test_sf.c

多个常用的特殊函数的例子

  sa += ( test_sf_frac_diff( sn, 0.8187707145344889190 ) > TEST_TOL0 );
  sa += ( test_sf_frac_diff( cn, 0.5741206467465548795 ) > TEST_TOL0 );
  sa += ( test_sf_frac_diff( dn, 0.8938033089590823040 ) > TEST_TOL0 );
  gsl_test(sa, "  gsl_sf_elljac_e(1.0|0.3)");
  s += sa;

  u = 1.0;
  m = 0.6;
  sa = 0;
  stat_ej = gsl_sf_elljac_e(u, m, &sn, &cn, &dn);
  sa += ( test_sf_frac_diff( sn, 0.7949388393365780943 ) > TEST_TOL0 );
  sa += ( test_sf_frac_diff( cn, 0.6066895760718277578 ) > TEST_TOL0 );
  sa += ( test_sf_frac_diff( dn, 0.7879361300438814425 ) > TEST_TOL0 );
  gsl_test(sa, "  gsl_sf_elljac_e(1.0|0.6)");
  s += sa;

  u = 3.0;
  m = 0.6;
  sa = 0;
  stat_ej = gsl_sf_elljac_e(u, m, &sn, &cn, &dn);
  sa += ( test_sf_frac_diff( sn,  0.7432676860864044186 ) > TEST_TOL0 );
  sa += ( test_sf_frac_diff( cn, -0.6689941306317733154 ) > TEST_TOL0 );
  sa += ( test_sf_frac_diff( dn,  0.8176379933025723259 ) > TEST_TOL0 );
  gsl_test(sa, "  gsl_sf_elljac_e(3.0|0.6)");
  s += sa;

  u = 2.0;
  m = 0.999999;
  sa = 0;
  stat_ej = gsl_sf_elljac_e(u, m, &sn, &cn, &dn);
  sa += ( test_sf_frac_diff( sn, 0.96402778575700186570 ) > TEST_TOL1 );
  sa += ( test_sf_frac_diff( cn, 0.26580148285600686381 ) > TEST_TOL1 );
  sa += ( test_sf_frac_diff( dn, 0.26580323105264131136 ) > TEST_TOL1 );
  gsl_test(sa, "  gsl_sf_elljac_e(2.0|0.999999)");
  s += sa;

  /* test supplied by Ivan Panchenko */
  u = 1.69695970624443;
  m = 0.270378013104138;
  sa = 0;
  stat_ej = gsl_sf_elljac_e(u, m, &sn, &cn, &dn);
  sa += ( test_sf_frac_diff( sn, 1.0 ) > TEST_TOL0 );
  sa += ( fabs(cn) > TEST_TOL1 );
  sa += ( test_sf_frac_diff( dn, 0.8541791304497336 ) > TEST_TOL1 );
  gsl_test(sa, "  gsl_sf_elljac_e(1.69695970624443|0.270378013104138)");
  s += sa;

  return s;
}


int test_laguerre(void)
{
  gsl_sf_result r;
  int s = 0;

