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Add some more functions to the tests.

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jzmaddock
2015-06-29 19:24:38 +01:00
parent 7318fc2663
commit bac9466df0
13 changed files with 1412 additions and 687 deletions
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22
reporting/accuracy/bindings.hpp
View File

@@ -15,6 +15,9 @@
#define TEST_LIBRARY_NAME "<tr1/cmath>"
#define LOG1P_FUNCTION_TO_TEST std::tr1::log1p
#define EXPM1_FUNCTION_TO_TEST std::tr1::log1p
#define CBRT_FUNCTION_TO_TEST std::tr1::cbrt
#define ERF_FUNCTION_TO_TEST std::tr1::erf
#define ERFC_FUNCTION_TO_TEST std::tr1::erfc
@@ -74,6 +77,9 @@ inline long double assoc_legendre_p_binder(int i, int j, long double d)
#ifdef _MSC_VER
#define LOG1P_FUNCTION_TO_TEST ::log1p
#define EXPM1_FUNCTION_TO_TEST ::expm1
#define CBRT_FUNCTION_TO_TEST ::cbrt
#define ERF_FUNCTION_TO_TEST ::erf
#define ERFC_FUNCTION_TO_TEST ::erfc
@@ -87,7 +93,10 @@ inline long double assoc_legendre_p_binder(int i, int j, long double d)
#else
#define CBRT_FUNCTION_TO_TEST ::cbrt
#define LOG1P_FUNCTION_TO_TEST ::log1pl
#define EXPM1_FUNCTION_TO_TEST ::expm1l
#define CBRT_FUNCTION_TO_TEST ::cbrtl
#define ERF_FUNCTION_TO_TEST ::erfl
#define ERFC_FUNCTION_TO_TEST ::erfcl
@@ -293,7 +302,10 @@ inline double legendre_q(unsigned n, double x) { return gsl_sf_legendre_Ql(n, x)
#define TEST_LIBRARY_NAME "boost"
#define CBRT_FUNCTION_TO_TEST boost::cbrt
#define LOG1P_FUNCTION_TO_TEST boost::math::log1p
#define EXPM1_FUNCTION_TO_TEST boost::math::expm1
#define CBRT_FUNCTION_TO_TEST boost::math::cbrt
#define ERF_FUNCTION_TO_TEST boost::math::erf
#define ERFC_FUNCTION_TO_TEST boost::math::erfc
#define ERF_INV_FUNCTION_TO_TEST boost::math::erf_inv
@@ -390,6 +402,12 @@ inline double legendre_q(unsigned n, double x) { return gsl_sf_legendre_Ql(n, x)
#define TRIGAMMA_RATIO_FUNCTION_TO_TEST boost::math::trigamma
#define ZETA_FUNCTION_TO_TEST boost::math::zeta
#define SQRT1PM1_FUNCTION_TO_TEST boost::math::sqrt1pm1
#define POWM1_FUNCTION_TO_TEST boost::math::powm1
#define OWENS_T_FUNCTION_TO_TEST boost::math::owens_t
#define SPHERICAL_HARMONIC_R_FUNCTION_TO_TEST boost::math::spherical_harmonic_r
#define SPHERICAL_HARMONIC_I_FUNCTION_TO_TEST boost::math::spherical_harmonic_i
#endif
#if defined(TYPE_TO_TEST) && !defined(NAME_OF_TYPE_TO_TEST)

