test_legendre.c

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  sa = 0;
  gsl_sf_legendre_Plm_deriv_array(100, 2, 0.999, L, DL);
  TEST_SF_VAL(sa, L[0],   +0.0,  0.00599700000000000000, TEST_TOL1);
  TEST_SF_VAL(sa, L[1],   +0.0,  0.02995501500000000000, TEST_TOL1 );
  TEST_SF_VAL(sa, DL[0],  +0.0,  -5.9940000000000000000, TEST_TOL1);
  TEST_SF_VAL(sa, DL[1],  +0.0,  -29.910045000000000000, TEST_TOL1 );
  TEST_SF_VAL(sa, DL[2],  +0.0,  -89.490629790000000000, TEST_TOL1 );
  TEST_SF_VAL(sa, DL[10], +0.0,  -5703.9461633355291972, TEST_TOL1 );
  TEST_SF_VAL(sa, DL[95], +0.0,  6.4518473603456858414E+06, TEST_TOL3);
  gsl_test(sa, "gsl_sf_legendre_Plm_deriv_array(100, 2, 0.999)");
  s += sa;

  sa = 0;
  gsl_sf_legendre_Plm_deriv_array(100, 2, 1.0 - 1.0e-15, L, DL);
  TEST_SF_VAL(sa, DL[0],  +0.0,  -5.9999999999999940000, TEST_TOL1);
  TEST_SF_VAL(sa, DL[1],  +0.0,  -29.999999999999910000, TEST_TOL1 );
  TEST_SF_VAL(sa, DL[2],  +0.0,  -89.999999999999490000, TEST_TOL1 );
  TEST_SF_VAL(sa, DL[10], +0.0,  -6005.9999999996936940, TEST_TOL1 );
  TEST_SF_VAL(sa, DL[95], +0.0,  -2.2586255999928454270e+07, TEST_TOL3);
  gsl_test(sa, "gsl_sf_legendre_Plm_deriv_array(100, 2, 1.0 - 1.0e-15)");
  s += sa;

  sa = 0;
  gsl_sf_legendre_Plm_deriv_array(100, 2, -1.0 + 1.0e-15, L, DL);
  TEST_SF_VAL(sa, DL[0],  +0.0,   5.9999999999999940000, TEST_TOL1);
  TEST_SF_VAL(sa, DL[1],  +0.0,  -29.999999999999910000, TEST_TOL1 );
  TEST_SF_VAL(sa, DL[95], +0.0,  -2.2586255999928454270e+07, TEST_TOL3);
  gsl_test(sa, "gsl_sf_legendre_Plm_deriv_array(100, 2, -1.0 + 1.0e-15)");
  s += sa;

  sa = 0;
  gsl_sf_legendre_Plm_deriv_array(100, 5, 0.999, L, DL);
  TEST_SF_VAL(sa, DL[0],  +0.0,  0.42187762481054616565, TEST_TOL1);
  TEST_SF_VAL(sa, DL[1],  +0.0,  4.6341560284340909936, TEST_TOL1 );
  TEST_SF_VAL(sa, DL[2],  +0.0,  27.759505566959219127, TEST_TOL1 );
  TEST_SF_VAL(sa, DL[10], +0.0,  76051.795860179545484, TEST_TOL1 );
  TEST_SF_VAL(sa, DL[95], +0.0,  3.0344503083851936814e+12, TEST_TOL3);
  gsl_test(sa, "gsl_sf_legendre_Plm_deriv_array(100, 5, 0.999)");
  s += sa;

  TEST_SF(s, gsl_sf_legendre_sphPlm_e, (10, 0, -0.5, &r), -0.24332702369300133776, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_legendre_sphPlm_e, (10, 0, 0.5, &r), -0.24332702369300133776, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_legendre_sphPlm_e, (10, 0, 0.999, &r), 1.2225754122797385990, TEST_TOL1, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_legendre_sphPlm_e, (10, 5, -0.5, &r),    -0.3725739049803293972,     TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_legendre_sphPlm_e, (10, 5, 1.0e-08, &r), -3.1377233589376792243e-08, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_legendre_sphPlm_e, (10, 5, 0.5, &r),      0.3725739049803293972,     TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_legendre_sphPlm_e, (10, 5, 0.999, &r),   -6.236870674727370094e-06,  TEST_TOL2, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_legendre_sphPlm_e, (10, 10, -0.5, &r), 0.12876871185785724117, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_legendre_sphPlm_e, (10, 10, 0.5, &r), 0.12876871185785724117,  TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_legendre_sphPlm_e, (10, 10, 0.999, &r), 1.7320802307583118647e-14, TEST_TOL2, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_legendre_sphPlm_e, (200, 1, -0.5, &r),   0.3302975570099492931, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_legendre_sphPlm_e, (200, 1, 0.5, &r),   -0.3302975570099492931, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_legendre_sphPlm_e, (200, 1, 0.999, &r), -1.4069792055546256912, TEST_TOL2, GSL_SUCCESS);

