_Mathworld_Data_Integer_Version_">And
2057                   other failures.</a>)</span>
2058                 </p>
2059               </td>
2060 <td>
2061                 <p>
2062                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
2063                   2.1:</em></span> Max = 6.9e+05&#949; (Mean = 2.53e+05&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__GSL_2_1_Bessel_JN_Mathworld_Data_Integer_Version_">And
2064                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
2065                   <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_JN_Mathworld_Data_Integer_Version_">And
2066                   other failures.</a>)</span>
2067                 </p>
2068               </td>
2069 <td>
2070                 <p>
2071                   <span class="blue">Max = 463&#949; (Mean = 112&#949;)</span>
2072                 </p>
2073               </td>
2074 <td>
2075                 <p>
2076                   <span class="blue">Max = 14.7&#949; (Mean = 5.4&#949;)</span><br> <br>
2077                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> <span class="red">Max =
2078                   +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_Microsoft_Visual_C_version_14_1_Win32_double_cyl_bessel_j_integer_orders___math_h__Bessel_JN_Mathworld_Data_Integer_Version_">And
2079                   other failures.</a>)</span>
2080                 </p>
2081               </td>
2082 </tr>
2083 </tbody>
2084 </table></div>
2085 </div>
2086 <br class="table-break"><div class="table">
2087 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_j_prime"></a><p class="title"><b>Table&#160;22.16.&#160;Error rates for cyl_bessel_j_prime</b></p>
2088 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j_prime">
2089 <colgroup>
2090 <col>
2091 <col>
2092 <col>
2093 <col>
2094 <col>
2095 </colgroup>
2096 <thead><tr>
2097 <th>
2098               </th>
2099 <th>
2100                 <p>
2101                   GNU C++ version 7.1.0<br> linux<br> double
2102                 </p>
2103               </th>
2104 <th>
2105                 <p>
2106                   GNU C++ version 7.1.0<br> linux<br> long double
2107                 </p>
2108               </th>
2109 <th>
2110                 <p>
2111                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
2112                 </p>
2113               </th>
2114 <th>
2115                 <p>
2116                   Microsoft Visual C++ version 14.1<br> Win32<br> double
2117                 </p>
2118               </th>
2119 </tr></thead>
2120 <tbody>
2121 <tr>
2122 <td>
2123                 <p>
2124                   Bessel J0': Mathworld Data
2125                 </p>
2126               </td>
2127 <td>
2128                 <p>
2129                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
2130                 </p>
2131               </td>
2132 <td>
2133                 <p>
2134                   <span class="blue">Max = 18.9&#949; (Mean = 6.82&#949;)</span>
2135                 </p>
2136               </td>
2137 <td>
2138                 <p>
2139                   <span class="blue">Max = 18.9&#949; (Mean = 6.72&#949;)</span>
2140                 </p>
2141               </td>
2142 <td>
2143                 <p>
2144                   <span class="blue">Max = 6.62&#949; (Mean = 2.55&#949;)</span>
2145                 </p>
2146               </td>
2147 </tr>
2148 <tr>
2149 <td>
2150                 <p>
2151                   Bessel J0': Mathworld Data (Tricky cases)
2152                 </p>
2153               </td>
2154 <td>
2155                 <p>
2156                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
2157                 </p>
2158               </td>
2159 <td>
2160                 <p>
2161                   <span class="blue">Max = 7.44&#949; (Mean = 3.34&#949;)</span>
2162                 </p>
2163               </td>
2164 <td>
2165                 <p>
2166                   <span class="blue">Max = 7.44&#949; (Mean = 3.31&#949;)</span>
2167                 </p>
2168               </td>
2169 <td>
2170                 <p>
2171                   <span class="blue">Max = 3.67&#949; (Mean = 1.74&#949;)</span>
2172                 </p>
2173               </td>
2174 </tr>
2175 <tr>
2176 <td>
2177                 <p>
2178                   Bessel J1': Mathworld Data
2179                 </p>
2180               </td>
2181 <td>
2182                 <p>
2183                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
2184                 </p>
2185               </td>
2186 <td>
2187                 <p>
2188                   <span class="blue">Max = 7.9&#949; (Mean = 3.37&#949;)</span>
2189                 </p>
2190               </td>
2191 <td>
2192                 <p>
2193                   <span class="blue">Max = 7.9&#949; (Mean = 3.37&#949;)</span>
2194                 </p>
2195               </td>
2196 <td>
2197                 <p>
2198                   <span class="blue">Max = 0.999&#949; (Mean = 0.627&#949;)</span>
2199                 </p>
2200               </td>
2201 </tr>
2202 <tr>
2203 <td>
2204                 <p>
2205                   Bessel J1': Mathworld Data (tricky cases)
2206                 </p>
2207               </td>
2208 <td>
2209                 <p>
2210                   <span class="blue">Max = 287&#949; (Mean = 129&#949;)</span>
2211                 </p>
2212               </td>
2213 <td>
2214                 <p>
2215                   <span class="blue">Max = 5.88e+05&#949; (Mean = 2.63e+05&#949;)</span>
2216                 </p>
2217               </td>
2218 <td>
2219                 <p>
2220                   <span class="blue">Max = 5.88e+05&#949; (Mean = 2.63e+05&#949;)</span>
2221                 </p>
2222               </td>
2223 <td>
2224                 <p>
2225                   <span class="blue">Max = 288&#949; (Mean = 129&#949;)</span>
2226                 </p>
2227               </td>
2228 </tr>
2229 <tr>
2230 <td>
2231                 <p>
2232                   Bessel JN': Mathworld Data
2233                 </p>
2234               </td>
2235 <td>
2236                 <p>
2237                   <span class="blue">Max = 0.527&#949; (Mean = 0.128&#949;)</span>
2238                 </p>
2239               </td>
2240 <td>
2241                 <p>
2242                   <span class="blue">Max = 1.29e+03&#949; (Mean = 312&#949;)</span>
2243                 </p>
2244               </td>
2245 <td>
2246                 <p>
2247                   <span class="blue">Max = 1.29e+03&#949; (Mean = 355&#949;)</span>
2248                 </p>
2249               </td>
2250 <td>
2251                 <p>
2252                   <span class="blue">Max = 14&#949; (Mean = 6.13&#949;)</span>
2253                 </p>
2254               </td>
2255 </tr>
2256 <tr>
2257 <td>
2258                 <p>
2259                   Bessel J': Mathworld Data
2260                 </p>
2261               </td>
2262 <td>
2263                 <p>
2264                   <span class="blue">Max = 21.5&#949; (Mean = 4.7&#949;)</span>
2265                 </p>
2266               </td>
2267 <td>
2268                 <p>
2269                   <span class="blue">Max = 42.5&#949; (Mean = 9.31&#949;)</span>
2270                 </p>
2271               </td>
2272 <td>
2273                 <p>
2274                   <span class="blue">Max = 42.5&#949; (Mean = 9.32&#949;)</span>
2275                 </p>
2276               </td>
2277 <td>
2278                 <p>
2279                   <span class="blue">Max = 23.7&#949; (Mean = 8&#949;)</span>
2280                 </p>
2281               </td>
2282 </tr>
2283 <tr>
2284 <td>
2285                 <p>
2286                   Bessel J': Mathworld Data (large values)
2287                 </p>
2288               </td>
2289 <td>
2290                 <p>
2291                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
2292                 </p>
2293               </td>
2294 <td>
2295                 <p>
2296                   <span class="blue">Max = 989&#949; (Mean = 495&#949;)</span>
2297                 </p>
2298               </td>
2299 <td>
2300                 <p>
2301                   <span class="blue">Max = 989&#949; (Mean = 495&#949;)</span>
2302                 </p>
2303               </td>
2304 <td>
2305                 <p>
2306                   <span class="blue">Max = 2.9&#949; (Mean = 1.61&#949;)</span>
2307                 </p>
2308               </td>
2309 </tr>
2310 <tr>
2311 <td>
2312                 <p>
2313                   Bessel JN': Random Data
2314                 </p>
2315               </td>
2316 <td>
2317                 <p>
2318                   <span class="blue">Max = 0.593&#949; (Mean = 0.0396&#949;)</span>
2319                 </p>
2320               </td>
2321 <td>
2322                 <p>
2323                   <span class="blue">Max = 11.3&#949; (Mean = 1.85&#949;)</span>
2324                 </p>
2325               </td>
2326 <td>
2327                 <p>
2328                   <span class="blue">Max = 79.4&#949; (Mean = 16.2&#949;)</span>
2329                 </p>
2330               </td>
2331 <td>
2332                 <p>
2333                   <span class="blue">Max = 6.34&#949; (Mean = 0.999&#949;)</span>
2334                 </p>
2335               </td>
2336 </tr>
2337 <tr>
2338 <td>
2339                 <p>
2340                   Bessel J': Random Data
2341                 </p>
2342               </td>
2343 <td>
2344                 <p>
2345                   <span class="blue">Max = 0.885&#949; (Mean = 0.033&#949;)</span>
2346                 </p>
2347               </td>
2348 <td>
2349                 <p>
2350                   <span class="blue">Max = 139&#949; (Mean = 6.47&#949;)</span>
2351                 </p>
2352               </td>
2353 <td>
2354                 <p>
2355                   <span class="blue">Max = 279&#949; (Mean = 27.2&#949;)</span>
2356                 </p>
2357               </td>
2358 <td>
2359                 <p>
2360                   <span class="blue">Max = 176&#949; (Mean = 9.75&#949;)</span>
2361                 </p>
2362               </td>
2363 </tr>
2364 <tr>
2365 <td>
2366                 <p>
2367                   Bessel J': Random Data (Tricky large values)
2368                 </p>
2369               </td>
2370 <td>
2371                 <p>
2372                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
2373                 </p>
2374               </td>
2375 <td>
2376                 <p>
2377                   <span class="blue">Max = 474&#949; (Mean = 62.2&#949;)</span>
2378                 </p>
2379               </td>
2380 <td>
2381                 <p>
2382                   <span class="blue">Max = 474&#949; (Mean = 64.5&#949;)</span>
2383                 </p>
2384               </td>
2385 <td>
2386                 <p>
2387                   <span class="blue">Max = 379&#949; (Mean = 45.4&#949;)</span>
2388                 </p>
2389               </td>
2390 </tr>
2391 </tbody>
2392 </table></div>
2393 </div>
2394 <br class="table-break"><div class="table">
2395 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_j_prime_integer_orders_"></a><p class="title"><b>Table&#160;22.17.&#160;Error rates for cyl_bessel_j_prime (integer orders)</b></p>
2396 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j_prime (integer orders)">
2397 <colgroup>
2398 <col>
2399 <col>
2400 <col>
2401 <col>
2402 <col>
2403 </colgroup>
2404 <thead><tr>
2405 <th>
2406               </th>
2407 <th>
2408                 <p>
2409                   GNU C++ version 7.1.0<br> linux<br> double
2410                 </p>
2411               </th>
2412 <th>
2413                 <p>
2414                   GNU C++ version 7.1.0<br> linux<br> long double
2415                 </p>
2416               </th>
2417 <th>
2418                 <p>
2419                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
2420                 </p>
2421               </th>
2422 <th>
2423                 <p>
2424                   Microsoft Visual C++ version 14.1<br> Win32<br> double
2425                 </p>
2426               </th>
2427 </tr></thead>
2428 <tbody>
2429 <tr>
2430 <td>
2431                 <p>
2432                   Bessel J0': Mathworld Data (Integer Version)
2433                 </p>
2434               </td>
2435 <td>
2436                 <p>
2437                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
2438                 </p>
2439               </td>
2440 <td>
2441                 <p>
2442                   <span class="blue">Max = 18.9&#949; (Mean = 6.82&#949;)</span>
2443                 </p>
2444               </td>
2445 <td>
2446                 <p>
2447                   <span class="blue">Max = 18.9&#949; (Mean = 6.72&#949;)</span>
2448                 </p>
2449               </td>
2450 <td>
2451                 <p>
2452                   <span class="blue">Max = 6.62&#949; (Mean = 2.55&#949;)</span>
2453                 </p>
2454               </td>
2455 </tr>
2456 <tr>
2457 <td>
2458                 <p>
2459                   Bessel J0': Mathworld Data (Tricky cases) (Integer Version)
2460                 </p>
2461               </td>
2462 <td>
2463                 <p>
2464                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
2465                 </p>
2466               </td>
2467 <td>
2468                 <p>
2469                   <span class="blue">Max = 7.44&#949; (Mean = 3.34&#949;)</span>
2470                 </p>
2471               </td>
2472 <td>
2473                 <p>
2474                   <span class="blue">Max = 7.44&#949; (Mean = 3.31&#949;)</span>
2475                 </p>
2476               </td>
2477 <td>
2478                 <p>
2479                   <span class="blue">Max = 3.67&#949; (Mean = 1.74&#949;)</span>
2480                 </p>
2481               </td>
2482 </tr>
2483 <tr>
2484 <td>
2485                 <p>
2486                   Bessel J1': Mathworld Data (Integer Version)
2487                 </p>
2488               </td>
2489 <td>
2490                 <p>
2491                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
2492                 </p>
2493               </td>
2494 <td>
2495                 <p>
2496                   <span class="blue">Max = 7.9&#949; (Mean = 3.37&#949;)</span>
2497                 </p>
2498               </td>
2499 <td>
2500                 <p>
2501                   <span class="blue">Max = 7.9&#949; (Mean = 3.37&#949;)</span>
2502                 </p>
2503               </td>
2504 <td>
2505                 <p>
2506                   <span class="blue">Max = 0.999&#949; (Mean = 0.627&#949;)</span>
2507                 </p>
2508               </td>
2509 </tr>
2510 <tr>
2511 <td>
2512                 <p>
2513                   Bessel J1': Mathworld Data (tricky cases) (Integer Version)
2514                 </p>
2515               </td>
2516 <td>
2517                 <p>
2518                   <span class="blue">Max = 287&#949; (Mean = 129&#949;)</span>
2519                 </p>
2520               </td>
2521 <td>
2522                 <p>
2523                   <span class="blue">Max = 5.88e+05&#949; (Mean = 2.63e+05&#949;)</span>
2524                 </p>
2525               </td>
2526 <td>
2527                 <p>
2528                   <span class="blue">Max = 5.88e+05&#949; (Mean = 2.63e+05&#949;)</span>
2529                 </p>
2530               </td>
2531 <td>
2532                 <p>
2533                   <span class="blue">Max = 288&#949; (Mean = 129&#949;)</span>
2534                 </p>
2535               </td>
2536 </tr>
2537 <tr>
2538 <td>
2539                 <p>
2540                   Bessel JN': Mathworld Data (Integer Version)
2541                 </p>
2542               </td>
2543 <td>
2544                 <p>
2545                   <span class="blue">Max = 0.527&#949; (Mean = 0.128&#949;)</span>
2546                 </p>
2547               </td>
2548 <td>
2549                 <p>
2550                   <span class="blue">Max = 1.29e+03&#949; (Mean = 312&#949;)</span>
2551                 </p>
2552               </td>
2553 <td>
2554                 <p>
2555                   <span class="blue">Max = 1.29e+03&#949; (Mean = 355&#949;)</span>
2556                 </p>
2557               </td>
2558 <td>
2559                 <p>
2560                   <span class="blue">Max = 14&#949; (Mean = 6.13&#949;)</span>
2561                 </p>
2562               </td>
2563 </tr>
2564 </tbody>
2565 </table></div>
2566 </div>
2567 <br class="table-break"><div class="table">
2568 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_k"></a><p class="title"><b>Table&#160;22.18.&#160;Error rates for cyl_bessel_k</b></p>
2569 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k">
2570 <colgroup>
2571 <col>
2572 <col>
2573 <col>
2574 <col>
2575 <col>
2576 </colgroup>
2577 <thead><tr>
2578 <th>
2579               </th>
2580 <th>
2581                 <p>
2582                   GNU C++ version 7.1.0<br> linux<br> long double
2583                 </p>
2584               </th>
2585 <th>
2586                 <p>
2587                   GNU C++ version 7.1.0<br> linux<br> double
2588                 </p>
2589               </th>
2590 <th>
2591                 <p>
2592                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
2593                 </p>
2594               </th>
2595 <th>
2596                 <p>
2597                   Microsoft Visual C++ version 14.1<br> Win32<br> double
2598                 </p>
2599               </th>
2600 </tr></thead>
2601 <tbody>
2602 <tr>
2603 <td>
2604                 <p>
2605                   Bessel K0: Mathworld Data
2606                 </p>
2607               </td>
2608 <td>
2609                 <p>
2610                   <span class="blue">Max = 0.833&#949; (Mean = 0.436&#949;)</span><br> <br>
2611                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 9.33&#949; (Mean = 3.25&#949;))
2612                 </p>
2613               </td>
2614 <td>
2615                 <p>
2616                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
2617                   2.1:</em></span> Max = 6.04&#949; (Mean = 2.16&#949;))<br> (<span class="emphasis"><em>Rmath
2618                   3.2.3:</em></span> Max = 0.833&#949; (Mean = 0.601&#949;))
2619                 </p>
2620               </td>
2621 <td>
2622                 <p>
2623                   <span class="blue">Max = 0.833&#949; (Mean = 0.436&#949;)</span>
2624                 </p>
2625               </td>
2626 <td>
2627                 <p>
2628                   <span class="blue">Max = 0.833&#949; (Mean = 0.552&#949;)</span>
2629                 </p>
2630               </td>
2631 </tr>
2632 <tr>
2633 <td>
2634                 <p>
2635                   Bessel K1: Mathworld Data
2636                 </p>
2637               </td>
2638 <td>
2639                 <p>
2640                   <span class="blue">Max = 0.786&#949; (Mean = 0.329&#949;)</span><br> <br>
2641                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 8.94&#949; (Mean = 3.19&#949;))
2642                 </p>
2643               </td>
2644 <td>
2645                 <p>
2646                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
2647                   2.1:</em></span> Max = 6.26&#949; (Mean = 2.21&#949;))<br> (<span class="emphasis"><em>Rmath
2648                   3.2.3:</em></span> Max = 0.894&#949; (Mean = 0.516&#949;))
2649                 </p>
2650               </td>
2651 <td>
2652                 <p>
2653                   <span class="blue">Max = 0.786&#949; (Mean = 0.329&#949;)</span>
2654                 </p>
2655               </td>
2656 <td>
2657                 <p>
2658                   <span class="blue">Max = 0.786&#949; (Mean = 0.39&#949;)</span>
2659                 </p>
2660               </td>
2661 </tr>
2662 <tr>
2663 <td>
2664                 <p>
2665                   Bessel Kn: Mathworld Data
2666                 </p>
2667               </td>
2668 <td>
2669                 <p>
2670                   <span class="blue">Max = 2.6&#949; (Mean = 1.21&#949;)</span><br> <br>
2671                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 12.9&#949; (Mean = 4.91&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kn_Mathworld_Data">And
2672                   other failures.</a>)
2673                 </p>
2674               </td>
2675 <td>
2676                 <p>
2677                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
2678                   2.1:</em></span> Max = 3.36&#949; (Mean = 1.43&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kn_Mathworld_Data">And
2679                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
2680                   Max = 8.48&#949; (Mean = 2.98&#949;))
2681                 </p>
2682               </td>
2683 <td>
2684                 <p>
2685                   <span class="blue">Max = 2.6&#949; (Mean = 1.21&#949;)</span>
2686                 </p>
2687               </td>
2688 <td>
2689                 <p>
2690                   <span class="blue">Max = 3.63&#949; (Mean = 1.46&#949;)</span>
2691                 </p>
2692               </td>
2693 </tr>
2694 <tr>
2695 <td>
2696                 <p>
2697                   Bessel Kv: Mathworld Data
2698                 </p>
2699               </td>
2700 <td>
2701                 <p>
2702                   <span class="blue">Max = 3.58&#949; (Mean = 2.39&#949;)</span><br> <br>
2703                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 13&#949; (Mean = 4.81&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Mathworld_Data">And
2704                   other failures.</a>)
2705                 </p>
2706               </td>
2707 <td>
2708                 <p>
2709                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
2710                   2.1:</em></span> Max = 5.47&#949; (Mean = 2.04&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Mathworld_Data">And
2711                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
2712                   Max = 3.15&#949; (Mean = 1.35&#949;))
2713                 </p>
2714               </td>
2715 <td>
2716                 <p>
2717                   <span class="blue">Max = 5.21&#949; (Mean = 2.53&#949;)</span>
2718                 </p>
2719               </td>
2720 <td>
2721                 <p>
2722                   <span class="blue">Max = 4.78&#949; (Mean = 2.19&#949;)</span>
2723                 </p>
2724               </td>
2725 </tr>
2726 <tr>
2727 <td>
2728                 <p>
2729                   Bessel Kv: Mathworld Data (large values)
2730                 </p>
2731               </td>
2732 <td>
2733                 <p>
2734                   <span class="blue">Max = 42.3&#949; (Mean = 21&#949;)</span><br> <br>
2735                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 42.3&#949; (Mean = 19.8&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Mathworld_Data_large_values_">And
2736                   other failures.</a>)
2737                 </p>
2738               </td>
2739 <td>
2740                 <p>
2741                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
2742                   2.1:</em></span> Max = 308&#949; (Mean = 142&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Mathworld_Data_large_values_">And
2743                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
2744                   Max = 84.6&#949; (Mean = 37.8&#949;))
2745                 </p>
2746               </td>
2747 <td>
2748                 <p>
2749                   <span class="blue">Max = 42.3&#949; (Mean = 21&#949;)</span>
2750                 </p>
2751               </td>
2752 <td>
2753                 <p>
2754                   <span class="blue">Max = 59.8&#949; (Mean = 26.9&#949;)</span>
2755                 </p>
2756               </td>
2757 </tr>
2758 <tr>
2759 <td>
2760                 <p>
2761                   Bessel Kn: Random Data
2762                 </p>
2763               </td>
2764 <td>
2765                 <p>
2766                   <span class="blue">Max = 4.55&#949; (Mean = 1.12&#949;)</span><br> <br>
2767                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 13.9&#949; (Mean = 2.91&#949;))
2768                 </p>
2769               </td>
2770 <td>
2771                 <p>
2772                   <span class="blue">Max = 0.764&#949; (Mean = 0.0348&#949;)</span><br>
2773                   <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.71&#949; (Mean = 1.76&#949;)
2774                   <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kn_Random_Data">And
2775                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
2776                   Max = 7.47&#949; (Mean = 1.34&#949;))
2777                 </p>
2778               </td>
2779 <td>
2780                 <p>
2781                   <span class="blue">Max = 4.55&#949; (Mean = 1.12&#949;)</span>
2782                 </p>
2783               </td>
2784 <td>
2785                 <p>
2786                   <span class="blue">Max = 9.34&#949; (Mean = 1.7&#949;)</span>
2787                 </p>
2788               </td>
2789 </tr>
2790 <tr>
2791 <td>
2792                 <p>
2793                   Bessel Kv: Random Data
2794                 </p>
2795               </td>
2796 <td>
2797                 <p>
2798                   <span class="blue">Max = 7.88&#949; (Mean = 1.48&#949;)</span><br> <br>
2799                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 13.6&#949; (Mean = 2.68&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Random_Data">And
2800                   other failures.</a>)
2801                 </p>
2802               </td>
2803 <td>
2804                 <p>
2805                   <span class="blue">Max = 0.507&#949; (Mean = 0.0313&#949;)</span><br>
2806                   <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 9.71&#949; (Mean = 1.47&#949;)
2807                   <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Random_Data">And
2808                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
2809                   Max = 7.37&#949; (Mean = 1.49&#949;))
2810                 </p>
2811               </td>
2812 <td>
2813                 <p>
2814                   <span class="blue">Max = 7.88&#949; (Mean = 1.47&#949;)</span>
2815                 </p>
2816               </td>
2817 <td>
2818                 <p>
2819                   <span class="blue">Max = 8.33&#949; (Mean = 1.62&#949;)</span>
2820                 </p>
2821               </td>
2822 </tr>
2823 </tbody>
2824 </table></div>
2825 </div>
2826 <br class="table-break"><div class="table">
2827 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_k_integer_orders_"></a><p class="title"><b>Table&#160;22.19.&#160;Error rates for cyl_bessel_k (integer orders)</b></p>
2828 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k (integer orders)">
2829 <colgroup>
2830 <col>
2831 <col>
2832 <col>
2833 <col>
2834 <col>
2835 </colgroup>
2836 <thead><tr>
2837 <th>
2838               </th>
2839 <th>
2840                 <p>
2841                   GNU C++ version 7.1.0<br> linux<br> long double
2842                 </p>
2843               </th>
2844 <th>
2845                 <p>
2846                   GNU C++ version 7.1.0<br> linux<br> double
2847                 </p>
2848               </th>
2849 <th>
2850                 <p>
2851                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
2852                 </p>
2853               </th>
2854 <th>
2855                 <p>
2856                   Microsoft Visual C++ version 14.1<br> Win32<br> double
2857                 </p>
2858               </th>
2859 </tr></thead>
2860 <tbody>
2861 <tr>
2862 <td>
2863                 <p>
2864                   Bessel K0: Mathworld Data (Integer Version)
2865                 </p>
2866               </td>
2867 <td>
2868                 <p>
2869                   <span class="blue">Max = 0.833&#949; (Mean = 0.436&#949;)</span><br> <br>
2870                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 9.33&#949; (Mean = 3.25&#949;))
2871                 </p>
2872               </td>
2873 <td>
2874                 <p>
2875                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
2876                   2.1:</em></span> Max = 1.2&#949; (Mean = 0.733&#949;))<br> (<span class="emphasis"><em>Rmath
2877                   3.2.3:</em></span> Max = 0.833&#949; (Mean = 0.601&#949;))
2878                 </p>
2879               </td>
2880 <td>
2881                 <p>
2882                   <span class="blue">Max = 0.833&#949; (Mean = 0.436&#949;)</span>
2883                 </p>
2884               </td>
2885 <td>
2886                 <p>
2887                   <span class="blue">Max = 0.833&#949; (Mean = 0.552&#949;)</span>
2888                 </p>
2889               </td>
2890 </tr>
2891 <tr>
2892 <td>
2893                 <p>
2894                   Bessel K1: Mathworld Data (Integer Version)
2895                 </p>
2896               </td>
2897 <td>
2898                 <p>
2899                   <span class="blue">Max = 0.786&#949; (Mean = 0.329&#949;)</span><br> <br>
2900                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 8.94&#949; (Mean = 3.19&#949;))
2901                 </p>
2902               </td>
2903 <td>
2904                 <p>
2905                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
2906                   2.1:</em></span> Max = 0.626&#949; (Mean = 0.333&#949;))<br> (<span class="emphasis"><em>Rmath
2907                   3.2.3:</em></span> Max = 0.894&#949; (Mean = 0.516&#949;))
2908                 </p>
2909               </td>
2910 <td>
2911                 <p>
2912                   <span class="blue">Max = 0.786&#949; (Mean = 0.329&#949;)</span>
2913                 </p>
2914               </td>
2915 <td>
2916                 <p>
2917                   <span class="blue">Max = 0.786&#949; (Mean = 0.39&#949;)</span>
2918                 </p>
2919               </td>
2920 </tr>
2921 <tr>
2922 <td>
2923                 <p>
2924                   Bessel Kn: Mathworld Data (Integer Version)
2925                 </p>
2926               </td>
2927 <td>
2928                 <p>
2929                   <span class="blue">Max = 2.6&#949; (Mean = 1.21&#949;)</span><br> <br>
2930                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 12.9&#949; (Mean = 4.91&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k_integer_orders___cmath__Bessel_Kn_Mathworld_Data_Integer_Version_">And
2931                   other failures.</a>)
2932                 </p>
2933               </td>
2934 <td>
2935                 <p>
2936                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
2937                   2.1:</em></span> Max = 168&#949; (Mean = 59.5&#949;))<br> (<span class="emphasis"><em>Rmath
2938                   3.2.3:</em></span> Max = 8.48&#949; (Mean = 2.98&#949;))
2939                 </p>
2940               </td>
2941 <td>
2942                 <p>
2943                   <span class="blue">Max = 2.6&#949; (Mean = 1.21&#949;)</span>
2944                 </p>
2945               </td>
2946 <td>
2947                 <p>
2948                   <span class="blue">Max = 3.63&#949; (Mean = 1.46&#949;)</span>
2949                 </p>
2950               </td>
2951 </tr>
2952 </tbody>
2953 </table></div>
2954 </div>
2955 <br class="table-break"><div class="table">
2956 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_k_prime"></a><p class="title"><b>Table&#160;22.20.&#160;Error rates for cyl_bessel_k_prime</b></p>
2957 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k_prime">
2958 <colgroup>
2959 <col>
2960 <col>
2961 <col>
2962 <col>
2963 <col>
2964 </colgroup>
2965 <thead><tr>
2966 <th>
2967               </th>
2968 <th>
2969                 <p>
2970                   GNU C++ version 7.1.0<br> linux<br> double
2971                 </p>
2972               </th>
2973 <th>
2974                 <p>
2975                   GNU C++ version 7.1.0<br> linux<br> long double
2976                 </p>
2977               </th>
2978 <th>
2979                 <p>
2980                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
2981                 </p>
2982               </th>
2983 <th>
2984                 <p>
2985                   Microsoft Visual C++ version 14.1<br> Win32<br> double
2986                 </p>
2987               </th>
2988 </tr></thead>
2989 <tbody>
2990 <tr>
2991 <td>
2992                 <p>
2993                   Bessel K'0: Mathworld Data
2994                 </p>
2995               </td>
2996 <td>
2997                 <p>
2998                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
2999                 </p>
3000               </td>
3001 <td>
3002                 <p>
3003                   <span class="blue">Max = 0.786&#949; (Mean = 0.329&#949;)</span>
3004                 </p>
3005               </td>
3006 <td>
3007                 <p>
3008                   <span class="blue">Max = 0.786&#949; (Mean = 0.329&#949;)</span>
3009                 </p>
3010               </td>
3011 <td>
3012                 <p>
3013                   <span class="blue">Max = 0.786&#949; (Mean = 0.39&#949;)</span>
3014                 </p>
3015               </td>
3016 </tr>
3017 <tr>
3018 <td>
3019                 <p>
3020                   Bessel K'1: Mathworld Data
3021                 </p>
3022               </td>
3023 <td>
3024                 <p>
3025                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
3026                 </p>
3027               </td>
3028 <td>
3029                 <p>
3030                   <span class="blue">Max = 0.736&#949; (Mean = 0.389&#949;)</span>
3031                 </p>
3032               </td>
3033 <td>
3034                 <p>
3035                   <span class="blue">Max = 0.736&#949; (Mean = 0.389&#949;)</span>
3036                 </p>
3037               </td>
3038 <td>
3039                 <p>
3040                   <span class="blue">Max = 0.761&#949; (Mean = 0.444&#949;)</span>
3041                 </p>
3042               </td>
3043 </tr>
3044 <tr>
3045 <td>
3046                 <p>
3047                   Bessel K'n: Mathworld Data
3048                 </p>
3049               </td>
3050 <td>
3051                 <p>
3052                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
3053                 </p>
3054               </td>
3055 <td>
3056                 <p>
3057                   <span class="blue">Max = 2.16&#949; (Mean = 1.08&#949;)</span>
3058                 </p>
3059               </td>
3060 <td>
3061                 <p>
3062                   <span class="blue">Max = 2.16&#949; (Mean = 1.08&#949;)</span>
3063                 </p>
3064               </td>
3065 <td>
3066                 <p>
3067                   <span class="blue">Max = 4.17&#949; (Mean = 1.75&#949;)</span>
3068                 </p>
3069               </td>
3070 </tr>
3071 <tr>
3072 <td>
3073                 <p>
3074                   Bessel K'v: Mathworld Data
3075                 </p>
3076               </td>
3077 <td>
3078                 <p>
3079                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
3080                 </p>
3081               </td>
3082 <td>
3083                 <p>
3084                   <span class="blue">Max = 3.94&#949; (Mean = 2.44&#949;)</span>
3085                 </p>
3086               </td>
3087 <td>
3088                 <p>
3089                   <span class="blue">Max = 3.94&#949; (Mean = 2.34&#949;)</span>
3090                 </p>
3091               </td>
3092 <td>
3093                 <p>
3094                   <span class="blue">Max = 3.94&#949; (Mean = 1.47&#949;)</span>
3095                 </p>
3096               </td>
3097 </tr>
3098 <tr>
3099 <td>
3100                 <p>
3101                   Bessel K'v: Mathworld Data (large values)
3102                 </p>
3103               </td>
3104 <td>
3105                 <p>
3106                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
3107                 </p>
3108               </td>
3109 <td>
3110                 <p>
3111                   <span class="blue">Max = 59.2&#949; (Mean = 42.9&#949;)</span>
3112                 </p>
3113               </td>
3114 <td>
3115                 <p>
3116                   <span class="blue">Max = 58.7&#949; (Mean = 42.6&#949;)</span>
3117                 </p>
3118               </td>
3119 <td>
3120                 <p>
3121                   <span class="blue">Max = 18.6&#949; (Mean = 11.8&#949;)</span>
3122                 </p>
3123               </td>
3124 </tr>
3125 <tr>
3126 <td>
3127                 <p>
3128                   Bessel K'n: Random Data
3129                 </p>
3130               </td>
3131 <td>
3132                 <p>
3133                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
3134                 </p>
3135               </td>
3136 <td>
3137                 <p>
3138                   <span class="blue">Max = 4.45&#949; (Mean = 1.19&#949;)</span>
3139                 </p>
3140               </td>
3141 <td>
3142                 <p>
3143                   <span class="blue">Max = 4.45&#949; (Mean = 1.19&#949;)</span>
3144                 </p>
3145               </td>
3146 <td>
3147                 <p>
3148                   <span class="blue">Max = 9.67&#949; (Mean = 1.73&#949;)</span>
3149                 </p>
3150               </td>
3151 </tr>
3152 <tr>
3153 <td>
3154                 <p>
3155                   Bessel K'v: Random Data
3156                 </p>
3157               </td>
3158 <td>
3159                 <p>
3160                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
3161                 </p>
3162               </td>
3163 <td>
3164                 <p>
3165                   <span class="blue">Max = 7.95&#949; (Mean = 1.53&#949;)</span>
3166                 </p>
3167               </td>
3168 <td>
3169                 <p>
3170                   <span class="blue">Max = 7.95&#949; (Mean = 1.52&#949;)</span>
3171                 </p>
3172               </td>
3173 <td>
3174                 <p>
3175                   <span class="blue">Max = 8.32&#949; (Mean = 1.65&#949;)</span>
3176                 </p>
3177               </td>
3178 </tr>
3179 </tbody>
3180 </table></div>
3181 </div>
3182 <br class="table-break"><div class="table">
3183 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_k_prime_integer_orders_"></a><p class="title"><b>Table&#160;22.21.&#160;Error rates for cyl_bessel_k_prime (integer orders)</b></p>
3184 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k_prime (integer orders)">
3185 <colgroup>
3186 <col>
3187 <col>
3188 <col>
3189 <col>
3190 <col>
3191 </colgroup>
3192 <thead><tr>
3193 <th>
3194               </th>
3195 <th>
3196                 <p>
3197                   GNU C++ version 7.1.0<br> linux<br> double
3198                 </p>
3199               </th>
3200 <th>
3201                 <p>
3202                   GNU C++ version 7.1.0<br> linux<br> long double
3203                 </p>
3204               </th>
3205 <th>
3206                 <p>
3207                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
3208                 </p>
3209               </th>
3210 <th>
3211                 <p>
3212                   Microsoft Visual C++ version 14.1<br> Win32<br> double
3213                 </p>
3214               </th>
3215 </tr></thead>
3216 <tbody>
3217 <tr>
3218 <td>
3219                 <p>
3220                   Bessel K'0: Mathworld Data (Integer Version)
3221                 </p>
3222               </td>
3223 <td>
3224                 <p>
3225                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
3226                 </p>
3227               </td>
3228 <td>
3229                 <p>
3230                   <span class="blue">Max = 0.786&#949; (Mean = 0.329&#949;)</span>
3231                 </p>
3232               </td>
3233 <td>
3234                 <p>
3235                   <span class="blue">Max = 0.786&#949; (Mean = 0.329&#949;)</span>
3236                 </p>
3237               </td>
3238 <td>
3239                 <p>
3240                   <span class="blue">Max = 0.786&#949; (Mean = 0.39&#949;)</span>
3241                 </p>
3242               </td>
3243 </tr>
3244 <tr>
3245 <td>
3246                 <p>
3247                   Bessel K'1: Mathworld Data (Integer Version)
3248                 </p>
3249               </td>
3250 <td>
3251                 <p>
3252                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
3253                 </p>
3254               </td>
3255 <td>
3256                 <p>
3257                   <span class="blue">Max = 0.736&#949; (Mean = 0.389&#949;)</span>
3258                 </p>
3259               </td>
3260 <td>
3261                 <p>
3262                   <span class="blue">Max = 0.736&#949; (Mean = 0.389&#949;)</span>
3263                 </p>
3264               </td>
3265 <td>
3266                 <p>
3267                   <span class="blue">Max = 0.761&#949; (Mean = 0.444&#949;)</span>
3268                 </p>
3269               </td>
3270 </tr>
3271 <tr>
3272 <td>
3273                 <p>
3274                   Bessel K'n: Mathworld Data (Integer Version)
3275                 </p>
3276               </td>
3277 <td>
3278                 <p>
3279                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
3280                 </p>
3281               </td>
3282 <td>
3283                 <p>
3284                   <span class="blue">Max = 2.16&#949; (Mean = 1.08&#949;)</span>
3285                 </p>
3286               </td>
3287 <td>
3288                 <p>
3289                   <span class="blue">Max = 2.16&#949; (Mean = 1.08&#949;)</span>
3290                 </p>
3291               </td>
3292 <td>
3293                 <p>
3294                   <span class="blue">Max = 4.17&#949; (Mean = 1.75&#949;)</span>
3295                 </p>
3296               </td>
3297 </tr>
3298 </tbody>
3299 </table></div>
3300 </div>
3301 <br class="table-break"><div class="table">
3302 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_neumann"></a><p class="title"><b>Table&#160;22.22.&#160;Error rates for cyl_neumann</b></p>
3303 <div class="table-contents"><table class="table" summary="Error rates for cyl_neumann">
3304 <colgroup>
3305 <col>
3306 <col>
3307 <col>
3308 <col>
3309 <col>
3310 </colgroup>
3311 <thead><tr>
3312 <th>
3313               </th>
3314 <th>
3315                 <p>
3316                   GNU C++ version 7.1.0<br> linux<br> long double
3317                 </p>
3318               </th>
3319 <th>
3320                 <p>
3321                   GNU C++ version 7.1.0<br> linux<br> double
3322                 </p>
3323               </th>
3324 <th>
3325                 <p>
3326                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
3327                 </p>
3328               </th>
3329 <th>
3330                 <p>
3331                   Microsoft Visual C++ version 14.1<br> Win32<br> double
3332                 </p>
3333               </th>
3334 </tr></thead>
3335 <tbody>
3336 <tr>
3337 <td>
3338                 <p>
3339                   Y0: Mathworld Data
3340                 </p>
3341               </td>
3342 <td>
3343                 <p>
3344                   <span class="blue">Max = 5.53&#949; (Mean = 2.4&#949;)</span><br> <br>
3345                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 2.05e+05&#949; (Mean = 6.87e+04&#949;))
3346                 </p>
3347               </td>
3348 <td>
3349                 <p>
3350                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
3351                   2.1:</em></span> Max = 60.9&#949; (Mean = 20.4&#949;))<br> (<span class="emphasis"><em>Rmath