660
reporting/accuracy/doc/accuracy_tables.qbk
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@@ -1,32 +1,42 @@
[/Cell Content:]
[template Microsoft_Visual_C_version_12_0_Win32_double_zeta_boost_Zeta_Integer_arguments[] [role blue Max = 6.5[epsilon] (Mean = 2.17[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_zeta_boost_Zeta_Values_close_to_and_less_than_1[] [role blue Max = 0.991[epsilon] (Mean = 0.375[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_zeta_boost_Zeta_Values_close_to_and_greater_than_1[] [role blue Max = 0.994[epsilon] (Mean = 0.421[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_zeta_boost_Zeta_Random_values_less_than_1[] [role blue Max = 7.03[epsilon] (Mean = 2.98[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_zeta_boost_Zeta_Random_values_greater_than_1[] [role blue Max = 0.836[epsilon] (Mean = 0.093[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_trigamma_boost_Mathematica_Data[] [role blue Max = 1[epsilon] (Mean = 0.382[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cos_pi_boost_sin_pi_and_cos_pi_near_integers_and_half_integers[] [role blue Max = 0.996[epsilon] (Mean = 0.298[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_sin_pi_boost_sin_pi_and_cos_pi_near_integers_and_half_integers[] [role blue Max = 0.996[epsilon] (Mean = 0.343[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cos_pi_boost_sin_pi_and_cos_pi[] [role blue Max = 0.996[epsilon] (Mean = 0.281[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_sin_pi_boost_sin_pi_and_cos_pi[] [role blue Max = 0.99[epsilon] (Mean = 0.328[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma_ratio_boost_tgamma_ratios[] [role blue Max = 3.66[epsilon] (Mean = 1.27[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma_delta_ratio_boost_integer_tgamma_ratios_negative_delta_[] [role blue Max = 0.974[epsilon] (Mean = 0.184[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma_delta_ratio_boost_integer_tgamma_ratios[] [role blue Max = 0.968[epsilon] (Mean = 0.386[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma_delta_ratio_boost_tgamma_small_integer_ratios_negative_delta_[] [role blue Max = 2.15[epsilon] (Mean = 0.685[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma_delta_ratio_boost_tgamma_small_integer_ratios[] [role blue Max = 2.74[epsilon] (Mean = 0.736[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma_delta_ratio_boost_tgamma_small_delta_ratios_negative_delta_[] [role blue Max = 8.04[epsilon] (Mean = 1.31[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma_delta_ratio_boost_tgamma_small_delta_ratios[] [role blue Max = 10.1[epsilon] (Mean = 1.25[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_polygamma_boost_Mathematica_Data_Large_orders_and_other_bug_cases[] [role blue Max = 200[epsilon] (Mean = 57.2[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_polygamma_boost_Mathematica_Data_small_arguments[] [role blue Max = 3[epsilon] (Mean = 0.496[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_polygamma_boost_Mathematica_Data_large_negative_arguments[] [role blue Max = 162[epsilon] (Mean = 101[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_polygamma_boost_Mathematica_Data_negative_arguments[] [role blue Max = 497[epsilon] (Mean = 129[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_polygamma_boost_Mathematica_Data_large_arguments[] [role blue Max = 150[epsilon] (Mean = 15.1[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_polygamma_boost_Mathematica_Data[] [role blue Max = 6.34[epsilon] (Mean = 1.53[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_legendre_p_associated__boost_Associated_Legendre_Polynomials_Small_Values[] [role blue Max = 121[epsilon] (Mean = 7.14[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_legendre_q_boost_Legendre_Polynomials_Large_Values[] [role blue Max = 4.6e+003[epsilon] (Mean = 366[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_legendre_p_boost_Legendre_Polynomials_Large_Values[] [role blue Max = 300[epsilon] (Mean = 33.2[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_legendre_q_boost_Legendre_Polynomials_Small_Values[] [role blue Max = 46.4[epsilon] (Mean = 7.32[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_legendre_p_boost_Legendre_Polynomials_Small_Values[] [role blue Max = 211[epsilon] (Mean = 20.4[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_powm1_boost_powm1[][role blue Max = 1.99[epsilon] (Mean = 0.461[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_sqrt1pm1_boost_sqrt1pm1[][role blue Max = 1.36[epsilon] (Mean = 0.44[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_expm1_boost_Random_test_data[][role blue Max = 0.996[epsilon] (Mean = 0.283[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_log1p_boost_Random_test_data[][role blue Max = 0.509[epsilon] (Mean = 0.057[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_expm1__math_h__Random_test_data[](<math.h> = Max = 1.31[epsilon] (Mean = 0.496[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_log1p__math_h__Random_test_data[](<math.h> = Max = 0.509[epsilon] (Mean = 0.057[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_spherical_harmonic_i_boost_Spherical_Harmonics[][role blue Max = 2.27e+004[epsilon] (Mean = 725[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_spherical_harmonic_r_boost_Spherical_Harmonics[][role blue Max = 2.27e+004[epsilon] (Mean = 725[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_boost_math_owens_t_boost_Owens_T_large_and_diverse_values_[][role blue Max = 3.78[epsilon] (Mean = 0.621[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_boost_math_owens_t_boost_Owens_T_medium_small_values_[][role blue Max = 4.37[epsilon] (Mean = 0.973[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_zeta_boost_Zeta_Integer_arguments[][role blue Max = 6.5[epsilon] (Mean = 2.17[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_zeta_boost_Zeta_Values_close_to_and_less_than_1[][role blue Max = 0.991[epsilon] (Mean = 0.375[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_zeta_boost_Zeta_Values_close_to_and_greater_than_1[][role blue Max = 0.994[epsilon] (Mean = 0.421[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_zeta_boost_Zeta_Random_values_less_than_1[][role blue Max = 7.03[epsilon] (Mean = 2.98[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_zeta_boost_Zeta_Random_values_greater_than_1[][role blue Max = 0.836[epsilon] (Mean = 0.093[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_trigamma_boost_Mathematica_Data[][role blue Max = 1[epsilon] (Mean = 0.382[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cos_pi_boost_sin_pi_and_cos_pi_near_integers_and_half_integers[][role blue Max = 0.996[epsilon] (Mean = 0.298[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_sin_pi_boost_sin_pi_and_cos_pi_near_integers_and_half_integers[][role blue Max = 0.996[epsilon] (Mean = 0.343[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cos_pi_boost_sin_pi_and_cos_pi[][role blue Max = 0.996[epsilon] (Mean = 0.281[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_sin_pi_boost_sin_pi_and_cos_pi[][role blue Max = 0.99[epsilon] (Mean = 0.328[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma_ratio_boost_tgamma_ratios[][role blue Max = 3.66[epsilon] (Mean = 1.27[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma_delta_ratio_boost_integer_tgamma_ratios_negative_delta_[][role blue Max = 0.974[epsilon] (Mean = 0.184[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma_delta_ratio_boost_integer_tgamma_ratios[][role blue Max = 0.968[epsilon] (Mean = 0.386[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma_delta_ratio_boost_tgamma_small_integer_ratios_negative_delta_[][role blue Max = 2.15[epsilon] (Mean = 0.685[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma_delta_ratio_boost_tgamma_small_integer_ratios[][role blue Max = 2.74[epsilon] (Mean = 0.736[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma_delta_ratio_boost_tgamma_small_delta_ratios_negative_delta_[][role blue Max = 8.04[epsilon] (Mean = 1.31[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma_delta_ratio_boost_tgamma_small_delta_ratios[][role blue Max = 10.1[epsilon] (Mean = 1.25[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_polygamma_boost_Mathematica_Data_Large_orders_and_other_bug_cases[][role blue Max = 200[epsilon] (Mean = 57.2[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_polygamma_boost_Mathematica_Data_small_arguments[][role blue Max = 3[epsilon] (Mean = 0.496[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_polygamma_boost_Mathematica_Data_large_negative_arguments[][role blue Max = 162[epsilon] (Mean = 101[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_polygamma_boost_Mathematica_Data_negative_arguments[][role blue Max = 497[epsilon] (Mean = 129[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_polygamma_boost_Mathematica_Data_large_arguments[][role blue Max = 150[epsilon] (Mean = 15.1[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_polygamma_boost_Mathematica_Data[][role blue Max = 6.34[epsilon] (Mean = 1.53[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_legendre_p_associated__boost_Associated_Legendre_Polynomials_Small_Values[][role blue Max = 121[epsilon] (Mean = 7.14[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_legendre_q_boost_Legendre_Polynomials_Large_Values[][role blue Max = 4.6e+003[epsilon] (Mean = 366[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_legendre_p_boost_Legendre_Polynomials_Large_Values[][role blue Max = 300[epsilon] (Mean = 33.2[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_legendre_q_boost_Legendre_Polynomials_Small_Values[][role blue Max = 46.4[epsilon] (Mean = 7.32[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_legendre_p_boost_Legendre_Polynomials_Small_Values[][role blue Max = 211[epsilon] (Mean = 20.4[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_jacobi_dn_boost_Jacobi_Elliptic_Large_Phi[][role blue Max = 1.67e+004[epsilon] (Mean = 1e+003[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_jacobi_cn_boost_Jacobi_Elliptic_Large_Phi[][role blue Max = 3.27e+004[epsilon] (Mean = 1.93e+003[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_jacobi_sn_boost_Jacobi_Elliptic_Large_Phi[][role blue Max = 4.36e+004[epsilon] (Mean = 2.54e+003[epsilon])]]
@@ -42,252 +52,302 @@
[template Microsoft_Visual_C_version_12_0_Win32_double_jacobi_dn_boost_Jacobi_Elliptic_Mathworld_Data[][role blue Max = 34.3[epsilon] (Mean = 8.71[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_jacobi_cn_boost_Jacobi_Elliptic_Mathworld_Data[][role blue Max = 45.8[epsilon] (Mean = 11.4[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_jacobi_sn_boost_Jacobi_Elliptic_Mathworld_Data[][role blue Max = 481[epsilon] (Mean = 113[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_gamma_q_inva_boost_Incomplete_gamma_inverses_[] [role blue Max = 5.64[epsilon] (Mean = 1.09[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_gamma_p_inva_boost_Incomplete_gamma_inverses_[] [role blue Max = 3.52[epsilon] (Mean = 0.997[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_gamma_q_inv_boost_incomplete_gamma_inverse_a_z_small_values[] [role blue Max = 451[epsilon] (Mean = 65[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_gamma_p_inv_boost_incomplete_gamma_inverse_a_z_small_values[] [role blue Max = 1.1e+003[epsilon] (Mean = 108[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_gamma_q_inv_boost_incomplete_gamma_inverse_a_z_large_values[] [role blue Max = 0.814[epsilon] (Mean = 0.0856[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_gamma_p_inv_boost_incomplete_gamma_inverse_a_z_large_values[] [role blue Max = 0.924[epsilon] (Mean = 0.118[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_gamma_q_inv_boost_incomplete_gamma_inverse_a_z_medium_values[] [role blue Max = 3.46[epsilon] (Mean = 0.475[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_gamma_p_inv_boost_incomplete_gamma_inverse_a_z_medium_values[] [role blue Max = 1.01[epsilon] (Mean = 0.307[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_gamma_p_boost_tgamma_a_z_integer_and_half_integer_values[] [role blue Max = 13[epsilon] (Mean = 2.93[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_gamma_q_boost_tgamma_a_z_integer_and_half_integer_values[] [role blue Max = 8.48[epsilon] (Mean = 1.42[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma_lower_boost_tgamma_a_z_integer_and_half_integer_values[] [role blue Max = 2.69[epsilon] (Mean = 0.866[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma_incomplete__boost_tgamma_a_z_integer_and_half_integer_values[] [role blue Max = 5.16[epsilon] (Mean = 1.44[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_gamma_p_boost_tgamma_a_z_large_values[] [role blue Max = 244[epsilon] (Mean = 20.2[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_gamma_q_boost_tgamma_a_z_large_values[] [role blue Max = 470[epsilon] (Mean = 31.5[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_gamma_p_boost_tgamma_a_z_small_values[] [role blue Max = 1.54[epsilon] (Mean = 0.439[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_gamma_q_boost_tgamma_a_z_small_values[] [role blue Max = 2.26[epsilon] (Mean = 0.732[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma_lower_boost_tgamma_a_z_small_values[] [role blue Max = 1.57[epsilon] (Mean = 0.527[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma_incomplete__boost_tgamma_a_z_small_values[] [role blue Max = 2.53[epsilon] (Mean = 0.66[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_gamma_p_boost_tgamma_a_z_medium_values[] [role blue Max = 35.1[epsilon] (Mean = 6.97[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_gamma_q_boost_tgamma_a_z_medium_values[] [role blue Max = 23.7[epsilon] (Mean = 4.03[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma_lower_boost_tgamma_a_z_medium_values[] [role blue Max = 5.62[epsilon] (Mean = 1.43[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma_incomplete__boost_tgamma_a_z_medium_values[] [role blue Max = 8.14[epsilon] (Mean = 1.71[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ibetac_inv_boost_Inverse_incomplete_beta[] [role blue Max = 5.53e+003[epsilon] (Mean = 220[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ibeta_inv_boost_Inverse_incomplete_beta[] [role blue Max = 7.08e+003[epsilon] (Mean = 244[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ibetac_boost_Incomplete_Beta_Function_Small_Integer_Values[] [role blue Max = 6.37[epsilon] (Mean = 1.03[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ibeta_boost_Incomplete_Beta_Function_Small_Integer_Values[] [role blue Max = 3.69[epsilon] (Mean = 0.765[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_betac_boost_Incomplete_Beta_Function_Small_Integer_Values[] [role blue Max = 26.7[epsilon] (Mean = 6.67[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_beta_incomplete__boost_Incomplete_Beta_Function_Small_Integer_Values[] [role blue Max = 26.8[epsilon] (Mean = 6.61[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ibetac_boost_Incomplete_Beta_Function_Large_and_Diverse_Values[] [role blue Max = 1.87e+003[epsilon] (Mean = 93.8[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ibeta_boost_Incomplete_Beta_Function_Large_and_Diverse_Values[] [role blue Max = 1.19e+003[epsilon] (Mean = 59.5[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_betac_boost_Incomplete_Beta_Function_Large_and_Diverse_Values[] [role blue Max = 3.72e+003[epsilon] (Mean = 113[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_beta_incomplete__boost_Incomplete_Beta_Function_Large_and_Diverse_Values[] [role blue Max = 635[epsilon] (Mean = 29.5[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ibetac_boost_Incomplete_Beta_Function_Medium_Values[] [role blue Max = 56.2[epsilon] (Mean = 14.1[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ibeta_boost_Incomplete_Beta_Function_Medium_Values[] [role blue Max = 108[epsilon] (Mean = 16.3[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_betac_boost_Incomplete_Beta_Function_Medium_Values[] [role blue Max = 91.3[epsilon] (Mean = 14.8[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_beta_incomplete__boost_Incomplete_Beta_Function_Medium_Values[] [role blue Max = 91.1[epsilon] (Mean = 12.7[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ibetac_boost_Incomplete_Beta_Function_Small_Values[] [role blue Max = 6.56[epsilon] (Mean = 1.88[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ibeta_boost_Incomplete_Beta_Function_Small_Values[] [role blue Max = 9.42[epsilon] (Mean = 2.24[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_betac_boost_Incomplete_Beta_Function_Small_Values[] [role blue Max = 12[epsilon] (Mean = 2.43[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_beta_incomplete__boost_Incomplete_Beta_Function_Small_Values[] [role blue Max = 11.1[epsilon] (Mean = 2.28[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_heuman_lambda_boost_Elliptic_Integral_Heuman_Lambda_Random_Data[] [role blue Max = 2.12[epsilon] (Mean = 0.59[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_heuman_lambda_boost_Elliptic_Integral_Jacobi_Zeta_Mathworld_Data[] [role blue Max = 1.08[epsilon] (Mean = 0.734[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_hermite_boost_Hermite_Polynomials[] [role blue Max = 4.46[epsilon] (Mean = 1.41[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_lgamma__math_h__near_55[] (<math.h> = Max = 249[epsilon] (Mean = 43.1[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma__math_h__near_55[] (<math.h> = Max = 3.87e+004[epsilon] (Mean = 6.71e+003[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_lgamma__math_h__near_10[] (<math.h> = Max = 0.997[epsilon] (Mean = 0.444[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma__math_h__near_10[] (<math.h> = Max = 0.866[epsilon] (Mean = 0.445[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_lgamma__math_h__near_2[] (<math.h> = Max = 0.741[epsilon] (Mean = 0.473[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma__math_h__near_2[] (<math.h> = Max = 0[epsilon] (Mean = 0[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_lgamma__math_h__near_1[] (<math.h> = Max = 0.906[epsilon] (Mean = 0.565[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma__math_h__near_1[] (<math.h> = Max = 1[epsilon] (Mean = 0.4[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_lgamma__math_h__near_0[] (<math.h> = Max = 0.962[epsilon] (Mean = 0.372[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma__math_h__near_0[] (<math.h> = Max = 1[epsilon] (Mean = 0.405[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_lgamma__math_h__factorials[] (<math.h> = Max = 0.958[epsilon] (Mean = 0.38[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma__math_h__factorials[] (<math.h> = Max = 3.17[epsilon] (Mean = 0.928[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma1pm1_boost_tgamma1pm1_dz_[] [role blue Max = 0.982[epsilon] (Mean = 0.399[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_lgamma_boost_near_55[] [role blue Max = 0.821[epsilon] (Mean = 0.419[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma_boost_near_55[] [role blue Max = 1.8[epsilon] (Mean = 0.817[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_lgamma_boost_near_10[] [role blue Max = 4.22[epsilon] (Mean = 1.33[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma_boost_near_10[] [role blue Max = 1.73[epsilon] (Mean = 0.729[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_lgamma_boost_near_2[] [role blue Max = 0.591[epsilon] (Mean = 0.159[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma_boost_near_2[] [role blue Max = 2[epsilon] (Mean = 0.995[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_lgamma_boost_near_1[] [role blue Max = 0.867[epsilon] (Mean = 0.468[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma_boost_near_1[] [role blue Max = 2[epsilon] (Mean = 0.865[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_lgamma_boost_near_0[] [role blue Max = 0.964[epsilon] (Mean = 0.462[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma_boost_near_0[] [role blue Max = 1.96[epsilon] (Mean = 0.684[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_lgamma_boost_factorials[] [role blue Max = 0.914[epsilon] (Mean = 0.167[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma_boost_factorials[] [role blue Max = 1.85[epsilon] (Mean = 0.491[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_expint_Ei__boost_Exponential_Integral_Ei_double_exponent_range[] [role blue Max = 1.7[epsilon] (Mean = 0.66[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_expint_Ei__boost_Exponential_Integral_Ei[] [role blue Max = 1.43[epsilon] (Mean = 0.541[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_expint_En__boost_Exponential_Integral_E1[] [role blue Max = 0.988[epsilon] (Mean = 0.486[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_expint_En__boost_Exponential_Integral_En_small_z_values[] [role blue Max = 2.62[epsilon] (Mean = 0.531[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_expint_En__boost_Exponential_Integral_En[] [role blue Max = 7.16[epsilon] (Mean = 1.85[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_erfc__math_h__Erf_Function_Large_Values[] (<math.h> = Max = 1.84[epsilon] (Mean = 0.331[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_erf__math_h__Erf_Function_Large_Values[] (<math.h> = Max = 0[epsilon] (Mean = 0[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_erfc__math_h__Erf_Function_Medium_Values[] (<math.h> = Max = 2.36[epsilon] (Mean = 0.539[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_erf__math_h__Erf_Function_Medium_Values[] (<math.h> = Max = 1.19[epsilon] (Mean = 0.244[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_erfc__math_h__Erf_Function_Small_Values[] (<math.h> = Max = 0[epsilon] (Mean = 0[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_erf__math_h__Erf_Function_Small_Values[] (<math.h> = Max = 1.57[epsilon] (Mean = 0.317[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_erfc_inv_boost_Inverse_Erfc_Function[] [role blue Max = 1[epsilon] (Mean = 0.491[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_erf_inv_boost_Inverse_Erf_Function[] [role blue Max = 1.09[epsilon] (Mean = 0.502[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_erfc_boost_Erf_Function_Large_Values[] [role blue Max = 1.14[epsilon] (Mean = 0.248[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_erf_boost_Erf_Function_Large_Values[] [role blue Max = 0[epsilon] (Mean = 0[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_erfc_boost_Erf_Function_Medium_Values[] [role blue Max = 1.65[epsilon] (Mean = 0.373[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_erf_boost_Erf_Function_Medium_Values[] [role blue Max = 1[epsilon] (Mean = 0.169[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_erfc_boost_Erf_Function_Small_Values[] [role blue Max = 0[epsilon] (Mean = 0[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_erf_boost_Erf_Function_Small_Values[] [role blue Max = 0.996[epsilon] (Mean = 0.182[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_d_complete__boost_Elliptic_Integral_D_Random_Data[] [role blue Max = 1.27[epsilon] (Mean = 0.355[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_d_complete__boost_Elliptic_Integral_E_Mathworld_Data[] [role blue Max = 0.637[epsilon] (Mean = 0.368[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_d_boost_Elliptic_Integral_D_Random_Data[] [role blue Max = 2.87[epsilon] (Mean = 0.805[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_d_boost_Elliptic_Integral_E_Mathworld_Data[] [role blue Max = 0.862[epsilon] (Mean = 0.457[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_3_complete__boost_Complete_Elliptic_Integral_PI_Random_Data[] [role blue Max = 2.46[epsilon] (Mean = 0.654[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_3_complete__boost_Complete_Elliptic_Integral_PI_Mathworld_Data[] [role blue Max = 0.971[epsilon] (Mean = 0.464[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_3_boost_Elliptic_Integral_PI_Large_Random_Data[] [role blue Max = 2.86[epsilon] (Mean = 0.944[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_3_boost_Elliptic_Integral_PI_Random_Data[] [role blue Max = 9.08[epsilon] (Mean = 0.99[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_3_boost_Elliptic_Integral_PI_Mathworld_Data[] [role blue Max = 565[epsilon] (Mean = 102[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_2_complete__boost_Elliptic_Integral_E_Random_Data[] [role blue Max = 1.71[epsilon] (Mean = 0.553[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_2_complete__boost_Elliptic_Integral_E_Mathworld_Data[] [role blue Max = 1.3[epsilon] (Mean = 0.615[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_2_boost_Elliptic_Integral_E_Random_Data[] [role blue Max = 2.23[epsilon] (Mean = 0.639[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_2_boost_Elliptic_Integral_E_Mathworld_Data[] [role blue Max = 1.31[epsilon] (Mean = 0.727[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_1_complete__boost_Elliptic_Integral_K_Random_Data[] [role blue Max = 0.958[epsilon] (Mean = 0.408[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_1_complete__boost_Elliptic_Integral_K_Mathworld_Data[] [role blue Max = 0.915[epsilon] (Mean = 0.547[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_1_boost_Elliptic_Integral_F_Random_Data[] [role blue Max = 2.26[epsilon] (Mean = 0.631[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_1_boost_Elliptic_Integral_F_Mathworld_Data[] [role blue Max = 0.919[epsilon] (Mean = 0.542[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_rg_boost_RG_one_value_zero[] [role blue Max = 1.96[epsilon] (Mean = 0.674[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_rg_boost_RG_two_values_the_same[] [role blue Max = 1.96[epsilon] (Mean = 0.374[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_rg_boost_RG_All_values_the_same_or_zero[] [role blue Max = 1.06[epsilon] (Mean = 0.348[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_rg_boost_RG_two_values_0[] [role blue Max = 0[epsilon] (Mean = 0[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_rg_boost_RG_Random_Data[] [role blue Max = 3.65[epsilon] (Mean = 0.929[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_rd_boost_RD_x_0[] [role blue Max = 2.64[epsilon] (Mean = 0.894[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_rd_boost_RD_x_y_z[] [role blue Max = 1.03[epsilon] (Mean = 0.418[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_rd_boost_RD_x_0_y_z[] [role blue Max = 1.16[epsilon] (Mean = 0.493[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_rd_boost_RD_x_y[] [role blue Max = 3.51[epsilon] (Mean = 0.816[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_rd_boost_RD_y_z[] [role blue Max = 16.5[epsilon] (Mean = 0.843[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_rd_boost_RD_Random_data[] [role blue Max = 2.16[epsilon] (Mean = 0.803[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_rj_boost_RJ_Equal_z_and_p[] [role blue Max = 15.4[epsilon] (Mean = 1.05[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_rj_boost_RJ_2_Equal_Values[] [role blue Max = 214[epsilon] (Mean = 5.05[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_rj_boost_RJ_3_Equal_Values[] [role blue Max = 39.9[epsilon] (Mean = 1.12[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_rj_boost_RJ_4_Equal_Values[] [role blue Max = 1.03[epsilon] (Mean = 0.418[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_rj_boost_RJ_Random_data[] [role blue Max = 119[epsilon] (Mean = 4.32[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_rc_boost_RC_Random_data[] [role blue Max = 0.962[epsilon] (Mean = 0.407[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_rf_boost_RF_z_0[] [role blue Max = 1.89[epsilon] (Mean = 0.587[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_rf_boost_RF_x_0_y_z[] [role blue Max = 0.999[epsilon] (Mean = 0.407[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_rf_boost_RF_x_y_or_y_z_or_x_z[] [role blue Max = 1.21[epsilon] (Mean = 0.394[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_rf_boost_RF_x_y_z[] [role blue Max = 0.999[epsilon] (Mean = 0.335[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_rf_boost_RF_Random_data[] [role blue Max = 2.02[epsilon] (Mean = 0.677[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_digamma_boost_Digamma_Function_Half_integer_arguments[] [role blue Max = 0.78[epsilon] (Mean = 