  sa = 0;
  gsl_sf_legendre_sphPlm_array(100, 5, 0.5, L);
  TEST_SF_VAL(sa, L[0],  +0.0, -0.22609703187800460722, TEST_TOL1);
  TEST_SF_VAL(sa, L[10], +0.0,  0.07452710323813558940, TEST_TOL1);
  TEST_SF_VAL(sa, L[95], +0.0,  0.25865355990880161717, TEST_TOL1);
  gsl_test(sa, "gsl_sf_legendre_sphPlm_array(100, 5, 0.5)");
  s += sa;

  sa = 0;
  gsl_sf_legendre_sphPlm_array(100, 2, 1.0 - 1.0/1125899906842624.0, L);
  TEST_SF_VAL(sa, L[0],  +0.0, 6.8616082064776657177e-16, TEST_TOL2);
  TEST_SF_VAL(sa, L[10], +0.0, 4.8543150313086787324e-14, TEST_TOL2);
  TEST_SF_VAL(sa, L[95], +0.0, 8.3138984963650838973e-12, TEST_TOL2);
  gsl_test(sa, "gsl_sf_legendre_sphPlm_array(100, 2, 1.0 - 2^(-50))");
  s += sa;

  sa = 0;
  gsl_sf_legendre_sphPlm_array(100, 2, -1.0 + 1.0/1125899906842624.0, L);
  TEST_SF_VAL(sa, L[0],  +0.0,  6.8616082064776657177e-16, TEST_TOL2);
  TEST_SF_VAL(sa, L[95], +0.0, -8.3138984963650838973e-12, TEST_TOL2);
  gsl_test(sa, "gsl_sf_legendre_sphPlm_array(100, 2, -1.0 + 2^(-50))");
  s += sa;

  sa = 0;
  gsl_sf_legendre_sphPlm_deriv_array(100, 0, 0.5, L, DL);
  TEST_SF_VAL(sa, DL[0],  +0.0,  0.0, TEST_TOL1);
  TEST_SF_VAL(sa, DL[10], +0.0, -2.9953934850252897591, TEST_TOL1);
  TEST_SF_VAL(sa, DL[95], +0.0, -36.411811015111761007, TEST_TOL1);
  gsl_test(sa, "gsl_sf_legendre_sphPlm_deriv_array(100, 0, 0.5)");
  s += sa;

  sa = 0;
  gsl_sf_legendre_sphPlm_deriv_array(100, 1, 0.5, L, DL);
  TEST_SF_VAL(sa, DL[0],  +0.0,  0.19947114020071633897, TEST_TOL1);
  TEST_SF_VAL(sa, DL[1],  +0.0, -0.44603102903819277863, TEST_TOL1);
  TEST_SF_VAL(sa, DL[10], +0.0,  1.3658895325030216565, TEST_TOL1);
  TEST_SF_VAL(sa, DL[99], +0.0, -27.925571865639037118, TEST_TOL1);
  gsl_test(sa, "gsl_sf_legendre_sphPlm_deriv_array(100, 1, 0.5)");
  s += sa;

  sa = 0;
  gsl_sf_legendre_sphPlm_deriv_array(100, 1, 1.0 - 1.0/1125899906842624.0, L, DL);
  TEST_SF_VAL(sa, DL[0],  +0.0,  8.1973898803378530946e+06, TEST_TOL1);
  TEST_SF_VAL(sa, DL[1],  +0.0,  1.8329921010504257405e+07, TEST_TOL1);
  TEST_SF_VAL(sa, DL[10], +0.0,  1.8439572562895384115e+08, TEST_TOL1);
  TEST_SF_VAL(sa, DL[99], +0.0,  4.7682463136232210552e+09, TEST_TOL3);
  gsl_test(sa, "gsl_sf_legendre_sphPlm_deriv_array(100, 1, 1.0 - 2^(-50))");
  s += sa;

  sa = 0;
  gsl_sf_legendre_sphPlm_deriv_array(100, 2, 0.5, L, DL);
  TEST_SF_VAL(sa, DL[0],  +0.0, -0.38627420202318958034, TEST_TOL1);
  TEST_SF_VAL(sa, DL[1],  +0.0,  0.25549636910832059085, TEST_TOL1);
  TEST_SF_VAL(sa, DL[2],  +0.0,  1.5053547230039006279, TEST_TOL1);
  TEST_SF_VAL(sa, DL[10], +0.0,  0.73576559668648243477, TEST_TOL1);
  TEST_SF_VAL(sa, DL[98], +0.0, 28.444589950264378407, TEST_TOL1);
  gsl_test(sa, "gsl_sf_legendre_sphPlm_deriv_array(100, 2, 0.5)");
  s += sa;

