libstdc++-v3/testsuite/special_functions/01_assoc_laguerre/check_value.cc

   1 // { dg-do run { target c++11 } }
   2 // { dg-options "-D__STDCPP_WANT_MATH_SPEC_FUNCS__" }
   3 //
   4 // Copyright (C) 2016-2017 Free Software Foundation, Inc.
   5 //
   6 // This file is part of the GNU ISO C++ Library.  This library is free
   7 // software; you can redistribute it and/or modify it under the
   8 // terms of the GNU General Public License as published by the
   9 // Free Software Foundation; either version 3, or (at your option)
  10 // any later version.
  11 //
  12 // This library is distributed in the hope that it will be useful,
  13 // but WITHOUT ANY WARRANTY; without even the implied warranty of
  14 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  15 // GNU General Public License for more details.
  16 //
  17 // You should have received a copy of the GNU General Public License along
  18 // with this library; see the file COPYING3.  If not see
  19 // <http://www.gnu.org/licenses/>.
  20
  21 //  assoc_laguerre
  22 //  Compare against values generated by the GNU Scientific Library.
  23 //  The GSL can be found on the web: http://www.gnu.org/software/gsl/
  24 #include <limits>
  25 #include <cmath>
  26 #if defined(__TEST_DEBUG)
  27 #  include <iostream>
  28 #  define VERIFY(A) \
  29   if (!(A)) \
  30     { \
  31       std::cout << "line " << __LINE__ \
  32         << "  max_abs_frac = " << max_abs_frac \
  33         << std::endl; \
  34     }
  35 #else
  36 #  include <testsuite_hooks.h>
  37 #endif
  38 #include <specfun_testcase.h>
  39
  40
  41 // Test data for n=0, m=0.
  42 // max(|f - f_GSL|): 0.0000000000000000
  43 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
  44 const testcase_assoc_laguerre<double>
  45 data001[11] =
  46 {
  47   { 1.0000000000000000, 0, 0,
  48           0.0000000000000000 },
  49   { 1.0000000000000000, 0, 0,
  50           10.000000000000000 },
  51   { 1.0000000000000000, 0, 0,
  52           20.000000000000000 },
  53   { 1.0000000000000000, 0, 0,
  54           30.000000000000000 },
  55   { 1.0000000000000000, 0, 0,
  56           40.000000000000000 },
  57   { 1.0000000000000000, 0, 0,
  58           50.000000000000000 },
  59   { 1.0000000000000000, 0, 0,
  60           60.000000000000000 },
  61   { 1.0000000000000000, 0, 0,
  62           70.000000000000000 },
  63   { 1.0000000000000000, 0, 0,
  64           80.000000000000000 },
  65   { 1.0000000000000000, 0, 0,
  66           90.000000000000000 },
  67   { 1.0000000000000000, 0, 0,
  68           100.00000000000000 },
  69 };
  70 const double toler001 = 2.5000000000000020e-13;
  71
  72 // Test data for n=0, m=1.
  73 // max(|f - f_GSL|): 0.0000000000000000
  74 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
  75 const testcase_assoc_laguerre<double>
  76 data002[11] =
  77 {
  78   { 1.0000000000000000, 0, 1,
  79           0.0000000000000000 },
  80   { 1.0000000000000000, 0, 1,
  81           10.000000000000000 },
  82   { 1.0000000000000000, 0, 1,
  83           20.000000000000000 },
  84   { 1.0000000000000000, 0, 1,
  85           30.000000000000000 },
  86   { 1.0000000000000000, 0, 1,
  87           40.000000000000000 },
  88   { 1.0000000000000000, 0, 1,
  89           50.000000000000000 },
  90   { 1.0000000000000000, 0, 1,
  91           60.000000000000000 },
  92   { 1.0000000000000000, 0, 1,
  93           70.000000000000000 },
  94   { 1.0000000000000000, 0, 1,
  95           80.000000000000000 },
  96   { 1.0000000000000000, 0, 1,
  97           90.000000000000000 },
  98   { 1.0000000000000000, 0, 1,
  99           100.00000000000000 },
 100 };
 101 const double toler002 = 2.5000000000000020e-13;
 102
 103 // Test data for n=0, m=2.
 104 // max(|f - f_GSL|): 0.0000000000000000
 105 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
 106 const testcase_assoc_laguerre<double>
 107 data003[11] =
 108 {
 109   { 1.0000000000000000, 0, 2,
 110           0.0000000000000000 },
 111   { 1.0000000000000000, 0, 2,
 112           10.000000000000000 },
 113   { 1.0000000000000000, 0, 2,
 114           20.000000000000000 },
 115   { 1.0000000000000000, 0, 2,
 116           30.000000000000000 },
 117   { 1.0000000000000000, 0, 2,
 118           40.000000000000000 },
 119   { 1.0000000000000000, 0, 2,
 120           50.000000000000000 },
 121   { 1.0000000000000000, 0, 2,
 122           60.000000000000000 },
 123   { 1.0000000000000000, 0, 2,
 124           70.000000000000000 },
 125   { 1.0000000000000000, 0, 2,
 126           80.000000000000000 },
 127   { 1.0000000000000000, 0, 2,
 128           90.000000000000000 },
 129   { 1.0000000000000000, 0, 2,
 130           100.00000000000000 },
 131 };
 132 const double toler003 = 2.5000000000000020e-13;
 133
 134 // Test data for n=0, m=5.
 135 // max(|f - f_GSL|): 0.0000000000000000
 136 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
 137 const testcase_assoc_laguerre<double>
 138 data004[11] =
 139 {
 140   { 1.0000000000000000, 0, 5,
 141           0.0000000000000000 },
 142   { 1.0000000000000000, 0, 5,
 143           10.000000000000000 },
 144   { 1.0000000000000000, 0, 5,
 145           20.000000000000000 },
 146   { 1.0000000000000000, 0, 5,
 147           30.000000000000000 },
 148   { 1.0000000000000000, 0, 5,
 149           40.000000000000000 },
 150   { 1.0000000000000000, 0, 5,
 151           50.000000000000000 },
 152   { 1.0000000000000000, 0, 5,
 153           60.000000000000000 },
 154   { 1.0000000000000000, 0, 5,
 155           70.000000000000000 },
 156   { 1.0000000000000000, 0, 5,
 157           80.000000000000000 },
 158   { 1.0000000000000000, 0, 5,
 159           90.000000000000000 },
 160   { 1.0000000000000000, 0, 5,
 161           100.00000000000000 },
 162 };
 163 const double toler004 = 2.5000000000000020e-13;
 164
 165 // Test data for n=0, m=10.
 166 // max(|f - f_GSL|): 0.0000000000000000
 167 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
 168 const testcase_assoc_laguerre<double>
 169 data005[11] =
 170 {
 171   { 1.0000000000000000, 0, 10,
 172           0.0000000000000000 },
 173   { 1.0000000000000000, 0, 10,
 174           10.000000000000000 },
 175   { 1.0000000000000000, 0, 10,
 176           20.000000000000000 },
 177   { 1.0000000000000000, 0, 10,
 178           30.000000000000000 },
 179   { 1.0000000000000000, 0, 10,
 180           40.000000000000000 },
 181   { 1.0000000000000000, 0, 10,
 182           50.000000000000000 },
 183   { 1.0000000000000000, 0, 10,
 184           60.000000000000000 },
 185   { 1.0000000000000000, 0, 10,
 186           70.000000000000000 },
 187   { 1.0000000000000000, 0, 10,
 188           80.000000000000000 },
 189   { 1.0000000000000000, 0, 10,
 190           90.000000000000000 },
 191   { 1.0000000000000000, 0, 10,
 192           100.00000000000000 },
 193 };
 194 const double toler005 = 2.5000000000000020e-13;
 195
 196 // Test data for n=0, m=20.
 197 // max(|f - f_GSL|): 0.0000000000000000
 198 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
 199 const testcase_assoc_laguerre<double>
 200 data006[11] =
 201 {
 202   { 1.0000000000000000, 0, 20,
 203           0.0000000000000000 },
 204   { 1.0000000000000000, 0, 20,
 205           10.000000000000000 },
 206   { 1.0000000000000000, 0, 20,
 207           20.000000000000000 },
 208   { 1.0000000000000000, 0, 20,
 209           30.000000000000000 },
 210   { 1.0000000000000000, 0, 20,
 211           40.000000000000000 },
 212   { 1.0000000000000000, 0, 20,
 213           50.000000000000000 },
 214   { 1.0000000000000000, 0, 20,
 215           60.000000000000000 },
 216   { 1.0000000000000000, 0, 20,
 217           70.000000000000000 },
 218   { 1.0000000000000000, 0, 20,
 219           80.000000000000000 },
 220   { 1.0000000000000000, 0, 20,
 221           90.000000000000000 },
 222   { 1.0000000000000000, 0, 20,
 223           100.00000000000000 },
 224 };
 225 const double toler006 = 2.5000000000000020e-13;
 226
 227 // Test data for n=0, m=50.
 228 // max(|f - f_GSL|): 0.0000000000000000
 229 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
 230 const testcase_assoc_laguerre<double>
 231 data007[11] =
 232 {
 233   { 1.0000000000000000, 0, 50,
 234           0.0000000000000000 },
 235   { 1.0000000000000000, 0, 50,
 236           10.000000000000000 },
 237   { 1.0000000000000000, 0, 50,
 238           20.000000000000000 },
 239   { 1.0000000000000000, 0, 50,
 240           30.000000000000000 },
 241   { 1.0000000000000000, 0, 50,
 242           40.000000000000000 },
 243   { 1.0000000000000000, 0, 50,
 244           50.000000000000000 },
 245   { 1.0000000000000000, 0, 50,
 246           60.000000000000000 },
 247   { 1.0000000000000000, 0, 50,
 248           70.000000000000000 },
 249   { 1.0000000000000000, 0, 50,
 250           80.000000000000000 },
 251   { 1.0000000000000000, 0, 50,
 252           90.000000000000000 },
 253   { 1.0000000000000000, 0, 50,
 254           100.00000000000000 },
 255 };
 256 const double toler007 = 2.5000000000000020e-13;
 257
 258 // Test data for n=0, m=100.