  TEST_SF(s, gsl_sf_laguerre_1_e, (0.5, -1.0, &r), 2.5, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_1_e, (0.5,  1.0, &r), 0.5, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_1_e, (1.0,  1.0, &r), 1.0, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_laguerre_2_e, ( 0.5, -1.0, &r), 4.875,  TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_2_e, ( 0.5,  1.0, &r), -0.125, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_2_e, ( 1.0,  1.0, &r),  0.5, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_2_e, (-1.0,  1.0, &r), -0.5, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_2_e, (-2.0,  1.0, &r),  0.5, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_2_e, (-3.0,  1.0, &r),  2.5, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_laguerre_3_e, (0.5, -1.0, &r), 8.479166666666666667,    TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_3_e, (0.5,  1.0, &r), -0.6041666666666666667,  TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_3_e, (1.0,  1.0, &r), -0.16666666666666666667, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_3_e, ( 2.0,  1.0, &r), 2.3333333333333333333,  TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_3_e, (-2.0,  1.0, &r), 1.0/3.0,  TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_3_e, (-3.0,  1.0, &r), -1.0/6.0, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_3_e, (-4.0,  1.0, &r), -8.0/3.0, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_laguerre_n_e, (1, 0.5, 1.0, &r), 0.5, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_n_e, (2, 1.0, 1.0, &r), 0.5, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_n_e, (3, 2.0, 1.0, &r), 2.3333333333333333333,   TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_n_e, (4, 2.0, 0.5, &r), 6.752604166666666667,    TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_n_e, (90, 2.0,  0.5, &r), -48.79047157201507897, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_n_e, (90, 2.0, -100.0, &r), 2.5295879275042410902e+63, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_n_e, (90, 2.0,  100.0, &r), -2.0929042259546928670e+20, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_n_e, (100, 2.0, -0.5, &r), 2.2521795545919391405e+07,  TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_n_e, (100, 2.0,  0.5, &r), -28.764832945909097418,     TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_n_e, (1000, 2.0, -0.5, &r), 2.4399915170947549589e+21, TEST_TOL3, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_n_e, (1000, 2.0,  0.5, &r), -306.77440254315317525,    TEST_TOL2, GSL_SUCCESS); /**/
  TEST_SF(s, gsl_sf_laguerre_n_e, (100000, 2.0, 1.0, &r), 5107.73491348319,         TEST_TOL4, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_laguerre_n_e, (1, -2.0, 1.0, &r),  -2.0,     TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_n_e, (2, -2.0, 1.0, &r),   0.5,     TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_n_e, (3, -2.0, 1.0, &r),   1.0/3.0, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_n_e, (10, -2.0, 1.0, &r), -0.04654954805996472663,   TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_n_e, (10, -5.0, 1.0, &r), -0.0031385030864197530864, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_n_e, (10, -9.0, 1.0, &r), -2.480158730158730159e-06, TEST_TOL5, GSL_SUCCESS);  
  TEST_SF(s, gsl_sf_laguerre_n_e, (10, -11.0,  1.0, &r), 2.7182818011463844797,    TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_n_e, (10, -11.0, -1.0, &r), 0.3678794642857142857,    TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_n_e, (100, -2.0,  1.0, &r),  -0.0027339992019526273866,  TEST_SQRT_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_n_e, (100, -2.0, -1.0, &r),   229923.09193402028290,     TEST_TOL5, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_n_e, (100, -10.0,  1.0, &r),  3.25966665871244092e-11,   TEST_TOL6, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_n_e, (100, -10.0, -1.0, &r),  0.00016484365618205810025, TEST_TOL6, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_n_e, (100, -20.0, 1.0, &r),  5.09567630343671251e-21,  TEST_TOL3, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_n_e, (100, -30.0, 1.0, &r),  3.46063150272466192e-34,  TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_n_e, (100, -50.0,  1.0, &r),  1.20981872933162889e-65,  TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_n_e, (100, -50.0, -1.0, &r),  8.60763477742332922e-65,  TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_n_e, (100, -50.5,  1.0, &r),  4.84021010426688393e-31,  TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_n_e, (100, -50.5, -1.0, &r),  8.49861345212160618e-33,  TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_n_e, (100, -101.0,  1.0, &r), 2.7182818284590452354,    TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_n_e, (100, -101.0, -1.0, &r), 0.3678794411714423216,    TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_n_e, (100, -102.0,  1.0, &r), 271.8281828459045235,    TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_n_e, (100, -102.0, -1.0, &r), 37.52370299948711680,    TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_n_e, (100, -110.0,  1.0, &r), 1.0666955248998831554e+13, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_n_e, (100, -110.0, -1.0, &r), 1.7028306108058225871e+12, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_n_e, (100, -200.0,  1.0, &r), 7.47851889721356628e+58,  TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_n_e, (100, -200.0, -1.0, &r), 2.73740299754732273e+58,  TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_n_e, (100, -50.0,  10.0, &r), 4.504712811317745591e-21,  TEST_SQRT_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_laguerre_n_e, (100, -50.0, -10.0, &r), 1.475165520610679937e-11,  TEST_TOL1, GSL_SUCCESS);


  return s;
}


int test_lambert(void)
{
  gsl_sf_result r;
  int s = 0;

  TEST_SF(s, gsl_sf_lambert_W0_e, (0.0, &r),  0.0,  TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_lambert_W0_e, (1.0, &r),  0.567143290409783872999969,  TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_lambert_W0_e, (2.0, &r),  0.852605502013725491346472,  TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_lambert_W0_e, (20.0, &r), 2.205003278024059970493066,  TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_lambert_W0_e, (1000.0, &r), 5.24960285240159622712606,  TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_lambert_W0_e, (1.0e+6, &r), 11.38335808614005262200016,  TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_lambert_W0_e, (1.0e+12, &r), 24.43500440493491313826305,  TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_lambert_W0_e, (1.0e+308, &r), 702.641362034106812081125,  TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_lambert_W0_e, (-1.0/M_E - GSL_DBL_EPSILON, &r), -1.0,  TEST_TOL0, GSL_EDOM);
  TEST_SF(s, gsl_sf_lambert_W0_e, (-1.0/M_E + 1.0/(1024.0*1024.0*1024.0), &r), -0.999928845560308370714970, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_lambert_W0_e, (-1.0/M_E + 1.0/(1024.0*1024.0), &r), -0.997724730359774141620354, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_lambert_W0_e, (-1.0/M_E + 1.0/512.0, &r), -0.900335676696088773044678, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_lambert_W0_e, (-1.0/M_E + 0.25, &r), -0.1349044682661213545487599, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_lambert_Wm1_e, (0.0, &r),  0.0,  TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_lambert_Wm1_e, (1.0, &r),  0.567143290409783872999969,  TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_lambert_Wm1_e, (2.0, &r),  0.852605502013725491346472,  TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_lambert_Wm1_e, (20.0, &r), 2.205003278024059970493066,  TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_lambert_Wm1_e, (-1.0/M_E - GSL_DBL_EPSILON, &r), -1.0,  TEST_TOL0, GSL_EDOM);
  TEST_SF(s, gsl_sf_lambert_Wm1_e, (-1.0/M_E + 1.0/(1024.0*1024.0*1024.0), &r), -1.000071157815154608049055, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_lambert_Wm1_e, (-1.0/M_E + 1.0/(1024.0*1024.0), &r), -1.002278726118593023934693, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_lambert_Wm1_e, (-1.0/M_E + 1.0/512.0, &r), -1.106761200865743124599130, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_lambert_Wm1_e, (-1.0/M_E + 1.0/64.0, &r), -1.324240940341812125489772, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_lambert_Wm1_e, (-1.0/M_E + 0.25, &r), -3.345798131120112, TEST_TOL1, GSL_SUCCESS);