3352                   3.2.3:</em></span> Max = 167&#949; (Mean = 56.5&#949;))
3353                 </p>
3354               </td>
3355 <td>
3356                 <p>
3357                   <span class="blue">Max = 5.53&#949; (Mean = 2.4&#949;)</span>
3358                 </p>
3359               </td>
3360 <td>
3361                 <p>
3362                   <span class="blue">Max = 4.61&#949; (Mean = 2.29&#949;)</span>
3363                 </p>
3364               </td>
3365 </tr>
3366 <tr>
3367 <td>
3368                 <p>
3369                   Y1: Mathworld Data
3370                 </p>
3371               </td>
3372 <td>
3373                 <p>
3374                   <span class="blue">Max = 6.33&#949; (Mean = 2.25&#949;)</span><br> <br>
3375                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 9.71e+03&#949; (Mean = 4.08e+03&#949;))
3376                 </p>
3377               </td>
3378 <td>
3379                 <p>
3380                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
3381                   2.1:</em></span> Max = 23.4&#949; (Mean = 8.1&#949;))<br> (<span class="emphasis"><em>Rmath
3382                   3.2.3:</em></span> Max = 193&#949; (Mean = 64.4&#949;))
3383                 </p>
3384               </td>
3385 <td>
3386                 <p>
3387                   <span class="blue">Max = 6.33&#949; (Mean = 2.29&#949;)</span>
3388                 </p>
3389               </td>
3390 <td>
3391                 <p>
3392                   <span class="blue">Max = 4.75&#949; (Mean = 1.72&#949;)</span>
3393                 </p>
3394               </td>
3395 </tr>
3396 <tr>
3397 <td>
3398                 <p>
3399                   Yn: Mathworld Data
3400                 </p>
3401               </td>
3402 <td>
3403                 <p>
3404                   <span class="blue">Max = 55.2&#949; (Mean = 17.8&#949;)</span><br> <br>
3405                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = 2.2e+20&#949; (Mean
3406                   = 6.97e+19&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yn_Mathworld_Data">And
3407                   other failures.</a>)</span>
3408                 </p>
3409               </td>
3410 <td>
3411                 <p>
3412                   <span class="blue">Max = 0.993&#949; (Mean = 0.314&#949;)</span><br> <br>
3413                   (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.41e+05&#949; (Mean = 7.62e+04&#949;)
3414                   <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yn_Mathworld_Data">And
3415                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
3416                   Max = 1.24e+04&#949; (Mean = 4e+03&#949;))
3417                 </p>
3418               </td>
3419 <td>
3420                 <p>
3421                   <span class="blue">Max = 55.2&#949; (Mean = 17.8&#949;)</span>
3422                 </p>
3423               </td>
3424 <td>
3425                 <p>
3426                   <span class="blue">Max = 35&#949; (Mean = 11.9&#949;)</span>
3427                 </p>
3428               </td>
3429 </tr>
3430 <tr>
3431 <td>
3432                 <p>
3433                   Yv: Mathworld Data
3434                 </p>
3435               </td>
3436 <td>
3437                 <p>
3438                   <span class="blue">Max = 10.7&#949; (Mean = 4.93&#949;)</span><br> <br>
3439                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = 3.49e+15&#949; (Mean
3440                   = 1.05e+15&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Mathworld_Data">And
3441                   other failures.</a>)</span>
3442                 </p>
3443               </td>
3444 <td>
3445                 <p>
3446                   <span class="blue">Max = 10&#949; (Mean = 3.02&#949;)</span><br> <br>
3447                   (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.07e+05&#949; (Mean = 3.22e+04&#949;)
3448                   <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yv_Mathworld_Data">And
3449                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
3450                   Max = 243&#949; (Mean = 73.9&#949;))
3451                 </p>
3452               </td>
3453 <td>
3454                 <p>
3455                   <span class="blue">Max = 10.7&#949; (Mean = 5.1&#949;)</span>
3456                 </p>
3457               </td>
3458 <td>
3459                 <p>
3460                   <span class="blue">Max = 7.89&#949; (Mean = 3.27&#949;)</span>
3461                 </p>
3462               </td>
3463 </tr>
3464 <tr>
3465 <td>
3466                 <p>
3467                   Yv: Mathworld Data (large values)
3468                 </p>
3469               </td>
3470 <td>
3471                 <p>
3472                   <span class="blue">Max = 1.7&#949; (Mean = 1.33&#949;)</span><br> <br>
3473                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 43.2&#949; (Mean = 16.3&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Mathworld_Data_large_values_">And
3474                   other failures.</a>)
3475                 </p>
3476               </td>
3477 <td>
3478                 <p>
3479                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
3480                   2.1:</em></span> Max = 60.8&#949; (Mean = 23&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yv_Mathworld_Data_large_values_">And
3481                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
3482                   Max = 0.682&#949; (Mean = 0.335&#949;))
3483                 </p>
3484               </td>
3485 <td>
3486                 <p>
3487                   <span class="blue">Max = 1.7&#949; (Mean = 1.33&#949;)</span>
3488                 </p>
3489               </td>
3490 <td>
3491                 <p>
3492                   <span class="blue">Max = 0.682&#949; (Mean = 0.423&#949;)</span>
3493                 </p>
3494               </td>
3495 </tr>
3496 <tr>
3497 <td>
3498                 <p>
3499                   Y0 and Y1: Random Data
3500                 </p>
3501               </td>
3502 <td>
3503                 <p>
3504                   <span class="blue">Max = 10.8&#949; (Mean = 3.04&#949;)</span><br> <br>
3505                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 2.59e+03&#949; (Mean = 500&#949;))
3506                 </p>
3507               </td>
3508 <td>
3509                 <p>
3510                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
3511                   2.1:</em></span> Max = 34.4&#949; (Mean = 8.9&#949;))<br> (<span class="emphasis"><em>Rmath
3512                   3.2.3:</em></span> Max = 83&#949; (Mean = 14.2&#949;))
3513                 </p>
3514               </td>
3515 <td>
3516                 <p>
3517                   <span class="blue">Max = 10.8&#949; (Mean = 3.04&#949;)</span>
3518                 </p>
3519               </td>
3520 <td>
3521                 <p>
3522                   <span class="blue">Max = 4.17&#949; (Mean = 1.24&#949;)</span>
3523                 </p>
3524               </td>
3525 </tr>
3526 <tr>
3527 <td>
3528                 <p>
3529                   Yn: Random Data
3530                 </p>
3531               </td>
3532 <td>
3533                 <p>
3534                   <span class="blue">Max = 338&#949; (Mean = 27.5&#949;)</span><br> <br>
3535                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 4.01e+03&#949; (Mean = 348&#949;))
3536                 </p>
3537               </td>
3538 <td>
3539                 <p>
3540                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
3541                   2.1:</em></span> Max = 500&#949; (Mean = 47.8&#949;))<br> (<span class="emphasis"><em>Rmath
3542                   3.2.3:</em></span> Max = 691&#949; (Mean = 67.9&#949;))
3543                 </p>
3544               </td>
3545 <td>
3546                 <p>
3547                   <span class="blue">Max = 338&#949; (Mean = 27.5&#949;)</span>
3548                 </p>
3549               </td>
3550 <td>
3551                 <p>
3552                   <span class="blue">Max = 117&#949; (Mean = 10.2&#949;)</span>
3553                 </p>
3554               </td>
3555 </tr>
3556 <tr>
3557 <td>
3558                 <p>
3559                   Yv: Random Data
3560                 </p>
3561               </td>
3562 <td>
3563                 <p>
3564                   <span class="blue">Max = 2.08e+03&#949; (Mean = 149&#949;)</span><br>
3565                   <br> (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max
3566                   = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Random_Data">And
3567                   other failures.</a>)</span>
3568                 </p>
3569               </td>
3570 <td>
3571                 <p>
3572                   <span class="blue">Max = 1.53&#949; (Mean = 0.102&#949;)</span><br> <br>
3573                   (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.41e+06&#949; (Mean = 7.67e+04&#949;))<br>
3574                   (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.79e+05&#949; (Mean = 9.64e+03&#949;))
3575                 </p>
3576               </td>
3577 <td>
3578                 <p>
3579                   <span class="blue">Max = 2.08e+03&#949; (Mean = 149&#949;)</span>
3580                 </p>
3581               </td>
3582 <td>
3583                 <p>
3584                   <span class="blue">Max = 1.23e+03&#949; (Mean = 69.9&#949;)</span>
3585                 </p>
3586               </td>
3587 </tr>
3588 </tbody>
3589 </table></div>
3590 </div>
3591 <br class="table-break"><div class="table">
3592 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_neumann_integer_orders_"></a><p class="title"><b>Table&#160;22.23.&#160;Error rates for cyl_neumann (integer orders)</b></p>
3593 <div class="table-contents"><table class="table" summary="Error rates for cyl_neumann (integer orders)">
3594 <colgroup>
3595 <col>
3596 <col>
3597 <col>
3598 <col>
3599 <col>
3600 </colgroup>
3601 <thead><tr>
3602 <th>
3603               </th>
3604 <th>
3605                 <p>
3606                   GNU C++ version 7.1.0<br> linux<br> long double
3607                 </p>
3608               </th>
3609 <th>
3610                 <p>
3611                   GNU C++ version 7.1.0<br> linux<br> double
3612                 </p>
3613               </th>
3614 <th>
3615                 <p>
3616                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
3617                 </p>
3618               </th>
3619 <th>
3620                 <p>
3621                   Microsoft Visual C++ version 14.1<br> Win32<br> double
3622                 </p>
3623               </th>
3624 </tr></thead>
3625 <tbody>
3626 <tr>
3627 <td>
3628                 <p>
3629                   Y0: Mathworld Data (Integer Version)
3630                 </p>
3631               </td>
3632 <td>
3633                 <p>
3634                   <span class="blue">Max = 5.53&#949; (Mean = 2.4&#949;)</span><br> <br>
3635                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 2.05e+05&#949; (Mean = 6.87e+04&#949;))
3636                 </p>
3637               </td>
3638 <td>
3639                 <p>
3640                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
3641                   2.1:</em></span> Max = 6.46&#949; (Mean = 2.38&#949;))<br> (<span class="emphasis"><em>Rmath
3642                   3.2.3:</em></span> Max = 167&#949; (Mean = 56.5&#949;))
3643                 </p>
3644               </td>
3645 <td>
3646                 <p>
3647                   <span class="blue">Max = 5.53&#949; (Mean = 2.4&#949;)</span>
3648                 </p>
3649               </td>
3650 <td>
3651                 <p>
3652                   <span class="blue">Max = 4.61&#949; (Mean = 2.29&#949;)</span><br> <br>
3653                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 5.37e+03&#949; (Mean = 1.81e+03&#949;))
3654                 </p>
3655               </td>
3656 </tr>
3657 <tr>
3658 <td>
3659                 <p>
3660                   Y1: Mathworld Data (Integer Version)
3661                 </p>
3662               </td>
3663 <td>
3664                 <p>
3665                   <span class="blue">Max = 6.33&#949; (Mean = 2.25&#949;)</span><br> <br>
3666                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 9.71e+03&#949; (Mean = 4.08e+03&#949;))
3667                 </p>
3668               </td>
3669 <td>
3670                 <p>
3671                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
3672                   2.1:</em></span> Max = 1.51&#949; (Mean = 0.839&#949;))<br> (<span class="emphasis"><em>Rmath
3673                   3.2.3:</em></span> Max = 193&#949; (Mean = 64.4&#949;))
3674                 </p>
3675               </td>
3676 <td>
3677                 <p>
3678                   <span class="blue">Max = 6.33&#949; (Mean = 2.29&#949;)</span>
3679                 </p>
3680               </td>
3681 <td>
3682                 <p>
3683                   <span class="blue">Max = 4.75&#949; (Mean = 1.72&#949;)</span><br> <br>
3684                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.86e+04&#949; (Mean = 6.2e+03&#949;))
3685                 </p>
3686               </td>
3687 </tr>
3688 <tr>
3689 <td>
3690                 <p>
3691                   Yn: Mathworld Data (Integer Version)
3692                 </p>
3693               </td>
3694 <td>
3695                 <p>
3696                   <span class="blue">Max = 55.2&#949; (Mean = 17.8&#949;)</span><br> <br>
3697                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = 2.2e+20&#949; (Mean
3698                   = 6.97e+19&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann_integer_orders___cmath__Yn_Mathworld_Data_Integer_Version_">And
3699                   other failures.</a>)</span>
3700                 </p>
3701               </td>
3702 <td>
3703                 <p>
3704                   <span class="blue">Max = 0.993&#949; (Mean = 0.314&#949;)</span><br> <br>
3705                   (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.41e+05&#949; (Mean = 7.62e+04&#949;))<br>
3706                   (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.24e+04&#949; (Mean = 4e+03&#949;))
3707                 </p>
3708               </td>
3709 <td>
3710                 <p>
3711                   <span class="blue">Max = 55.2&#949; (Mean = 17.8&#949;)</span>
3712                 </p>
3713               </td>
3714 <td>
3715                 <p>
3716                   <span class="blue">Max = 35&#949; (Mean = 11.9&#949;)</span><br> <br>
3717                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 2.49e+05&#949; (Mean = 8.14e+04&#949;))
3718                 </p>
3719               </td>
3720 </tr>
3721 </tbody>
3722 </table></div>
3723 </div>
3724 <br class="table-break"><div class="table">
3725 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_neumann_prime"></a><p class="title"><b>Table&#160;22.24.&#160;Error rates for cyl_neumann_prime</b></p>
3726 <div class="table-contents"><table class="table" summary="Error rates for cyl_neumann_prime">
3727 <colgroup>
3728 <col>
3729 <col>
3730 <col>
3731 <col>
3732 <col>
3733 </colgroup>
3734 <thead><tr>
3735 <th>
3736               </th>
3737 <th>
3738                 <p>
3739                   GNU C++ version 7.1.0<br> linux<br> double
3740                 </p>
3741               </th>
3742 <th>
3743                 <p>
3744                   GNU C++ version 7.1.0<br> linux<br> long double
3745                 </p>
3746               </th>
3747 <th>
3748                 <p>
3749                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
3750                 </p>
3751               </th>
3752 <th>
3753                 <p>
3754                   Microsoft Visual C++ version 14.1<br> Win32<br> double
3755                 </p>
3756               </th>
3757 </tr></thead>
3758 <tbody>
3759 <tr>
3760 <td>
3761                 <p>
3762                   Y'0: Mathworld Data
3763                 </p>
3764               </td>
3765 <td>
3766                 <p>
3767                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
3768                 </p>
3769               </td>
3770 <td>
3771                 <p>
3772                   <span class="blue">Max = 6.33&#949; (Mean = 3.12&#949;)</span>
3773                 </p>
3774               </td>
3775 <td>
3776                 <p>
3777                   <span class="blue">Max = 6.33&#949; (Mean = 3.14&#949;)</span>
3778                 </p>
3779               </td>
3780 <td>
3781                 <p>
3782                   <span class="blue">Max = 4.75&#949; (Mean = 1.75&#949;)</span>
3783                 </p>
3784               </td>
3785 </tr>
3786 <tr>
3787 <td>
3788                 <p>
3789                   Y'1: Mathworld Data
3790                 </p>
3791               </td>
3792 <td>
3793                 <p>
3794                   <span class="blue">Max = 0.58&#949; (Mean = 0.193&#949;)</span>
3795                 </p>
3796               </td>
3797 <td>
3798                 <p>
3799                   <span class="blue">Max = 37.1&#949; (Mean = 12.8&#949;)</span>
3800                 </p>
3801               </td>
3802 <td>
3803                 <p>
3804                   <span class="blue">Max = 34&#949; (Mean = 11.8&#949;)</span>
3805                 </p>
3806               </td>
3807 <td>
3808                 <p>
3809                   <span class="blue">Max = 3.08&#949; (Mean = 1.2&#949;)</span>
3810                 </p>
3811               </td>
3812 </tr>
3813 <tr>
3814 <td>
3815                 <p>
3816                   Y'n: Mathworld Data
3817                 </p>
3818               </td>
3819 <td>
3820                 <p>
3821                   <span class="blue">Max = 2.05&#949; (Mean = 0.677&#949;)</span>
3822                 </p>
3823               </td>
3824 <td>
3825                 <p>
3826                   <span class="blue">Max = 56&#949; (Mean = 18.2&#949;)</span>
3827                 </p>
3828               </td>
3829 <td>
3830                 <p>
3831                   <span class="blue">Max = 56&#949; (Mean = 21.3&#949;)</span>
3832                 </p>
3833               </td>
3834 <td>
3835                 <p>
3836                   <span class="blue">Max = 563&#949; (Mean = 178&#949;)</span>
3837                 </p>
3838               </td>
3839 </tr>
3840 <tr>
3841 <td>
3842                 <p>
3843                   Y'v: Mathworld Data
3844                 </p>
3845               </td>
3846 <td>
3847                 <p>
3848                   <span class="blue">Max = 21.5&#949; (Mean = 6.49&#949;)</span>
3849                 </p>
3850               </td>
3851 <td>
3852                 <p>
3853                   <span class="blue">Max = 42.5&#949; (Mean = 13.4&#949;)</span>
3854                 </p>
3855               </td>
3856 <td>
3857                 <p>
3858                   <span class="blue">Max = 42.5&#949; (Mean = 13.6&#949;)</span>
3859                 </p>
3860               </td>
3861 <td>
3862                 <p>
3863                   <span class="blue">Max = 23.7&#949; (Mean = 10.1&#949;)</span>
3864                 </p>
3865               </td>
3866 </tr>
3867 <tr>
3868 <td>
3869                 <p>
3870                   Y'v: Mathworld Data (large values)
3871                 </p>
3872               </td>
3873 <td>
3874                 <p>
3875                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
3876                 </p>
3877               </td>
3878 <td>
3879                 <p>
3880                   <span class="blue">Max = 1.57&#949; (Mean = 1.24&#949;)</span>
3881                 </p>
3882               </td>
3883 <td>
3884                 <p>
3885                   <span class="blue">Max = 1.57&#949; (Mean = 1.24&#949;)</span>
3886                 </p>
3887               </td>
3888 <td>
3889                 <p>
3890                   <span class="blue">Max = 0.627&#949; (Mean = 0.237&#949;)</span>
3891                 </p>
3892               </td>
3893 </tr>
3894 <tr>
3895 <td>
3896                 <p>
3897                   Y'0 and Y'1: Random Data
3898                 </p>
3899               </td>
3900 <td>
3901                 <p>
3902                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
3903                 </p>
3904               </td>
3905 <td>
3906                 <p>
3907                   <span class="blue">Max = 23.8&#949; (Mean = 3.69&#949;)</span>
3908                 </p>
3909               </td>
3910 <td>
3911                 <p>
3912                   <span class="blue">Max = 23.8&#949; (Mean = 3.69&#949;)</span>
3913                 </p>
3914               </td>
3915 <td>
3916                 <p>
3917                   <span class="blue">Max = 5.95&#949; (Mean = 1.36&#949;)</span>
3918                 </p>
3919               </td>
3920 </tr>
3921 <tr>
3922 <td>
3923                 <p>
3924                   Y'n: Random Data
3925                 </p>
3926               </td>
3927 <td>
3928                 <p>
3929                   <span class="blue">Max = 1.53&#949; (Mean = 0.0885&#949;)</span>
3930                 </p>
3931               </td>
3932 <td>
3933                 <p>
3934                   <span class="blue">Max = 2.35e+03&#949; (Mean = 136&#949;)</span>
3935                 </p>
3936               </td>
3937 <td>
3938                 <p>
3939                   <span class="blue">Max = 2.35e+03&#949; (Mean = 136&#949;)</span>
3940                 </p>
3941               </td>
3942 <td>
3943                 <p>
3944                   <span class="blue">Max = 621&#949; (Mean = 36&#949;)</span>
3945                 </p>
3946               </td>
3947 </tr>
3948 <tr>
3949 <td>
3950                 <p>
3951                   Y'v: Random Data
3952                 </p>
3953               </td>
3954 <td>
3955                 <p>
3956                   <span class="blue">Max = 56.8&#949; (Mean = 2.59&#949;)</span>
3957                 </p>
3958               </td>
3959 <td>
3960                 <p>
3961                   <span class="blue">Max = 1.16e+05&#949; (Mean = 5.28e+03&#949;)</span>
3962                 </p>
3963               </td>
3964 <td>
3965                 <p>
3966                   <span class="blue">Max = 1.16e+05&#949; (Mean = 5.28e+03&#949;)</span>
3967                 </p>
3968               </td>
3969 <td>
3970                 <p>
3971                   <span class="blue">Max = 3.23e+04&#949; (Mean = 1.13e+03&#949;)</span>
3972                 </p>
3973               </td>
3974 </tr>
3975 </tbody>
3976 </table></div>
3977 </div>
3978 <br class="table-break"><div class="table">
3979 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_neumann_prime_integer_orders_"></a><p class="title"><b>Table&#160;22.25.&#160;Error rates for cyl_neumann_prime (integer orders)</b></p>
3980 <div class="table-contents"><table class="table" summary="Error rates for cyl_neumann_prime (integer orders)">
3981 <colgroup>
3982 <col>
3983 <col>
3984 <col>
3985 <col>
3986 <col>
3987 </colgroup>
3988 <thead><tr>
3989 <th>
3990               </th>
3991 <th>
3992                 <p>
3993                   GNU C++ version 7.1.0<br> linux<br> double
3994                 </p>
3995               </th>
3996 <th>
3997                 <p>
3998                   GNU C++ version 7.1.0<br> linux<br> long double
3999                 </p>
4000               </th>
4001 <th>
4002                 <p>
4003                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
4004                 </p>
4005               </th>
4006 <th>
4007                 <p>
4008                   Microsoft Visual C++ version 14.1<br> Win32<br> double
4009                 </p>
4010               </th>
4011 </tr></thead>
4012 <tbody>
4013 <tr>
4014 <td>
4015                 <p>
4016                   Y'0: Mathworld Data (Integer Version)
4017                 </p>
4018               </td>
4019 <td>
4020                 <p>
4021                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
4022                 </p>
4023               </td>
4024 <td>
4025                 <p>
4026                   <span class="blue">Max = 6.33&#949; (Mean = 3.12&#949;)</span>
4027                 </p>
4028               </td>
4029 <td>
4030                 <p>
4031                   <span class="blue">Max = 6.33&#949; (Mean = 3.14&#949;)</span>
4032                 </p>
4033               </td>
4034 <td>
4035                 <p>
4036                   <span class="blue">Max = 4.75&#949; (Mean = 1.75&#949;)</span>
4037                 </p>
4038               </td>
4039 </tr>
4040 <tr>
4041 <td>
4042                 <p>
4043                   Y'1: Mathworld Data (Integer Version)
4044                 </p>
4045               </td>
4046 <td>
4047                 <p>
4048                   <span class="blue">Max = 0.58&#949; (Mean = 0.193&#949;)</span>
4049                 </p>
4050               </td>
4051 <td>
4052                 <p>
4053                   <span class="blue">Max = 37.1&#949; (Mean = 12.8&#949;)</span>
4054                 </p>
4055               </td>
4056 <td>
4057                 <p>
4058                   <span class="blue">Max = 34&#949; (Mean = 11.8&#949;)</span>
4059                 </p>
4060               </td>
4061 <td>
4062                 <p>
4063                   <span class="blue">Max = 3.08&#949; (Mean = 1.2&#949;)</span>
4064                 </p>
4065               </td>
4066 </tr>
4067 <tr>
4068 <td>
4069                 <p>
4070                   Y'n: Mathworld Data (Integer Version)
4071                 </p>
4072               </td>
4073 <td>
4074                 <p>
4075                   <span class="blue">Max = 2.05&#949; (Mean = 0.677&#949;)</span>
4076                 </p>
4077               </td>
4078 <td>
4079                 <p>
4080                   <span class="blue">Max = 56&#949; (Mean = 18.2&#949;)</span>
4081                 </p>
4082               </td>
4083 <td>
4084                 <p>
4085                   <span class="blue">Max = 56&#949; (Mean = 21.3&#949;)</span>
4086                 </p>
4087               </td>
4088 <td>
4089                 <p>
4090                   <span class="blue">Max = 563&#949; (Mean = 178&#949;)</span>
4091                 </p>
4092               </td>
4093 </tr>
4094 </tbody>
4095 </table></div>
4096 </div>
4097 <br class="table-break"><div class="table">
4098 <a name="math_toolkit.logs_and_tables.all_table.table_digamma"></a><p class="title"><b>Table&#160;22.26.&#160;Error rates for digamma</b></p>
4099 <div class="table-contents"><table class="table" summary="Error rates for digamma">
4100 <colgroup>
4101 <col>
4102 <col>
4103 <col>
4104 <col>
4105 <col>
4106 </colgroup>
4107 <thead><tr>
4108 <th>
4109               </th>
4110 <th>
4111                 <p>
4112                   GNU C++ version 7.1.0<br> linux<br> double
4113                 </p>
4114               </th>
4115 <th>
4116                 <p>
4117                   GNU C++ version 7.1.0<br> linux<br> long double
4118                 </p>
4119               </th>
4120 <th>
4121                 <p>
4122                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
4123                 </p>
4124               </th>
4125 <th>
4126                 <p>
4127                   Microsoft Visual C++ version 14.1<br> Win32<br> double
4128                 </p>
4129               </th>
4130 </tr></thead>
4131 <tbody>
4132 <tr>
4133 <td>
4134                 <p>
4135                   Digamma Function: Large Values
4136                 </p>
4137               </td>
4138 <td>
4139                 <p>
4140                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
4141                   2.1:</em></span> Max = 1.84&#949; (Mean = 0.71&#949;))<br> (<span class="emphasis"><em>Rmath
4142                   3.2.3:</em></span> Max = 1.18&#949; (Mean = 0.331&#949;))
4143                 </p>
4144               </td>
4145 <td>
4146                 <p>
4147                   <span class="blue">Max = 1.39&#949; (Mean = 0.413&#949;)</span>
4148                 </p>
4149               </td>
4150 <td>
4151                 <p>
4152                   <span class="blue">Max = 1.39&#949; (Mean = 0.413&#949;)</span>
4153                 </p>
4154               </td>
4155 <td>
4156                 <p>
4157                   <span class="blue">Max = 0.98&#949; (Mean = 0.369&#949;)</span>
4158                 </p>
4159               </td>
4160 </tr>
4161 <tr>
4162 <td>
4163                 <p>
4164                   Digamma Function: Near the Positive Root
4165                 </p>
4166               </td>
4167 <td>
4168                 <p>
4169                   <span class="blue">Max = 0.891&#949; (Mean = 0.0995&#949;)</span><br>
4170                   <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 135&#949; (Mean = 11.9&#949;))<br>
4171                   (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.02e+03&#949; (Mean = 256&#949;))
4172                 </p>
4173               </td>
4174 <td>
4175                 <p>
4176                   <span class="blue">Max = 1.37&#949; (Mean = 0.477&#949;)</span>
4177                 </p>
4178               </td>
4179 <td>
4180                 <p>
4181                   <span class="blue">Max = 1.31&#949; (Mean = 0.471&#949;)</span>
4182                 </p>
4183               </td>
4184 <td>
4185                 <p>
4186                   <span class="blue">Max = 0.997&#949; (Mean = 0.527&#949;)</span>
4187                 </p>
4188               </td>
4189 </tr>
4190 <tr>
4191 <td>
4192                 <p>
4193                   Digamma Function: Near Zero
4194                 </p>
4195               </td>
4196 <td>
4197                 <p>
4198                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
4199                   2.1:</em></span> Max = 0.953&#949; (Mean = 0.348&#949;))<br> (<span class="emphasis"><em>Rmath
4200                   3.2.3:</em></span> Max = 1.17&#949; (Mean = 0.564&#949;))
4201                 </p>
4202               </td>
4203 <td>
4204                 <p>
4205                   <span class="blue">Max = 0.984&#949; (Mean = 0.361&#949;)</span>
4206                 </p>
4207               </td>
4208 <td>
4209                 <p>
4210                   <span class="blue">Max = 0.984&#949; (Mean = 0.361&#949;)</span>
4211                 </p>
4212               </td>
4213 <td>
4214                 <p>
4215                   <span class="blue">Max = 0.953&#949; (Mean = 0.337&#949;)</span>
4216                 </p>
4217               </td>
4218 </tr>
4219 <tr>
4220 <td>
4221                 <p>
4222                   Digamma Function: Negative Values
4223                 </p>
4224               </td>
4225 <td>
4226                 <p>
4227                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
4228                   2.1:</em></span> Max = 4.56e+04&#949; (Mean = 3.91e+03&#949;))<br> (<span class="emphasis"><em>Rmath
4229                   3.2.3:</em></span> Max = 4.6e+04&#949; (Mean = 3.94e+03&#949;))
4230                 </p>
4231               </td>
4232 <td>
4233                 <p>
4234                   <span class="blue">Max = 180&#949; (Mean = 13&#949;)</span>
4235                 </p>
4236               </td>
4237 <td>
4238                 <p>
4239                   <span class="blue">Max = 180&#949; (Mean = 13&#949;)</span>
4240                 </p>
4241               </td>
4242 <td>
4243                 <p>
4244                   <span class="blue">Max = 214&#949; (Mean = 16.1&#949;)</span>
4245                 </p>
4246               </td>
4247 </tr>
4248 <tr>
4249 <td>
4250                 <p>
4251                   Digamma Function: Values near 0
4252                 </p>
4253               </td>
4254 <td>
4255                 <p>
4256                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
4257                   2.1:</em></span> Max = 0.866&#949; (Mean = 0.387&#949;))<br> (<span class="emphasis"><em>Rmath
4258                   3.2.3:</em></span> Max = 3.58e+05&#949; (Mean = 1.6e+05&#949;))
4259                 </p>
4260               </td>
4261 <td>
4262                 <p>
4263                   <span class="blue">Max = 1&#949; (Mean = 0.592&#949;)</span>
4264                 </p>
4265               </td>
4266 <td>
4267                 <p>
4268                   <span class="blue">Max = 1&#949; (Mean = 0.592&#949;)</span>
4269                 </p>
4270               </td>
4271 <td>
4272                 <p>
4273                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
4274                 </p>
4275               </td>
4276 </tr>
4277 <tr>
4278 <td>
4279                 <p>
4280                   Digamma Function: Integer arguments
4281                 </p>
4282               </td>
4283 <td>
4284                 <p>
4285                   <span class="blue">Max = 0.992&#949; (Mean = 0.215&#949;)</span><br> <br>
4286                   (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.18&#949; (Mean = 0.607&#949;))<br>
4287                   (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 4.33&#949; (Mean = 0.982&#949;))
4288                 </p>
4289               </td>
4290 <td>
4291                 <p>
4292                   <span class="blue">Max = 0.888&#949; (Mean = 0.403&#949;)</span>
4293                 </p>
4294               </td>
4295 <td>
4296                 <p>
4297                   <span class="blue">Max = 0.888&#949; (Mean = 0.403&#949;)</span>
4298                 </p>
4299               </td>
4300 <td>
4301                 <p>
4302                   <span class="blue">Max = 0.992&#949; (Mean = 0.452&#949;)</span>
4303                 </p>
4304               </td>
4305 </tr>
4306 <tr>
4307 <td>
4308                 <p>
4309                   Digamma Function: Half integer arguments
4310                 </p>
4311               </td>
4312 <td>
4313                 <p>
4314                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
4315                   2.1:</em></span> Max = 1.09&#949; (Mean = 0.531&#949;))<br> (<span class="emphasis"><em>Rmath
4316                   3.2.3:</em></span> Max = 46.2&#949; (Mean = 7.24&#949;))
4317                 </p>
4318               </td>
4319 <td>
4320                 <p>
4321                   <span class="blue">Max = 0.906&#949; (Mean = 0.409&#949;)</span>
4322                 </p>
4323               </td>
4324 <td>
4325                 <p>
4326                   <span class="blue">Max = 0.906&#949; (Mean = 0.409&#949;)</span>
4327                 </p>
4328               </td>
4329 <td>
4330                 <p>
4331                   <span class="blue">Max = 0.78&#949; (Mean = 0.314&#949;)</span>
4332                 </p>
4333               </td>
4334 </tr>
4335 </tbody>
4336 </table></div>
4337 </div>
4338 <br class="table-break"><div class="table">
4339 <a name="math_toolkit.logs_and_tables.all_table.table_ellint_1"></a><p class="title"><b>Table&#160;22.27.&#160;Error rates for ellint_1</b></p>
4340 <div class="table-contents"><table class="table" summary="Error rates for ellint_1">
4341 <colgroup>
4342 <col>
4343 <col>
4344 <col>
4345 <col>
4346 <col>
4347 </colgroup>
4348 <thead><tr>
4349 <th>
4350               </th>
4351 <th>
4352                 <p>
4353                   GNU C++ version 7.1.0<br> linux<br> long double
4354                 </p>
4355               </th>
4356 <th>
4357                 <p>
4358                   GNU C++ version 7.1.0<br> linux<br> double
4359                 </p>
4360               </th>
4361 <th>
4362                 <p>
4363                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
4364                 </p>
4365               </th>
4366 <th>
4367                 <p>
4368                   Microsoft Visual C++ version 14.1<br> Win32<br> double
4369                 </p>
4370               </th>
4371 </tr></thead>
4372 <tbody>
4373 <tr>
4374 <td>
4375                 <p>
4376                   Elliptic Integral F: Mathworld Data
4377                 </p>
4378               </td>
4379 <td>
4380                 <p>
4381                   <span class="blue">Max = 0.94&#949; (Mean = 0.509&#949;)</span><br> <br>
4382                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = +INF&#949; (Mean
4383                   = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_1__cmath__Elliptic_Integral_F_Mathworld_Data">And
4384                   other failures.</a>)</span>
4385                 </p>
4386               </td>
4387 <td>
4388                 <p>
4389                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
4390                   2.1:</em></span> Max = 0.919&#949; (Mean = 0.544&#949;))
4391                 </p>
4392               </td>
4393 <td>
4394                 <p>
4395                   <span class="blue">Max = 0.94&#949; (Mean = 0.509&#949;)</span>
4396                 </p>
4397               </td>
4398 <td>
4399                 <p>
4400                   <span class="blue">Max = 0.919&#949; (Mean = 0.542&#949;)</span>
4401                 </p>
4402               </td>
4403 </tr>
4404 <tr>
4405 <td>
4406                 <p>
4407                   Elliptic Integral F: Random Data
4408                 </p>
4409               </td>
4410 <td>
4411                 <p>
4412                   <span class="blue">Max = 1.57&#949; (Mean = 0.56&#949;)</span><br> <br>
4413                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 2.56&#949; (Mean = 0.816&#949;))
4414                 </p>
4415               </td>
4416 <td>
4417                 <p>
4418                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
4419                   2.1:</em></span> Max = 2.99&#949; (Mean = 0.797&#949;))
4420                 </p>
4421               </td>
4422 <td>
4423                 <p>
4424                   <span class="blue">Max = 1.57&#949; (Mean = 0.561&#949;)</span>
4425                 </p>
4426               </td>
4427 <td>
4428                 <p>
4429                   <span class="blue">Max = 2.26&#949; (Mean = 0.631&#949;)</span>
4430                 </p>
4431               </td>
4432 </tr>
4433 </tbody>
4434 </table></div>
4435 </div>
4436 <br class="table-break"><div class="table">
4437 <a name="math_toolkit.logs_and_tables.all_table.table_ellint_1_complete_"></a><p class="title"><b>Table&#160;22.28.&#160;Error rates for ellint_1 (complete)</b></p>
4438 <div class="table-contents"><table class="table" summary="Error rates for ellint_1 (complete)">
4439 <colgroup>
4440 <col>
4441 <col>
4442 <col>
4443 <col>
4444 <col>
4445 </colgroup>
4446 <thead><tr>
4447 <th>
4448               </th>
4449 <th>
4450                 <p>
4451                   GNU C++ version 7.1.0<br> linux<br> long double
4452                 </p>
4453               </th>
4454 <th>
4455                 <p>
4456                   GNU C++ version 7.1.0<br> linux<br> double
4457                 </p>
4458               </th>
4459 <th>
4460                 <p>
4461                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
4462                 </p>
4463               </th>
4464 <th>
4465                 <p>
4466                   Microsoft Visual C++ version 14.1<br> Win32<br> double
4467                 </p>
4468               </th>
4469 </tr></thead>
4470 <tbody>
4471 <tr>
4472 <td>
4473                 <p>
4474                   Elliptic Integral K: Mathworld Data
4475                 </p>
4476               </td>
4477 <td>
4478                 <p>
4479                   <span class="blue">Max = 0.887&#949; (Mean = 0.296&#949;)</span><br> <br>
4480                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.19&#949; (Mean = 0.765&#949;))
4481                 </p>
4482               </td>
4483 <td>
4484                 <p>
4485                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
4486                   2.1:</em></span> Max = 0.623&#949; (Mean = 0.393&#949;))
4487                 </p>
4488               </td>
4489 <td>
4490                 <p>
4491                   <span class="blue">Max = 0.887&#949; (Mean = 0.296&#949;)</span>
4492                 </p>
4493               </td>
4494 <td>
4495                 <p>
4496                   <span class="blue">Max = 0.915&#949; (Mean = 0.547&#949;)</span>
4497                 </p>
4498               </td>
4499 </tr>
4500 <tr>
4501 <td>
4502                 <p>
4503                   Elliptic Integral K: Random Data
4504                 </p>
4505               </td>
4506 <td>
4507                 <p>
4508                   <span class="blue">Max = 1.27&#949; (Mean = 0.473&#949;)</span><br> <br>
4509                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 2.19&#949; (Mean = 0.694&#949;))
4510                 </p>
4511               </td>
4512 <td>
4513                 <p>
4514                   <span class="blue">Max = 0.851&#949; (Mean = 0.0851&#949;)</span><br>
4515                   <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.32&#949; (Mean = 0.688&#949;))
4516                 </p>
4517               </td>
4518 <td>
4519                 <p>
4520                   <span class="blue">Max = 1.27&#949; (Mean = 0.473&#949;)</span>
4521                 </p>
4522               </td>
4523 <td>
4524                 <p>
4525                   <span class="blue">Max = 0.958&#949; (Mean = 0.408&#949;)</span>
4526                 </p>
4527               </td>
4528 </tr>
4529 </tbody>
4530 </table></div>
4531 </div>
4532 <br class="table-break"><div class="table">
4533 <a name="math_toolkit.logs_and_tables.all_table.table_ellint_2"></a><p class="title"><b>Table&#160;22.29.&#160;Error rates for ellint_2</b></p>
4534 <div class="table-contents"><table class="table" summary="Error rates for ellint_2">
4535 <colgroup>
4536 <col>
4537 <col>
4538 <col>
4539 <col>
4540 <col>
4541 </colgroup>
4542 <thead><tr>
4543 <th>
4544               </th>
4545 <th>
4546                 <p>
4547                   GNU C++ version 7.1.0<br> linux<br> double
4548                 </p>
4549               </th>
4550 <th>
4551                 <p>
4552                   GNU C++ version 7.1.0<br> linux<br> long double
4553                 </p>
4554               </th>
4555 <th>
4556                 <p>
4557                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
4558                 </p>
4559               </th>
4560 <th>
4561                 <p>
4562                   Microsoft Visual C++ version 14.1<br> Win32<br> double
4563                 </p>
4564               </th>
4565 </tr></thead>
4566 <tbody>
4567 <tr>
4568 <td>
4569                 <p>
4570                   Elliptic Integral E: Mathworld Data
4571                 </p>
4572               </td>
4573 <td>
4574                 <p>
4575                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
4576                   2.1:</em></span> Max = 0.63&#949; (Mean = 0.325&#949;))
4577                 </p>
4578               </td>
4579 <td>
4580                 <p>
4581                   <span class="blue">Max = 0.656&#949; (Mean = 0.317&#949;)</span><br> <br>
4582                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = +INF&#949; (Mean
4583                   = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_2__cmath__Elliptic_Integral_E_Mathworld_Data">And
4584                   other failures.</a>)</span>
4585                 </p>
4586               </td>
4587 <td>
4588                 <p>
4589                   <span class="blue">Max = 0.656&#949; (Mean = 0.317&#949;)</span>
4590                 </p>
4591               </td>
4592 <td>
4593                 <p>
4594                   <span class="blue">Max = 1.31&#949; (Mean = 0.727&#949;)</span>
4595                 </p>
4596               </td>
4597 </tr>
4598 <tr>
4599 <td>
4600                 <p>
4601                   Elliptic Integral E: Random Data