 259 // max(|f - f_GSL|): 0.0000000000000000
 260 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
 261 const testcase_assoc_laguerre<double>
 262 data008[11] =
 263 {
 264   { 1.0000000000000000, 0, 100,
 265           0.0000000000000000 },
 266   { 1.0000000000000000, 0, 100,
 267           10.000000000000000 },
 268   { 1.0000000000000000, 0, 100,
 269           20.000000000000000 },
 270   { 1.0000000000000000, 0, 100,
 271           30.000000000000000 },
 272   { 1.0000000000000000, 0, 100,
 273           40.000000000000000 },
 274   { 1.0000000000000000, 0, 100,
 275           50.000000000000000 },
 276   { 1.0000000000000000, 0, 100,
 277           60.000000000000000 },
 278   { 1.0000000000000000, 0, 100,
 279           70.000000000000000 },
 280   { 1.0000000000000000, 0, 100,
 281           80.000000000000000 },
 282   { 1.0000000000000000, 0, 100,
 283           90.000000000000000 },
 284   { 1.0000000000000000, 0, 100,
 285           100.00000000000000 },
 286 };
 287 const double toler008 = 2.5000000000000020e-13;
 288
 289 // Test data for n=1, m=0.
 290 // max(|f - f_GSL|): 0.0000000000000000
 291 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
 292 const testcase_assoc_laguerre<double>
 293 data009[11] =
 294 {
 295   { 1.0000000000000000, 1, 0,
 296           0.0000000000000000 },
 297   { -9.0000000000000000, 1, 0,
 298           10.000000000000000 },
 299   { -19.000000000000000, 1, 0,
 300           20.000000000000000 },
 301   { -29.000000000000000, 1, 0,
 302           30.000000000000000 },
 303   { -39.000000000000000, 1, 0,
 304           40.000000000000000 },
 305   { -49.000000000000000, 1, 0,
 306           50.000000000000000 },
 307   { -59.000000000000000, 1, 0,
 308           60.000000000000000 },
 309   { -69.000000000000000, 1, 0,
 310           70.000000000000000 },
 311   { -79.000000000000000, 1, 0,
 312           80.000000000000000 },
 313   { -89.000000000000000, 1, 0,
 314           90.000000000000000 },
 315   { -99.000000000000000, 1, 0,
 316           100.00000000000000 },
 317 };
 318 const double toler009 = 2.5000000000000020e-13;
 319
 320 // Test data for n=1, m=1.
 321 // max(|f - f_GSL|): 0.0000000000000000
 322 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
 323 const testcase_assoc_laguerre<double>
 324 data010[11] =
 325 {
 326   { 2.0000000000000000, 1, 1,
 327           0.0000000000000000 },
 328   { -8.0000000000000000, 1, 1,
 329           10.000000000000000 },
 330   { -18.000000000000000, 1, 1,
 331           20.000000000000000 },
 332   { -28.000000000000000, 1, 1,
 333           30.000000000000000 },
 334   { -38.000000000000000, 1, 1,
 335           40.000000000000000 },
 336   { -48.000000000000000, 1, 1,
 337           50.000000000000000 },
 338   { -58.000000000000000, 1, 1,
 339           60.000000000000000 },
 340   { -68.000000000000000, 1, 1,
 341           70.000000000000000 },
 342   { -78.000000000000000, 1, 1,
 343           80.000000000000000 },
 344   { -88.000000000000000, 1, 1,
 345           90.000000000000000 },
 346   { -98.000000000000000, 1, 1,
 347           100.00000000000000 },
 348 };
 349 const double toler010 = 2.5000000000000020e-13;
 350
 351 // Test data for n=1, m=2.
 352 // max(|f - f_GSL|): 0.0000000000000000
 353 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
 354 const testcase_assoc_laguerre<double>
 355 data011[11] =
 356 {
 357   { 3.0000000000000000, 1, 2,
 358           0.0000000000000000 },
 359   { -7.0000000000000000, 1, 2,
 360           10.000000000000000 },
 361   { -17.000000000000000, 1, 2,
 362           20.000000000000000 },
 363   { -27.000000000000000, 1, 2,
 364           30.000000000000000 },
 365   { -37.000000000000000, 1, 2,
 366           40.000000000000000 },
 367   { -47.000000000000000, 1, 2,
 368           50.000000000000000 },
 369   { -57.000000000000000, 1, 2,
 370           60.000000000000000 },
 371   { -67.000000000000000, 1, 2,
 372           70.000000000000000 },
 373   { -77.000000000000000, 1, 2,
 374           80.000000000000000 },
 375   { -87.000000000000000, 1, 2,
 376           90.000000000000000 },
 377   { -97.000000000000000, 1, 2,
 378           100.00000000000000 },
 379 };
 380 const double toler011 = 2.5000000000000020e-13;
 381
 382 // Test data for n=1, m=5.
 383 // max(|f - f_GSL|): 0.0000000000000000
 384 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
 385 const testcase_assoc_laguerre<double>
 386 data012[11] =
 387 {
 388   { 6.0000000000000000, 1, 5,
 389           0.0000000000000000 },
 390   { -4.0000000000000000, 1, 5,
 391           10.000000000000000 },
 392   { -14.000000000000000, 1, 5,
 393           20.000000000000000 },
 394   { -24.000000000000000, 1, 5,
 395           30.000000000000000 },
 396   { -34.000000000000000, 1, 5,
 397           40.000000000000000 },
 398   { -44.000000000000000, 1, 5,
 399           50.000000000000000 },
 400   { -54.000000000000000, 1, 5,
 401           60.000000000000000 },
 402   { -64.000000000000000, 1, 5,
 403           70.000000000000000 },
 404   { -74.000000000000000, 1, 5,
 405           80.000000000000000 },
 406   { -84.000000000000000, 1, 5,
 407           90.000000000000000 },
 408   { -94.000000000000000, 1, 5,
 409           100.00000000000000 },
 410 };
 411 const double toler012 = 2.5000000000000020e-13;
 412
 413 // Test data for n=1, m=10.
 414 // max(|f - f_GSL|): 0.0000000000000000
 415 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
 416 const testcase_assoc_laguerre<double>
 417 data013[11] =
 418 {
 419   { 11.000000000000000, 1, 10,
 420           0.0000000000000000 },
 421   { 1.0000000000000000, 1, 10,
 422           10.000000000000000 },
 423   { -9.0000000000000000, 1, 10,
 424           20.000000000000000 },
 425   { -19.000000000000000, 1, 10,
 426           30.000000000000000 },
 427   { -29.000000000000000, 1, 10,
 428           40.000000000000000 },
 429   { -39.000000000000000, 1, 10,
 430           50.000000000000000 },
 431   { -49.000000000000000, 1, 10,
 432           60.000000000000000 },
 433   { -59.000000000000000, 1, 10,
 434           70.000000000000000 },
 435   { -69.000000000000000, 1, 10,
 436           80.000000000000000 },
 437   { -79.000000000000000, 1, 10,
 438           90.000000000000000 },
 439   { -89.000000000000000, 1, 10,
 440           100.00000000000000 },
 441 };
 442 const double toler013 = 2.5000000000000020e-13;
 443
 444 // Test data for n=1, m=20.
 445 // max(|f - f_GSL|): 0.0000000000000000
 446 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
 447 const testcase_assoc_laguerre<double>
 448 data014[11] =
 449 {
 450   { 21.000000000000000, 1, 20,
 451           0.0000000000000000 },
 452   { 11.000000000000000, 1, 20,
 453           10.000000000000000 },
 454   { 1.0000000000000000, 1, 20,
 455           20.000000000000000 },
 456   { -9.0000000000000000, 1, 20,
 457           30.000000000000000 },
 458   { -19.000000000000000, 1, 20,
 459           40.000000000000000 },
 460   { -29.000000000000000, 1, 20,
 461           50.000000000000000 },
 462   { -39.000000000000000, 1, 20,
 463           60.000000000000000 },
 464   { -49.000000000000000, 1, 20,
 465           70.000000000000000 },
 466   { -59.000000000000000, 1, 20,
 467           80.000000000000000 },
 468   { -69.000000000000000, 1, 20,
 469           90.000000000000000 },
 470   { -79.000000000000000, 1, 20,
 471           100.00000000000000 },
 472 };
 473 const double toler014 = 2.5000000000000020e-13;
 474
 475 // Test data for n=1, m=50.
 476 // max(|f - f_GSL|): 0.0000000000000000
 477 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
 478 const testcase_assoc_laguerre<double>
 479 data015[11] =
 480 {
 481   { 51.000000000000000, 1, 50,
 482           0.0000000000000000 },
 483   { 41.000000000000000, 1, 50,
 484           10.000000000000000 },
 485   { 31.000000000000000, 1, 50,
 486           20.000000000000000 },
 487   { 21.000000000000000, 1, 50,
 488           30.000000000000000 },
 489   { 11.000000000000000, 1, 50,
 490           40.000000000000000 },
 491   { 1.0000000000000000, 1, 50,
 492           50.000000000000000 },
 493   { -9.0000000000000000, 1, 50,
 494           60.000000000000000 },
 495   { -19.000000000000000, 1, 50,
 496           70.000000000000000 },
 497   { -29.000000000000000, 1, 50,
 498           80.000000000000000 },
 499   { -39.000000000000000, 1, 50,
 500           90.000000000000000 },
 501   { -49.000000000000000, 1, 50,
 502           100.00000000000000 },
 503 };
 504 const double toler015 = 2.5000000000000020e-13;
 505
 506 // Test data for n=1, m=100.
 507 // max(|f - f_GSL|): 0.0000000000000000
 508 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
 509 const testcase_assoc_laguerre<double>
 510 data016[11] =
 511 {
 512   { 101.00000000000000, 1, 100,
 513           0.0000000000000000 },
 514   { 91.000000000000000, 1, 100,
 515           10.000000000000000 },
 516   { 81.000000000000000, 1, 100,
 517           20.000000000000000 },
 518   { 71.000000000000000, 1, 100,
 519           30.000000000000000 },
 520   { 61.000000000000000, 1, 100,
 521           40.000000000000000 },
 522   { 51.000000000000000, 1, 100,
 523           50.000000000000000 },
 524   { 41.000000000000000, 1, 100,
 525           60.000000000000000 },
 526   { 31.000000000000000, 1, 100,
 527           70.000000000000000 },
 528   { 21.000000000000000, 1, 100,
 529           80.000000000000000 },
 530   { 11.000000000000000, 1, 100,
 531           90.000000000000000 },
 532   { 1.0000000000000000, 1, 100,
 533           100.00000000000000 },
 534 };
 535 const double toler016 = 2.5000000000000020e-13;
 536
 537 // Test data for n=2, m=0.
