libstdc++-v3/testsuite/special_functions/02_assoc_legendre/check_value.cc

   1 // { dg-do run { target c++11 } }
   2 // { dg-options "-D__STDCPP_WANT_MATH_SPEC_FUNCS__ -ffp-contract=off" }
   3
   4 // Copyright (C) 2016 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_legendre
  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 l=0, m=0.
  42 // max(|f - f_GSL|): 0.0000000000000000
  43 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
  44 const testcase_assoc_legendre<double>
  45 data001[21] =
  46 {
  47   { 1.0000000000000000, 0, 0,
  48           -1.0000000000000000 },
  49   { 1.0000000000000000, 0, 0,
  50           -0.90000000000000002 },
  51   { 1.0000000000000000, 0, 0,
  52           -0.80000000000000004 },
  53   { 1.0000000000000000, 0, 0,
  54           -0.69999999999999996 },
  55   { 1.0000000000000000, 0, 0,
  56           -0.59999999999999998 },
  57   { 1.0000000000000000, 0, 0,
  58           -0.50000000000000000 },
  59   { 1.0000000000000000, 0, 0,
  60           -0.40000000000000002 },
  61   { 1.0000000000000000, 0, 0,
  62           -0.30000000000000004 },
  63   { 1.0000000000000000, 0, 0,
  64           -0.19999999999999996 },
  65   { 1.0000000000000000, 0, 0,
  66           -0.099999999999999978 },
  67   { 1.0000000000000000, 0, 0,
  68           0.0000000000000000 },
  69   { 1.0000000000000000, 0, 0,
  70           0.10000000000000009 },
  71   { 1.0000000000000000, 0, 0,
  72           0.19999999999999996 },
  73   { 1.0000000000000000, 0, 0,
  74           0.30000000000000004 },
  75   { 1.0000000000000000, 0, 0,
  76           0.39999999999999991 },
  77   { 1.0000000000000000, 0, 0,
  78           0.50000000000000000 },
  79   { 1.0000000000000000, 0, 0,
  80           0.60000000000000009 },
  81   { 1.0000000000000000, 0, 0,
  82           0.69999999999999996 },
  83   { 1.0000000000000000, 0, 0,
  84           0.80000000000000004 },
  85   { 1.0000000000000000, 0, 0,
  86           0.89999999999999991 },
  87   { 1.0000000000000000, 0, 0,
  88           1.0000000000000000 },
  89 };
  90 const double toler001 = 2.5000000000000020e-13;
  91
  92 // Test data for l=1, m=0.
  93 // max(|f - f_GSL|): 0.0000000000000000
  94 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
  95 const testcase_assoc_legendre<double>
  96 data002[21] =
  97 {
  98   { -1.0000000000000000, 1, 0,
  99           -1.0000000000000000 },
 100   { -0.90000000000000002, 1, 0,
 101           -0.90000000000000002 },
 102   { -0.80000000000000004, 1, 0,
 103           -0.80000000000000004 },
 104   { -0.69999999999999996, 1, 0,
 105           -0.69999999999999996 },
 106   { -0.59999999999999998, 1, 0,
 107           -0.59999999999999998 },
 108   { -0.50000000000000000, 1, 0,
 109           -0.50000000000000000 },
 110   { -0.40000000000000002, 1, 0,
 111           -0.40000000000000002 },
 112   { -0.30000000000000004, 1, 0,
 113           -0.30000000000000004 },
 114   { -0.19999999999999996, 1, 0,
 115           -0.19999999999999996 },
 116   { -0.099999999999999978, 1, 0,
 117           -0.099999999999999978 },
 118   { 0.0000000000000000, 1, 0,
 119           0.0000000000000000 },
 120   { 0.10000000000000009, 1, 0,
 121           0.10000000000000009 },
 122   { 0.19999999999999996, 1, 0,
 123           0.19999999999999996 },
 124   { 0.30000000000000004, 1, 0,
 125           0.30000000000000004 },
 126   { 0.39999999999999991, 1, 0,
 127           0.39999999999999991 },
 128   { 0.50000000000000000, 1, 0,
 129           0.50000000000000000 },
 130   { 0.60000000000000009, 1, 0,
 131           0.60000000000000009 },
 132   { 0.69999999999999996, 1, 0,
 133           0.69999999999999996 },
 134   { 0.80000000000000004, 1, 0,
 135           0.80000000000000004 },
 136   { 0.89999999999999991, 1, 0,
 137           0.89999999999999991 },
 138   { 1.0000000000000000, 1, 0,
 139           1.0000000000000000 },
 140 };
 141 const double toler002 = 2.5000000000000020e-13;
 142
 143 // Test data for l=1, m=1.
 144 // max(|f - f_GSL|): 0.0000000000000000
 145 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
 146 const testcase_assoc_legendre<double>
 147 data003[21] =
 148 {
 149   { -0.0000000000000000, 1, 1,
 150           -1.0000000000000000 },
 151   { -0.43588989435406728, 1, 1,
 152           -0.90000000000000002 },
 153   { -0.59999999999999987, 1, 1,
 154           -0.80000000000000004 },
 155   { -0.71414284285428509, 1, 1,
 156           -0.69999999999999996 },
 157   { -0.80000000000000004, 1, 1,
 158           -0.59999999999999998 },
 159   { -0.86602540378443860, 1, 1,
 160           -0.50000000000000000 },
 161   { -0.91651513899116799, 1, 1,
 162           -0.40000000000000002 },
 163   { -0.95393920141694577, 1, 1,
 164           -0.30000000000000004 },
 165   { -0.97979589711327120, 1, 1,
 166           -0.19999999999999996 },
 167   { -0.99498743710661997, 1, 1,
 168           -0.099999999999999978 },
 169   { -1.0000000000000000, 1, 1,
 170           0.0000000000000000 },
 171   { -0.99498743710661997, 1, 1,
 172           0.10000000000000009 },
 173   { -0.97979589711327120, 1, 1,
 174           0.19999999999999996 },
 175   { -0.95393920141694577, 1, 1,
 176           0.30000000000000004 },
 177   { -0.91651513899116799, 1, 1,
 178           0.39999999999999991 },
 179   { -0.86602540378443860, 1, 1,
 180           0.50000000000000000 },
 181   { -0.79999999999999993, 1, 1,
 182           0.60000000000000009 },
 183   { -0.71414284285428509, 1, 1,
 184           0.69999999999999996 },
 185   { -0.59999999999999987, 1, 1,
 186           0.80000000000000004 },
 187   { -0.43588989435406750, 1, 1,
 188           0.89999999999999991 },
 189   { -0.0000000000000000, 1, 1,
 190           1.0000000000000000 },
 191 };
 192 const double toler003 = 2.5000000000000020e-13;
 193
 194 // Test data for l=2, m=0.
 195 // max(|f - f_GSL|): 1.1102230246251565e-16
 196 // max(|f - f_GSL| / |f_GSL|): 1.3877787807814482e-15
 197 const testcase_assoc_legendre<double>
 198 data004[21] =
 199 {
 200   { 1.0000000000000000, 2, 0,
 201           -1.0000000000000000 },
 202   { 0.71500000000000008, 2, 0,
 203           -0.90000000000000002 },
 204   { 0.46000000000000019, 2, 0,
 205           -0.80000000000000004 },
 206   { 0.23499999999999988, 2, 0,
 207           -0.69999999999999996 },
 208   { 0.039999999999999925, 2, 0,
 209           -0.59999999999999998 },
 210   { -0.12500000000000000, 2, 0,
 211           -0.50000000000000000 },
 212   { -0.25999999999999995, 2, 0,
 213           -0.40000000000000002 },
 214   { -0.36499999999999999, 2, 0,
 215           -0.30000000000000004 },
 216   { -0.44000000000000006, 2, 0,
 217           -0.19999999999999996 },
 218   { -0.48499999999999999, 2, 0,
 219           -0.099999999999999978 },
 220   { -0.50000000000000000, 2, 0,
 221           0.0000000000000000 },
 222   { -0.48499999999999999, 2, 0,
 223           0.10000000000000009 },
 224   { -0.44000000000000006, 2, 0,
 225           0.19999999999999996 },
 226   { -0.36499999999999999, 2, 0,
 227           0.30000000000000004 },
 228   { -0.26000000000000012, 2, 0,
 229           0.39999999999999991 },
 230   { -0.12500000000000000, 2, 0,
 231           0.50000000000000000 },
 232   { 0.040000000000000147, 2, 0,
 233           0.60000000000000009 },
 234   { 0.23499999999999988, 2, 0,
 235           0.69999999999999996 },
 236   { 0.46000000000000019, 2, 0,
 237           0.80000000000000004 },
 238   { 0.71499999999999986, 2, 0,
 239           0.89999999999999991 },
 240   { 1.0000000000000000, 2, 0,
 241           1.0000000000000000 },
 242 };
 243 const double toler004 = 2.5000000000000020e-13;
 244
 245 // Test data for l=2, m=1.
 246 // max(|f - f_GSL|): 0.0000000000000000
 247 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
 248 const testcase_assoc_legendre<double>
 249 data005[21] =
 250 {
 251   { 0.0000000000000000, 2, 1,
 252           -1.0000000000000000 },
 253   { 1.1769027147559816, 2, 1,
 254           -0.90000000000000002 },
 255   { 1.4399999999999999, 2, 1,
 256           -0.80000000000000004 },
 257   { 1.4996999699939983, 2, 1,
 258           -0.69999999999999996 },
 259   { 1.4399999999999999, 2, 1,
 260           -0.59999999999999998 },
 261   { 1.2990381056766580, 2, 1,
 262           -0.50000000000000000 },
 263   { 1.0998181667894018, 2, 1,
 264           -0.40000000000000002 },
 265   { 0.85854528127525132, 2, 1,
 266           -0.30000000000000004 },
 267   { 0.58787753826796263, 2, 1,
 268           -0.19999999999999996 },
 269   { 0.29849623113198592, 2, 1,
 270           -0.099999999999999978 },
 271   { -0.0000000000000000, 2, 1,
 272           0.0000000000000000 },
 273   { -0.29849623113198626, 2, 1,
 274           0.10000000000000009 },
 275   { -0.58787753826796263, 2, 1,
 276           0.19999999999999996 },
 277   { -0.85854528127525132, 2, 1,
 278           0.30000000000000004 },
 279   { -1.0998181667894014, 2, 1,
 280           0.39999999999999991 },
 281   { -1.2990381056766580, 2, 1,
 282           0.50000000000000000 },
 283   { -1.4400000000000002, 2, 1,
 284           0.60000000000000009 },
 285   { -1.4996999699939983, 2, 1,
 286           0.69999999999999996 },
 287   { -1.4399999999999999, 2, 1,
 288           0.80000000000000004 },
 289   { -1.1769027147559821, 2, 1,
 290           0.89999999999999991 },
 291   { -0.0000000000000000, 2, 1,
 292           1.0000000000000000 },
 293 };
 294 const double toler005 = 2.5000000000000020e-13;
 295
 296 // Test data for l=2, m=2.