4602                 </p>
4603               </td>
4604 <td>
4605                 <p>
4606                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
4607                   2.1:</em></span> Max = 4.4&#949; (Mean = 1.16&#949;))
4608                 </p>
4609               </td>
4610 <td>
4611                 <p>
4612                   <span class="blue">Max = 2.05&#949; (Mean = 0.632&#949;)</span><br> <br>
4613                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 3.08e+04&#949; (Mean = 3.84e+03&#949;))
4614                 </p>
4615               </td>
4616 <td>
4617                 <p>
4618                   <span class="blue">Max = 2.05&#949; (Mean = 0.632&#949;)</span>
4619                 </p>
4620               </td>
4621 <td>
4622                 <p>
4623                   <span class="blue">Max = 2.23&#949; (Mean = 0.639&#949;)</span>
4624                 </p>
4625               </td>
4626 </tr>
4627 <tr>
4628 <td>
4629                 <p>
4630                   Elliptic Integral E: Small Angles
4631                 </p>
4632               </td>
4633 <td>
4634                 <p>
4635                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
4636                   2.1:</em></span> Max = 0.5&#949; (Mean = 0.118&#949;))
4637                 </p>
4638               </td>
4639 <td>
4640                 <p>
4641                   <span class="blue">Max = 1&#949; (Mean = 0.283&#949;)</span><br> <br>
4642                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 2&#949; (Mean = 0.333&#949;))
4643                 </p>
4644               </td>
4645 <td>
4646                 <p>
4647                   <span class="blue">Max = 1&#949; (Mean = 0.283&#949;)</span>
4648                 </p>
4649               </td>
4650 <td>
4651                 <p>
4652                   <span class="blue">Max = 1&#949; (Mean = 0.421&#949;)</span>
4653                 </p>
4654               </td>
4655 </tr>
4656 </tbody>
4657 </table></div>
4658 </div>
4659 <br class="table-break"><div class="table">
4660 <a name="math_toolkit.logs_and_tables.all_table.table_ellint_2_complete_"></a><p class="title"><b>Table&#160;22.30.&#160;Error rates for ellint_2 (complete)</b></p>
4661 <div class="table-contents"><table class="table" summary="Error rates for ellint_2 (complete)">
4662 <colgroup>
4663 <col>
4664 <col>
4665 <col>
4666 <col>
4667 <col>
4668 </colgroup>
4669 <thead><tr>
4670 <th>
4671               </th>
4672 <th>
4673                 <p>
4674                   GNU C++ version 7.1.0<br> linux<br> double
4675                 </p>
4676               </th>
4677 <th>
4678                 <p>
4679                   GNU C++ version 7.1.0<br> linux<br> long double
4680                 </p>
4681               </th>
4682 <th>
4683                 <p>
4684                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
4685                 </p>
4686               </th>
4687 <th>
4688                 <p>
4689                   Microsoft Visual C++ version 14.1<br> Win32<br> double
4690                 </p>
4691               </th>
4692 </tr></thead>
4693 <tbody>
4694 <tr>
4695 <td>
4696                 <p>
4697                   Elliptic Integral E: Mathworld Data
4698                 </p>
4699               </td>
4700 <td>
4701                 <p>
4702                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
4703                   2.1:</em></span> Max = 3.09&#949; (Mean = 1.04&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_ellint_2_complete__GSL_2_1_Elliptic_Integral_E_Mathworld_Data">And
4704                   other failures.</a>)
4705                 </p>
4706               </td>
4707 <td>
4708                 <p>
4709                   <span class="blue">Max = 0.836&#949; (Mean = 0.469&#949;)</span><br> <br>
4710                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 170&#949; (Mean = 55.1&#949;))
4711                 </p>
4712               </td>
4713 <td>
4714                 <p>
4715                   <span class="blue">Max = 0.836&#949; (Mean = 0.469&#949;)</span>
4716                 </p>
4717               </td>
4718 <td>
4719                 <p>
4720                   <span class="blue">Max = 1.3&#949; (Mean = 0.615&#949;)</span>
4721                 </p>
4722               </td>
4723 </tr>
4724 <tr>
4725 <td>
4726                 <p>
4727                   Elliptic Integral E: Random Data
4728                 </p>
4729               </td>
4730 <td>
4731                 <p>
4732                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
4733                   2.1:</em></span> Max = 4.34&#949; (Mean = 1.18&#949;))
4734                 </p>
4735               </td>
4736 <td>
4737                 <p>
4738                   <span class="blue">Max = 1.97&#949; (Mean = 0.629&#949;)</span><br> <br>
4739                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 2.49e+04&#949; (Mean = 3.39e+03&#949;))
4740                 </p>
4741               </td>
4742 <td>
4743                 <p>
4744                   <span class="blue">Max = 1.97&#949; (Mean = 0.629&#949;)</span>
4745                 </p>
4746               </td>
4747 <td>
4748                 <p>
4749                   <span class="blue">Max = 1.71&#949; (Mean = 0.553&#949;)</span>
4750                 </p>
4751               </td>
4752 </tr>
4753 </tbody>
4754 </table></div>
4755 </div>
4756 <br class="table-break"><div class="table">
4757 <a name="math_toolkit.logs_and_tables.all_table.table_ellint_3"></a><p class="title"><b>Table&#160;22.31.&#160;Error rates for ellint_3</b></p>
4758 <div class="table-contents"><table class="table" summary="Error rates for ellint_3">
4759 <colgroup>
4760 <col>
4761 <col>
4762 <col>
4763 <col>
4764 <col>
4765 </colgroup>
4766 <thead><tr>
4767 <th>
4768               </th>
4769 <th>
4770                 <p>
4771                   GNU C++ version 7.1.0<br> linux<br> long double
4772                 </p>
4773               </th>
4774 <th>
4775                 <p>
4776                   GNU C++ version 7.1.0<br> linux<br> double
4777                 </p>
4778               </th>
4779 <th>
4780                 <p>
4781                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
4782                 </p>
4783               </th>
4784 <th>
4785                 <p>
4786                   Microsoft Visual C++ version 14.1<br> Win32<br> double
4787                 </p>
4788               </th>
4789 </tr></thead>
4790 <tbody>
4791 <tr>
4792 <td>
4793                 <p>
4794                   Elliptic Integral PI: Mathworld Data
4795                 </p>
4796               </td>
4797 <td>
4798                 <p>
4799                   <span class="blue">Max = 475&#949; (Mean = 86.3&#949;)</span><br> <br>
4800                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = +INF&#949; (Mean
4801                   = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Mathworld_Data">And
4802                   other failures.</a>)</span>
4803                 </p>
4804               </td>
4805 <td>
4806                 <p>
4807                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
4808                   2.1:</em></span> Max = 1.48e+05&#949; (Mean = 2.54e+04&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_ellint_3_GSL_2_1_Elliptic_Integral_PI_Mathworld_Data">And
4809                   other failures.</a>)
4810                 </p>
4811               </td>
4812 <td>
4813                 <p>
4814                   <span class="blue">Max = 475&#949; (Mean = 86.3&#949;)</span>
4815                 </p>
4816               </td>
4817 <td>
4818                 <p>
4819                   <span class="blue">Max = 565&#949; (Mean = 102&#949;)</span>
4820                 </p>
4821               </td>
4822 </tr>
4823 <tr>
4824 <td>
4825                 <p>
4826                   Elliptic Integral PI: Random Data
4827                 </p>
4828               </td>
4829 <td>
4830                 <p>
4831                   <span class="blue">Max = 4.54&#949; (Mean = 0.895&#949;)</span><br> <br>
4832                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = 3.37e+20&#949; (Mean
4833                   = 3.47e+19&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Random_Data">And
4834                   other failures.</a>)</span>
4835                 </p>
4836               </td>
4837 <td>
4838                 <p>
4839                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
4840                   2.1:</em></span> Max = 633&#949; (Mean = 50.1&#949;))
4841                 </p>
4842               </td>
4843 <td>
4844                 <p>
4845                   <span class="blue">Max = 4.49&#949; (Mean = 0.885&#949;)</span>
4846                 </p>
4847               </td>
4848 <td>
4849                 <p>
4850                   <span class="blue">Max = 8.33&#949; (Mean = 0.971&#949;)</span>
4851                 </p>
4852               </td>
4853 </tr>
4854 <tr>
4855 <td>
4856                 <p>
4857                   Elliptic Integral PI: Large Random Data
4858                 </p>
4859               </td>
4860 <td>
4861                 <p>
4862                   <span class="blue">Max = 3.7&#949; (Mean = 0.893&#949;)</span><br> <br>
4863                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = 2.52e+18&#949; (Mean
4864                   = 4.83e+17&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Large_Random_Data">And
4865                   other failures.</a>)</span>
4866                 </p>
4867               </td>
4868 <td>
4869                 <p>
4870                   <span class="blue">Max = 0.557&#949; (Mean = 0.0389&#949;)</span><br>
4871                   <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 40.1&#949; (Mean = 7.77&#949;))
4872                 </p>
4873               </td>
4874 <td>
4875                 <p>
4876                   <span class="blue">Max = 3.7&#949; (Mean = 0.892&#949;)</span>
4877                 </p>
4878               </td>
4879 <td>
4880                 <p>
4881                   <span class="blue">Max = 2.86&#949; (Mean = 0.944&#949;)</span>
4882                 </p>
4883               </td>
4884 </tr>
4885 </tbody>
4886 </table></div>
4887 </div>
4888 <br class="table-break"><div class="table">
4889 <a name="math_toolkit.logs_and_tables.all_table.table_ellint_3_complete_"></a><p class="title"><b>Table&#160;22.32.&#160;Error rates for ellint_3 (complete)</b></p>
4890 <div class="table-contents"><table class="table" summary="Error rates for ellint_3 (complete)">
4891 <colgroup>
4892 <col>
4893 <col>
4894 <col>
4895 <col>
4896 <col>
4897 </colgroup>
4898 <thead><tr>
4899 <th>
4900               </th>
4901 <th>
4902                 <p>
4903                   GNU C++ version 7.1.0<br> linux<br> long double
4904                 </p>
4905               </th>
4906 <th>
4907                 <p>
4908                   GNU C++ version 7.1.0<br> linux<br> double
4909                 </p>
4910               </th>
4911 <th>
4912                 <p>
4913                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
4914                 </p>
4915               </th>
4916 <th>
4917                 <p>
4918                   Microsoft Visual C++ version 14.1<br> Win32<br> double
4919                 </p>
4920               </th>
4921 </tr></thead>
4922 <tbody>
4923 <tr>
4924 <td>
4925                 <p>
4926                   Complete Elliptic Integral PI: Mathworld Data
4927                 </p>
4928               </td>
4929 <td>
4930                 <p>
4931                   <span class="blue">Max = 1.4&#949; (Mean = 0.575&#949;)</span><br> <br>
4932                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = 6.31e+20&#949; (Mean
4933                   = 1.53e+20&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3_complete___cmath__Complete_Elliptic_Integral_PI_Mathworld_Data">And
4934                   other failures.</a>)</span>
4935                 </p>
4936               </td>
4937 <td>
4938                 <p>
4939                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
4940                   2.1:</em></span> Max = 6.33e+04&#949; (Mean = 1.54e+04&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_ellint_3_complete__GSL_2_1_Complete_Elliptic_Integral_PI_Mathworld_Data">And
4941                   other failures.</a>)
4942                 </p>
4943               </td>
4944 <td>
4945                 <p>
4946                   <span class="blue">Max = 1.4&#949; (Mean = 0.575&#949;)</span>
4947                 </p>
4948               </td>
4949 <td>
4950                 <p>
4951                   <span class="blue">Max = 0.971&#949; (Mean = 0.464&#949;)</span>
4952                 </p>
4953               </td>
4954 </tr>
4955 <tr>
4956 <td>
4957                 <p>
4958                   Complete Elliptic Integral PI: Random Data
4959                 </p>
4960               </td>
4961 <td>
4962                 <p>
4963                   <span class="blue">Max = 2.45&#949; (Mean = 0.696&#949;)</span><br> <br>
4964                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = 8.78e+20&#949; (Mean
4965                   = 1.02e+20&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3_complete___cmath__Complete_Elliptic_Integral_PI_Random_Data">And
4966                   other failures.</a>)</span>
4967                 </p>
4968               </td>
4969 <td>
4970                 <p>
4971                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
4972                   2.1:</em></span> Max = 24&#949; (Mean = 2.99&#949;))
4973                 </p>
4974               </td>
4975 <td>
4976                 <p>
4977                   <span class="blue">Max = 2.4&#949; (Mean = 0.677&#949;)</span>
4978                 </p>
4979               </td>
4980 <td>
4981                 <p>
4982                   <span class="blue">Max = 2.46&#949; (Mean = 0.657&#949;)</span>
4983                 </p>
4984               </td>
4985 </tr>
4986 </tbody>
4987 </table></div>
4988 </div>
4989 <br class="table-break"><div class="table">
4990 <a name="math_toolkit.logs_and_tables.all_table.table_ellint_d"></a><p class="title"><b>Table&#160;22.33.&#160;Error rates for ellint_d</b></p>
4991 <div class="table-contents"><table class="table" summary="Error rates for ellint_d">
4992 <colgroup>
4993 <col>
4994 <col>
4995 <col>
4996 <col>
4997 <col>
4998 </colgroup>
4999 <thead><tr>
5000 <th>
5001               </th>
5002 <th>
5003                 <p>
5004                   GNU C++ version 7.1.0<br> linux<br> double
5005                 </p>
5006               </th>
5007 <th>
5008                 <p>
5009                   GNU C++ version 7.1.0<br> linux<br> long double
5010                 </p>
5011               </th>
5012 <th>
5013                 <p>
5014                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
5015                 </p>
5016               </th>
5017 <th>
5018                 <p>
5019                   Microsoft Visual C++ version 14.1<br> Win32<br> double
5020                 </p>
5021               </th>
5022 </tr></thead>
5023 <tbody>
5024 <tr>
5025 <td>
5026                 <p>
5027                   Elliptic Integral E: Mathworld Data
5028                 </p>
5029               </td>
5030 <td>
5031                 <p>
5032                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5033                   2.1:</em></span> Max = 0.862&#949; (Mean = 0.568&#949;))
5034                 </p>
5035               </td>
5036 <td>
5037                 <p>
5038                   <span class="blue">Max = 1.3&#949; (Mean = 0.813&#949;)</span>
5039                 </p>
5040               </td>
5041 <td>
5042                 <p>
5043                   <span class="blue">Max = 1.3&#949; (Mean = 0.813&#949;)</span>
5044                 </p>
5045               </td>
5046 <td>
5047                 <p>
5048                   <span class="blue">Max = 0.862&#949; (Mean = 0.457&#949;)</span>
5049                 </p>
5050               </td>
5051 </tr>
5052 <tr>
5053 <td>
5054                 <p>
5055                   Elliptic Integral D: Random Data
5056                 </p>
5057               </td>
5058 <td>
5059                 <p>
5060                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5061                   2.1:</em></span> Max = 3.01&#949; (Mean = 0.928&#949;))
5062                 </p>
5063               </td>
5064 <td>
5065                 <p>
5066                   <span class="blue">Max = 2.51&#949; (Mean = 0.883&#949;)</span>
5067                 </p>
5068               </td>
5069 <td>
5070                 <p>
5071                   <span class="blue">Max = 2.51&#949; (Mean = 0.883&#949;)</span>
5072                 </p>
5073               </td>
5074 <td>
5075                 <p>
5076                   <span class="blue">Max = 2.87&#949; (Mean = 0.805&#949;)</span>
5077                 </p>
5078               </td>
5079 </tr>
5080 </tbody>
5081 </table></div>
5082 </div>
5083 <br class="table-break"><div class="table">
5084 <a name="math_toolkit.logs_and_tables.all_table.table_ellint_d_complete_"></a><p class="title"><b>Table&#160;22.34.&#160;Error rates for ellint_d (complete)</b></p>
5085 <div class="table-contents"><table class="table" summary="Error rates for ellint_d (complete)">
5086 <colgroup>
5087 <col>
5088 <col>
5089 <col>
5090 <col>
5091 <col>
5092 </colgroup>
5093 <thead><tr>
5094 <th>
5095               </th>
5096 <th>
5097                 <p>
5098                   GNU C++ version 7.1.0<br> linux<br> double
5099                 </p>
5100               </th>
5101 <th>
5102                 <p>
5103                   GNU C++ version 7.1.0<br> linux<br> long double
5104                 </p>
5105               </th>
5106 <th>
5107                 <p>
5108                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
5109                 </p>
5110               </th>
5111 <th>
5112                 <p>
5113                   Microsoft Visual C++ version 14.1<br> Win32<br> double
5114                 </p>
5115               </th>
5116 </tr></thead>
5117 <tbody>
5118 <tr>
5119 <td>
5120                 <p>
5121                   Elliptic Integral E: Mathworld Data
5122                 </p>
5123               </td>
5124 <td>
5125                 <p>
5126                   <span class="blue">Max = 0.637&#949; (Mean = 0.368&#949;)</span>
5127                 </p>
5128               </td>
5129 <td>
5130                 <p>
5131                   <span class="blue">Max = 1.27&#949; (Mean = 0.735&#949;)</span>
5132                 </p>
5133               </td>
5134 <td>
5135                 <p>
5136                   <span class="blue">Max = 1.27&#949; (Mean = 0.735&#949;)</span>
5137                 </p>
5138               </td>
5139 <td>
5140                 <p>
5141                   <span class="blue">Max = 0.637&#949; (Mean = 0.368&#949;)</span>
5142                 </p>
5143               </td>
5144 </tr>
5145 <tr>
5146 <td>
5147                 <p>
5148                   Elliptic Integral D: Random Data
5149                 </p>
5150               </td>
5151 <td>
5152                 <p>
5153                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
5154                 </p>
5155               </td>
5156 <td>
5157                 <p>
5158                   <span class="blue">Max = 1.27&#949; (Mean = 0.334&#949;)</span>
5159                 </p>
5160               </td>
5161 <td>
5162                 <p>
5163                   <span class="blue">Max = 1.27&#949; (Mean = 0.334&#949;)</span>
5164                 </p>
5165               </td>
5166 <td>
5167                 <p>
5168                   <span class="blue">Max = 1.27&#949; (Mean = 0.355&#949;)</span>
5169                 </p>
5170               </td>
5171 </tr>
5172 </tbody>
5173 </table></div>
5174 </div>
5175 <br class="table-break"><div class="table">
5176 <a name="math_toolkit.logs_and_tables.all_table.table_ellint_rc"></a><p class="title"><b>Table&#160;22.35.&#160;Error rates for ellint_rc</b></p>
5177 <div class="table-contents"><table class="table" summary="Error rates for ellint_rc">
5178 <colgroup>
5179 <col>
5180 <col>
5181 <col>
5182 <col>
5183 </colgroup>
5184 <thead><tr>
5185 <th>
5186               </th>
5187 <th>
5188                 <p>
5189                   GNU C++ version 7.1.0<br> linux<br> double
5190                 </p>
5191               </th>
5192 <th>
5193                 <p>
5194                   GNU C++ version 7.1.0<br> linux<br> long double
5195                 </p>
5196               </th>
5197 <th>
5198                 <p>
5199                   Microsoft Visual C++ version 14.1<br> Win32<br> double
5200                 </p>
5201               </th>
5202 </tr></thead>
5203 <tbody><tr>
5204 <td>
5205                 <p>
5206                   RC: Random data
5207                 </p>
5208               </td>
5209 <td>
5210                 <p>
5211                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5212                   2.1:</em></span> Max = 2.4&#949; (Mean = 0.624&#949;))
5213                 </p>
5214               </td>
5215 <td>
5216                 <p>
5217                   <span class="blue">Max = 0.995&#949; (Mean = 0.433&#949;)</span>
5218                 </p>
5219               </td>
5220 <td>
5221                 <p>
5222                   <span class="blue">Max = 0.962&#949; (Mean = 0.407&#949;)</span>
5223                 </p>
5224               </td>
5225 </tr></tbody>
5226 </table></div>
5227 </div>
5228 <br class="table-break"><div class="table">
5229 <a name="math_toolkit.logs_and_tables.all_table.table_ellint_rd"></a><p class="title"><b>Table&#160;22.36.&#160;Error rates for ellint_rd</b></p>
5230 <div class="table-contents"><table class="table" summary="Error rates for ellint_rd">
5231 <colgroup>
5232 <col>
5233 <col>
5234 <col>
5235 <col>
5236 </colgroup>
5237 <thead><tr>
5238 <th>
5239               </th>
5240 <th>
5241                 <p>
5242                   GNU C++ version 7.1.0<br> linux<br> double
5243                 </p>
5244               </th>
5245 <th>
5246                 <p>
5247                   GNU C++ version 7.1.0<br> linux<br> long double
5248                 </p>
5249               </th>
5250 <th>
5251                 <p>
5252                   Microsoft Visual C++ version 14.1<br> Win32<br> double
5253                 </p>
5254               </th>
5255 </tr></thead>
5256 <tbody>
5257 <tr>
5258 <td>
5259                 <p>
5260                   RD: Random data
5261                 </p>
5262               </td>
5263 <td>
5264                 <p>
5265                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5266                   2.1:</em></span> Max = 2.59&#949; (Mean = 0.878&#949;))
5267                 </p>
5268               </td>
5269 <td>
5270                 <p>
5271                   <span class="blue">Max = 2.73&#949; (Mean = 0.831&#949;)</span>
5272                 </p>
5273               </td>
5274 <td>
5275                 <p>
5276                   <span class="blue">Max = 2.16&#949; (Mean = 0.803&#949;)</span>
5277                 </p>
5278               </td>
5279 </tr>
5280 <tr>
5281 <td>
5282                 <p>
5283                   RD: y = z
5284                 </p>
5285               </td>
5286 <td>
5287                 <p>
5288                   <span class="blue">Max = 0.896&#949; (Mean = 0.022&#949;)</span><br> <br>
5289                   (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.88&#949; (Mean = 0.839&#949;))
5290                 </p>
5291               </td>
5292 <td>
5293                 <p>
5294                   <span class="blue">Max = 2.65&#949; (Mean = 0.82&#949;)</span>
5295                 </p>
5296               </td>
5297 <td>
5298                 <p>
5299                   <span class="blue">Max = 16.5&#949; (Mean = 0.843&#949;)</span>
5300                 </p>
5301               </td>
5302 </tr>
5303 <tr>
5304 <td>
5305                 <p>
5306                   RD: x = y
5307                 </p>
5308               </td>
5309 <td>
5310                 <p>
5311                   <span class="blue">Max = 0.824&#949; (Mean = 0.0272&#949;)</span><br>
5312                   <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.74&#949; (Mean = 0.84&#949;))
5313                 </p>
5314               </td>
5315 <td>
5316                 <p>
5317                   <span class="blue">Max = 2.85&#949; (Mean = 0.865&#949;)</span>
5318                 </p>
5319               </td>
5320 <td>
5321                 <p>
5322                   <span class="blue">Max = 3.51&#949; (Mean = 0.816&#949;)</span>
5323                 </p>
5324               </td>
5325 </tr>
5326 <tr>
5327 <td>
5328                 <p>
5329                   RD: x = 0, y = z
5330                 </p>
5331               </td>
5332 <td>
5333                 <p>
5334                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5335                   2.1:</em></span> Max = 2&#949; (Mean = 0.656&#949;))
5336                 </p>
5337               </td>
5338 <td>
5339                 <p>
5340                   <span class="blue">Max = 1.19&#949; (Mean = 0.522&#949;)</span>
5341                 </p>
5342               </td>
5343 <td>
5344                 <p>
5345                   <span class="blue">Max = 1.16&#949; (Mean = 0.497&#949;)</span>
5346                 </p>
5347               </td>
5348 </tr>
5349 <tr>
5350 <td>
5351                 <p>
5352                   RD: x = y = z
5353                 </p>
5354               </td>
5355 <td>
5356                 <p>
5357                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5358                   2.1:</em></span> Max = 1.03&#949; (Mean = 0.418&#949;))
5359                 </p>
5360               </td>
5361 <td>
5362                 <p>
5363                   <span class="blue">Max = 0.998&#949; (Mean = 0.387&#949;)</span>
5364                 </p>
5365               </td>
5366 <td>
5367                 <p>
5368                   <span class="blue">Max = 1.03&#949; (Mean = 0.418&#949;)</span>
5369                 </p>
5370               </td>
5371 </tr>
5372 <tr>
5373 <td>
5374                 <p>
5375                   RD: x = 0
5376                 </p>
5377               </td>
5378 <td>
5379                 <p>
5380                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5381                   2.1:</em></span> Max = 2.85&#949; (Mean = 0.781&#949;))
5382                 </p>
5383               </td>
5384 <td>
5385                 <p>
5386                   <span class="blue">Max = 2.79&#949; (Mean = 0.883&#949;)</span>
5387                 </p>
5388               </td>
5389 <td>
5390                 <p>
5391                   <span class="blue">Max = 2.64&#949; (Mean = 0.894&#949;)</span>
5392                 </p>
5393               </td>
5394 </tr>
5395 </tbody>
5396 </table></div>
5397 </div>
5398 <br class="table-break"><div class="table">
5399 <a name="math_toolkit.logs_and_tables.all_table.table_ellint_rf"></a><p class="title"><b>Table&#160;22.37.&#160;Error rates for ellint_rf</b></p>
5400 <div class="table-contents"><table class="table" summary="Error rates for ellint_rf">
5401 <colgroup>
5402 <col>
5403 <col>
5404 <col>
5405 <col>
5406 </colgroup>
5407 <thead><tr>
5408 <th>
5409               </th>
5410 <th>
5411                 <p>
5412                   GNU C++ version 7.1.0<br> linux<br> double
5413                 </p>
5414               </th>
5415 <th>
5416                 <p>
5417                   GNU C++ version 7.1.0<br> linux<br> long double
5418                 </p>
5419               </th>
5420 <th>
5421                 <p>
5422                   Microsoft Visual C++ version 14.1<br> Win32<br> double
5423                 </p>
5424               </th>
5425 </tr></thead>
5426 <tbody>
5427 <tr>
5428 <td>
5429                 <p>
5430                   RF: Random data
5431                 </p>
5432               </td>
5433 <td>
5434                 <p>
5435                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5436                   2.1:</em></span> Max = 2.73&#949; (Mean = 0.804&#949;))
5437                 </p>
5438               </td>
5439 <td>
5440                 <p>
5441                   <span class="blue">Max = 2.54&#949; (Mean = 0.674&#949;)</span>
5442                 </p>
5443               </td>
5444 <td>
5445                 <p>
5446                   <span class="blue">Max = 2.02&#949; (Mean = 0.677&#949;)</span>
5447                 </p>
5448               </td>
5449 </tr>
5450 <tr>
5451 <td>
5452                 <p>
5453                   RF: x = y = z
5454                 </p>
5455               </td>
5456 <td>
5457                 <p>
5458                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5459                   2.1:</em></span> Max = 0.999&#949; (Mean = 0.34&#949;))
5460                 </p>
5461               </td>
5462 <td>
5463                 <p>
5464                   <span class="blue">Max = 0.991&#949; (Mean = 0.345&#949;)</span>
5465                 </p>
5466               </td>
5467 <td>
5468                 <p>
5469                   <span class="blue">Max = 0.999&#949; (Mean = 0.34&#949;)</span>
5470                 </p>
5471               </td>
5472 </tr>
5473 <tr>
5474 <td>
5475                 <p>
5476                   RF: x = y or y = z or x = z
5477                 </p>
5478               </td>
5479 <td>
5480                 <p>
5481                   <span class="blue">Max = 0.536&#949; (Mean = 0.00658&#949;)</span><br>
5482                   <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.89&#949; (Mean = 0.749&#949;))
5483                 </p>
5484               </td>
5485 <td>
5486                 <p>
5487                   <span class="blue">Max = 1.95&#949; (Mean = 0.418&#949;)</span>
5488                 </p>
5489               </td>
5490 <td>
5491                 <p>
5492                   <span class="blue">Max = 1.21&#949; (Mean = 0.394&#949;)</span>
5493                 </p>
5494               </td>
5495 </tr>
5496 <tr>
5497 <td>
5498                 <p>
5499                   RF: x = 0, y = z
5500                 </p>
5501               </td>
5502 <td>
5503                 <p>
5504                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5505                   2.1:</em></span> Max = 1.29&#949; (Mean = 0.527&#949;))
5506                 </p>
5507               </td>
5508 <td>
5509                 <p>
5510                   <span class="blue">Max = 0.894&#949; (Mean = 0.338&#949;)</span>
5511                 </p>
5512               </td>
5513 <td>
5514                 <p>
5515                   <span class="blue">Max = 0.999&#949; (Mean = 0.407&#949;)</span>
5516                 </p>
5517               </td>
5518 </tr>
5519 <tr>
5520 <td>
5521                 <p>
5522                   RF: z = 0
5523                 </p>
5524               </td>
5525 <td>
5526                 <p>
5527                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5528                   2.1:</em></span> Max = 2.54&#949; (Mean = 0.781&#949;))
5529                 </p>
5530               </td>
5531 <td>
5532                 <p>
5533                   <span class="blue">Max = 1.7&#949; (Mean = 0.539&#949;)</span>
5534                 </p>
5535               </td>
5536 <td>
5537                 <p>
5538                   <span class="blue">Max = 1.89&#949; (Mean = 0.587&#949;)</span>
5539                 </p>
5540               </td>
5541 </tr>
5542 </tbody>
5543 </table></div>
5544 </div>
5545 <br class="table-break"><div class="table">
5546 <a name="math_toolkit.logs_and_tables.all_table.table_ellint_rg"></a><p class="title"><b>Table&#160;22.38.&#160;Error rates for ellint_rg</b></p>
5547 <div class="table-contents"><table class="table" summary="Error rates for ellint_rg">
5548 <colgroup>
5549 <col>
5550 <col>
5551 <col>
5552 <col>
5553 </colgroup>
5554 <thead><tr>
5555 <th>
5556               </th>
5557 <th>
5558                 <p>
5559                   GNU C++ version 7.1.0<br> linux<br> double
5560                 </p>
5561               </th>
5562 <th>
5563                 <p>
5564                   GNU C++ version 7.1.0<br> linux<br> long double
5565                 </p>
5566               </th>
5567 <th>
5568                 <p>
5569                   Microsoft Visual C++ version 14.1<br> Win32<br> double
5570                 </p>
5571               </th>
5572 </tr></thead>
5573 <tbody>
5574 <tr>
5575 <td>
5576                 <p>
5577                   RG: Random Data
5578                 </p>
5579               </td>
5580 <td>
5581                 <p>
5582                   <span class="blue">Max = 0.983&#949; (Mean = 0.0172&#949;)</span><br>
5583                   <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.983&#949; (Mean = 0.0172&#949;))
5584                 </p>
5585               </td>
5586 <td>
5587                 <p>
5588                   <span class="blue">Max = 3.95&#949; (Mean = 0.951&#949;)</span>
5589                 </p>
5590               </td>
5591 <td>
5592                 <p>
5593                   <span class="blue">Max = 3.65&#949; (Mean = 0.929&#949;)</span>
5594                 </p>
5595               </td>
5596 </tr>
5597 <tr>
5598 <td>
5599                 <p>
5600                   RG: two values 0
5601                 </p>
5602               </td>
5603 <td>
5604                 <p>
5605                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5606                   2.1:</em></span> Max = 0&#949; (Mean = 0&#949;))
5607                 </p>
5608               </td>
5609 <td>
5610                 <p>
5611                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
5612                 </p>
5613               </td>
5614 <td>
5615                 <p>
5616                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
5617                 </p>
5618               </td>
5619 </tr>
5620 <tr>
5621 <td>
5622                 <p>
5623                   RG: All values the same or zero
5624                 </p>
5625               </td>
5626 <td>
5627                 <p>
5628                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5629                   2.1:</em></span> Max = 0&#949; (Mean = 0&#949;))
5630                 </p>
5631               </td>
5632 <td>
5633                 <p>
5634                   <span class="blue">Max = 0.992&#949; (Mean = 0.288&#949;)</span>
5635                 </p>
5636               </td>
5637 <td>
5638                 <p>
5639                   <span class="blue">Max = 1.06&#949; (Mean = 0.348&#949;)</span>
5640                 </p>
5641               </td>
5642 </tr>
5643 <tr>
5644 <td>
5645                 <p>
5646                   RG: two values the same
5647                 </p>
5648               </td>
5649 <td>
5650                 <p>
5651                   <span class="blue">Max = 0.594&#949; (Mean = 0.0103&#949;)</span><br>
5652                   <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.594&#949; (Mean = 0.0103&#949;))
5653                 </p>
5654               </td>
5655 <td>
5656                 <p>
5657                   <span class="blue">Max = 1.51&#949; (Mean = 0.404&#949;)</span>
5658                 </p>
5659               </td>
5660 <td>
5661                 <p>
5662                   <span class="blue">Max = 1.96&#949; (Mean = 0.374&#949;)</span>
5663                 </p>
5664               </td>
5665 </tr>
5666 <tr>
5667 <td>
5668                 <p>
5669                   RG: one value zero
5670                 </p>
5671               </td>
5672 <td>
5673                 <p>
5674                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5675                   2.1:</em></span> Max = 0&#949; (Mean = 0&#949;))
5676                 </p>
5677               </td>
5678 <td>
5679                 <p>
5680                   <span class="blue">Max = 2.14&#949; (Mean = 0.722&#949;)</span>
5681                 </p>
5682               </td>
5683 <td>
5684                 <p>
5685                   <span class="blue">Max = 1.96&#949; (Mean = 0.674&#949;)</span>
5686                 </p>
5687               </td>
5688 </tr>
5689 </tbody>
5690 </table></div>
5691 </div>
5692 <br class="table-break"><div class="table">
5693 <a name="math_toolkit.logs_and_tables.all_table.table_ellint_rj"></a><p class="title"><b>Table&#160;22.39.&#160;Error rates for ellint_rj</b></p>
5694 <div class="table-contents"><table class="table" summary="Error rates for ellint_rj">
5695 <colgroup>
5696 <col>
5697 <col>
5698 <col>
5699 <col>
5700 </colgroup>
5701 <thead><tr>
5702 <th>
5703               </th>
5704 <th>
5705                 <p>
5706                   GNU C++ version 7.1.0<br> linux<br> double
5707                 </p>
5708               </th>
5709 <th>
5710                 <p>
5711                   GNU C++ version 7.1.0<br> linux<br> long double
5712                 </p>
5713               </th>
5714 <th>
5715                 <p>
5716                   Microsoft Visual C++ version 14.1<br> Win32<br> double
5717                 </p>
5718               </th>
5719 </tr></thead>
5720 <tbody>
5721 <tr>
5722 <td>
5723                 <p>
5724                   RJ: Random data
5725                 </p>
5726               </td>
5727 <td>
5728                 <p>
5729                   <span class="blue">Max = 0.52&#949; (Mean = 0.0184&#949;)</span><br> <br>
5730                   (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.57&#949; (Mean = 0.704&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_ellint_rj_GSL_2_1_RJ_Random_data">And
5731                   other failures.</a>)
5732                 </p>
5733               </td>
5734 <td>
5735                 <p>
5736                   <span class="blue">Max = 186&#949; (Mean = 6.67&#949;)</span>
5737                 </p>
5738               </td>
5739 <td>
5740                 <p>
5741                   <span class="blue">Max = 215&#949; (Mean = 7.66&#949;)</span>
5742                 </p>
5743               </td>
5744 </tr>
5745 <tr>
5746 <td>
5747                 <p>
5748                   RJ: 4 Equal Values
5749                 </p>
5750               </td>
5751 <td>
5752                 <p>
5753                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5754                   2.1:</em></span> Max = 1.03&#949; (Mean = 0.418&#949;))
5755                 </p>
5756               </td>
5757 <td>
5758                 <p>
5759                   <span class="blue">Max = 0.998&#949; (Mean = 0.387&#949;)</span>
5760                 </p>
5761               </td>
5762 <td>
5763                 <p>
5764                   <span class="blue">Max = 1.03&#949; (Mean = 0.418&#949;)</span>
5765                 </p>
5766               </td>
5767 </tr>
5768 <tr>
5769 <td>
5770                 <p>
5771                   RJ: 3 Equal Values
5772                 </p>
5773               </td>
5774 <td>
5775                 <p>
5776                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5777                   2.1:</em></span> Max = 3.96&#949; (Mean = 1.06&#949;))
5778                 </p>
5779               </td>
5780 <td>
5781                 <p>
5782                   <span class="blue">Max = 20.8&#949; (Mean = 0.986&#949;)</span>
5783                 </p>
5784               </td>
5785 <td>
5786                 <p>
5787                   <span class="blue">Max = 39.9&#949; (Mean = 1.17&#949;)</span>
5788                 </p>
5789               </td>
5790 </tr>
5791 <tr>
5792 <td>
5793                 <p>
5794                   RJ: 2 Equal Values
5795                 </p>
5796               </td>
5797 <td>
5798                 <p>
5799                   <span class="blue">Max = 0.6&#949; (Mean = 0.0228&#949;)</span><br> <br>
5800                   (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.57&#949; (Mean = 0.754&#949;))
5801                 </p>
5802               </td>
5803 <td>
5804                 <p>
5805                   <span class="blue">Max = 220&#949; (Mean = 6.64&#949;)</span>
5806                 </p>
5807               </td>
5808 <td>
5809                 <p>
5810                   <span class="blue">Max = 214&#949; (Mean = 5.28&#949;)</span>
5811                 </p>
5812               </td>
5813 </tr>
5814 <tr>
5815 <td>
5816                 <p>
5817                   RJ: Equal z and p
5818                 </p>
5819               </td>
5820 <td>
5821                 <p>
5822                   <span class="blue">Max = 0.742&#949; (Mean = 0.0166&#949;)</span><br>
5823                   <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.62&#949; (Mean = 0.699&#949;))
5824                 </p>
5825               </td>
5826 <td>
5827                 <p>
5828                   <span class="blue">Max = 17.2&#949; (Mean = 1.16&#949;)</span>
5829                 </p>
5830               </td>
5831 <td>
5832                 <p>
5833                   <span class="blue">Max = 16.1&#949; (Mean = 1.14&#949;)</span>
5834                 </p>
5835               </td>
5836 </tr>
5837 </tbody>
5838 </table></div>
5839 </div>
5840 <br class="table-break"><div class="table">
5841 <a name="math_toolkit.logs_and_tables.all_table.table_erf"></a><p class="title"><b>Table&#160;22.40.&#160;Error rates for erf</b></p>
5842 <div class="table-contents"><table class="table" summary="Error rates for erf">
5843 <colgroup>
5844 <col>
5845 <col>
5846 <col>
5847 <col>
5848 <col>
5849 </colgroup>
5850 <thead><tr>
5851 <th>
5852               </th>
5853 <th>
5854                 <p>
5855                   GNU C++ version 7.1.0<br> linux<br> long double
5856                 </p>
5857               </th>
5858 <th>
5859                 <p>
5860                   GNU C++ version 7.1.0<br> linux<br> double
5861                 </p>
5862               </th>
5863 <th>
5864                 <p>
5865                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
5866                 </p>
5867               </th>
5868 <th>
5869                 <p>
5870                   Microsoft Visual C++ version 14.1<br> Win32<br> double
5871                 </p>
5872               </th>
5873 </tr></thead>
5874 <tbody>
5875 <tr>
5876 <td>
5877                 <p>
5878                   Erf Function: Small Values
5879                 </p>
5880               </td>
5881 <td>
5882                 <p>
5883                   <span class="blue">Max = 0.925&#949; (Mean = 0.193&#949;)</span><br> <br>
5884                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 0.944&#949; (Mean = 0.191&#949;))<br>
5885                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.944&#949; (Mean = 0.191&#949;))
5886                 </p>
5887               </td>
5888 <td>
5889                 <p>
5890                   <span class="blue">Max = 0.841&#949; (Mean = 0.0687&#949;)</span><br>
5891                   <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.06&#949; (Mean = 0.319&#949;))
5892                 </p>
5893               </td>
5894 <td>
5895                 <p>
5896                   <span class="blue">Max = 0.925&#949; (Mean = 0.193&#949;)</span><br> <br>
5897                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.944&#949; (Mean = 0.194&#949;))
5898                 </p>
5899               </td>
5900 <td>
5901                 <p>
5902                   <span class="blue">Max = 0.996&#949; (Mean = 0.182&#949;)</span><br> <br>
5903                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.57&#949; (Mean = 0.317&#949;))
5904                 </p>
5905               </td>
5906 </tr>
5907 <tr>
5908 <td>
5909                 <p>
5910                   Erf Function: Medium Values
5911                 </p>
5912               </td>