 538 // max(|f - f_GSL|): 0.0000000000000000
 539 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
 540 const testcase_assoc_laguerre<double>
 541 data017[11] =
 542 {
 543   { 1.0000000000000000, 2, 0,
 544           0.0000000000000000 },
 545   { 31.000000000000000, 2, 0,
 546           10.000000000000000 },
 547   { 161.00000000000000, 2, 0,
 548           20.000000000000000 },
 549   { 391.00000000000000, 2, 0,
 550           30.000000000000000 },
 551   { 721.00000000000000, 2, 0,
 552           40.000000000000000 },
 553   { 1151.0000000000000, 2, 0,
 554           50.000000000000000 },
 555   { 1681.0000000000000, 2, 0,
 556           60.000000000000000 },
 557   { 2311.0000000000000, 2, 0,
 558           70.000000000000000 },
 559   { 3041.0000000000000, 2, 0,
 560           80.000000000000000 },
 561   { 3871.0000000000000, 2, 0,
 562           90.000000000000000 },
 563   { 4801.0000000000000, 2, 0,
 564           100.00000000000000 },
 565 };
 566 const double toler017 = 2.5000000000000020e-13;
 567
 568 // Test data for n=2, m=1.
 569 // max(|f - f_GSL|): 0.0000000000000000
 570 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
 571 const testcase_assoc_laguerre<double>
 572 data018[11] =
 573 {
 574   { 3.0000000000000000, 2, 1,
 575           0.0000000000000000 },
 576   { 23.000000000000000, 2, 1,
 577           10.000000000000000 },
 578   { 143.00000000000000, 2, 1,
 579           20.000000000000000 },
 580   { 363.00000000000000, 2, 1,
 581           30.000000000000000 },
 582   { 683.00000000000000, 2, 1,
 583           40.000000000000000 },
 584   { 1103.0000000000000, 2, 1,
 585           50.000000000000000 },
 586   { 1623.0000000000000, 2, 1,
 587           60.000000000000000 },
 588   { 2243.0000000000000, 2, 1,
 589           70.000000000000000 },
 590   { 2963.0000000000000, 2, 1,
 591           80.000000000000000 },
 592   { 3783.0000000000000, 2, 1,
 593           90.000000000000000 },
 594   { 4703.0000000000000, 2, 1,
 595           100.00000000000000 },
 596 };
 597 const double toler018 = 2.5000000000000020e-13;
 598
 599 // Test data for n=2, m=2.
 600 // max(|f - f_GSL|): 0.0000000000000000
 601 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
 602 const testcase_assoc_laguerre<double>
 603 data019[11] =
 604 {
 605   { 6.0000000000000000, 2, 2,
 606           0.0000000000000000 },
 607   { 16.000000000000000, 2, 2,
 608           10.000000000000000 },
 609   { 126.00000000000000, 2, 2,
 610           20.000000000000000 },
 611   { 336.00000000000000, 2, 2,
 612           30.000000000000000 },
 613   { 646.00000000000000, 2, 2,
 614           40.000000000000000 },
 615   { 1056.0000000000000, 2, 2,
 616           50.000000000000000 },
 617   { 1566.0000000000000, 2, 2,
 618           60.000000000000000 },
 619   { 2176.0000000000000, 2, 2,
 620           70.000000000000000 },
 621   { 2886.0000000000000, 2, 2,
 622           80.000000000000000 },
 623   { 3696.0000000000000, 2, 2,
 624           90.000000000000000 },
 625   { 4606.0000000000000, 2, 2,
 626           100.00000000000000 },
 627 };
 628 const double toler019 = 2.5000000000000020e-13;
 629
 630 // Test data for n=2, m=5.
 631 // max(|f - f_GSL|): 4.5519144009631418e-15
 632 // max(|f - f_GSL| / |f_GSL|): 4.5519144009631623e-15
 633 const testcase_assoc_laguerre<double>
 634 data020[11] =
 635 {
 636   { 21.000000000000000, 2, 5,
 637           0.0000000000000000 },
 638   { 0.99999999999999545, 2, 5,
 639           10.000000000000000 },
 640   { 81.000000000000000, 2, 5,
 641           20.000000000000000 },
 642   { 261.00000000000000, 2, 5,
 643           30.000000000000000 },
 644   { 541.00000000000000, 2, 5,
 645           40.000000000000000 },
 646   { 921.00000000000000, 2, 5,
 647           50.000000000000000 },
 648   { 1401.0000000000000, 2, 5,
 649           60.000000000000000 },
 650   { 1981.0000000000000, 2, 5,
 651           70.000000000000000 },
 652   { 2661.0000000000000, 2, 5,
 653           80.000000000000000 },
 654   { 3441.0000000000000, 2, 5,
 655           90.000000000000000 },
 656   { 4321.0000000000000, 2, 5,
 657           100.00000000000000 },
 658 };
 659 const double toler020 = 2.5000000000000020e-13;
 660
 661 // Test data for n=2, m=10.
 662 // max(|f - f_GSL|): 3.5527136788005009e-14
 663 // max(|f - f_GSL| / |f_GSL|): 2.4424906541753385e-15
 664 const testcase_assoc_laguerre<double>
 665 data021[11] =
 666 {
 667   { 66.000000000000000, 2, 10,
 668           0.0000000000000000 },
 669   { -4.0000000000000098, 2, 10,
 670           10.000000000000000 },
 671   { 25.999999999999964, 2, 10,
 672           20.000000000000000 },
 673   { 156.00000000000000, 2, 10,
 674           30.000000000000000 },
 675   { 386.00000000000000, 2, 10,
 676           40.000000000000000 },
 677   { 716.00000000000000, 2, 10,
 678           50.000000000000000 },
 679   { 1146.0000000000000, 2, 10,
 680           60.000000000000000 },
 681   { 1676.0000000000000, 2, 10,
 682           70.000000000000000 },
 683   { 2306.0000000000000, 2, 10,
 684           80.000000000000000 },
 685   { 3036.0000000000000, 2, 10,
 686           90.000000000000000 },
 687   { 3866.0000000000000, 2, 10,
 688           100.00000000000000 },
 689 };
 690 const double toler021 = 2.5000000000000020e-13;
 691
 692 // Test data for n=2, m=20.
 693 // max(|f - f_GSL|): 5.6843418860808015e-13
 694 // max(|f - f_GSL| / |f_GSL|): 5.9211894646674663e-15
 695 const testcase_assoc_laguerre<double>
 696 data022[11] =
 697 {
 698   { 231.00000000000000, 2, 20,
 699           0.0000000000000000 },
 700   { 61.000000000000206, 2, 20,
 701           10.000000000000000 },
 702   { -9.0000000000000053, 2, 20,
 703           20.000000000000000 },
 704   { 21.000000000000124, 2, 20,
 705           30.000000000000000 },
 706   { 151.00000000000057, 2, 20,
 707           40.000000000000000 },
 708   { 381.00000000000000, 2, 20,
 709           50.000000000000000 },
 710   { 711.00000000000000, 2, 20,
 711           60.000000000000000 },
 712   { 1141.0000000000000, 2, 20,
 713           70.000000000000000 },
 714   { 1670.9999999999998, 2, 20,
 715           80.000000000000000 },
 716   { 2301.0000000000000, 2, 20,
 717           90.000000000000000 },
 718   { 3031.0000000000000, 2, 20,
 719           100.00000000000000 },
 720 };
 721 const double toler022 = 5.0000000000000039e-13;
 722
 723 // Test data for n=2, m=50.
 724 // max(|f - f_GSL|): 3.6379788070917130e-12
 725 // max(|f - f_GSL| / |f_GSL|): 1.9243865760169750e-14
 726 const testcase_assoc_laguerre<double>
 727 data023[11] =
 728 {
 729   { 1326.0000000000000, 2, 50,
 730           0.0000000000000000 },
 731   { 855.99999999999693, 2, 50,
 732           10.000000000000000 },
 733   { 485.99999999999835, 2, 50,
 734           20.000000000000000 },
 735   { 215.99999999999937, 2, 50,
 736           30.000000000000000 },
 737   { 45.999999999999829, 2, 50,
 738           40.000000000000000 },
 739   { -23.999999999999538, 2, 50,
 740           50.000000000000000 },
 741   { 6.0000000000001057, 2, 50,
 742           60.000000000000000 },
 743   { 135.99999999999963, 2, 50,
 744           70.000000000000000 },
 745   { 365.99999999999892, 2, 50,
 746           80.000000000000000 },
 747   { 695.99999999999784, 2, 50,
 748           90.000000000000000 },
 749   { 1125.9999999999964, 2, 50,
 750           100.00000000000000 },
 751 };
 752 const double toler023 = 1.0000000000000008e-12;
 753
 754 // Test data for n=2, m=100.
 755 // max(|f - f_GSL|): 6.5483618527650833e-11
 756 // max(|f - f_GSL| / |f_GSL|): 1.6416871873157281e-14
 757 const testcase_assoc_laguerre<double>
 758 data024[11] =
 759 {
 760   { 5151.0000000000000, 2, 100,
 761           0.0000000000000000 },
 762   { 4181.0000000000655, 2, 100,
 763           10.000000000000000 },
 764   { 3311.0000000000518, 2, 100,
 765           20.000000000000000 },
 766   { 2541.0000000000400, 2, 100,
 767           30.000000000000000 },
 768   { 1871.0000000000291, 2, 100,
 769           40.000000000000000 },
 770   { 1301.0000000000207, 2, 100,
 771           50.000000000000000 },
 772   { 831.00000000001364, 2, 100,
 773           60.000000000000000 },
 774   { 461.00000000000682, 2, 100,
 775           70.000000000000000 },
 776   { 191.00000000000250, 2, 100,
 777           80.000000000000000 },
 778   { 21.000000000000046, 2, 100,
 779           90.000000000000000 },
 780   { -48.999999999999915, 2, 100,
 781           100.00000000000000 },
 782 };
 783 const double toler024 = 1.0000000000000008e-12;
 784
 785 // Test data for n=5, m=0.
 786 // max(|f - f_GSL|): 7.4505805969238281e-09
 787 // max(|f - f_GSL| / |f_GSL|): 1.9501553136894460e-16
 788 const testcase_assoc_laguerre<double>
 789 data025[11] =
 790 {
 791   { 1.0000000000000000, 5, 0,
 792           0.0000000000000000 },
 793   { 34.333333333333329, 5, 0,
 794           10.000000000000000 },
 795   { -4765.6666666666670, 5, 0,
 796           20.000000000000000 },
 797   { -74399.000000000000, 5, 0,
 798           30.000000000000000 },
 799   { -418865.66666666663, 5, 0,
 800           40.000000000000000 },
 801   { -1498165.6666666665, 5, 0,
 802           50.000000000000000 },
 803   { -4122299.0000000000, 5, 0,
 804           60.000000000000000 },
 805   { -9551265.6666666679, 5, 0,
 806           70.000000000000000 },
 807   { -19595065.666666664, 5, 0,
 808           80.000000000000000 },
 809   { -36713699.000000000, 5, 0,
 810           90.000000000000000 },
 811   { -64117165.666666664, 5, 0,
 812           100.00000000000000 },
 813 };
 814 const double toler025 = 2.5000000000000020e-13;
 815
 816 // Test data for n=5, m=1.