 297 // max(|f - f_GSL|): 0.0000000000000000
 298 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
 299 const testcase_assoc_legendre<double>
 300 data006[21] =
 301 {
 302   { 0.0000000000000000, 2, 2,
 303           -1.0000000000000000 },
 304   { 0.56999999999999984, 2, 2,
 305           -0.90000000000000002 },
 306   { 1.0799999999999996, 2, 2,
 307           -0.80000000000000004 },
 308   { 1.5300000000000005, 2, 2,
 309           -0.69999999999999996 },
 310   { 1.9200000000000004, 2, 2,
 311           -0.59999999999999998 },
 312   { 2.2500000000000000, 2, 2,
 313           -0.50000000000000000 },
 314   { 2.5200000000000000, 2, 2,
 315           -0.40000000000000002 },
 316   { 2.7300000000000004, 2, 2,
 317           -0.30000000000000004 },
 318   { 2.8799999999999999, 2, 2,
 319           -0.19999999999999996 },
 320   { 2.9700000000000002, 2, 2,
 321           -0.099999999999999978 },
 322   { 3.0000000000000000, 2, 2,
 323           0.0000000000000000 },
 324   { 2.9700000000000002, 2, 2,
 325           0.10000000000000009 },
 326   { 2.8799999999999999, 2, 2,
 327           0.19999999999999996 },
 328   { 2.7300000000000004, 2, 2,
 329           0.30000000000000004 },
 330   { 2.5200000000000000, 2, 2,
 331           0.39999999999999991 },
 332   { 2.2500000000000000, 2, 2,
 333           0.50000000000000000 },
 334   { 1.9199999999999997, 2, 2,
 335           0.60000000000000009 },
 336   { 1.5300000000000005, 2, 2,
 337           0.69999999999999996 },
 338   { 1.0799999999999996, 2, 2,
 339           0.80000000000000004 },
 340   { 0.57000000000000040, 2, 2,
 341           0.89999999999999991 },
 342   { 0.0000000000000000, 2, 2,
 343           1.0000000000000000 },
 344 };
 345 const double toler006 = 2.5000000000000020e-13;
 346
 347 // Test data for l=5, m=0.
 348 // max(|f - f_GSL|): 2.0122792321330962e-16
 349 // max(|f - f_GSL| / |f_GSL|): 4.8911475274404243e-15
 350 const testcase_assoc_legendre<double>
 351 data007[21] =
 352 {
 353   { -1.0000000000000000, 5, 0,
 354           -1.0000000000000000 },
 355   { 0.041141250000000087, 5, 0,
 356           -0.90000000000000002 },
 357   { 0.39951999999999993, 5, 0,
 358           -0.80000000000000004 },
 359   { 0.36519874999999991, 5, 0,
 360           -0.69999999999999996 },
 361   { 0.15263999999999994, 5, 0,
 362           -0.59999999999999998 },
 363   { -0.089843750000000000, 5, 0,
 364           -0.50000000000000000 },
 365   { -0.27063999999999994, 5, 0,
 366           -0.40000000000000002 },
 367   { -0.34538625000000001, 5, 0,
 368           -0.30000000000000004 },
 369   { -0.30751999999999996, 5, 0,
 370           -0.19999999999999996 },
 371   { -0.17882874999999995, 5, 0,
 372           -0.099999999999999978 },
 373   { 0.0000000000000000, 5, 0,
 374           0.0000000000000000 },
 375   { 0.17882875000000015, 5, 0,
 376           0.10000000000000009 },
 377   { 0.30751999999999996, 5, 0,
 378           0.19999999999999996 },
 379   { 0.34538625000000001, 5, 0,
 380           0.30000000000000004 },
 381   { 0.27064000000000010, 5, 0,
 382           0.39999999999999991 },
 383   { 0.089843750000000000, 5, 0,
 384           0.50000000000000000 },
 385   { -0.15264000000000016, 5, 0,
 386           0.60000000000000009 },
 387   { -0.36519874999999991, 5, 0,
 388           0.69999999999999996 },
 389   { -0.39951999999999993, 5, 0,
 390           0.80000000000000004 },
 391   { -0.041141250000000261, 5, 0,
 392           0.89999999999999991 },
 393   { 1.0000000000000000, 5, 0,
 394           1.0000000000000000 },
 395 };
 396 const double toler007 = 2.5000000000000020e-13;
 397
 398 // Test data for l=5, m=1.
 399 // max(|f - f_GSL|): 0.0000000000000000
 400 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
 401 const testcase_assoc_legendre<double>
 402 data008[21] =
 403 {
 404   { 0.0000000000000000, 5, 1,
 405           -1.0000000000000000 },
 406   { -2.8099369608350981, 5, 1,
 407           -0.90000000000000002 },
 408   { -0.72180000000000089, 5, 1,
 409           -0.80000000000000004 },
 410   { 1.0951826834447254, 5, 1,
 411           -0.69999999999999996 },
 412   { 1.9775999999999998, 5, 1,
 413           -0.59999999999999998 },
 414   { 1.9282596881137892, 5, 1,
 415           -0.50000000000000000 },
 416   { 1.2070504380513685, 5, 1,
 417           -0.40000000000000002 },
 418   { 0.16079837663884422, 5, 1,
 419           -0.30000000000000004 },
 420   { -0.87005875663658538, 5, 1,
 421           -0.19999999999999996 },
 422   { -1.6083350053680323, 5, 1,
 423           -0.099999999999999978 },
 424   { -1.8750000000000000, 5, 1,
 425           0.0000000000000000 },
 426   { -1.6083350053680314, 5, 1,
 427           0.10000000000000009 },
 428   { -0.87005875663658538, 5, 1,
 429           0.19999999999999996 },
 430   { 0.16079837663884422, 5, 1,
 431           0.30000000000000004 },
 432   { 1.2070504380513671, 5, 1,
 433           0.39999999999999991 },
 434   { 1.9282596881137892, 5, 1,
 435           0.50000000000000000 },
 436   { 1.9775999999999998, 5, 1,
 437           0.60000000000000009 },
 438   { 1.0951826834447254, 5, 1,
 439           0.69999999999999996 },
 440   { -0.72180000000000089, 5, 1,
 441           0.80000000000000004 },
 442   { -2.8099369608350973, 5, 1,
 443           0.89999999999999991 },
 444   { 0.0000000000000000, 5, 1,
 445           1.0000000000000000 },
 446 };
 447 const double toler008 = 2.5000000000000020e-13;
 448
 449 // Test data for l=5, m=2.
 450 // max(|f - f_GSL|): 0.0000000000000000
 451 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
 452 const testcase_assoc_legendre<double>
 453 data009[21] =
 454 {
 455   { 0.0000000000000000, 5, 2,
 456           -1.0000000000000000 },
 457   { -12.837825000000000, 5, 2,
 458           -0.90000000000000002 },
 459   { -13.910400000000001, 5, 2,
 460           -0.80000000000000004 },
 461   { -8.8089749999999967, 5, 2,
 462           -0.69999999999999996 },
 463   { -1.6128000000000000, 5, 2,
 464           -0.59999999999999998 },
 465   { 4.9218750000000000, 5, 2,
 466           -0.50000000000000000 },
 467   { 9.1728000000000005, 5, 2,
 468           -0.40000000000000002 },
 469   { 10.462725000000001, 5, 2,
 470           -0.30000000000000004 },
 471   { 8.8703999999999983, 5, 2,
 472           -0.19999999999999996 },
 473   { 5.0415749999999990, 5, 2,
 474           -0.099999999999999978 },
 475   { -0.0000000000000000, 5, 2,
 476           0.0000000000000000 },
 477   { -5.0415750000000044, 5, 2,
 478           0.10000000000000009 },
 479   { -8.8703999999999983, 5, 2,
 480           0.19999999999999996 },
 481   { -10.462725000000001, 5, 2,
 482           0.30000000000000004 },
 483   { -9.1728000000000005, 5, 2,
 484           0.39999999999999991 },
 485   { -4.9218750000000000, 5, 2,
 486           0.50000000000000000 },
 487   { 1.6128000000000047, 5, 2,
 488           0.60000000000000009 },
 489   { 8.8089749999999967, 5, 2,
 490           0.69999999999999996 },
 491   { 13.910400000000001, 5, 2,
 492           0.80000000000000004 },
 493   { 12.837825000000004, 5, 2,
 494           0.89999999999999991 },
 495   { 0.0000000000000000, 5, 2,
 496           1.0000000000000000 },
 497 };
 498 const double toler009 = 2.5000000000000020e-13;
 499
 500 // Test data for l=5, m=5.