5913 <td>
5914                 <p>
5915                   <span class="blue">Max = 1.5&#949; (Mean = 0.193&#949;)</span><br> <br>
5916                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 0.921&#949; (Mean = 0.0723&#949;))<br>
5917                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.921&#949; (Mean = 0.0723&#949;))
5918                 </p>
5919               </td>
5920 <td>
5921                 <p>
5922                   <span class="blue">Max = 1&#949; (Mean = 0.119&#949;)</span><br> <br>
5923                   (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.31&#949; (Mean = 0.368&#949;))
5924                 </p>
5925               </td>
5926 <td>
5927                 <p>
5928                   <span class="blue">Max = 1.5&#949; (Mean = 0.197&#949;)</span><br> <br>
5929                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.921&#949; (Mean = 0.071&#949;))
5930                 </p>
5931               </td>
5932 <td>
5933                 <p>
5934                   <span class="blue">Max = 1&#949; (Mean = 0.171&#949;)</span><br> <br>
5935                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.19&#949; (Mean = 0.244&#949;))
5936                 </p>
5937               </td>
5938 </tr>
5939 <tr>
5940 <td>
5941                 <p>
5942                   Erf Function: Large Values
5943                 </p>
5944               </td>
5945 <td>
5946                 <p>
5947                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;cmath&gt;:</em></span>
5948                   Max = 0&#949; (Mean = 0&#949;))<br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span>
5949                   Max = 0&#949; (Mean = 0&#949;))
5950                 </p>
5951               </td>
5952 <td>
5953                 <p>
5954                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5955                   2.1:</em></span> Max = 0&#949; (Mean = 0&#949;))
5956                 </p>
5957               </td>
5958 <td>
5959                 <p>
5960                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span>
5961                   Max = 0&#949; (Mean = 0&#949;))
5962                 </p>
5963               </td>
5964 <td>
5965                 <p>
5966                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span>
5967                   Max = 0&#949; (Mean = 0&#949;))
5968                 </p>
5969               </td>
5970 </tr>
5971 </tbody>
5972 </table></div>
5973 </div>
5974 <br class="table-break"><div class="table">
5975 <a name="math_toolkit.logs_and_tables.all_table.table_erf_inv"></a><p class="title"><b>Table&#160;22.41.&#160;Error rates for erf_inv</b></p>
5976 <div class="table-contents"><table class="table" summary="Error rates for erf_inv">
5977 <colgroup>
5978 <col>
5979 <col>
5980 <col>
5981 <col>
5982 <col>
5983 </colgroup>
5984 <thead><tr>
5985 <th>
5986               </th>
5987 <th>
5988                 <p>
5989                   GNU C++ version 7.1.0<br> linux<br> double
5990                 </p>
5991               </th>
5992 <th>
5993                 <p>
5994                   GNU C++ version 7.1.0<br> linux<br> long double
5995                 </p>
5996               </th>
5997 <th>
5998                 <p>
5999                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
6000                 </p>
6001               </th>
6002 <th>
6003                 <p>
6004                   Microsoft Visual C++ version 14.1<br> Win32<br> double
6005                 </p>
6006               </th>
6007 </tr></thead>
6008 <tbody><tr>
6009 <td>
6010                 <p>
6011                   Inverse Erf Function
6012                 </p>
6013               </td>
6014 <td>
6015                 <p>
6016                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
6017                 </p>
6018               </td>
6019 <td>
6020                 <p>
6021                   <span class="blue">Max = 0.996&#949; (Mean = 0.389&#949;)</span>
6022                 </p>
6023               </td>
6024 <td>
6025                 <p>
6026                   <span class="blue">Max = 1.08&#949; (Mean = 0.395&#949;)</span>
6027                 </p>
6028               </td>
6029 <td>
6030                 <p>
6031                   <span class="blue">Max = 1.09&#949; (Mean = 0.502&#949;)</span>
6032                 </p>
6033               </td>
6034 </tr></tbody>
6035 </table></div>
6036 </div>
6037 <br class="table-break"><div class="table">
6038 <a name="math_toolkit.logs_and_tables.all_table.table_erfc"></a><p class="title"><b>Table&#160;22.42.&#160;Error rates for erfc</b></p>
6039 <div class="table-contents"><table class="table" summary="Error rates for erfc">
6040 <colgroup>
6041 <col>
6042 <col>
6043 <col>
6044 <col>
6045 <col>
6046 </colgroup>
6047 <thead><tr>
6048 <th>
6049               </th>
6050 <th>
6051                 <p>
6052                   GNU C++ version 7.1.0<br> linux<br> long double
6053                 </p>
6054               </th>
6055 <th>
6056                 <p>
6057                   GNU C++ version 7.1.0<br> linux<br> double
6058                 </p>
6059               </th>
6060 <th>
6061                 <p>
6062                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
6063                 </p>
6064               </th>
6065 <th>
6066                 <p>
6067                   Microsoft Visual C++ version 14.1<br> Win32<br> double
6068                 </p>
6069               </th>
6070 </tr></thead>
6071 <tbody>
6072 <tr>
6073 <td>
6074                 <p>
6075                   Erf Function: Small Values
6076                 </p>
6077               </td>
6078 <td>
6079                 <p>
6080                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;cmath&gt;:</em></span>
6081                   Max = 0&#949; (Mean = 0&#949;))<br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span>
6082                   Max = 0&#949; (Mean = 0&#949;))
6083                 </p>
6084               </td>
6085 <td>
6086                 <p>
6087                   <span class="blue">Max = 0.658&#949; (Mean = 0.0537&#949;)</span><br>
6088                   <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.01&#949; (Mean = 0.485&#949;))
6089                 </p>
6090               </td>
6091 <td>
6092                 <p>
6093                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span>
6094                   Max = 0&#949; (Mean = 0&#949;))
6095                 </p>
6096               </td>
6097 <td>
6098                 <p>
6099                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span>
6100                   Max = 0&#949; (Mean = 0&#949;))
6101                 </p>
6102               </td>
6103 </tr>
6104 <tr>
6105 <td>
6106                 <p>
6107                   Erf Function: Medium Values
6108                 </p>
6109               </td>
6110 <td>
6111                 <p>
6112                   <span class="blue">Max = 1.76&#949; (Mean = 0.365&#949;)</span><br> <br>
6113                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.35&#949; (Mean = 0.307&#949;))<br>
6114                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.35&#949; (Mean = 0.307&#949;))
6115                 </p>
6116               </td>
6117 <td>
6118                 <p>
6119                   <span class="blue">Max = 0.983&#949; (Mean = 0.213&#949;)</span><br> <br>
6120                   (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.64&#949; (Mean = 0.662&#949;))
6121                 </p>
6122               </td>
6123 <td>
6124                 <p>
6125                   <span class="blue">Max = 1.76&#949; (Mean = 0.38&#949;)</span><br> <br>
6126                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 2.81&#949; (Mean = 0.739&#949;))
6127                 </p>
6128               </td>
6129 <td>
6130                 <p>
6131                   <span class="blue">Max = 1.65&#949; (Mean = 0.373&#949;)</span><br> <br>
6132                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 2.36&#949; (Mean = 0.539&#949;))
6133                 </p>
6134               </td>
6135 </tr>
6136 <tr>
6137 <td>
6138                 <p>
6139                   Erf Function: Large Values
6140                 </p>
6141               </td>
6142 <td>
6143                 <p>
6144                   <span class="blue">Max = 1.57&#949; (Mean = 0.542&#949;)</span><br> <br>
6145                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.26&#949; (Mean = 0.441&#949;))<br>
6146                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.26&#949; (Mean = 0.441&#949;))
6147                 </p>
6148               </td>
6149 <td>
6150                 <p>
6151                   <span class="blue">Max = 0.868&#949; (Mean = 0.147&#949;)</span><br> <br>
6152                   (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.9&#949; (Mean = 0.472&#949;))
6153                 </p>
6154               </td>
6155 <td>
6156                 <p>
6157                   <span class="blue">Max = 1.57&#949; (Mean = 0.564&#949;)</span><br> <br>
6158                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 4.91&#949; (Mean = 1.54&#949;))
6159                 </p>
6160               </td>
6161 <td>
6162                 <p>
6163                   <span class="blue">Max = 1.14&#949; (Mean = 0.248&#949;)</span><br> <br>
6164                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.84&#949; (Mean = 0.331&#949;))
6165                 </p>
6166               </td>
6167 </tr>
6168 </tbody>
6169 </table></div>
6170 </div>
6171 <br class="table-break"><div class="table">
6172 <a name="math_toolkit.logs_and_tables.all_table.table_erfc_inv"></a><p class="title"><b>Table&#160;22.43.&#160;Error rates for erfc_inv</b></p>
6173 <div class="table-contents"><table class="table" summary="Error rates for erfc_inv">
6174 <colgroup>
6175 <col>
6176 <col>
6177 <col>
6178 <col>
6179 <col>
6180 </colgroup>
6181 <thead><tr>
6182 <th>
6183               </th>
6184 <th>
6185                 <p>
6186                   GNU C++ version 7.1.0<br> linux<br> double
6187                 </p>
6188               </th>
6189 <th>
6190                 <p>
6191                   GNU C++ version 7.1.0<br> linux<br> long double
6192                 </p>
6193               </th>
6194 <th>
6195                 <p>
6196                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
6197                 </p>
6198               </th>
6199 <th>
6200                 <p>
6201                   Microsoft Visual C++ version 14.1<br> Win32<br> double
6202                 </p>
6203               </th>
6204 </tr></thead>
6205 <tbody>
6206 <tr>
6207 <td>
6208                 <p>
6209                   Inverse Erfc Function
6210                 </p>
6211               </td>
6212 <td>
6213                 <p>
6214                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
6215                 </p>
6216               </td>
6217 <td>
6218                 <p>
6219                   <span class="blue">Max = 0.996&#949; (Mean = 0.397&#949;)</span>
6220                 </p>
6221               </td>
6222 <td>
6223                 <p>
6224                   <span class="blue">Max = 1.08&#949; (Mean = 0.403&#949;)</span>
6225                 </p>
6226               </td>
6227 <td>
6228                 <p>
6229                   <span class="blue">Max = 1&#949; (Mean = 0.491&#949;)</span>
6230                 </p>
6231               </td>
6232 </tr>
6233 <tr>
6234 <td>
6235                 <p>
6236                   Inverse Erfc Function: extreme values
6237                 </p>
6238               </td>
6239 <td>
6240               </td>
6241 <td>
6242                 <p>
6243                   <span class="blue">Max = 1.62&#949; (Mean = 0.383&#949;)</span>
6244                 </p>
6245               </td>
6246 <td>
6247                 <p>
6248                   <span class="blue">Max = 1.62&#949; (Mean = 0.383&#949;)</span>
6249                 </p>
6250               </td>
6251 <td>
6252               </td>
6253 </tr>
6254 </tbody>
6255 </table></div>
6256 </div>
6257 <br class="table-break"><div class="table">
6258 <a name="math_toolkit.logs_and_tables.all_table.table_expint_Ei_"></a><p class="title"><b>Table&#160;22.44.&#160;Error rates for expint (Ei)</b></p>
6259 <div class="table-contents"><table class="table" summary="Error rates for expint (Ei)">
6260 <colgroup>
6261 <col>
6262 <col>
6263 <col>
6264 <col>
6265 <col>
6266 </colgroup>
6267 <thead><tr>
6268 <th>
6269               </th>
6270 <th>
6271                 <p>
6272                   GNU C++ version 7.1.0<br> linux<br> long double
6273                 </p>
6274               </th>
6275 <th>
6276                 <p>
6277                   GNU C++ version 7.1.0<br> linux<br> double
6278                 </p>
6279               </th>
6280 <th>
6281                 <p>
6282                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
6283                 </p>
6284               </th>
6285 <th>
6286                 <p>
6287                   Microsoft Visual C++ version 14.1<br> Win32<br> double
6288                 </p>
6289               </th>
6290 </tr></thead>
6291 <tbody>
6292 <tr>
6293 <td>
6294                 <p>
6295                   Exponential Integral Ei
6296                 </p>
6297               </td>
6298 <td>
6299                 <p>
6300                   <span class="blue">Max = 5.05&#949; (Mean = 0.821&#949;)</span><br> <br>
6301                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 14.1&#949; (Mean = 2.43&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_expint_Ei___cmath__Exponential_Integral_Ei">And
6302                   other failures.</a>)
6303                 </p>
6304               </td>
6305 <td>
6306                 <p>
6307                   <span class="blue">Max = 0.994&#949; (Mean = 0.142&#949;)</span><br> <br>
6308                   (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.96&#949; (Mean = 0.703&#949;))
6309                 </p>
6310               </td>
6311 <td>
6312                 <p>
6313                   <span class="blue">Max = 5.05&#949; (Mean = 0.835&#949;)</span>
6314                 </p>
6315               </td>
6316 <td>
6317                 <p>
6318                   <span class="blue">Max = 1.43&#949; (Mean = 0.54&#949;)</span>
6319                 </p>
6320               </td>
6321 </tr>
6322 <tr>
6323 <td>
6324                 <p>
6325                   Exponential Integral Ei: double exponent range
6326                 </p>
6327               </td>
6328 <td>
6329                 <p>
6330                   <span class="blue">Max = 1.72&#949; (Mean = 0.593&#949;)</span><br> <br>
6331                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 3.11&#949; (Mean = 1.13&#949;))
6332                 </p>
6333               </td>
6334 <td>
6335                 <p>
6336                   <span class="blue">Max = 0.998&#949; (Mean = 0.156&#949;)</span><br> <br>
6337                   (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.5&#949; (Mean = 0.612&#949;))
6338                 </p>
6339               </td>
6340 <td>
6341                 <p>
6342                   <span class="blue">Max = 1.72&#949; (Mean = 0.607&#949;)</span>
6343                 </p>
6344               </td>
6345 <td>
6346                 <p>
6347                   <span class="blue">Max = 1.7&#949; (Mean = 0.66&#949;)</span>
6348                 </p>
6349               </td>
6350 </tr>
6351 <tr>
6352 <td>
6353                 <p>
6354                   Exponential Integral Ei: long exponent range
6355                 </p>
6356               </td>
6357 <td>
6358                 <p>
6359                   <span class="blue">Max = 1.98&#949; (Mean = 0.595&#949;)</span><br> <br>
6360                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.93&#949; (Mean = 0.855&#949;))
6361                 </p>
6362               </td>
6363 <td>
6364               </td>
6365 <td>
6366                 <p>
6367                   <span class="blue">Max = 1.98&#949; (Mean = 0.575&#949;)</span>
6368                 </p>
6369               </td>
6370 <td>
6371               </td>
6372 </tr>
6373 </tbody>
6374 </table></div>
6375 </div>
6376 <br class="table-break"><div class="table">
6377 <a name="math_toolkit.logs_and_tables.all_table.table_expint_En_"></a><p class="title"><b>Table&#160;22.45.&#160;Error rates for expint (En)</b></p>
6378 <div class="table-contents"><table class="table" summary="Error rates for expint (En)">
6379 <colgroup>
6380 <col>
6381 <col>
6382 <col>
6383 <col>
6384 <col>
6385 </colgroup>
6386 <thead><tr>
6387 <th>
6388               </th>
6389 <th>
6390                 <p>
6391                   GNU C++ version 7.1.0<br> linux<br> double
6392                 </p>
6393               </th>
6394 <th>
6395                 <p>
6396                   GNU C++ version 7.1.0<br> linux<br> long double
6397                 </p>
6398               </th>
6399 <th>
6400                 <p>
6401                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
6402                 </p>
6403               </th>
6404 <th>
6405                 <p>
6406                   Microsoft Visual C++ version 14.1<br> Win32<br> double
6407                 </p>
6408               </th>
6409 </tr></thead>
6410 <tbody>
6411 <tr>
6412 <td>
6413                 <p>
6414                   Exponential Integral En
6415                 </p>
6416               </td>
6417 <td>
6418                 <p>
6419                   <span class="blue">Max = 0.589&#949; (Mean = 0.0331&#949;)</span><br>
6420                   <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 58.5&#949; (Mean = 17.1&#949;))
6421                 </p>
6422               </td>
6423 <td>
6424                 <p>
6425                   <span class="blue">Max = 9.97&#949; (Mean = 2.13&#949;)</span>
6426                 </p>
6427               </td>
6428 <td>
6429                 <p>
6430                   <span class="blue">Max = 9.97&#949; (Mean = 2.13&#949;)</span>
6431                 </p>
6432               </td>
6433 <td>
6434                 <p>
6435                   <span class="blue">Max = 7.16&#949; (Mean = 1.85&#949;)</span>
6436                 </p>
6437               </td>
6438 </tr>
6439 <tr>
6440 <td>
6441                 <p>
6442                   Exponential Integral En: small z values
6443                 </p>
6444               </td>
6445 <td>
6446                 <p>
6447                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
6448                   2.1:</em></span> Max = 115&#949; (Mean = 23.6&#949;))
6449                 </p>
6450               </td>
6451 <td>
6452                 <p>
6453                   <span class="blue">Max = 1.99&#949; (Mean = 0.559&#949;)</span>
6454                 </p>
6455               </td>
6456 <td>
6457                 <p>
6458                   <span class="blue">Max = 1.99&#949; (Mean = 0.559&#949;)</span>
6459                 </p>
6460               </td>
6461 <td>
6462                 <p>
6463                   <span class="blue">Max = 2.62&#949; (Mean = 0.531&#949;)</span>
6464                 </p>
6465               </td>
6466 </tr>
6467 <tr>
6468 <td>
6469                 <p>
6470                   Exponential Integral E1
6471                 </p>
6472               </td>
6473 <td>
6474                 <p>
6475                   <span class="blue">Max = 0.556&#949; (Mean = 0.0625&#949;)</span><br>
6476                   <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.988&#949; (Mean = 0.469&#949;))
6477                 </p>
6478               </td>
6479 <td>
6480                 <p>
6481                   <span class="blue">Max = 0.965&#949; (Mean = 0.414&#949;)</span>
6482                 </p>
6483               </td>
6484 <td>
6485                 <p>
6486                   <span class="blue">Max = 0.965&#949; (Mean = 0.408&#949;)</span>
6487                 </p>
6488               </td>
6489 <td>
6490                 <p>
6491                   <span class="blue">Max = 0.988&#949; (Mean = 0.486&#949;)</span>
6492                 </p>
6493               </td>
6494 </tr>
6495 </tbody>
6496 </table></div>
6497 </div>
6498 <br class="table-break"><div class="table">
6499 <a name="math_toolkit.logs_and_tables.all_table.table_expm1"></a><p class="title"><b>Table&#160;22.46.&#160;Error rates for expm1</b></p>
6500 <div class="table-contents"><table class="table" summary="Error rates for expm1">
6501 <colgroup>
6502 <col>
6503 <col>
6504 <col>
6505 <col>
6506 <col>
6507 </colgroup>
6508 <thead><tr>
6509 <th>
6510               </th>
6511 <th>
6512                 <p>
6513                   GNU C++ version 7.1.0<br> linux<br> long double
6514                 </p>
6515               </th>
6516 <th>
6517                 <p>
6518                   GNU C++ version 7.1.0<br> linux<br> double
6519                 </p>
6520               </th>
6521 <th>
6522                 <p>
6523                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
6524                 </p>
6525               </th>
6526 <th>
6527                 <p>
6528                   Microsoft Visual C++ version 14.1<br> Win32<br> double
6529                 </p>
6530               </th>
6531 </tr></thead>
6532 <tbody><tr>
6533 <td>
6534                 <p>
6535                   Random test data
6536                 </p>
6537               </td>
6538 <td>
6539                 <p>
6540                   <span class="blue">Max = 0.992&#949; (Mean = 0.402&#949;)</span><br> <br>
6541                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 0.992&#949; (Mean = 0.402&#949;))<br>
6542                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.992&#949; (Mean = 0.402&#949;))
6543                 </p>
6544               </td>
6545 <td>
6546                 <p>
6547                   <span class="blue">Max = 0.793&#949; (Mean = 0.126&#949;)</span><br> <br>
6548                   (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 0.793&#949; (Mean = 0.126&#949;))
6549                 </p>
6550               </td>
6551 <td>
6552                 <p>
6553                   <span class="blue">Max = 1.31&#949; (Mean = 0.428&#949;)</span><br> <br>
6554                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.996&#949; (Mean = 0.426&#949;))
6555                 </p>
6556               </td>
6557 <td>
6558                 <p>
6559                   <span class="blue">Max = 1.31&#949; (Mean = 0.496&#949;)</span><br> <br>
6560                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.31&#949; (Mean = 0.496&#949;))
6561                 </p>
6562               </td>
6563 </tr></tbody>
6564 </table></div>
6565 </div>
6566 <br class="table-break"><div class="table">
6567 <a name="math_toolkit.logs_and_tables.all_table.table_gamma_p"></a><p class="title"><b>Table&#160;22.47.&#160;Error rates for gamma_p</b></p>
6568 <div class="table-contents"><table class="table" summary="Error rates for gamma_p">
6569 <colgroup>
6570 <col>
6571 <col>
6572 <col>
6573 <col>
6574 <col>
6575 </colgroup>
6576 <thead><tr>
6577 <th>
6578               </th>
6579 <th>
6580                 <p>
6581                   GNU C++ version 7.1.0<br> linux<br> double
6582                 </p>
6583               </th>
6584 <th>
6585                 <p>
6586                   GNU C++ version 7.1.0<br> linux<br> long double
6587                 </p>
6588               </th>
6589 <th>
6590                 <p>
6591                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
6592                 </p>
6593               </th>
6594 <th>
6595                 <p>
6596                   Microsoft Visual C++ version 14.1<br> Win32<br> double
6597                 </p>
6598               </th>
6599 </tr></thead>
6600 <tbody>
6601 <tr>
6602 <td>
6603                 <p>
6604                   tgamma(a, z) medium values
6605                 </p>
6606               </td>
6607 <td>
6608                 <p>
6609                   <span class="blue">Max = 0.955&#949; (Mean = 0.05&#949;)</span><br> <br>
6610                   (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 342&#949; (Mean = 45.8&#949;))<br> (<span class="emphasis"><em>Rmath
6611                   3.2.3:</em></span> Max = 389&#949; (Mean = 44&#949;))
6612                 </p>
6613               </td>
6614 <td>
6615                 <p>
6616                   <span class="blue">Max = 41.6&#949; (Mean = 8.09&#949;)</span>
6617                 </p>
6618               </td>
6619 <td>
6620                 <p>
6621                   <span class="blue">Max = 239&#949; (Mean = 30.2&#949;)</span>
6622                 </p>
6623               </td>
6624 <td>
6625                 <p>
6626                   <span class="blue">Max = 35.1&#949; (Mean = 6.98&#949;)</span>
6627                 </p>
6628               </td>
6629 </tr>
6630 <tr>
6631 <td>
6632                 <p>
6633                   tgamma(a, z) small values
6634                 </p>
6635               </td>
6636 <td>
6637                 <p>
6638                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
6639                   2.1:</em></span> Max = 4.82&#949; (Mean = 0.758&#949;))<br> (<span class="emphasis"><em>Rmath
6640                   3.2.3:</em></span> Max = 1.01&#949; (Mean = 0.306&#949;))
6641                 </p>
6642               </td>
6643 <td>
6644                 <p>
6645                   <span class="blue">Max = 2&#949; (Mean = 0.464&#949;)</span>
6646                 </p>
6647               </td>
6648 <td>
6649                 <p>
6650                   <span class="blue">Max = 2&#949; (Mean = 0.461&#949;)</span>
6651                 </p>
6652               </td>
6653 <td>
6654                 <p>
6655                   <span class="blue">Max = 1.54&#949; (Mean = 0.439&#949;)</span>
6656                 </p>
6657               </td>
6658 </tr>
6659 <tr>
6660 <td>
6661                 <p>
6662                   tgamma(a, z) large values
6663                 </p>
6664               </td>
6665 <td>
6666                 <p>
6667                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
6668                   2.1:</em></span> Max = 1.02e+03&#949; (Mean = 105&#949;))<br> (<span class="emphasis"><em>Rmath
6669                   3.2.3:</em></span> Max = 1.11e+03&#949; (Mean = 67.5&#949;))
6670                 </p>
6671               </td>
6672 <td>
6673                 <p>
6674                   <span class="blue">Max = 3.08e+04&#949; (Mean = 1.86e+03&#949;)</span>
6675                 </p>
6676               </td>
6677 <td>
6678                 <p>
6679                   <span class="blue">Max = 3.02e+04&#949; (Mean = 1.91e+03&#949;)</span>
6680                 </p>
6681               </td>
6682 <td>
6683                 <p>
6684                   <span class="blue">Max = 243&#949; (Mean = 20.2&#949;)</span>
6685                 </p>
6686               </td>
6687 </tr>
6688 <tr>
6689 <td>
6690                 <p>
6691                   tgamma(a, z) integer and half integer values
6692                 </p>
6693               </td>
6694 <td>
6695                 <p>
6696                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
6697                   2.1:</em></span> Max = 128&#949; (Mean = 22.6&#949;))<br> (<span class="emphasis"><em>Rmath
6698                   3.2.3:</em></span> Max = 66.2&#949; (Mean = 12.2&#949;))
6699                 </p>
6700               </td>
6701 <td>
6702                 <p>
6703                   <span class="blue">Max = 11.8&#949; (Mean = 2.66&#949;)</span>
6704                 </p>
6705               </td>
6706 <td>
6707                 <p>
6708                   <span class="blue">Max = 71.6&#949; (Mean = 9.47&#949;)</span>
6709                 </p>
6710               </td>
6711 <td>
6712                 <p>
6713                   <span class="blue">Max = 13&#949; (Mean = 2.97&#949;)</span>
6714                 </p>
6715               </td>
6716 </tr>
6717 </tbody>
6718 </table></div>
6719 </div>
6720 <br class="table-break"><div class="table">
6721 <a name="math_toolkit.logs_and_tables.all_table.table_gamma_p_inv"></a><p class="title"><b>Table&#160;22.48.&#160;Error rates for gamma_p_inv</b></p>
6722 <div class="table-contents"><table class="table" summary="Error rates for gamma_p_inv">
6723 <colgroup>
6724 <col>
6725 <col>
6726 <col>
6727 <col>
6728 <col>
6729 </colgroup>
6730 <thead><tr>
6731 <th>
6732               </th>
6733 <th>
6734                 <p>
6735                   GNU C++ version 7.1.0<br> linux<br> double
6736                 </p>
6737               </th>
6738 <th>
6739                 <p>
6740                   GNU C++ version 7.1.0<br> linux<br> long double
6741                 </p>
6742               </th>
6743 <th>
6744                 <p>
6745                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
6746                 </p>
6747               </th>
6748 <th>
6749                 <p>
6750                   Microsoft Visual C++ version 14.1<br> Win32<br> double
6751                 </p>
6752               </th>
6753 </tr></thead>
6754 <tbody>
6755 <tr>
6756 <td>
6757                 <p>
6758                   incomplete gamma inverse(a, z) medium values
6759                 </p>
6760               </td>
6761 <td>
6762                 <p>
6763                   <span class="blue">Max = 0.993&#949; (Mean = 0.15&#949;)</span><br> <br>
6764                   (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 4.88&#949; (Mean = 0.868&#949;))
6765                 </p>
6766               </td>
6767 <td>
6768                 <p>
6769                   <span class="blue">Max = 1.8&#949; (Mean = 0.406&#949;)</span>
6770                 </p>
6771               </td>
6772 <td>
6773                 <p>
6774                   <span class="blue">Max = 1.89&#949; (Mean = 0.466&#949;)</span>
6775                 </p>
6776               </td>
6777 <td>
6778                 <p>
6779                   <span class="blue">Max = 1.71&#949; (Mean = 0.34&#949;)</span>
6780                 </p>
6781               </td>
6782 </tr>
6783 <tr>
6784 <td>
6785                 <p>
6786                   incomplete gamma inverse(a, z) large values
6787                 </p>
6788               </td>
6789 <td>
6790                 <p>
6791                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>Rmath
6792                   3.2.3:</em></span> Max = 0.816&#949; (Mean = 0.0874&#949;))
6793                 </p>
6794               </td>
6795 <td>
6796                 <p>
6797                   <span class="blue">Max = 0.509&#949; (Mean = 0.0447&#949;)</span>
6798                 </p>
6799               </td>
6800 <td>
6801                 <p>
6802                   <span class="blue">Max = 0.509&#949; (Mean = 0.0447&#949;)</span>
6803                 </p>
6804               </td>
6805 <td>
6806                 <p>
6807                   <span class="blue">Max = 0.924&#949; (Mean = 0.108&#949;)</span>
6808                 </p>
6809               </td>
6810 </tr>
6811 <tr>
6812 <td>
6813                 <p>
6814                   incomplete gamma inverse(a, z) small values
6815                 </p>
6816               </td>
6817 <td>
6818                 <p>
6819                   <span class="blue">Max = 441&#949; (Mean = 53.9&#949;)</span><br> <br>
6820                   (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 547&#949; (Mean = 61.6&#949;))
6821                 </p>
6822               </td>
6823 <td>
6824                 <p>
6825                   <span class="blue">Max = 9.17e+03&#949; (Mean = 1.45e+03&#949;)</span>
6826                 </p>
6827               </td>
6828 <td>
6829                 <p>
6830                   <span class="blue">Max = 1.09e+04&#949; (Mean = 1.3e+03&#949;)</span>
6831                 </p>
6832               </td>
6833 <td>
6834                 <p>
6835                   <span class="blue">Max = 1.1e+03&#949; (Mean = 131&#949;)</span>
6836                 </p>
6837               </td>
6838 </tr>
6839 </tbody>
6840 </table></div>
6841 </div>
6842 <br class="table-break"><div class="table">
6843 <a name="math_toolkit.logs_and_tables.all_table.table_gamma_p_inva"></a><p class="title"><b>Table&#160;22.49.&#160;Error rates for gamma_p_inva</b></p>
6844 <div class="table-contents"><table class="table" summary="Error rates for gamma_p_inva">
6845 <colgroup>
6846 <col>
6847 <col>
6848 <col>
6849 <col>
6850 <col>
6851 </colgroup>
6852 <thead><tr>
6853 <th>
6854               </th>
6855 <th>
6856                 <p>
6857                   GNU C++ version 7.1.0<br> linux<br> double
6858                 </p>
6859               </th>
6860 <th>
6861                 <p>
6862                   GNU C++ version 7.1.0<br> linux<br> long double
6863                 </p>
6864               </th>
6865 <th>
6866                 <p>
6867                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
6868                 </p>
6869               </th>
6870 <th>
6871                 <p>
6872                   Microsoft Visual C++ version 14.1<br> Win32<br> double
6873                 </p>
6874               </th>
6875 </tr></thead>
6876 <tbody><tr>
6877 <td>
6878                 <p>
6879                   Incomplete gamma inverses.
6880                 </p>
6881               </td>
6882 <td>
6883                 <p>
6884                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
6885                 </p>
6886               </td>
6887 <td>
6888                 <p>
6889                   <span class="blue">Max = 7.87&#949; (Mean = 1.15&#949;)</span>
6890                 </p>
6891               </td>
6892 <td>
6893                 <p>
6894                   <span class="blue">Max = 4.08&#949; (Mean = 1.12&#949;)</span>
6895                 </p>
6896               </td>
6897 <td>
6898                 <p>
6899                   <span class="blue">Max = 4.92&#949; (Mean = 1.03&#949;)</span>
6900                 </p>
6901               </td>
6902 </tr></tbody>
6903 </table></div>
6904 </div>
6905 <br class="table-break"><div class="table">
6906 <a name="math_toolkit.logs_and_tables.all_table.table_gamma_q"></a><p class="title"><b>Table&#160;22.50.&#160;Error rates for gamma_q</b></p>
6907 <div class="table-contents"><table class="table" summary="Error rates for gamma_q">
6908 <colgroup>
6909 <col>
6910 <col>
6911 <col>
6912 <col>
6913 <col>
6914 </colgroup>
6915 <thead><tr>
6916 <th>
6917               </th>
6918 <th>
6919                 <p>
6920                   GNU C++ version 7.1.0<br> linux<br> double
6921                 </p>
6922               </th>
6923 <th>
6924                 <p>
6925                   GNU C++ version 7.1.0<br> linux<br> long double
6926                 </p>
6927               </th>
6928 <th>
6929                 <p>
6930                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
6931                 </p>
6932               </th>
6933 <th>
6934                 <p>
6935                   Microsoft Visual C++ version 14.1<br> Win32<br> double
6936                 </p>
6937               </th>
6938 </tr></thead>
6939 <tbody>
6940 <tr>
6941 <td>
6942                 <p>
6943                   tgamma(a, z) medium values
6944                 </p>
6945               </td>
6946 <td>
6947                 <p>
6948                   <span class="blue">Max = 0.927&#949; (Mean = 0.035&#949;)</span><br> <br>
6949                   (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 201&#949; (Mean = 13.5&#949;))<br> (<span class="emphasis"><em>Rmath
6950                   3.2.3:</em></span> Max = 131&#949; (Mean = 12.7&#949;))
6951                 </p>
6952               </td>
6953 <td>
6954                 <p>
6955                   <span class="blue">Max = 32.3&#949; (Mean = 6.61&#949;)</span>
6956                 </p>
6957               </td>
6958 <td>
6959                 <p>
6960                   <span class="blue">Max = 199&#949; (Mean = 26.6&#949;)</span>
6961                 </p>
6962               </td>
6963 <td>
6964                 <p>
6965                   <span class="blue">Max = 23.7&#949; (Mean = 4&#949;)</span>
6966                 </p>
6967               </td>
6968 </tr>
6969 <tr>
6970 <td>
6971                 <p>
6972                   tgamma(a, z) small values
6973                 </p>
6974               </td>
6975 <td>
6976                 <p>
6977                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
6978                   2.1:</em></span> <span class="red">Max = 1.38e+10&#949; (Mean = 1.05e+09&#949;))</span><br>
6979                   (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 65.6&#949; (Mean = 11&#949;))
6980                 </p>
6981               </td>
6982 <td>
6983                 <p>
6984                   <span class="blue">Max = 2.45&#949; (Mean = 0.885&#949;)</span>
6985                 </p>
6986               </td>
6987 <td>
6988                 <p>
6989                   <span class="blue">Max = 2.45&#949; (Mean = 0.819&#949;)</span>
6990                 </p>
6991               </td>
6992 <td>
6993                 <p>
6994                   <span class="blue">Max = 2.26&#949; (Mean = 0.74&#949;)</span>
6995                 </p>
6996               </td>
6997 </tr>
6998 <tr>
6999 <td>
7000                 <p>
7001                   tgamma(a, z) large values
7002                 </p>
7003               </td>
7004 <td>
7005                 <p>
7006                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
7007                   2.1:</em></span> Max = 2.71e+04&#949; (Mean = 2.16e+03&#949;))<br> (<span class="emphasis"><em>Rmath
7008                   3.2.3:</em></span> Max = 1.02e+03&#949; (Mean = 62.7&#949;))
7009                 </p>
7010               </td>
7011 <td>
7012                 <p>
7013                   <span class="blue">Max = 6.82e+03&#949; (Mean = 414&#949;)</span>
7014                 </p>
7015               </td>
7016 <td>
7017                 <p>
7018                   <span class="blue">Max = 1.15e+04&#949; (Mean = 733&#949;)</span>
7019                 </p>
7020               </td>
7021 <td>
7022                 <p>
7023                   <span class="blue">Max = 469&#949; (Mean = 31.5&#949;)</span>
7024                 </p>
7025               </td>
7026 </tr>
7027 <tr>
7028 <td>
7029                 <p>
7030                   tgamma(a, z) integer and half integer values
7031                 </p>
7032               </td>
7033 <td>
7034                 <p>
7035                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
7036                   2.1:</em></span> Max = 118&#949; (Mean = 12.5&#949;))<br> (<span class="emphasis"><em>Rmath
7037                   3.2.3:</em></span> Max = 138&#949; (Mean = 16.9&#949;))
7038                 </p>
7039               </td>
7040 <td>
7041                 <p>
7042                   <span class="blue">Max = 11.1&#949; (Mean = 2.07&#949;)</span>
7043                 </p>
7044               </td>
7045 <td>
7046                 <p>
7047                   <span class="blue">Max = 54.7&#949; (Mean = 6.16&#949;)</span>
7048                 </p>
7049               </td>
7050 <td>
7051                 <p>
7052                   <span class="blue">Max = 8.72&#949; (Mean = 1.48&#949;)</span>
7053                 </p>
7054               </td>
7055 </tr>
7056 </tbody>
7057 </table></div>
7058 </div>
7059 <br class="table-break"><div class="table">
7060 <a name="math_toolkit.logs_and_tables.all_table.table_gamma_q_inv"></a><p class="title"><b>Table&#160;22.51.&#160;Error rates for gamma_q_inv</b></p>
7061 <div class="table-contents"><table class="table" summary="Error rates for gamma_q_inv">
7062 <colgroup>
7063 <col>
7064 <col>
7065 <col>
7066 <col>
7067 <col>
7068 </colgroup>
7069 <thead><tr>
7070 <th>
7071               </th>
7072 <th>
7073                 <p>
7074                   GNU C++ version 7.1.0<br> linux<br> double
7075                 </p>
7076               </th>
7077 <th>
7078                 <p>
7079                   GNU C++ version 7.1.0<br> linux<br> long double
7080                 </p>
7081               </th>
7082 <th>
7083                 <p>
7084                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
7085                 </p>
7086               </th>
7087 <th>
7088                 <p>
7089                   Microsoft Visual C++ version 14.1<br> Win32<br> double
7090                 </p>
7091               </th>
7092 </tr></thead>
7093 <tbody>
7094 <tr>
7095 <td>
7096                 <p>
7097                   incomplete gamma inverse(a, z) medium values
7098                 </p>
7099               </td>
7100 <td>
7101                 <p>
7102                   <span class="blue">Max = 0.912&#949; (Mean = 0.154&#949;)</span><br> <br>
7103                   (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 4.66&#949; (Mean = 0.792&#949;))
7104                 </p>
7105               </td>
7106 <td>
7107                 <p>
7108                   <span class="blue">Max = 6.2&#949; (Mean = 0.627&#949;)</span>
7109                 </p>
7110               </td>
7111 <td>
7112                 <p>
7113                   <span class="blue">Max = 6.2&#949; (Mean = 0.683&#949;)</span>
7114                 </p>
7115               </td>
7116 <td>
7117                 <p>
7118                   <span class="blue">Max = 2.88&#949; (Mean = 0.469&#949;)</span>
7119                 </p>
7120               </td>
7121 </tr>
7122 <tr>
7123 <td>
7124                 <p>
7125                   incomplete gamma inverse(a, z) large values
7126                 </p>
7127               </td>
7128 <td>
7129                 <p>
7130                   <span class="blue">Max = 0.894&#949; (Mean = 0.0915&#949;)</span><br>
7131                   <br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 0.894&#949; (Mean = 0.106&#949;))
7132                 </p>
7133               </td>
7134 <td>
7135                 <p>
7136                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
7137                 </p>
7138               </td>
7139 <td>
7140                 <p>
7141                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
7142                 </p>
7143               </td>
7144 <td>
7145                 <p>
7146                   <span class="blue">Max = 0.814&#949; (Mean = 0.0856&#949;)</span>
7147                 </p>
7148               </td>
7149 </tr>
7150 <tr>
7151 <td>
7152                 <p>
7153                   incomplete gamma inverse(a, z) small values
7154                 </p>
7155               </td>
7156 <td>
7157                 <p>
7158                   <span class="blue">Max = 292&#949; (Mean = 36.4&#949;)</span><br> <br>
7159                   (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 415&#949; (Mean = 48.7&#949;))
7160                 </p>
7161               </td>
7162 <td>
7163                 <p>
7164                   <span class="blue">Max = 8.28e+03&#949; (Mean = 1.09e+03&#949;)</span>
7165                 </p>
7166               </td>
7167 <td>
7168                 <p>
7169                   <span class="blue">Max = 8.98e+03&#949; (Mean = 877&#949;)</span>
7170                 </p>
7171               </td>
7172 <td>
7173                 <p>
7174                   <span class="blue">Max = 451&#949; (Mean = 64.7&#949;)</span>
7175                 </p>
7176               </td>
7177 </tr>
7178 </tbody>
7179 </table></div>
7180 </div>
7181 <br class="table-break"><div class="table">
7182 <a name="math_toolkit.logs_and_tables.all_table.table_gamma_q_inva"></a><p class="title"><b>Table&#160;22.52.&#160;Error rates for gamma_q_inva</b></p>
7183 <div class="table-contents"><table class="table" summary="Error rates for gamma_q_inva">