0.314[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_digamma_boost_Digamma_Function_Integer_arguments[] [role blue Max = 0.992[epsilon] (Mean = 0.452[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_digamma_boost_Digamma_Function_Values_near_0[] [role blue Max = 0[epsilon] (Mean = 0[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_digamma_boost_Digamma_Function_Negative_Values[] [role blue Max = 214[epsilon] (Mean = 16.1[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_digamma_boost_Digamma_Function_Near_Zero[] [role blue Max = 0.953[epsilon] (Mean = 0.337[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_digamma_boost_Digamma_Function_Near_the_Positive_Root[] [role blue Max = 0.997[epsilon] (Mean = 0.527[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_digamma_boost_Digamma_Function_Large_Values[] [role blue Max = 0.98[epsilon] (Mean = 0.369[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cbrt__math_h__cbrt_Function[] (<math.h> = Max = 1.7[epsilon] (Mean = 0.565[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_cbrt_boost_cbrt_Function[] [role blue Max = 1.7[epsilon] (Mean = 0.565[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_binomial_coefficient_boost_Binomials_large_arguments[] [role blue Max = 24.3[epsilon] (Mean = 6.3[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_binomial_coefficient_boost_Binomials_small_arguments[] [role blue Max = 1[epsilon] (Mean = 0.369[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_beta_boost_Beta_Function_Divergent_Values[] [role blue Max = 10.7[epsilon] (Mean = 2.22[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_beta_boost_Beta_Function_Medium_Values[] [role blue Max = 99.1[epsilon] (Mean = 22.4[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_beta_boost_Beta_Function_Small_Values[] [role blue Max = 1.75[epsilon] (Mean = 0.828[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_sph_neumann_prime_boost_y_Random_Data[] [role blue Max = 296[epsilon] (Mean = 25.6[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_prime_boost_Y_v_Random_Data[] [role blue Max = 3.23e+004[epsilon] (Mean = 1.13e+003[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_prime_boost_Y_n_Random_Data[] [role blue Max = 621[epsilon] (Mean = 36[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_prime_boost_Y_0_and_Y_1_Random_Data[] [role blue Max = 5.95[epsilon] (Mean = 1.36[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_prime_boost_Y_v_Mathworld_Data_large_values_[] [role blue Max = 0.627[epsilon] (Mean = 0.237[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_prime_boost_Y_v_Mathworld_Data[] [role blue Max = 23.7[epsilon] (Mean = 10.1[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_prime_integer_orders__boost_Y_n_Mathworld_Data_Integer_Version_[] [role blue Max = 563[epsilon] (Mean = 178[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_prime_integer_orders__boost_Y_1_Mathworld_Data_Integer_Version_[] [role blue Max = 3.08[epsilon] (Mean = 1.2[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_prime_integer_orders__boost_Y_0_Mathworld_Data_Integer_Version_[] [role blue Max = 4.75[epsilon] (Mean = 1.75[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_prime_boost_Y_n_Mathworld_Data[] [role blue Max = 563[epsilon] (Mean = 178[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_prime_boost_Y_1_Mathworld_Data[] [role blue Max = 3.08[epsilon] (Mean = 1.2[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_prime_boost_Y_0_Mathworld_Data[] [role blue Max = 4.75[epsilon] (Mean = 1.75[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_integer_orders___math_h__Yn_Mathworld_Data_Integer_Version_[] (<math.h> = Max = 2.49e+005[epsilon] (Mean = 8.14e+004[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_integer_orders___math_h__Y1_Mathworld_Data_Integer_Version_[] (<math.h> = Max = 1.86e+004[epsilon] (Mean = 6.2e+003[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_integer_orders___math_h__Y0_Mathworld_Data_Integer_Version_[] (<math.h> = Max = 5.37e+003[epsilon] (Mean = 1.81e+003[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_sph_neumann_boost_y_Random_Data[] [role blue Max = 281[epsilon] (Mean = 31.1[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_boost_Yv_Random_Data[] [role blue Max = 1.23e+003[epsilon] (Mean = 69.9[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_boost_Yn_Random_Data[] [role blue Max = 117[epsilon] (Mean = 10.2[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_boost_Y0_and_Y1_Random_Data[] [role blue Max = 4.17[epsilon] (Mean = 1.24[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_boost_Yv_Mathworld_Data_large_values_[] [role blue Max = 0.682[epsilon] (Mean = 0.35[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_boost_Yv_Mathworld_Data[] [role blue Max = 7.89[epsilon] (Mean = 3.27[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_integer_orders__boost_Yn_Mathworld_Data_Integer_Version_[] [role blue Max = 35[epsilon] (Mean = 11.8[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_integer_orders__boost_Y1_Mathworld_Data_Integer_Version_[] [role blue Max = 4.75[epsilon] (Mean = 1.72[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_integer_orders__boost_Y0_Mathworld_Data_Integer_Version_[] [role blue Max = 4.61[epsilon] (Mean = 2.29[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_boost_Yn_Mathworld_Data[] [role blue Max = 35[epsilon] (Mean = 11.8[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_boost_Y1_Mathworld_Data[] [role blue Max = 4.75[epsilon] (Mean = 1.72[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_boost_Y0_Mathworld_Data[] [role blue Max = 4.61[epsilon] (Mean = 2.29[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_k_prime_boost_Bessel_K_v_Random_Data[] [role blue Max = 8.32[epsilon] (Mean = 1.65[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_k_prime_boost_Bessel_K_n_Random_Data[] [role blue Max = 8.18[epsilon] (Mean = 1.45[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_k_prime_boost_Bessel_K_v_Mathworld_Data_large_values_[] [role blue Max = 18.6[epsilon] (Mean = 12.1[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_k_prime_boost_Bessel_K_v_Mathworld_Data[] [role blue Max = 3.94[epsilon] (Mean = 1.43[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_k_prime_integer_orders__boost_Bessel_K_n_Mathworld_Data_Integer_Version_[] [role blue Max = 4.17[epsilon] (Mean = 1.74[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_k_prime_integer_orders__boost_Bessel_K_1_Mathworld_Data_Integer_Version_[] [role blue Max = 1.09[epsilon] (Mean = 0.607[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_k_prime_integer_orders__boost_Bessel_K_0_Mathworld_Data_Integer_Version_[] [role blue Max = 1[epsilon] (Mean = 0.573[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_k_prime_boost_Bessel_K_n_Mathworld_Data[] [role blue Max = 4.17[epsilon] (Mean = 1.74[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_k_prime_boost_Bessel_K_1_Mathworld_Data[] [role blue Max = 1.09[epsilon] (Mean = 0.607[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_k_prime_boost_Bessel_K_0_Mathworld_Data[] [role blue Max = 1[epsilon] (Mean = 0.573[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_k_boost_Bessel_Kv_Random_Data[] [role blue Max = 8.33[epsilon] (Mean = 1.62[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_k_boost_Bessel_Kn_Random_Data[] [role blue Max = 7.47[epsilon] (Mean = 1.4[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_k_boost_Bessel_Kv_Mathworld_Data_large_values_[] [role blue Max = 59.8[epsilon] (Mean = 26.9[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_k_boost_Bessel_Kv_Mathworld_Data[] [role blue Max = 4.78[epsilon] (Mean = 2.2[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_k_integer_orders__boost_Bessel_Kn_Mathworld_Data_Integer_Version_[] [role blue Max = 3.63[epsilon] (Mean = 1.46[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_k_integer_orders__boost_Bessel_K1_Mathworld_Data_Integer_Version_[] [role blue Max = 1[epsilon] (Mean = 0.573[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_k_integer_orders__boost_Bessel_K0_Mathworld_Data_Integer_Version_[] [role blue Max = 1.55[epsilon] (Mean = 0.837[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_k_boost_Bessel_Kn_Mathworld_Data[] [role blue Max = 3.63[epsilon] (Mean = 1.46[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_k_boost_Bessel_K1_Mathworld_Data[] [role blue Max = 1[epsilon] (Mean = 0.573[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_k_boost_Bessel_K0_Mathworld_Data[] [role blue Max = 1.55[epsilon] (Mean = 0.837[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_sph_bessel_prime_boost_Bessel_j_Random_Data[] [role blue Max = 307[epsilon] (Mean = 25.2[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_prime_boost_Bessel_J_Random_Data_Tricky_large_values_[] [role blue Max = 379[epsilon] (Mean = 45.4[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_prime_boost_Bessel_J_Random_Data[] [role blue Max = 176[epsilon] (Mean = 9.76[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_prime_boost_Bessel_JN_Random_Data[] [role blue Max = 6.34[epsilon] (Mean = 0.997[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_prime_boost_Bessel_J_Mathworld_Data_large_values_[] [role blue Max = 2.9[epsilon] (Mean = 1.61[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_prime_boost_Bessel_J_Mathworld_Data[] [role blue Max = 23.7[epsilon] (Mean = 8.01[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_prime_integer_orders__boost_Bessel_JN_Mathworld_Data_Integer_Version_[] [role blue Max = 14[epsilon] (Mean = 6.13[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_prime_integer_orders__boost_Bessel_J1_Mathworld_Data_tricky_cases_Integer_Version_[] [role blue Max = 288[epsilon] (Mean = 129[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_prime_integer_orders__boost_Bessel_J1_Mathworld_Data_Integer_Version_[] [role blue Max = 0.999[epsilon] (Mean = 0.627[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_prime_integer_orders__boost_Bessel_J0_Mathworld_Data_Tricky_cases_Integer_Version_[] [role blue Max = 3.67[epsilon] (Mean = 1.74[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_prime_integer_orders__boost_Bessel_J0_Mathworld_Data_Integer_Version_[] [role blue Max = 6.62[epsilon] (Mean = 2.55[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_prime_boost_Bessel_JN_Mathworld_Data[] [role blue Max = 14[epsilon] (Mean = 6.13[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_prime_boost_Bessel_J1_Mathworld_Data_tricky_cases_[] [role blue Max = 288[epsilon] (Mean = 129[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_prime_boost_Bessel_J1_Mathworld_Data[] [role blue Max = 0.999[epsilon] (Mean = 0.627[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_prime_boost_Bessel_J0_Mathworld_Data_Tricky_cases_[] [role blue Max = 3.67[epsilon] (Mean = 1.74[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_prime_boost_Bessel_J0_Mathworld_Data[] [role blue Max = 6.62[epsilon] (Mean = 2.55[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_integer_orders___math_h__Bessel_JN_Mathworld_Data_Integer_Version_[] (<math.h> = [role red Max = +INF[epsilon] (Mean = +INF[epsilon]) [link errors_Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_integer_orders___math_h__Bessel_JN_Mathworld_Data_Integer_Version_ And other failures.])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_integer_orders___math_h__Bessel_J1_Mathworld_Data_tricky_cases_Integer_Version_[] (<math.h> = Max = 1.44e+007[epsilon] (Mean = 6.5e+006[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_integer_orders___math_h__Bessel_J1_Mathworld_Data_Integer_Version_[] (<math.h> = Max = 11.4[epsilon] (Mean = 4.15[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_integer_orders___math_h__Bessel_J0_Mathworld_Data_Tricky_cases_Integer_Version_[] (<math.h> = [role red Max = 2.54e+008[epsilon] (Mean = 1.04e+008[epsilon]))]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_integer_orders___math_h__Bessel_J0_Mathworld_Data_Integer_Version_[] (<math.h> = Max = 1.89[epsilon] (Mean = 0.988[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_sph_bessel_boost_Bessel_j_Random_Data[] [role blue Max = 245[epsilon] (Mean = 16.3[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_boost_Bessel_J_Random_Data_Tricky_large_values_[] [role blue Max = 59.2[epsilon] (Mean = 8.67[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_boost_Bessel_J_Random_Data[] [role blue Max = 9.24[epsilon] (Mean = 1.36[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_boost_Bessel_JN_Random_Data[] [role blue Max = 17.5[epsilon] (Mean = 1.46[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_boost_Bessel_J_Mathworld_Data_large_values_[] [role blue Max = 9.31[epsilon] (Mean = 5.52[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_boost_Bessel_J_Mathworld_Data[] [role blue Max = 14.9[epsilon] (Mean = 3.82[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_integer_orders__boost_Bessel_JN_Mathworld_Data_Integer_Version_[] [role blue Max = 14.7[epsilon] (Mean = 5.4[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_integer_orders__boost_Bessel_J1_Mathworld_Data_tricky_cases_Integer_Version_[] [role blue Max = 3.23e+004[epsilon] (Mean = 1.45e+004[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_integer_orders__boost_Bessel_J1_Mathworld_Data_Integer_Version_[] [role blue Max = 1.73[epsilon] (Mean = 0.976[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_integer_orders__boost_Bessel_J0_Mathworld_Data_Tricky_cases_Integer_Version_[] [role blue Max = 1e+007[epsilon] (Mean = 4.09e+006[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_integer_orders__boost_Bessel_J0_Mathworld_Data_Integer_Version_[] [role blue Max = 2.52[epsilon] (Mean = 1.2[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_boost_Bessel_JN_Mathworld_Data[] [role blue Max = 14.7[epsilon] (Mean = 5.4[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_boost_Bessel_J1_Mathworld_Data_tricky_cases_[] [role blue Max = 3.23e+004[epsilon] (Mean = 1.45e+004[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_boost_Bessel_J1_Mathworld_Data[] [role blue Max = 1.73[epsilon] (Mean = 0.976[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_boost_Bessel_J0_Mathworld_Data_Tricky_cases_[] [role blue Max = 1e+007[epsilon] (Mean = 4.09e+006[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_boost_Bessel_J0_Mathworld_Data[] [role blue Max = 2.52[epsilon] (Mean = 1.2[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_i_prime_boost_Bessel_I_v_Mathworld_Data_large_values_[] [role blue Max = 59.5[epsilon] (Mean = 26.8[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_i_prime_boost_Bessel_I_v_Random_Data[] [role blue Max = 14[epsilon] (Mean = 2.46[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_i_prime_boost_Bessel_I_n_Random_Data[] [role blue Max = 9.85[epsilon] (Mean = 1.83[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_i_prime_boost_Bessel_I_v_Mathworld_Data[] [role blue Max = 3.76e+003[epsilon] (Mean = 1.19e+003[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_i_prime_integer_orders__boost_Bessel_I_n_Mathworld_Data_Integer_Version_[] [role blue Max = 3.61[epsilon] (Mean = 1.22[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_i_prime_integer_orders__boost_Bessel_I_1_Mathworld_Data_Integer_Version_[] [role blue Max = 1.61[epsilon] (Mean = 0.786[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_i_prime_integer_orders__boost_Bessel_I_0_Mathworld_Data_Integer_Version_[] [role blue Max = 0.885[epsilon] (Mean = 0.567[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_i_prime_boost_Bessel_I_n_Mathworld_Data[] [role blue Max = 3.61[epsilon] (Mean = 1.22[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_i_prime_boost_Bessel_I_1_Mathworld_Data[] [role blue Max = 1.61[epsilon] (Mean = 0.786[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_i_prime_boost_Bessel_I_0_Mathworld_Data[] [role blue Max = 0.885[epsilon] (Mean = 0.567[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_i_boost_Bessel_Iv_Mathworld_Data_large_values_[] [role blue Max = 3.67[epsilon] (Mean = 1.64[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_i_boost_Bessel_Iv_Random_Data[] [role blue Max = 7.46[epsilon] (Mean = 1.54[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_i_boost_Bessel_In_Random_Data[] [role blue Max = 9.67[epsilon] (Mean = 1.89[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_i_boost_Bessel_Iv_Mathworld_Data[] [role blue Max = 2.97[epsilon] (Mean = 1.33[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_i_integer_orders__boost_Bessel_In_Mathworld_Data_Integer_Version_[] [role blue Max = 3.46[epsilon] (Mean = 1.32[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_i_integer_orders__boost_Bessel_I1_Mathworld_Data_Integer_Version_[] [role blue Max = 0.885[epsilon] (Mean = 0.55[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_i_integer_orders__boost_Bessel_I0_Mathworld_Data_Integer_Version_[] [role blue Max = 0.877[epsilon] (Mean = 0.549[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_i_boost_Bessel_In_Mathworld_Data[] [role blue Max = 3.46[epsilon] (Mean = 1.32[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_i_boost_Bessel_I1_Mathworld_Data[] [role blue Max = 0.885[epsilon] (Mean = 0.55[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_i_boost_Bessel_I0_Mathworld_Data[] [role blue Max = 0.877[epsilon] (Mean = 0.549[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_gamma_q_inva_boost_Incomplete_gamma_inverses_[][role blue Max = 5.64[epsilon] (Mean = 1.09[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_gamma_p_inva_boost_Incomplete_gamma_inverses_[][role blue Max = 3.52[epsilon] (Mean = 0.997[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_gamma_q_inv_boost_incomplete_gamma_inverse_a_z_small_values[][role blue Max = 451[epsilon] (Mean = 65[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_gamma_p_inv_boost_incomplete_gamma_inverse_a_z_small_values[][role blue Max = 1.1e+003[epsilon] (Mean = 108[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_gamma_q_inv_boost_incomplete_gamma_inverse_a_z_large_values[][role blue Max = 0.814[epsilon] (Mean = 0.0856[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_gamma_p_inv_boost_incomplete_gamma_inverse_a_z_large_values[][role blue Max = 0.924[epsilon] (Mean = 0.118[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_gamma_q_inv_boost_incomplete_gamma_inverse_a_z_medium_values[][role blue Max = 3.46[epsilon] (Mean = 0.475[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_gamma_p_inv_boost_incomplete_gamma_inverse_a_z_medium_values[][role blue Max = 1.01[epsilon] (Mean = 0.307[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_gamma_p_boost_tgamma_a_z_integer_and_half_integer_values[][role blue Max = 13[epsilon] (Mean = 2.93[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_gamma_q_boost_tgamma_a_z_integer_and_half_integer_values[][role blue Max = 8.48[epsilon] (Mean = 1.42[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma_lower_boost_tgamma_a_z_integer_and_half_integer_values[][role blue Max = 2.69[epsilon] (Mean = 0.866[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma_incomplete__boost_tgamma_a_z_integer_and_half_integer_values[][role blue Max = 5.16[epsilon] (Mean = 1.44[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_gamma_p_boost_tgamma_a_z_large_values[][role blue Max = 244[epsilon] (Mean = 20.2[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_gamma_q_boost_tgamma_a_z_large_values[][role blue Max = 470[epsilon] (Mean = 31.5[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_gamma_p_boost_tgamma_a_z_small_values[][role blue Max = 1.54[epsilon] (Mean = 0.439[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_gamma_q_boost_tgamma_a_z_small_values[][role blue Max = 2.26[epsilon] (Mean = 0.732[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma_lower_boost_tgamma_a_z_small_values[][role blue Max = 1.57[epsilon] (Mean = 0.527[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma_incomplete__boost_tgamma_a_z_small_values[][role blue Max = 2.53[epsilon] (Mean = 0.66[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_gamma_p_boost_tgamma_a_z_medium_values[][role blue Max = 35.1[epsilon] (Mean = 6.97[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_gamma_q_boost_tgamma_a_z_medium_values[][role blue Max = 23.7[epsilon] (Mean = 4.03[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma_lower_boost_tgamma_a_z_medium_values[][role blue Max = 5.62[epsilon] (Mean = 1.43[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma_incomplete__boost_tgamma_a_z_medium_values[][role blue Max = 8.14[epsilon] (Mean = 1.71[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ibetac_inv_boost_Inverse_incomplete_beta[][role blue Max = 5.53e+003[epsilon] (Mean = 220[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ibeta_inv_boost_Inverse_incomplete_beta[][role blue Max = 7.08e+003[epsilon] (Mean = 244[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ibetac_boost_Incomplete_Beta_Function_Small_Integer_Values[][role blue Max = 6.37[epsilon] (Mean = 1.03[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ibeta_boost_Incomplete_Beta_Function_Small_Integer_Values[][role blue Max = 3.69[epsilon] (Mean = 0.765[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_betac_boost_Incomplete_Beta_Function_Small_Integer_Values[][role blue Max = 26.7[epsilon] (Mean = 6.67[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_beta_incomplete__boost_Incomplete_Beta_Function_Small_Integer_Values[][role blue Max = 26.8[epsilon] (Mean = 6.61[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ibetac_boost_Incomplete_Beta_Function_Large_and_Diverse_Values[][role blue Max = 1.87e+003[epsilon] (Mean = 93.8[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ibeta_boost_Incomplete_Beta_Function_Large_and_Diverse_Values[][role blue Max = 1.19e+003[epsilon] (Mean = 59.5[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_betac_boost_Incomplete_Beta_Function_Large_and_Diverse_Values[][role blue Max = 3.72e+003[epsilon] (Mean = 113[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_beta_incomplete__boost_Incomplete_Beta_Function_Large_and_Diverse_Values[][role blue Max = 635[epsilon] (Mean = 29.5[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ibetac_boost_Incomplete_Beta_Function_Medium_Values[][role blue Max = 56.2[epsilon] (Mean = 14.1[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ibeta_boost_Incomplete_Beta_Function_Medium_Values[][role blue Max = 108[epsilon] (Mean = 16.3[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_betac_boost_Incomplete_Beta_Function_Medium_Values[][role blue Max = 91.3[epsilon] (Mean = 14.8[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_beta_incomplete__boost_Incomplete_Beta_Function_Medium_Values[][role blue Max = 91.1[epsilon] (Mean = 12.7[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ibetac_boost_Incomplete_Beta_Function_Small_Values[][role blue Max = 6.56[epsilon] (Mean = 1.88[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ibeta_boost_Incomplete_Beta_Function_Small_Values[][role blue Max = 9.42[epsilon] (Mean = 2.24[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_betac_boost_Incomplete_Beta_Function_Small_Values[][role blue Max = 12[epsilon] (Mean = 2.43[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_beta_incomplete__boost_Incomplete_Beta_Function_Small_Values[][role blue Max = 11.1[epsilon] (Mean = 2.28[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_heuman_lambda_boost_Elliptic_Integral_Heuman_Lambda_Random_Data[][role blue Max = 2.12[epsilon] (Mean = 0.59[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_heuman_lambda_boost_Elliptic_Integral_Jacobi_Zeta_Mathworld_Data[][role blue Max = 1.08[epsilon] (Mean = 0.734[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_hermite_boost_Hermite_Polynomials[][role blue Max = 4.46[epsilon] (Mean = 1.41[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_lgamma__math_h__near_55[](<math.h> = Max = 249[epsilon] (Mean = 43.1[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma__math_h__near_55[](<math.h> = Max = 3.87e+004[epsilon] (Mean = 6.71e+003[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_lgamma__math_h__near_10[](<math.h> = Max = 0.997[epsilon] (Mean = 0.444[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma__math_h__near_10[](<math.h> = Max = 0.866[epsilon] (Mean = 0.445[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_lgamma__math_h__near_2[](<math.h> = Max = 0.741[epsilon] (Mean = 0.473[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma__math_h__near_2[](<math.h> = Max = 0[epsilon] (Mean = 0[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_lgamma__math_h__near_1[](<math.h> = Max = 0.906[epsilon] (Mean = 0.565[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma__math_h__near_1[](<math.h> = Max = 1[epsilon] (Mean = 0.4[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_lgamma__math_h__near_0[](<math.h> = Max = 0.962[epsilon] (Mean = 0.372[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma__math_h__near_0[](<math.h> = Max = 1[epsilon] (Mean = 0.405[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_lgamma__math_h__factorials[](<math.h> = Max = 0.958[epsilon] (Mean = 0.38[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma__math_h__factorials[](<math.h> = Max = 3.17[epsilon] (Mean = 0.928[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma1pm1_boost_tgamma1pm1_dz_[][role blue Max = 0.982[epsilon] (Mean = 0.399[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_lgamma_boost_near_55[][role blue Max = 0.821[epsilon] (Mean = 0.419[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma_boost_near_55[][role blue Max = 1.8[epsilon] (Mean = 0.817[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_lgamma_boost_near_10[][role blue Max = 4.22[epsilon] (Mean = 1.33[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma_boost_near_10[][role blue Max = 1.73[epsilon] (Mean = 0.729[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_lgamma_boost_near_2[][role blue Max = 0.591[epsilon] (Mean = 0.159[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma_boost_near_2[][role blue Max = 2[epsilon] (Mean = 0.995[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_lgamma_boost_near_1[][role blue Max = 0.867[epsilon] (Mean = 0.468[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma_boost_near_1[][role blue Max = 2[epsilon] (Mean = 0.865[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_lgamma_boost_near_0[][role blue Max = 0.964[epsilon] (Mean = 0.462[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma_boost_near_0[][role blue Max = 1.96[epsilon] (Mean = 0.684[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_lgamma_boost_factorials[][role blue Max = 0.914[epsilon] (Mean = 0.167[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_tgamma_boost_factorials[][role blue Max = 1.85[epsilon] (Mean = 0.491[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_expint_Ei__boost_Exponential_Integral_Ei_double_exponent_range[][role blue Max = 1.7[epsilon] (Mean = 0.66[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_expint_Ei__boost_Exponential_Integral_Ei[][role blue Max = 1.43[epsilon] (Mean = 0.541[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_expint_En__boost_Exponential_Integral_E1[][role blue Max = 0.988[epsilon] (Mean = 0.486[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_expint_En__boost_Exponential_Integral_En_small_z_values[][role blue Max = 2.62[epsilon] (Mean = 0.531[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_expint_En__boost_Exponential_Integral_En[][role blue Max = 7.16[epsilon] (Mean = 1.85[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_erfc__math_h__Erf_Function_Large_Values[](<math.h> = Max = 1.84[epsilon] (Mean = 0.331[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_erf__math_h__Erf_Function_Large_Values[](<math.h> = Max = 0[epsilon] (Mean = 0[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_erfc__math_h__Erf_Function_Medium_Values[](<math.h> = Max = 2.36[epsilon] (Mean = 0.539[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_erf__math_h__Erf_Function_Medium_Values[](<math.h> = Max = 1.19[epsilon] (Mean = 0.244[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_erfc__math_h__Erf_Function_Small_Values[](<math.h> = Max = 0[epsilon] (Mean = 0[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_erf__math_h__Erf_Function_Small_Values[](<math.h> = Max = 