 817 // max(|f - f_GSL|): 3.7252902984619141e-09
 818 // max(|f - f_GSL| / |f_GSL|): 3.1347473636475015e-16
 819 const testcase_assoc_laguerre<double>
 820 data026[11] =
 821 {
 822   { 6.0000000000000000, 5, 1,
 823           0.0000000000000000 },
 824   { 22.666666666666661, 5, 1,
 825           10.000000000000000 },
 826   { -2960.6666666666661, 5, 1,
 827           20.000000000000000 },
 828   { -58944.000000000000, 5, 1,
 829           30.000000000000000 },
 830   { -357927.33333333326, 5, 1,
 831           40.000000000000000 },
 832   { -1329910.6666666665, 5, 1,
 833           50.000000000000000 },
 834   { -3744894.0000000000, 5, 1,
 835           60.000000000000000 },
 836   { -8812877.3333333321, 5, 1,
 837           70.000000000000000 },
 838   { -18283860.666666664, 5, 1,
 839           80.000000000000000 },
 840   { -34547844.000000000, 5, 1,
 841           90.000000000000000 },
 842   { -60734827.333333336, 5, 1,
 843           100.00000000000000 },
 844 };
 845 const double toler026 = 2.5000000000000020e-13;
 846
 847 // Test data for n=5, m=2.
 848 // max(|f - f_GSL|): 0.0000000000000000
 849 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
 850 const testcase_assoc_laguerre<double>
 851 data027[11] =
 852 {
 853   { 21.000000000000000, 5, 2,
 854           0.0000000000000000 },
 855   { 4.3333333333333339, 5, 2,
 856           10.000000000000000 },
 857   { -1679.0000000000000, 5, 2,
 858           20.000000000000000 },
 859   { -46029.000000000000, 5, 2,
 860           30.000000000000000 },
 861   { -304045.66666666669, 5, 2,
 862           40.000000000000000 },
 863   { -1176729.0000000002, 5, 2,
 864           50.000000000000000 },
 865   { -3395079.0000000000, 5, 2,
 866           60.000000000000000 },
 867   { -8120095.6666666660, 5, 2,
 868           70.000000000000000 },
 869   { -17042778.999999996, 5, 2,
 870           80.000000000000000 },
 871   { -32484129.000000000, 5, 2,
 872           90.000000000000000 },
 873   { -57495145.666666664, 5, 2,
 874           100.00000000000000 },
 875 };
 876 const double toler027 = 2.5000000000000020e-13;
 877
 878 // Test data for n=5, m=5.
 879 // max(|f - f_GSL|): 7.4505805969238281e-09
 880 // max(|f - f_GSL| / |f_GSL|): 1.7763568394002536e-15
 881 const testcase_assoc_laguerre<double>
 882 data028[11] =
 883 {
 884   { 252.00000000000000, 5, 5,
 885           0.0000000000000000 },
 886   { -14.666666666666654, 5, 5,
 887           10.000000000000000 },
 888   { 51.999999999999908, 5, 5,
 889           20.000000000000000 },
 890   { -19548.000000000000, 5, 5,
 891           30.000000000000000 },
 892   { -178814.66666666660, 5, 5,
 893           40.000000000000000 },
 894   { -797747.99999999977, 5, 5,
 895           50.000000000000000 },
 896   { -2496348.0000000000, 5, 5,
 897           60.000000000000000 },
 898   { -6294614.6666666660, 5, 5,
 899           70.000000000000000 },
 900   { -13712547.999999996, 5, 5,
 901           80.000000000000000 },
 902   { -26870147.999999993, 5, 5,
 903           90.000000000000000 },
 904   { -48587414.666666672, 5, 5,
 905           100.00000000000000 },
 906 };
 907 const double toler028 = 2.5000000000000020e-13;
 908
 909 // Test data for n=5, m=10.
 910 // max(|f - f_GSL|): 7.4505805969238281e-09
 911 // max(|f - f_GSL| / |f_GSL|): 1.9556222085140405e-15
 912 const testcase_assoc_laguerre<double>
 913 data029[11] =
 914 {
 915   { 3003.0000000000000, 5, 10,
 916           0.0000000000000000 },
 917   { 19.666666666666668, 5, 10,
 918           10.000000000000000 },
 919   { 36.333333333333272, 5, 10,
 920           20.000000000000000 },
 921   { -1947.0000000000000, 5, 10,
 922           30.000000000000000 },
 923   { -60930.333333333314, 5, 10,
 924           40.000000000000000 },
 925   { -381913.66666666651, 5, 10,
 926           50.000000000000000 },
 927   { -1419897.0000000000, 5, 10,
 928           60.000000000000000 },
 929   { -3979880.3333333330, 5, 10,
 930           70.000000000000000 },
 931   { -9316863.6666666642, 5, 10,
 932           80.000000000000000 },
 933   { -19235847.000000000, 5, 10,
 934           90.000000000000000 },
 935   { -36191830.333333328, 5, 10,
 936           100.00000000000000 },
 937 };
 938 const double toler029 = 2.5000000000000020e-13;
 939
 940 // Test data for n=5, m=20.
 941 // max(|f - f_GSL|): 1.8626451492309570e-09
 942 // max(|f - f_GSL| / |f_GSL|): 2.8421709430404088e-15
 943 const testcase_assoc_laguerre<double>
 944 data030[11] =
 945 {
 946   { 53130.000000000000, 5, 20,
 947           0.0000000000000000 },
 948   { 1213.3333333333335, 5, 20,
 949           10.000000000000000 },
 950   { 129.99999999999963, 5, 20,
 951           20.000000000000000 },
 952   { -119.99999999999974, 5, 20,
 953           30.000000000000000 },
 954   { 463.33333333333320, 5, 20,
 955           40.000000000000000 },
 956   { -48120.000000000015, 5, 20,
 957           50.000000000000000 },
 958   { -345870.00000000017, 5, 20,
 959           60.000000000000000 },
 960   { -1342786.6666666667, 5, 20,
 961           70.000000000000000 },
 962   { -3838870.0000000009, 5, 20,
 963           80.000000000000000 },
 964   { -9084120.0000000000, 5, 20,
 965           90.000000000000000 },
 966   { -18878536.666666668, 5, 20,
 967           100.00000000000000 },
 968 };
 969 const double toler030 = 2.5000000000000020e-13;
 970
 971 // Test data for n=5, m=50.
 972 // max(|f - f_GSL|): 5.8207660913467407e-11
 973 // max(|f - f_GSL| / |f_GSL|): 8.3212917817998576e-15
 974 const testcase_assoc_laguerre<double>
 975 data031[11] =
 976 {
 977   { 3478761.0000000000, 5, 50,
 978           0.0000000000000000 },
 979   { 1154544.3333333335, 5, 50,
 980           10.000000000000000 },
 981   { 264661.00000000006, 5, 50,
 982           20.000000000000000 },
 983   { 24111.000000000033, 5, 50,
 984           30.000000000000000 },
 985   { -2105.6666666666665, 5, 50,
 986           40.000000000000000 },
 987   { 1010.9999999999916, 5, 50,
 988           50.000000000000000 },
 989   { -1538.9999999999955, 5, 50,
 990           60.000000000000000 },
 991   { 5244.3333333333449, 5, 50,
 992           70.000000000000000 },
 993   { -13639.000000000011, 5, 50,
 994           80.000000000000000 },
 995   { -243189.00000000006, 5, 50,
 996           90.000000000000000 },
 997   { -1118405.6666666667, 5, 50,
 998           100.00000000000000 },
 999 };
1000 const double toler031 = 5.0000000000000039e-13;
1001
1002 // Test data for n=5, m=100.
1003 // max(|f - f_GSL|): 1.4901161193847656e-08
1004 // max(|f - f_GSL| / |f_GSL|): 4.3934583843896481e-16
1005 const testcase_assoc_laguerre<double>
1006 data032[11] =
1007 {
1008   { 96560646.000000000, 5, 100,
1009           0.0000000000000000 },
1010   { 57264262.666666649, 5, 100,
1011           10.000000000000000 },
1012   { 31841379.333333332, 5, 100,
1013           20.000000000000000 },
1014   { 16281996.000000000, 5, 100,
1015           30.000000000000000 },
1016   { 7426112.6666666670, 5, 100,
1017           40.000000000000000 },
1018   { 2863729.3333333330, 5, 100,
1019           50.000000000000000 },
1020   { 834846.00000000000, 5, 100,
1021           60.000000000000000 },
1022   { 129462.66666666663, 5, 100,
1023           70.000000000000000 },
1024   { -12420.666666666668, 5, 100,
1025           80.000000000000000 },
1026   { -804.00000000000000, 5, 100,
1027           90.000000000000000 },
1028   { 4312.6666666666670, 5, 100,
1029           100.00000000000000 },
1030 };
1031 const double toler032 = 2.5000000000000020e-13;
1032
1033 // Test data for n=10, m=0.
1034 // max(|f - f_GSL|): 6.1035156250000000e-05
1035 // max(|f - f_GSL| / |f_GSL|): 6.1315986390500118e-15
1036 const testcase_assoc_laguerre<double>
1037 data033[11] =
1038 {
1039   { 1.0000000000000000, 10, 0,
1040           0.0000000000000000 },
1041   { 27.984126984126977, 10, 0,
1042           10.000000000000000 },
1043   { 3227.8077601410932, 10, 0,
1044           20.000000000000000 },
1045   { 15129.571428571455, 10, 0,
1046           30.000000000000000 },
1047   { 79724066.608465582, 10, 0,
1048           40.000000000000000 },
1049   { 2037190065.3738980, 10, 0,
1050           50.000000000000000 },
1051   { 21804200401.000000, 10, 0,
1052           60.000000000000000 },
1053   { 144688291819.51855, 10, 0,
1054           70.000000000000000 },
1055   { 703324772760.08276, 10, 0,
1056           80.000000000000000 },
1057   { 2741055412243.8569, 10, 0,
1058           90.000000000000000 },
1059   { 9051283795429.5723, 10, 0,
1060           100.00000000000000 },
1061 };
1062 const double toler033 = 5.0000000000000039e-13;
1063
1064 // Test data for n=10, m=1.