  sa = 0;
  gsl_sf_legendre_sphPlm_deriv_array(100, 5, 0.5, L, DL);
  TEST_SF_VAL(sa, DL[0],  +0.0,  0.75365677292668202407, TEST_TOL1);
  TEST_SF_VAL(sa, DL[1],  +0.0,  0.54346962777757450534, TEST_TOL1);
  TEST_SF_VAL(sa, DL[2],  +0.0, -0.98309969029001383773, TEST_TOL1);
  TEST_SF_VAL(sa, DL[3],  +0.0, -2.7728270988954534293, TEST_TOL1);
  TEST_SF_VAL(sa, DL[10], +0.0, -5.7407133315443482193, TEST_TOL1);
  TEST_SF_VAL(sa, DL[95], +0.0, -25.893934624747394561, TEST_TOL1);
  gsl_test(sa, "gsl_sf_legendre_sphPlm_deriv_array(100, 5, 0.5)");
  s += sa;
  sa = 0;

  gsl_sf_legendre_sphPlm_deriv_array(100, 5, 1.0 - 1.0/1125899906842624.0, L, DL);
  TEST_SF_VAL(sa, DL[0],  +0.0,  1.7374288379067753301e-22, TEST_TOL1);
  TEST_SF_VAL(sa, DL[1],  +0.0,  6.2643887625426827113e-22, TEST_TOL1);
  TEST_SF_VAL(sa, DL[2],  +0.0,  1.6482697200734667281e-21, TEST_TOL1);
  TEST_SF_VAL(sa, DL[95], +0.0,  3.9890549466071349506e-15, TEST_TOL2);
  gsl_test(sa, "gsl_sf_legendre_sphPlm_deriv_array(100, 5, 1.0 - 2^(-50))");
  s += sa;

  gsl_sf_legendre_sphPlm_deriv_array(100, 5, -1.0 + 1.0/1125899906842624.0, L, DL);
  TEST_SF_VAL(sa, DL[0],  +0.0, -1.7374288379067753301e-22, TEST_TOL1);
  TEST_SF_VAL(sa, DL[1],  +0.0,  6.2643887625426827113e-22, TEST_TOL1);
  TEST_SF_VAL(sa, DL[2],  +0.0, -1.6482697200734667281e-21, TEST_TOL1);
  TEST_SF_VAL(sa, DL[95], +0.0,  3.9890549466071349506e-15, TEST_TOL3);
  gsl_test(sa, "gsl_sf_legendre_sphPlm_deriv_array(100, 5, -1.0 + 2^(-50))");
  s += sa;

  TEST_SF(s, gsl_sf_conicalP_half_e, (0.0, -0.5, &r),   0.8573827581049917129, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_half_e, (0.0,  0.5, &r),   0.8573827581049917129, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_half_e, (0.0,  2.0, &r),   0.6062611623284649811, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_half_e, (0.0,  100.0, &r), 0.07979045091636735635, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_conicalP_half_e, (10.0, -0.5, &r),    5.345484922591867188e+08, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_half_e, (10.0,  0.5, &r),    15137.910380385258370, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_half_e, (10.0,  2.0, &r),    0.4992680691891618544, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_half_e, (10.0,  100.0, &r), -0.07272008163718195685, TEST_TOL2, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_conicalP_half_e, (200.0, -1.0e-3, &r),  1.3347639529084185010e+136, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_half_e, (200.0,  1.0e-8, &r),  1.0928098010940058507e+136, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_half_e, (200.0,  0.5, &r),     3.895546021611205442e+90,   TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_half_e, (200.0,  10.0, &r),   -0.04308567180833581268,     TEST_TOL3, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_half_e, (200.0,  100.0, &r),  -0.04694669186576399194,     TEST_TOL3, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_half_e, (200.0,  1000.0, &r),  0.023698140704121273277,    TEST_TOL3, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_half_e, (200.0,  1.0e+8, &r), -0.00006790983312124277891,  TEST_TOL3, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_conicalP_half_e, (1.0e+8,  1.1, &r),   1.1599311133054742944,  TEST_SQRT_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_half_e, (1.0e+8,  100.0, &r), 0.07971967557381557875, TEST_SQRT_TOL0, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_conicalP_mhalf_e, (0.0, -0.5, &r),  1.7956982494514644808, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_mhalf_e, (0.0,  0.5, &r),  0.8978491247257322404, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_mhalf_e, (0.0,  2.0, &r),  0.7984204253272901551, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_mhalf_e, (0.0,  100.0, &r),  0.4227531369388072584, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_conicalP_mhalf_e, (10.0, -0.5, &r),  5.345484922591867181e+07, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_mhalf_e, (10.0,  0.5, &r),  1513.7910356104985334, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_mhalf_e, (10.0,  2.0, &r),  0.03439243987215615642, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_mhalf_e, (10.0,  100.0, &r),  0.003283756665952609624, TEST_TOL2, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_conicalP_mhalf_e, (200.0, -0.5, &r),  1.7699538115312304280e+179, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_mhalf_e, (200.0,  1.0e-8, &r),  5.464049005470029253e+133, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_mhalf_e, (200.0,  0.5, &r),  1.9477730108056027211e+88, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_mhalf_e, (200.0,  10.0, &r),  0.0012462575917716355362, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_mhalf_e, (200.0,  100.0, &r),  -0.0003225881344802625149, TEST_TOL2, GSL_SUCCESS);