1.57[epsilon] (Mean = 0.317[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_erfc_inv_boost_Inverse_Erfc_Function[][role blue Max = 1[epsilon] (Mean = 0.491[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_erf_inv_boost_Inverse_Erf_Function[][role blue Max = 1.09[epsilon] (Mean = 0.502[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_erfc_boost_Erf_Function_Large_Values[][role blue Max = 1.14[epsilon] (Mean = 0.248[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_erf_boost_Erf_Function_Large_Values[][role blue Max = 0[epsilon] (Mean = 0[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_erfc_boost_Erf_Function_Medium_Values[][role blue Max = 1.65[epsilon] (Mean = 0.373[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_erf_boost_Erf_Function_Medium_Values[][role blue Max = 1[epsilon] (Mean = 0.169[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_erfc_boost_Erf_Function_Small_Values[][role blue Max = 0[epsilon] (Mean = 0[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_erf_boost_Erf_Function_Small_Values[][role blue Max = 0.996[epsilon] (Mean = 0.182[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_d_complete__boost_Elliptic_Integral_D_Random_Data[][role blue Max = 1.27[epsilon] (Mean = 0.355[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_d_complete__boost_Elliptic_Integral_E_Mathworld_Data[][role blue Max = 0.637[epsilon] (Mean = 0.368[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_d_boost_Elliptic_Integral_D_Random_Data[][role blue Max = 2.87[epsilon] (Mean = 0.805[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_d_boost_Elliptic_Integral_E_Mathworld_Data[][role blue Max = 0.862[epsilon] (Mean = 0.457[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_3_complete__boost_Complete_Elliptic_Integral_PI_Random_Data[][role blue Max = 2.46[epsilon] (Mean = 0.654[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_3_complete__boost_Complete_Elliptic_Integral_PI_Mathworld_Data[][role blue Max = 0.971[epsilon] (Mean = 0.464[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_3_boost_Elliptic_Integral_PI_Large_Random_Data[][role blue Max = 2.86[epsilon] (Mean = 0.944[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_3_boost_Elliptic_Integral_PI_Random_Data[][role blue Max = 9.08[epsilon] (Mean = 0.99[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_3_boost_Elliptic_Integral_PI_Mathworld_Data[][role blue Max = 565[epsilon] (Mean = 102[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_2_complete__boost_Elliptic_Integral_E_Random_Data[][role blue Max = 1.71[epsilon] (Mean = 0.553[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_2_complete__boost_Elliptic_Integral_E_Mathworld_Data[][role blue Max = 1.3[epsilon] (Mean = 0.615[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_2_boost_Elliptic_Integral_E_Random_Data[][role blue Max = 2.23[epsilon] (Mean = 0.639[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_2_boost_Elliptic_Integral_E_Mathworld_Data[][role blue Max = 1.31[epsilon] (Mean = 0.727[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_1_complete__boost_Elliptic_Integral_K_Random_Data[][role blue Max = 0.958[epsilon] (Mean = 0.408[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_1_complete__boost_Elliptic_Integral_K_Mathworld_Data[][role blue Max = 0.915[epsilon] (Mean = 0.547[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_1_boost_Elliptic_Integral_F_Random_Data[][role blue Max = 2.26[epsilon] (Mean = 0.631[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_1_boost_Elliptic_Integral_F_Mathworld_Data[][role blue Max = 0.919[epsilon] (Mean = 0.542[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_rg_boost_RG_one_value_zero[][role blue Max = 1.96[epsilon] (Mean = 0.674[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_rg_boost_RG_two_values_the_same[][role blue Max = 1.96[epsilon] (Mean = 0.374[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_rg_boost_RG_All_values_the_same_or_zero[][role blue Max = 1.06[epsilon] (Mean = 0.348[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_rg_boost_RG_two_values_0[][role blue Max = 0[epsilon] (Mean = 0[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_rg_boost_RG_Random_Data[][role blue Max = 3.65[epsilon] (Mean = 0.929[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_rd_boost_RD_x_0[][role blue Max = 2.64[epsilon] (Mean = 0.894[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_rd_boost_RD_x_y_z[][role blue Max = 1.03[epsilon] (Mean = 0.418[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_rd_boost_RD_x_0_y_z[][role blue Max = 1.16[epsilon] (Mean = 0.493[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_rd_boost_RD_x_y[][role blue Max = 3.51[epsilon] (Mean = 0.816[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_rd_boost_RD_y_z[][role blue Max = 16.5[epsilon] (Mean = 0.843[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_rd_boost_RD_Random_data[][role blue Max = 2.16[epsilon] (Mean = 0.803[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_rj_boost_RJ_Equal_z_and_p[][role blue Max = 15.4[epsilon] (Mean = 1.05[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_rj_boost_RJ_2_Equal_Values[][role blue Max = 214[epsilon] (Mean = 5.05[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_rj_boost_RJ_3_Equal_Values[][role blue Max = 39.9[epsilon] (Mean = 1.12[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_rj_boost_RJ_4_Equal_Values[][role blue Max = 1.03[epsilon] (Mean = 0.418[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_rj_boost_RJ_Random_data[][role blue Max = 119[epsilon] (Mean = 4.32[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_rc_boost_RC_Random_data[][role blue Max = 0.962[epsilon] (Mean = 0.407[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_rf_boost_RF_z_0[][role blue Max = 1.89[epsilon] (Mean = 0.587[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_rf_boost_RF_x_0_y_z[][role blue Max = 0.999[epsilon] (Mean = 0.407[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_rf_boost_RF_x_y_or_y_z_or_x_z[][role blue Max = 1.21[epsilon] (Mean = 0.394[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_rf_boost_RF_x_y_z[][role blue Max = 0.999[epsilon] (Mean = 0.335[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_ellint_rf_boost_RF_Random_data[][role blue Max = 2.02[epsilon] (Mean = 0.677[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_digamma_boost_Digamma_Function_Half_integer_arguments[][role blue Max = 0.78[epsilon] (Mean = 0.314[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_digamma_boost_Digamma_Function_Integer_arguments[][role blue Max = 0.992[epsilon] (Mean = 0.452[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_digamma_boost_Digamma_Function_Values_near_0[][role blue Max = 0[epsilon] (Mean = 0[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_digamma_boost_Digamma_Function_Negative_Values[][role blue Max = 214[epsilon] (Mean = 16.1[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_digamma_boost_Digamma_Function_Near_Zero[][role blue Max = 0.953[epsilon] (Mean = 0.337[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_digamma_boost_Digamma_Function_Near_the_Positive_Root[][role blue Max = 0.997[epsilon] (Mean = 0.527[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_digamma_boost_Digamma_Function_Large_Values[][role blue Max = 0.98[epsilon] (Mean = 0.369[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cbrt__math_h__cbrt_Function[](<math.h> = Max = 1.7[epsilon] (Mean = 0.565[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_cbrt_boost_cbrt_Function[][role blue Max = 1.7[epsilon] (Mean = 0.565[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_binomial_coefficient_boost_Binomials_large_arguments[][role blue Max = 24.3[epsilon] (Mean = 6.3[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_binomial_coefficient_boost_Binomials_small_arguments[][role blue Max = 1[epsilon] (Mean = 0.369[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_beta_boost_Beta_Function_Divergent_Values[][role blue Max = 10.7[epsilon] (Mean = 2.22[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_beta_boost_Beta_Function_Medium_Values[][role blue Max = 99.1[epsilon] (Mean = 22.4[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_beta_boost_Beta_Function_Small_Values[][role blue Max = 1.75[epsilon] (Mean = 0.828[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_sph_neumann_prime_boost_y_Random_Data[][role blue Max = 296[epsilon] (Mean = 25.6[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_prime_boost_Y_v_Random_Data[][role blue Max = 3.23e+004[epsilon] (Mean = 1.13e+003[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_prime_boost_Y_n_Random_Data[][role blue Max = 621[epsilon] (Mean = 36[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_prime_boost_Y_0_and_Y_1_Random_Data[][role blue Max = 5.95[epsilon] (Mean = 1.36[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_prime_boost_Y_v_Mathworld_Data_large_values_[][role blue Max = 0.627[epsilon] (Mean = 0.237[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_prime_boost_Y_v_Mathworld_Data[][role blue Max = 23.7[epsilon] (Mean = 10.1[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_prime_integer_orders__boost_Y_n_Mathworld_Data_Integer_Version_[][role blue Max = 563[epsilon] (Mean = 178[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_prime_integer_orders__boost_Y_1_Mathworld_Data_Integer_Version_[][role blue Max = 3.08[epsilon] (Mean = 1.2[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_prime_integer_orders__boost_Y_0_Mathworld_Data_Integer_Version_[][role blue Max = 4.75[epsilon] (Mean = 1.75[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_prime_boost_Y_n_Mathworld_Data[][role blue Max = 563[epsilon] (Mean = 178[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_prime_boost_Y_1_Mathworld_Data[][role blue Max = 3.08[epsilon] (Mean = 1.2[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_prime_boost_Y_0_Mathworld_Data[][role blue Max = 4.75[epsilon] (Mean = 1.75[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_integer_orders___math_h__Yn_Mathworld_Data_Integer_Version_[](<math.h> = Max = 2.49e+005[epsilon] (Mean = 8.14e+004[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_integer_orders___math_h__Y1_Mathworld_Data_Integer_Version_[](<math.h> = Max = 1.86e+004[epsilon] (Mean = 6.2e+003[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_integer_orders___math_h__Y0_Mathworld_Data_Integer_Version_[](<math.h> = Max = 5.37e+003[epsilon] (Mean = 1.81e+003[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_sph_neumann_boost_y_Random_Data[][role blue Max = 281[epsilon] (Mean = 31.1[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_boost_Yv_Random_Data[][role blue Max = 1.23e+003[epsilon] (Mean = 69.9[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_boost_Yn_Random_Data[][role blue Max = 117[epsilon] (Mean = 10.2[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_boost_Y0_and_Y1_Random_Data[][role blue Max = 4.17[epsilon] (Mean = 1.24[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_boost_Yv_Mathworld_Data_large_values_[][role blue Max = 0.682[epsilon] (Mean = 0.35[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_boost_Yv_Mathworld_Data[][role blue Max = 7.89[epsilon] (Mean = 3.27[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_integer_orders__boost_Yn_Mathworld_Data_Integer_Version_[][role blue Max = 35[epsilon] (Mean = 11.8[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_integer_orders__boost_Y1_Mathworld_Data_Integer_Version_[][role blue Max = 4.75[epsilon] (Mean = 1.72[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_integer_orders__boost_Y0_Mathworld_Data_Integer_Version_[][role blue Max = 4.61[epsilon] (Mean = 2.29[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_boost_Yn_Mathworld_Data[][role blue Max = 35[epsilon] (Mean = 11.8[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_boost_Y1_Mathworld_Data[][role blue Max = 4.75[epsilon] (Mean = 1.72[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_neumann_boost_Y0_Mathworld_Data[][role blue Max = 4.61[epsilon] (Mean = 2.29[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_k_prime_boost_Bessel_K_v_Random_Data[][role blue Max = 8.32[epsilon] (Mean = 1.65[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_k_prime_boost_Bessel_K_n_Random_Data[][role blue Max = 8.18[epsilon] (Mean = 1.45[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_k_prime_boost_Bessel_K_v_Mathworld_Data_large_values_[][role blue Max = 18.6[epsilon] (Mean = 12.1[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_k_prime_boost_Bessel_K_v_Mathworld_Data[][role blue Max = 3.94[epsilon] (Mean = 1.43[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_k_prime_integer_orders__boost_Bessel_K_n_Mathworld_Data_Integer_Version_[][role blue Max = 4.17[epsilon] (Mean = 1.74[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_k_prime_integer_orders__boost_Bessel_K_1_Mathworld_Data_Integer_Version_[][role blue Max = 1.09[epsilon] (Mean = 0.607[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_k_prime_integer_orders__boost_Bessel_K_0_Mathworld_Data_Integer_Version_[][role blue Max = 1[epsilon] (Mean = 0.573[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_k_prime_boost_Bessel_K_n_Mathworld_Data[][role blue Max = 4.17[epsilon] (Mean = 1.74[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_k_prime_boost_Bessel_K_1_Mathworld_Data[][role blue Max = 1.09[epsilon] (Mean = 0.607[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_k_prime_boost_Bessel_K_0_Mathworld_Data[][role blue Max = 1[epsilon] (Mean = 0.573[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_k_boost_Bessel_Kv_Random_Data[][role blue Max = 8.33[epsilon] (Mean = 1.62[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_k_boost_Bessel_Kn_Random_Data[][role blue Max = 7.47[epsilon] (Mean = 1.4[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_k_boost_Bessel_Kv_Mathworld_Data_large_values_[][role blue Max = 59.8[epsilon] (Mean = 26.9[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_k_boost_Bessel_Kv_Mathworld_Data[][role blue Max = 4.78[epsilon] (Mean = 2.2[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_k_integer_orders__boost_Bessel_Kn_Mathworld_Data_Integer_Version_[][role blue Max = 3.63[epsilon] (Mean = 1.46[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_k_integer_orders__boost_Bessel_K1_Mathworld_Data_Integer_Version_[][role blue Max = 1[epsilon] (Mean = 0.573[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_k_integer_orders__boost_Bessel_K0_Mathworld_Data_Integer_Version_[][role blue Max = 1.55[epsilon] (Mean = 0.837[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_k_boost_Bessel_Kn_Mathworld_Data[][role blue Max = 3.63[epsilon] (Mean = 1.46[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_k_boost_Bessel_K1_Mathworld_Data[][role blue Max = 1[epsilon] (Mean = 0.573[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_k_boost_Bessel_K0_Mathworld_Data[][role blue Max = 1.55[epsilon] (Mean = 0.837[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_sph_bessel_prime_boost_Bessel_j_Random_Data[][role blue Max = 307[epsilon] (Mean = 25.2[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_prime_boost_Bessel_J_Random_Data_Tricky_large_values_[][role blue Max = 379[epsilon] (Mean = 45.4[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_prime_boost_Bessel_J_Random_Data[][role blue Max = 176[epsilon] (Mean = 9.76[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_prime_boost_Bessel_JN_Random_Data[][role blue Max = 6.34[epsilon] (Mean = 0.997[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_prime_boost_Bessel_J_Mathworld_Data_large_values_[][role blue Max = 2.9[epsilon] (Mean = 1.61[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_prime_boost_Bessel_J_Mathworld_Data[][role blue Max = 23.7[epsilon] (Mean = 8.01[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_prime_integer_orders__boost_Bessel_JN_Mathworld_Data_Integer_Version_[][role blue Max = 14[epsilon] (Mean = 6.13[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_prime_integer_orders__boost_Bessel_J1_Mathworld_Data_tricky_cases_Integer_Version_[][role blue Max = 288[epsilon] (Mean = 129[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_prime_integer_orders__boost_Bessel_J1_Mathworld_Data_Integer_Version_[][role blue Max = 0.999[epsilon] (Mean = 0.627[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_prime_integer_orders__boost_Bessel_J0_Mathworld_Data_Tricky_cases_Integer_Version_[][role blue Max = 3.67[epsilon] (Mean = 1.74[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_prime_integer_orders__boost_Bessel_J0_Mathworld_Data_Integer_Version_[][role blue Max = 6.62[epsilon] (Mean = 2.55[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_prime_boost_Bessel_JN_Mathworld_Data[][role blue Max = 14[epsilon] (Mean = 6.13[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_prime_boost_Bessel_J1_Mathworld_Data_tricky_cases_[][role blue Max = 288[epsilon] (Mean = 129[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_prime_boost_Bessel_J1_Mathworld_Data[][role blue Max = 0.999[epsilon] (Mean = 0.627[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_prime_boost_Bessel_J0_Mathworld_Data_Tricky_cases_[][role blue Max = 3.67[epsilon] (Mean = 1.74[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_prime_boost_Bessel_J0_Mathworld_Data[][role blue Max = 6.62[epsilon] (Mean = 2.55[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_integer_orders___math_h__Bessel_JN_Mathworld_Data_Integer_Version_[](<math.h> = [role red Max = +INF[epsilon] (Mean = +INF[epsilon]) [link errors_Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_integer_orders___math_h__Bessel_JN_Mathworld_Data_Integer_Version_ And other failures.])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_integer_orders___math_h__Bessel_J1_Mathworld_Data_tricky_cases_Integer_Version_[](<math.h> = Max = 1.44e+007[epsilon] (Mean = 6.5e+006[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_integer_orders___math_h__Bessel_J1_Mathworld_Data_Integer_Version_[](<math.h> = Max = 11.4[epsilon] (Mean = 4.15[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_integer_orders___math_h__Bessel_J0_Mathworld_Data_Tricky_cases_Integer_Version_[](<math.h> = [role red Max = 2.54e+008[epsilon] (Mean = 1.04e+008[epsilon]))]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_integer_orders___math_h__Bessel_J0_Mathworld_Data_Integer_Version_[](<math.h> = Max = 1.89[epsilon] (Mean = 0.988[epsilon]))]
[template Microsoft_Visual_C_version_12_0_Win32_double_sph_bessel_boost_Bessel_j_Random_Data[][role blue Max = 245[epsilon] (Mean = 16.3[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_boost_Bessel_J_Random_Data_Tricky_large_values_[][role blue Max = 59.2[epsilon] (Mean = 8.67[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_boost_Bessel_J_Random_Data[][role blue Max = 9.24[epsilon] (Mean = 1.36[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_boost_Bessel_JN_Random_Data[][role blue Max = 17.5[epsilon] (Mean = 1.46[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_boost_Bessel_J_Mathworld_Data_large_values_[][role blue Max = 9.31[epsilon] (Mean = 5.52[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_boost_Bessel_J_Mathworld_Data[][role blue Max = 14.9[epsilon] (Mean = 3.82[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_integer_orders__boost_Bessel_JN_Mathworld_Data_Integer_Version_[][role blue Max = 14.7[epsilon] (Mean = 5.4[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_integer_orders__boost_Bessel_J1_Mathworld_Data_tricky_cases_Integer_Version_[][role blue Max = 3.23e+004[epsilon] (Mean = 1.45e+004[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_integer_orders__boost_Bessel_J1_Mathworld_Data_Integer_Version_[][role blue Max = 1.73[epsilon] (Mean = 0.976[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_integer_orders__boost_Bessel_J0_Mathworld_Data_Tricky_cases_Integer_Version_[][role blue Max = 1e+007[epsilon] (Mean = 4.09e+006[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_integer_orders__boost_Bessel_J0_Mathworld_Data_Integer_Version_[][role blue Max = 2.52[epsilon] (Mean = 1.2[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_boost_Bessel_JN_Mathworld_Data[][role blue Max = 14.7[epsilon] (Mean = 5.4[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_boost_Bessel_J1_Mathworld_Data_tricky_cases_[][role blue Max = 3.23e+004[epsilon] (Mean = 1.45e+004[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_boost_Bessel_J1_Mathworld_Data[][role blue Max = 1.73[epsilon] (Mean = 0.976[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_boost_Bessel_J0_Mathworld_Data_Tricky_cases_[][role blue Max = 1e+007[epsilon] (Mean = 4.09e+006[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_boost_Bessel_J0_Mathworld_Data[][role blue Max = 2.52[epsilon] (Mean = 1.2[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_i_prime_boost_Bessel_I_v_Mathworld_Data_large_values_[][role blue Max = 59.5[epsilon] (Mean = 26.8[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_i_prime_boost_Bessel_I_v_Random_Data[][role blue Max = 14[epsilon] (Mean = 2.46[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_i_prime_boost_Bessel_I_n_Random_Data[][role blue Max = 9.85[epsilon] (Mean = 1.83[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_i_prime_boost_Bessel_I_v_Mathworld_Data[][role blue Max = 3.76e+003[epsilon] (Mean = 1.19e+003[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_i_prime_integer_orders__boost_Bessel_I_n_Mathworld_Data_Integer_Version_[][role blue Max = 3.61[epsilon] (Mean = 1.22[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_i_prime_integer_orders__boost_Bessel_I_1_Mathworld_Data_Integer_Version_[][role blue Max = 1.61[epsilon] (Mean = 0.786[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_i_prime_integer_orders__boost_Bessel_I_0_Mathworld_Data_Integer_Version_[][role blue Max = 0.885[epsilon] (Mean = 0.567[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_i_prime_boost_Bessel_I_n_Mathworld_Data[][role blue Max = 3.61[epsilon] (Mean = 1.22[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_i_prime_boost_Bessel_I_1_Mathworld_Data[][role blue Max = 1.61[epsilon] (Mean = 0.786[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_i_prime_boost_Bessel_I_0_Mathworld_Data[][role blue Max = 0.885[epsilon] (Mean = 0.567[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_i_boost_Bessel_Iv_Mathworld_Data_large_values_[][role blue Max = 3.67[epsilon] (Mean = 1.64[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_i_boost_Bessel_Iv_Random_Data[][role blue Max = 7.46[epsilon] (Mean = 1.54[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_i_boost_Bessel_In_Random_Data[][role blue Max = 9.67[epsilon] (Mean = 1.89[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_i_boost_Bessel_Iv_Mathworld_Data[][role blue Max = 2.97[epsilon] (Mean = 1.33[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_i_integer_orders__boost_Bessel_In_Mathworld_Data_Integer_Version_[][role blue Max = 3.46[epsilon] (Mean = 1.32[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_i_integer_orders__boost_Bessel_I1_Mathworld_Data_Integer_Version_[][role blue Max = 0.885[epsilon] (Mean = 0.55[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_i_integer_orders__boost_Bessel_I0_Mathworld_Data_Integer_Version_[][role blue Max = 0.877[epsilon] (Mean = 0.549[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_i_boost_Bessel_In_Mathworld_Data[][role blue Max = 3.46[epsilon] (Mean = 1.32[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_i_boost_Bessel_I1_Mathworld_Data[][role blue Max = 0.885[epsilon] (Mean = 0.55[epsilon])]]
[template Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_i_boost_Bessel_I0_Mathworld_Data[][role blue Max = 0.877[epsilon] (Mean = 0.549[epsilon])]]
[/tables:]
[template table_powm1[]
[table:table_powm1 Error rates for powm1
[[][Microsoft Visual C++ version 12.0[br]Win32[br]double]]
[[powm1][[Microsoft_Visual_C_version_12_0_Win32_double_powm1_boost_powm1]]]
]
]
[template table_sqrt1pm1[]
[table:table_sqrt1pm1 Error rates for sqrt1pm1
[[][Microsoft Visual C++ version 12.0[br]Win32[br]double]]
[[sqrt1pm1][[Microsoft_Visual_C_version_12_0_Win32_double_sqrt1pm1_boost_sqrt1pm1]]]
]
]
[template table_expm1[]
[table:table_expm1 Error rates for expm1
[[][Microsoft Visual C++ version 12.0[br]Win32[br]double]]
[[Random test data][[Microsoft_Visual_C_version_12_0_Win32_double_expm1_boost_Random_test_data][br][br][Microsoft_Visual_C_version_12_0_Win32_double_expm1__math_h__Random_test_data]]]
]
]
[template table_log1p[]
[table:table_log1p Error rates for log1p
[[][Microsoft Visual C++ version 12.0[br]Win32[br]double]]
[[Random test data][[Microsoft_Visual_C_version_12_0_Win32_double_log1p_boost_Random_test_data][br][br][Microsoft_Visual_C_version_12_0_Win32_double_log1p__math_h__Random_test_data]]]
]
]
[template table_spherical_harmonic_i[]
[table:table_spherical_harmonic_i Error rates for spherical_harmonic_i
[[][Microsoft Visual C++ version 12.0[br]Win32[br]double]]
[[Spherical Harmonics][[Microsoft_Visual_C_version_12_0_Win32_double_spherical_harmonic_i_boost_Spherical_Harmonics]]]
]
]
[template table_spherical_harmonic_r[]
[table:table_spherical_harmonic_r Error rates for spherical_harmonic_r
[[][Microsoft Visual C++ version 12.0[br]Win32[br]double]]
[[Spherical Harmonics][[Microsoft_Visual_C_version_12_0_Win32_double_spherical_harmonic_r_boost_Spherical_Harmonics]]]
]
]
[template table_boost_math_owens_t[]
[table:table_boost_math_owens_t Error rates for boost::math::owens_t
[[][Microsoft Visual C++ version 12.0[br]Win32[br]double]]
[[Owens T (medium small values)][[Microsoft_Visual_C_version_12_0_Win32_double_boost_math_owens_t_boost_Owens_T_medium_small_values_]]]
[[Owens T (large and diverse values)][[Microsoft_Visual_C_version_12_0_Win32_double_boost_math_owens_t_boost_Owens_T_large_and_diverse_values_]]]
]
]
[template table_zeta[]
[table:table_zeta Error rates for zeta
[[][Microsoft Visual C++ version 12.0[br]Win32[br]double]]
@@ -1001,6 +1061,48 @@
[/sections:]
[template section_powm1[]
[section:section_powm1 powm1]
[table_powm1]
[endsect]
]
[template section_sqrt1pm1[]
[section:section_sqrt1pm1 sqrt1pm1]
[table_sqrt1pm1]
[endsect]
]
[template section_expm1[]
[section:section_expm1 expm1]
[table_expm1]
[endsect]
]
[template section_log1p[]
[section:section_log1p log1p]
[table_log1p]
[endsect]
]
[template section_spherical_harmonic_i[]
[section:section_spherical_harmonic_i spherical_harmonic_i]
[table_spherical_harmonic_i]
[endsect]
]
[template section_spherical_harmonic_r[]
[section:section_spherical_harmonic_r spherical_harmonic_r]
[table_spherical_harmonic_r]
[endsect]
]
[template section_boost_math_owens_t[]
[section:section_boost_math_owens_t boost::math::owens_t]
[table_boost_math_owens_t]
[endsect]
]
[template section_zeta[]
[section:section_zeta zeta]
[table_zeta]
@@ -1457,6 +1559,7 @@
[section_beta_incomplete_]
[section_betac]
[section_binomial_coefficient]
[section_boost_math_owens_t]
[section_cbrt]
[section_cos_pi]
[section_cyl_bessel_i]
@@ -1495,6 +1598,7 @@
[section_erfc_inv]
[section_expint_Ei_]
[section_expint_En_]
[section_expm1]
[section_gamma_p]
[section_gamma_p_inv]
[section_gamma_p_inva]
@@ -1514,12 +1618,17 @@
[section_legendre_p_associated_]
[section_legendre_q]
[section_lgamma]
[section_log1p]
[section_polygamma]
[section_powm1]
[section_sin_pi]
[section_sph_bessel]
[section_sph_bessel_prime]
[section_sph_neumann]
[section_sph_neumann_prime]
[section_spherical_harmonic_i]
[section_spherical_harmonic_r]
[section_sqrt1pm1]
[section_tgamma]
[section_tgamma1pm1]
[section_tgamma_delta_ratio]
@@ -1531,6 +1640,10 @@
]
[/error_content:]
[template errors_Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_integer_orders___math_h__Bessel_JN_Mathworld_Data_Integer_Version_[]
[h4 Error Output For cyl_bessel_j (integer orders) with compiler Microsoft Visual C++ version 12.0 and library <math.h> and test data Bessel JN: Mathworld Data (Integer Version)]
@@ -1538,9 +1651,10 @@
CAUTION: Found non-finite result, when a finite value was expected at entry 16[br]Found: -1.#IND Expected 0 Error: 1.79769e+308[br]10, 1e-100, 0[br]CAUTION: Gross error found at entry 16.[br]Found: -1.#IND Expected 0 Error: 1.79769e+308[br]10, 1e-100, 0[br]
]
[template all_errors[]
[errors_Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_integer_orders___math_h__Bessel_JN_Mathworld_Data_Integer_Version_]
]