7184 <colgroup>
7185 <col>
7186 <col>
7187 <col>
7188 <col>
7189 <col>
7190 </colgroup>
7191 <thead><tr>
7192 <th>
7193               </th>
7194 <th>
7195                 <p>
7196                   GNU C++ version 7.1.0<br> linux<br> double
7197                 </p>
7198               </th>
7199 <th>
7200                 <p>
7201                   GNU C++ version 7.1.0<br> linux<br> long double
7202                 </p>
7203               </th>
7204 <th>
7205                 <p>
7206                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
7207                 </p>
7208               </th>
7209 <th>
7210                 <p>
7211                   Microsoft Visual C++ version 14.1<br> Win32<br> double
7212                 </p>
7213               </th>
7214 </tr></thead>
7215 <tbody><tr>
7216 <td>
7217                 <p>
7218                   Incomplete gamma inverses.
7219                 </p>
7220               </td>
7221 <td>
7222                 <p>
7223                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
7224                 </p>
7225               </td>
7226 <td>
7227                 <p>
7228                   <span class="blue">Max = 8.42&#949; (Mean = 1.3&#949;)</span>
7229                 </p>
7230               </td>
7231 <td>
7232                 <p>
7233                   <span class="blue">Max = 7.86&#949; (Mean = 1.24&#949;)</span>
7234                 </p>
7235               </td>
7236 <td>
7237                 <p>
7238                   <span class="blue">Max = 5.05&#949; (Mean = 1.08&#949;)</span>
7239                 </p>
7240               </td>
7241 </tr></tbody>
7242 </table></div>
7243 </div>
7244 <br class="table-break"><div class="table">
7245 <a name="math_toolkit.logs_and_tables.all_table.table_hermite"></a><p class="title"><b>Table&#160;22.53.&#160;Error rates for hermite</b></p>
7246 <div class="table-contents"><table class="table" summary="Error rates for hermite">
7247 <colgroup>
7248 <col>
7249 <col>
7250 <col>
7251 <col>
7252 <col>
7253 </colgroup>
7254 <thead><tr>
7255 <th>
7256               </th>
7257 <th>
7258                 <p>
7259                   GNU C++ version 7.1.0<br> linux<br> double
7260                 </p>
7261               </th>
7262 <th>
7263                 <p>
7264                   GNU C++ version 7.1.0<br> linux<br> long double
7265                 </p>
7266               </th>
7267 <th>
7268                 <p>
7269                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
7270                 </p>
7271               </th>
7272 <th>
7273                 <p>
7274                   Microsoft Visual C++ version 14.1<br> Win32<br> double
7275                 </p>
7276               </th>
7277 </tr></thead>
7278 <tbody><tr>
7279 <td>
7280                 <p>
7281                   Hermite Polynomials
7282                 </p>
7283               </td>
7284 <td>
7285                 <p>
7286                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
7287                 </p>
7288               </td>
7289 <td>
7290                 <p>
7291                   <span class="blue">Max = 6.24&#949; (Mean = 2.07&#949;)</span>
7292                 </p>
7293               </td>
7294 <td>
7295                 <p>
7296                   <span class="blue">Max = 6.24&#949; (Mean = 2.07&#949;)</span>
7297                 </p>
7298               </td>
7299 <td>
7300                 <p>
7301                   <span class="blue">Max = 4.46&#949; (Mean = 1.41&#949;)</span>
7302                 </p>
7303               </td>
7304 </tr></tbody>
7305 </table></div>
7306 </div>
7307 <br class="table-break"><div class="table">
7308 <a name="math_toolkit.logs_and_tables.all_table.table_heuman_lambda"></a><p class="title"><b>Table&#160;22.54.&#160;Error rates for heuman_lambda</b></p>
7309 <div class="table-contents"><table class="table" summary="Error rates for heuman_lambda">
7310 <colgroup>
7311 <col>
7312 <col>
7313 <col>
7314 <col>
7315 <col>
7316 </colgroup>
7317 <thead><tr>
7318 <th>
7319               </th>
7320 <th>
7321                 <p>
7322                   GNU C++ version 7.1.0<br> linux<br> double
7323                 </p>
7324               </th>
7325 <th>
7326                 <p>
7327                   GNU C++ version 7.1.0<br> linux<br> long double
7328                 </p>
7329               </th>
7330 <th>
7331                 <p>
7332                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
7333                 </p>
7334               </th>
7335 <th>
7336                 <p>
7337                   Microsoft Visual C++ version 14.1<br> Win32<br> double
7338                 </p>
7339               </th>
7340 </tr></thead>
7341 <tbody>
7342 <tr>
7343 <td>
7344                 <p>
7345                   Elliptic Integral Jacobi Zeta: Mathworld Data
7346                 </p>
7347               </td>
7348 <td>
7349                 <p>
7350                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
7351                 </p>
7352               </td>
7353 <td>
7354                 <p>
7355                   <span class="blue">Max = 1.89&#949; (Mean = 0.887&#949;)</span>
7356                 </p>
7357               </td>
7358 <td>
7359                 <p>
7360                   <span class="blue">Max = 1.89&#949; (Mean = 0.887&#949;)</span>
7361                 </p>
7362               </td>
7363 <td>
7364                 <p>
7365                   <span class="blue">Max = 1.08&#949; (Mean = 0.734&#949;)</span>
7366                 </p>
7367               </td>
7368 </tr>
7369 <tr>
7370 <td>
7371                 <p>
7372                   Elliptic Integral Heuman Lambda: Random Data
7373                 </p>
7374               </td>
7375 <td>
7376                 <p>
7377                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
7378                 </p>
7379               </td>
7380 <td>
7381                 <p>
7382                   <span class="blue">Max = 3.82&#949; (Mean = 0.609&#949;)</span>
7383                 </p>
7384               </td>
7385 <td>
7386                 <p>
7387                   <span class="blue">Max = 3.82&#949; (Mean = 0.608&#949;)</span>
7388                 </p>
7389               </td>
7390 <td>
7391                 <p>
7392                   <span class="blue">Max = 2.12&#949; (Mean = 0.588&#949;)</span>
7393                 </p>
7394               </td>
7395 </tr>
7396 </tbody>
7397 </table></div>
7398 </div>
7399 <br class="table-break"><div class="table">
7400 <a name="math_toolkit.logs_and_tables.all_table.table_ibeta"></a><p class="title"><b>Table&#160;22.55.&#160;Error rates for ibeta</b></p>
7401 <div class="table-contents"><table class="table" summary="Error rates for ibeta">
7402 <colgroup>
7403 <col>
7404 <col>
7405 <col>
7406 <col>
7407 <col>
7408 </colgroup>
7409 <thead><tr>
7410 <th>
7411               </th>
7412 <th>
7413                 <p>
7414                   GNU C++ version 7.1.0<br> linux<br> double
7415                 </p>
7416               </th>
7417 <th>
7418                 <p>
7419                   GNU C++ version 7.1.0<br> linux<br> long double
7420                 </p>
7421               </th>
7422 <th>
7423                 <p>
7424                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
7425                 </p>
7426               </th>
7427 <th>
7428                 <p>
7429                   Microsoft Visual C++ version 14.1<br> Win32<br> double
7430                 </p>
7431               </th>
7432 </tr></thead>
7433 <tbody>
7434 <tr>
7435 <td>
7436                 <p>
7437                   Incomplete Beta Function: Small Values
7438                 </p>
7439               </td>
7440 <td>
7441                 <p>
7442                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
7443                   2.1:</em></span> Max = 682&#949; (Mean = 32.6&#949;))<br> (<span class="emphasis"><em>Rmath
7444                   3.2.3:</em></span> Max = 22.9&#949; (Mean = 3.35&#949;))
7445                 </p>
7446               </td>
7447 <td>
7448                 <p>
7449                   <span class="blue">Max = 8.97&#949; (Mean = 2.09&#949;)</span>
7450                 </p>
7451               </td>
7452 <td>
7453                 <p>
7454                   <span class="blue">Max = 21.3&#949; (Mean = 2.75&#949;)</span>
7455                 </p>
7456               </td>
7457 <td>
7458                 <p>
7459                   <span class="blue">Max = 8.4&#949; (Mean = 1.93&#949;)</span>
7460                 </p>
7461               </td>
7462 </tr>
7463 <tr>
7464 <td>
7465                 <p>
7466                   Incomplete Beta Function: Medium Values
7467                 </p>
7468               </td>
7469 <td>
7470                 <p>
7471                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
7472                   2.1:</em></span> Max = 690&#949; (Mean = 151&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
7473                   Max = 232&#949; (Mean = 27.9&#949;))
7474                 </p>
7475               </td>
7476 <td>
7477                 <p>
7478                   <span class="blue">Max = 50&#949; (Mean = 12.1&#949;)</span>
7479                 </p>
7480               </td>
7481 <td>
7482                 <p>
7483                   <span class="blue">Max = 124&#949; (Mean = 18.4&#949;)</span>
7484                 </p>
7485               </td>
7486 <td>
7487                 <p>
7488                   <span class="blue">Max = 106&#949; (Mean = 16.3&#949;)</span>
7489                 </p>
7490               </td>
7491 </tr>
7492 <tr>
7493 <td>
7494                 <p>
7495                   Incomplete Beta Function: Large and Diverse Values
7496                 </p>
7497               </td>
7498 <td>
7499                 <p>
7500                   <span class="blue">Max = 1.26&#949; (Mean = 0.063&#949;)</span><br> <br>
7501                   (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.9e+05&#949; (Mean = 1.82e+04&#949;)
7502                   <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_ibeta_GSL_2_1_Incomplete_Beta_Function_Large_and_Diverse_Values">And
7503                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
7504                   Max = 574&#949; (Mean = 49.4&#949;))
7505                 </p>
7506               </td>
7507 <td>
7508                 <p>
7509                   <span class="blue">Max = 1.96e+04&#949; (Mean = 997&#949;)</span>
7510                 </p>
7511               </td>
7512 <td>
7513                 <p>
7514                   <span class="blue">Max = 4.98e+04&#949; (Mean = 2.07e+03&#949;)</span>
7515                 </p>
7516               </td>
7517 <td>
7518                 <p>
7519                   <span class="blue">Max = 1.32e+03&#949; (Mean = 68.5&#949;)</span>
7520                 </p>
7521               </td>
7522 </tr>
7523 <tr>
7524 <td>
7525                 <p>
7526                   Incomplete Beta Function: Small Integer Values
7527                 </p>
7528               </td>
7529 <td>
7530                 <p>
7531                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
7532                   2.1:</em></span> Max = 254&#949; (Mean = 50.9&#949;))<br> (<span class="emphasis"><em>Rmath
7533                   3.2.3:</em></span> Max = 62.2&#949; (Mean = 8.95&#949;))
7534                 </p>
7535               </td>
7536 <td>
7537                 <p>
7538                   <span class="blue">Max = 4.45&#949; (Mean = 0.814&#949;)</span>
7539                 </p>
7540               </td>
7541 <td>
7542                 <p>
7543                   <span class="blue">Max = 44.5&#949; (Mean = 10.1&#949;)</span>
7544                 </p>
7545               </td>
7546 <td>
7547                 <p>
7548                   <span class="blue">Max = 3.85&#949; (Mean = 0.791&#949;)</span>
7549                 </p>
7550               </td>
7551 </tr>
7552 </tbody>
7553 </table></div>
7554 </div>
7555 <br class="table-break"><div class="table">
7556 <a name="math_toolkit.logs_and_tables.all_table.table_ibeta_inv"></a><p class="title"><b>Table&#160;22.56.&#160;Error rates for ibeta_inv</b></p>
7557 <div class="table-contents"><table class="table" summary="Error rates for ibeta_inv">
7558 <colgroup>
7559 <col>
7560 <col>
7561 <col>
7562 <col>
7563 <col>
7564 </colgroup>
7565 <thead><tr>
7566 <th>
7567               </th>
7568 <th>
7569                 <p>
7570                   GNU C++ version 7.1.0<br> linux<br> double
7571                 </p>
7572               </th>
7573 <th>
7574                 <p>
7575                   GNU C++ version 7.1.0<br> linux<br> long double
7576                 </p>
7577               </th>
7578 <th>
7579                 <p>
7580                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
7581                 </p>
7582               </th>
7583 <th>
7584                 <p>
7585                   Microsoft Visual C++ version 14.1<br> Win32<br> double
7586                 </p>
7587               </th>
7588 </tr></thead>
7589 <tbody><tr>
7590 <td>
7591                 <p>
7592                   Inverse incomplete beta
7593                 </p>
7594               </td>
7595 <td>
7596                 <p>
7597                   <span class="blue">Max = 11&#949; (Mean = 0.345&#949;)</span><br> <br>
7598                   (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 1.14e+121&#949; (Mean
7599                   = 3.28e+119&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_ibeta_inv_Rmath_3_2_3_Inverse_incomplete_beta">And
7600                   other failures.</a>)</span>
7601                 </p>
7602               </td>
7603 <td>
7604                 <p>
7605                   <span class="blue">Max = 3.8e+04&#949; (Mean = 2.66e+03&#949;)</span>
7606                 </p>
7607               </td>
7608 <td>
7609                 <p>
7610                   <span class="blue">Max = 4.07e+04&#949; (Mean = 2.86e+03&#949;)</span>
7611                 </p>
7612               </td>
7613 <td>
7614                 <p>
7615                   <span class="blue">Max = 8.59e+03&#949; (Mean = 277&#949;)</span>
7616                 </p>
7617               </td>
7618 </tr></tbody>
7619 </table></div>
7620 </div>
7621 <br class="table-break"><div class="table">
7622 <a name="math_toolkit.logs_and_tables.all_table.table_ibeta_inva"></a><p class="title"><b>Table&#160;22.57.&#160;Error rates for ibeta_inva</b></p>
7623 <div class="table-contents"><table class="table" summary="Error rates for ibeta_inva">
7624 <colgroup>
7625 <col>
7626 <col>
7627 <col>
7628 <col>
7629 <col>
7630 </colgroup>
7631 <thead><tr>
7632 <th>
7633               </th>
7634 <th>
7635                 <p>
7636                   GNU C++ version 7.1.0<br> linux<br> double
7637                 </p>
7638               </th>
7639 <th>
7640                 <p>
7641                   GNU C++ version 7.1.0<br> linux<br> long double
7642                 </p>
7643               </th>
7644 <th>
7645                 <p>
7646                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
7647                 </p>
7648               </th>
7649 <th>
7650                 <p>
7651                   Microsoft Visual C++ version 14.1<br> Win32<br> double
7652                 </p>
7653               </th>
7654 </tr></thead>
7655 <tbody><tr>
7656 <td>
7657                 <p>
7658                   Inverse incomplete beta
7659                 </p>
7660               </td>
7661 <td>
7662                 <p>
7663                   <span class="blue">Max = 0.602&#949; (Mean = 0.0239&#949;)</span>
7664                 </p>
7665               </td>
7666 <td>
7667                 <p>
7668                   <span class="blue">Max = 377&#949; (Mean = 24.4&#949;)</span>
7669                 </p>
7670               </td>
7671 <td>
7672                 <p>
7673                   <span class="blue">Max = 438&#949; (Mean = 31.3&#949;)</span>
7674                 </p>
7675               </td>
7676 <td>
7677                 <p>
7678                   <span class="blue">Max = 242&#949; (Mean = 22.9&#949;)</span>
7679                 </p>
7680               </td>
7681 </tr></tbody>
7682 </table></div>
7683 </div>
7684 <br class="table-break"><div class="table">
7685 <a name="math_toolkit.logs_and_tables.all_table.table_ibeta_invb"></a><p class="title"><b>Table&#160;22.58.&#160;Error rates for ibeta_invb</b></p>
7686 <div class="table-contents"><table class="table" summary="Error rates for ibeta_invb">
7687 <colgroup>
7688 <col>
7689 <col>
7690 <col>
7691 <col>
7692 <col>
7693 </colgroup>
7694 <thead><tr>
7695 <th>
7696               </th>
7697 <th>
7698                 <p>
7699                   GNU C++ version 7.1.0<br> linux<br> double
7700                 </p>
7701               </th>
7702 <th>
7703                 <p>
7704                   GNU C++ version 7.1.0<br> linux<br> long double
7705                 </p>
7706               </th>
7707 <th>
7708                 <p>
7709                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
7710                 </p>
7711               </th>
7712 <th>
7713                 <p>
7714                   Microsoft Visual C++ version 14.1<br> Win32<br> double
7715                 </p>
7716               </th>
7717 </tr></thead>
7718 <tbody><tr>
7719 <td>
7720                 <p>
7721                   Inverse incomplete beta
7722                 </p>
7723               </td>
7724 <td>
7725                 <p>
7726                   <span class="blue">Max = 0.765&#949; (Mean = 0.0422&#949;)</span>
7727                 </p>
7728               </td>
7729 <td>
7730                 <p>
7731                   <span class="blue">Max = 407&#949; (Mean = 27.2&#949;)</span>
7732                 </p>
7733               </td>
7734 <td>
7735                 <p>
7736                   <span class="blue">Max = 407&#949; (Mean = 24.4&#949;)</span>
7737                 </p>
7738               </td>
7739 <td>
7740                 <p>
7741                   <span class="blue">Max = 409&#949; (Mean = 19.3&#949;)</span>
7742                 </p>
7743               </td>
7744 </tr></tbody>
7745 </table></div>
7746 </div>
7747 <br class="table-break"><div class="table">
7748 <a name="math_toolkit.logs_and_tables.all_table.table_ibetac"></a><p class="title"><b>Table&#160;22.59.&#160;Error rates for ibetac</b></p>
7749 <div class="table-contents"><table class="table" summary="Error rates for ibetac">
7750 <colgroup>
7751 <col>
7752 <col>
7753 <col>
7754 <col>
7755 <col>
7756 </colgroup>
7757 <thead><tr>
7758 <th>
7759               </th>
7760 <th>
7761                 <p>
7762                   GNU C++ version 7.1.0<br> linux<br> double
7763                 </p>
7764               </th>
7765 <th>
7766                 <p>
7767                   GNU C++ version 7.1.0<br> linux<br> long double
7768                 </p>
7769               </th>
7770 <th>
7771                 <p>
7772                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
7773                 </p>
7774               </th>
7775 <th>
7776                 <p>
7777                   Microsoft Visual C++ version 14.1<br> Win32<br> double
7778                 </p>
7779               </th>
7780 </tr></thead>
7781 <tbody>
7782 <tr>
7783 <td>
7784                 <p>
7785                   Incomplete Beta Function: Small Values
7786                 </p>
7787               </td>
7788 <td>
7789                 <p>
7790                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>Rmath
7791                   3.2.3:</em></span> Max = 22.4&#949; (Mean = 3.67&#949;))
7792                 </p>
7793               </td>
7794 <td>
7795                 <p>
7796                   <span class="blue">Max = 10.6&#949; (Mean = 2.22&#949;)</span>
7797                 </p>
7798               </td>
7799 <td>
7800                 <p>
7801                   <span class="blue">Max = 13.8&#949; (Mean = 2.68&#949;)</span>
7802                 </p>
7803               </td>
7804 <td>
7805                 <p>
7806                   <span class="blue">Max = 6.94&#949; (Mean = 1.71&#949;)</span>
7807                 </p>
7808               </td>
7809 </tr>
7810 <tr>
7811 <td>
7812                 <p>
7813                   Incomplete Beta Function: Medium Values
7814                 </p>
7815               </td>
7816 <td>
7817                 <p>
7818                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>Rmath
7819                   3.2.3:</em></span> Max = 204&#949; (Mean = 25.8&#949;))
7820                 </p>
7821               </td>
7822 <td>
7823                 <p>
7824                   <span class="blue">Max = 73.9&#949; (Mean = 11.2&#949;)</span>
7825                 </p>
7826               </td>
7827 <td>
7828                 <p>
7829                   <span class="blue">Max = 132&#949; (Mean = 19.8&#949;)</span>
7830                 </p>
7831               </td>
7832 <td>
7833                 <p>
7834                   <span class="blue">Max = 56.7&#949; (Mean = 14.3&#949;)</span>
7835                 </p>
7836               </td>
7837 </tr>
7838 <tr>
7839 <td>
7840                 <p>
7841                   Incomplete Beta Function: Large and Diverse Values
7842                 </p>
7843               </td>
7844 <td>
7845                 <p>
7846                   <span class="blue">Max = 0.981&#949; (Mean = 0.0573&#949;)</span><br>
7847                   <br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 889&#949; (Mean = 68.4&#949;))
7848                 </p>
7849               </td>
7850 <td>
7851                 <p>
7852                   <span class="blue">Max = 3.45e+04&#949; (Mean = 1.32e+03&#949;)</span>
7853                 </p>
7854               </td>
7855 <td>
7856                 <p>
7857                   <span class="blue">Max = 6.31e+04&#949; (Mean = 2.04e+03&#949;)</span>
7858                 </p>
7859               </td>
7860 <td>
7861                 <p>
7862                   <span class="blue">Max = 1.88e+03&#949; (Mean = 82.7&#949;)</span>
7863                 </p>
7864               </td>
7865 </tr>
7866 <tr>
7867 <td>
7868                 <p>
7869                   Incomplete Beta Function: Small Integer Values
7870                 </p>
7871               </td>
7872 <td>
7873                 <p>
7874                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>Rmath
7875                   3.2.3:</em></span> Max = 84.6&#949; (Mean = 18&#949;))
7876                 </p>
7877               </td>
7878 <td>
7879                 <p>
7880                   <span class="blue">Max = 5.34&#949; (Mean = 1.11&#949;)</span>
7881                 </p>
7882               </td>
7883 <td>
7884                 <p>
7885                   <span class="blue">Max = 107&#949; (Mean = 17.1&#949;)</span>
7886                 </p>
7887               </td>
7888 <td>
7889                 <p>
7890                   <span class="blue">Max = 6.37&#949; (Mean = 1.03&#949;)</span>
7891                 </p>
7892               </td>
7893 </tr>
7894 </tbody>
7895 </table></div>
7896 </div>
7897 <br class="table-break"><div class="table">
7898 <a name="math_toolkit.logs_and_tables.all_table.table_ibetac_inv"></a><p class="title"><b>Table&#160;22.60.&#160;Error rates for ibetac_inv</b></p>
7899 <div class="table-contents"><table class="table" summary="Error rates for ibetac_inv">
7900 <colgroup>
7901 <col>
7902 <col>
7903 <col>
7904 <col>
7905 <col>
7906 </colgroup>
7907 <thead><tr>
7908 <th>
7909               </th>
7910 <th>
7911                 <p>
7912                   GNU C++ version 7.1.0<br> linux<br> double
7913                 </p>
7914               </th>
7915 <th>
7916                 <p>
7917                   GNU C++ version 7.1.0<br> linux<br> long double
7918                 </p>
7919               </th>
7920 <th>
7921                 <p>
7922                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
7923                 </p>
7924               </th>
7925 <th>
7926                 <p>
7927                   Microsoft Visual C++ version 14.1<br> Win32<br> double
7928                 </p>
7929               </th>
7930 </tr></thead>
7931 <tbody><tr>
7932 <td>
7933                 <p>
7934                   Inverse incomplete beta
7935                 </p>
7936               </td>
7937 <td>
7938                 <p>
7939                   <span class="blue">Max = 0.977&#949; (Mean = 0.0976&#949;)</span><br>
7940                   <br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max
7941                   = 3.01e+132&#949; (Mean = 8.65e+130&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_ibetac_inv_Rmath_3_2_3_Inverse_incomplete_beta">And
7942                   other failures.</a>)</span>
7943                 </p>
7944               </td>
7945 <td>
7946                 <p>
7947                   <span class="blue">Max = 4.88e+04&#949; (Mean = 3.16e+03&#949;)</span>
7948                 </p>
7949               </td>
7950 <td>
7951                 <p>
7952                   <span class="blue">Max = 5.05e+04&#949; (Mean = 3.33e+03&#949;)</span>
7953                 </p>
7954               </td>
7955 <td>
7956                 <p>
7957                   <span class="blue">Max = 2.93e+03&#949; (Mean = 198&#949;)</span>
7958                 </p>
7959               </td>
7960 </tr></tbody>
7961 </table></div>
7962 </div>
7963 <br class="table-break"><div class="table">
7964 <a name="math_toolkit.logs_and_tables.all_table.table_ibetac_inva"></a><p class="title"><b>Table&#160;22.61.&#160;Error rates for ibetac_inva</b></p>
7965 <div class="table-contents"><table class="table" summary="Error rates for ibetac_inva">
7966 <colgroup>
7967 <col>
7968 <col>
7969 <col>
7970 <col>
7971 <col>
7972 </colgroup>
7973 <thead><tr>
7974 <th>
7975               </th>
7976 <th>
7977                 <p>
7978                   GNU C++ version 7.1.0<br> linux<br> double
7979                 </p>
7980               </th>
7981 <th>
7982                 <p>
7983                   GNU C++ version 7.1.0<br> linux<br> long double
7984                 </p>
7985               </th>
7986 <th>
7987                 <p>
7988                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
7989                 </p>
7990               </th>
7991 <th>
7992                 <p>
7993                   Microsoft Visual C++ version 14.1<br> Win32<br> double
7994                 </p>
7995               </th>
7996 </tr></thead>
7997 <tbody><tr>
7998 <td>
7999                 <p>
8000                   Inverse incomplete beta
8001                 </p>
8002               </td>
8003 <td>
8004                 <p>
8005                   <span class="blue">Max = 0.683&#949; (Mean = 0.0314&#949;)</span>
8006                 </p>
8007               </td>
8008 <td>
8009                 <p>
8010                   <span class="blue">Max = 382&#949; (Mean = 22.2&#949;)</span>
8011                 </p>
8012               </td>
8013 <td>
8014                 <p>
8015                   <span class="blue">Max = 315&#949; (Mean = 23.7&#949;)</span>
8016                 </p>
8017               </td>
8018 <td>
8019                 <p>
8020                   <span class="blue">Max = 408&#949; (Mean = 26.7&#949;)</span>
8021                 </p>
8022               </td>
8023 </tr></tbody>
8024 </table></div>
8025 </div>
8026 <br class="table-break"><div class="table">
8027 <a name="math_toolkit.logs_and_tables.all_table.table_ibetac_invb"></a><p class="title"><b>Table&#160;22.62.&#160;Error rates for ibetac_invb</b></p>
8028 <div class="table-contents"><table class="table" summary="Error rates for ibetac_invb">
8029 <colgroup>
8030 <col>
8031 <col>
8032 <col>
8033 <col>
8034 <col>
8035 </colgroup>
8036 <thead><tr>
8037 <th>
8038               </th>
8039 <th>
8040                 <p>
8041                   GNU C++ version 7.1.0<br> linux<br> double
8042                 </p>
8043               </th>
8044 <th>
8045                 <p>
8046                   GNU C++ version 7.1.0<br> linux<br> long double
8047                 </p>
8048               </th>
8049 <th>
8050                 <p>
8051                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
8052                 </p>
8053               </th>
8054 <th>
8055                 <p>
8056                   Microsoft Visual C++ version 14.1<br> Win32<br> double
8057                 </p>
8058               </th>
8059 </tr></thead>
8060 <tbody><tr>
8061 <td>
8062                 <p>
8063                   Inverse incomplete beta
8064                 </p>
8065               </td>
8066 <td>
8067                 <p>
8068                   <span class="blue">Max = 0.724&#949; (Mean = 0.0303&#949;)</span>
8069                 </p>
8070               </td>
8071 <td>
8072                 <p>
8073                   <span class="blue">Max = 317&#949; (Mean = 19.8&#949;)</span>
8074                 </p>
8075               </td>
8076 <td>
8077                 <p>
8078                   <span class="blue">Max = 369&#949; (Mean = 22.6&#949;)</span>
8079                 </p>
8080               </td>
8081 <td>
8082                 <p>
8083                   <span class="blue">Max = 271&#949; (Mean = 16.4&#949;)</span>
8084                 </p>
8085               </td>
8086 </tr></tbody>
8087 </table></div>
8088 </div>
8089 <br class="table-break"><div class="table">
8090 <a name="math_toolkit.logs_and_tables.all_table.table_jacobi_cn"></a><p class="title"><b>Table&#160;22.63.&#160;Error rates for jacobi_cn</b></p>
8091 <div class="table-contents"><table class="table" summary="Error rates for jacobi_cn">
8092 <colgroup>
8093 <col>
8094 <col>
8095 <col>
8096 <col>
8097 <col>
8098 </colgroup>
8099 <thead><tr>
8100 <th>
8101               </th>
8102 <th>
8103                 <p>
8104                   GNU C++ version 7.1.0<br> linux<br> double
8105                 </p>
8106               </th>
8107 <th>
8108                 <p>
8109                   GNU C++ version 7.1.0<br> linux<br> long double
8110                 </p>
8111               </th>
8112 <th>
8113                 <p>
8114                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
8115                 </p>
8116               </th>
8117 <th>
8118                 <p>
8119                   Microsoft Visual C++ version 14.1<br> Win32<br> double
8120                 </p>
8121               </th>
8122 </tr></thead>
8123 <tbody>
8124 <tr>
8125 <td>
8126                 <p>
8127                   Jacobi Elliptic: Mathworld Data
8128                 </p>
8129               </td>
8130 <td>
8131                 <p>
8132                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
8133                   2.1:</em></span> Max = 17.3&#949; (Mean = 4.29&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data">And
8134                   other failures.</a>)
8135                 </p>
8136               </td>
8137 <td>
8138                 <p>
8139                   <span class="blue">Max = 71.6&#949; (Mean = 19.3&#949;)</span>
8140                 </p>
8141               </td>
8142 <td>
8143                 <p>
8144                   <span class="blue">Max = 71.6&#949; (Mean = 19.4&#949;)</span>
8145                 </p>
8146               </td>
8147 <td>
8148                 <p>
8149                   <span class="blue">Max = 45.8&#949; (Mean = 11.4&#949;)</span>
8150                 </p>
8151               </td>
8152 </tr>
8153 <tr>
8154 <td>
8155                 <p>
8156                   Jacobi Elliptic: Random Data
8157                 </p>
8158               </td>
8159 <td>
8160                 <p>
8161                   <span class="blue">Max = 0.816&#949; (Mean = 0.0563&#949;)</span><br>
8162                   <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.43&#949; (Mean = 0.803&#949;))
8163                 </p>
8164               </td>
8165 <td>
8166                 <p>
8167                   <span class="blue">Max = 1.68&#949; (Mean = 0.443&#949;)</span>
8168                 </p>
8169               </td>
8170 <td>
8171                 <p>
8172                   <span class="blue">Max = 1.68&#949; (Mean = 0.454&#949;)</span>
8173                 </p>
8174               </td>
8175 <td>
8176                 <p>
8177                   <span class="blue">Max = 1.83&#949; (Mean = 0.455&#949;)</span>
8178                 </p>
8179               </td>
8180 </tr>
8181 <tr>
8182 <td>
8183                 <p>
8184                   Jacobi Elliptic: Random Small Values
8185                 </p>
8186               </td>
8187 <td>
8188                 <p>
8189                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
8190                   2.1:</em></span> Max = 55.2&#949; (Mean = 1.64&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values">And
8191                   other failures.</a>)
8192                 </p>
8193               </td>
8194 <td>
8195                 <p>
8196                   <span class="blue">Max = 10.4&#949; (Mean = 0.594&#949;)</span>
8197                 </p>
8198               </td>
8199 <td>
8200                 <p>
8201                   <span class="blue">Max = 10.4&#949; (Mean = 0.602&#949;)</span>
8202                 </p>
8203               </td>
8204 <td>
8205                 <p>
8206                   <span class="blue">Max = 26.2&#949; (Mean = 1.17&#949;)</span>
8207                 </p>
8208               </td>
8209 </tr>
8210 <tr>
8211 <td>
8212                 <p>
8213                   Jacobi Elliptic: Modulus near 1
8214                 </p>
8215               </td>
8216 <td>
8217                 <p>
8218                   <span class="blue">Max = 0.919&#949; (Mean = 0.127&#949;)</span><br> <br>
8219                   (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0&#949; (Mean = 0&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1">And
8220                   other failures.</a>)
8221                 </p>
8222               </td>
8223 <td>
8224                 <p>
8225                   <span class="blue">Max = 675&#949; (Mean = 87.1&#949;)</span>
8226                 </p>
8227               </td>
8228 <td>
8229                 <p>
8230                   <span class="blue">Max = 675&#949; (Mean = 86.8&#949;)</span>
8231                 </p>
8232               </td>
8233 <td>
8234                 <p>
8235                   <span class="blue">Max = 513&#949; (Mean = 126&#949;)</span>
8236                 </p>
8237               </td>
8238 </tr>
8239 <tr>
8240 <td>
8241                 <p>
8242                   Jacobi Elliptic: Large Phi
8243                 </p>
8244               </td>
8245 <td>
8246                 <p>
8247                   <span class="blue">Max = 14.2&#949; (Mean = 0.927&#949;)</span><br> <br>
8248                   (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 5.92e+03&#949; (Mean = 477&#949;))
8249                 </p>
8250               </td>
8251 <td>
8252                 <p>
8253                   <span class="blue">Max = 2.97e+04&#949; (Mean = 1.9e+03&#949;)</span>
8254                 </p>
8255               </td>
8256 <td>
8257                 <p>
8258                   <span class="blue">Max = 2.97e+04&#949; (Mean = 1.9e+03&#949;)</span>
8259                 </p>
8260               </td>
8261 <td>
8262                 <p>
8263                   <span class="blue">Max = 3.27e+04&#949; (Mean = 1.93e+03&#949;)</span>
8264                 </p>
8265               </td>
8266 </tr>
8267 </tbody>
8268 </table></div>
8269 </div>
8270 <br class="table-break"><div class="table">
8271 <a name="math_toolkit.logs_and_tables.all_table.table_jacobi_dn"></a><p class="title"><b>Table&#160;22.64.&#160;Error rates for jacobi_dn</b></p>
8272 <div class="table-contents"><table class="table" summary="Error rates for jacobi_dn">
8273 <colgroup>
8274 <col>
8275 <col>
8276 <col>
8277 <col>
8278 <col>
8279 </colgroup>
8280 <thead><tr>
8281 <th>
8282               </th>
8283 <th>
8284                 <p>
8285                   GNU C++ version 7.1.0<br> linux<br> double
8286                 </p>
8287               </th>
8288 <th>
8289                 <p>
8290                   GNU C++ version 7.1.0<br> linux<br> long double
8291                 </p>
8292               </th>
8293 <th>
8294                 <p>
8295                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
8296                 </p>
8297               </th>
8298 <th>
8299                 <p>
8300                   Microsoft Visual C++ version 14.1<br> Win32<br> double
8301                 </p>
8302               </th>
8303 </tr></thead>
8304 <tbody>
8305 <tr>
8306 <td>
8307                 <p>
8308                   Jacobi Elliptic: Mathworld Data
8309                 </p>
8310               </td>
8311 <td>
8312                 <p>
8313                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
8314                   2.1:</em></span> Max = 2.82&#949; (Mean = 1.18&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data">And
8315                   other failures.</a>)
8316                 </p>
8317               </td>
8318 <td>
8319                 <p>
8320                   <span class="blue">Max = 49&#949; (Mean = 14&#949;)</span>
8321                 </p>
8322               </td>
8323 <td>
8324                 <p>
8325                   <span class="blue">Max = 49&#949; (Mean = 14&#949;)</span>
8326                 </p>
8327               </td>
8328 <td>
8329                 <p>
8330                   <span class="blue">Max = 34.3&#949; (Mean = 8.71&#949;)</span>
8331                 </p>
8332               </td>
8333 </tr>
8334 <tr>
8335 <td>
8336                 <p>
8337                   Jacobi Elliptic: Random Data
8338                 </p>
8339               </td>
8340 <td>
8341                 <p>
8342                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
8343                   2.1:</em></span> Max = 3&#949; (Mean = 0.61&#949;))
8344                 </p>
8345               </td>
8346 <td>
8347                 <p>
8348                   <span class="blue">Max = 1.53&#949; (Mean = 0.473&#949;)</span>
8349                 </p>
8350               </td>
8351 <td>
8352                 <p>
8353                   <span class="blue">Max = 1.53&#949; (Mean = 0.481&#949;)</span>
8354                 </p>
8355               </td>
8356 <td>
8357                 <p>
8358                   <span class="blue">Max = 1.52&#949; (Mean = 0.466&#949;)</span>
8359                 </p>
8360               </td>
8361 </tr>
8362 <tr>
8363 <td>
8364                 <p>
8365                   Jacobi Elliptic: Random Small Values
8366                 </p>
8367               </td>
8368 <td>
8369                 <p>
8370                   <span class="blue">Max = 0.5&#949; (Mean = 0.0122&#949;)</span><br> <br>
8371                   (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.5&#949; (Mean = 0.391&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values">And
8372                   other failures.</a>)
8373                 </p>
8374               </td>
8375 <td>
8376                 <p>
8377                   <span class="blue">Max = 22.4&#949; (Mean = 0.777&#949;)</span>
8378                 </p>
8379               </td>
8380 <td>
8381                 <p>
8382                   <span class="blue">Max = 22.4&#949; (Mean = 0.763&#949;)</span>
8383                 </p>
8384               </td>
8385 <td>
8386                 <p>
8387                   <span class="blue">Max = 16.1&#949; (Mean = 0.685&#949;)</span>
8388                 </p>
8389               </td>
8390 </tr>
8391 <tr>
8392 <td>
8393                 <p>
8394                   Jacobi Elliptic: Modulus near 1
8395                 </p>
8396               </td>
8397 <td>
8398                 <p>
8399                   <span class="blue">Max = 2.28&#949; (Mean = 0.194&#949;)</span><br> <br>
8400                   (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0&#949; (Mean = 0&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1">And
8401                   other failures.</a>)
8402                 </p>
8403               </td>
8404 <td>
8405                 <p>
8406                   <span class="blue">Max = 3.75e+03&#949; (Mean = 293&#949;)</span>
8407                 </p>
8408               </td>
8409 <td>
8410                 <p>
8411                   <span class="blue">Max = 3.75e+03&#949; (Mean = 293&#949;)</span>
8412                 </p>
8413               </td>
8414 <td>
8415                 <p>
8416                   <span class="blue">Max = 6.24e+03&#949; (Mean = 482&#949;)</span>
8417                 </p>
8418               </td>
8419 </tr>
8420 <tr>
8421 <td>
8422                 <p>
8423                   Jacobi Elliptic: Large Phi
8424                 </p>
8425               </td>
8426 <td>
8427                 <p>
8428                   <span class="blue">Max = 14.1&#949; (Mean = 0.897&#949;)</span><br> <br>
8429                   (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 121&#949; (Mean = 22&#949;))
8430                 </p>
8431               </td>
8432 <td>
8433                 <p>
8434                   <span class="blue">Max = 2.82e+04&#949; (Mean = 1.79e+03&#949;)</span>
8435                 </p>
8436               </td>
8437 <td>
8438                 <p>
8439                   <span class="blue">Max = 2.82e+04&#949; (Mean = 1.79e+03&#949;)</span>
8440                 </p>
8441               </td>
8442 <td>
8443                 <p>
8444                   <span class="blue">Max = 1.67e+04&#949; (Mean = 1e+03&#949;)</span>
8445                 </p>
8446               </td>
8447 </tr>
8448 </tbody>
8449 </table></div>
8450 </div>
8451 <br class="table-break"><div class="table">
8452 <a name="math_toolkit.logs_and_tables.all_table.table_jacobi_sn"></a><p class="title"><b>Table&#160;22.65.&#160;Error rates for jacobi_sn</b></p>
8453 <div class="table-contents"><table class="table" summary="Error rates for jacobi_sn">
8454 <colgroup>
8455 <col>
8456 <col>
8457 <col>
8458 <col>
8459 <col>
8460 </colgroup>
8461 <thead><tr>
8462 <th>
8463               </th>
8464 <th>
8465                 <p>
8466                   GNU C++ version 7.1.0<br> linux<br> double
8467                 </p>