 501 // max(|f - f_GSL|): 0.0000000000000000
 502 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
 503 const testcase_assoc_legendre<double>
 504 data010[21] =
 505 {
 506   { -0.0000000000000000, 5, 5,
 507           -1.0000000000000000 },
 508   { -14.870165800941818, 5, 5,
 509           -0.90000000000000002 },
 510   { -73.483199999999925, 5, 5,
 511           -0.80000000000000004 },
 512   { -175.53238298794764, 5, 5,
 513           -0.69999999999999996 },
 514   { -309.65760000000006, 5, 5,
 515           -0.59999999999999998 },
 516   { -460.34662869916559, 5, 5,
 517           -0.50000000000000000 },
 518   { -611.12496255819883, 5, 5,
 519           -0.40000000000000002 },
 520   { -746.50941479523760, 5, 5,
 521           -0.30000000000000004 },
 522   { -853.31600434671316, 5, 5,
 523           -0.19999999999999996 },
 524   { -921.55189181724734, 5, 5,
 525           -0.099999999999999978 },
 526   { -945.00000000000000, 5, 5,
 527           0.0000000000000000 },
 528   { -921.55189181724734, 5, 5,
 529           0.10000000000000009 },
 530   { -853.31600434671316, 5, 5,
 531           0.19999999999999996 },
 532   { -746.50941479523760, 5, 5,
 533           0.30000000000000004 },
 534   { -611.12496255819883, 5, 5,
 535           0.39999999999999991 },
 536   { -460.34662869916559, 5, 5,
 537           0.50000000000000000 },
 538   { -309.65759999999989, 5, 5,
 539           0.60000000000000009 },
 540   { -175.53238298794764, 5, 5,
 541           0.69999999999999996 },
 542   { -73.483199999999925, 5, 5,
 543           0.80000000000000004 },
 544   { -14.870165800941855, 5, 5,
 545           0.89999999999999991 },
 546   { -0.0000000000000000, 5, 5,
 547           1.0000000000000000 },
 548 };
 549 const double toler010 = 2.5000000000000020e-13;
 550
 551 // Test data for l=10, m=0.
 552 // max(|f - f_GSL|): 2.7755575615628914e-16
 553 // max(|f - f_GSL| / |f_GSL|): 1.0547610802636413e-15
 554 const testcase_assoc_legendre<double>
 555 data011[21] =
 556 {
 557   { 1.0000000000000000, 10, 0,
 558           -1.0000000000000000 },
 559   { -0.26314561785585960, 10, 0,
 560           -0.90000000000000002 },
 561   { 0.30052979560000004, 10, 0,
 562           -0.80000000000000004 },
 563   { 0.085805795531640333, 10, 0,
 564           -0.69999999999999996 },
 565   { -0.24366274560000001, 10, 0,
 566           -0.59999999999999998 },
 567   { -0.18822860717773438, 10, 0,
 568           -0.50000000000000000 },
 569   { 0.096839064399999925, 10, 0,
 570           -0.40000000000000002 },
 571   { 0.25147634951601561, 10, 0,
 572           -0.30000000000000004 },
 573   { 0.12907202559999983, 10, 0,
 574           -0.19999999999999996 },
 575   { -0.12212499738710943, 10, 0,
 576           -0.099999999999999978 },
 577   { -0.24609375000000000, 10, 0,
 578           0.0000000000000000 },
 579   { -0.12212499738710922, 10, 0,
 580           0.10000000000000009 },
 581   { 0.12907202559999983, 10, 0,
 582           0.19999999999999996 },
 583   { 0.25147634951601561, 10, 0,
 584           0.30000000000000004 },
 585   { 0.096839064400000258, 10, 0,
 586           0.39999999999999991 },
 587   { -0.18822860717773438, 10, 0,
 588           0.50000000000000000 },
 589   { -0.24366274559999984, 10, 0,
 590           0.60000000000000009 },
 591   { 0.085805795531640333, 10, 0,
 592           0.69999999999999996 },
 593   { 0.30052979560000004, 10, 0,
 594           0.80000000000000004 },
 595   { -0.26314561785585899, 10, 0,
 596           0.89999999999999991 },
 597   { 1.0000000000000000, 10, 0,
 598           1.0000000000000000 },
 599 };
 600 const double toler011 = 2.5000000000000020e-13;
 601
 602 // Test data for l=10, m=1.
 603 // max(|f - f_GSL|): 0.0000000000000000
 604 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
 605 const testcase_assoc_legendre<double>
 606 data012[21] =
 607 {
 608   { -0.0000000000000000, 10, 1,
 609           -1.0000000000000000 },
 610   { -3.0438748781479039, 10, 1,
 611           -0.90000000000000002 },
 612   { -0.87614260800000254, 10, 1,
 613           -0.80000000000000004 },
 614   { 2.9685359952934527, 10, 1,
 615           -0.69999999999999996 },
 616   { 1.2511825919999997, 10, 1,
 617           -0.59999999999999998 },
 618   { -2.0066877394361260, 10, 1,
 619           -0.50000000000000000 },
 620   { -2.4822196173476661, 10, 1,
 621           -0.40000000000000002 },
 622   { -0.12309508907433910, 10, 1,
 623           -0.30000000000000004 },
 624   { 2.2468221751958413, 10, 1,
 625           -0.19999999999999996 },
 626   { 2.2472659777983512, 10, 1,
 627           -0.099999999999999978 },
 628   { -0.0000000000000000, 10, 1,
 629           0.0000000000000000 },
 630   { -2.2472659777983535, 10, 1,
 631           0.10000000000000009 },
 632   { -2.2468221751958413, 10, 1,
 633           0.19999999999999996 },
 634   { 0.12309508907433910, 10, 1,
 635           0.30000000000000004 },
 636   { 2.4822196173476647, 10, 1,
 637           0.39999999999999991 },
 638   { 2.0066877394361260, 10, 1,
 639           0.50000000000000000 },
 640   { -1.2511825920000037, 10, 1,
 641           0.60000000000000009 },
 642   { -2.9685359952934527, 10, 1,
 643           0.69999999999999996 },
 644   { 0.87614260800000254, 10, 1,
 645           0.80000000000000004 },
 646   { 3.0438748781479115, 10, 1,
 647           0.89999999999999991 },
 648   { 0.0000000000000000, 10, 1,
 649           1.0000000000000000 },
 650 };
 651 const double toler012 = 2.5000000000000020e-13;
 652
 653 // Test data for l=10, m=2.
 654 // max(|f - f_GSL|): 0.0000000000000000
 655 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
 656 const testcase_assoc_legendre<double>
 657 data013[21] =
 658 {
 659   { 0.0000000000000000, 10, 2,
 660           -1.0000000000000000 },
 661   { 16.376387762496137, 10, 2,
 662           -0.90000000000000002 },
 663   { -35.394657804000005, 10, 2,
 664           -0.80000000000000004 },
 665   { -3.6191429423788648, 10, 2,
 666           -0.69999999999999996 },
 667   { 28.679675904000014, 10, 2,
 668           -0.59999999999999998 },
 669   { 18.388023376464844, 10, 2,
 670           -0.50000000000000000 },
 671   { -12.818955995999994, 10, 2,
 672           -0.40000000000000002 },
 673   { -27.739821675972664, 10, 2,
 674           -0.30000000000000004 },
 675   { -13.280661503999987, 10, 2,
 676           -0.19999999999999996 },
 677   { 13.885467170308601, 10, 2,
 678           -0.099999999999999978 },
 679   { 27.070312500000000, 10, 2,
 680           0.0000000000000000 },
 681   { 13.885467170308573, 10, 2,
 682           0.10000000000000009 },
 683   { -13.280661503999987, 10, 2,
 684           0.19999999999999996 },
 685   { -27.739821675972664, 10, 2,
 686           0.30000000000000004 },
 687   { -12.818955996000021, 10, 2,
 688           0.39999999999999991 },
 689   { 18.388023376464844, 10, 2,
 690           0.50000000000000000 },
 691   { 28.679675904000000, 10, 2,
 692           0.60000000000000009 },
 693   { -3.6191429423788648, 10, 2,
 694           0.69999999999999996 },
 695   { -35.394657804000005, 10, 2,
 696           0.80000000000000004 },
 697   { 16.376387762496009, 10, 2,
 698           0.89999999999999991 },
 699   { 0.0000000000000000, 10, 2,
 700           1.0000000000000000 },
 701 };
 702 const double toler013 = 2.5000000000000020e-13;
 703
 704 // Test data for l=10, m=5.
 705 // max(|f - f_GSL|): 0.0000000000000000
 706 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
 707 const testcase_assoc_legendre<double>
 708 data014[21] =
 709 {
 710   { 0.0000000000000000, 10, 5,
 711           -1.0000000000000000 },
 712   { 21343.618518164680, 10, 5,
 713           -0.90000000000000002 },
 714   { 40457.016407807983, 10, 5,
 715           -0.80000000000000004 },
 716   { 20321.279317331315, 10, 5,
 717           -0.69999999999999996 },
 718   { -14410.820616192004, 10, 5,
 719           -0.59999999999999998 },
 720   { -30086.169706116176, 10, 5,
 721           -0.50000000000000000 },
 722   { -17177.549337582859, 10, 5,
 723           -0.40000000000000002 },
 724   { 9272.5119495412364, 10, 5,
 725           -0.30000000000000004 },
 726   { 26591.511184414714, 10, 5,
 727           -0.19999999999999996 },
 728   { 21961.951238504211, 10, 5,
 729           -0.099999999999999978 },
 730   { -0.0000000000000000, 10, 5,
 731           0.0000000000000000 },
 732   { -21961.951238504229, 10, 5,
 733           0.10000000000000009 },
 734   { -26591.511184414714, 10, 5,
 735           0.19999999999999996 },
 736   { -9272.5119495412364, 10, 5,
 737           0.30000000000000004 },
 738   { 17177.549337582834, 10, 5,
 739           0.39999999999999991 },
 740   { 30086.169706116176, 10, 5,
 741           0.50000000000000000 },
 742   { 14410.820616191972, 10, 5,
 743           0.60000000000000009 },
 744   { -20321.279317331315, 10, 5,
 745           0.69999999999999996 },
 746   { -40457.016407807983, 10, 5,
 747           0.80000000000000004 },
 748   { -21343.618518164694, 10, 5,
 749           0.89999999999999991 },
 750   { 0.0000000000000000, 10, 5,
 751           1.0000000000000000 },
 752 };
 753 const double toler014 = 2.5000000000000020e-13;
 754
 755 // Test data for l=10, m=10.