419
reporting/accuracy/html/index.html
View File

@@ -39,6 +39,7 @@
(incomplete)</a></span></dt>
<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_betac">betac</a></span></dt>
<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_binomial_coefficient">binomial_coefficient</a></span></dt>
<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_boost_math_owens_t">boost::math::owens_t</a></span></dt>
<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cbrt">cbrt</a></span></dt>
<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cos_pi">cos_pi</a></span></dt>
<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_i">cyl_bessel_i</a></span></dt>
@@ -91,6 +92,7 @@
(Ei)</a></span></dt>
<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_expint_En_">expint
(En)</a></span></dt>
<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_expm1">expm1</a></span></dt>
<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_gamma_p">gamma_p</a></span></dt>
<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_gamma_p_inv">gamma_p_inv</a></span></dt>
<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_gamma_p_inva">gamma_p_inva</a></span></dt>
@@ -111,12 +113,17 @@
(associated)</a></span></dt>
<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_legendre_q">legendre_q</a></span></dt>
<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_lgamma">lgamma</a></span></dt>
<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_log1p">log1p</a></span></dt>
<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_polygamma">polygamma</a></span></dt>
<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_powm1">powm1</a></span></dt>
<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_sin_pi">sin_pi</a></span></dt>
<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_sph_bessel">sph_bessel</a></span></dt>
<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_sph_bessel_prime">sph_bessel_prime</a></span></dt>
<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_sph_neumann">sph_neumann</a></span></dt>
<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_sph_neumann_prime">sph_neumann_prime</a></span></dt>
<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_spherical_harmonic_i">spherical_harmonic_i</a></span></dt>
<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_spherical_harmonic_r">spherical_harmonic_r</a></span></dt>
<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_sqrt1pm1">sqrt1pm1</a></span></dt>
<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_tgamma">tgamma</a></span></dt>
<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_tgamma1pm1">tgamma1pm1</a></span></dt>
<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_tgamma_delta_ratio">tgamma_delta_ratio</a></span></dt>
@@ -392,10 +399,60 @@
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="special_function_error_rates_rep.section_boost_math_owens_t"></a><a class="link" href="index.html#special_function_error_rates_rep.section_boost_math_owens_t" title="boost::math::owens_t">boost::math::owens_t</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_boost_math_owens_t.table_boost_math_owens_t"></a><p class="title"><b>Table&#160;5.&#160;Error rates for boost::math::owens_t</b></p>
<div class="table-contents"><table class="table" summary="Error rates for boost::math::owens_t">
<colgroup>
<col>
<col>
</colgroup>
<thead><tr>
<th>
</th>
<th>
<p>
Microsoft Visual C++ version 12.0<br> Win32<br> double
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
Owens T (medium small values)
</p>
</td>
<td>
<p>
<span class="blue">Max = 4.37&#949; (Mean = 0.973&#949;)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
Owens T (large and diverse values)
</p>
</td>
<td>
<p>
<span class="blue">Max = 3.78&#949; (Mean = 0.621&#949;)</span>
</p>
</td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break">
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="special_function_error_rates_rep.section_cbrt"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cbrt" title="cbrt">cbrt</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_cbrt.table_cbrt"></a><p class="title"><b>Table&#160;5.&#160;Error rates for cbrt</b></p>
<a name="special_function_error_rates_rep.section_cbrt.table_cbrt"></a><p class="title"><b>Table&#160;6.&#160;Error rates for cbrt</b></p>
<div class="table-contents"><table class="table" summary="Error rates for cbrt">
<colgroup>
<col>
@@ -432,7 +489,7 @@
<a name="special_function_error_rates_rep.section_cos_pi"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cos_pi" title="cos_pi">cos_pi</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_cos_pi.table_cos_pi"></a><p class="title"><b>Table&#160;6.&#160;Error rates for cos_pi</b></p>
<a name="special_function_error_rates_rep.section_cos_pi.table_cos_pi"></a><p class="title"><b>Table&#160;7.&#160;Error rates for cos_pi</b></p>
<div class="table-contents"><table class="table" summary="Error rates for cos_pi">
<colgroup>
<col>
@@ -482,7 +539,7 @@
<a name="special_function_error_rates_rep.section_cyl_bessel_i"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_i" title="cyl_bessel_i">cyl_bessel_i</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_cyl_bessel_i.table_cyl_bessel_i"></a><p class="title"><b>Table&#160;7.&#160;Error rates for cyl_bessel_i</b></p>
<a name="special_function_error_rates_rep.section_cyl_bessel_i.table_cyl_bessel_i"></a><p class="title"><b>Table&#160;8.&#160;Error rates for cyl_bessel_i</b></p>
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i">
<colgroup>
<col>
@@ -593,7 +650,7 @@
(integer orders)</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_cyl_bessel_i_integer_orders_.table_cyl_bessel_i_integer_orders_"></a><p class="title"><b>Table&#160;8.&#160;Error rates for cyl_bessel_i (integer orders)</b></p>
<a name="special_function_error_rates_rep.section_cyl_bessel_i_integer_orders_.table_cyl_bessel_i_integer_orders_"></a><p class="title"><b>Table&#160;9.&#160;Error rates for cyl_bessel_i (integer orders)</b></p>
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i (integer orders)">
<colgroup>
<col>
@@ -655,7 +712,7 @@
<a name="special_function_error_rates_rep.section_cyl_bessel_i_prime"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_i_prime" title="cyl_bessel_i_prime">cyl_bessel_i_prime</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_cyl_bessel_i_prime.table_cyl_bessel_i_prime"></a><p class="title"><b>Table&#160;9.&#160;Error rates for cyl_bessel_i_prime</b></p>
<a name="special_function_error_rates_rep.section_cyl_bessel_i_prime.table_cyl_bessel_i_prime"></a><p class="title"><b>Table&#160;10.&#160;Error rates for cyl_bessel_i_prime</b></p>
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i_prime">
<colgroup>
<col>
@@ -766,7 +823,7 @@
(integer orders)</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_cyl_bessel_i_prime_integer_orders_.table_cyl_bessel_i_prime_integer_orders_"></a><p class="title"><b>Table&#160;10.&#160;Error rates for cyl_bessel_i_prime (integer orders)</b></p>
<a name="special_function_error_rates_rep.section_cyl_bessel_i_prime_integer_orders_.table_cyl_bessel_i_prime_integer_orders_"></a><p class="title"><b>Table&#160;11.&#160;Error rates for cyl_bessel_i_prime (integer orders)</b></p>
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i_prime (integer orders)">
<colgroup>
<col>
@@ -828,7 +885,7 @@
<a name="special_function_error_rates_rep.section_cyl_bessel_j"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_j" title="cyl_bessel_j">cyl_bessel_j</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_cyl_bessel_j.table_cyl_bessel_j"></a><p class="title"><b>Table&#160;11.&#160;Error rates for cyl_bessel_j</b></p>
<a name="special_function_error_rates_rep.section_cyl_bessel_j.table_cyl_bessel_j"></a><p class="title"><b>Table&#160;12.&#160;Error rates for cyl_bessel_j</b></p>
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j">
<colgroup>
<col>
@@ -975,7 +1032,7 @@
(integer orders)</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_cyl_bessel_j_integer_orders_.table_cyl_bessel_j_integer_orders_"></a><p class="title"><b>Table&#160;12.&#160;Error rates for cyl_bessel_j (integer orders)</b></p>
<a name="special_function_error_rates_rep.section_cyl_bessel_j_integer_orders_.table_cyl_bessel_j_integer_orders_"></a><p class="title"><b>Table&#160;13.&#160;Error rates for cyl_bessel_j (integer orders)</b></p>
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j (integer orders)">
<colgroup>
<col>
@@ -1068,7 +1125,7 @@
<a name="special_function_error_rates_rep.section_cyl_bessel_j_prime"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_j_prime" title="cyl_bessel_j_prime">cyl_bessel_j_prime</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_cyl_bessel_j_prime.table_cyl_bessel_j_prime"></a><p class="title"><b>Table&#160;13.&#160;Error rates for cyl_bessel_j_prime</b></p>
<a name="special_function_error_rates_rep.section_cyl_bessel_j_prime.table_cyl_bessel_j_prime"></a><p class="title"><b>Table&#160;14.&#160;Error rates for cyl_bessel_j_prime</b></p>
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j_prime">
<colgroup>
<col>
@@ -1215,7 +1272,7 @@
(integer orders)</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_cyl_bessel_j_prime_integer_orders_.table_cyl_bessel_j_prime_integer_orders_"></a><p class="title"><b>Table&#160;14.&#160;Error rates for cyl_bessel_j_prime (integer orders)</b></p>
<a name="special_function_error_rates_rep.section_cyl_bessel_j_prime_integer_orders_.table_cyl_bessel_j_prime_integer_orders_"></a><p class="title"><b>Table&#160;15.&#160;Error rates for cyl_bessel_j_prime (integer orders)</b></p>
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j_prime (integer orders)">
<colgroup>
<col>
@@ -1301,7 +1358,7 @@
<a name="special_function_error_rates_rep.section_cyl_bessel_k"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_k" title="cyl_bessel_k">cyl_bessel_k</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_cyl_bessel_k.table_cyl_bessel_k"></a><p class="title"><b>Table&#160;15.&#160;Error rates for cyl_bessel_k</b></p>
<a name="special_function_error_rates_rep.section_cyl_bessel_k.table_cyl_bessel_k"></a><p class="title"><b>Table&#160;16.&#160;Error rates for cyl_bessel_k</b></p>
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k">
<colgroup>
<col>
@@ -1412,7 +1469,7 @@
(integer orders)</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_cyl_bessel_k_integer_orders_.table_cyl_bessel_k_integer_orders_"></a><p class="title"><b>Table&#160;16.&#160;Error rates for cyl_bessel_k (integer orders)</b></p>
<a name="special_function_error_rates_rep.section_cyl_bessel_k_integer_orders_.table_cyl_bessel_k_integer_orders_"></a><p class="title"><b>Table&#160;17.&#160;Error rates for cyl_bessel_k (integer orders)</b></p>
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k (integer orders)">
<colgroup>
<col>
@@ -1474,7 +1531,7 @@
<a name="special_function_error_rates_rep.section_cyl_bessel_k_prime"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_k_prime" title="cyl_bessel_k_prime">cyl_bessel_k_prime</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_cyl_bessel_k_prime.table_cyl_bessel_k_prime"></a><p class="title"><b>Table&#160;17.&#160;Error rates for cyl_bessel_k_prime</b></p>
<a name="special_function_error_rates_rep.section_cyl_bessel_k_prime.table_cyl_bessel_k_prime"></a><p class="title"><b>Table&#160;18.&#160;Error rates for cyl_bessel_k_prime</b></p>
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k_prime">
<colgroup>
<col>
@@ -1585,7 +1642,7 @@
(integer orders)</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_cyl_bessel_k_prime_integer_orders_.table_cyl_bessel_k_prime_integer_orders_"></a><p class="title"><b>Table&#160;18.&#160;Error rates for cyl_bessel_k_prime (integer orders)</b></p>
<a name="special_function_error_rates_rep.section_cyl_bessel_k_prime_integer_orders_.table_cyl_bessel_k_prime_integer_orders_"></a><p class="title"><b>Table&#160;19.&#160;Error rates for cyl_bessel_k_prime (integer orders)</b></p>
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k_prime (integer orders)">
<colgroup>
<col>
@@ -1647,7 +1704,7 @@
<a name="special_function_error_rates_rep.section_cyl_neumann"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_neumann" title="cyl_neumann">cyl_neumann</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_cyl_neumann.table_cyl_neumann"></a><p class="title"><b>Table&#160;19.&#160;Error rates for cyl_neumann</b></p>
<a name="special_function_error_rates_rep.section_cyl_neumann.table_cyl_neumann"></a><p class="title"><b>Table&#160;20.&#160;Error rates for cyl_neumann</b></p>
<div class="table-contents"><table class="table" summary="Error rates for cyl_neumann">
<colgroup>
<col>
@@ -1770,7 +1827,7 @@
(integer orders)</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_cyl_neumann_integer_orders_.table_cyl_neumann_integer_orders_"></a><p class="title"><b>Table&#160;20.&#160;Error rates for cyl_neumann (integer orders)</b></p>
<a name="special_function_error_rates_rep.section_cyl_neumann_integer_orders_.table_cyl_neumann_integer_orders_"></a><p class="title"><b>Table&#160;21.&#160;Error rates for cyl_neumann (integer orders)</b></p>
<div class="table-contents"><table class="table" summary="Error rates for cyl_neumann (integer orders)">
<colgroup>
<col>
@@ -1835,7 +1892,7 @@
<a name="special_function_error_rates_rep.section_cyl_neumann_prime"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_neumann_prime" title="cyl_neumann_prime">cyl_neumann_prime</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_cyl_neumann_prime.table_cyl_neumann_prime"></a><p class="title"><b>Table&#160;21.&#160;Error rates for cyl_neumann_prime</b></p>
<a name="special_function_error_rates_rep.section_cyl_neumann_prime.table_cyl_neumann_prime"></a><p class="title"><b>Table&#160;22.&#160;Error rates for cyl_neumann_prime</b></p>
<div class="table-contents"><table class="table" summary="Error rates for cyl_neumann_prime">
<colgroup>
<col>
@@ -1958,7 +2015,7 @@
(integer orders)</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_cyl_neumann_prime_integer_orders_.table_cyl_neumann_prime_integer_orders_"></a><p class="title"><b>Table&#160;22.&#160;Error rates for cyl_neumann_prime (integer orders)</b></p>
<a name="special_function_error_rates_rep.section_cyl_neumann_prime_integer_orders_.table_cyl_neumann_prime_integer_orders_"></a><p class="title"><b>Table&#160;23.&#160;Error rates for cyl_neumann_prime (integer orders)</b></p>
<div class="table-contents"><table class="table" summary="Error rates for cyl_neumann_prime (integer orders)">
<colgroup>
<col>
@@ -2020,7 +2077,7 @@
<a name="special_function_error_rates_rep.section_digamma"></a><a class="link" href="index.html#special_function_error_rates_rep.section_digamma" title="digamma">digamma</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_digamma.table_digamma"></a><p class="title"><b>Table&#160;23.&#160;Error rates for digamma</b></p>
<a name="special_function_error_rates_rep.section_digamma.table_digamma"></a><p class="title"><b>Table&#160;24.&#160;Error rates for digamma</b></p>
<div class="table-contents"><table class="table" summary="Error rates for digamma">
<colgroup>
<col>
@@ -2130,7 +2187,7 @@
<a name="special_function_error_rates_rep.section_ellint_1"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_1" title="ellint_1">ellint_1</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_ellint_1.table_ellint_1"></a><p class="title"><b>Table&#160;24.&#160;Error rates for ellint_1</b></p>
<a name="special_function_error_rates_rep.section_ellint_1.table_ellint_1"></a><p class="title"><b>Table&#160;25.&#160;Error rates for ellint_1</b></p>
<div class="table-contents"><table class="table" summary="Error rates for ellint_1">
<colgroup>
<col>
@@ -2181,7 +2238,7 @@
(complete)</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_ellint_1_complete_.table_ellint_1_complete_"></a><p class="title"><b>Table&#160;25.&#160;Error rates for ellint_1 (complete)</b></p>
<a name="special_function_error_rates_rep.section_ellint_1_complete_.table_ellint_1_complete_"></a><p class="title"><b>Table&#160;26.&#160;Error rates for ellint_1 (complete)</b></p>
<div class="table-contents"><table class="table" summary="Error rates for ellint_1 (complete)">
<colgroup>
<col>
@@ -2231,7 +2288,7 @@
<a name="special_function_error_rates_rep.section_ellint_2"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_2" title="ellint_2">ellint_2</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_ellint_2.table_ellint_2"></a><p class="title"><b>Table&#160;26.&#160;Error rates for ellint_2</b></p>
<a name="special_function_error_rates_rep.section_ellint_2.table_ellint_2"></a><p class="title"><b>Table&#160;27.&#160;Error rates for ellint_2</b></p>
<div class="table-contents"><table class="table" summary="Error rates for ellint_2">
<colgroup>
<col>
@@ -2282,7 +2339,7 @@
(complete)</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_ellint_2_complete_.table_ellint_2_complete_"></a><p class="title"><b>Table&#160;27.&#160;Error rates for ellint_2 (complete)</b></p>
<a name="special_function_error_rates_rep.section_ellint_2_complete_.table_ellint_2_complete_"></a><p class="title"><b>Table&#160;28.&#160;Error rates for ellint_2 (complete)</b></p>
<div class="table-contents"><table class="table" summary="Error rates for ellint_2 (complete)">
<colgroup>
<col>
@@ -2332,7 +2389,7 @@
<a name="special_function_error_rates_rep.section_ellint_3"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_3" title="ellint_3">ellint_3</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_ellint_3.table_ellint_3"></a><p class="title"><b>Table&#160;28.&#160;Error rates for ellint_3</b></p>
<a name="special_function_error_rates_rep.section_ellint_3.table_ellint_3"></a><p class="title"><b>Table&#160;29.&#160;Error rates for ellint_3</b></p>
<div class="table-contents"><table class="table" summary="Error rates for ellint_3">
<colgroup>
<col>
@@ -2395,7 +2452,7 @@
(complete)</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_ellint_3_complete_.table_ellint_3_complete_"></a><p class="title"><b>Table&#160;29.&#160;Error rates for ellint_3 (complete)</b></p>
<a name="special_function_error_rates_rep.section_ellint_3_complete_.table_ellint_3_complete_"></a><p class="title"><b>Table&#160;30.&#160;Error rates for ellint_3 (complete)</b></p>
<div class="table-contents"><table class="table" summary="Error rates for ellint_3 (complete)">
<colgroup>
<col>
@@ -2445,7 +2502,7 @@
<a name="special_function_error_rates_rep.section_ellint_d"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_d" title="ellint_d">ellint_d</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_ellint_d.table_ellint_d"></a><p class="title"><b>Table&#160;30.&#160;Error rates for ellint_d</b></p>
<a name="special_function_error_rates_rep.section_ellint_d.table_ellint_d"></a><p class="title"><b>Table&#160;31.&#160;Error rates for ellint_d</b></p>
<div class="table-contents"><table class="table" summary="Error rates for ellint_d">
<colgroup>
<col>
@@ -2496,7 +2553,7 @@
(complete)</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_ellint_d_complete_.table_ellint_d_complete_"></a><p class="title"><b>Table&#160;31.&#160;Error rates for ellint_d (complete)</b></p>
<a name="special_function_error_rates_rep.section_ellint_d_complete_.table_ellint_d_complete_"></a><p class="title"><b>Table&#160;32.&#160;Error rates for ellint_d (complete)</b></p>
<div class="table-contents"><table class="table" summary="Error rates for ellint_d (complete)">
<colgroup>
<col>
@@ -2546,7 +2603,7 @@
<a name="special_function_error_rates_rep.section_ellint_rc"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_rc" title="ellint_rc">ellint_rc</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_ellint_rc.table_ellint_rc"></a><p class="title"><b>Table&#160;32.&#160;Error rates for ellint_rc</b></p>
<a name="special_function_error_rates_rep.section_ellint_rc.table_ellint_rc"></a><p class="title"><b>Table&#160;33.&#160;Error rates for ellint_rc</b></p>
<div class="table-contents"><table class="table" summary="Error rates for ellint_rc">
<colgroup>
<col>
@@ -2582,7 +2639,7 @@
<a name="special_function_error_rates_rep.section_ellint_rd"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_rd" title="ellint_rd">ellint_rd</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_ellint_rd.table_ellint_rd"></a><p class="title"><b>Table&#160;33.&#160;Error rates for ellint_rd</b></p>
<a name="special_function_error_rates_rep.section_ellint_rd.table_ellint_rd"></a><p class="title"><b>Table&#160;34.&#160;Error rates for ellint_rd</b></p>
<div class="table-contents"><table class="table" summary="Error rates for ellint_rd">
<colgroup>
<col>
@@ -2680,7 +2737,7 @@
<a name="special_function_error_rates_rep.section_ellint_rf"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_rf" title="ellint_rf">ellint_rf</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_ellint_rf.table_ellint_rf"></a><p class="title"><b>Table&#160;34.&#160;Error rates for ellint_rf</b></p>
<a name="special_function_error_rates_rep.section_ellint_rf.table_ellint_rf"></a><p class="title"><b>Table&#160;35.&#160;Error rates for ellint_rf</b></p>
<div class="table-contents"><table class="table" summary="Error rates for ellint_rf">
<colgroup>
<col>
@@ -2766,7 +2823,7 @@
<a name="special_function_error_rates_rep.section_ellint_rg"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_rg" title="ellint_rg">ellint_rg</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_ellint_rg.table_ellint_rg"></a><p class="title"><b>Table&#160;35.&#160;Error rates for ellint_rg</b></p>
<a name="special_function_error_rates_rep.section_ellint_rg.table_ellint_rg"></a><p class="title"><b>Table&#160;36.&#160;Error rates for ellint_rg</b></p>
<div class="table-contents"><table class="table" summary="Error rates for ellint_rg">
<colgroup>
<col>
@@ -2852,7 +2909,7 @@
<a name="special_function_error_rates_rep.section_ellint_rj"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_rj" title="ellint_rj">ellint_rj</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_ellint_rj.table_ellint_rj"></a><p class="title"><b>Table&#160;36.&#160;Error rates for ellint_rj</b></p>
<a name="special_function_error_rates_rep.section_ellint_rj.table_ellint_rj"></a><p class="title"><b>Table&#160;37.&#160;Error rates for ellint_rj</b></p>
<div class="table-contents"><table class="table" summary="Error rates for ellint_rj">
<colgroup>
<col>
@@ -2938,7 +2995,7 @@
<a name="special_function_error_rates_rep.section_erf"></a><a class="link" href="index.html#special_function_error_rates_rep.section_erf" title="erf">erf</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_erf.table_erf"></a><p class="title"><b>Table&#160;37.&#160;Error rates for erf</b></p>
<a name="special_function_error_rates_rep.section_erf.table_erf"></a><p class="title"><b>Table&#160;38.&#160;Error rates for erf</b></p>
<div class="table-contents"><table class="table" summary="Error rates for erf">
<colgroup>
<col>
@@ -3003,7 +3060,7 @@
<a name="special_function_error_rates_rep.section_erf_inv"></a><a class="link" href="index.html#special_function_error_rates_rep.section_erf_inv" title="erf_inv">erf_inv</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_erf_inv.table_erf_inv"></a><p class="title"><b>Table&#160;38.&#160;Error rates for erf_inv</b></p>
<a name="special_function_error_rates_rep.section_erf_inv.table_erf_inv"></a><p class="title"><b>Table&#160;39.&#160;Error rates for erf_inv</b></p>
<div class="table-contents"><table class="table" summary="Error rates for erf_inv">
<colgroup>
<col>
@@ -3039,7 +3096,7 @@
<a name="special_function_error_rates_rep.section_erfc"></a><a class="link" href="index.html#special_function_error_rates_rep.section_erfc" title="erfc">erfc</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_erfc.table_erfc"></a><p class="title"><b>Table&#160;39.&#160;Error rates for erfc</b></p>
<a name="special_function_error_rates_rep.section_erfc.table_erfc"></a><p class="title"><b>Table&#160;40.&#160;Error rates for erfc</b></p>
<div class="table-contents"><table class="table" summary="Error rates for erfc">
<colgroup>
<col>
@@ -3104,7 +3161,7 @@
<a name="special_function_error_rates_rep.section_erfc_inv"></a><a class="link" href="index.html#special_function_error_rates_rep.section_erfc_inv" title="erfc_inv">erfc_inv</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_erfc_inv.table_erfc_inv"></a><p class="title"><b>Table&#160;40.&#160;Error rates for erfc_inv</b></p>
<a name="special_function_error_rates_rep.section_erfc_inv.table_erfc_inv"></a><p class="title"><b>Table&#160;41.&#160;Error rates for erfc_inv</b></p>
<div class="table-contents"><table class="table" summary="Error rates for erfc_inv">
<colgroup>
<col>
@@ -3141,7 +3198,7 @@
(Ei)</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_expint_Ei_.table_expint_Ei_"></a><p class="title"><b>Table&#160;41.&#160;Error rates for expint (Ei)</b></p>
<a name="special_function_error_rates_rep.section_expint_Ei_.table_expint_Ei_"></a><p class="title"><b>Table&#160;42.&#160;Error rates for expint (Ei)</b></p>
<div class="table-contents"><table class="table" summary="Error rates for expint (Ei)">
<colgroup>
<col>
@@ -3192,7 +3249,7 @@
(En)</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_expint_En_.table_expint_En_"></a><p class="title"><b>Table&#160;42.&#160;Error rates for expint (En)</b></p>
<a name="special_function_error_rates_rep.section_expint_En_.table_expint_En_"></a><p class="title"><b>Table&#160;43.&#160;Error rates for expint (En)</b></p>
<div class="table-contents"><table class="table" summary="Error rates for expint (En)">
<colgroup>
<col>
@@ -3251,10 +3308,47 @@
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="special_function_error_rates_rep.section_expm1"></a><a class="link" href="index.html#special_function_error_rates_rep.section_expm1" title="expm1">expm1</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_expm1.table_expm1"></a><p class="title"><b>Table&#160;44.&#160;Error rates for expm1</b></p>
<div class="table-contents"><table class="table" summary="Error rates for expm1">
<colgroup>
<col>
<col>
</colgroup>
<thead><tr>
<th>
</th>
<th>
<p>
Microsoft Visual C++ version 12.0<br> Win32<br> double
</p>
</th>
</tr></thead>
<tbody><tr>
<td>
<p>
Random test data
</p>
</td>
<td>
<p>
<span class="blue">Max = 0.996&#949; (Mean = 0.283&#949;)</span><br> <br>
(&lt;math.h&gt; = Max = 1.31&#949; (Mean = 0.496&#949;))
</p>
</td>
</tr></tbody>
</table></div>
</div>
<br class="table-break">
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="special_function_error_rates_rep.section_gamma_p"></a><a class="link" href="index.html#special_function_error_rates_rep.section_gamma_p" title="gamma_p">gamma_p</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_gamma_p.table_gamma_p"></a><p class="title"><b>Table&#160;43.&#160;Error rates for gamma_p</b></p>
<a name="special_function_error_rates_rep.section_gamma_p.table_gamma_p"></a><p class="title"><b>Table&#160;45.&#160;Error rates for gamma_p</b></p>
<div class="table-contents"><table class="table" summary="Error rates for gamma_p">
<colgroup>
<col>
@@ -3328,7 +3422,7 @@
<a name="special_function_error_rates_rep.section_gamma_p_inv"></a><a class="link" href="index.html#special_function_error_rates_rep.section_gamma_p_inv" title="gamma_p_inv">gamma_p_inv</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_gamma_p_inv.table_gamma_p_inv"></a><p class="title"><b>Table&#160;44.&#160;Error rates for gamma_p_inv</b></p>
<a name="special_function_error_rates_rep.section_gamma_p_inv.table_gamma_p_inv"></a><p class="title"><b>Table&#160;46.&#160;Error rates for gamma_p_inv</b></p>
<div class="table-contents"><table class="table" summary="Error rates for gamma_p_inv">
<colgroup>
<col>
@@ -3390,7 +3484,7 @@
<a name="special_function_error_rates_rep.section_gamma_p_inva"></a><a class="link" href="index.html#special_function_error_rates_rep.section_gamma_p_inva" title="gamma_p_inva">gamma_p_inva</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_gamma_p_inva.table_gamma_p_inva"></a><p class="title"><b>Table&#160;45.&#160;Error rates for gamma_p_inva</b></p>
<a name="special_function_error_rates_rep.section_gamma_p_inva.table_gamma_p_inva"></a><p class="title"><b>Table&#160;47.&#160;Error rates for gamma_p_inva</b></p>
<div class="table-contents"><table class="table" summary="Error rates for gamma_p_inva">
<colgroup>
<col>
@@ -3426,7 +3520,7 @@
<a name="special_function_error_rates_rep.section_gamma_q"></a><a class="link" href="index.html#special_function_error_rates_rep.section_gamma_q" title="gamma_q">gamma_q</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_gamma_q.table_gamma_q"></a><p class="title"><b>Table&#160;46.&#160;Error rates for gamma_q</b></p>
<a name="special_function_error_rates_rep.section_gamma_q.table_gamma_q"></a><p class="title"><b>Table&#160;48.&#160;Error rates for gamma_q</b></p>
<div class="table-contents"><table class="table" summary="Error rates for gamma_q">
<colgroup>
<col>
@@ -3500,7 +3594,7 @@
<a name="special_function_error_rates_rep.section_gamma_q_inv"></a><a class="link" href="index.html#special_function_error_rates_rep.section_gamma_q_inv" title="gamma_q_inv">gamma_q_inv</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_gamma_q_inv.table_gamma_q_inv"></a><p class="title"><b>Table&#160;47.&#160;Error rates for gamma_q_inv</b></p>
<a name="special_function_error_rates_rep.section_gamma_q_inv.table_gamma_q_inv"></a><p class="title"><b>Table&#160;49.&#160;Error rates for gamma_q_inv</b></p>
<div class="table-contents"><table class="table" summary="Error rates for gamma_q_inv">
<colgroup>
<col>
@@ -3562,7 +3656,7 @@
<a name="special_function_error_rates_rep.section_gamma_q_inva"></a><a class="link" href="index.html#special_function_error_rates_rep.section_gamma_q_inva" title="gamma_q_inva">gamma_q_inva</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_gamma_q_inva.table_gamma_q_inva"></a><p class="title"><b>Table&#160;48.&#160;Error rates for gamma_q_inva</b></p>
<a name="special_function_error_rates_rep.section_gamma_q_inva.table_gamma_q_inva"></a><p class="title"><b>Table&#160;50.&#160;Error rates for gamma_q_inva</b></p>
<div class="table-contents"><table class="table" summary="Error rates for gamma_q_inva">
<colgroup>
<col>
@@ -3598,7 +3692,7 @@
<a name="special_function_error_rates_rep.section_hermite"></a><a class="link" href="index.html#special_function_error_rates_rep.section_hermite" title="hermite">hermite</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_hermite.table_hermite"></a><p class="title"><b>Table&#160;49.&#160;Error rates for hermite</b></p>
<a name="special_function_error_rates_rep.section_hermite.table_hermite"></a><p class="title"><b>Table&#160;51.&#160;Error rates for hermite</b></p>
<div class="table-contents"><table class="table" summary="Error rates for hermite">
<colgroup>
<col>
@@ -3634,7 +3728,7 @@
<a name="special_function_error_rates_rep.section_heuman_lambda"></a><a class="link" href="index.html#special_function_error_rates_rep.section_heuman_lambda" title="heuman_lambda">heuman_lambda</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_heuman_lambda.table_heuman_lambda"></a><p class="title"><b>Table&#160;50.&#160;Error rates for heuman_lambda</b></p>
<a name="special_function_error_rates_rep.section_heuman_lambda.table_heuman_lambda"></a><p class="title"><b>Table&#160;52.&#160;Error rates for heuman_lambda</b></p>
<div class="table-contents"><table class="table" summary="Error rates for heuman_lambda">
<colgroup>
<col>
@@ -3684,7 +3778,7 @@
<a name="special_function_error_rates_rep.section_ibeta"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ibeta" title="ibeta">ibeta</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_ibeta.table_ibeta"></a><p class="title"><b>Table&#160;51.&#160;Error rates for ibeta</b></p>
<a name="special_function_error_rates_rep.section_ibeta.table_ibeta"></a><p class="title"><b>Table&#160;53.&#160;Error rates for ibeta</b></p>
<div class="table-contents"><table class="table" summary="Error rates for ibeta">
<colgroup>
<col>
@@ -3758,7 +3852,7 @@
<a name="special_function_error_rates_rep.section_ibeta_inv"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ibeta_inv" title="ibeta_inv">ibeta_inv</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_ibeta_inv.table_ibeta_inv"></a><p class="title"><b>Table&#160;52.&#160;Error rates for ibeta_inv</b></p>
<a name="special_function_error_rates_rep.section_ibeta_inv.table_ibeta_inv"></a><p class="title"><b>Table&#160;54.&#160;Error rates for ibeta_inv</b></p>
<div class="table-contents"><table class="table" summary="Error rates for ibeta_inv">
<colgroup>
<col>
@@ -3794,7 +3888,7 @@
<a name="special_function_error_rates_rep.section_ibetac"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ibetac" title="ibetac">ibetac</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_ibetac.table_ibetac"></a><p class="title"><b>Table&#160;53.&#160;Error rates for ibetac</b></p>
<a name="special_function_error_rates_rep.section_ibetac.table_ibetac"></a><p class="title"><b>Table&#160;55.&#160;Error rates for ibetac</b></p>
<div class="table-contents"><table class="table" summary="Error rates for ibetac">
<colgroup>
<col>
@@ -3868,7 +3962,7 @@
<a name="special_function_error_rates_rep.section_ibetac_inv"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ibetac_inv" title="ibetac_inv">ibetac_inv</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_ibetac_inv.table_ibetac_inv"></a><p class="title"><b>Table&#160;54.&#160;Error rates for ibetac_inv</b></p>
<a name="special_function_error_rates_rep.section_ibetac_inv.table_ibetac_inv"></a><p class="title"><b>Table&#160;56.&#160;Error rates for ibetac_inv</b></p>
<div class="table-contents"><table class="table" summary="Error rates for ibetac_inv">
<colgroup>
<col>
@@ -3904,7 +3998,7 @@
<a name="special_function_error_rates_rep.section_jacobi_cn"></a><a class="link" href="index.html#special_function_error_rates_rep.section_jacobi_cn" title="jacobi_cn">jacobi_cn</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_jacobi_cn.table_jacobi_cn"></a><p class="title"><b>Table&#160;55.&#160;Error rates for jacobi_cn</b></p>
<a name="special_function_error_rates_rep.section_jacobi_cn.table_jacobi_cn"></a><p class="title"><b>Table&#160;57.&#160;Error rates for jacobi_cn</b></p>
<div class="table-contents"><table class="table" summary="Error rates for jacobi_cn">
<colgroup>
<col>
@@ -3990,7 +4084,7 @@
<a name="special_function_error_rates_rep.section_jacobi_dn"></a><a class="link" href="index.html#special_function_error_rates_rep.section_jacobi_dn" title="jacobi_dn">jacobi_dn</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_jacobi_dn.table_jacobi_dn"></a><p class="title"><b>Table&#160;56.&#160;Error rates for jacobi_dn</b></p>
<a name="special_function_error_rates_rep.section_jacobi_dn.table_jacobi_dn"></a><p class="title"><b>Table&#160;58.&#160;Error rates for jacobi_dn</b></p>
<div class="table-contents"><table class="table" summary="Error rates for jacobi_dn">
<colgroup>
<col>
@@ -4076,7 +4170,7 @@
<a name="special_function_error_rates_rep.section_jacobi_sn"></a><a class="link" href="index.html#special_function_error_rates_rep.section_jacobi_sn" title="jacobi_sn">jacobi_sn</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_jacobi_sn.table_jacobi_sn"></a><p class="title"><b>Table&#160;57.&#160;Error rates for jacobi_sn</b></p>
<a name="special_function_error_rates_rep.section_jacobi_sn.table_jacobi_sn"></a><p class="title"><b>Table&#160;59.&#160;Error rates for jacobi_sn</b></p>
<div class="table-contents"><table class="table" summary="Error rates for jacobi_sn">
<colgroup>
<col>
@@ -4162,7 +4256,7 @@
<a name="special_function_error_rates_rep.section_legendre_p"></a><a class="link" href="index.html#special_function_error_rates_rep.section_legendre_p" title="legendre_p">legendre_p</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_legendre_p.table_legendre_p"></a><p class="title"><b>Table&#160;58.&#160;Error rates for legendre_p</b></p>
<a name="special_function_error_rates_rep.section_legendre_p.table_legendre_p"></a><p class="title"><b>Table&#160;60.&#160;Error rates for legendre_p</b></p>
<div class="table-contents"><table class="table" summary="Error rates for legendre_p">
<colgroup>
<col>
@@ -4213,7 +4307,7 @@
(associated)</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_legendre_p_associated_.table_legendre_p_associated_"></a><p class="title"><b>Table&#160;59.&#160;Error rates for legendre_p (associated)</b></p>
<a name="special_function_error_rates_rep.section_legendre_p_associated_.table_legendre_p_associated_"></a><p class="title"><b>Table&#160;61.&#160;Error rates for legendre_p (associated)</b></p>
<div class="table-contents"><table class="table" summary="Error rates for legendre_p (associated)">
<colgroup>
<col>
@@ -4249,7 +4343,7 @@
<a name="special_function_error_rates_rep.section_legendre_q"></a><a class="link" href="index.html#special_function_error_rates_rep.section_legendre_q" title="legendre_q">legendre_q</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_legendre_q.table_legendre_q"></a><p class="title"><b>Table&#160;60.&#160;Error rates for legendre_q</b></p>
<a name="special_function_error_rates_rep.section_legendre_q.table_legendre_q"></a><p class="title"><b>Table&#160;62.&#160;Error rates for legendre_q</b></p>
<div class="table-contents"><table class="table" summary="Error rates for legendre_q">
<colgroup>
<col>
@@ -4299,7 +4393,7 @@
<a name="special_function_error_rates_rep.section_lgamma"></a><a class="link" href="index.html#special_function_error_rates_rep.section_lgamma" title="lgamma">lgamma</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_lgamma.table_lgamma"></a><p class="title"><b>Table&#160;61.&#160;Error rates for lgamma</b></p>
<a name="special_function_error_rates_rep.section_lgamma.table_lgamma"></a><p class="title"><b>Table&#160;63.&#160;Error rates for lgamma</b></p>
<div class="table-contents"><table class="table" summary="Error rates for lgamma">
<colgroup>
<col>
@@ -4400,10 +4494,47 @@
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="special_function_error_rates_rep.section_log1p"></a><a class="link" href="index.html#special_function_error_rates_rep.section_log1p" title="log1p">log1p</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_log1p.table_log1p"></a><p class="title"><b>Table&#160;64.&#160;Error rates for log1p</b></p>
<div class="table-contents"><table class="table" summary="Error rates for log1p">
<colgroup>
<col>
<col>
</colgroup>
<thead><tr>
<th>
</th>
<th>
<p>
Microsoft Visual C++ version 12.0<br> Win32<br> double
</p>
</th>
</tr></thead>
<tbody><tr>
<td>
<p>
Random test data
</p>
</td>
<td>
<p>
<span class="blue">Max = 0.509&#949; (Mean = 0.057&#949;)</span><br> <br>
(&lt;math.h&gt; = Max = 0.509&#949; (Mean = 0.057&#949;))
</p>
</td>
</tr></tbody>
</table></div>
</div>
<br class="table-break">
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="special_function_error_rates_rep.section_polygamma"></a><a class="link" href="index.html#special_function_error_rates_rep.section_polygamma" title="polygamma">polygamma</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_polygamma.table_polygamma"></a><p class="title"><b>Table&#160;62.&#160;Error rates for polygamma</b></p>
<a name="special_function_error_rates_rep.section_polygamma.table_polygamma"></a><p class="title"><b>Table&#160;65.&#160;Error rates for polygamma</b></p>
<div class="table-contents"><table class="table" summary="Error rates for polygamma">
<colgroup>
<col>
@@ -4498,10 +4629,46 @@
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="special_function_error_rates_rep.section_powm1"></a><a class="link" href="index.html#special_function_error_rates_rep.section_powm1" title="powm1">powm1</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_powm1.table_powm1"></a><p class="title"><b>Table&#160;66.&#160;Error rates for powm1</b></p>
<div class="table-contents"><table class="table" summary="Error rates for powm1">
<colgroup>
<col>
<col>
</colgroup>
<thead><tr>
<th>
</th>
<th>
<p>
Microsoft Visual C++ version 12.0<br> Win32<br> double
</p>
</th>
</tr></thead>
<tbody><tr>
<td>
<p>
powm1
</p>
</td>
<td>
<p>
<span class="blue">Max = 1.99&#949; (Mean = 0.461&#949;)</span>
</p>
</td>
</tr></tbody>
</table></div>
</div>
<br class="table-break">
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="special_function_error_rates_rep.section_sin_pi"></a><a class="link" href="index.html#special_function_error_rates_rep.section_sin_pi" title="sin_pi">sin_pi</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_sin_pi.table_sin_pi"></a><p class="title"><b>Table&#160;63.&#160;Error rates for sin_pi</b></p>
<a name="special_function_error_rates_rep.section_sin_pi.table_sin_pi"></a><p class="title"><b>Table&#160;67.&#160;Error rates for sin_pi</b></p>
<div class="table-contents"><table class="table" summary="Error rates for sin_pi">
<colgroup>
<col>
@@ -4551,7 +4718,7 @@
<a name="special_function_error_rates_rep.section_sph_bessel"></a><a class="link" href="index.html#special_function_error_rates_rep.section_sph_bessel" title="sph_bessel">sph_bessel</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_sph_bessel.table_sph_bessel"></a><p class="title"><b>Table&#160;64.&#160;Error rates for sph_bessel</b></p>
<a name="special_function_error_rates_rep.section_sph_bessel.table_sph_bessel"></a><p class="title"><b>Table&#160;68.&#160;Error rates for sph_bessel</b></p>
<div class="table-contents"><table class="table" summary="Error rates for sph_bessel">
<colgroup>
<col>
@@ -4587,7 +4754,7 @@
<a name="special_function_error_rates_rep.section_sph_bessel_prime"></a><a class="link" href="index.html#special_function_error_rates_rep.section_sph_bessel_prime" title="sph_bessel_prime">sph_bessel_prime</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_sph_bessel_prime.table_sph_bessel_prime"></a><p class="title"><b>Table&#160;65.&#160;Error rates for sph_bessel_prime</b></p>
<a name="special_function_error_rates_rep.section_sph_bessel_prime.table_sph_bessel_prime"></a><p class="title"><b>Table&#160;69.&#160;Error rates for sph_bessel_prime</b></p>
<div class="table-contents"><table class="table" summary="Error rates for sph_bessel_prime">
<colgroup>
<col>
@@ -4623,7 +4790,7 @@
<a name="special_function_error_rates_rep.section_sph_neumann"></a><a class="link" href="index.html#special_function_error_rates_rep.section_sph_neumann" title="sph_neumann">sph_neumann</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_sph_neumann.table_sph_neumann"></a><p class="title"><b>Table&#160;66.&#160;Error rates for sph_neumann</b></p>
<a name="special_function_error_rates_rep.section_sph_neumann.table_sph_neumann"></a><p class="title"><b>Table&#160;70.&#160;Error rates for sph_neumann</b></p>
<div class="table-contents"><table class="table" summary="Error rates for sph_neumann">
<colgroup>
<col>
@@ -4659,7 +4826,7 @@
<a name="special_function_error_rates_rep.section_sph_neumann_prime"></a><a class="link" href="index.html#special_function_error_rates_rep.section_sph_neumann_prime" title="sph_neumann_prime">sph_neumann_prime</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_sph_neumann_prime.table_sph_neumann_prime"></a><p class="title"><b>Table&#160;67.&#160;Error rates for sph_neumann_prime</b></p>
<a name="special_function_error_rates_rep.section_sph_neumann_prime.table_sph_neumann_prime"></a><p class="title"><b>Table&#160;71.&#160;Error rates for sph_neumann_prime</b></p>
<div class="table-contents"><table class="table" summary="Error rates for sph_neumann_prime">
<colgroup>
<col>
@@ -4692,10 +4859,118 @@
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="special_function_error_rates_rep.section_spherical_harmonic_i"></a><a class="link" href="index.html#special_function_error_rates_rep.section_spherical_harmonic_i" title="spherical_harmonic_i">spherical_harmonic_i</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_spherical_harmonic_i.table_spherical_harmonic_i"></a><p class="title"><b>Table&#160;72.&#160;Error rates for spherical_harmonic_i</b></p>
<div class="table-contents"><table class="table" summary="Error rates for spherical_harmonic_i">
<colgroup>
<col>
<col>
</colgroup>
<thead><tr>
<th>
</th>
<th>
<p>
Microsoft Visual C++ version 12.0<br> Win32<br> double
</p>
</th>
</tr></thead>
<tbody><tr>
<td>
<p>
Spherical Harmonics
</p>
</td>
<td>
<p>
<span class="blue">Max = 2.27e+004&#949; (Mean = 725&#949;)</span>
</p>
</td>
</tr></tbody>
</table></div>
</div>
<br class="table-break">
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="special_function_error_rates_rep.section_spherical_harmonic_r"></a><a class="link" href="index.html#special_function_error_rates_rep.section_spherical_harmonic_r" title="spherical_harmonic_r">spherical_harmonic_r</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_spherical_harmonic_r.table_spherical_harmonic_r"></a><p class="title"><b>Table&#160;73.&#160;Error rates for spherical_harmonic_r</b></p>
<div class="table-contents"><table class="table" summary="Error rates for spherical_harmonic_r">
<colgroup>
<col>
<col>
</colgroup>
<thead><tr>
<th>
</th>
<th>
<p>
Microsoft Visual C++ version 12.0<br> Win32<br> double
</p>
</th>
</tr></thead>
<tbody><tr>
<td>
<p>
Spherical Harmonics
</p>
</td>
<td>
<p>
<span class="blue">Max = 2.27e+004&#949; (Mean = 725&#949;)</span>
</p>
</td>
</tr></tbody>
</table></div>
</div>
<br class="table-break">
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="special_function_error_rates_rep.section_sqrt1pm1"></a><a class="link" href="index.html#special_function_error_rates_rep.section_sqrt1pm1" title="sqrt1pm1">sqrt1pm1</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_sqrt1pm1.table_sqrt1pm1"></a><p class="title"><b>Table&#160;74.&#160;Error rates for sqrt1pm1</b></p>
<div class="table-contents"><table class="table" summary="Error rates for sqrt1pm1">
<colgroup>
<col>
<col>
</colgroup>
<thead><tr>
<th>
</th>
<th>
<p>
Microsoft Visual C++ version 12.0<br> Win32<br> double
</p>
</th>
</tr></thead>
<tbody><tr>
<td>
<p>
sqrt1pm1
</p>
</td>
<td>
<p>
<span class="blue">Max = 1.36&#949; (Mean = 0.44&#949;)</span>
</p>
</td>
</tr></tbody>
</table></div>
</div>
<br class="table-break">
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="special_function_error_rates_rep.section_tgamma"></a><a class="link" href="index.html#special_function_error_rates_rep.section_tgamma" title="tgamma">tgamma</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_tgamma.table_tgamma"></a><p class="title"><b>Table&#160;68.&#160;Error rates for tgamma</b></p>
<a name="special_function_error_rates_rep.section_tgamma.table_tgamma"></a><p class="title"><b>Table&#160;75.&#160;Error rates for tgamma</b></p>
<div class="table-contents"><table class="table" summary="Error rates for tgamma">
<colgroup>
<col>
@@ -4799,7 +5074,7 @@
<a name="special_function_error_rates_rep.section_tgamma1pm1"></a><a class="link" href="index.html#special_function_error_rates_rep.section_tgamma1pm1" title="tgamma1pm1">tgamma1pm1</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_tgamma1pm1.table_tgamma1pm1"></a><p class="title"><b>Table&#160;69.&#160;Error rates for tgamma1pm1</b></p>
<a name="special_function_error_rates_rep.section_tgamma1pm1.table_tgamma1pm1"></a><p class="title"><b>Table&#160;76.&#160;Error rates for tgamma1pm1</b></p>
<div class="table-contents"><table class="table" summary="Error rates for tgamma1pm1">
<colgroup>
<col>
@@ -4835,7 +5110,7 @@
<a name="special_function_error_rates_rep.section_tgamma_delta_ratio"></a><a class="link" href="index.html#special_function_error_rates_rep.section_tgamma_delta_ratio" title="tgamma_delta_ratio">tgamma_delta_ratio</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_tgamma_delta_ratio.table_tgamma_delta_ratio"></a><p class="title"><b>Table&#160;70.&#160;Error rates for tgamma_delta_ratio</b></p>
<a name="special_function_error_rates_rep.section_tgamma_delta_ratio.table_tgamma_delta_ratio"></a><p class="title"><b>Table&#160;77.&#160;Error rates for tgamma_delta_ratio</b></p>
<div class="table-contents"><table class="table" summary="Error rates for tgamma_delta_ratio">
<colgroup>
<col>
@@ -4934,7 +5209,7 @@
(incomplete)</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_tgamma_incomplete_.table_tgamma_incomplete_"></a><p class="title"><b>Table&#160;71.&#160;Error rates for tgamma (incomplete)</b></p>
<a name="special_function_error_rates_rep.section_tgamma_incomplete_.table_tgamma_incomplete_"></a><p class="title"><b>Table&#160;78.&#160;Error rates for tgamma (incomplete)</b></p>
<div class="table-contents"><table class="table" summary="Error rates for tgamma (incomplete)">
<colgroup>
<col>
@@ -4996,7 +5271,7 @@
<a name="special_function_error_rates_rep.section_tgamma_lower"></a><a class="link" href="index.html#special_function_error_rates_rep.section_tgamma_lower" title="tgamma_lower">tgamma_lower</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_tgamma_lower.table_tgamma_lower"></a><p class="title"><b>Table&#160;72.&#160;Error rates for tgamma_lower</b></p>
<a name="special_function_error_rates_rep.section_tgamma_lower.table_tgamma_lower"></a><p class="title"><b>Table&#160;79.&#160;Error rates for tgamma_lower</b></p>
<div class="table-contents"><table class="table" summary="Error rates for tgamma_lower">
<colgroup>
<col>
@@ -5058,7 +5333,7 @@
<a name="special_function_error_rates_rep.section_tgamma_ratio"></a><a class="link" href="index.html#special_function_error_rates_rep.section_tgamma_ratio" title="tgamma_ratio">tgamma_ratio</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_tgamma_ratio.table_tgamma_ratio"></a><p class="title"><b>Table&#160;73.&#160;Error rates for tgamma_ratio</b></p>
<a name="special_function_error_rates_rep.section_tgamma_ratio.table_tgamma_ratio"></a><p class="title"><b>Table&#160;80.&#160;Error rates for tgamma_ratio</b></p>
<div class="table-contents"><table class="table" summary="Error rates for tgamma_ratio">
<colgroup>
<col>
@@ -5094,7 +5369,7 @@
<a name="special_function_error_rates_rep.section_trigamma"></a><a class="link" href="index.html#special_function_error_rates_rep.section_trigamma" title="trigamma">trigamma</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_trigamma.table_trigamma"></a><p class="title"><b>Table&#160;74.&#160;Error rates for trigamma</b></p>
<a name="special_function_error_rates_rep.section_trigamma.table_trigamma"></a><p class="title"><b>Table&#160;81.&#160;Error rates for trigamma</b></p>
<div class="table-contents"><table class="table" summary="Error rates for trigamma">
<colgroup>
<col>
@@ -5130,7 +5405,7 @@
<a name="special_function_error_rates_rep.section_zeta"></a><a class="link" href="index.html#special_function_error_rates_rep.section_zeta" title="zeta">zeta</a>
</h2></div></div></div>
<div class="table">
<a name="special_function_error_rates_rep.section_zeta.table_zeta"></a><p class="title"><b>Table&#160;75.&#160;Error rates for zeta</b></p>
<a name="special_function_error_rates_rep.section_zeta.table_zeta"></a><p class="title"><b>Table&#160;82.&#160;Error rates for zeta</b></p>
<div class="table-contents"><table class="table" summary="Error rates for zeta">
<colgroup>
<col>
@@ -5232,7 +5507,7 @@
</div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"><p><small>Last revised: June 29, 2015 at 10:52:00 GMT</small></p></td>
<td align="left"><p><small>Last revised: June 29, 2015 at 18:21:41 GMT</small></p></td>
<td align="right"><div class="copyright-footer"></div></td>
</tr></table>
<hr>