8468               </th>
8469 <th>
8470                 <p>
8471                   GNU C++ version 7.1.0<br> linux<br> long double
8472                 </p>
8473               </th>
8474 <th>
8475                 <p>
8476                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
8477                 </p>
8478               </th>
8479 <th>
8480                 <p>
8481                   Microsoft Visual C++ version 14.1<br> Win32<br> double
8482                 </p>
8483               </th>
8484 </tr></thead>
8485 <tbody>
8486 <tr>
8487 <td>
8488                 <p>
8489                   Jacobi Elliptic: Mathworld Data
8490                 </p>
8491               </td>
8492 <td>
8493                 <p>
8494                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
8495                   2.1:</em></span> Max = 588&#949; (Mean = 146&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data">And
8496                   other failures.</a>)
8497                 </p>
8498               </td>
8499 <td>
8500                 <p>
8501                   <span class="blue">Max = 341&#949; (Mean = 80.7&#949;)</span>
8502                 </p>
8503               </td>
8504 <td>
8505                 <p>
8506                   <span class="blue">Max = 341&#949; (Mean = 80.7&#949;)</span>
8507                 </p>
8508               </td>
8509 <td>
8510                 <p>
8511                   <span class="blue">Max = 481&#949; (Mean = 113&#949;)</span>
8512                 </p>
8513               </td>
8514 </tr>
8515 <tr>
8516 <td>
8517                 <p>
8518                   Jacobi Elliptic: Random Data
8519                 </p>
8520               </td>
8521 <td>
8522                 <p>
8523                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
8524                   2.1:</em></span> Max = 4.02&#949; (Mean = 1.07&#949;))
8525                 </p>
8526               </td>
8527 <td>
8528                 <p>
8529                   <span class="blue">Max = 2.01&#949; (Mean = 0.584&#949;)</span>
8530                 </p>
8531               </td>
8532 <td>
8533                 <p>
8534                   <span class="blue">Max = 2.01&#949; (Mean = 0.593&#949;)</span>
8535                 </p>
8536               </td>
8537 <td>
8538                 <p>
8539                   <span class="blue">Max = 1.92&#949; (Mean = 0.567&#949;)</span>
8540                 </p>
8541               </td>
8542 </tr>
8543 <tr>
8544 <td>
8545                 <p>
8546                   Jacobi Elliptic: Random Small Values
8547                 </p>
8548               </td>
8549 <td>
8550                 <p>
8551                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
8552                   2.1:</em></span> Max = 11.7&#949; (Mean = 1.65&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values">And
8553                   other failures.</a>)
8554                 </p>
8555               </td>
8556 <td>
8557                 <p>
8558                   <span class="blue">Max = 1.99&#949; (Mean = 0.347&#949;)</span>
8559                 </p>
8560               </td>
8561 <td>
8562                 <p>
8563                   <span class="blue">Max = 1.99&#949; (Mean = 0.347&#949;)</span>
8564                 </p>
8565               </td>
8566 <td>
8567                 <p>
8568                   <span class="blue">Max = 2.11&#949; (Mean = 0.385&#949;)</span>
8569                 </p>
8570               </td>
8571 </tr>
8572 <tr>
8573 <td>
8574                 <p>
8575                   Jacobi Elliptic: Modulus near 1
8576                 </p>
8577               </td>
8578 <td>
8579                 <p>
8580                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
8581                   2.1:</em></span> Max = 0&#949; (Mean = 0&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1">And
8582                   other failures.</a>)
8583                 </p>
8584               </td>
8585 <td>
8586                 <p>
8587                   <span class="blue">Max = 109&#949; (Mean = 7.35&#949;)</span>
8588                 </p>
8589               </td>
8590 <td>
8591                 <p>
8592                   <span class="blue">Max = 109&#949; (Mean = 7.38&#949;)</span>
8593                 </p>
8594               </td>
8595 <td>
8596                 <p>
8597                   <span class="blue">Max = 23.2&#949; (Mean = 1.85&#949;)</span>
8598                 </p>
8599               </td>
8600 </tr>
8601 <tr>
8602 <td>
8603                 <p>
8604                   Jacobi Elliptic: Large Phi
8605                 </p>
8606               </td>
8607 <td>
8608                 <p>
8609                   <span class="blue">Max = 12&#949; (Mean = 0.771&#949;)</span><br> <br>
8610                   (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 4.54e+04&#949; (Mean = 2.63e+03&#949;))
8611                 </p>
8612               </td>
8613 <td>
8614                 <p>
8615                   <span class="blue">Max = 2.45e+04&#949; (Mean = 1.51e+03&#949;)</span>
8616                 </p>
8617               </td>
8618 <td>
8619                 <p>
8620                   <span class="blue">Max = 2.45e+04&#949; (Mean = 1.51e+03&#949;)</span>
8621                 </p>
8622               </td>
8623 <td>
8624                 <p>
8625                   <span class="blue">Max = 4.36e+04&#949; (Mean = 2.54e+03&#949;)</span>
8626                 </p>
8627               </td>
8628 </tr>
8629 </tbody>
8630 </table></div>
8631 </div>
8632 <br class="table-break"><div class="table">
8633 <a name="math_toolkit.logs_and_tables.all_table.table_jacobi_zeta"></a><p class="title"><b>Table&#160;22.66.&#160;Error rates for jacobi_zeta</b></p>
8634 <div class="table-contents"><table class="table" summary="Error rates for jacobi_zeta">
8635 <colgroup>
8636 <col>
8637 <col>
8638 <col>
8639 <col>
8640 <col>
8641 </colgroup>
8642 <thead><tr>
8643 <th>
8644               </th>
8645 <th>
8646                 <p>
8647                   GNU C++ version 7.1.0<br> linux<br> double
8648                 </p>
8649               </th>
8650 <th>
8651                 <p>
8652                   GNU C++ version 7.1.0<br> linux<br> long double
8653                 </p>
8654               </th>
8655 <th>
8656                 <p>
8657                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
8658                 </p>
8659               </th>
8660 <th>
8661                 <p>
8662                   Microsoft Visual C++ version 14.1<br> Win32<br> double
8663                 </p>
8664               </th>
8665 </tr></thead>
8666 <tbody>
8667 <tr>
8668 <td>
8669                 <p>
8670                   Elliptic Integral Jacobi Zeta: Mathworld Data
8671                 </p>
8672               </td>
8673 <td>
8674                 <p>
8675                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
8676                 </p>
8677               </td>
8678 <td>
8679                 <p>
8680                   <span class="blue">Max = 1.66&#949; (Mean = 0.48&#949;)</span>
8681                 </p>
8682               </td>
8683 <td>
8684                 <p>
8685                   <span class="blue">Max = 1.66&#949; (Mean = 0.48&#949;)</span>
8686                 </p>
8687               </td>
8688 <td>
8689                 <p>
8690                   <span class="blue">Max = 1.52&#949; (Mean = 0.357&#949;)</span>
8691                 </p>
8692               </td>
8693 </tr>
8694 <tr>
8695 <td>
8696                 <p>
8697                   Elliptic Integral Jacobi Zeta: Random Data
8698                 </p>
8699               </td>
8700 <td>
8701                 <p>
8702                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
8703                 </p>
8704               </td>
8705 <td>
8706                 <p>
8707                   <span class="blue">Max = 2.99&#949; (Mean = 0.824&#949;)</span>
8708                 </p>
8709               </td>
8710 <td>
8711                 <p>
8712                   <span class="blue">Max = 3.96&#949; (Mean = 1.06&#949;)</span>
8713                 </p>
8714               </td>
8715 <td>
8716                 <p>
8717                   <span class="blue">Max = 3.89&#949; (Mean = 0.824&#949;)</span>
8718                 </p>
8719               </td>
8720 </tr>
8721 <tr>
8722 <td>
8723                 <p>
8724                   Elliptic Integral Jacobi Zeta: Large Phi Values
8725                 </p>
8726               </td>
8727 <td>
8728                 <p>
8729                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
8730                 </p>
8731               </td>
8732 <td>
8733                 <p>
8734                   <span class="blue">Max = 2.92&#949; (Mean = 0.951&#949;)</span>
8735                 </p>
8736               </td>
8737 <td>
8738                 <p>
8739                   <span class="blue">Max = 3.05&#949; (Mean = 1.13&#949;)</span>
8740                 </p>
8741               </td>
8742 <td>
8743                 <p>
8744                   <span class="blue">Max = 2.52&#949; (Mean = 0.977&#949;)</span>
8745                 </p>
8746               </td>
8747 </tr>
8748 </tbody>
8749 </table></div>
8750 </div>
8751 <br class="table-break"><div class="table">
8752 <a name="math_toolkit.logs_and_tables.all_table.table_laguerre_n_m_x_"></a><p class="title"><b>Table&#160;22.67.&#160;Error rates for laguerre(n, m, x)</b></p>
8753 <div class="table-contents"><table class="table" summary="Error rates for laguerre(n, m, x)">
8754 <colgroup>
8755 <col>
8756 <col>
8757 <col>
8758 <col>
8759 <col>
8760 </colgroup>
8761 <thead><tr>
8762 <th>
8763               </th>
8764 <th>
8765                 <p>
8766                   GNU C++ version 7.1.0<br> linux<br> double
8767                 </p>
8768               </th>
8769 <th>
8770                 <p>
8771                   GNU C++ version 7.1.0<br> linux<br> long double
8772                 </p>
8773               </th>
8774 <th>
8775                 <p>
8776                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
8777                 </p>
8778               </th>
8779 <th>
8780                 <p>
8781                   Microsoft Visual C++ version 14.1<br> Win32<br> double
8782                 </p>
8783               </th>
8784 </tr></thead>
8785 <tbody><tr>
8786 <td>
8787                 <p>
8788                   Associated Laguerre Polynomials
8789                 </p>
8790               </td>
8791 <td>
8792                 <p>
8793                   <span class="blue">Max = 0.84&#949; (Mean = 0.0358&#949;)</span><br> <br>
8794                   (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 434&#949; (Mean = 10.7&#949;))
8795                 </p>
8796               </td>
8797 <td>
8798                 <p>
8799                   <span class="blue">Max = 167&#949; (Mean = 6.38&#949;)</span><br> <br>
8800                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 206&#949; (Mean = 6.86&#949;))
8801                 </p>
8802               </td>
8803 <td>
8804                 <p>
8805                   <span class="blue">Max = 167&#949; (Mean = 6.38&#949;)</span>
8806                 </p>
8807               </td>
8808 <td>
8809                 <p>
8810                   <span class="blue">Max = 434&#949; (Mean = 11.1&#949;)</span>
8811                 </p>
8812               </td>
8813 </tr></tbody>
8814 </table></div>
8815 </div>
8816 <br class="table-break"><div class="table">
8817 <a name="math_toolkit.logs_and_tables.all_table.table_laguerre_n_x_"></a><p class="title"><b>Table&#160;22.68.&#160;Error rates for laguerre(n, x)</b></p>
8818 <div class="table-contents"><table class="table" summary="Error rates for laguerre(n, x)">
8819 <colgroup>
8820 <col>
8821 <col>
8822 <col>
8823 <col>
8824 <col>
8825 </colgroup>
8826 <thead><tr>
8827 <th>
8828               </th>
8829 <th>
8830                 <p>
8831                   GNU C++ version 7.1.0<br> linux<br> double
8832                 </p>
8833               </th>
8834 <th>
8835                 <p>
8836                   GNU C++ version 7.1.0<br> linux<br> long double
8837                 </p>
8838               </th>
8839 <th>
8840                 <p>
8841                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
8842                 </p>
8843               </th>
8844 <th>
8845                 <p>
8846                   Microsoft Visual C++ version 14.1<br> Win32<br> double
8847                 </p>
8848               </th>
8849 </tr></thead>
8850 <tbody><tr>
8851 <td>
8852                 <p>
8853                   Laguerre Polynomials
8854                 </p>
8855               </td>
8856 <td>
8857                 <p>
8858                   <span class="blue">Max = 6.82&#949; (Mean = 0.408&#949;)</span><br> <br>
8859                   (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.1e+03&#949; (Mean = 185&#949;))
8860                 </p>
8861               </td>
8862 <td>
8863                 <p>
8864                   <span class="blue">Max = 1.39e+04&#949; (Mean = 828&#949;)</span><br>
8865                   <br> (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 4.2e+03&#949; (Mean
8866                   = 251&#949;))
8867                 </p>
8868               </td>
8869 <td>
8870                 <p>
8871                   <span class="blue">Max = 1.39e+04&#949; (Mean = 828&#949;)</span>
8872                 </p>
8873               </td>
8874 <td>
8875                 <p>
8876                   <span class="blue">Max = 3.1e+03&#949; (Mean = 185&#949;)</span>
8877                 </p>
8878               </td>
8879 </tr></tbody>
8880 </table></div>
8881 </div>
8882 <br class="table-break"><div class="table">
8883 <a name="math_toolkit.logs_and_tables.all_table.table_legendre_p"></a><p class="title"><b>Table&#160;22.69.&#160;Error rates for legendre_p</b></p>
8884 <div class="table-contents"><table class="table" summary="Error rates for legendre_p">
8885 <colgroup>
8886 <col>
8887 <col>
8888 <col>
8889 <col>
8890 <col>
8891 </colgroup>
8892 <thead><tr>
8893 <th>
8894               </th>
8895 <th>
8896                 <p>
8897                   GNU C++ version 7.1.0<br> linux<br> double
8898                 </p>
8899               </th>
8900 <th>
8901                 <p>
8902                   GNU C++ version 7.1.0<br> linux<br> long double
8903                 </p>
8904               </th>
8905 <th>
8906                 <p>
8907                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
8908                 </p>
8909               </th>
8910 <th>
8911                 <p>
8912                   Microsoft Visual C++ version 14.1<br> Win32<br> double
8913                 </p>
8914               </th>
8915 </tr></thead>
8916 <tbody>
8917 <tr>
8918 <td>
8919                 <p>
8920                   Legendre Polynomials: Small Values
8921                 </p>
8922               </td>
8923 <td>
8924                 <p>
8925                   <span class="blue">Max = 0.732&#949; (Mean = 0.0619&#949;)</span><br>
8926                   <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 211&#949; (Mean = 20.4&#949;))
8927                 </p>
8928               </td>
8929 <td>
8930                 <p>
8931                   <span class="blue">Max = 69.2&#949; (Mean = 9.58&#949;)</span><br> <br>
8932                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 124&#949; (Mean = 13.2&#949;))
8933                 </p>
8934               </td>
8935 <td>
8936                 <p>
8937                   <span class="blue">Max = 69.2&#949; (Mean = 9.58&#949;)</span>
8938                 </p>
8939               </td>
8940 <td>
8941                 <p>
8942                   <span class="blue">Max = 211&#949; (Mean = 20.4&#949;)</span>
8943                 </p>
8944               </td>
8945 </tr>
8946 <tr>
8947 <td>
8948                 <p>
8949                   Legendre Polynomials: Large Values
8950                 </p>
8951               </td>
8952 <td>
8953                 <p>
8954                   <span class="blue">Max = 0.632&#949; (Mean = 0.0693&#949;)</span><br>
8955                   <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 300&#949; (Mean = 33.2&#949;))
8956                 </p>
8957               </td>
8958 <td>
8959                 <p>
8960                   <span class="blue">Max = 699&#949; (Mean = 59.6&#949;)</span><br> <br>
8961                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 343&#949; (Mean = 32.1&#949;))
8962                 </p>
8963               </td>
8964 <td>
8965                 <p>
8966                   <span class="blue">Max = 699&#949; (Mean = 59.6&#949;)</span>
8967                 </p>
8968               </td>
8969 <td>
8970                 <p>
8971                   <span class="blue">Max = 300&#949; (Mean = 33.2&#949;)</span>
8972                 </p>
8973               </td>
8974 </tr>
8975 </tbody>
8976 </table></div>
8977 </div>
8978 <br class="table-break"><div class="table">
8979 <a name="math_toolkit.logs_and_tables.all_table.table_legendre_p_associated_"></a><p class="title"><b>Table&#160;22.70.&#160;Error rates for legendre_p (associated)</b></p>
8980 <div class="table-contents"><table class="table" summary="Error rates for legendre_p (associated)">
8981 <colgroup>
8982 <col>
8983 <col>
8984 <col>
8985 <col>
8986 <col>
8987 </colgroup>
8988 <thead><tr>
8989 <th>
8990               </th>
8991 <th>
8992                 <p>
8993                   GNU C++ version 7.1.0<br> linux<br> double
8994                 </p>
8995               </th>
8996 <th>
8997                 <p>
8998                   GNU C++ version 7.1.0<br> linux<br> long double
8999                 </p>
9000               </th>
9001 <th>
9002                 <p>
9003                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
9004                 </p>
9005               </th>
9006 <th>
9007                 <p>
9008                   Microsoft Visual C++ version 14.1<br> Win32<br> double
9009                 </p>
9010               </th>
9011 </tr></thead>
9012 <tbody><tr>
9013 <td>
9014                 <p>
9015                   Associated Legendre Polynomials: Small Values
9016                 </p>
9017               </td>
9018 <td>
9019                 <p>
9020                   <span class="blue">Max = 0.999&#949; (Mean = 0.05&#949;)</span><br> <br>
9021                   (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 121&#949; (Mean = 6.75&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_legendre_p_associated__GSL_2_1_Associated_Legendre_Polynomials_Small_Values">And
9022                   other failures.</a>)
9023                 </p>
9024               </td>
9025 <td>
9026                 <p>
9027                   <span class="blue">Max = 175&#949; (Mean = 9.88&#949;)</span><br> <br>
9028                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 175&#949; (Mean = 9.36&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_legendre_p_associated___cmath__Associated_Legendre_Polynomials_Small_Values">And
9029                   other failures.</a>)
9030                 </p>
9031               </td>
9032 <td>
9033                 <p>
9034                   <span class="blue">Max = 77.7&#949; (Mean = 5.59&#949;)</span>
9035                 </p>
9036               </td>
9037 <td>
9038                 <p>
9039                   <span class="blue">Max = 121&#949; (Mean = 7.14&#949;)</span>
9040                 </p>
9041               </td>
9042 </tr></tbody>
9043 </table></div>
9044 </div>
9045 <br class="table-break"><div class="table">
9046 <a name="math_toolkit.logs_and_tables.all_table.table_legendre_q"></a><p class="title"><b>Table&#160;22.71.&#160;Error rates for legendre_q</b></p>
9047 <div class="table-contents"><table class="table" summary="Error rates for legendre_q">
9048 <colgroup>
9049 <col>
9050 <col>
9051 <col>
9052 <col>
9053 <col>
9054 </colgroup>
9055 <thead><tr>
9056 <th>
9057               </th>
9058 <th>
9059                 <p>
9060                   GNU C++ version 7.1.0<br> linux<br> double
9061                 </p>
9062               </th>
9063 <th>
9064                 <p>
9065                   GNU C++ version 7.1.0<br> linux<br> long double
9066                 </p>
9067               </th>
9068 <th>
9069                 <p>
9070                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
9071                 </p>
9072               </th>
9073 <th>
9074                 <p>
9075                   Microsoft Visual C++ version 14.1<br> Win32<br> double
9076                 </p>
9077               </th>
9078 </tr></thead>
9079 <tbody>
9080 <tr>
9081 <td>
9082                 <p>
9083                   Legendre Polynomials: Small Values
9084                 </p>
9085               </td>
9086 <td>
9087                 <p>
9088                   <span class="blue">Max = 0.612&#949; (Mean = 0.0517&#949;)</span><br>
9089                   <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 46.4&#949; (Mean = 7.46&#949;))
9090                 </p>
9091               </td>
9092 <td>
9093                 <p>
9094                   <span class="blue">Max = 50.9&#949; (Mean = 9&#949;)</span>
9095                 </p>
9096               </td>
9097 <td>
9098                 <p>
9099                   <span class="blue">Max = 50.9&#949; (Mean = 8.98&#949;)</span>
9100                 </p>
9101               </td>
9102 <td>
9103                 <p>
9104                   <span class="blue">Max = 46.4&#949; (Mean = 7.32&#949;)</span>
9105                 </p>
9106               </td>
9107 </tr>
9108 <tr>
9109 <td>
9110                 <p>
9111                   Legendre Polynomials: Large Values
9112                 </p>
9113               </td>
9114 <td>
9115                 <p>
9116                   <span class="blue">Max = 2.49&#949; (Mean = 0.202&#949;)</span><br> <br>
9117                   (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 4.6e+03&#949; (Mean = 366&#949;))
9118                 </p>
9119               </td>
9120 <td>
9121                 <p>
9122                   <span class="blue">Max = 5.98e+03&#949; (Mean = 478&#949;)</span>
9123                 </p>
9124               </td>
9125 <td>
9126                 <p>
9127                   <span class="blue">Max = 5.98e+03&#949; (Mean = 478&#949;)</span>
9128                 </p>
9129               </td>
9130 <td>
9131                 <p>
9132                   <span class="blue">Max = 4.6e+03&#949; (Mean = 366&#949;)</span>
9133                 </p>
9134               </td>
9135 </tr>
9136 </tbody>
9137 </table></div>
9138 </div>
9139 <br class="table-break"><div class="table">
9140 <a name="math_toolkit.logs_and_tables.all_table.table_lgamma"></a><p class="title"><b>Table&#160;22.72.&#160;Error rates for lgamma</b></p>
9141 <div class="table-contents"><table class="table" summary="Error rates for lgamma">
9142 <colgroup>
9143 <col>
9144 <col>
9145 <col>
9146 <col>
9147 <col>
9148 </colgroup>
9149 <thead><tr>
9150 <th>
9151               </th>
9152 <th>
9153                 <p>
9154                   GNU C++ version 7.1.0<br> linux<br> double
9155                 </p>
9156               </th>
9157 <th>
9158                 <p>
9159                   GNU C++ version 7.1.0<br> linux<br> long double
9160                 </p>
9161               </th>
9162 <th>
9163                 <p>
9164                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
9165                 </p>
9166               </th>
9167 <th>
9168                 <p>
9169                   Microsoft Visual C++ version 14.1<br> Win32<br> double
9170                 </p>
9171               </th>
9172 </tr></thead>
9173 <tbody>
9174 <tr>
9175 <td>
9176                 <p>
9177                   factorials
9178                 </p>
9179               </td>
9180 <td>
9181                 <p>
9182                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
9183                   2.1:</em></span> Max = 33.6&#949; (Mean = 2.78&#949;))<br> (<span class="emphasis"><em>Rmath
9184                   3.2.3:</em></span> Max = 1.55&#949; (Mean = 0.592&#949;))
9185                 </p>
9186               </td>
9187 <td>
9188                 <p>
9189                   <span class="blue">Max = 0.991&#949; (Mean = 0.308&#949;)</span><br> <br>
9190                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.67&#949; (Mean = 0.487&#949;))<br>
9191                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.67&#949; (Mean = 0.487&#949;))
9192                 </p>
9193               </td>
9194 <td>
9195                 <p>
9196                   <span class="blue">Max = 0.991&#949; (Mean = 0.383&#949;)</span><br> <br>
9197                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.36&#949; (Mean = 0.476&#949;))
9198                 </p>
9199               </td>
9200 <td>
9201                 <p>
9202                   <span class="blue">Max = 0.914&#949; (Mean = 0.175&#949;)</span><br> <br>
9203                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.958&#949; (Mean = 0.38&#949;))
9204                 </p>
9205               </td>
9206 </tr>
9207 <tr>
9208 <td>
9209                 <p>
9210                   near 0
9211                 </p>
9212               </td>
9213 <td>
9214                 <p>
9215                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
9216                   2.1:</em></span> Max = 5.21&#949; (Mean = 1.57&#949;))<br> (<span class="emphasis"><em>Rmath
9217                   3.2.3:</em></span> Max = 0&#949; (Mean = 0&#949;))
9218                 </p>
9219               </td>
9220 <td>
9221                 <p>
9222                   <span class="blue">Max = 1.42&#949; (Mean = 0.566&#949;)</span><br> <br>
9223                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 0.964&#949; (Mean = 0.543&#949;))<br>
9224                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.964&#949; (Mean = 0.543&#949;))
9225                 </p>
9226               </td>
9227 <td>
9228                 <p>
9229                   <span class="blue">Max = 1.42&#949; (Mean = 0.566&#949;)</span><br> <br>
9230                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.964&#949; (Mean = 0.543&#949;))
9231                 </p>
9232               </td>
9233 <td>
9234                 <p>
9235                   <span class="blue">Max = 0.964&#949; (Mean = 0.462&#949;)</span><br> <br>
9236                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.962&#949; (Mean = 0.372&#949;))
9237                 </p>
9238               </td>
9239 </tr>
9240 <tr>
9241 <td>
9242                 <p>
9243                   near 1
9244                 </p>
9245               </td>
9246 <td>
9247                 <p>
9248                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
9249                   2.1:</em></span> Max = 442&#949; (Mean = 88.8&#949;))<br> (<span class="emphasis"><em>Rmath
9250                   3.2.3:</em></span> Max = 7.99e+04&#949; (Mean = 1.68e+04&#949;))
9251                 </p>
9252               </td>
9253 <td>
9254                 <p>
9255                   <span class="blue">Max = 0.948&#949; (Mean = 0.36&#949;)</span><br> <br>
9256                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 0.615&#949; (Mean = 0.096&#949;))<br>
9257                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.615&#949; (Mean = 0.096&#949;))
9258                 </p>
9259               </td>
9260 <td>
9261                 <p>
9262                   <span class="blue">Max = 0.948&#949; (Mean = 0.36&#949;)</span><br> <br>
9263                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.71&#949; (Mean = 0.581&#949;))
9264                 </p>
9265               </td>
9266 <td>
9267                 <p>
9268                   <span class="blue">Max = 0.867&#949; (Mean = 0.468&#949;)</span><br> <br>
9269                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.906&#949; (Mean = 0.565&#949;))
9270                 </p>
9271               </td>
9272 </tr>
9273 <tr>
9274 <td>
9275                 <p>
9276                   near 2
9277                 </p>
9278               </td>
9279 <td>
9280                 <p>
9281                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
9282                   2.1:</em></span> Max = 1.17e+03&#949; (Mean = 274&#949;))<br> (<span class="emphasis"><em>Rmath
9283                   3.2.3:</em></span> Max = 2.63e+05&#949; (Mean = 5.84e+04&#949;))
9284                 </p>
9285               </td>
9286 <td>
9287                 <p>
9288                   <span class="blue">Max = 0.878&#949; (Mean = 0.242&#949;)</span><br> <br>
9289                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 0.741&#949; (Mean = 0.263&#949;))<br>
9290                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.741&#949; (Mean = 0.263&#949;))
9291                 </p>
9292               </td>
9293 <td>
9294                 <p>
9295                   <span class="blue">Max = 0.878&#949; (Mean = 0.242&#949;)</span><br> <br>
9296                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.598&#949; (Mean = 0.235&#949;))
9297                 </p>
9298               </td>
9299 <td>
9300                 <p>
9301                   <span class="blue">Max = 0.591&#949; (Mean = 0.159&#949;)</span><br> <br>
9302                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.741&#949; (Mean = 0.473&#949;))
9303                 </p>
9304               </td>
9305 </tr>
9306 <tr>
9307 <td>
9308                 <p>
9309                   near -10
9310                 </p>
9311               </td>
9312 <td>
9313                 <p>
9314                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
9315                   2.1:</em></span> Max = 24.9&#949; (Mean = 4.6&#949;))<br> (<span class="emphasis"><em>Rmath
9316                   3.2.3:</em></span> Max = 4.22&#949; (Mean = 1.26&#949;))
9317                 </p>
9318               </td>
9319 <td>
9320                 <p>
9321                   <span class="blue">Max = 3.81&#949; (Mean = 1.01&#949;)</span><br> <br>
9322                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 0.997&#949; (Mean = 0.412&#949;))<br>
9323                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.997&#949; (Mean = 0.412&#949;))
9324                 </p>
9325               </td>
9326 <td>
9327                 <p>
9328                   <span class="blue">Max = 3.81&#949; (Mean = 1.01&#949;)</span><br> <br>
9329                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 3.04&#949; (Mean = 1.01&#949;))
9330                 </p>
9331               </td>
9332 <td>
9333                 <p>
9334                   <span class="blue">Max = 4.22&#949; (Mean = 1.33&#949;)</span><br> <br>
9335                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.997&#949; (Mean = 0.444&#949;))
9336                 </p>
9337               </td>
9338 </tr>
9339 <tr>
9340 <td>
9341                 <p>
9342                   near -55
9343                 </p>
9344               </td>
9345 <td>
9346                 <p>
9347                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
9348                   2.1:</em></span> Max = 7.02&#949; (Mean = 1.47&#949;))<br> (<span class="emphasis"><em>Rmath
9349                   3.2.3:</em></span> Max = 250&#949; (Mean = 60.9&#949;))
9350                 </p>
9351               </td>
9352 <td>
9353                 <p>
9354                   <span class="blue">Max = 0.821&#949; (Mean = 0.513&#949;)</span><br> <br>
9355                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.58&#949; (Mean = 0.672&#949;))<br>
9356                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.58&#949; (Mean = 0.672&#949;))
9357                 </p>
9358               </td>
9359 <td>
9360                 <p>
9361                   <span class="blue">Max = 1.59&#949; (Mean = 0.587&#949;)</span><br> <br>
9362                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.821&#949; (Mean = 0.674&#949;))
9363                 </p>
9364               </td>
9365 <td>
9366                 <p>
9367                   <span class="blue">Max = 0.821&#949; (Mean = 0.419&#949;)</span><br> <br>
9368                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 249&#949; (Mean = 43.1&#949;))
9369                 </p>
9370               </td>
9371 </tr>
9372 </tbody>
9373 </table></div>
9374 </div>
9375 <br class="table-break"><div class="table">
9376 <a name="math_toolkit.logs_and_tables.all_table.table_log1p"></a><p class="title"><b>Table&#160;22.73.&#160;Error rates for log1p</b></p>
9377 <div class="table-contents"><table class="table" summary="Error rates for log1p">
9378 <colgroup>
9379 <col>
9380 <col>
9381 <col>
9382 <col>
9383 <col>
9384 </colgroup>
9385 <thead><tr>
9386 <th>
9387               </th>
9388 <th>
9389                 <p>
9390                   GNU C++ version 7.1.0<br> linux<br> long double
9391                 </p>
9392               </th>
9393 <th>
9394                 <p>
9395                   GNU C++ version 7.1.0<br> linux<br> double
9396                 </p>
9397               </th>
9398 <th>
9399                 <p>
9400                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
9401                 </p>
9402               </th>
9403 <th>
9404                 <p>
9405                   Microsoft Visual C++ version 14.1<br> Win32<br> double
9406                 </p>
9407               </th>
9408 </tr></thead>
9409 <tbody><tr>
9410 <td>
9411                 <p>
9412                   Random test data
9413                 </p>
9414               </td>
9415 <td>
9416                 <p>
9417                   <span class="blue">Max = 0.818&#949; (Mean = 0.227&#949;)</span><br> <br>
9418                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 0.818&#949; (Mean = 0.227&#949;))<br>
9419                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.818&#949; (Mean = 0.227&#949;))
9420                 </p>
9421               </td>
9422 <td>
9423                 <p>
9424                   <span class="blue">Max = 0.846&#949; (Mean = 0.153&#949;)</span><br> <br>
9425                   (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 0.846&#949; (Mean = 0.153&#949;))
9426                 </p>
9427               </td>
9428 <td>
9429                 <p>
9430                   <span class="blue">Max = 2.3&#949; (Mean = 0.66&#949;)</span><br> <br>
9431                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.818&#949; (Mean = 0.249&#949;))
9432                 </p>
9433               </td>
9434 <td>
9435                 <p>
9436                   <span class="blue">Max = 0.509&#949; (Mean = 0.057&#949;)</span><br> <br>
9437                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.509&#949; (Mean = 0.057&#949;))
9438                 </p>
9439               </td>
9440 </tr></tbody>
9441 </table></div>
9442 </div>
9443 <br class="table-break"><div class="table">
9444 <a name="math_toolkit.logs_and_tables.all_table.table_non_central_beta_CDF"></a><p class="title"><b>Table&#160;22.74.&#160;Error rates for non central beta CDF</b></p>
9445 <div class="table-contents"><table class="table" summary="Error rates for non central beta CDF">
9446 <colgroup>
9447 <col>
9448 <col>
9449 <col>
9450 <col>
9451 <col>
9452 </colgroup>
9453 <thead><tr>
9454 <th>
9455               </th>
9456 <th>
9457                 <p>
9458                   GNU C++ version 7.1.0<br> linux<br> double
9459                 </p>
9460               </th>
9461 <th>
9462                 <p>
9463                   GNU C++ version 7.1.0<br> linux<br> long double
9464                 </p>
9465               </th>
9466 <th>
9467                 <p>
9468                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
9469                 </p>
9470               </th>
9471 <th>
9472                 <p>
9473                   Microsoft Visual C++ version 14.1<br> Win32<br> double
9474                 </p>
9475               </th>
9476 </tr></thead>
9477 <tbody>
9478 <tr>
9479 <td>
9480                 <p>
9481                   Non Central Beta, medium parameters
9482                 </p>
9483               </td>
9484 <td>
9485                 <p>
9486                   <span class="blue">Max = 0.998&#949; (Mean = 0.0649&#949;)</span><br>
9487                   <br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max
9488                   = 1.46e+26&#949; (Mean = 3.5e+24&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_Rmath_3_2_3_Non_Central_Beta_medium_parameters">And
9489                   other failures.</a>)</span>
9490                 </p>
9491               </td>
9492 <td>
9493                 <p>
9494                   <span class="blue">Max = 824&#949; (Mean = 27.4&#949;)</span>
9495                 </p>
9496               </td>
9497 <td>
9498                 <p>
9499                   <span class="blue">Max = 832&#949; (Mean = 38.1&#949;)</span>
9500                 </p>
9501               </td>
9502 <td>
9503                 <p>
9504                   <span class="blue">Max = 242&#949; (Mean = 31&#949;)</span>
9505                 </p>
9506               </td>
9507 </tr>
9508 <tr>
9509 <td>
9510                 <p>
9511                   Non Central Beta, large parameters
9512                 </p>
9513               </td>
9514 <td>
9515                 <p>
9516                   <span class="blue">Max = 1.18&#949; (Mean = 0.175&#949;)</span><br> <br>
9517                   (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 1.01e+36&#949; (Mean
9518                   = 1.19e+35&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_Rmath_3_2_3_Non_Central_Beta_large_parameters">And
9519                   other failures.</a>)</span>
9520                 </p>
9521               </td>
9522 <td>
9523                 <p>
9524                   <span class="blue">Max = 2.5e+04&#949; (Mean = 3.78e+03&#949;)</span>
9525                 </p>
9526               </td>
9527 <td>
9528                 <p>
9529                   <span class="blue">Max = 2.57e+04&#949; (Mean = 4.45e+03&#949;)</span>
9530                 </p>
9531               </td>
9532 <td>
9533                 <p>
9534                   <span class="blue">Max = 3.66e+03&#949; (Mean = 500&#949;)</span>
9535                 </p>
9536               </td>
9537 </tr>
9538 </tbody>
9539 </table></div>
9540 </div>
9541 <br class="table-break"><div class="table">
9542 <a name="math_toolkit.logs_and_tables.all_table.table_non_central_beta_CDF_complement"></a><p class="title"><b>Table&#160;22.75.&#160;Error rates for non central beta CDF complement</b></p>
9543 <div class="table-contents"><table class="table" summary="Error rates for non central beta CDF complement">
9544 <colgroup>
9545 <col>
9546 <col>
9547 <col>
9548 <col>
9549 <col>
9550 </colgroup>
9551 <thead><tr>
9552 <th>
9553               </th>
9554 <th>
9555                 <p>
9556                   GNU C++ version 7.1.0<br> linux<br> double
9557                 </p>
9558               </th>
9559 <th>
9560                 <p>
9561                   GNU C++ version 7.1.0<br> linux<br> long double
9562                 </p>
9563               </th>
9564 <th>
9565                 <p>
9566                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
9567                 </p>
9568               </th>
9569 <th>
9570                 <p>
9571                   Microsoft Visual C++ version 14.1<br> Win32<br> double
9572                 </p>
9573               </th>
9574 </tr></thead>
9575 <tbody>
9576 <tr>
9577 <td>
9578                 <p>
9579                   Non Central Beta, medium parameters
9580                 </p>
9581               </td>
9582 <td>
9583                 <p>
9584                   <span class="blue">Max = 0.998&#949; (Mean = 0.0936&#949;)</span><br>
9585                   <br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max
9586                   = 7.5e+97&#949; (Mean = 1.37e+96&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_complement_Rmath_3_2_3_Non_Central_Beta_medium_parameters">And
9587                   other failures.</a>)</span>
9588                 </p>
9589               </td>
9590 <td>
9591                 <p>
9592                   <span class="blue">Max = 396&#949; (Mean = 50.7&#949;)</span>
9593                 </p>
9594               </td>
9595 <td>
9596                 <p>
9597                   <span class="blue">Max = 554&#949; (Mean = 57.2&#949;)</span>
9598                 </p>
9599               </td>
9600 <td>
9601                 <p>
9602                   <span class="blue">Max = 624&#949; (Mean = 62.7&#949;)</span>
9603                 </p>
9604               </td>
9605 </tr>
9606 <tr>
9607 <td>
9608                 <p>
9609                   Non Central Beta, large parameters
9610                 </p>
9611               </td>
9612 <td>
9613                 <p>
9614                   <span class="blue">Max = 0.986&#949; (Mean = 0.188&#949;)</span><br> <br>
9615                   (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = +INF&#949; (Mean
9616                   = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_complement_Rmath_3_2_3_Non_Central_Beta_large_parameters">And
9617                   other failures.</a>)</span>
9618                 </p>
9619               </td>
9620 <td>
9621                 <p>
9622                   <span class="blue">Max = 6.83e+03&#949; (Mean = 993&#949;)</span>
9623                 </p>
9624               </td>
9625 <td>
9626                 <p>
9627                   <span class="blue">Max = 3.56e+03&#949; (Mean = 707&#949;)</span>
9628                 </p>
9629               </td>
9630 <td>
9631                 <p>
9632                   <span class="blue">Max = 1.25e+04&#949; (Mean = 1.49e+03&#949;)</span>
9633                 </p>
9634               </td>
9635 </tr>
9636 </tbody>
9637 </table></div>
9638 </div>
9639 <br class="table-break"><div class="table">