1065 // max(|f - f_GSL|): 0.0019531250000000000
1066 // max(|f - f_GSL| / |f_GSL|): 3.2082933888884751e-16
1067 const testcase_assoc_laguerre<double>
1068 data034[11] =
1069 {
1070   { 11.000000000000000, 10, 1,
1071           0.0000000000000000 },
1072   { 14.791887125220455, 10, 1,
1073           10.000000000000000 },
1074   { 2704.6507936507933, 10, 1,
1075           20.000000000000000 },
1076   { -182924.71428571423, 10, 1,
1077           30.000000000000000 },
1078   { 48066036.749559075, 10, 1,
1079           40.000000000000000 },
1080   { 1486264192.2169311, 10, 1,
1081           50.000000000000000 },
1082   { 17239562282.428574, 10, 1,
1083           60.000000000000000 },
1084   { 119837491630.13579, 10, 1,
1085           70.000000000000000 },
1086   { 600681375251.21167, 10, 1,
1087           80.000000000000000 },
1088   { 2392908405632.4287, 10, 1,
1089           90.000000000000000 },
1090   { 8033035722509.2373, 10, 1,
1091           100.00000000000000 },
1092 };
1093 const double toler034 = 2.5000000000000020e-13;
1094
1095 // Test data for n=10, m=2.
1096 // max(|f - f_GSL|): 0.00012207031250000000
1097 // max(|f - f_GSL| / |f_GSL|): 3.0884259455918855e-16
1098 const testcase_assoc_laguerre<double>
1099 data035[11] =
1100 {
1101   { 66.000000000000000, 10, 2,
1102           0.0000000000000000 },
1103   { -14.511463844797181, 10, 2,
1104           10.000000000000000 },
1105   { 1064.5890652557316, 10, 2,
1106           20.000000000000000 },
1107   { -194569.71428571429, 10, 2,
1108           30.000000000000000 },
1109   { 27343569.350970022, 10, 2,
1110           40.000000000000000 },
1111   { 1067807661.6790125, 10, 2,
1112           50.000000000000000 },
1113   { 13529451580.285711, 10, 2,
1114           60.000000000000000 },
1115   { 98812724224.641937, 10, 2,
1116           70.000000000000000 },
1117   { 511482736187.34021, 10, 2,
1118           80.000000000000000 },
1119   { 2084478393087.4285, 10, 2,
1120           90.000000000000000 },
1121   { 7117724862237.0752, 10, 2,
1122           100.00000000000000 },
1123 };
1124 const double toler035 = 2.5000000000000020e-13;
1125
1126 // Test data for n=10, m=5.
1127 // max(|f - f_GSL|): 0.0019531250000000000
1128 // max(|f - f_GSL| / |f_GSL|): 5.4929549774030811e-15
1129 const testcase_assoc_laguerre<double>
1130 data036[11] =
1131 {
1132   { 3003.0000000000000, 10, 5,
1133           0.0000000000000000 },
1134   { 11.641975308642031, 10, 5,
1135           10.000000000000000 },
1136   { -1137.5643738977069, 10, 5,
1137           20.000000000000000 },
1138   { -9254.1428571428605, 10, 5,
1139           30.000000000000000 },
1140   { 2121878.8377425023, 10, 5,
1141           40.000000000000000 },
1142   { 352060171.43033499, 10, 5,
1143           50.000000000000000 },
1144   { 6212028560.1428576, 10, 5,
1145           60.000000000000000 },
1146   { 53782171674.604919, 10, 5,
1147           70.000000000000000 },
1148   { 309720255837.56775, 10, 5,
1149           80.000000000000000 },
1150   { 1359043035731.5713, 10, 5,
1151           90.000000000000000 },
1152   { 4900625954398.9434, 10, 5,
1153           100.00000000000000 },
1154 };
1155 const double toler036 = 5.0000000000000039e-13;
1156
1157 // Test data for n=10, m=10.
1158 // max(|f - f_GSL|): 0.00048828125000000000
1159 // max(|f - f_GSL| / |f_GSL|): 1.2999856205575476e-15
1160 const testcase_assoc_laguerre<double>
1161 data037[11] =
1162 {
1163   { 184756.00000000000, 10, 10,
1164           0.0000000000000000 },
1165   { -210.84303350970018, 10, 10,
1166           10.000000000000000 },
1167   { 508.38095238095184, 10, 10,
1168           20.000000000000000 },
1169   { 2098.8571428571431, 10, 10,
1170           30.000000000000000 },
1171   { -536338.88536155177, 10, 10,
1172           40.000000000000000 },
1173   { 24865988.804232784, 10, 10,
1174           50.000000000000000 },
1175   { 1343756013.1428571, 10, 10,
1176           60.000000000000000 },
1177   { 17298791247.358025, 10, 10,
1178           70.000000000000000 },
1179   { 124528450897.79892, 10, 10,
1180           80.000000000000000 },
1181   { 632674413641.71423, 10, 10,
1182           90.000000000000000 },
1183   { 2533008935405.0298, 10, 10,
1184           100.00000000000000 },
1185 };
1186 const double toler037 = 2.5000000000000020e-13;
1187
1188 // Test data for n=10, m=20.
1189 // max(|f - f_GSL|): 1.1444091796875000e-05
1190 // max(|f - f_GSL| / |f_GSL|): 1.3165826881543491e-14
1191 const testcase_assoc_laguerre<double>
1192 data038[11] =
1193 {
1194   { 30045014.999999993, 10, 20,
1195           0.0000000000000000 },
1196   { -23087.733686067022, 10, 20,
1197           10.000000000000000 },
1198   { 207.23985890652330, 10, 20,
1199           20.000000000000000 },
1200   { 1407.8571428571508, 10, 20,
1201           30.000000000000000 },
1202   { -44618.156966490322, 10, 20,
1203           40.000000000000000 },
1204   { 158690.04409171100, 10, 20,
1205           50.000000000000000 },
1206   { -6870413.5714285728, 10, 20,
1207           60.000000000000000 },
1208   { 793841351.41975331, 10, 20,
1209           70.000000000000000 },
1210   { 13358288958.562618, 10, 20,
1211           80.000000000000000 },
1212   { 106073722407.85715, 10, 20,
1213           90.000000000000000 },
1214   { 566337213392.42493, 10, 20,
1215           100.00000000000000 },
1216 };
1217 const double toler038 = 1.0000000000000008e-12;
1218
1219 // Test data for n=10, m=50.
1220 // max(|f - f_GSL|): 1.7881393432617188e-07
1221 // max(|f - f_GSL| / |f_GSL|): 1.9220038158581863e-14
1222 const testcase_assoc_laguerre<double>
1223 data039[11] =
1224 {
1225   { 75394027566.000000, 10, 50,
1226           0.0000000000000000 },
1227   { 8048106183.3721361, 10, 50,
1228           10.000000000000000 },
1229   { 328045023.84832460, 10, 50,
1230           20.000000000000000 },
1231   { -2568769.7142857178, 10, 50,
1232           30.000000000000000 },
1233   { 6971.9964726631533, 10, 50,
1234           40.000000000000000 },
1235   { 136111.41446207993, 10, 50,
1236           50.000000000000000 },
1237   { -62462.571428570242, 10, 50,
1238           60.000000000000000 },
1239   { -248167.95061728527, 10, 50,
1240           70.000000000000000 },
1241   { 1941270.4091710770, 10, 50,
1242           80.000000000000000 },
1243   { -8643512.5714285765, 10, 50,
1244           90.000000000000000 },
1245   { -140863522.18342152, 10, 50,
1246           100.00000000000000 },
1247 };
1248 const double toler039 = 1.0000000000000008e-12;
1249
1250 // Test data for n=10, m=100.
1251 // max(|f - f_GSL|): 0.0019531250000000000
1252 // max(|f - f_GSL| / |f_GSL|): 8.5796208358610616e-15
1253 const testcase_assoc_laguerre<double>
1254 data040[11] =
1255 {
1256   { 46897636623981.000, 10, 100,
1257           0.0000000000000000 },
1258   { 16444031323272.084, 10, 100,
1259           10.000000000000000 },
1260   { 5020343986463.5391, 10, 100,
1261           20.000000000000000 },
1262   { 1270977490645.2859, 10, 100,
1263           30.000000000000000 },
1264   { 244835756822.62262, 10, 100,
1265           40.000000000000000 },
1266   { 29786827693.962959, 10, 100,
1267           50.000000000000000 },
1268   { 1127612095.2857144, 10, 100,
1269           60.000000000000000 },
1270   { -66370555.419753075, 10, 100,
1271           70.000000000000000 },
1272   { 10420852.957671870, 10, 100,
1273           80.000000000000000 },
1274   { -3373097.5714285718, 10, 100,
1275           90.000000000000000 },
1276   { 2065423.6807760145, 10, 100,
1277           100.00000000000000 },
1278 };
1279 const double toler040 = 5.0000000000000039e-13;
1280
1281 // Test data for n=20, m=0.
1282 // max(|f - f_GSL|): 20.000000000000000
1283 // max(|f - f_GSL| / |f_GSL|): 4.7350442720305269e-15
1284 const testcase_assoc_laguerre<double>
1285 data041[11] =
1286 {
1287   { 1.0000000000000000, 20, 0,
1288           0.0000000000000000 },
1289   { -11.961333867812119, 20, 0,
1290           10.000000000000000 },
1291   { 2829.4728613531743, 20, 0,
1292           20.000000000000000 },
1293   { -18439.424502520938, 20, 0,
1294           30.000000000000000 },
1295   { 24799805.877530713, 20, 0,
1296           40.000000000000000 },
1297   { 7551960453.7672548, 20, 0,
1298           50.000000000000000 },
1299   { -1379223608444.9155, 20, 0,
1300           60.000000000000000 },
1301   { 165423821874449.94, 20, 0,
1302           70.000000000000000 },
1303   { 29500368536981676., 20, 0,
1304           80.000000000000000 },
1305   { 1.1292309514432901e+18, 20, 0,
1306           90.000000000000000 },
1307   { 2.2061882785931735e+19, 20, 0,
1308           100.00000000000000 },
1309 };
1310 const double toler041 = 2.5000000000000020e-13;
1311
1312 // Test data for n=20, m=1.
1313 // max(|f - f_GSL|): 8192.0000000000000
1314 // max(|f - f_GSL| / |f_GSL|): 2.0583579235866667e-15
1315 const testcase_assoc_laguerre<double>
1316 data042[11] =
1317 {
1318   { 21.000000000000000, 20, 1,
1319           0.0000000000000000 },
1320   { 19.900488129734079, 20, 1,
1321           10.000000000000000 },
1322   { 2208.0318569557585, 20, 1,
1323           20.000000000000000 },
1324   { 263690.96303121914, 20, 1,
1325           30.000000000000000 },
1326   { 40667285.630564235, 20, 1,
1327           40.000000000000000 },
1328   { 1737442572.8115399, 20, 1,
1329           50.000000000000000 },
1330   { -588280953643.28125, 20, 1,
1331           60.000000000000000 },
1332   { 45617733778241.328, 20, 1,
1333           70.000000000000000 },
1334   { 17293487114876864., 20, 1,
1335           80.000000000000000 },
1336   { 7.6219135858585062e+17, 20, 1,
1337           90.000000000000000 },
1338   { 1.6037288204336759e+19, 20, 1,
1339           100.00000000000000 },
1340 };
1341 const double toler042 = 2.5000000000000020e-13;
1342
1343 // Test data for n=20, m=2.