 756 // max(|f - f_GSL|): 0.0000000000000000
 757 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
 758 const testcase_assoc_legendre<double>
 759 data015[21] =
 760 {
 761   { 0.0000000000000000, 10, 10,
 762           -1.0000000000000000 },
 763   { 162117.40078784220, 10, 10,
 764           -0.90000000000000002 },
 765   { 3958896.3481267113, 10, 10,
 766           -0.80000000000000004 },
 767   { 22589806.343887307, 10, 10,
 768           -0.69999999999999996 },
 769   { 70300999.121633321, 10, 10,
 770           -0.59999999999999998 },
 771   { 155370278.54003900, 10, 10,
 772           -0.50000000000000000 },
 773   { 273815518.20150518, 10, 10,
 774           -0.40000000000000002 },
 775   { 408571989.13158917, 10, 10,
 776           -0.30000000000000004 },
 777   { 533848212.07990247, 10, 10,
 778           -0.19999999999999996 },
 779   { 622640835.70523083, 10, 10,
 780           -0.099999999999999978 },
 781   { 654729075.00000000, 10, 10,
 782           0.0000000000000000 },
 783   { 622640835.70523083, 10, 10,
 784           0.10000000000000009 },
 785   { 533848212.07990247, 10, 10,
 786           0.19999999999999996 },
 787   { 408571989.13158917, 10, 10,
 788           0.30000000000000004 },
 789   { 273815518.20150518, 10, 10,
 790           0.39999999999999991 },
 791   { 155370278.54003900, 10, 10,
 792           0.50000000000000000 },
 793   { 70300999.121633217, 10, 10,
 794           0.60000000000000009 },
 795   { 22589806.343887307, 10, 10,
 796           0.69999999999999996 },
 797   { 3958896.3481267113, 10, 10,
 798           0.80000000000000004 },
 799   { 162117.40078784304, 10, 10,
 800           0.89999999999999991 },
 801   { 0.0000000000000000, 10, 10,
 802           1.0000000000000000 },
 803 };
 804 const double toler015 = 2.5000000000000020e-13;
 805
 806 // Test data for l=20, m=0.
 807 // max(|f - f_GSL|): 3.3306690738754696e-16
 808 // max(|f - f_GSL| / |f_GSL|): 2.2307336678138069e-15
 809 const testcase_assoc_legendre<double>
 810 data016[21] =
 811 {
 812   { 1.0000000000000000, 20, 0,
 813           -1.0000000000000000 },
 814   { -0.14930823530984835, 20, 0,
 815           -0.90000000000000002 },
 816   { 0.22420460541741347, 20, 0,
 817           -0.80000000000000004 },
 818   { -0.20457394463834172, 20, 0,
 819           -0.69999999999999996 },
 820   { 0.15916752910098109, 20, 0,
 821           -0.59999999999999998 },
 822   { -0.048358381067373557, 20, 0,
 823           -0.50000000000000000 },
 824   { -0.10159261558628156, 20, 0,
 825           -0.40000000000000002 },
 826   { 0.18028715947998042, 20, 0,
 827           -0.30000000000000004 },
 828   { -0.098042194344594796, 20, 0,
 829           -0.19999999999999996 },
 830   { -0.082077130944527663, 20, 0,
 831           -0.099999999999999978 },
 832   { 0.17619705200195312, 20, 0,
 833           0.0000000000000000 },
 834   { -0.082077130944528023, 20, 0,
 835           0.10000000000000009 },
 836   { -0.098042194344594796, 20, 0,
 837           0.19999999999999996 },
 838   { 0.18028715947998042, 20, 0,
 839           0.30000000000000004 },
 840   { -0.10159261558628112, 20, 0,
 841           0.39999999999999991 },
 842   { -0.048358381067373557, 20, 0,
 843           0.50000000000000000 },
 844   { 0.15916752910098075, 20, 0,
 845           0.60000000000000009 },
 846   { -0.20457394463834172, 20, 0,
 847           0.69999999999999996 },
 848   { 0.22420460541741347, 20, 0,
 849           0.80000000000000004 },
 850   { -0.14930823530984924, 20, 0,
 851           0.89999999999999991 },
 852   { 1.0000000000000000, 20, 0,
 853           1.0000000000000000 },
 854 };
 855 const double toler016 = 2.5000000000000020e-13;
 856
 857 // Test data for l=20, m=1.
 858 // max(|f - f_GSL|): 0.0000000000000000
 859 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
 860 const testcase_assoc_legendre<double>
 861 data017[21] =
 862 {
 863   { 0.0000000000000000, 20, 1,
 864           -1.0000000000000000 },
 865   { 4.3838334818220499, 20, 1,
 866           -0.90000000000000002 },
 867   { -0.63138296146340844, 20, 1,
 868           -0.80000000000000004 },
 869   { 0.72274871413391395, 20, 1,
 870           -0.69999999999999996 },
 871   { -2.3203528743824910, 20, 1,
 872           -0.59999999999999998 },
 873   { 3.7399919228791405, 20, 1,
 874           -0.50000000000000000 },
 875   { -3.1692202279270041, 20, 1,
 876           -0.40000000000000002 },
 877   { 0.15804468835344135, 20, 1,
 878           -0.30000000000000004 },
 879   { 3.0366182393271171, 20, 1,
 880           -0.19999999999999996 },
 881   { -3.2115523815580209, 20, 1,
 882           -0.099999999999999978 },
 883   { 0.0000000000000000, 20, 1,
 884           0.0000000000000000 },
 885   { 3.2115523815580169, 20, 1,
 886           0.10000000000000009 },
 887   { -3.0366182393271171, 20, 1,
 888           0.19999999999999996 },
 889   { -0.15804468835344135, 20, 1,
 890           0.30000000000000004 },
 891   { 3.1692202279270085, 20, 1,
 892           0.39999999999999991 },
 893   { -3.7399919228791405, 20, 1,
 894           0.50000000000000000 },
 895   { 2.3203528743824995, 20, 1,
 896           0.60000000000000009 },
 897   { -0.72274871413391395, 20, 1,
 898           0.69999999999999996 },
 899   { 0.63138296146340844, 20, 1,
 900           0.80000000000000004 },
 901   { -4.3838334818220339, 20, 1,
 902           0.89999999999999991 },
 903   { 0.0000000000000000, 20, 1,
 904           1.0000000000000000 },
 905 };
 906 const double toler017 = 2.5000000000000020e-13;
 907
 908 // Test data for l=20, m=2.
 909 // max(|f - f_GSL|): 0.0000000000000000
 910 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
 911 const testcase_assoc_legendre<double>
 912 data018[21] =
 913 {
 914   { 0.0000000000000000, 20, 2,
 915           -1.0000000000000000 },
 916   { 80.812425587310102, 20, 2,
 917           -0.90000000000000002 },
 918   { -95.849622172549374, 20, 2,
 919           -0.80000000000000004 },
 920   { 87.337927630325510, 20, 2,
 921           -0.69999999999999996 },
 922   { -70.330891533985834, 20, 2,
 923           -0.59999999999999998 },
 924   { 24.629090735179489, 20, 2,
 925           -0.50000000000000000 },
 926   { 39.902576338912425, 20, 2,
 927           -0.40000000000000002 },
 928   { -75.621201471396603, 20, 2,
 929           -0.30000000000000004 },
 930   { 42.417415829726494, 20, 2,
 931           -0.19999999999999996 },
 932   { 33.826848678871293, 20, 2,
 933           -0.099999999999999978 },
 934   { -74.002761840820312, 20, 2,
 935           0.0000000000000000 },
 936   { 33.826848678871464, 20, 2,
 937           0.10000000000000009 },
 938   { 42.417415829726494, 20, 2,
 939           0.19999999999999996 },
 940   { -75.621201471396603, 20, 2,
 941           0.30000000000000004 },
 942   { 39.902576338912247, 20, 2,
 943           0.39999999999999991 },
 944   { 24.629090735179489, 20, 2,
 945           0.50000000000000000 },
 946   { -70.330891533985721, 20, 2,
 947           0.60000000000000009 },
 948   { 87.337927630325510, 20, 2,
 949           0.69999999999999996 },
 950   { -95.849622172549374, 20, 2,
 951           0.80000000000000004 },
 952   { 80.812425587310500, 20, 2,
 953           0.89999999999999991 },
 954   { 0.0000000000000000, 20, 2,
 955           1.0000000000000000 },
 956 };
 957 const double toler018 = 2.5000000000000020e-13;
 958
 959 // Test data for l=20, m=5.
 960 // max(|f - f_GSL|): 0.0000000000000000
 961 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
 962 const testcase_assoc_legendre<double>
 963 data019[21] =
 964 {
 965   { -0.0000000000000000, 20, 5,
 966           -1.0000000000000000 },
 967   { -315702.32715134218, 20, 5,
 968           -0.90000000000000002 },
 969   { 503060.91484852589, 20, 5,
 970           -0.80000000000000004 },
 971   { -298127.28360361955, 20, 5,
 972           -0.69999999999999996 },
 973   { -114444.61447464029, 20, 5,
 974           -0.59999999999999998 },
 975   { 543428.40914592845, 20, 5,
 976           -0.50000000000000000 },
 977   { -613842.07728185470, 20, 5,
 978           -0.40000000000000002 },
 979   { 143765.42411270936, 20, 5,
 980           -0.30000000000000004 },
 981   { 472600.45321372285, 20, 5,
 982           -0.19999999999999996 },
 983   { -563861.76771496492, 20, 5,
 984           -0.099999999999999978 },
 985   { 0.0000000000000000, 20, 5,
 986           0.0000000000000000 },
 987   { 563861.76771496458, 20, 5,
 988           0.10000000000000009 },
 989   { -472600.45321372285, 20, 5,
 990           0.19999999999999996 },
 991   { -143765.42411270936, 20, 5,
 992           0.30000000000000004 },
 993   { 613842.07728185481, 20, 5,
 994           0.39999999999999991 },
 995   { -543428.40914592845, 20, 5,
 996           0.50000000000000000 },
 997   { 114444.61447464178, 20, 5,
 998           0.60000000000000009 },
 999   { 298127.28360361955, 20, 5,
1000           0.69999999999999996 },
1001   { -503060.91484852589, 20, 5,
1002           0.80000000000000004 },
1003   { 315702.32715134491, 20, 5,
1004           0.89999999999999991 },
1005   { 0.0000000000000000, 20, 5,
1006           1.0000000000000000 },
1007 };
1008 const double toler019 = 2.5000000000000020e-13;
1009
1010 // Test data for l=20, m=10.