65
reporting/accuracy/test_log1p_expm1.cpp Normal file
View File

@@ -0,0 +1,65 @@
// Copyright John Maddock 2006-15.
// Copyright Paul A. Bristow 2007
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0. (See accompanying file
// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
#include "bindings.hpp"
#include "../../test/log1p_expm1_test.hpp"
#include <boost/math/special_functions/expm1.hpp>
#include <boost/math/special_functions/log1p.hpp>
#define BOOST_TEST_MAIN
#include <boost/test/unit_test.hpp>
BOOST_AUTO_TEST_CASE(test_main, *boost::unit_test::expected_failures(10000))
{
BOOST_MATH_CONTROL_FP;
error_stream_replacer rep;
#ifdef TYPE_TO_TEST
test(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST);
#else
bool test_float = false;
bool test_double = false;
bool test_long_double = false;
if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits)
{
//
// Don't bother with long double, it's the same as double:
//
if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false)
test_float = true;
test_double = true;
}
else
{
if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false)
test_float = true;
if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false)
test_double = true;
test_long_double = true;
}
#ifdef ALWAYS_TEST_DOUBLE
test_double = true;
#endif
if(test_float)
test(0.0f, "float");
if(test_double)
test(0.0, "double");
if(test_long_double)
test(0.0L, "long double");
#ifdef BOOST_MATH_USE_FLOAT128
//test(0.0Q, "__float128");
#endif
#endif
}

63
reporting/accuracy/test_owens_t.cpp Normal file
View File

@@ -0,0 +1,63 @@
// Copyright John Maddock 2006-15.
// Copyright Paul A. Bristow 2007
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0. (See accompanying file
// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
#define BOOST_TEST_MAIN
#include "bindings.hpp"
#include "../../test/test_owens_t.hpp"
#include <boost/math/special_functions/owens_t.hpp> // for owens_t function.
#include <boost/test/unit_test.hpp>
BOOST_AUTO_TEST_CASE(test_main, *boost::unit_test::expected_failures(10000))
{
BOOST_MATH_CONTROL_FP;
error_stream_replacer rep;
#ifdef TYPE_TO_TEST
test_owens_t(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST);
#else
bool test_float = false;
bool test_double = false;
bool test_long_double = false;
if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits)
{
//
// Don't bother with long double, it's the same as double:
//
if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false)
test_float = true;
test_double = true;
}
else
{
if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false)
test_float = true;
if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false)
test_double = true;
test_long_double = true;
}
#ifdef ALWAYS_TEST_DOUBLE
test_double = true;
#endif
if(test_float)
test_owens_t(0.0f, "float");
if(test_double)
test_owens_t(0.0, "double");
if(test_long_double)
test_owens_t(0.0L, "long double");
#ifdef BOOST_MATH_USE_FLOAT128
//test_owens_t(0.0Q, "__float128");
#endif
#endif
}