9640 <a name="math_toolkit.logs_and_tables.all_table.table_non_central_chi_squared_CDF"></a><p class="title"><b>Table&#160;22.76.&#160;Error rates for non central chi squared CDF</b></p>
9641 <div class="table-contents"><table class="table" summary="Error rates for non central chi squared CDF">
9642 <colgroup>
9643 <col>
9644 <col>
9645 <col>
9646 <col>
9647 <col>
9648 </colgroup>
9649 <thead><tr>
9650 <th>
9651               </th>
9652 <th>
9653                 <p>
9654                   GNU C++ version 7.1.0<br> linux<br> double
9655                 </p>
9656               </th>
9657 <th>
9658                 <p>
9659                   GNU C++ version 7.1.0<br> linux<br> long double
9660                 </p>
9661               </th>
9662 <th>
9663                 <p>
9664                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
9665                 </p>
9666               </th>
9667 <th>
9668                 <p>
9669                   Microsoft Visual C++ version 14.1<br> Win32<br> double
9670                 </p>
9671               </th>
9672 </tr></thead>
9673 <tbody>
9674 <tr>
9675 <td>
9676                 <p>
9677                   Non Central Chi Squared, medium parameters
9678                 </p>
9679               </td>
9680 <td>
9681                 <p>
9682                   <span class="blue">Max = 0.99&#949; (Mean = 0.0544&#949;)</span><br> <br>
9683                   (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 727&#949; (Mean = 121&#949;))
9684                 </p>
9685               </td>
9686 <td>
9687                 <p>
9688                   <span class="blue">Max = 46.5&#949; (Mean = 10.3&#949;)</span>
9689                 </p>
9690               </td>
9691 <td>
9692                 <p>
9693                   <span class="blue">Max = 115&#949; (Mean = 13.9&#949;)</span>
9694                 </p>
9695               </td>
9696 <td>
9697                 <p>
9698                   <span class="blue">Max = 48.9&#949; (Mean = 10&#949;)</span>
9699                 </p>
9700               </td>
9701 </tr>
9702 <tr>
9703 <td>
9704                 <p>
9705                   Non Central Chi Squared, large parameters
9706                 </p>
9707               </td>
9708 <td>
9709                 <p>
9710                   <span class="blue">Max = 1.07&#949; (Mean = 0.102&#949;)</span><br> <br>
9711                   (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 3.27e+08&#949; (Mean
9712                   = 2.23e+07&#949;))</span>
9713                 </p>
9714               </td>
9715 <td>
9716                 <p>
9717                   <span class="blue">Max = 3.07e+03&#949; (Mean = 336&#949;)</span>
9718                 </p>
9719               </td>
9720 <td>
9721                 <p>
9722                   <span class="blue">Max = 6.17e+03&#949; (Mean = 677&#949;)</span>
9723                 </p>
9724               </td>
9725 <td>
9726                 <p>
9727                   <span class="blue">Max = 9.79e+03&#949; (Mean = 723&#949;)</span>
9728                 </p>
9729               </td>
9730 </tr>
9731 </tbody>
9732 </table></div>
9733 </div>
9734 <br class="table-break"><div class="table">
9735 <a name="math_toolkit.logs_and_tables.all_table.table_non_central_chi_squared_CDF_complement"></a><p class="title"><b>Table&#160;22.77.&#160;Error rates for non central chi squared CDF complement</b></p>
9736 <div class="table-contents"><table class="table" summary="Error rates for non central chi squared CDF complement">
9737 <colgroup>
9738 <col>
9739 <col>
9740 <col>
9741 <col>
9742 <col>
9743 </colgroup>
9744 <thead><tr>
9745 <th>
9746               </th>
9747 <th>
9748                 <p>
9749                   GNU C++ version 7.1.0<br> linux<br> double
9750                 </p>
9751               </th>
9752 <th>
9753                 <p>
9754                   GNU C++ version 7.1.0<br> linux<br> long double
9755                 </p>
9756               </th>
9757 <th>
9758                 <p>
9759                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
9760                 </p>
9761               </th>
9762 <th>
9763                 <p>
9764                   Microsoft Visual C++ version 14.1<br> Win32<br> double
9765                 </p>
9766               </th>
9767 </tr></thead>
9768 <tbody>
9769 <tr>
9770 <td>
9771                 <p>
9772                   Non Central Chi Squared, medium parameters
9773                 </p>
9774               </td>
9775 <td>
9776                 <p>
9777                   <span class="blue">Max = 0.96&#949; (Mean = 0.0635&#949;)</span><br> <br>
9778                   (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = +INF&#949; (Mean
9779                   = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_non_central_chi_squared_CDF_complement_Rmath_3_2_3_Non_Central_Chi_Squared_medium_parameters">And
9780                   other failures.</a>)</span>
9781                 </p>
9782               </td>
9783 <td>
9784                 <p>
9785                   <span class="blue">Max = 107&#949; (Mean = 17.2&#949;)</span>
9786                 </p>
9787               </td>
9788 <td>
9789                 <p>
9790                   <span class="blue">Max = 171&#949; (Mean = 22.8&#949;)</span>
9791                 </p>
9792               </td>
9793 <td>
9794                 <p>
9795                   <span class="blue">Max = 98.6&#949; (Mean = 15.8&#949;)</span>
9796                 </p>
9797               </td>
9798 </tr>
9799 <tr>
9800 <td>
9801                 <p>
9802                   Non Central Chi Squared, large parameters
9803                 </p>
9804               </td>
9805 <td>
9806                 <p>
9807                   <span class="blue">Max = 2.11&#949; (Mean = 0.278&#949;)</span><br> <br>
9808                   (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = +INF&#949; (Mean
9809                   = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_non_central_chi_squared_CDF_complement_Rmath_3_2_3_Non_Central_Chi_Squared_large_parameters">And
9810                   other failures.</a>)</span>
9811                 </p>
9812               </td>
9813 <td>
9814                 <p>
9815                   <span class="blue">Max = 5.02e+03&#949; (Mean = 630&#949;)</span>
9816                 </p>
9817               </td>
9818 <td>
9819                 <p>
9820                   <span class="blue">Max = 5.1e+03&#949; (Mean = 577&#949;)</span>
9821                 </p>
9822               </td>
9823 <td>
9824                 <p>
9825                   <span class="blue">Max = 5.43e+03&#949; (Mean = 705&#949;)</span>
9826                 </p>
9827               </td>
9828 </tr>
9829 </tbody>
9830 </table></div>
9831 </div>
9832 <br class="table-break"><div class="table">
9833 <a name="math_toolkit.logs_and_tables.all_table.table_non_central_t_CDF"></a><p class="title"><b>Table&#160;22.78.&#160;Error rates for non central t CDF</b></p>
9834 <div class="table-contents"><table class="table" summary="Error rates for non central t CDF">
9835 <colgroup>
9836 <col>
9837 <col>
9838 <col>
9839 <col>
9840 <col>
9841 </colgroup>
9842 <thead><tr>
9843 <th>
9844               </th>
9845 <th>
9846                 <p>
9847                   GNU C++ version 7.1.0<br> linux<br> double
9848                 </p>
9849               </th>
9850 <th>
9851                 <p>
9852                   GNU C++ version 7.1.0<br> linux<br> long double
9853                 </p>
9854               </th>
9855 <th>
9856                 <p>
9857                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
9858                 </p>
9859               </th>
9860 <th>
9861                 <p>
9862                   Microsoft Visual C++ version 14.1<br> Win32<br> double
9863                 </p>
9864               </th>
9865 </tr></thead>
9866 <tbody>
9867 <tr>
9868 <td>
9869                 <p>
9870                   Non Central T
9871                 </p>
9872               </td>
9873 <td>
9874                 <p>
9875                   <span class="blue">Max = 0.796&#949; (Mean = 0.0691&#949;)</span><br>
9876                   <br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max
9877                   = 5.28e+15&#949; (Mean = 8.49e+14&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_non_central_t_CDF_Rmath_3_2_3_Non_Central_T">And
9878                   other failures.</a>)</span>
9879                 </p>
9880               </td>
9881 <td>
9882                 <p>
9883                   <span class="blue">Max = 139&#949; (Mean = 31&#949;)</span>
9884                 </p>
9885               </td>
9886 <td>
9887                 <p>
9888                   <span class="blue">Max = 145&#949; (Mean = 30.9&#949;)</span>
9889                 </p>
9890               </td>
9891 <td>
9892                 <p>
9893                   <span class="blue">Max = 135&#949; (Mean = 32.1&#949;)</span>
9894                 </p>
9895               </td>
9896 </tr>
9897 <tr>
9898 <td>
9899                 <p>
9900                   Non Central T (small non-centrality)
9901                 </p>
9902               </td>
9903 <td>
9904                 <p>
9905                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>Rmath
9906                   3.2.3:</em></span> Max = 2.09e+03&#949; (Mean = 244&#949;))
9907                 </p>
9908               </td>
9909 <td>
9910                 <p>
9911                   <span class="blue">Max = 3.86&#949; (Mean = 1.4&#949;)</span>
9912                 </p>
9913               </td>
9914 <td>
9915                 <p>
9916                   <span class="blue">Max = 9.15&#949; (Mean = 2.13&#949;)</span>
9917                 </p>
9918               </td>
9919 <td>
9920                 <p>
9921                   <span class="blue">Max = 6.17&#949; (Mean = 1.45&#949;)</span>
9922                 </p>
9923               </td>
9924 </tr>
9925 <tr>
9926 <td>
9927                 <p>
9928                   Non Central T (large parameters)
9929                 </p>
9930               </td>
9931 <td>
9932                 <p>
9933                   <span class="blue">Max = 257&#949; (Mean = 72.1&#949;)</span><br> <br>
9934                   (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.46&#949; (Mean = 0.657&#949;))
9935                 </p>
9936               </td>
9937 <td>
9938                 <p>
9939                   <span class="blue">Max = 5.26e+05&#949; (Mean = 1.48e+05&#949;)</span>
9940                 </p>
9941               </td>
9942 <td>
9943                 <p>
9944                   <span class="blue">Max = 5.24e+05&#949; (Mean = 1.47e+05&#949;)</span>
9945                 </p>
9946               </td>
9947 <td>
9948                 <p>
9949                   <span class="blue">Max = 286&#949; (Mean = 62.8&#949;)</span>
9950                 </p>
9951               </td>
9952 </tr>
9953 </tbody>
9954 </table></div>
9955 </div>
9956 <br class="table-break"><div class="table">
9957 <a name="math_toolkit.logs_and_tables.all_table.table_non_central_t_CDF_complement"></a><p class="title"><b>Table&#160;22.79.&#160;Error rates for non central t CDF complement</b></p>
9958 <div class="table-contents"><table class="table" summary="Error rates for non central t CDF complement">
9959 <colgroup>
9960 <col>
9961 <col>
9962 <col>
9963 <col>
9964 <col>
9965 </colgroup>
9966 <thead><tr>
9967 <th>
9968               </th>
9969 <th>
9970                 <p>
9971                   GNU C++ version 7.1.0<br> linux<br> double
9972                 </p>
9973               </th>
9974 <th>
9975                 <p>
9976                   GNU C++ version 7.1.0<br> linux<br> long double
9977                 </p>
9978               </th>
9979 <th>
9980                 <p>
9981                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
9982                 </p>
9983               </th>
9984 <th>
9985                 <p>
9986                   Microsoft Visual C++ version 14.1<br> Win32<br> double
9987                 </p>
9988               </th>
9989 </tr></thead>
9990 <tbody>
9991 <tr>
9992 <td>
9993                 <p>
9994                   Non Central T
9995                 </p>
9996               </td>
9997 <td>
9998                 <p>
9999                   <span class="blue">Max = 0.707&#949; (Mean = 0.0497&#949;)</span><br>
10000                   <br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max
10001                   = 6.19e+15&#949; (Mean = 6.72e+14&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_non_central_t_CDF_complement_Rmath_3_2_3_Non_Central_T">And
10002                   other failures.</a>)</span>
10003                 </p>
10004               </td>
10005 <td>
10006                 <p>
10007                   <span class="blue">Max = 201&#949; (Mean = 31.7&#949;)</span>
10008                 </p>
10009               </td>
10010 <td>
10011                 <p>
10012                   <span class="blue">Max = 340&#949; (Mean = 43.2&#949;)</span>
10013                 </p>
10014               </td>
10015 <td>
10016                 <p>
10017                   <span class="blue">Max = 154&#949; (Mean = 32.1&#949;)</span>
10018                 </p>
10019               </td>
10020 </tr>
10021 <tr>
10022 <td>
10023                 <p>
10024                   Non Central T (small non-centrality)
10025                 </p>
10026               </td>
10027 <td>
10028                 <p>
10029                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>Rmath
10030                   3.2.3:</em></span> Max = 1.87e+03&#949; (Mean = 263&#949;))
10031                 </p>
10032               </td>
10033 <td>
10034                 <p>
10035                   <span class="blue">Max = 10.5&#949; (Mean = 2.13&#949;)</span>
10036                 </p>
10037               </td>
10038 <td>
10039                 <p>
10040                   <span class="blue">Max = 10.5&#949; (Mean = 2.39&#949;)</span>
10041                 </p>
10042               </td>
10043 <td>
10044                 <p>
10045                   <span class="blue">Max = 4.6&#949; (Mean = 1.63&#949;)</span>
10046                 </p>
10047               </td>
10048 </tr>
10049 <tr>
10050 <td>
10051                 <p>
10052                   Non Central T (large parameters)
10053                 </p>
10054               </td>
10055 <td>
10056                 <p>
10057                   <span class="blue">Max = 478&#949; (Mean = 96.3&#949;)</span><br> <br>
10058                   (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.24&#949; (Mean = 0.945&#949;))
10059                 </p>
10060               </td>
10061 <td>
10062                 <p>
10063                   <span class="blue">Max = 9.79e+05&#949; (Mean = 1.97e+05&#949;)</span>
10064                 </p>
10065               </td>
10066 <td>
10067                 <p>
10068                   <span class="blue">Max = 9.79e+05&#949; (Mean = 1.97e+05&#949;)</span>
10069                 </p>
10070               </td>
10071 <td>
10072                 <p>
10073                   <span class="blue">Max = 227&#949; (Mean = 50.4&#949;)</span>
10074                 </p>
10075               </td>
10076 </tr>
10077 </tbody>
10078 </table></div>
10079 </div>
10080 <br class="table-break"><div class="table">
10081 <a name="math_toolkit.logs_and_tables.all_table.table_owens_t"></a><p class="title"><b>Table&#160;22.80.&#160;Error rates for owens_t</b></p>
10082 <div class="table-contents"><table class="table" summary="Error rates for owens_t">
10083 <colgroup>
10084 <col>
10085 <col>
10086 <col>
10087 <col>
10088 <col>
10089 </colgroup>
10090 <thead><tr>
10091 <th>
10092               </th>
10093 <th>
10094                 <p>
10095                   GNU C++ version 7.1.0<br> linux<br> double
10096                 </p>
10097               </th>
10098 <th>
10099                 <p>
10100                   GNU C++ version 7.1.0<br> linux<br> long double
10101                 </p>
10102               </th>
10103 <th>
10104                 <p>
10105                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
10106                 </p>
10107               </th>
10108 <th>
10109                 <p>
10110                   Microsoft Visual C++ version 14.1<br> Win32<br> double
10111                 </p>
10112               </th>
10113 </tr></thead>
10114 <tbody>
10115 <tr>
10116 <td>
10117                 <p>
10118                   Owens T (medium small values)
10119                 </p>
10120               </td>
10121 <td>
10122                 <p>
10123                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
10124                 </p>
10125               </td>
10126 <td>
10127                 <p>
10128                   <span class="blue">Max = 3.34&#949; (Mean = 0.944&#949;)</span>
10129                 </p>
10130               </td>
10131 <td>
10132                 <p>
10133                   <span class="blue">Max = 3.34&#949; (Mean = 0.911&#949;)</span>
10134                 </p>
10135               </td>
10136 <td>
10137                 <p>
10138                   <span class="blue">Max = 4.37&#949; (Mean = 0.98&#949;)</span>
10139                 </p>
10140               </td>
10141 </tr>
10142 <tr>
10143 <td>
10144                 <p>
10145                   Owens T (large and diverse values)
10146                 </p>
10147               </td>
10148 <td>
10149                 <p>
10150                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
10151                 </p>
10152               </td>
10153 <td>
10154                 <p>
10155                   <span class="blue">Max = 49&#949; (Mean = 2.16&#949;)</span>
10156                 </p>
10157               </td>
10158 <td>
10159                 <p>
10160                   <span class="blue">Max = 24.5&#949; (Mean = 1.39&#949;)</span>
10161                 </p>
10162               </td>
10163 <td>
10164                 <p>
10165                   <span class="blue">Max = 3.78&#949; (Mean = 0.621&#949;)</span>
10166                 </p>
10167               </td>
10168 </tr>
10169 </tbody>
10170 </table></div>
10171 </div>
10172 <br class="table-break"><div class="table">
10173 <a name="math_toolkit.logs_and_tables.all_table.table_polygamma"></a><p class="title"><b>Table&#160;22.81.&#160;Error rates for polygamma</b></p>
10174 <div class="table-contents"><table class="table" summary="Error rates for polygamma">
10175 <colgroup>
10176 <col>
10177 <col>
10178 <col>
10179 <col>
10180 <col>
10181 </colgroup>
10182 <thead><tr>
10183 <th>
10184               </th>
10185 <th>
10186                 <p>
10187                   GNU C++ version 7.1.0<br> linux<br> double
10188                 </p>
10189               </th>
10190 <th>
10191                 <p>
10192                   GNU C++ version 7.1.0<br> linux<br> long double
10193                 </p>
10194               </th>
10195 <th>
10196                 <p>
10197                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
10198                 </p>
10199               </th>
10200 <th>
10201                 <p>
10202                   Microsoft Visual C++ version 14.1<br> Win32<br> double
10203                 </p>
10204               </th>
10205 </tr></thead>
10206 <tbody>
10207 <tr>
10208 <td>
10209                 <p>
10210                   Mathematica Data
10211                 </p>
10212               </td>
10213 <td>
10214                 <p>
10215                   <span class="blue">Max = 0.824&#949; (Mean = 0.0574&#949;)</span><br>
10216                   <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 62.9&#949; (Mean = 12.8&#949;))<br>
10217                   (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 108&#949; (Mean = 15.2&#949;))
10218                 </p>
10219               </td>
10220 <td>
10221                 <p>
10222                   <span class="blue">Max = 7.38&#949; (Mean = 1.84&#949;)</span>
10223                 </p>
10224               </td>
10225 <td>
10226                 <p>
10227                   <span class="blue">Max = 34.3&#949; (Mean = 7.65&#949;)</span>
10228                 </p>
10229               </td>
10230 <td>
10231                 <p>
10232                   <span class="blue">Max = 9.32&#949; (Mean = 1.95&#949;)</span>
10233                 </p>
10234               </td>
10235 </tr>
10236 <tr>
10237 <td>
10238                 <p>
10239                   Mathematica Data - large arguments
10240                 </p>
10241               </td>
10242 <td>
10243                 <p>
10244                   <span class="blue">Max = 0.998&#949; (Mean = 0.0592&#949;)</span><br>
10245                   <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 244&#949; (Mean = 32.8&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_large_arguments">And
10246                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
10247                   <span class="red">Max = 1.71e+56&#949; (Mean = 1.01e+55&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_large_arguments">And
10248                   other failures.</a>)</span>
10249                 </p>
10250               </td>
10251 <td>
10252                 <p>
10253                   <span class="blue">Max = 2.23&#949; (Mean = 0.323&#949;)</span>
10254                 </p>
10255               </td>
10256 <td>
10257                 <p>
10258                   <span class="blue">Max = 11.1&#949; (Mean = 0.848&#949;)</span>
10259                 </p>
10260               </td>
10261 <td>
10262                 <p>
10263                   <span class="blue">Max = 150&#949; (Mean = 13.9&#949;)</span>
10264                 </p>
10265               </td>
10266 </tr>
10267 <tr>
10268 <td>
10269                 <p>
10270                   Mathematica Data - negative arguments
10271                 </p>
10272               </td>
10273 <td>
10274                 <p>
10275                   <span class="blue">Max = 0.516&#949; (Mean = 0.022&#949;)</span><br> <br>
10276                   (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 36.6&#949; (Mean = 3.04&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_negative_arguments">And
10277                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
10278                   Max = 0&#949; (Mean = 0&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_negative_arguments">And
10279                   other failures.</a>)
10280                 </p>
10281               </td>
10282 <td>
10283                 <p>
10284                   <span class="blue">Max = 269&#949; (Mean = 87.7&#949;)</span>
10285                 </p>
10286               </td>
10287 <td>
10288                 <p>
10289                   <span class="blue">Max = 269&#949; (Mean = 88.4&#949;)</span>
10290                 </p>
10291               </td>
10292 <td>
10293                 <p>
10294                   <span class="blue">Max = 497&#949; (Mean = 129&#949;)</span>
10295                 </p>
10296               </td>
10297 </tr>
10298 <tr>
10299 <td>
10300                 <p>
10301                   Mathematica Data - large negative arguments
10302                 </p>
10303               </td>
10304 <td>
10305                 <p>
10306                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
10307                   2.1:</em></span> Max = 1.79&#949; (Mean = 0.197&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_large_negative_arguments">And
10308                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
10309                   Max = 0&#949; (Mean = 0&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_large_negative_arguments">And
10310                   other failures.</a>)
10311                 </p>
10312               </td>
10313 <td>
10314                 <p>
10315                   <span class="blue">Max = 155&#949; (Mean = 96.4&#949;)</span>
10316                 </p>
10317               </td>
10318 <td>
10319                 <p>
10320                   <span class="blue">Max = 155&#949; (Mean = 96.4&#949;)</span>
10321                 </p>
10322               </td>
10323 <td>
10324                 <p>
10325                   <span class="blue">Max = 162&#949; (Mean = 101&#949;)</span>
10326                 </p>
10327               </td>
10328 </tr>
10329 <tr>
10330 <td>
10331                 <p>
10332                   Mathematica Data - small arguments
10333                 </p>
10334               </td>
10335 <td>
10336                 <p>
10337                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
10338                   2.1:</em></span> Max = 15.2&#949; (Mean = 5.03&#949;))<br> (<span class="emphasis"><em>Rmath
10339                   3.2.3:</em></span> Max = 106&#949; (Mean = 20&#949;))
10340                 </p>
10341               </td>
10342 <td>
10343                 <p>
10344                   <span class="blue">Max = 3.33&#949; (Mean = 0.75&#949;)</span>
10345                 </p>
10346               </td>
10347 <td>
10348                 <p>
10349                   <span class="blue">Max = 3.33&#949; (Mean = 0.75&#949;)</span>
10350                 </p>
10351               </td>
10352 <td>
10353                 <p>
10354                   <span class="blue">Max = 3&#949; (Mean = 0.496&#949;)</span>
10355                 </p>
10356               </td>
10357 </tr>
10358 <tr>
10359 <td>
10360                 <p>
10361                   Mathematica Data - Large orders and other bug cases
10362                 </p>
10363               </td>
10364 <td>
10365                 <p>
10366                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
10367                   2.1:</em></span> Max = 151&#949; (Mean = 39.3&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_Large_orders_and_other_bug_cases">And
10368                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
10369                   <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_Large_orders_and_other_bug_cases">And
10370                   other failures.</a>)</span>
10371                 </p>
10372               </td>
10373 <td>
10374                 <p>
10375                   <span class="blue">Max = 54.5&#949; (Mean = 13.3&#949;)</span>
10376                 </p>
10377               </td>
10378 <td>
10379                 <p>
10380                   <span class="blue">Max = 145&#949; (Mean = 55.9&#949;)</span>
10381                 </p>
10382               </td>
10383 <td>
10384                 <p>
10385                   <span class="blue">Max = 200&#949; (Mean = 57.2&#949;)</span>
10386                 </p>
10387               </td>
10388 </tr>
10389 </tbody>
10390 </table></div>
10391 </div>
10392 <br class="table-break"><div class="table">
10393 <a name="math_toolkit.logs_and_tables.all_table.table_powm1"></a><p class="title"><b>Table&#160;22.82.&#160;Error rates for powm1</b></p>
10394 <div class="table-contents"><table class="table" summary="Error rates for powm1">
10395 <colgroup>
10396 <col>
10397 <col>
10398 <col>
10399 <col>
10400 <col>
10401 </colgroup>
10402 <thead><tr>
10403 <th>
10404               </th>
10405 <th>
10406                 <p>
10407                   GNU C++ version 7.1.0<br> linux<br> double
10408                 </p>
10409               </th>
10410 <th>
10411                 <p>
10412                   GNU C++ version 7.1.0<br> linux<br> long double
10413                 </p>
10414               </th>
10415 <th>
10416                 <p>
10417                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
10418                 </p>
10419               </th>
10420 <th>
10421                 <p>
10422                   Microsoft Visual C++ version 14.1<br> Win32<br> double
10423                 </p>
10424               </th>
10425 </tr></thead>
10426 <tbody><tr>
10427 <td>
10428                 <p>
10429                   powm1
10430                 </p>
10431               </td>
10432 <td>
10433                 <p>
10434                   <span class="blue">Max = 1.06&#949; (Mean = 0.425&#949;)</span>
10435                 </p>
10436               </td>
10437 <td>
10438                 <p>
10439                   <span class="blue">Max = 2.04&#949; (Mean = 0.493&#949;)</span>
10440                 </p>
10441               </td>
10442 <td>
10443                 <p>
10444                   <span class="blue">Max = 1.88&#949; (Mean = 0.49&#949;)</span>
10445                 </p>
10446               </td>
10447 <td>
10448                 <p>
10449                   <span class="blue">Max = 1.84&#949; (Mean = 0.486&#949;)</span>
10450                 </p>
10451               </td>
10452 </tr></tbody>
10453 </table></div>
10454 </div>
10455 <br class="table-break"><div class="table">
10456 <a name="math_toolkit.logs_and_tables.all_table.table_sin_pi"></a><p class="title"><b>Table&#160;22.83.&#160;Error rates for sin_pi</b></p>
10457 <div class="table-contents"><table class="table" summary="Error rates for sin_pi">
10458 <colgroup>
10459 <col>
10460 <col>
10461 <col>
10462 <col>
10463 <col>
10464 </colgroup>
10465 <thead><tr>
10466 <th>
10467               </th>
10468 <th>
10469                 <p>
10470                   GNU C++ version 7.1.0<br> linux<br> double
10471                 </p>
10472               </th>
10473 <th>
10474                 <p>
10475                   GNU C++ version 7.1.0<br> linux<br> long double
10476                 </p>
10477               </th>
10478 <th>
10479                 <p>
10480                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
10481                 </p>
10482               </th>
10483 <th>
10484                 <p>
10485                   Microsoft Visual C++ version 14.1<br> Win32<br> double
10486                 </p>
10487               </th>
10488 </tr></thead>
10489 <tbody>
10490 <tr>
10491 <td>
10492                 <p>
10493                   sin_pi and cos_pi
10494                 </p>
10495               </td>
10496 <td>
10497                 <p>
10498                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
10499                 </p>
10500               </td>
10501 <td>
10502                 <p>
10503                   <span class="blue">Max = 0.996&#949; (Mean = 0.335&#949;)</span>
10504                 </p>
10505               </td>
10506 <td>
10507                 <p>
10508                   <span class="blue">Max = 0.996&#949; (Mean = 0.336&#949;)</span>
10509                 </p>
10510               </td>
10511 <td>
10512                 <p>
10513                   <span class="blue">Max = 0.99&#949; (Mean = 0.328&#949;)</span>
10514                 </p>
10515               </td>
10516 </tr>
10517 <tr>
10518 <td>
10519                 <p>
10520                   sin_pi and cos_pi near integers and half integers
10521                 </p>
10522               </td>
10523 <td>
10524                 <p>
10525                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
10526                 </p>
10527               </td>
10528 <td>
10529                 <p>
10530                   <span class="blue">Max = 0.976&#949; (Mean = 0.293&#949;)</span>
10531                 </p>
10532               </td>
10533 <td>
10534                 <p>
10535                   <span class="blue">Max = 0.976&#949; (Mean = 0.293&#949;)</span>
10536                 </p>
10537               </td>
10538 <td>
10539                 <p>
10540                   <span class="blue">Max = 0.996&#949; (Mean = 0.343&#949;)</span>
10541                 </p>
10542               </td>
10543 </tr>
10544 </tbody>
10545 </table></div>
10546 </div>
10547 <br class="table-break"><div class="table">
10548 <a name="math_toolkit.logs_and_tables.all_table.table_sph_bessel"></a><p class="title"><b>Table&#160;22.84.&#160;Error rates for sph_bessel</b></p>
10549 <div class="table-contents"><table class="table" summary="Error rates for sph_bessel">
10550 <colgroup>
10551 <col>
10552 <col>
10553 <col>
10554 <col>
10555 <col>
10556 </colgroup>
10557 <thead><tr>
10558 <th>
10559               </th>
10560 <th>
10561                 <p>
10562                   GNU C++ version 7.1.0<br> linux<br> long double
10563                 </p>
10564               </th>
10565 <th>
10566                 <p>
10567                   GNU C++ version 7.1.0<br> linux<br> double
10568                 </p>
10569               </th>
10570 <th>
10571                 <p>
10572                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
10573                 </p>
10574               </th>
10575 <th>
10576                 <p>
10577                   Microsoft Visual C++ version 14.1<br> Win32<br> double
10578                 </p>
10579               </th>
10580 </tr></thead>
10581 <tbody><tr>
10582 <td>
10583                 <p>
10584                   Bessel j: Random Data
10585                 </p>
10586               </td>
10587 <td>
10588                 <p>
10589                   <span class="blue">Max = 243&#949; (Mean = 13.3&#949;)</span><br> <br>
10590                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.91e+06&#949; (Mean = 1.09e+05&#949;))
10591                 </p>
10592               </td>
10593 <td>
10594                 <p>
10595                   <span class="blue">Max = 0.978&#949; (Mean = 0.0445&#949;)</span><br>
10596                   <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.79e+03&#949; (Mean = 107&#949;))
10597                 </p>
10598               </td>
10599 <td>
10600                 <p>
10601                   <span class="blue">Max = 243&#949; (Mean = 33.7&#949;)</span>
10602                 </p>
10603               </td>
10604 <td>
10605                 <p>
10606                   <span class="blue">Max = 245&#949; (Mean = 16.3&#949;)</span>
10607                 </p>
10608               </td>
10609 </tr></tbody>
10610 </table></div>
10611 </div>
10612 <br class="table-break"><div class="table">
10613 <a name="math_toolkit.logs_and_tables.all_table.table_sph_bessel_prime"></a><p class="title"><b>Table&#160;22.85.&#160;Error rates for sph_bessel_prime</b></p>
10614 <div class="table-contents"><table class="table" summary="Error rates for sph_bessel_prime">
10615 <colgroup>
10616 <col>
10617 <col>
10618 <col>
10619 <col>
10620 <col>
10621 </colgroup>
10622 <thead><tr>
10623 <th>
10624               </th>
10625 <th>
10626                 <p>
10627                   GNU C++ version 7.1.0<br> linux<br> double
10628                 </p>
10629               </th>
10630 <th>
10631                 <p>
10632                   GNU C++ version 7.1.0<br> linux<br> long double
10633                 </p>
10634               </th>
10635 <th>
10636                 <p>
10637                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
10638                 </p>
10639               </th>
10640 <th>
10641                 <p>
10642                   Microsoft Visual C++ version 14.1<br> Win32<br> double
10643                 </p>
10644               </th>
10645 </tr></thead>
10646 <tbody><tr>
10647 <td>
10648                 <p>
10649                   Bessel j': Random Data
10650                 </p>
10651               </td>
10652 <td>
10653                 <p>
10654                   <span class="blue">Max = 0.753&#949; (Mean = 0.0343&#949;)</span>
10655                 </p>
10656               </td>
10657 <td>
10658                 <p>
10659                   <span class="blue">Max = 167&#949; (Mean = 12&#949;)</span>
10660                 </p>
10661               </td>
10662 <td>
10663                 <p>
10664                   <span class="blue">Max = 167&#949; (Mean = 33.2&#949;)</span>
10665                 </p>
10666               </td>
10667 <td>
10668                 <p>
10669                   <span class="blue">Max = 307&#949; (Mean = 25.2&#949;)</span>
10670                 </p>
10671               </td>
10672 </tr></tbody>
10673 </table></div>
10674 </div>
10675 <br class="table-break"><div class="table">
10676 <a name="math_toolkit.logs_and_tables.all_table.table_sph_neumann"></a><p class="title"><b>Table&#160;22.86.&#160;Error rates for sph_neumann</b></p>
10677 <div class="table-contents"><table class="table" summary="Error rates for sph_neumann">
10678 <colgroup>
10679 <col>
10680 <col>
10681 <col>
10682 <col>
10683 <col>
10684 </colgroup>
10685 <thead><tr>
10686 <th>
10687               </th>
10688 <th>
10689                 <p>
10690                   GNU C++ version 7.1.0<br> linux<br> long double
10691                 </p>
10692               </th>
10693 <th>
10694                 <p>
10695                   GNU C++ version 7.1.0<br> linux<br> double
10696                 </p>
10697               </th>
10698 <th>
10699                 <p>
10700                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
10701                 </p>
10702               </th>
10703 <th>
10704                 <p>
10705                   Microsoft Visual C++ version 14.1<br> Win32<br> double
10706                 </p>
10707               </th>
10708 </tr></thead>
10709 <tbody><tr>
10710 <td>
10711                 <p>
10712                   y: Random Data
10713                 </p>
10714               </td>
10715 <td>
10716                 <p>
10717                   <span class="blue">Max = 234&#949; (Mean = 19.5&#949;)</span><br> <br>
10718                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.6e+06&#949; (Mean = 1.4e+05&#949;))
10719                 </p>
10720               </td>
10721 <td>
10722                 <p>
10723                   <span class="blue">Max = 0.995&#949; (Mean = 0.0665&#949;)</span><br>
10724                   <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.5e+04&#949; (Mean = 5.33e+03&#949;))
10725                 </p>
10726               </td>
10727 <td>
10728                 <p>
10729                   <span class="blue">Max = 234&#949; (Mean = 19.8&#949;)</span>
10730                 </p>
10731               </td>
10732 <td>
10733                 <p>
10734                   <span class="blue">Max = 281&#949; (Mean = 31.1&#949;)</span>
10735                 </p>
10736               </td>
10737 </tr></tbody>
10738 </table></div>
10739 </div>
10740 <br class="table-break"><div class="table">
10741 <a name="math_toolkit.logs_and_tables.all_table.table_sph_neumann_prime"></a><p class="title"><b>Table&#160;22.87.&#160;Error rates for sph_neumann_prime</b></p>
10742 <div class="table-contents"><table class="table" summary="Error rates for sph_neumann_prime">
10743 <colgroup>
10744 <col>
10745 <col>
10746 <col>
10747 <col>
10748 <col>
10749 </colgroup>
10750 <thead><tr>
10751 <th>
10752               </th>
10753 <th>
10754                 <p>
10755                   GNU C++ version 7.1.0<br> linux<br> double
10756                 </p>
10757               </th>
10758 <th>
10759                 <p>
10760                   GNU C++ version 7.1.0<br> linux<br> long double
10761                 </p>
10762               </th>
10763 <th>
10764                 <p>
10765                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
10766                 </p>
10767               </th>
10768 <th>
10769                 <p>
10770                   Microsoft Visual C++ version 14.1<br> Win32<br> double
10771                 </p>
10772               </th>
10773 </tr></thead>
10774 <tbody><tr>
10775 <td>
10776                 <p>
10777                   y': Random Data
10778                 </p>
10779               </td>
10780 <td>
10781                 <p>
10782                   <span class="blue">Max = 0.988&#949; (Mean = 0.0869&#949;)</span>
10783                 </p>
10784               </td>
10785 <td>
10786                 <p>
10787                   <span class="blue">Max = 158&#949; (Mean = 18.8&#949;)</span>
10788                 </p>
10789               </td>
10790 <td>
10791                 <p>
10792                   <span class="blue">Max = 158&#949; (Mean = 20.2&#949;)</span>
10793                 </p>
10794               </td>
10795 <td>
10796                 <p>
10797                   <span class="blue">Max = 296&#949; (Mean = 25.6&#949;)</span>
10798                 </p>
10799               </td>
10800 </tr></tbody>
10801 </table></div>
10802 </div>
10803 <br class="table-break"><div class="table">
10804 <a name="math_toolkit.logs_and_tables.all_table.table_spherical_harmonic_i"></a><p class="title"><b>Table&#160;22.88.&#160;Error rates for spherical_harmonic_i</b></p>
10805 <div class="table-contents"><table class="table" summary="Error rates for spherical_harmonic_i">
10806 <colgroup>
10807 <col>
10808 <col>
10809 <col>
10810 <col>
10811 <col>
10812 </colgroup>
10813 <thead><tr>
10814 <th>
10815               </th>
10816 <th>
10817                 <p>
10818                   GNU C++ version 7.1.0<br> linux<br> double
10819                 </p>
10820               </th>
10821 <th>
10822                 <p>
10823                   GNU C++ version 7.1.0<br> linux<br> long double
10824                 </p>
10825               </th>
10826 <th>
10827                 <p>
10828                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
10829                 </p>
10830               </th>
10831 <th>
10832                 <p>
10833                   Microsoft Visual C++ version 14.1<br> Win32<br> double
10834                 </p>
10835               </th>
10836 </tr></thead>
10837 <tbody><tr>
10838 <td>
10839                 <p>
10840                   Spherical Harmonics
10841                 </p>
10842               </td>
10843 <td>
10844                 <p>
10845                   <span class="blue">Max = 1.36&#949; (Mean = 0.0765&#949;)</span>
10846                 </p>
10847               </td>
10848 <td>
10849                 <p>
10850                   <span class="blue">Max = 2.89e+03&#949; (Mean = 108&#949;)</span>
10851                 </p>
10852               </td>
10853 <td>
10854                 <p>
10855                   <span class="blue">Max = 1.03e+04&#949; (Mean = 327&#949;)</span>
10856                 </p>
10857               </td>
10858 <td>
10859                 <p>
10860                   <span class="blue">Max = 2.27e+04&#949; (Mean = 725&#949;)</span>
10861                 </p>
10862               </td>
10863 </tr></tbody>
10864 </table></div>
10865 </div>