1011 // max(|f - f_GSL|): 0.0000000000000000
1012 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
1013 const testcase_assoc_legendre<double>
1014 data020[21] =
1015 {
1016   { -0.0000000000000000, 20, 10,
1017           -1.0000000000000000 },
1018   { 990017476694.99084, 20, 10,
1019           -0.90000000000000002 },
1020   { 2392757933281.0498, 20, 10,
1021           -0.80000000000000004 },
1022   { -1548364524949.5808, 20, 10,
1023           -0.69999999999999996 },
1024   { -424471915195.05627, 20, 10,
1025           -0.59999999999999998 },
1026   { 1744502295946.2073, 20, 10,
1027           -0.50000000000000000 },
1028   { -899973487310.55212, 20, 10,
1029           -0.40000000000000002 },
1030   { -1092420454297.7161, 20, 10,
1031           -0.30000000000000004 },
1032   { 1466609267659.8816, 20, 10,
1033           -0.19999999999999996 },
1034   { 356041756390.71674, 20, 10,
1035           -0.099999999999999978 },
1036   { -1612052956674.3164, 20, 10,
1037           0.0000000000000000 },
1038   { 356041756390.71985, 20, 10,
1039           0.10000000000000009 },
1040   { 1466609267659.8816, 20, 10,
1041           0.19999999999999996 },
1042   { -1092420454297.7161, 20, 10,
1043           0.30000000000000004 },
1044   { -899973487310.55530, 20, 10,
1045           0.39999999999999991 },
1046   { 1744502295946.2073, 20, 10,
1047           0.50000000000000000 },
1048   { -424471915195.05896, 20, 10,
1049           0.60000000000000009 },
1050   { -1548364524949.5808, 20, 10,
1051           0.69999999999999996 },
1052   { 2392757933281.0498, 20, 10,
1053           0.80000000000000004 },
1054   { 990017476694.99316, 20, 10,
1055           0.89999999999999991 },
1056   { 0.0000000000000000, 20, 10,
1057           1.0000000000000000 },
1058 };
1059 const double toler020 = 2.5000000000000020e-13;
1060
1061 // Test data for l=20, m=20.
1062 // max(|f - f_GSL|): 0.0000000000000000
1063 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
1064 const testcase_assoc_legendre<double>
1065 data021[21] =
1066 {
1067   { 0.0000000000000000, 20, 20,
1068           -1.0000000000000000 },
1069   { 19609049712023808., 20, 20,
1070           -0.90000000000000002 },
1071   { 1.1693527616833221e+19, 20, 20,
1072           -0.80000000000000004 },
1073   { 3.8073455880620691e+20, 20, 20,
1074           -0.69999999999999996 },
1075   { 3.6874002249007927e+21, 20, 20,
1076           -0.59999999999999998 },
1077   { 1.8010806978179592e+22, 20, 20,
1078           -0.50000000000000000 },
1079   { 5.5938832584012466e+22, 20, 20,
1080           -0.40000000000000002 },
1081   { 1.2454734132297811e+23, 20, 20,
1082           -0.30000000000000004 },
1083   { 2.1263407800797497e+23, 20, 20,
1084           -0.19999999999999996 },
1085   { 2.8924941146976873e+23, 20, 20,
1086           -0.099999999999999978 },
1087   { 3.1983098677287775e+23, 20, 20,
1088           0.0000000000000000 },
1089   { 2.8924941146976873e+23, 20, 20,
1090           0.10000000000000009 },
1091   { 2.1263407800797497e+23, 20, 20,
1092           0.19999999999999996 },
1093   { 1.2454734132297811e+23, 20, 20,
1094           0.30000000000000004 },
1095   { 5.5938832584012466e+22, 20, 20,
1096           0.39999999999999991 },
1097   { 1.8010806978179592e+22, 20, 20,
1098           0.50000000000000000 },
1099   { 3.6874002249007807e+21, 20, 20,
1100           0.60000000000000009 },
1101   { 3.8073455880620691e+20, 20, 20,
1102           0.69999999999999996 },
1103   { 1.1693527616833221e+19, 20, 20,
1104           0.80000000000000004 },
1105   { 19609049712024020., 20, 20,
1106           0.89999999999999991 },
1107   { 0.0000000000000000, 20, 20,
1108           1.0000000000000000 },
1109 };
1110 const double toler021 = 2.5000000000000020e-13;
1111
1112 // Test data for l=50, m=0.
1113 // max(|f - f_GSL|): 3.6082248300317588e-16
1114 // max(|f - f_GSL| / |f_GSL|): 2.1700196856209138e-15
1115 const testcase_assoc_legendre<double>
1116 data022[21] =
1117 {
1118   { 1.0000000000000000, 50, 0,
1119           -1.0000000000000000 },
1120   { -0.17003765994383671, 50, 0,
1121           -0.90000000000000002 },
1122   { 0.13879737345093113, 50, 0,
1123           -0.80000000000000004 },
1124   { -0.014572731645892852, 50, 0,
1125           -0.69999999999999996 },
1126   { -0.058860798844002096, 50, 0,
1127           -0.59999999999999998 },
1128   { -0.031059099239609811, 50, 0,
1129           -0.50000000000000000 },
1130   { 0.041569033381825375, 50, 0,
1131           -0.40000000000000002 },
1132   { 0.10911051574714797, 50, 0,
1133           -0.30000000000000004 },
1134   { 0.083432272204197494, 50, 0,
1135           -0.19999999999999996 },
1136   { -0.038205812661313600, 50, 0,
1137           -0.099999999999999978 },
1138   { -0.11227517265921705, 50, 0,
1139           0.0000000000000000 },
1140   { -0.038205812661314155, 50, 0,
1141           0.10000000000000009 },
1142   { 0.083432272204197494, 50, 0,
1143           0.19999999999999996 },
1144   { 0.10911051574714797, 50, 0,
1145           0.30000000000000004 },
1146   { 0.041569033381824674, 50, 0,
1147           0.39999999999999991 },
1148   { -0.031059099239609811, 50, 0,
1149           0.50000000000000000 },
1150   { -0.058860798844001430, 50, 0,
1151           0.60000000000000009 },
1152   { -0.014572731645892852, 50, 0,
1153           0.69999999999999996 },
1154   { 0.13879737345093113, 50, 0,
1155           0.80000000000000004 },
1156   { -0.17003765994383657, 50, 0,
1157           0.89999999999999991 },
1158   { 1.0000000000000000, 50, 0,
1159           1.0000000000000000 },
1160 };
1161 const double toler022 = 2.5000000000000020e-13;
1162
1163 // Test data for l=50, m=1.
1164 // max(|f - f_GSL|): 0.0000000000000000
1165 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
1166 const testcase_assoc_legendre<double>
1167 data023[21] =
1168 {
1169   { 0.0000000000000000, 50, 1,
1170           -1.0000000000000000 },
1171   { -0.13424149984449490, 50, 1,
1172           -0.90000000000000002 },
1173   { 2.2011219672413018, 50, 1,
1174           -0.80000000000000004 },
1175   { 6.6622414993232004, 50, 1,
1176           -0.69999999999999996 },
1177   { 5.5772846936919249, 50, 1,
1178           -0.59999999999999998 },
1179   { 5.8787148815607608, 50, 1,
1180           -0.50000000000000000 },
1181   { 5.5473459458633974, 50, 1,
1182           -0.40000000000000002 },
1183   { 1.8444956647619930, 50, 1,
1184           -0.30000000000000004 },
1185   { -3.8722014306642127, 50, 1,
1186           -0.19999999999999996 },
1187   { -5.3488751322285628, 50, 1,
1188           -0.099999999999999978 },
1189   { -0.0000000000000000, 50, 1,
1190           0.0000000000000000 },
1191   { 5.3488751322285522, 50, 1,
1192           0.10000000000000009 },
1193   { 3.8722014306642127, 50, 1,
1194           0.19999999999999996 },
1195   { -1.8444956647619930, 50, 1,
1196           0.30000000000000004 },
1197   { -5.5473459458634080, 50, 1,
1198           0.39999999999999991 },
1199   { -5.8787148815607608, 50, 1,
1200           0.50000000000000000 },
1201   { -5.5772846936919453, 50, 1,
1202           0.60000000000000009 },
1203   { -6.6622414993232004, 50, 1,
1204           0.69999999999999996 },
1205   { -2.2011219672413018, 50, 1,
1206           0.80000000000000004 },
1207   { 0.13424149984462019, 50, 1,
1208           0.89999999999999991 },
1209   { 0.0000000000000000, 50, 1,
1210           1.0000000000000000 },
1211 };
1212 const double toler023 = 2.5000000000000020e-13;
1213
1214 // Test data for l=50, m=2.