1344 // max(|f - f_GSL|): 6144.0000000000000
1345 // max(|f - f_GSL| / |f_GSL|): 9.3068805041852228e-15
1346 const testcase_assoc_laguerre<double>
1347 data043[11] =
1348 {
1349   { 231.00000000000003, 20, 2,
1350           0.0000000000000000 },
1351   { 47.009338065112921, 20, 2,
1352           10.000000000000000 },
1353   { -652.51305461728589, 20, 2,
1354           20.000000000000000 },
1355   { 285388.25895069109, 20, 2,
1356           30.000000000000000 },
1357   { 28664069.685624730, 20, 2,
1358           40.000000000000000 },
1359   { -1399631966.3144732, 20, 2,
1360           50.000000000000000 },
1361   { -115357373248.28194, 20, 2,
1362           60.000000000000000 },
1363   { -3357730872975.8750, 20, 2,
1364           70.000000000000000 },
1365   { 9765808962855122.0, 20, 2,
1366           80.000000000000000 },
1367   { 5.0717292945559181e+17, 20, 2,
1368           90.000000000000000 },
1369   { 1.1564665701334456e+19, 20, 2,
1370           100.00000000000000 },
1371 };
1372 const double toler043 = 5.0000000000000039e-13;
1373
1374 // Test data for n=20, m=5.
1375 // max(|f - f_GSL|): 16.000000000000000
1376 // max(|f - f_GSL| / |f_GSL|): 3.5731302592472765e-15
1377 const testcase_assoc_laguerre<double>
1378 data044[11] =
1379 {
1380   { 53130.000000000000, 20, 5,
1381           0.0000000000000000 },
1382   { -158.69554500944142, 20, 5,
1383           10.000000000000000 },
1384   { 334.08012288038952, 20, 5,
1385           20.000000000000000 },
1386   { -198372.47662554163, 20, 5,
1387           30.000000000000000 },
1388   { -13627144.088579426, 20, 5,
1389           40.000000000000000 },
1390   { -780579985.44731510, 20, 5,
1391           50.000000000000000 },
1392   { 116648634237.73535, 20, 5,
1393           60.000000000000000 },
1394   { -12347348707739.742, 20, 5,
1395           70.000000000000000 },
1396   { 1199516248034090.8, 20, 5,
1397           80.000000000000000 },
1398   { 1.3451503195078531e+17, 20, 5,
1399           90.000000000000000 },
1400   { 4.1058904276111483e+18, 20, 5,
1401           100.00000000000000 },
1402 };
1403 const double toler044 = 2.5000000000000020e-13;
1404
1405 // Test data for n=20, m=10.
1406 // max(|f - f_GSL|): 64.000000000000000
1407 // max(|f - f_GSL| / |f_GSL|): 1.0709209504860220e-15
1408 const testcase_assoc_laguerre<double>
1409 data045[11] =
1410 {
1411   { 30045015.000000000, 20, 10,
1412           0.0000000000000000 },
1413   { -1755.6226861258601, 20, 10,
1414           10.000000000000000 },
1415   { -9081.6726644737901, 20, 10,
1416           20.000000000000000 },
1417   { 95771.650912113109, 20, 10,
1418           30.000000000000000 },
1419   { 5089151.9272779236, 20, 10,
1420           40.000000000000000 },
1421   { 97400399.450206712, 20, 10,
1422           50.000000000000000 },
1423   { -16009352450.477026, 20, 10,
1424           60.000000000000000 },
1425   { 842271286905.01050, 20, 10,
1426           70.000000000000000 },
1427   { -79901725466796.938, 20, 10,
1428           80.000000000000000 },
1429   { 7944103675858637.0, 20, 10,
1430           90.000000000000000 },
1431   { 5.7429821893388288e+17, 20, 10,
1432           100.00000000000000 },
1433 };
1434 const double toler045 = 2.5000000000000020e-13;
1435
1436 // Test data for n=20, m=20.
1437 // max(|f - f_GSL|): 2.1250000000000000
1438 // max(|f - f_GSL| / |f_GSL|): 1.1968937782285294e-14
1439 const testcase_assoc_laguerre<double>
1440 data046[11] =
1441 {
1442   { 137846528819.99994, 20, 20,
1443           0.0000000000000000 },
1444   { -136976.49571333229, 20, 20,
1445           10.000000000000000 },
1446   { 113878.49908041643, 20, 20,
1447           20.000000000000000 },
1448   { -342529.21778796182, 20, 20,
1449           30.000000000000000 },
1450   { -350112.66981443466, 20, 20,
1451           40.000000000000000 },
1452   { -10791735.172977809, 20, 20,
1453           50.000000000000000 },
1454   { -1038073940.0811402, 20, 20,
1455           60.000000000000000 },
1456   { 667312550.63616335, 20, 20,
1457           70.000000000000000 },
1458   { 741537869902.29028, 20, 20,
1459           80.000000000000000 },
1460   { -32378376755737.418, 20, 20,
1461           90.000000000000000 },
1462   { -601760332167937.62, 20, 20,
1463           100.00000000000000 },
1464 };
1465 const double toler046 = 1.0000000000000008e-12;
1466
1467 // Test data for n=20, m=50.
1468 // max(|f - f_GSL|): 0.25000000000000000
1469 // max(|f - f_GSL| / |f_GSL|): 1.2103144092558234e-14
1470 const testcase_assoc_laguerre<double>
1471 data047[11] =
1472 {
1473   { 1.6188460366265789e+17, 20, 50,
1474           0.0000000000000000 },
1475   { 1599011936804291.5, 20, 50,
1476           10.000000000000000 },
1477   { -131273880831.42432, 20, 50,
1478           20.000000000000000 },
1479   { -3133213093.6903548, 20, 50,
1480           30.000000000000000 },
1481   { -213935628.04985175, 20, 50,
1482           40.000000000000000 },
1483   { -47375578.495921060, 20, 50,
1484           50.000000000000000 },
1485   { -115731015.14034876, 20, 50,
1486           60.000000000000000 },
1487   { -737415147.29420292, 20, 50,
1488           70.000000000000000 },
1489   { -2123455626.8621769, 20, 50,
1490           80.000000000000000 },
1491   { 29801266858.608929, 20, 50,
1492           90.000000000000000 },
1493   { -132886631026.82553, 20, 50,
1494           100.00000000000000 },
1495 };
1496 const double toler047 = 1.0000000000000008e-12;
1497
1498 // Test data for n=20, m=100.
1499 // max(|f - f_GSL|): 1572864.0000000000
1500 // max(|f - f_GSL| / |f_GSL|): 3.6621229371267356e-14
1501 const testcase_assoc_laguerre<double>
1502 data048[11] =
1503 {
1504   { 2.9462227291176643e+22, 20, 100,
1505           0.0000000000000000 },
1506   { 3.5777890748701244e+21, 20, 100,
1507           10.000000000000000 },
1508   { 3.1584925521456759e+20, 20, 100,
1509           20.000000000000000 },
1510   { 1.7389599388424864e+19, 20, 100,
1511           30.000000000000000 },
1512   { 4.1401342745980634e+17, 20, 100,
1513           40.000000000000000 },
1514   { -79359706102062.594, 20, 100,
1515           50.000000000000000 },
1516   { 22736203650743.145, 20, 100,
1517           60.000000000000000 },
1518   { 65679006380.095703, 20, 100,
1519           70.000000000000000 },
1520   { -236263257610.77792, 20, 100,
1521           80.000000000000000 },
1522   { -38072644585.303101, 20, 100,
1523           90.000000000000000 },
1524   { 68236474365.173973, 20, 100,
1525           100.00000000000000 },
1526 };
1527 const double toler048 = 2.5000000000000015e-12;
1528
1529 // Test data for n=50, m=0.
1530 // max(|f - f_GSL|): 196608.00000000000
1531 // max(|f - f_GSL| / |f_GSL|): 4.2910775919271532e-15
1532 const testcase_assoc_laguerre<double>
1533 data049[11] =
1534 {
1535   { 1.0000000000000000, 50, 0,
1536           0.0000000000000000 },
1537   { 17.534183446338233, 50, 0,
1538           10.000000000000000 },
1539   { 980.26961889791028, 50, 0,
1540           20.000000000000000 },
1541   { 293000.50735962362, 50, 0,
1542           30.000000000000000 },
1543   { -14896937.968694873, 50, 0,
1544           40.000000000000000 },
1545   { 2513677852.6916871, 50, 0,
1546           50.000000000000000 },
1547   { -883876565337.99219, 50, 0,
1548           60.000000000000000 },
1549   { -80967880733583.234, 50, 0,
1550           70.000000000000000 },
1551   { -8217471769564841.0, 50, 0,
1552           80.000000000000000 },
1553   { -2.1140031308048891e+18, 50, 0,
1554           90.000000000000000 },
1555   { -3.9710103487094692e+20, 50, 0,
1556           100.00000000000000 },
1557 };
1558 const double toler049 = 2.5000000000000020e-13;
1559
1560 // Test data for n=50, m=1.
1561 // max(|f - f_GSL|): 311296.00000000000
1562 // max(|f - f_GSL| / |f_GSL|): 4.3113718426975911e-14
1563 const testcase_assoc_laguerre<double>
1564 data050[11] =
1565 {
1566   { 51.000000000000021, 50, 1,
1567           0.0000000000000000 },
1568   { 1.4214573271639575, 50, 1,
1569           10.000000000000000 },
1570   { -2574.8072295127827, 50, 1,
1571           20.000000000000000 },
1572   { 35846.479728359205, 50, 1,
1573           30.000000000000000 },
1574   { -48263698.768318526, 50, 1,
1575           40.000000000000000 },
1576   { 6161525870.2738533, 50, 1,
1577           50.000000000000000 },
1578   { -382655486658.47125, 50, 1,
1579           60.000000000000000 },
1580   { -109635579833241.72, 50, 1,
1581           70.000000000000000 },
1582   { -14623805817283490., 50, 1,
1583           80.000000000000000 },
1584   { -2.0666847190878152e+18, 50, 1,
1585           90.000000000000000 },
1586   { -1.4385187953997626e+20, 50, 1,
1587           100.00000000000000 },
1588 };
1589 const double toler050 = 2.5000000000000015e-12;
1590
1591 // Test data for n=50, m=2.