64
reporting/accuracy/test_powm1.cpp Normal file
View File

@@ -0,0 +1,64 @@
// Copyright John Maddock 2006-15.
// Copyright Paul A. Bristow 2007
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0. (See accompanying file
// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
#define BOOST_TEST_MAIN
#include "bindings.hpp"
#include "../../test/powm1_sqrtp1m1_test.hpp"
#include <boost/math/special_functions/powm1.hpp>
#include <boost/math/special_functions/sqrt1pm1.hpp>
#include <boost/test/unit_test.hpp>
BOOST_AUTO_TEST_CASE(test_main, *boost::unit_test::expected_failures(10000))
{
BOOST_MATH_CONTROL_FP;
error_stream_replacer rep;
#ifdef TYPE_TO_TEST
test_powm1_sqrtp1m1(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST);
#else
bool test_float = false;
bool test_double = false;
bool test_long_double = false;
if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits)
{
//
// Don't bother with long double, it's the same as double:
//
if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false)
test_float = true;
test_double = true;
}
else
{
if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false)
test_float = true;
if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false)
test_double = true;
test_long_double = true;
}
#ifdef ALWAYS_TEST_DOUBLE
test_double = true;
#endif
if(test_float)
test_powm1_sqrtp1m1(0.0f, "float");
if(test_double)
test_powm1_sqrtp1m1(0.0, "double");
if(test_long_double)
test_powm1_sqrtp1m1(0.0L, "long double");
#ifdef BOOST_MATH_USE_FLOAT128
//test_powm1_sqrtp1m1(0.0Q, "__float128");
#endif
#endif
}

63
reporting/accuracy/test_spherical_harmonic.cpp Normal file
View File

@@ -0,0 +1,63 @@
// Copyright John Maddock 2006-15.
// Copyright Paul A. Bristow 2007
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0. (See accompanying file
// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
#include "bindings.hpp"
#include "../../test/test_spherical_harmonic.hpp"
#include <boost/math/special_functions/spherical_harmonic.hpp>
#define BOOST_TEST_MAIN
#include <boost/test/unit_test.hpp>
BOOST_AUTO_TEST_CASE(test_main, *boost::unit_test::expected_failures(10000))
{
BOOST_MATH_CONTROL_FP;
error_stream_replacer rep;
#ifdef TYPE_TO_TEST
test_spherical_harmonic(static_cast<TYPE_TO_TEST>(0), NAME_OF_TYPE_TO_TEST);
#else
bool test_float = false;
bool test_double = false;
bool test_long_double = false;
if(std::numeric_limits<long double>::digits == std::numeric_limits<double>::digits)
{
//
// Don't bother with long double, it's the same as double:
//
if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false)
test_float = true;
test_double = true;
}
else
{
if(BOOST_MATH_PROMOTE_FLOAT_POLICY == false)
test_float = true;
if(BOOST_MATH_PROMOTE_DOUBLE_POLICY == false)
test_double = true;
test_long_double = true;
}
#ifdef ALWAYS_TEST_DOUBLE
test_double = true;
#endif
if(test_float)
test_spherical_harmonic(0.0f, "float");
if(test_double)
test_spherical_harmonic(0.0, "double");
if(test_long_double)
test_spherical_harmonic(0.0L, "long double");
#ifdef BOOST_MATH_USE_FLOAT128
//test_spherical_harmonic(0.0Q, "__float128");
#endif
#endif
}

21
test/log1p_expm1_test.hpp
View File

@@ -17,7 +17,9 @@ void do_test(const T& data, const char* type_name, const char* test_name)
typedef Real value_type;
typedef value_type (*pg)(value_type);
#if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
#ifdef LOG1P_FUNCTION_TO_TEST
pg funcp = LOG1P_FUNCTION_TO_TEST;
#elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
pg funcp = &boost::math::log1p<value_type>;
#else
pg funcp = &boost::math::log1p;
@@ -29,21 +31,21 @@ void do_test(const T& data, const char* type_name, const char* test_name)
//
// test log1p against data:
//
#if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
funcp = boost::math::log1p<value_type>;
#else
funcp = &boost::math::log1p;
#endif
#if !(defined(ERROR_REPORTING_MODE) && !defined(LOG1P_FUNCTION_TO_TEST))
result = boost::math::tools::test_hetero<Real>(
data,
bind_func<Real>(funcp, 0),
extract_result<Real>(1));
handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::log1p", "log1p and expm1");
handle_test_result(result, data[result.worst()], result.worst(), type_name, "log1p", "Random test data");
std::cout << std::endl;
#endif
#if !(defined(ERROR_REPORTING_MODE) && !defined(EXPM1_FUNCTION_TO_TEST))
//
// test expm1 against data:
//
#if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
#ifdef EXPM1_FUNCTION_TO_TEST
funcp = EXPM1_FUNCTION_TO_TEST;
#elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
funcp = boost::math::expm1<value_type>;
#else
funcp = boost::math::expm1;
@@ -52,8 +54,9 @@ void do_test(const T& data, const char* type_name, const char* test_name)
data,
bind_func<Real>(funcp, 0),
extract_result<Real>(2));
handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::expm1", "log1p and expm1");
handle_test_result(result, data[result.worst()], result.worst(), type_name, "expm1", "Random test data");
std::cout << std::endl;
#endif
}
template <class T>

17
test/powm1_sqrtp1m1_test.hpp
View File

@@ -1568,8 +1568,13 @@ void test_powm1_sqrtp1m1(T, const char* type_name)
using namespace std;
typedef T (*func_t)(const T&);
#ifdef SQRT1PM1_FUNCTION_TO_TEST
func_t f = SQRT1PM1_FUNCTION_TO_TEST;
#else
func_t f = &boost::math::sqrt1pm1<T>;
#endif
#if !(defined(ERROR_REPORTING_MODE) && !defined(SQRT1PM1_FUNCTION_TO_TEST))
boost::math::tools::test_result<T> result = boost::math::tools::test_hetero<T>(
sqrtp1m1_data,
bind_func<T>(f, 0),
@@ -1577,14 +1582,22 @@ void test_powm1_sqrtp1m1(T, const char* type_name)
std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n"
"Test results for type " << type_name << std::endl << std::endl;
handle_test_result(result, sqrtp1m1_data[result.worst()], result.worst(), type_name, "boost::math::sqrt1pm1", "sqrt1pm1");
handle_test_result(result, sqrtp1m1_data[result.worst()], result.worst(), type_name, "sqrt1pm1", "sqrt1pm1");
#endif
#if !(defined(ERROR_REPORTING_MODE) && !defined(POWM1_FUNCTION_TO_TEST))
typedef T (*func2_t)(T const, T const);
#ifdef POWM1_FUNCTION_TO_TEST
func2_t f2 = POWM1_FUNCTION_TO_TEST;
#else
func2_t f2 = &boost::math::powm1<T,T>;
#endif
result = boost::math::tools::test_hetero<T>(
powm1_data,
bind_func<T>(f2, 0, 1),
extract_result<T>(2));
handle_test_result(result, powm1_data[result.worst()], result.worst(), type_name, "boost::math::powm1", "powm1");
handle_test_result(result, powm1_data[result.worst()], result.worst(), type_name, "powm1", "powm1");
#endif
}

143
test/test_owens_t.cpp
View File

@@ -125,149 +125,6 @@ void expected_results()
<< BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
}
template <class RealType>
void test_spot(
RealType h, //
RealType a, //
RealType tol) // Test tolerance
{
BOOST_CHECK_CLOSE_FRACTION(owens_t(h, a), 3.89119302347013668966224771378e-2L, tol);
}
template <class RealType> // Any floating-point type RealType.
void test_spots(RealType)
{
// Basic sanity checks, test data is as accurate as long double,
// so set tolerance to a few epsilon expressed as a fraction.
RealType tolerance = boost::math::tools::epsilon<RealType>() * 30; // most OK with 3 eps tolerance.
cout << "Tolerance = " << tolerance << "." << endl;
using ::boost::math::owens_t;
using ::boost::math::normal_distribution;
BOOST_MATH_STD_USING // ADL of std names.
// Checks of six sub-methods T1 to T6.
BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(0.0625L), static_cast<RealType>(0.25L)), static_cast<RealType>(3.89119302347013668966224771378e-2L), tolerance); // T1
BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(6.5L), static_cast<RealType>(0.4375L)), static_cast<RealType>(2.00057730485083154100907167685E-11L), tolerance); // T2
BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(7L), static_cast<RealType>( 0.96875L)), static_cast<RealType>(6.39906271938986853083219914429E-13L), tolerance); // T3
BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(4.78125L), static_cast<RealType>(0.0625L)), static_cast<RealType>(1.06329748046874638058307112826E-7L), tolerance); // T4
BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(2.L), static_cast<RealType>(0.5L)), static_cast<RealType>(8.62507798552150713113488319155E-3L), tolerance); // T5
BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(1.L), static_cast<RealType>(0.9999975L)), static_cast<RealType>(6.67418089782285927715589822405E-2L), tolerance); // T6
//BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(L), static_cast<RealType>(L)), static_cast<RealType>(L), tolerance);
// BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(L), static_cast<RealType>(L)), static_cast<RealType>(L), tolerance);
// Spots values using Mathematica
BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(6.5L), static_cast<RealType>(0.4375L)), static_cast<RealType>(2.00057730485083154100907167684918851101649922551817956120806662022118024594547E-11L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(0.4375L), static_cast<RealType>(6.5L)), static_cast<RealType>(0.16540130125449396247498691826626273249659241838438244251206819782787761751256L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(7.L), static_cast<RealType>(0.96875L)), static_cast<RealType>(6.39906271938986853083219914428916013764797190941459233223182225724846022843930e-13L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(0.96875L), static_cast<RealType>(7.L)), static_cast<RealType>(0.08316748474602973770533230453272140919966614259525787470390475393923633179072L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(4.78125L), static_cast<RealType>(0.0625L)), static_cast<RealType>(1.06329748046874638058307112826015825291136503488102191050906959246644942646701e-7L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(0.0625L), static_cast<RealType>(4.78125L)), static_cast<RealType>(0.21571185819897989857261253680409017017649352928888660746045361855686569265171L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(2.L), static_cast<RealType>(0.5L)), static_cast<RealType>(0.00862507798552150713113488319154637187875641190390854291100809449487812876461L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(0.5L), static_cast<RealType>(2L)), static_cast<RealType>(0.14158060365397839346662819588111542648867283386549027383784843786494855594607L), tolerance);
// check basic properties
BOOST_CHECK_EQUAL(owens_t(static_cast<RealType>(0.5L), static_cast<RealType>(2L)), owens_t(static_cast<RealType>(-0.5L), static_cast<RealType>(2L)));
BOOST_CHECK_EQUAL(owens_t(static_cast<RealType>(0.5L), static_cast<RealType>(2L)), -owens_t(static_cast<RealType>(0.5L), static_cast<RealType>(-2L)));
BOOST_CHECK_EQUAL(owens_t(static_cast<RealType>(0.5L), static_cast<RealType>(2L)), -owens_t(static_cast<RealType>(-0.5L), static_cast<RealType>(-2L)));
// Special relations from Owen's original paper:
BOOST_CHECK_EQUAL(owens_t(static_cast<RealType>(0.5), static_cast<RealType>(0)), static_cast<RealType>(0));
BOOST_CHECK_EQUAL(owens_t(static_cast<RealType>(10), static_cast<RealType>(0)), static_cast<RealType>(0));
BOOST_CHECK_EQUAL(owens_t(static_cast<RealType>(10000), static_cast<RealType>(0)), static_cast<RealType>(0));
BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(0), static_cast<RealType>(2L)), atan(static_cast<RealType>(2L)) / (boost::math::constants::pi<RealType>() * 2), tolerance);
BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(0), static_cast<RealType>(0.5L)), atan(static_cast<RealType>(0.5L)) / (boost::math::constants::pi<RealType>() * 2), tolerance);
BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(0), static_cast<RealType>(2000L)), atan(static_cast<RealType>(2000L)) / (boost::math::constants::pi<RealType>() * 2), tolerance);
BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(5), static_cast<RealType>(1)), cdf(normal_distribution<RealType>(), 5) * cdf(complement(normal_distribution<RealType>(), 5)) / 2, tolerance);
BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(0.125), static_cast<RealType>(1)), cdf(normal_distribution<RealType>(), 0.125) * cdf(complement(normal_distribution<RealType>(), 0.125)) / 2, tolerance);
if(std::numeric_limits<RealType>::has_infinity)
{
BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(0.125), std::numeric_limits<RealType>::infinity()), cdf(complement(normal_distribution<RealType>(), 0.125)) / 2, tolerance);
BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(5), std::numeric_limits<RealType>::infinity()), cdf(complement(normal_distribution<RealType>(), 5)) / 2, tolerance);
BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(-0.125), std::numeric_limits<RealType>::infinity()), cdf(normal_distribution<RealType>(), -0.125) / 2, tolerance);
BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(-5), std::numeric_limits<RealType>::infinity()), cdf(normal_distribution<RealType>(), -5) / 2, tolerance);
}
} // template <class RealType>void test_spots(RealType)
template <class RealType> // Any floating-point type RealType.
void check_against_T7(RealType)
{
// Basic sanity checks, test data is as accurate as long double,
// so set tolerance to a few epsilon expressed as a fraction.
RealType tolerance = boost::math::tools::epsilon<RealType>() * 150; // most OK with 3 eps tolerance.
cout << "Tolerance = " << tolerance << "." << endl;
using ::boost::math::owens_t;
using namespace std; // ADL of std names.
// apply log scale because points near zero are more interesting
for(RealType a = static_cast<RealType>(-10.0l); a < static_cast<RealType>(3l); a+= static_cast<RealType>(0.2l))
for(RealType h = static_cast<RealType>(-10.0l); h < static_cast<RealType>(3.5l); h+= static_cast<RealType>(0.2l))
{
const RealType expa = exp(a);
const RealType exph = exp(h);
const RealType t = boost::math::owens_t(exph, expa);
RealType t7 = boost::math::owens_t_T7(exph,expa);
//if(!(boost::math::isnormal)(t) || !(boost::math::isnormal)(t7))
// std::cout << "a = " << expa << " h = " << exph << " t = " << t << " t7 = " << t7 << std::endl;
BOOST_CHECK_CLOSE_FRACTION(t, t7, tolerance);
}
} // template <class RealType>void test_spots(RealType)
template <class Real, class T>
void do_test_owens_t(const T& data, const char* type_name, const char* test_name)
{
typedef typename T::value_type row_type;
typedef Real value_type;
typedef value_type (*pg)(value_type, value_type);
#if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
pg funcp = boost::math::owens_t<value_type>;
#else
pg funcp = boost::math::owens_t;
#endif
boost::math::tools::test_result<value_type> result;
std::cout << "Testing " << test_name << " with type " << type_name
<< "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
//
// test hermite against data:
//
result = boost::math::tools::test_hetero<Real>(
data,
bind_func<Real>(funcp, 0, 1),
extract_result<Real>(2));
handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::owens_t", test_name);
std::cout << std::endl;
}
template <class T>
void test_owens_t(T, const char* name)
{
//
// The actual test data is rather verbose, so it's in a separate file
//
// The contents are as follows, each row of data contains
// three items, input value a, input value b and erf(a, b):
//
# include "owens_t.ipp"
do_test_owens_t<T>(owens_t, name, "Owens T (medium small values)");
#include "owens_t_large_data.ipp"
do_test_owens_t<T>(owens_t_large_data, name, "Owens T (large and diverse values)");
}
BOOST_AUTO_TEST_CASE( test_main )
{
BOOST_MATH_CONTROL_FP;

162
test/test_owens_t.hpp Normal file
View File

@@ -0,0 +1,162 @@
// (C) Copyright John Maddock 2007.
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0. (See accompanying file
// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
#include <boost/math/concepts/real_concept.hpp>
#define BOOST_TEST_MAIN
#include <boost/test/unit_test.hpp>
#include <boost/test/floating_point_comparison.hpp>
#include <boost/math/special_functions/math_fwd.hpp>
#include <boost/type_traits/is_floating_point.hpp>
#include <boost/array.hpp>
#include "functor.hpp"
#include "handle_test_result.hpp"
#include "table_type.hpp"
template <class RealType>
void test_spot(
RealType h, //
RealType a, //
RealType tol) // Test tolerance
{
BOOST_CHECK_CLOSE_FRACTION(owens_t(h, a), 3.89119302347013668966224771378e-2L, tol);
}
template <class RealType> // Any floating-point type RealType.
void test_spots(RealType)
{
// Basic sanity checks, test data is as accurate as long double,
// so set tolerance to a few epsilon expressed as a fraction.
RealType tolerance = boost::math::tools::epsilon<RealType>() * 30; // most OK with 3 eps tolerance.
cout << "Tolerance = " << tolerance << "." << endl;
using ::boost::math::owens_t;
using ::boost::math::normal_distribution;
BOOST_MATH_STD_USING // ADL of std names.
// Checks of six sub-methods T1 to T6.
BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(0.0625L), static_cast<RealType>(0.25L)), static_cast<RealType>(3.89119302347013668966224771378e-2L), tolerance); // T1
BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(6.5L), static_cast<RealType>(0.4375L)), static_cast<RealType>(2.00057730485083154100907167685E-11L), tolerance); // T2
BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(7L), static_cast<RealType>(0.96875L)), static_cast<RealType>(6.39906271938986853083219914429E-13L), tolerance); // T3
BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(4.78125L), static_cast<RealType>(0.0625L)), static_cast<RealType>(1.06329748046874638058307112826E-7L), tolerance); // T4
BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(2.L), static_cast<RealType>(0.5L)), static_cast<RealType>(8.62507798552150713113488319155E-3L), tolerance); // T5
BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(1.L), static_cast<RealType>(0.9999975L)), static_cast<RealType>(6.67418089782285927715589822405E-2L), tolerance); // T6
//BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(L), static_cast<RealType>(L)), static_cast<RealType>(L), tolerance);
// BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(L), static_cast<RealType>(L)), static_cast<RealType>(L), tolerance);
// Spots values using Mathematica
BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(6.5L), static_cast<RealType>(0.4375L)), static_cast<RealType>(2.00057730485083154100907167684918851101649922551817956120806662022118024594547E-11L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(0.4375L), static_cast<RealType>(6.5L)), static_cast<RealType>(0.16540130125449396247498691826626273249659241838438244251206819782787761751256L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(7.L), static_cast<RealType>(0.96875L)), static_cast<RealType>(6.39906271938986853083219914428916013764797190941459233223182225724846022843930e-13L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(0.96875L), static_cast<RealType>(7.L)), static_cast<RealType>(0.08316748474602973770533230453272140919966614259525787470390475393923633179072L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(4.78125L), static_cast<RealType>(0.0625L)), static_cast<RealType>(1.06329748046874638058307112826015825291136503488102191050906959246644942646701e-7L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(0.0625L), static_cast<RealType>(4.78125L)), static_cast<RealType>(0.21571185819897989857261253680409017017649352928888660746045361855686569265171L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(2.L), static_cast<RealType>(0.5L)), static_cast<RealType>(0.00862507798552150713113488319154637187875641190390854291100809449487812876461L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(0.5L), static_cast<RealType>(2L)), static_cast<RealType>(0.14158060365397839346662819588111542648867283386549027383784843786494855594607L), tolerance);
// check basic properties
BOOST_CHECK_EQUAL(owens_t(static_cast<RealType>(0.5L), static_cast<RealType>(2L)), owens_t(static_cast<RealType>(-0.5L), static_cast<RealType>(2L)));
BOOST_CHECK_EQUAL(owens_t(static_cast<RealType>(0.5L), static_cast<RealType>(2L)), -owens_t(static_cast<RealType>(0.5L), static_cast<RealType>(-2L)));
BOOST_CHECK_EQUAL(owens_t(static_cast<RealType>(0.5L), static_cast<RealType>(2L)), -owens_t(static_cast<RealType>(-0.5L), static_cast<RealType>(-2L)));
// Special relations from Owen's original paper:
BOOST_CHECK_EQUAL(owens_t(static_cast<RealType>(0.5), static_cast<RealType>(0)), static_cast<RealType>(0));
BOOST_CHECK_EQUAL(owens_t(static_cast<RealType>(10), static_cast<RealType>(0)), static_cast<RealType>(0));
BOOST_CHECK_EQUAL(owens_t(static_cast<RealType>(10000), static_cast<RealType>(0)), static_cast<RealType>(0));
BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(0), static_cast<RealType>(2L)), atan(static_cast<RealType>(2L)) / (boost::math::constants::pi<RealType>() * 2), tolerance);
BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(0), static_cast<RealType>(0.5L)), atan(static_cast<RealType>(0.5L)) / (boost::math::constants::pi<RealType>() * 2), tolerance);
BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(0), static_cast<RealType>(2000L)), atan(static_cast<RealType>(2000L)) / (boost::math::constants::pi<RealType>() * 2), tolerance);
BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(5), static_cast<RealType>(1)), cdf(normal_distribution<RealType>(), 5) * cdf(complement(normal_distribution<RealType>(), 5)) / 2, tolerance);
BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(0.125), static_cast<RealType>(1)), cdf(normal_distribution<RealType>(), 0.125) * cdf(complement(normal_distribution<RealType>(), 0.125)) / 2, tolerance);
if(std::numeric_limits<RealType>::has_infinity)
{
BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(0.125), std::numeric_limits<RealType>::infinity()), cdf(complement(normal_distribution<RealType>(), 0.125)) / 2, tolerance);
BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(5), std::numeric_limits<RealType>::infinity()), cdf(complement(normal_distribution<RealType>(), 5)) / 2, tolerance);
BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(-0.125), std::numeric_limits<RealType>::infinity()), cdf(normal_distribution<RealType>(), -0.125) / 2, tolerance);
BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast<RealType>(-5), std::numeric_limits<RealType>::infinity()), cdf(normal_distribution<RealType>(), -5) / 2, tolerance);
}
} // template <class RealType>void test_spots(RealType)
template <class RealType> // Any floating-point type RealType.
void check_against_T7(RealType)
{
// Basic sanity checks, test data is as accurate as long double,
// so set tolerance to a few epsilon expressed as a fraction.
RealType tolerance = boost::math::tools::epsilon<RealType>() * 150; // most OK with 3 eps tolerance.
cout << "Tolerance = " << tolerance << "." << endl;
using ::boost::math::owens_t;
using namespace std; // ADL of std names.
// apply log scale because points near zero are more interesting
for(RealType a = static_cast<RealType>(-10.0l); a < static_cast<RealType>(3l); a += static_cast<RealType>(0.2l))
for(RealType h = static_cast<RealType>(-10.0l); h < static_cast<RealType>(3.5l); h += static_cast<RealType>(0.2l))
{
const RealType expa = exp(a);
const RealType exph = exp(h);
const RealType t = boost::math::owens_t(exph, expa);
RealType t7 = boost::math::owens_t_T7(exph, expa);
//if(!(boost::math::isnormal)(t) || !(boost::math::isnormal)(t7))
// std::cout << "a = " << expa << " h = " << exph << " t = " << t << " t7 = " << t7 << std::endl;
BOOST_CHECK_CLOSE_FRACTION(t, t7, tolerance);
}
} // template <class RealType>void test_spots(RealType)
template <class Real, class T>
void do_test_owens_t(const T& data, const char* type_name, const char* test_name)
{
#if !(defined(ERROR_REPORTING_MODE) && !defined(OWENS_T_FUNCTION_TO_TEST))
typedef typename T::value_type row_type;
typedef Real value_type;
typedef value_type(*pg)(value_type, value_type);
#ifdef OWENS_T_FUNCTION_TO_TEST
pg funcp = OWENS_T_FUNCTION_TO_TEST;
#elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
pg funcp = boost::math::owens_t<value_type>;
#else
pg funcp = boost::math::owens_t;
#endif
boost::math::tools::test_result<value_type> result;
std::cout << "Testing " << test_name << " with type " << type_name
<< "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
//
// test owens_t against data:
//
result = boost::math::tools::test_hetero<Real>(
data,
bind_func<Real>(funcp, 0, 1),
extract_result<Real>(2));
handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::owens_t", test_name);
std::cout << std::endl;
#endif
}
template <class T>
void test_owens_t(T, const char* name)
{
//
// The actual test data is rather verbose, so it's in a separate file
//
// The contents are as follows, each row of data contains
// three items, input value a, input value b and erf(a, b):
//
# include "owens_t.ipp"
do_test_owens_t<T>(owens_t, name, "Owens T (medium small values)");
#include "owens_t_large_data.ipp"
do_test_owens_t<T>(owens_t_large_data, name, "Owens T (large and diverse values)");
}