1215 // max(|f - f_GSL|): 0.0000000000000000
1216 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
1217 const testcase_assoc_legendre<double>
1218 data024[21] =
1219 {
1220   { 0.0000000000000000, 50, 2,
1221           -1.0000000000000000 },
1222   { 433.04168483713511, 50, 2,
1223           -0.90000000000000002 },
1224   { -348.06364372056424, 50, 2,
1225           -0.80000000000000004 },
1226   { 50.221071418108444, 50, 2,
1227           -0.69999999999999996 },
1228   { 158.46096409274352, 50, 2,
1229           -0.59999999999999998 },
1230   { 85.988858299721457, 50, 2,
1231           -0.50000000000000000 },
1232   { -101.15891460879270, 50, 2,
1233           -0.40000000000000002 },
1234   { -277.07168105316617, 50, 2,
1235           -0.30000000000000004 },
1236   { -214.33311373510401, 50, 2,
1237           -0.19999999999999996 },
1238   { 96.349657930951665, 50, 2,
1239           -0.099999999999999978 },
1240   { 286.30169028100346, 50, 2,
1241           0.0000000000000000 },
1242   { 96.349657930953242, 50, 2,
1243           0.10000000000000009 },
1244   { -214.33311373510401, 50, 2,
1245           0.19999999999999996 },
1246   { -277.07168105316617, 50, 2,
1247           0.30000000000000004 },
1248   { -101.15891460879088, 50, 2,
1249           0.39999999999999991 },
1250   { 85.988858299721457, 50, 2,
1251           0.50000000000000000 },
1252   { 158.46096409274153, 50, 2,
1253           0.60000000000000009 },
1254   { 50.221071418108444, 50, 2,
1255           0.69999999999999996 },
1256   { -348.06364372056424, 50, 2,
1257           0.80000000000000004 },
1258   { 433.04168483713374, 50, 2,
1259           0.89999999999999991 },
1260   { 0.0000000000000000, 50, 2,
1261           1.0000000000000000 },
1262 };
1263 const double toler024 = 2.5000000000000020e-13;
1264
1265 // Test data for l=50, m=5.
1266 // max(|f - f_GSL|): 0.0000000000000000
1267 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
1268 const testcase_assoc_legendre<double>
1269 data025[21] =
1270 {
1271   { -0.0000000000000000, 50, 5,
1272           -1.0000000000000000 },
1273   { -27340473.952132829, 50, 5,
1274           -0.90000000000000002 },
1275   { 27753716.768532373, 50, 5,
1276           -0.80000000000000004 },
1277   { 40808153.913493633, 50, 5,
1278           -0.69999999999999996 },
1279   { 32071189.035790090, 50, 5,
1280           -0.59999999999999998 },
1281   { 36265736.218529105, 50, 5,
1282           -0.50000000000000000 },
1283   { 37089596.700204901, 50, 5,
1284           -0.40000000000000002 },
1285   { 14562029.629244499, 50, 5,
1286           -0.30000000000000004 },
1287   { -23686895.217517190, 50, 5,
1288           -0.19999999999999996 },
1289   { -34878992.965676002, 50, 5,
1290           -0.099999999999999978 },
1291   { -0.0000000000000000, 50, 5,
1292           0.0000000000000000 },
1293   { 34878992.965675958, 50, 5,
1294           0.10000000000000009 },
1295   { 23686895.217517190, 50, 5,
1296           0.19999999999999996 },
1297   { -14562029.629244499, 50, 5,
1298           0.30000000000000004 },
1299   { -37089596.700204931, 50, 5,
1300           0.39999999999999991 },
1301   { -36265736.218529105, 50, 5,
1302           0.50000000000000000 },
1303   { -32071189.035790242, 50, 5,
1304           0.60000000000000009 },
1305   { -40808153.913493633, 50, 5,
1306           0.69999999999999996 },
1307   { -27753716.768532373, 50, 5,
1308           0.80000000000000004 },
1309   { 27340473.952133428, 50, 5,
1310           0.89999999999999991 },
1311   { 0.0000000000000000, 50, 5,
1312           1.0000000000000000 },
1313 };
1314 const double toler025 = 2.5000000000000020e-13;
1315
1316 // Test data for l=50, m=10.
1317 // max(|f - f_GSL|): 0.0000000000000000
1318 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
1319 const testcase_assoc_legendre<double>
1320 data026[21] =
1321 {
1322   { -0.0000000000000000, 50, 10,
1323           -1.0000000000000000 },
1324   { -8994661710093155.0, 50, 10,
1325           -0.90000000000000002 },
1326   { 932311375306569.62, 50, 10,
1327           -0.80000000000000004 },
1328   { 12153535011507012., 50, 10,
1329           -0.69999999999999996 },
1330   { 12176690755542240., 50, 10,
1331           -0.59999999999999998 },
1332   { 9180035388465754.0, 50, 10,
1333           -0.50000000000000000 },
1334   { 889201701866910.38, 50, 10,
1335           -0.40000000000000002 },
1336   { -9451384032851604.0, 50, 10,
1337           -0.30000000000000004 },
1338   { -9926439446673564.0, 50, 10,
1339           -0.19999999999999996 },
1340   { 2794368162749970.5, 50, 10,
1341           -0.099999999999999978 },
1342   { 11452238249246346., 50, 10,
1343           0.0000000000000000 },
1344   { 2794368162750031.0, 50, 10,
1345           0.10000000000000009 },
1346   { -9926439446673564.0, 50, 10,
1347           0.19999999999999996 },
1348   { -9451384032851604.0, 50, 10,
1349           0.30000000000000004 },
1350   { 889201701866984.00, 50, 10,
1351           0.39999999999999991 },
1352   { 9180035388465754.0, 50, 10,
1353           0.50000000000000000 },
1354   { 12176690755542214., 50, 10,
1355           0.60000000000000009 },
1356   { 12153535011507012., 50, 10,
1357           0.69999999999999996 },
1358   { 932311375306569.62, 50, 10,
1359           0.80000000000000004 },
1360   { -8994661710093362.0, 50, 10,
1361           0.89999999999999991 },
1362   { 0.0000000000000000, 50, 10,
1363           1.0000000000000000 },
1364 };
1365 const double toler026 = 2.5000000000000020e-13;
1366
1367 // Test data for l=50, m=20.
1368 // max(|f - f_GSL|): 0.0000000000000000
1369 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
1370 const testcase_assoc_legendre<double>
1371 data027[21] =
1372 {
1373   { 0.0000000000000000, 50, 20,
1374           -1.0000000000000000 },
1375   { 1.6630925158645501e+33, 50, 20,
1376           -0.90000000000000002 },
1377   { 1.0622676657892052e+33, 50, 20,
1378           -0.80000000000000004 },
1379   { 8.6022521164717112e+32, 50, 20,
1380           -0.69999999999999996 },
1381   { 4.0860128756808466e+32, 50, 20,
1382           -0.59999999999999998 },
1383   { -4.0169860814274459e+32, 50, 20,
1384           -0.50000000000000000 },
1385   { -8.2324325279774037e+32, 50, 20,
1386           -0.40000000000000002 },
1387   { -4.0054067236243731e+31, 50, 20,
1388           -0.30000000000000004 },
1389   { 7.9309266056434309e+32, 50, 20,
1390           -0.19999999999999996 },
1391   { 5.4151358290898977e+31, 50, 20,
1392           -0.099999999999999978 },
1393   { -7.8735935697332210e+32, 50, 20,
1394           0.0000000000000000 },
1395   { 5.4151358290894924e+31, 50, 20,
1396           0.10000000000000009 },
1397   { 7.9309266056434309e+32, 50, 20,
1398           0.19999999999999996 },
1399   { -4.0054067236243731e+31, 50, 20,
1400           0.30000000000000004 },
1401   { -8.2324325279773994e+32, 50, 20,
1402           0.39999999999999991 },
1403   { -4.0169860814274459e+32, 50, 20,
1404           0.50000000000000000 },
1405   { 4.0860128756807846e+32, 50, 20,
1406           0.60000000000000009 },
1407   { 8.6022521164717112e+32, 50, 20,
1408           0.69999999999999996 },
1409   { 1.0622676657892052e+33, 50, 20,
1410           0.80000000000000004 },
1411   { 1.6630925158645483e+33, 50, 20,
1412           0.89999999999999991 },
1413   { 0.0000000000000000, 50, 20,
1414           1.0000000000000000 },
1415 };
1416 const double toler027 = 2.5000000000000020e-13;
1417
1418 // Test data for l=50, m=50.
1419 // max(|f - f_GSL|): 0.0000000000000000
1420 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
1421 const testcase_assoc_legendre<double>
1422 data028[21] =
1423 {
1424   { 0.0000000000000000, 50, 50,
1425           -1.0000000000000000 },
1426   { 2.5366994974431341e+60, 50, 50,
1427           -0.90000000000000002 },
1428   { 2.2028834403101213e+67, 50, 50,
1429           -0.80000000000000004 },
1430   { 1.3325496559566651e+71, 50, 50,
1431           -0.69999999999999996 },
1432   { 3.8898096431781969e+73, 50, 50,
1433           -0.59999999999999998 },
1434   { 2.0509760257037188e+75, 50, 50,
1435           -0.50000000000000000 },
1436   { 3.4866724533443283e+76, 50, 50,
1437           -0.40000000000000002 },
1438   { 2.5790740224150207e+77, 50, 50,
1439           -0.30000000000000004 },
1440   { 9.8222237931680989e+77, 50, 50,
1441           -0.19999999999999996 },
1442   { 2.1198682190366617e+78, 50, 50,
1443           -0.099999999999999978 },
1444   { 2.7253921397507295e+78, 50, 50,
1445           0.0000000000000000 },
1446   { 2.1198682190366617e+78, 50, 50,
1447           0.10000000000000009 },
1448   { 9.8222237931680989e+77, 50, 50,
1449           0.19999999999999996 },
1450   { 2.5790740224150207e+77, 50, 50,
1451           0.30000000000000004 },
1452   { 3.4866724533443283e+76, 50, 50,
1453           0.39999999999999991 },
1454   { 2.0509760257037188e+75, 50, 50,
1455           0.50000000000000000 },
1456   { 3.8898096431781724e+73, 50, 50,
1457           0.60000000000000009 },
1458   { 1.3325496559566651e+71, 50, 50,
1459           0.69999999999999996 },
1460   { 2.2028834403101213e+67, 50, 50,
1461           0.80000000000000004 },
1462   { 2.5366994974431990e+60, 50, 50,
1463           0.89999999999999991 },
1464   { 0.0000000000000000, 50, 50,
1465           1.0000000000000000 },
1466 };
1467 const double toler028 = 2.5000000000000020e-13;
1468
1469 // Test data for l=100, m=0.