10866 <br class="table-break"><div class="table">
10867 <a name="math_toolkit.logs_and_tables.all_table.table_spherical_harmonic_r"></a><p class="title"><b>Table&#160;22.89.&#160;Error rates for spherical_harmonic_r</b></p>
10868 <div class="table-contents"><table class="table" summary="Error rates for spherical_harmonic_r">
10869 <colgroup>
10870 <col>
10871 <col>
10872 <col>
10873 <col>
10874 <col>
10875 </colgroup>
10876 <thead><tr>
10877 <th>
10878               </th>
10879 <th>
10880                 <p>
10881                   GNU C++ version 7.1.0<br> linux<br> double
10882                 </p>
10883               </th>
10884 <th>
10885                 <p>
10886                   GNU C++ version 7.1.0<br> linux<br> long double
10887                 </p>
10888               </th>
10889 <th>
10890                 <p>
10891                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
10892                 </p>
10893               </th>
10894 <th>
10895                 <p>
10896                   Microsoft Visual C++ version 14.1<br> Win32<br> double
10897                 </p>
10898               </th>
10899 </tr></thead>
10900 <tbody><tr>
10901 <td>
10902                 <p>
10903                   Spherical Harmonics
10904                 </p>
10905               </td>
10906 <td>
10907                 <p>
10908                   <span class="blue">Max = 1.58&#949; (Mean = 0.0707&#949;)</span>
10909                 </p>
10910               </td>
10911 <td>
10912                 <p>
10913                   <span class="blue">Max = 2.89e+03&#949; (Mean = 108&#949;)</span>
10914                 </p>
10915               </td>
10916 <td>
10917                 <p>
10918                   <span class="blue">Max = 1.03e+04&#949; (Mean = 327&#949;)</span>
10919                 </p>
10920               </td>
10921 <td>
10922                 <p>
10923                   <span class="blue">Max = 2.27e+04&#949; (Mean = 725&#949;)</span>
10924                 </p>
10925               </td>
10926 </tr></tbody>
10927 </table></div>
10928 </div>
10929 <br class="table-break"><div class="table">
10930 <a name="math_toolkit.logs_and_tables.all_table.table_sqrt1pm1"></a><p class="title"><b>Table&#160;22.90.&#160;Error rates for sqrt1pm1</b></p>
10931 <div class="table-contents"><table class="table" summary="Error rates for sqrt1pm1">
10932 <colgroup>
10933 <col>
10934 <col>
10935 <col>
10936 <col>
10937 <col>
10938 </colgroup>
10939 <thead><tr>
10940 <th>
10941               </th>
10942 <th>
10943                 <p>
10944                   GNU C++ version 7.1.0<br> linux<br> double
10945                 </p>
10946               </th>
10947 <th>
10948                 <p>
10949                   GNU C++ version 7.1.0<br> linux<br> long double
10950                 </p>
10951               </th>
10952 <th>
10953                 <p>
10954                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
10955                 </p>
10956               </th>
10957 <th>
10958                 <p>
10959                   Microsoft Visual C++ version 14.1<br> Win32<br> double
10960                 </p>
10961               </th>
10962 </tr></thead>
10963 <tbody><tr>
10964 <td>
10965                 <p>
10966                   sqrt1pm1
10967                 </p>
10968               </td>
10969 <td>
10970                 <p>
10971                   <span class="blue">Max = 1.3&#949; (Mean = 0.404&#949;)</span>
10972                 </p>
10973               </td>
10974 <td>
10975                 <p>
10976                   <span class="blue">Max = 1.33&#949; (Mean = 0.404&#949;)</span>
10977                 </p>
10978               </td>
10979 <td>
10980                 <p>
10981                   <span class="blue">Max = 1.54&#949; (Mean = 0.563&#949;)</span>
10982                 </p>
10983               </td>
10984 <td>
10985                 <p>
10986                   <span class="blue">Max = 1.35&#949; (Mean = 0.497&#949;)</span>
10987                 </p>
10988               </td>
10989 </tr></tbody>
10990 </table></div>
10991 </div>
10992 <br class="table-break"><div class="table">
10993 <a name="math_toolkit.logs_and_tables.all_table.table_tgamma"></a><p class="title"><b>Table&#160;22.91.&#160;Error rates for tgamma</b></p>
10994 <div class="table-contents"><table class="table" summary="Error rates for tgamma">
10995 <colgroup>
10996 <col>
10997 <col>
10998 <col>
10999 <col>
11000 <col>
11001 </colgroup>
11002 <thead><tr>
11003 <th>
11004               </th>
11005 <th>
11006                 <p>
11007                   GNU C++ version 7.1.0<br> linux<br> double
11008                 </p>
11009               </th>
11010 <th>
11011                 <p>
11012                   GNU C++ version 7.1.0<br> linux<br> long double
11013                 </p>
11014               </th>
11015 <th>
11016                 <p>
11017                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
11018                 </p>
11019               </th>
11020 <th>
11021                 <p>
11022                   Microsoft Visual C++ version 14.1<br> Win32<br> double
11023                 </p>
11024               </th>
11025 </tr></thead>
11026 <tbody>
11027 <tr>
11028 <td>
11029                 <p>
11030                   factorials
11031                 </p>
11032               </td>
11033 <td>
11034                 <p>
11035                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
11036                   2.1:</em></span> Max = 3.95&#949; (Mean = 0.783&#949;))<br> (<span class="emphasis"><em>Rmath
11037                   3.2.3:</em></span> Max = 314&#949; (Mean = 93.4&#949;))
11038                 </p>
11039               </td>
11040 <td>
11041                 <p>
11042                   <span class="blue">Max = 2.67&#949; (Mean = 0.617&#949;)</span><br> <br>
11043                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.66&#949; (Mean = 0.584&#949;))<br>
11044                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.66&#949; (Mean = 0.584&#949;))
11045                 </p>
11046               </td>
11047 <td>
11048                 <p>
11049                   <span class="blue">Max = 172&#949; (Mean = 41&#949;)</span><br> <br>
11050                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0&#949; (Mean = 0&#949;))
11051                 </p>
11052               </td>
11053 <td>
11054                 <p>
11055                   <span class="blue">Max = 1.85&#949; (Mean = 0.566&#949;)</span><br> <br>
11056                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 3.17&#949; (Mean = 0.928&#949;))
11057                 </p>
11058               </td>
11059 </tr>
11060 <tr>
11061 <td>
11062                 <p>
11063                   near 0
11064                 </p>
11065               </td>
11066 <td>
11067                 <p>
11068                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
11069                   2.1:</em></span> Max = 4.51&#949; (Mean = 1.92&#949;))<br> (<span class="emphasis"><em>Rmath
11070                   3.2.3:</em></span> Max = 1&#949; (Mean = 0.335&#949;))
11071                 </p>
11072               </td>
11073 <td>
11074                 <p>
11075                   <span class="blue">Max = 2&#949; (Mean = 0.608&#949;)</span><br> <br>
11076                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1&#949; (Mean = 0.376&#949;))<br>
11077                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1&#949; (Mean = 0.376&#949;))
11078                 </p>
11079               </td>
11080 <td>
11081                 <p>
11082                   <span class="blue">Max = 2&#949; (Mean = 0.647&#949;)</span><br> <br>
11083                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.5&#949; (Mean = 0.0791&#949;))
11084                 </p>
11085               </td>
11086 <td>
11087                 <p>
11088                   <span class="blue">Max = 1.5&#949; (Mean = 0.635&#949;)</span><br> <br>
11089                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1&#949; (Mean = 0.405&#949;))
11090                 </p>
11091               </td>
11092 </tr>
11093 <tr>
11094 <td>
11095                 <p>
11096                   near 1
11097                 </p>
11098               </td>
11099 <td>
11100                 <p>
11101                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
11102                   2.1:</em></span> Max = 4.41&#949; (Mean = 1.81&#949;))<br> (<span class="emphasis"><em>Rmath
11103                   3.2.3:</em></span> Max = 1&#949; (Mean = 0.32&#949;))
11104                 </p>
11105               </td>
11106 <td>
11107                 <p>
11108                   <span class="blue">Max = 2.51&#949; (Mean = 1.02&#949;)</span><br> <br>
11109                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 0.918&#949; (Mean = 0.203&#949;))<br>
11110                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.918&#949; (Mean = 0.203&#949;))
11111                 </p>
11112               </td>
11113 <td>
11114                 <p>
11115                   <span class="blue">Max = 3.01&#949; (Mean = 1.06&#949;)</span><br> <br>
11116                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1&#949; (Mean = 0.175&#949;))
11117                 </p>
11118               </td>
11119 <td>
11120                 <p>
11121                   <span class="blue">Max = 1.1&#949; (Mean = 0.59&#949;)</span><br> <br>
11122                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1&#949; (Mean = 0.4&#949;))
11123                 </p>
11124               </td>
11125 </tr>
11126 <tr>
11127 <td>
11128                 <p>
11129                   near 2
11130                 </p>
11131               </td>
11132 <td>
11133                 <p>
11134                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
11135                   2.1:</em></span> Max = 7.95&#949; (Mean = 3.12&#949;))<br> (<span class="emphasis"><em>Rmath
11136                   3.2.3:</em></span> Max = 1&#949; (Mean = 0.191&#949;))
11137                 </p>
11138               </td>
11139 <td>
11140                 <p>
11141                   <span class="blue">Max = 4.1&#949; (Mean = 1.55&#949;)</span><br> <br>
11142                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 0.558&#949; (Mean = 0.298&#949;))<br>
11143                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.558&#949; (Mean = 0.298&#949;))
11144                 </p>
11145               </td>
11146 <td>
11147                 <p>
11148                   <span class="blue">Max = 5.01&#949; (Mean = 1.89&#949;)</span><br> <br>
11149                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0&#949; (Mean = 0&#949;))
11150                 </p>
11151               </td>
11152 <td>
11153                 <p>
11154                   <span class="blue">Max = 2&#949; (Mean = 0.733&#949;)</span><br> <br>
11155                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0&#949; (Mean = 0&#949;))
11156                 </p>
11157               </td>
11158 </tr>
11159 <tr>
11160 <td>
11161                 <p>
11162                   near -10
11163                 </p>
11164               </td>
11165 <td>
11166                 <p>
11167                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
11168                   2.1:</em></span> Max = 2.6&#949; (Mean = 1.05&#949;))<br> (<span class="emphasis"><em>Rmath
11169                   3.2.3:</em></span> Max = 34.9&#949; (Mean = 9.2&#949;))
11170                 </p>
11171               </td>
11172 <td>
11173                 <p>
11174                   <span class="blue">Max = 1.75&#949; (Mean = 0.895&#949;)</span><br> <br>
11175                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 2.26&#949; (Mean = 1.08&#949;))<br>
11176                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 2.26&#949; (Mean = 1.08&#949;))
11177                 </p>
11178               </td>
11179 <td>
11180                 <p>
11181                   <span class="blue">Max = 1.75&#949; (Mean = 0.819&#949;)</span><br> <br>
11182                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0&#949; (Mean = 0&#949;))
11183                 </p>
11184               </td>
11185 <td>
11186                 <p>
11187                   <span class="blue">Max = 1.86&#949; (Mean = 0.881&#949;)</span><br> <br>
11188                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.866&#949; (Mean = 0.445&#949;))
11189                 </p>
11190               </td>
11191 </tr>
11192 <tr>
11193 <td>
11194                 <p>
11195                   near -55
11196                 </p>
11197               </td>
11198 <td>
11199                 <p>
11200                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
11201                   2.1:</em></span> Max = 1.8&#949; (Mean = 0.782&#949;))<br> (<span class="emphasis"><em>Rmath
11202                   3.2.3:</em></span> Max = 3.89e+04&#949; (Mean = 9.52e+03&#949;))
11203                 </p>
11204               </td>
11205 <td>
11206                 <p>
11207                   <span class="blue">Max = 2.69&#949; (Mean = 1.09&#949;)</span><br> <br>
11208                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.79&#949; (Mean = 0.75&#949;))<br>
11209                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.79&#949; (Mean = 0.75&#949;))
11210                 </p>
11211               </td>
11212 <td>
11213                 <p>
11214                   <span class="blue">Max = 98.5&#949; (Mean = 53.4&#949;)</span><br> <br>
11215                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0&#949; (Mean = 0&#949;))
11216                 </p>
11217               </td>
11218 <td>
11219                 <p>
11220                   <span class="blue">Max = 2.7&#949; (Mean = 1.35&#949;)</span><br> <br>
11221                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 3.87e+04&#949; (Mean = 6.71e+03&#949;))
11222                 </p>
11223               </td>
11224 </tr>
11225 </tbody>
11226 </table></div>
11227 </div>
11228 <br class="table-break"><div class="table">
11229 <a name="math_toolkit.logs_and_tables.all_table.table_tgamma1pm1"></a><p class="title"><b>Table&#160;22.92.&#160;Error rates for tgamma1pm1</b></p>
11230 <div class="table-contents"><table class="table" summary="Error rates for tgamma1pm1">
11231 <colgroup>
11232 <col>
11233 <col>
11234 <col>
11235 <col>
11236 <col>
11237 </colgroup>
11238 <thead><tr>
11239 <th>
11240               </th>
11241 <th>
11242                 <p>
11243                   GNU C++ version 7.1.0<br> linux<br> double
11244                 </p>
11245               </th>
11246 <th>
11247                 <p>
11248                   GNU C++ version 7.1.0<br> linux<br> long double
11249                 </p>
11250               </th>
11251 <th>
11252                 <p>
11253                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
11254                 </p>
11255               </th>
11256 <th>
11257                 <p>
11258                   Microsoft Visual C++ version 14.1<br> Win32<br> double
11259                 </p>
11260               </th>
11261 </tr></thead>
11262 <tbody><tr>
11263 <td>
11264                 <p>
11265                   tgamma1pm1(dz)
11266                 </p>
11267               </td>
11268 <td>
11269                 <p>
11270                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
11271                 </p>
11272               </td>
11273 <td>
11274                 <p>
11275                   <span class="blue">Max = 1.12&#949; (Mean = 0.49&#949;)</span>
11276                 </p>
11277               </td>
11278 <td>
11279                 <p>
11280                   <span class="blue">Max = 6.61&#949; (Mean = 0.84&#949;)</span>
11281                 </p>
11282               </td>
11283 <td>
11284                 <p>
11285                   <span class="blue">Max = 3.31&#949; (Mean = 0.517&#949;)</span>
11286                 </p>
11287               </td>
11288 </tr></tbody>
11289 </table></div>
11290 </div>
11291 <br class="table-break"><div class="table">
11292 <a name="math_toolkit.logs_and_tables.all_table.table_tgamma_delta_ratio"></a><p class="title"><b>Table&#160;22.93.&#160;Error rates for tgamma_delta_ratio</b></p>
11293 <div class="table-contents"><table class="table" summary="Error rates for tgamma_delta_ratio">
11294 <colgroup>
11295 <col>
11296 <col>
11297 <col>
11298 <col>
11299 <col>
11300 </colgroup>
11301 <thead><tr>
11302 <th>
11303               </th>
11304 <th>
11305                 <p>
11306                   GNU C++ version 7.1.0<br> linux<br> double
11307                 </p>
11308               </th>
11309 <th>
11310                 <p>
11311                   GNU C++ version 7.1.0<br> linux<br> long double
11312                 </p>
11313               </th>
11314 <th>
11315                 <p>
11316                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
11317                 </p>
11318               </th>
11319 <th>
11320                 <p>
11321                   Microsoft Visual C++ version 14.1<br> Win32<br> double
11322                 </p>
11323               </th>
11324 </tr></thead>
11325 <tbody>
11326 <tr>
11327 <td>
11328                 <p>
11329                   tgamma + small delta ratios
11330                 </p>
11331               </td>
11332 <td>
11333                 <p>
11334                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
11335                 </p>
11336               </td>
11337 <td>
11338                 <p>
11339                   <span class="blue">Max = 5.83&#949; (Mean = 1.3&#949;)</span>
11340                 </p>
11341               </td>
11342 <td>
11343                 <p>
11344                   <span class="blue">Max = 15.4&#949; (Mean = 2.09&#949;)</span>
11345                 </p>
11346               </td>
11347 <td>
11348                 <p>
11349                   <span class="blue">Max = 7.56&#949; (Mean = 1.31&#949;)</span>
11350                 </p>
11351               </td>
11352 </tr>
11353 <tr>
11354 <td>
11355                 <p>
11356                   tgamma + small delta ratios (negative delta)
11357                 </p>
11358               </td>
11359 <td>
11360                 <p>
11361                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
11362                 </p>
11363               </td>
11364 <td>
11365                 <p>
11366                   <span class="blue">Max = 7.94&#949; (Mean = 1.4&#949;)</span>
11367                 </p>
11368               </td>
11369 <td>
11370                 <p>
11371                   <span class="blue">Max = 18.3&#949; (Mean = 2.03&#949;)</span>
11372                 </p>
11373               </td>
11374 <td>
11375                 <p>
11376                   <span class="blue">Max = 7.43&#949; (Mean = 1.42&#949;)</span>
11377                 </p>
11378               </td>
11379 </tr>
11380 <tr>
11381 <td>
11382                 <p>
11383                   tgamma + small integer ratios
11384                 </p>
11385               </td>
11386 <td>
11387                 <p>
11388                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
11389                 </p>
11390               </td>
11391 <td>
11392                 <p>
11393                   <span class="blue">Max = 1.96&#949; (Mean = 0.677&#949;)</span>
11394                 </p>
11395               </td>
11396 <td>
11397                 <p>
11398                   <span class="blue">Max = 1.96&#949; (Mean = 0.677&#949;)</span>
11399                 </p>
11400               </td>
11401 <td>
11402                 <p>
11403                   <span class="blue">Max = 2.74&#949; (Mean = 0.736&#949;)</span>
11404                 </p>
11405               </td>
11406 </tr>
11407 <tr>
11408 <td>
11409                 <p>
11410                   tgamma + small integer ratios (negative delta)
11411                 </p>
11412               </td>
11413 <td>
11414                 <p>
11415                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
11416                 </p>
11417               </td>
11418 <td>
11419                 <p>
11420                   <span class="blue">Max = 1.62&#949; (Mean = 0.451&#949;)</span>
11421                 </p>
11422               </td>
11423 <td>
11424                 <p>
11425                   <span class="blue">Max = 1.62&#949; (Mean = 0.451&#949;)</span>
11426                 </p>
11427               </td>
11428 <td>
11429                 <p>
11430                   <span class="blue">Max = 2.15&#949; (Mean = 0.685&#949;)</span>
11431                 </p>
11432               </td>
11433 </tr>
11434 <tr>
11435 <td>
11436                 <p>
11437                   integer tgamma ratios
11438                 </p>
11439               </td>
11440 <td>
11441                 <p>
11442                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
11443                 </p>
11444               </td>
11445 <td>
11446                 <p>
11447                   <span class="blue">Max = 0.997&#949; (Mean = 0.4&#949;)</span>
11448                 </p>
11449               </td>
11450 <td>
11451                 <p>
11452                   <span class="blue">Max = 0.997&#949; (Mean = 0.4&#949;)</span>
11453                 </p>
11454               </td>
11455 <td>
11456                 <p>
11457                   <span class="blue">Max = 0.968&#949; (Mean = 0.386&#949;)</span>
11458                 </p>
11459               </td>
11460 </tr>
11461 <tr>
11462 <td>
11463                 <p>
11464                   integer tgamma ratios (negative delta)
11465                 </p>
11466               </td>
11467 <td>
11468                 <p>
11469                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
11470                 </p>
11471               </td>
11472 <td>
11473                 <p>
11474                   <span class="blue">Max = 0.853&#949; (Mean = 0.176&#949;)</span>
11475                 </p>
11476               </td>
11477 <td>
11478                 <p>
11479                   <span class="blue">Max = 0.853&#949; (Mean = 0.176&#949;)</span>
11480                 </p>
11481               </td>
11482 <td>
11483                 <p>
11484                   <span class="blue">Max = 0.974&#949; (Mean = 0.175&#949;)</span>
11485                 </p>
11486               </td>
11487 </tr>
11488 </tbody>
11489 </table></div>
11490 </div>
11491 <br class="table-break"><div class="table">
11492 <a name="math_toolkit.logs_and_tables.all_table.table_tgamma_incomplete_"></a><p class="title"><b>Table&#160;22.94.&#160;Error rates for tgamma (incomplete)</b></p>
11493 <div class="table-contents"><table class="table" summary="Error rates for tgamma (incomplete)">
11494 <colgroup>
11495 <col>
11496 <col>
11497 <col>
11498 <col>
11499 <col>
11500 </colgroup>
11501 <thead><tr>
11502 <th>
11503               </th>
11504 <th>
11505                 <p>
11506                   GNU C++ version 7.1.0<br> linux<br> double
11507                 </p>
11508               </th>
11509 <th>
11510                 <p>
11511                   GNU C++ version 7.1.0<br> linux<br> long double
11512                 </p>
11513               </th>
11514 <th>
11515                 <p>
11516                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
11517                 </p>
11518               </th>
11519 <th>
11520                 <p>
11521                   Microsoft Visual C++ version 14.1<br> Win32<br> double
11522                 </p>
11523               </th>
11524 </tr></thead>
11525 <tbody>
11526 <tr>
11527 <td>
11528                 <p>
11529                   tgamma(a, z) medium values
11530                 </p>
11531               </td>
11532 <td>
11533                 <p>
11534                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
11535                   2.1:</em></span> Max = 200&#949; (Mean = 13.3&#949;))
11536                 </p>
11537               </td>
11538 <td>
11539                 <p>
11540                   <span class="blue">Max = 8.47&#949; (Mean = 1.9&#949;)</span>
11541                 </p>
11542               </td>
11543 <td>
11544                 <p>
11545                   <span class="blue">Max = 412&#949; (Mean = 95.5&#949;)</span>
11546                 </p>
11547               </td>
11548 <td>
11549                 <p>
11550                   <span class="blue">Max = 8.14&#949; (Mean = 1.76&#949;)</span>
11551                 </p>
11552               </td>
11553 </tr>
11554 <tr>
11555 <td>
11556                 <p>
11557                   tgamma(a, z) small values
11558                 </p>
11559               </td>
11560 <td>
11561                 <p>
11562                   <span class="blue">Max = 0.753&#949; (Mean = 0.0474&#949;)</span><br>
11563                   <br> (<span class="emphasis"><em>GSL 2.1:</em></span> <span class="red">Max =
11564                   1.38e+10&#949; (Mean = 1.05e+09&#949;))</span>
11565                 </p>
11566               </td>
11567 <td>
11568                 <p>
11569                   <span class="blue">Max = 2.31&#949; (Mean = 0.775&#949;)</span>
11570                 </p>
11571               </td>
11572 <td>
11573                 <p>
11574                   <span class="blue">Max = 2.13&#949; (Mean = 0.717&#949;)</span>
11575                 </p>
11576               </td>
11577 <td>
11578                 <p>
11579                   <span class="blue">Max = 2.53&#949; (Mean = 0.66&#949;)</span>
11580                 </p>
11581               </td>
11582 </tr>
11583 <tr>
11584 <td>
11585                 <p>
11586                   tgamma(a, z) integer and half integer values
11587                 </p>
11588               </td>
11589 <td>
11590                 <p>
11591                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
11592                   2.1:</em></span> Max = 117&#949; (Mean = 12.5&#949;))
11593                 </p>
11594               </td>
11595 <td>
11596                 <p>
11597                   <span class="blue">Max = 5.52&#949; (Mean = 1.48&#949;)</span>
11598                 </p>
11599               </td>
11600 <td>
11601                 <p>
11602                   <span class="blue">Max = 79.6&#949; (Mean = 20.9&#949;)</span>
11603                 </p>
11604               </td>
11605 <td>
11606                 <p>
11607                   <span class="blue">Max = 5.16&#949; (Mean = 1.33&#949;)</span>
11608                 </p>
11609               </td>
11610 </tr>
11611 </tbody>
11612 </table></div>
11613 </div>
11614 <br class="table-break"><div class="table">
11615 <a name="math_toolkit.logs_and_tables.all_table.table_tgamma_lower"></a><p class="title"><b>Table&#160;22.95.&#160;Error rates for tgamma_lower</b></p>
11616 <div class="table-contents"><table class="table" summary="Error rates for tgamma_lower">
11617 <colgroup>
11618 <col>
11619 <col>
11620 <col>
11621 <col>
11622 <col>
11623 </colgroup>
11624 <thead><tr>
11625 <th>
11626               </th>
11627 <th>
11628                 <p>
11629                   GNU C++ version 7.1.0<br> linux<br> double
11630                 </p>
11631               </th>
11632 <th>
11633                 <p>
11634                   GNU C++ version 7.1.0<br> linux<br> long double
11635                 </p>
11636               </th>
11637 <th>
11638                 <p>
11639                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
11640                 </p>
11641               </th>
11642 <th>
11643                 <p>
11644                   Microsoft Visual C++ version 14.1<br> Win32<br> double
11645                 </p>
11646               </th>
11647 </tr></thead>
11648 <tbody>
11649 <tr>
11650 <td>
11651                 <p>
11652                   tgamma(a, z) medium values
11653                 </p>
11654               </td>
11655 <td>
11656                 <p>
11657                   <span class="blue">Max = 0.833&#949; (Mean = 0.0315&#949;)</span><br>
11658                   <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.833&#949; (Mean = 0.0315&#949;))
11659                 </p>
11660               </td>
11661 <td>
11662                 <p>
11663                   <span class="blue">Max = 6.79&#949; (Mean = 1.46&#949;)</span>
11664                 </p>
11665               </td>
11666 <td>
11667                 <p>
11668                   <span class="blue">Max = 363&#949; (Mean = 63.8&#949;)</span>
11669                 </p>
11670               </td>
11671 <td>
11672                 <p>
11673                   <span class="blue">Max = 5.62&#949; (Mean = 1.49&#949;)</span>
11674                 </p>
11675               </td>
11676 </tr>
11677 <tr>
11678 <td>
11679                 <p>
11680                   tgamma(a, z) small values
11681                 </p>
11682               </td>
11683 <td>
11684                 <p>
11685                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
11686                   2.1:</em></span> Max = 0&#949; (Mean = 0&#949;))
11687                 </p>
11688               </td>
11689 <td>
11690                 <p>
11691                   <span class="blue">Max = 1.97&#949; (Mean = 0.555&#949;)</span>
11692                 </p>
11693               </td>
11694 <td>
11695                 <p>
11696                   <span class="blue">Max = 1.97&#949; (Mean = 0.558&#949;)</span>
11697                 </p>
11698               </td>
11699 <td>
11700                 <p>
11701                   <span class="blue">Max = 1.57&#949; (Mean = 0.525&#949;)</span>
11702                 </p>
11703               </td>
11704 </tr>
11705 <tr>
11706 <td>
11707                 <p>
11708                   tgamma(a, z) integer and half integer values
11709                 </p>
11710               </td>
11711 <td>
11712                 <p>
11713                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
11714                   2.1:</em></span> Max = 0&#949; (Mean = 0&#949;))
11715                 </p>
11716               </td>
11717 <td>
11718                 <p>
11719                   <span class="blue">Max = 4.83&#949; (Mean = 1.15&#949;)</span>
11720                 </p>
11721               </td>
11722 <td>
11723                 <p>
11724                   <span class="blue">Max = 84.7&#949; (Mean = 17.5&#949;)</span>
11725                 </p>
11726               </td>
11727 <td>
11728                 <p>
11729                   <span class="blue">Max = 2.69&#949; (Mean = 0.849&#949;)</span>
11730                 </p>
11731               </td>
11732 </tr>
11733 </tbody>
11734 </table></div>
11735 </div>
11736 <br class="table-break"><div class="table">
11737 <a name="math_toolkit.logs_and_tables.all_table.table_tgamma_ratio"></a><p class="title"><b>Table&#160;22.96.&#160;Error rates for tgamma_ratio</b></p>
11738 <div class="table-contents"><table class="table" summary="Error rates for tgamma_ratio">
11739 <colgroup>
11740 <col>
11741 <col>
11742 <col>
11743 <col>
11744 <col>
11745 </colgroup>
11746 <thead><tr>
11747 <th>
11748               </th>
11749 <th>
11750                 <p>
11751                   GNU C++ version 7.1.0<br> linux<br> double
11752                 </p>
11753               </th>
11754 <th>
11755                 <p>
11756                   GNU C++ version 7.1.0<br> linux<br> long double
11757                 </p>
11758               </th>
11759 <th>
11760                 <p>
11761                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
11762                 </p>
11763               </th>
11764 <th>
11765                 <p>
11766                   Microsoft Visual C++ version 14.1<br> Win32<br> double
11767                 </p>
11768               </th>
11769 </tr></thead>
11770 <tbody><tr>
11771 <td>
11772                 <p>
11773                   tgamma ratios
11774                 </p>
11775               </td>
11776 <td>
11777                 <p>
11778                   <span class="blue">Max = 0.694&#949; (Mean = 0.0347&#949;)</span>
11779                 </p>
11780               </td>
11781 <td>
11782                 <p>
11783                   <span class="blue">Max = 2.99&#949; (Mean = 1.15&#949;)</span>
11784                 </p>
11785               </td>
11786 <td>
11787                 <p>
11788                   <span class="blue">Max = 174&#949; (Mean = 61.2&#949;)</span>
11789                 </p>
11790               </td>
11791 <td>
11792                 <p>
11793                   <span class="blue">Max = 3.28&#949; (Mean = 1.12&#949;)</span>
11794                 </p>
11795               </td>
11796 </tr></tbody>
11797 </table></div>
11798 </div>
11799 <br class="table-break"><div class="table">
11800 <a name="math_toolkit.logs_and_tables.all_table.table_trigamma"></a><p class="title"><b>Table&#160;22.97.&#160;Error rates for trigamma</b></p>
11801 <div class="table-contents"><table class="table" summary="Error rates for trigamma">
11802 <colgroup>
11803 <col>
11804 <col>
11805 <col>
11806 <col>
11807 <col>
11808 </colgroup>
11809 <thead><tr>
11810 <th>
11811               </th>
11812 <th>
11813                 <p>
11814                   GNU C++ version 7.1.0<br> linux<br> double
11815                 </p>
11816               </th>
11817 <th>
11818                 <p>
11819                   GNU C++ version 7.1.0<br> linux<br> long double
11820                 </p>
11821               </th>
11822 <th>
11823                 <p>
11824                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
11825                 </p>
11826               </th>
11827 <th>
11828                 <p>
11829                   Microsoft Visual C++ version 14.1<br> Win32<br> double
11830                 </p>
11831               </th>
11832 </tr></thead>
11833 <tbody><tr>
11834 <td>
11835                 <p>
11836                   Mathematica Data
11837                 </p>
11838               </td>
11839 <td>
11840                 <p>
11841                   <span class="blue">Max = 0.998&#949; (Mean = 0.105&#949;)</span><br> <br>
11842                   (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.34e+04&#949; (Mean = 1.49e+03&#949;))<br>
11843                   (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.34e+04&#949; (Mean = 1.51e+03&#949;))
11844                 </p>
11845               </td>
11846 <td>
11847                 <p>
11848                   <span class="blue">Max = 1.28&#949; (Mean = 0.449&#949;)</span>
11849                 </p>
11850               </td>
11851 <td>
11852                 <p>
11853                   <span class="blue">Max = 1.28&#949; (Mean = 0.449&#949;)</span>
11854                 </p>
11855               </td>
11856 <td>
11857                 <p>
11858                   <span class="blue">Max = 1&#949; (Mean = 0.382&#949;)</span>
11859                 </p>
11860               </td>
11861 </tr></tbody>
11862 </table></div>
11863 </div>
11864 <br class="table-break"><div class="table">
11865 <a name="math_toolkit.logs_and_tables.all_table.table_zeta"></a><p class="title"><b>Table&#160;22.98.&#160;Error rates for zeta</b></p>
11866 <div class="table-contents"><table class="table" summary="Error rates for zeta">
11867 <colgroup>
11868 <col>
11869 <col>
11870 <col>
11871 <col>
11872 <col>
11873 </colgroup>
11874 <thead><tr>
11875 <th>
11876               </th>
11877 <th>
11878                 <p>
11879                   GNU C++ version 7.1.0<br> linux<br> long double
11880                 </p>
11881               </th>
11882 <th>
11883                 <p>
11884                   GNU C++ version 7.1.0<br> linux<br> double
11885                 </p>
11886               </th>
11887 <th>
11888                 <p>
11889                   Sun compiler version 0x5150<br> Sun Solaris<br> long double
11890                 </p>
11891               </th>
11892 <th>
11893                 <p>
11894                   Microsoft Visual C++ version 14.1<br> Win32<br> double
11895                 </p>
11896               </th>
11897 </tr></thead>
11898 <tbody>
11899 <tr>
11900 <td>
11901                 <p>
11902                   Zeta: Random values greater than 1
11903                 </p>
11904               </td>
11905 <td>
11906                 <p>
11907                   <span class="blue">Max = 0.846&#949; (Mean = 0.0833&#949;)</span><br>
11908                   <br> (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 5.45&#949; (Mean = 1&#949;))
11909                 </p>
11910               </td>
11911 <td>
11912                 <p>
11913                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
11914                   2.1:</em></span> Max = 8.69&#949; (Mean = 1.03&#949;))
11915                 </p>
11916               </td>
11917 <td>
11918                 <p>
11919                   <span class="blue">Max = 0.846&#949; (Mean = 0.0833&#949;)</span>
11920                 </p>
11921               </td>
11922 <td>
11923                 <p>
11924                   <span class="blue">Max = 0.836&#949; (Mean = 0.093&#949;)</span>
11925                 </p>
11926               </td>
11927 </tr>
11928 <tr>
11929 <td>
11930                 <p>
11931                   Zeta: Random values less than 1
11932                 </p>
11933               </td>
11934 <td>
11935                 <p>
11936                   <span class="blue">Max = 7.03&#949; (Mean = 2.93&#949;)</span><br> <br>
11937                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 538&#949; (Mean = 59.3&#949;))
11938                 </p>
11939               </td>
11940 <td>
11941                 <p>
11942                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
11943                   2.1:</em></span> Max = 137&#949; (Mean = 13.8&#949;))
11944                 </p>
11945               </td>
11946 <td>
11947                 <p>
11948                   <span class="blue">Max = 70.1&#949; (Mean = 17.1&#949;)</span>
11949                 </p>
11950               </td>
11951 <td>
11952                 <p>
11953                   <span class="blue">Max = 6.84&#949; (Mean = 3.12&#949;)</span>
11954                 </p>
11955               </td>
11956 </tr>
11957 <tr>
11958 <td>
11959                 <p>
11960                   Zeta: Values close to and greater than 1
11961                 </p>
11962               </td>
11963 <td>
11964                 <p>
11965                   <span class="blue">Max = 0.995&#949; (Mean = 0.5&#949;)</span><br> <br>
11966                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.9e+06&#949; (Mean = 5.11e+05&#949;))
11967                 </p>
11968               </td>
11969 <td>
11970                 <p>
11971                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
11972                   2.1:</em></span> Max = 7.73&#949; (Mean = 4.07&#949;))
11973                 </p>
11974               </td>
11975 <td>
11976                 <p>
11977                   <span class="blue">Max = 0.995&#949; (Mean = 0.5&#949;)</span>
11978                 </p>
11979               </td>
11980 <td>
11981                 <p>
11982                   <span class="blue">Max = 0.994&#949; (Mean = 0.421&#949;)</span>
11983                 </p>
11984               </td>
11985 </tr>
11986 <tr>
11987 <td>
11988                 <p>
11989                   Zeta: Values close to and less than 1
11990                 </p>
11991               </td>
11992 <td>
11993                 <p>
11994                   <span class="blue">Max = 0.998&#949; (Mean = 0.508&#949;)</span><br> <br>
11995                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 8.53e+06&#949; (Mean = 1.87e+06&#949;))
11996                 </p>
11997               </td>
11998 <td>
11999                 <p>
12000                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
12001                   2.1:</em></span> Max = 0.991&#949; (Mean = 0.28&#949;))
12002                 </p>
12003               </td>
12004 <td>
12005                 <p>
12006                   <span class="blue">Max = 0.998&#949; (Mean = 0.508&#949;)</span>
12007                 </p>
12008               </td>
12009 <td>
12010                 <p>
12011                   <span class="blue">Max = 0.991&#949; (Mean = 0.375&#949;)</span>
12012                 </p>
12013               </td>
12014 </tr>
12015 <tr>
12016 <td>
12017                 <p>
12018                   Zeta: Integer arguments
12019                 </p>
12020               </td>
12021 <td>
12022                 <p>
12023                   <span class="blue">Max = 9&#949; (Mean = 3.06&#949;)</span><br> <br>
12024                   (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 70.3&#949; (Mean = 17.4&#949;))
12025                 </p>
12026               </td>
12027 <td>
12028                 <p>
12029                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
12030                   2.1:</em></span> Max = 3.75&#949; (Mean = 1.1&#949;))
12031                 </p>
12032               </td>
12033 <td>
12034                 <p>
12035                   <span class="blue">Max = 28&#949; (Mean = 5.62&#949;)</span>
12036                 </p>
12037               </td>
12038 <td>
12039                 <p>
12040                   <span class="blue">Max = 9&#949; (Mean = 3&#949;)</span>
12041                 </p>
12042               </td>
12043 </tr>
12044 </tbody>
12045 </table></div>
12046 </div>
12047 <br class="table-break">
12048 </div>
12049 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
12050 <td align="left"></td>
12051 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
12052       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
12053       Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
12054       R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
12055       Daryle Walker and Xiaogang Zhang<p>
12056         Distributed under the Boost Software License, Version 1.0. (See accompanying
12057         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
12058       </p>
12059 </div></td>
12060 </tr></table>
12061 <hr>
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