1592 // max(|f - f_GSL|): 139264.00000000000
1593 // max(|f - f_GSL| / |f_GSL|): 2.5437687254653283e-15
1594 const testcase_assoc_laguerre<double>
1595 data051[11] =
1596 {
1597   { 1326.0000000000000, 50, 2,
1598           0.0000000000000000 },
1599   { -87.860732516444529, 50, 2,
1600           10.000000000000000 },
1601   { -5203.2351191780917, 50, 2,
1602           20.000000000000000 },
1603   { -461059.50012538867, 50, 2,
1604           30.000000000000000 },
1605   { -30476695.327440590, 50, 2,
1606           40.000000000000000 },
1607   { 3720804977.9338136, 50, 2,
1608           50.000000000000000 },
1609   { 362262002434.51453, 50, 2,
1610           60.000000000000000 },
1611   { -52210917867820.227, 50, 2,
1612           70.000000000000000 },
1613   { -9567965136901914.0, 50, 2,
1614           80.000000000000000 },
1615   { -8.9171277517712883e+17, 50, 2,
1616           90.000000000000000 },
1617   { 5.7231129448806982e+19, 50, 2,
1618           100.00000000000000 },
1619 };
1620 const double toler051 = 2.5000000000000020e-13;
1621
1622 // Test data for n=50, m=5.
1623 // max(|f - f_GSL|): 81920.000000000000
1624 // max(|f - f_GSL| / |f_GSL|): 2.6215979818234617e-15
1625 const testcase_assoc_laguerre<double>
1626 data052[11] =
1627 {
1628   { 3478761.0000000000, 50, 5,
1629           0.0000000000000000 },
1630   { 1055.8381917651498, 50, 5,
1631           10.000000000000000 },
1632   { 15264.646660345055, 50, 5,
1633           20.000000000000000 },
1634   { 1229651.8966600848, 50, 5,
1635           30.000000000000000 },
1636   { 39270451.823656842, 50, 5,
1637           40.000000000000000 },
1638   { -4424062601.1152029, 50, 5,
1639           50.000000000000000 },
1640   { -186017434284.19223, 50, 5,
1641           60.000000000000000 },
1642   { 50972853949302.609, 50, 5,
1643           70.000000000000000 },
1644   { 6530702754012517.0, 50, 5,
1645           80.000000000000000 },
1646   { 6.8387592714678029e+17, 50, 5,
1647           90.000000000000000 },
1648   { 3.9198742504338391e+19, 50, 5,
1649           100.00000000000000 },
1650 };
1651 const double toler052 = 2.5000000000000020e-13;
1652
1653 // Test data for n=50, m=10.
1654 // max(|f - f_GSL|): 192.00000000000000
1655 // max(|f - f_GSL| / |f_GSL|): 3.6229303412867937e-15
1656 const testcase_assoc_laguerre<double>
1657 data053[11] =
1658 {
1659   { 75394027565.999985, 50, 10,
1660           0.0000000000000000 },
1661   { 91833.924098770178, 50, 10,
1662           10.000000000000000 },
1663   { 330501.87929778261, 50, 10,
1664           20.000000000000000 },
1665   { 3625088.1635972536, 50, 10,
1666           30.000000000000000 },
1667   { 213954727.28632012, 50, 10,
1668           40.000000000000000 },
1669   { -9381006937.7517681, 50, 10,
1670           50.000000000000000 },
1671   { 535333683777.48615, 50, 10,
1672           60.000000000000000 },
1673   { 18824406573722.172, 50, 10,
1674           70.000000000000000 },
1675   { -533858276780013.12, 50, 10,
1676           80.000000000000000 },
1677   { -52995774666704016., 50, 10,
1678           90.000000000000000 },
1679   { 6.0504182862448783e+18, 50, 10,
1680           100.00000000000000 },
1681 };
1682 const double toler053 = 2.5000000000000020e-13;
1683
1684 // Test data for n=50, m=20.
1685 // max(|f - f_GSL|): 512.00000000000000
1686 // max(|f - f_GSL| / |f_GSL|): 9.6616871455409171e-14
1687 const testcase_assoc_laguerre<double>
1688 data054[11] =
1689 {
1690   { 1.6188460366265779e+17, 50, 20,
1691           0.0000000000000000 },
1692   { -307637087.25169408, 50, 20,
1693           10.000000000000000 },
1694   { 12524651.102974586, 50, 20,
1695           20.000000000000000 },
1696   { -315460483.86210561, 50, 20,
1697           30.000000000000000 },
1698   { -1889683587.3459988, 50, 20,
1699           40.000000000000000 },
1700   { 37457044404.200348, 50, 20,
1701           50.000000000000000 },
1702   { -843831858224.71802, 50, 20,
1703           60.000000000000000 },
1704   { -92231643172.307495, 50, 20,
1705           70.000000000000000 },
1706   { 904211757769501.00, 50, 20,
1707           80.000000000000000 },
1708   { 46508193600283272., 50, 20,
1709           90.000000000000000 },
1710   { 2.3216887928162719e+18, 50, 20,
1711           100.00000000000000 },
1712 };
1713 const double toler054 = 5.0000000000000029e-12;
1714
1715 // Test data for n=50, m=50.
1716 // max(|f - f_GSL|): 989855744.00000000
1717 // max(|f - f_GSL| / |f_GSL|): 1.1139535389485780e-14
1718 const testcase_assoc_laguerre<double>
1719 data055[11] =
1720 {
1721   { 1.0089134454556417e+29, 50, 50,
1722           0.0000000000000000 },
1723   { 1.3822795753070493e+23, 50, 50,
1724           10.000000000000000 },
1725   { 95817260381628336., 50, 50,
1726           20.000000000000000 },
1727   { -910798580856015.38, 50, 50,
1728           30.000000000000000 },
1729   { 50513254049166.922, 50, 50,
1730           40.000000000000000 },
1731   { 84159703903348.938, 50, 50,
1732           50.000000000000000 },
1733   { -138805244691822.72, 50, 50,
1734           60.000000000000000 },
1735   { 181046391269246.25, 50, 50,
1736           70.000000000000000 },
1737   { 2086884905317107.5, 50, 50,
1738           80.000000000000000 },
1739   { -2765620139862428.0, 50, 50,
1740           90.000000000000000 },
1741   { -1.3706751678146290e+17, 50, 50,
1742           100.00000000000000 },
1743 };
1744 const double toler055 = 1.0000000000000008e-12;
1745
1746 // Test data for n=50, m=100.
1747 // max(|f - f_GSL|): 1.8889465931478581e+22
1748 // max(|f - f_GSL| / |f_GSL|): 2.2737143709403468e-14
1749 const testcase_assoc_laguerre<double>
1750 data056[11] =
1751 {
1752   { 2.0128660909731929e+40, 50, 100,
1753           0.0000000000000000 },
1754   { 9.3675094807695474e+37, 50, 100,
1755           10.000000000000000 },
1756   { 1.3009321481877196e+35, 50, 100,
1757           20.000000000000000 },
1758   { 7.3720026893233823e+30, 50, 100,
1759           30.000000000000000 },
1760   { -6.0824679079634667e+25, 50, 100,
1761           40.000000000000000 },
1762   { -6.0053188793543450e+23, 50, 100,
1763           50.000000000000000 },
1764   { 1.4178129287264692e+22, 50, 100,
1765           60.000000000000000 },
1766   { -5.4652099341566706e+20, 50, 100,
1767           70.000000000000000 },
1768   { -1.0817271759263274e+20, 50, 100,
1769           80.000000000000000 },
1770   { 3.8058734007924195e+19, 50, 100,
1771           90.000000000000000 },
1772   { 4.7439240848028344e+19, 50, 100,
1773           100.00000000000000 },
1774 };
1775 const double toler056 = 2.5000000000000015e-12;
1776
1777 // Test data for n=100, m=0.
1778 // max(|f - f_GSL|): 98304.000000000000
1779 // max(|f - f_GSL| / |f_GSL|): 3.8776197831393928e-15
1780 const testcase_assoc_laguerre<double>
1781 data057[11] =
1782 {
1783   { 1.0000000000000000, 100, 0,
1784           0.0000000000000000 },
1785   { 13.277662844303450, 100, 0,
1786           10.000000000000000 },
1787   { 1854.0367283243388, 100, 0,
1788           20.000000000000000 },
1789   { 170141.86987046551, 100, 0,
1790           30.000000000000000 },
1791   { -7272442.3156006960, 100, 0,
1792           40.000000000000000 },
1793   { 4847420871.2690506, 100, 0,
1794           50.000000000000000 },
1795   { 693492765740.29688, 100, 0,
1796           60.000000000000000 },
1797   { 17125518672239.770, 100, 0,
1798           70.000000000000000 },
1799   { -13763178176383768., 100, 0,
1800           80.000000000000000 },
1801   { 2.1307220490380173e+18, 100, 0,
1802           90.000000000000000 },
1803   { -2.6292260693068916e+20, 100, 0,
1804           100.00000000000000 },
1805 };
1806 const double toler057 = 2.5000000000000020e-13;
1807
1808 // Test data for n=100, m=1.
1809 // max(|f - f_GSL|): 245760.00000000000
1810 // max(|f - f_GSL| / |f_GSL|): 1.4500034612453474e-14
1811 const testcase_assoc_laguerre<double>
1812 data058[11] =
1813 {
1814   { 101.00000000000003, 100, 1,
1815           0.0000000000000000 },
1816   { -14.650661983680420, 100, 1,
1817           10.000000000000000 },
1818   { 1626.5010939361582, 100, 1,
1819           20.000000000000000 },
1820   { 417884.77658268728, 100, 1,
1821           30.000000000000000 },
1822   { -55617646.951649837, 100, 1,
1823           40.000000000000000 },
1824   { 884829874.26626217, 100, 1,
1825           50.000000000000000 },
1826   { 154466082750.32202, 100, 1,
1827           60.000000000000000 },
1828   { -101423973484646.00, 100, 1,
1829           70.000000000000000 },
1830   { -1388352348671756.8, 100, 1,
1831           80.000000000000000 },
1832   { 7.8048705513268582e+17, 100, 1,
1833           90.000000000000000 },
1834   { 1.6948925059042755e+19, 100, 1,
1835           100.00000000000000 },
1836 };
1837 const double toler058 = 1.0000000000000008e-12;
1838
1839 // Test data for n=100, m=2.