1470 // max(|f - f_GSL|): 3.4694469519536142e-16
1471 // max(|f - f_GSL| / |f_GSL|): 6.8214063779431592e-15
1472 const testcase_assoc_legendre<double>
1473 data029[21] =
1474 {
1475   { 1.0000000000000000, 100, 0,
1476           -1.0000000000000000 },
1477   { 0.10226582055871893, 100, 0,
1478           -0.90000000000000002 },
1479   { 0.050861167913584228, 100, 0,
1480           -0.80000000000000004 },
1481   { -0.077132507199778641, 100, 0,
1482           -0.69999999999999996 },
1483   { -0.023747023905133141, 100, 0,
1484           -0.59999999999999998 },
1485   { -0.060518025961861198, 100, 0,
1486           -0.50000000000000000 },
1487   { -0.072258202125684470, 100, 0,
1488           -0.40000000000000002 },
1489   { 0.057127392202801566, 100, 0,
1490           -0.30000000000000004 },
1491   { 0.014681835355659706, 100, 0,
1492           -0.19999999999999996 },
1493   { -0.063895098434750205, 100, 0,
1494           -0.099999999999999978 },
1495   { 0.079589237387178727, 100, 0,
1496           0.0000000000000000 },
1497   { -0.063895098434749761, 100, 0,
1498           0.10000000000000009 },
1499   { 0.014681835355659706, 100, 0,
1500           0.19999999999999996 },
1501   { 0.057127392202801566, 100, 0,
1502           0.30000000000000004 },
1503   { -0.072258202125685025, 100, 0,
1504           0.39999999999999991 },
1505   { -0.060518025961861198, 100, 0,
1506           0.50000000000000000 },
1507   { -0.023747023905134217, 100, 0,
1508           0.60000000000000009 },
1509   { -0.077132507199778641, 100, 0,
1510           0.69999999999999996 },
1511   { 0.050861167913584228, 100, 0,
1512           0.80000000000000004 },
1513   { 0.10226582055871711, 100, 0,
1514           0.89999999999999991 },
1515   { 1.0000000000000000, 100, 0,
1516           1.0000000000000000 },
1517 };
1518 const double toler029 = 5.0000000000000039e-13;
1519
1520 // Test data for l=100, m=1.
1521 // max(|f - f_GSL|): 0.0000000000000000
1522 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
1523 const testcase_assoc_legendre<double>
1524 data030[21] =
1525 {
1526   { -0.0000000000000000, 100, 1,
1527           -1.0000000000000000 },
1528   { 6.5200167187780345, 100, 1,
1529           -0.90000000000000002 },
1530   { 9.0065170007027486, 100, 1,
1531           -0.80000000000000004 },
1532   { -5.4690908541180976, 100, 1,
1533           -0.69999999999999996 },
1534   { -8.6275439170430790, 100, 1,
1535           -0.59999999999999998 },
1536   { -6.0909031663448454, 100, 1,
1537           -0.50000000000000000 },
1538   { 4.1160338699561212, 100, 1,
1539           -0.40000000000000002 },
1540   { 5.8491043010758013, 100, 1,
1541           -0.30000000000000004 },
1542   { -7.9435138723089826, 100, 1,
1543           -0.19999999999999996 },
1544   { 4.7996285823989355, 100, 1,
1545           -0.099999999999999978 },
1546   { 0.0000000000000000, 100, 1,
1547           0.0000000000000000 },
1548   { -4.7996285823990101, 100, 1,
1549           0.10000000000000009 },
1550   { 7.9435138723089826, 100, 1,
1551           0.19999999999999996 },
1552   { -5.8491043010758013, 100, 1,
1553           0.30000000000000004 },
1554   { -4.1160338699560395, 100, 1,
1555           0.39999999999999991 },
1556   { 6.0909031663448454, 100, 1,
1557           0.50000000000000000 },
1558   { 8.6275439170430470, 100, 1,
1559           0.60000000000000009 },
1560   { 5.4690908541180976, 100, 1,
1561           0.69999999999999996 },
1562   { -9.0065170007027486, 100, 1,
1563           0.80000000000000004 },
1564   { -6.5200167187783542, 100, 1,
1565           0.89999999999999991 },
1566   { 0.0000000000000000, 100, 1,
1567           1.0000000000000000 },
1568 };
1569 const double toler030 = 2.5000000000000020e-13;
1570
1571 // Test data for l=100, m=2.
1572 // max(|f - f_GSL|): 0.0000000000000000
1573 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
1574 const testcase_assoc_legendre<double>
1575 data031[21] =
1576 {
1577   { 0.0000000000000000, 100, 2,
1578           -1.0000000000000000 },
1579   { -1005.9604880761002, 100, 2,
1580           -0.90000000000000002 },
1581   { -489.68041725865947, 100, 2,
1582           -0.80000000000000004 },
1583   { 768.31676011669924, 100, 2,
1584           -0.69999999999999996 },
1585   { 226.90362556627937, 100, 2,
1586           -0.59999999999999998 },
1587   { 604.19889304940341, 100, 2,
1588           -0.50000000000000000 },
1589   { 733.40061037838029, 100, 2,
1590           -0.40000000000000002 },
1591   { -573.30774483996390, 100, 2,
1592           -0.30000000000000004 },
1593   { -151.52946305080880, 100, 2,
1594           -0.19999999999999996 },
1595   { 646.30525583587985, 100, 2,
1596           -0.099999999999999978 },
1597   { -803.85129761050518, 100, 2,
1598           0.0000000000000000 },
1599   { 646.30525583587439, 100, 2,
1600           0.10000000000000009 },
1601   { -151.52946305080880, 100, 2,
1602           0.19999999999999996 },
1603   { -573.30774483996390, 100, 2,
1604           0.30000000000000004 },
1605   { 733.40061037838518, 100, 2,
1606           0.39999999999999991 },
1607   { 604.19889304940341, 100, 2,
1608           0.50000000000000000 },
1609   { 226.90362556629168, 100, 2,
1610           0.60000000000000009 },
1611   { 768.31676011669924, 100, 2,
1612           0.69999999999999996 },
1613   { -489.68041725865947, 100, 2,
1614           0.80000000000000004 },
1615   { -1005.9604880760779, 100, 2,
1616           0.89999999999999991 },
1617   { 0.0000000000000000, 100, 2,
1618           1.0000000000000000 },
1619 };
1620 const double toler031 = 2.5000000000000020e-13;
1621
1622 // Test data for l=100, m=5.
1623 // max(|f - f_GSL|): 0.0000000000000000
1624 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
1625 const testcase_assoc_legendre<double>
1626 data032[21] =
1627 {
1628   { 0.0000000000000000, 100, 5,
1629           -1.0000000000000000 },
1630   { 900551126.09653807, 100, 5,
1631           -0.90000000000000002 },
1632   { 988567431.55756140, 100, 5,
1633           -0.80000000000000004 },
1634   { -645646451.90344620, 100, 5,
1635           -0.69999999999999996 },
1636   { -897114585.29920685, 100, 5,
1637           -0.59999999999999998 },
1638   { -661710744.42483854, 100, 5,
1639           -0.50000000000000000 },
1640   { 380163158.51425636, 100, 5,
1641           -0.40000000000000002 },
1642   { 617391071.36632574, 100, 5,
1643           -0.30000000000000004 },
1644   { -805288801.85509109, 100, 5,
1645           -0.19999999999999996 },
1646   { 481041740.16728652, 100, 5,
1647           -0.099999999999999978 },
1648   { 0.0000000000000000, 100, 5,
1649           0.0000000000000000 },
1650   { -481041740.16729391, 100, 5,
1651           0.10000000000000009 },
1652   { 805288801.85509109, 100, 5,
1653           0.19999999999999996 },
1654   { -617391071.36632574, 100, 5,
1655           0.30000000000000004 },
1656   { -380163158.51424754, 100, 5,
1657           0.39999999999999991 },
1658   { 661710744.42483854, 100, 5,
1659           0.50000000000000000 },
1660   { 897114585.29920483, 100, 5,
1661           0.60000000000000009 },
1662   { 645646451.90344620, 100, 5,
1663           0.69999999999999996 },
1664   { -988567431.55756140, 100, 5,
1665           0.80000000000000004 },
1666   { -900551126.09655857, 100, 5,
1667           0.89999999999999991 },
1668   { 0.0000000000000000, 100, 5,
1669           1.0000000000000000 },
1670 };
1671 const double toler032 = 2.5000000000000020e-13;
1672
1673 // Test data for l=100, m=10.
1674 // max(|f - f_GSL|): 0.0000000000000000
1675 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
1676 const testcase_assoc_legendre<double>
1677 data033[21] =
1678 {
1679   { 0.0000000000000000, 100, 10,
1680           -1.0000000000000000 },
1681   { 2.5643395957658602e+17, 100, 10,
1682           -0.90000000000000002 },
1683   { 1.5778673545673485e+18, 100, 10,
1684           -0.80000000000000004 },
1685   { 4.4355048487496801e+18, 100, 10,
1686           -0.69999999999999996 },
1687   { -9.5936111659124288e+17, 100, 10,
1688           -0.59999999999999998 },
1689   { 4.2387123021963438e+18, 100, 10,
1690           -0.50000000000000000 },
1691   { 8.2370834618426542e+18, 100, 10,
1692           -0.40000000000000002 },
1693   { -4.9089358388052941e+18, 100, 10,
1694           -0.30000000000000004 },
1695   { -2.3468810358091274e+18, 100, 10,
1696           -0.19999999999999996 },
1697   { 6.8627855225034568e+18, 100, 10,
1698           -0.099999999999999978 },
1699   { -8.2494597181670380e+18, 100, 10,
1700           0.0000000000000000 },
1701   { 6.8627855225034056e+18, 100, 10,
1702           0.10000000000000009 },
1703   { -2.3468810358091274e+18, 100, 10,
1704           0.19999999999999996 },
1705   { -4.9089358388052941e+18, 100, 10,
1706           0.30000000000000004 },
1707   { 8.2370834618426767e+18, 100, 10,
1708           0.39999999999999991 },
1709   { 4.2387123021963438e+18, 100, 10,
1710           0.50000000000000000 },
1711   { -9.5936111659112640e+17, 100, 10,
1712           0.60000000000000009 },
1713   { 4.4355048487496801e+18, 100, 10,
1714           0.69999999999999996 },
1715   { 1.5778673545673485e+18, 100, 10,
1716           0.80000000000000004 },
1717   { 2.5643395957697341e+17, 100, 10,
1718           0.89999999999999991 },
1719   { 0.0000000000000000, 100, 10,
1720           1.0000000000000000 },
1721 };
1722 const double toler033 = 2.5000000000000020e-13;
1723
1724 // Test data for l=100, m=20.