  return s;
}


int test_log(void)
{
  gsl_sf_result r;
  gsl_sf_result r1, r2;
  int s = 0;

  TEST_SF(s, gsl_sf_log_e, (0.1, &r), -2.3025850929940456840,  TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_log_e, (1.1, &r), 0.09531017980432486004,  TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_log_e, (1000.0, &r), 6.907755278982137052, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_log_abs_e, (-0.1, &r), -2.3025850929940456840,  TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_log_abs_e, (-1.1, &r), 0.09531017980432486004,  TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_log_abs_e, (-1000.0, &r), 6.907755278982137052, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_log_abs_e, (0.1, &r), -2.3025850929940456840,  TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_log_abs_e, (1.1, &r), 0.09531017980432486004,  TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_log_abs_e, (1000.0, &r), 6.907755278982137052, TEST_TOL0, GSL_SUCCESS);

  TEST_SF_2(s, gsl_sf_complex_log_e, (1.0, 1.0, &r1, &r2),
            0.3465735902799726547, TEST_TOL0,
	    0.7853981633974483096, TEST_TOL0,
            GSL_SUCCESS);

  TEST_SF_2(s, gsl_sf_complex_log_e, (1.0, -1.0, &r1, &r2),
             0.3465735902799726547, TEST_TOL0,
	    -0.7853981633974483096, TEST_TOL0,
            GSL_SUCCESS);

  TEST_SF_2(s, gsl_sf_complex_log_e, (1.0, 100.0, &r1, &r2),
            4.605220183488258022, TEST_TOL0,
	    1.560796660108231381, TEST_TOL0,
            GSL_SUCCESS);

  TEST_SF_2(s, gsl_sf_complex_log_e, (-1000.0, -1.0, &r1, &r2),
             6.907755778981887052, TEST_TOL0,
	    -3.1405926539231263718, TEST_TOL0,
            GSL_SUCCESS);

  TEST_SF_2(s, gsl_sf_complex_log_e, (-1.0, 0.0, &r1, &r2),
             0.0, TEST_TOL0,
	     3.1415926535897932385, TEST_TOL0,
             GSL_SUCCESS);


  TEST_SF(s,  gsl_sf_log_1plusx_e, (1.0e-10, &r), 9.999999999500000000e-11, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_log_1plusx_e, (1.0e-8, &r), 9.999999950000000333e-09, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_log_1plusx_e, (1.0e-4, &r), 0.00009999500033330833533, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_log_1plusx_e, (0.1, &r), 0.09531017980432486004, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_log_1plusx_e, (0.49, &r), 0.3987761199573677730, TEST_TOL0, GSL_SUCCESS);
  
  TEST_SF(s,  gsl_sf_log_1plusx_e, (-0.49, &r), -0.6733445532637655964, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_log_1plusx_e, (1.0, &r), M_LN2, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_log_1plusx_e, (-0.99, &r), -4.605170185988091368, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_log_1plusx_mx_e, (1.0e-10, &r), -4.999999999666666667e-21, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_log_1plusx_mx_e, (1.0e-8, &r), -4.999999966666666917e-17, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_log_1plusx_mx_e, (1.0e-4, &r), -4.999666691664666833e-09, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_log_1plusx_mx_e, (0.1, &r), -0.004689820195675139956, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_log_1plusx_mx_e, (0.49, &r), -0.09122388004263222704, TEST_TOL0, GSL_SUCCESS);
  
  TEST_SF(s,  gsl_sf_log_1plusx_mx_e, (-0.49, &r), -0.18334455326376559639, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_log_1plusx_mx_e, (1.0, &r), M_LN2-1.0, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_log_1plusx_mx_e, (-0.99, &r), -3.615170185988091368, TEST_TOL0, GSL_SUCCESS);

  return s;
}


int test_pow_int(void)
{
  gsl_sf_result r;
  int status = 0;
  int s = 0;
  
  TEST_SF(s,  gsl_sf_pow_int_e, (2.0, 3, &r), 8.0, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_pow_int_e, (-2.0, 3, &r), -8.0, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_pow_int_e, (2.0, -3, &r), 1.0/8.0, TE