1840 // max(|f - f_GSL|): 557056.00000000000
1841 // max(|f - f_GSL| / |f_GSL|): 5.1603746667135714e-15
1842 const testcase_assoc_laguerre<double>
1843 data059[11] =
1844 {
1845   { 5151.0000000000055, 100, 2,
1846           0.0000000000000000 },
1847   { -150.22012290951324, 100, 2,
1848           10.000000000000000 },
1849   { -7655.0593294049449, 100, 2,
1850           20.000000000000000 },
1851   { -140996.69276179091, 100, 2,
1852           30.000000000000000 },
1853   { -38645171.278549351, 100, 2,
1854           40.000000000000000 },
1855   { -8889263688.2118931, 100, 2,
1856           50.000000000000000 },
1857   { -1010338971533.3400, 100, 2,
1858           60.000000000000000 },
1859   { -127582564332943.91, 100, 2,
1860           70.000000000000000 },
1861   { 15970305694654312., 100, 2,
1862           80.000000000000000 },
1863   { -1.6019844992862820e+18, 100, 2,
1864           90.000000000000000 },
1865   { 2.8267024730962955e+20, 100, 2,
1866           100.00000000000000 },
1867 };
1868 const double toler059 = 5.0000000000000039e-13;
1869
1870 // Test data for n=100, m=5.
1871 // max(|f - f_GSL|): 393216.00000000000
1872 // max(|f - f_GSL| / |f_GSL|): 8.0946565190235238e-15
1873 const testcase_assoc_laguerre<double>
1874 data060[11] =
1875 {
1876   { 96560646.000000030, 100, 5,
1877           0.0000000000000000 },
1878   { 2430.6732236677612, 100, 5,
1879           10.000000000000000 },
1880   { 111162.32026994647, 100, 5,
1881           20.000000000000000 },
1882   { 4036708.2599413628, 100, 5,
1883           30.000000000000000 },
1884   { -34055982.664405443, 100, 5,
1885           40.000000000000000 },
1886   { 30110688343.562328, 100, 5,
1887           50.000000000000000 },
1888   { 2651429940558.2974, 100, 5,
1889           60.000000000000000 },
1890   { 192108556058943.09, 100, 5,
1891           70.000000000000000 },
1892   { -25410533973455528., 100, 5,
1893           80.000000000000000 },
1894   { 2.1072955633564431e+18, 100, 5,
1895           90.000000000000000 },
1896   { -2.9434005355877289e+20, 100, 5,
1897           100.00000000000000 },
1898 };
1899 const double toler060 = 5.0000000000000039e-13;
1900
1901 // Test data for n=100, m=10.
1902 // max(|f - f_GSL|): 155648.00000000000
1903 // max(|f - f_GSL| / |f_GSL|): 5.1685581852917721e-15
1904 const testcase_assoc_laguerre<double>
1905 data061[11] =
1906 {
1907   { 46897636623981.039, 100, 10,
1908           0.0000000000000000 },
1909   { 529208.11550990329, 100, 10,
1910           10.000000000000000 },
1911   { 7402892.1748803817, 100, 10,
1912           20.000000000000000 },
1913   { 88369632.083243579, 100, 10,
1914           30.000000000000000 },
1915   { 822187797.59096563, 100, 10,
1916           40.000000000000000 },
1917   { 180231446033.06866, 100, 10,
1918           50.000000000000000 },
1919   { 7922942703798.1309, 100, 10,
1920           60.000000000000000 },
1921   { 784424250559042.12, 100, 10,
1922           70.000000000000000 },
1923   { -16325634720239370., 100, 10,
1924           80.000000000000000 },
1925   { -1.0879588307443162e+18, 100, 10,
1926           90.000000000000000 },
1927   { 3.0114394463610642e+19, 100, 10,
1928           100.00000000000000 },
1929 };
1930 const double toler061 = 5.0000000000000039e-13;
1931
1932 // Test data for n=100, m=20.
1933 // max(|f - f_GSL|): 524288.00000000000
1934 // max(|f - f_GSL| / |f_GSL|): 3.7005989410347388e-14
1935 const testcase_assoc_laguerre<double>
1936 data062[11] =
1937 {
1938   { 2.9462227291176614e+22, 100, 20,
1939           0.0000000000000000 },
1940   { 313694958939.90405, 100, 20,
1941           10.000000000000000 },
1942   { 45396489338.096191, 100, 20,
1943           20.000000000000000 },
1944   { -7215826758.0081253, 100, 20,
1945           30.000000000000000 },
1946   { 825949194005.88855, 100, 20,
1947           40.000000000000000 },
1948   { -2764742119971.0811, 100, 20,
1949           50.000000000000000 },
1950   { -219802198273516.03, 100, 20,
1951           60.000000000000000 },
1952   { -1699053306145262.0, 100, 20,
1953           70.000000000000000 },
1954   { 3.5495709345023846e+17, 100, 20,
1955           80.000000000000000 },
1956   { -9.6128675110292419e+18, 100, 20,
1957           90.000000000000000 },
1958   { 4.3619868422072212e+20, 100, 20,
1959           100.00000000000000 },
1960 };
1961 const double toler062 = 2.5000000000000015e-12;
1962
1963 // Test data for n=100, m=50.
1964 // max(|f - f_GSL|): 316659348799488.00
1965 // max(|f - f_GSL| / |f_GSL|): 1.1554040570270351e-14
1966 const testcase_assoc_laguerre<double>
1967 data063[11] =
1968 {
1969   { 2.0128660909731931e+40, 100, 50,
1970           0.0000000000000000 },
1971   { -4.0151443913473373e+28, 100, 50,
1972           10.000000000000000 },
1973   { 3.2199632594551924e+22, 100, 50,
1974           20.000000000000000 },
1975   { -2.7568702092659756e+20, 100, 50,
1976           30.000000000000000 },
1977   { 7.5553066015421563e+19, 100, 50,
1978           40.000000000000000 },
1979   { -2.7651625252387734e+19, 100, 50,
1980           50.000000000000000 },
1981   { -5.8963680147283804e+19, 100, 50,
1982           60.000000000000000 },
1983   { -1.8082798163033106e+20, 100, 50,
1984           70.000000000000000 },
1985   { -3.9044276986817249e+20, 100, 50,
1986           80.000000000000000 },
1987   { 6.9926310700401904e+21, 100, 50,
1988           90.000000000000000 },
1989   { -5.5727272809923646e+22, 100, 50,
1990           100.00000000000000 },
1991 };
1992 const double toler063 = 1.0000000000000008e-12;
1993
1994 // Test data for n=100, m=100.
1995 // max(|f - f_GSL|): 2.3819765684465692e+39
1996 // max(|f - f_GSL| / |f_GSL|): 1.9897039067343855e-14
1997 const testcase_assoc_laguerre<double>
1998 data064[11] =
1999 {
2000   { 9.0548514656103225e+58, 100, 100,
2001           0.0000000000000000 },
2002   { 1.3334078033060556e+54, 100, 100,
2003           10.000000000000000 },
2004   { 2.1002639254211340e+46, 100, 100,
2005           20.000000000000000 },
2006   { -1.1073158068796292e+39, 100, 100,
2007           30.000000000000000 },
2008   { -8.3640937363981346e+35, 100, 100,
2009           40.000000000000000 },
2010   { -6.5879339429312686e+32, 100, 100,
2011           50.000000000000000 },
2012   { -2.4190645077698771e+30, 100, 100,
2013           60.000000000000000 },
2014   { -7.9224960465662171e+29, 100, 100,
2015           70.000000000000000 },
2016   { -2.8605772478408694e+29, 100, 100,
2017           80.000000000000000 },
2018   { 2.4149589189609957e+28, 100, 100,
2019           90.000000000000000 },
2020   { 5.1146476014859021e+28, 100, 100,
2021           100.00000000000000 },
2022 };
2023 const double toler064 = 1.0000000000000008e-12;
2024
2025 template<typename Tp, unsigned int Num>
2026   void
2027   test(const testcase_assoc_laguerre<Tp> (&data)[Num], Tp toler)
2028   {
2029     const Tp eps = std::numeric_limits<Tp>::epsilon();
2030     Tp max_abs_diff = -Tp(1);
2031     Tp max_abs_frac = -Tp(1);
2032     unsigned int num_datum = Num;
2033     for (unsigned int i = 0; i < num_datum; ++i)
2034          {
2035         const Tp f = std::assoc_laguerre(data[i].n, data[i].m,
2036                      data[i].x);
2037         const Tp f0 = data[i].f0;
2038         const Tp diff = f - f0;
2039         if (std::abs(diff) > max_abs_diff)
2040           max_abs_diff = std::abs(diff);
2041         if (std::abs(f0) > Tp(10) * eps
2042          && std::abs(f) > Tp(10) * eps)
2043           {
2044             const Tp frac = diff / f0;
2045             if (std::abs(frac) > max_abs_frac)
2046               max_abs_frac = std::abs(frac);
2047           }
2048       }
2049     VERIFY(max_abs_frac < toler);
2050   }
2051
2052 int
2053 main()
2054 {
2055   test(data001, toler001);
2056   test(data002, toler002);
2057   test(data003, toler003);
2058   test(data004, toler004);
2059   test(data005, toler005);
2060   test(data006, toler006);
2061   test(data007, toler007);
2062   test(data008, toler008);
2063   test(data009, toler009);
2064   test(data010, toler010);
2065   test(data011, toler011);
2066   test(data012, toler012);
2067   test(data013, toler013);
2068   test(data014, toler014);
2069   test(data015, toler015);
2070   test(data016, toler016);
2071   test(data017, toler017);
2072   test(data018, toler018);
2073   test(data019, toler019);
2074   test(data020, toler020);
2075   test(data021, toler021);
2076   test(data022, toler022);
2077   test(data023, toler023);
2078   test(data024, toler024);
2079   test(data025, toler025);
2080   test(data026, toler026);
2081   test(data027, toler027);
2082   test(data028, toler028);
2083   test(data029, toler029);
2084   test(data030, toler030);
2085   test(data031, toler031);
2086   test(data032, toler032);
2087   test(data033, toler033);
2088   test(data034, toler034);
2089   test(data035, toler035);
2090   test(data036, toler036);
2091   test(data037, toler037);
2092   test(data038, toler038);
2093   test(data039, toler039);
2094   test(data040, toler040);
2095   test(data041, toler041);
2096   test(data042, toler042);
2097   test(data043, toler043);
2098   test(data044, toler044);
2099   test(data045, toler045);
2100   test(data046, toler046);
2101   test(data047, toler047);
2102   test(data048, toler048);
2103   test(data049, toler049);
2104   test(data050, toler050);
2105   test(data051, toler051);
2106   test(data052, toler052);
2107   test(data053, toler053);
2108   test(data054, toler054);
2109   test(data055, toler055);
2110   test(data056, toler056);
2111   test(data057, toler057);
2112   test(data058, toler058);
2113   test(data059, toler059);
2114   test(data060, toler060);
2115   test(data061, toler061);
2116   test(data062, toler062);
2117   test(data063, toler063);
2118   test(data064, toler064);
2119   return 0;
2120 }