1725 // max(|f - f_GSL|): 0.0000000000000000
1726 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
1727 const testcase_assoc_legendre<double>
1728 data034[21] =
1729 {
1730   { 0.0000000000000000, 100, 20,
1731           -1.0000000000000000 },
1732   { 7.1604344878780134e+37, 100, 20,
1733           -0.90000000000000002 },
1734   { -8.3963895116962231e+38, 100, 20,
1735           -0.80000000000000004 },
1736   { 7.9022236853110145e+38, 100, 20,
1737           -0.69999999999999996 },
1738   { 8.2680005574121013e+38, 100, 20,
1739           -0.59999999999999998 },
1740   { 3.0750497039999552e+38, 100, 20,
1741           -0.50000000000000000 },
1742   { -7.6120586043843889e+38, 100, 20,
1743           -0.40000000000000002 },
1744   { 1.1474496891901797e+38, 100, 20,
1745           -0.30000000000000004 },
1746   { 4.3966251307444241e+38, 100, 20,
1747           -0.19999999999999996 },
1748   { -7.0503266451702591e+38, 100, 20,
1749           -0.099999999999999978 },
1750   { 7.7727439836159581e+38, 100, 20,
1751           0.0000000000000000 },
1752   { -7.0503266451702213e+38, 100, 20,
1753           0.10000000000000009 },
1754   { 4.3966251307444241e+38, 100, 20,
1755           0.19999999999999996 },
1756   { 1.1474496891901797e+38, 100, 20,
1757           0.30000000000000004 },
1758   { -7.6120586043843556e+38, 100, 20,
1759           0.39999999999999991 },
1760   { 3.0750497039999552e+38, 100, 20,
1761           0.50000000000000000 },
1762   { 8.2680005574120394e+38, 100, 20,
1763           0.60000000000000009 },
1764   { 7.9022236853110145e+38, 100, 20,
1765           0.69999999999999996 },
1766   { -8.3963895116962231e+38, 100, 20,
1767           0.80000000000000004 },
1768   { 7.1604344878812652e+37, 100, 20,
1769           0.89999999999999991 },
1770   { 0.0000000000000000, 100, 20,
1771           1.0000000000000000 },
1772 };
1773 const double toler034 = 2.5000000000000020e-13;
1774
1775 // Test data for l=100, m=50.
1776 // max(|f - f_GSL|): 0.0000000000000000
1777 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
1778 const testcase_assoc_legendre<double>
1779 data035[21] =
1780 {
1781   { 0.0000000000000000, 100, 50,
1782           -1.0000000000000000 },
1783   { 9.3231278516893716e+96, 100, 50,
1784           -0.90000000000000002 },
1785   { -1.1029797977454281e+98, 100, 50,
1786           -0.80000000000000004 },
1787   { 1.8089333903465606e+97, 100, 50,
1788           -0.69999999999999996 },
1789   { 5.9364045925669405e+97, 100, 50,
1790           -0.59999999999999998 },
1791   { -8.2252620339727118e+97, 100, 50,
1792           -0.50000000000000000 },
1793   { 7.1431385093739863e+97, 100, 50,
1794           -0.40000000000000002 },
1795   { -3.3520602067479344e+97, 100, 50,
1796           -0.30000000000000004 },
1797   { -2.7791149588121382e+97, 100, 50,
1798           -0.19999999999999996 },
1799   { 9.0119338550180417e+97, 100, 50,
1800           -0.099999999999999978 },
1801   { -1.1712145031578381e+98, 100, 50,
1802           0.0000000000000000 },
1803   { 9.0119338550181207e+97, 100, 50,
1804           0.10000000000000009 },
1805   { -2.7791149588121382e+97, 100, 50,
1806           0.19999999999999996 },
1807   { -3.3520602067479344e+97, 100, 50,
1808           0.30000000000000004 },
1809   { 7.1431385093740728e+97, 100, 50,
1810           0.39999999999999991 },
1811   { -8.2252620339727118e+97, 100, 50,
1812           0.50000000000000000 },
1813   { 5.9364045925668024e+97, 100, 50,
1814           0.60000000000000009 },
1815   { 1.8089333903465606e+97, 100, 50,
1816           0.69999999999999996 },
1817   { -1.1029797977454281e+98, 100, 50,
1818           0.80000000000000004 },
1819   { 9.3231278516894968e+96, 100, 50,
1820           0.89999999999999991 },
1821   { 0.0000000000000000, 100, 50,
1822           1.0000000000000000 },
1823 };
1824 const double toler035 = 2.5000000000000020e-13;
1825
1826 // Test data for l=100, m=100.
1827 // max(|f - f_GSL|): 0.0000000000000000
1828 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
1829 const testcase_assoc_legendre<double>
1830 data036[21] =
1831 {
1832   { 0.0000000000000000, 100, 100,
1833           -1.0000000000000000 },
1834   { 5.7751792255758316e+150, 100, 100,
1835           -0.90000000000000002 },
1836   { 4.3552236041585515e+164, 100, 100,
1837           -0.80000000000000004 },
1838   { 1.5936546850595123e+172, 100, 100,
1839           -0.69999999999999996 },
1840   { 1.3579510590289176e+177, 100, 100,
1841           -0.59999999999999998 },
1842   { 3.7752749682889513e+180, 100, 100,
1843           -0.50000000000000000 },
1844   { 1.0910627330458913e+183, 100, 100,
1845           -0.40000000000000002 },
1846   { 5.9697347526822483e+184, 100, 100,
1847           -0.30000000000000004 },
1848   { 8.6585879147526714e+185, 100, 100,
1849           -0.19999999999999996 },
1850   { 4.0331571908057011e+186, 100, 100,
1851           -0.099999999999999978 },
1852   { 6.6663086700729543e+186, 100, 100,
1853           0.0000000000000000 },
1854   { 4.0331571908057011e+186, 100, 100,
1855           0.10000000000000009 },
1856   { 8.6585879147526714e+185, 100, 100,
1857           0.19999999999999996 },
1858   { 5.9697347526822483e+184, 100, 100,
1859           0.30000000000000004 },
1860   { 1.0910627330458913e+183, 100, 100,
1861           0.39999999999999991 },
1862   { 3.7752749682889513e+180, 100, 100,
1863           0.50000000000000000 },
1864   { 1.3579510590289000e+177, 100, 100,
1865           0.60000000000000009 },
1866   { 1.5936546850595123e+172, 100, 100,
1867           0.69999999999999996 },
1868   { 4.3552236041585515e+164, 100, 100,
1869           0.80000000000000004 },
1870   { 5.7751792255761289e+150, 100, 100,
1871           0.89999999999999991 },
1872   { 0.0000000000000000, 100, 100,
1873           1.0000000000000000 },
1874 };
1875 const double toler036 = 2.5000000000000020e-13;
1876
1877 template<typename Tp, unsigned int Num>
1878   void
1879   test(const testcase_assoc_legendre<Tp> (&data)[Num], Tp toler)
1880   {
1881     bool test __attribute__((unused)) = true;
1882     const Tp eps = std::numeric_limits<Tp>::epsilon();
1883     Tp max_abs_diff = -Tp(1);
1884     Tp max_abs_frac = -Tp(1);
1885     unsigned int num_datum = Num;
1886     for (unsigned int i = 0; i < num_datum; ++i)
1887          {
1888         const Tp f = std::assoc_legendre(data[i].l, data[i].m,
1889                      data[i].x);
1890         const Tp f0 = data[i].f0;
1891         const Tp diff = f - f0;
1892         if (std::abs(diff) > max_abs_diff)
1893           max_abs_diff = std::abs(diff);
1894         if (std::abs(f0) > Tp(10) * eps
1895          && std::abs(f) > Tp(10) * eps)
1896           {
1897             const Tp frac = diff / f0;
1898             if (std::abs(frac) > max_abs_frac)
1899               max_abs_frac = std::abs(frac);
1900           }
1901       }
1902     VERIFY(max_abs_frac < toler);
1903   }
1904
1905 int
1906 main()
1907 {
1908   test(data001, toler001);
1909   test(data002, toler002);
1910   test(data003, toler003);
1911   test(data004, toler004);
1912   test(data005, toler005);
1913   test(data006, toler006);
1914   test(data007, toler007);
1915   test(data008, toler008);
1916   test(data009, toler009);
1917   test(data010, toler010);
1918   test(data011, toler011);
1919   test(data012, toler012);
1920   test(data013, toler013);
1921   test(data014, toler014);
1922   test(data015, toler015);
1923   test(data016, toler016);
1924   test(data017, toler017);
1925   test(data018, toler018);
1926   test(data019, toler019);
1927   test(data020, toler020);
1928   test(data021, toler021);
1929   test(data022, toler022);
1930   test(data023, toler023);
1931   test(data024, toler024);
1932   test(data025, toler025);
1933   test(data026, toler026);
1934   test(data027, toler027);
1935   test(data028, toler028);
1936   test(data029, toler029);
1937   test(data030, toler030);
1938   test(data031, toler031);
1939   test(data032, toler032);
1940   test(data033, toler033);
1941   test(data034, toler034);
1942   test(data035, toler035);
1943   test(data036, toler036);
1944   return 0;
1945 }