187
test/test_spherical_harmonic.cpp
View File

@@ -16,6 +16,7 @@
#include "handle_test_result.hpp"
#include "table_type.hpp"
#include "test_spherical_harmonic.hpp"
//
// DESCRIPTION:
@@ -98,192 +99,6 @@ void expected_results()
<< BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
}
template <class Real, class T>
void do_test_spherical_harmonic(const T& data, const char* type_name, const char* test_name)
{
typedef Real value_type;
typedef value_type (*pg)(unsigned, int, value_type, value_type);
#if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
pg funcp = boost::math::spherical_harmonic_r<value_type, value_type>;
#else
pg funcp = boost::math::spherical_harmonic_r;
#endif
boost::math::tools::test_result<value_type> result;
std::cout << "Testing " << test_name << " with type " << type_name
<< "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
//
// test Spheric Harmonic against data:
//
result = boost::math::tools::test_hetero<Real>(
data,
bind_func_int2<Real>(funcp, 0, 1, 2, 3),
extract_result<Real>(4));
handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::spherical_harmonic_r", test_name);
#if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
funcp = boost::math::spherical_harmonic_i<value_type, value_type>;
#else
funcp = boost::math::spherical_harmonic_i;
#endif
//
// test Spheric Harmonic against data:
//
result = boost::math::tools::test_hetero<Real>(
data,
bind_func_int2<Real>(funcp, 0, 1, 2, 3),
extract_result<Real>(5));
handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::spherical_harmonic_i", test_name);
std::cout << std::endl;
}
template <class Real, class T>
void test_complex_spherical_harmonic(const T& data, const char* /* name */, boost::mpl::true_ const &)
{
typedef Real value_type;
for(unsigned i = 0; i < sizeof(data) / sizeof(data[0]); ++i)
{
//
// Sanity check that the complex version does the same thing as the real
// and imaginary versions:
//
std::complex<value_type> r = boost::math::spherical_harmonic(
boost::math::tools::real_cast<unsigned>(data[i][0]),
boost::math::tools::real_cast<unsigned>(data[i][1]),
Real(data[i][2]),
Real(data[i][3]));
value_type re = boost::math::spherical_harmonic_r(
boost::math::tools::real_cast<unsigned>(data[i][0]),
boost::math::tools::real_cast<unsigned>(data[i][1]),
Real(data[i][2]),
Real(data[i][3]));
value_type im = boost::math::spherical_harmonic_i(
boost::math::tools::real_cast<unsigned>(data[i][0]),
boost::math::tools::real_cast<unsigned>(data[i][1]),
Real(data[i][2]),
Real(data[i][3]));
BOOST_CHECK_CLOSE_FRACTION(std::real(r), re, value_type(5));
BOOST_CHECK_CLOSE_FRACTION(std::imag(r), im, value_type(5));
}
}
template <class Real, class T>
void test_complex_spherical_harmonic(const T& /* data */, const char* /* name */, boost::mpl::false_ const &)
{
// T is not a built in type, can't use std::complex with it...
}
template <class T>
void test_spherical_harmonic(T, const char* name)
{
//
// The actual test data is rather verbose, so it's in a separate file
//
// The contents are as follows, each row of data contains
// three items, input value a, input value b and erf(a, b):
//
# include "spherical_harmonic.ipp"
do_test_spherical_harmonic<T>(spherical_harmonic, name, "Spherical Harmonics");
test_complex_spherical_harmonic<T>(spherical_harmonic, name, boost::is_floating_point<T>());
}
template <class T>
void test_spots(T, const char* t)
{
std::cout << "Testing basic sanity checks for type " << t << std::endl;
//
// basic sanity checks, tolerance is 100 epsilon:
//
T tolerance = boost::math::tools::epsilon<T>() * 100;
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(3, 2, static_cast<T>(0.5), static_cast<T>(0)), static_cast<T>(0.2061460599687871330692286791802688341213L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(20, 10, static_cast<T>(0.75), static_cast<T>(-0.25)), static_cast<T>(0.06197787102219208244041677775577045124092L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(20, 10, static_cast<T>(0.75), static_cast<T>(-0.25)), static_cast<T>(0.04629885158895932341185988759669916977920L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(40, 15, static_cast<T>(-0.75), static_cast<T>(2.25)), static_cast<T>(0.2806904825045745687343492963236868973484L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(40, 15, static_cast<T>(-0.75), static_cast<T>(2.25)), static_cast<T>(-0.2933918444656603582282372590387544902135L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(40, 15, static_cast<T>(-0.75), static_cast<T>(-2.25)), static_cast<T>(0.2806904825045745687343492963236868973484L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(40, 15, static_cast<T>(-0.75), static_cast<T>(-2.25)), static_cast<T>(0.2933918444656603582282372590387544902135L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(40, 15, static_cast<T>(0.75), static_cast<T>(-2.25)), static_cast<T>(-0.2806904825045745687343492963236868973484L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(40, 15, static_cast<T>(0.75), static_cast<T>(-2.25)), static_cast<T>(-0.2933918444656603582282372590387544902135L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(40, 15, static_cast<T>(0.75), static_cast<T>(2.25)), static_cast<T>(-0.2806904825045745687343492963236868973484L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(40, 15, static_cast<T>(0.75), static_cast<T>(2.25)), static_cast<T>(0.2933918444656603582282372590387544902135L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(20, 14, static_cast<T>(-0.75), static_cast<T>(2.25)), static_cast<T>(0.3479218186133435466692822481919867452442L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(20, 14, static_cast<T>(-0.75), static_cast<T>(2.25)), static_cast<T>(0.0293201066685263879566422194539567289974L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(20, 14, static_cast<T>(-0.75), static_cast<T>(-2.25)), static_cast<T>(0.3479218186133435466692822481919867452442L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(20, 14, static_cast<T>(-0.75), static_cast<T>(-2.25)), static_cast<T>(-0.0293201066685263879566422194539567289974L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(20, 14, static_cast<T>(0.75), static_cast<T>(-2.25)), static_cast<T>(0.3479218186133435466692822481919867452442L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(20, 14, static_cast<T>(0.75), static_cast<T>(-2.25)), static_cast<T>(-0.0293201066685263879566422194539567289974L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(20, 14, static_cast<T>(0.75), static_cast<T>(2.25)), static_cast<T>(0.3479218186133435466692822481919867452442L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(20, 14, static_cast<T>(0.75), static_cast<T>(2.25)), static_cast<T>(0.0293201066685263879566422194539567289974L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(39, 15, static_cast<T>(-0.75), static_cast<T>(2.25)), static_cast<T>(0.1757594233240278196989039119899901986211L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(39, 15, static_cast<T>(-0.75), static_cast<T>(2.25)), static_cast<T>(-0.1837126108841860058078729532035715580790L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(39, 15, static_cast<T>(-0.75), static_cast<T>(-2.25)), static_cast<T>(0.1757594233240278196989039119899901986211L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(39, 15, static_cast<T>(-0.75), static_cast<T>(-2.25)), static_cast<T>(0.1837126108841860058078729532035715580790L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(39, 15, static_cast<T>(0.75), static_cast<T>(-2.25)), static_cast<T>(-0.1757594233240278196989039119899901986211L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(39, 15, static_cast<T>(0.75), static_cast<T>(-2.25)), static_cast<T>(-0.1837126108841860058078729532035715580790L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(39, 15, static_cast<T>(0.75), static_cast<T>(2.25)), static_cast<T>(-0.1757594233240278196989039119899901986211L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(39, 15, static_cast<T>(0.75), static_cast<T>(2.25)), static_cast<T>(0.1837126108841860058078729532035715580790L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(19, 14, static_cast<T>(-0.75), static_cast<T>(2.25)), static_cast<T>(0.2341701030303444033808969389588343934828L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(19, 14, static_cast<T>(-0.75), static_cast<T>(2.25)), static_cast<T>(0.0197340092863212879172432610952871202640L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(19, 14, static_cast<T>(-0.75), static_cast<T>(-2.25)), static_cast<T>(0.2341701030303444033808969389588343934828L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(19, 14, static_cast<T>(-0.75), static_cast<T>(-2.25)), static_cast<T>(-0.0197340092863212879172432610952871202640L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(19, 14, static_cast<T>(0.75), static_cast<T>(-2.25)), static_cast<T>(0.2341701030303444033808969389588343934828L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(19, 14, static_cast<T>(0.75), static_cast<T>(-2.25)), static_cast<T>(-0.0197340092863212879172432610952871202640L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(19, 14, static_cast<T>(0.75), static_cast<T>(2.25)), static_cast<T>(0.2341701030303444033808969389588343934828L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(19, 14, static_cast<T>(0.75), static_cast<T>(2.25)), static_cast<T>(0.0197340092863212879172432610952871202640L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(40, -15, static_cast<T>(-0.75), static_cast<T>(2.25)), static_cast<T>(-0.2806904825045745687343492963236868973484L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(40, -15, static_cast<T>(-0.75), static_cast<T>(2.25)), static_cast<T>(-0.2933918444656603582282372590387544902135L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(40, -15, static_cast<T>(-0.75), static_cast<T>(-2.25)), static_cast<T>(-0.2806904825045745687343492963236868973484L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(40, -15, static_cast<T>(-0.75), static_cast<T>(-2.25)), static_cast<T>(0.2933918444656603582282372590387544902135L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(40, -15, static_cast<T>(0.75), static_cast<T>(-2.25)), static_cast<T>(0.2806904825045745687343492963236868973484L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(40, -15, static_cast<T>(0.75), static_cast<T>(-2.25)), static_cast<T>(-0.2933918444656603582282372590387544902135L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(40, -15, static_cast<T>(0.75), static_cast<T>(2.25)), static_cast<T>(0.2806904825045745687343492963236868973484L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(40, -15, static_cast<T>(0.75), static_cast<T>(2.25)), static_cast<T>(0.2933918444656603582282372590387544902135L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(20, -14, static_cast<T>(-0.75), static_cast<T>(2.25)), static_cast<T>(0.3479218186133435466692822481919867452442L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(20, -14, static_cast<T>(-0.75), static_cast<T>(2.25)), static_cast<T>(-0.0293201066685263879566422194539567289974L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(20, -14, static_cast<T>(-0.75), static_cast<T>(-2.25)), static_cast<T>(0.3479218186133435466692822481919867452442L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(20, -14, static_cast<T>(-0.75), static_cast<T>(-2.25)), static_cast<T>(0.0293201066685263879566422194539567289974L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(20, -14, static_cast<T>(0.75), static_cast<T>(-2.25)), static_cast<T>(0.3479218186133435466692822481919867452442L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(20, -14, static_cast<T>(0.75), static_cast<T>(-2.25)), static_cast<T>(0.0293201066685263879566422194539567289974L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(20, -14, static_cast<T>(0.75), static_cast<T>(2.25)), static_cast<T>(0.3479218186133435466692822481919867452442L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(20, -14, static_cast<T>(0.75), static_cast<T>(2.25)), static_cast<T>(-0.0293201066685263879566422194539567289974L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(20, 14, static_cast<T>(-4), static_cast<T>(2.25)), static_cast<T>(0.5253373768014719124617844890495875474590L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(20, 14, static_cast<T>(-4), static_cast<T>(2.25)), static_cast<T>(0.0442712905622650144694916590407495495699L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(20, 14, static_cast<T>(-4), static_cast<T>(-2.25)), static_cast<T>(0.5253373768014719124617844890495875474590L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(20, 14, static_cast<T>(-4), static_cast<T>(-2.25)), static_cast<T>(-0.0442712905622650144694916590407495495699L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(20, 14, static_cast<T>(4), static_cast<T>(-2.25)), static_cast<T>(0.5253373768014719124617844890495875474590L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(20, 14, static_cast<T>(4), static_cast<T>(-2.25)), static_cast<T>(-0.0442712905622650144694916590407495495699L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(20, 14, static_cast<T>(4), static_cast<T>(2.25)), static_cast<T>(0.5253373768014719124617844890495875474590L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(20, 14, static_cast<T>(4), static_cast<T>(2.25)), static_cast<T>(0.0442712905622650144694916590407495495699L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(20, 15, static_cast<T>(-4), static_cast<T>(2.25)), static_cast<T>(-0.2991140325667575801827063718821420263438L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(20, 15, static_cast<T>(-4), static_cast<T>(2.25)), static_cast<T>(0.3126490678888350710506307405826667514065L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(20, 15, static_cast<T>(-4), static_cast<T>(-2.25)), static_cast<T>(-0.2991140325667575801827063718821420263438L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(20, 15, static_cast<T>(-4), static_cast<T>(-2.25)), static_cast<T>(-0.3126490678888350710506307405826667514065L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(20, 15, static_cast<T>(4), static_cast<T>(-2.25)), static_cast<T>(0.2991140325667575801827063718821420263438L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(20, 15, static_cast<T>(4), static_cast<T>(-2.25)), static_cast<T>(0.3126490678888350710506307405826667514065L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(20, 15, static_cast<T>(4), static_cast<T>(2.25)), static_cast<T>(0.2991140325667575801827063718821420263438L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(20, 15, static_cast<T>(4), static_cast<T>(2.25)), static_cast<T>(-0.3126490678888350710506307405826667514065L), tolerance);
BOOST_CHECK_EQUAL(::boost::math::spherical_harmonic_r(10, 15, static_cast<T>(-0.75), static_cast<T>(2.25)), static_cast<T>(0));
BOOST_CHECK_EQUAL(::boost::math::spherical_harmonic_i(10, 15, static_cast<T>(-0.75), static_cast<T>(2.25)), static_cast<T>(0));
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(53, 42, static_cast<T>(-8.75), static_cast<T>(-2.25)), static_cast<T>(-0.0008147976618889536159592309471859037113647L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(53, 42, static_cast<T>(-8.75), static_cast<T>(-2.25)), static_cast<T>(0.0002099802242493057018193798824353982612756L), tolerance);
}
BOOST_AUTO_TEST_CASE( test_main )
{
BOOST_MATH_CONTROL_FP;

213
test/test_spherical_harmonic.hpp Normal file
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// (C) Copyright John Maddock 2007.
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0. (See accompanying file
// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
#include <boost/math/concepts/real_concept.hpp>
#define BOOST_TEST_MAIN
#include <boost/test/unit_test.hpp>
#include <boost/test/floating_point_comparison.hpp>
#include <boost/math/special_functions/math_fwd.hpp>
#include <boost/type_traits/is_floating_point.hpp>
#include <boost/array.hpp>
#include "functor.hpp"
#include "handle_test_result.hpp"
#include "table_type.hpp"
template <class Real, class T>
void do_test_spherical_harmonic(const T& data, const char* type_name, const char* test_name)
{
typedef Real value_type;
typedef value_type(*pg)(unsigned, int, value_type, value_type);
#ifdef SPHERICAL_HARMONIC_R_FUNCTION_TO_TEST
pg funcp = SPHERICAL_HARMONIC_R_FUNCTION_TO_TEST;
#elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
pg funcp = boost::math::spherical_harmonic_r<value_type, value_type>;
#else
pg funcp = boost::math::spherical_harmonic_r;
#endif
boost::math::tools::test_result<value_type> result;
std::cout << "Testing " << test_name << " with type " << type_name
<< "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
//
// test Spheric Harmonic against data:
//
#if !(defined(ERROR_REPORTING_MODE) && !defined(SPHERICAL_HARMONIC_R_FUNCTION_TO_TEST))
result = boost::math::tools::test_hetero<Real>(
data,
bind_func_int2<Real>(funcp, 0, 1, 2, 3),
extract_result<Real>(4));
handle_test_result(result, data[result.worst()], result.worst(), type_name, "spherical_harmonic_r", test_name);
#endif
#if !(defined(ERROR_REPORTING_MODE) && !defined(SPHERICAL_HARMONIC_I_FUNCTION_TO_TEST))
#ifdef SPHERICAL_HARMONIC_I_FUNCTION_TO_TEST
funcp = SPHERICAL_HARMONIC_I_FUNCTION_TO_TEST;
#elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
funcp = boost::math::spherical_harmonic_i<value_type, value_type>;
#else
funcp = boost::math::spherical_harmonic_i;
#endif
//
// test Spheric Harmonic against data:
//
result = boost::math::tools::test_hetero<Real>(
data,
bind_func_int2<Real>(funcp, 0, 1, 2, 3),
extract_result<Real>(5));
handle_test_result(result, data[result.worst()], result.worst(), type_name, "spherical_harmonic_i", test_name);
std::cout << std::endl;
#endif
}
template <class Real, class T>
void test_complex_spherical_harmonic(const T& data, const char* /* name */, boost::mpl::true_ const &)
{
typedef Real value_type;
for(unsigned i = 0; i < sizeof(data) / sizeof(data[0]); ++i)
{
//
// Sanity check that the complex version does the same thing as the real
// and imaginary versions:
//
std::complex<value_type> r = boost::math::spherical_harmonic(
boost::math::tools::real_cast<unsigned>(data[i][0]),
boost::math::tools::real_cast<unsigned>(data[i][1]),
Real(data[i][2]),
Real(data[i][3]));
value_type re = boost::math::spherical_harmonic_r(
boost::math::tools::real_cast<unsigned>(data[i][0]),
boost::math::tools::real_cast<unsigned>(data[i][1]),
Real(data[i][2]),
Real(data[i][3]));
value_type im = boost::math::spherical_harmonic_i(
boost::math::tools::real_cast<unsigned>(data[i][0]),
boost::math::tools::real_cast<unsigned>(data[i][1]),
Real(data[i][2]),
Real(data[i][3]));
BOOST_CHECK_CLOSE_FRACTION(std::real(r), re, value_type(5));
BOOST_CHECK_CLOSE_FRACTION(std::imag(r), im, value_type(5));
}
}
template <class Real, class T>
void test_complex_spherical_harmonic(const T& /* data */, const char* /* name */, boost::mpl::false_ const &)
{
// T is not a built in type, can't use std::complex with it...
}
template <class T>
void test_spherical_harmonic(T, const char* name)
{
//
// The actual test data is rather verbose, so it's in a separate file
//
// The contents are as follows, each row of data contains
// 6 items, the 4 input values, plus the real and imaginary results:
//
# include "spherical_harmonic.ipp"
do_test_spherical_harmonic<T>(spherical_harmonic, name, "Spherical Harmonics");
test_complex_spherical_harmonic<T>(spherical_harmonic, name, boost::is_floating_point<T>());
}
template <class T>
void test_spots(T, const char* t)
{
std::cout << "Testing basic sanity checks for type " << t << std::endl;
//
// basic sanity checks, tolerance is 100 epsilon:
//
T tolerance = boost::math::tools::epsilon<T>() * 100;
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(3, 2, static_cast<T>(0.5), static_cast<T>(0)), static_cast<T>(0.2061460599687871330692286791802688341213L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(20, 10, static_cast<T>(0.75), static_cast<T>(-0.25)), static_cast<T>(0.06197787102219208244041677775577045124092L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(20, 10, static_cast<T>(0.75), static_cast<T>(-0.25)), static_cast<T>(0.04629885158895932341185988759669916977920L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(40, 15, static_cast<T>(-0.75), static_cast<T>(2.25)), static_cast<T>(0.2806904825045745687343492963236868973484L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(40, 15, static_cast<T>(-0.75), static_cast<T>(2.25)), static_cast<T>(-0.2933918444656603582282372590387544902135L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(40, 15, static_cast<T>(-0.75), static_cast<T>(-2.25)), static_cast<T>(0.2806904825045745687343492963236868973484L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(40, 15, static_cast<T>(-0.75), static_cast<T>(-2.25)), static_cast<T>(0.2933918444656603582282372590387544902135L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(40, 15, static_cast<T>(0.75), static_cast<T>(-2.25)), static_cast<T>(-0.2806904825045745687343492963236868973484L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(40, 15, static_cast<T>(0.75), static_cast<T>(-2.25)), static_cast<T>(-0.2933918444656603582282372590387544902135L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(40, 15, static_cast<T>(0.75), static_cast<T>(2.25)), static_cast<T>(-0.2806904825045745687343492963236868973484L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(40, 15, static_cast<T>(0.75), static_cast<T>(2.25)), static_cast<T>(0.2933918444656603582282372590387544902135L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(20, 14, static_cast<T>(-0.75), static_cast<T>(2.25)), static_cast<T>(0.3479218186133435466692822481919867452442L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(20, 14, static_cast<T>(-0.75), static_cast<T>(2.25)), static_cast<T>(0.0293201066685263879566422194539567289974L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(20, 14, static_cast<T>(-0.75), static_cast<T>(-2.25)), static_cast<T>(0.3479218186133435466692822481919867452442L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(20, 14, static_cast<T>(-0.75), static_cast<T>(-2.25)), static_cast<T>(-0.0293201066685263879566422194539567289974L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(20, 14, static_cast<T>(0.75), static_cast<T>(-2.25)), static_cast<T>(0.3479218186133435466692822481919867452442L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(20, 14, static_cast<T>(0.75), static_cast<T>(-2.25)), static_cast<T>(-0.0293201066685263879566422194539567289974L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(20, 14, static_cast<T>(0.75), static_cast<T>(2.25)), static_cast<T>(0.3479218186133435466692822481919867452442L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(20, 14, static_cast<T>(0.75), static_cast<T>(2.25)), static_cast<T>(0.0293201066685263879566422194539567289974L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(39, 15, static_cast<T>(-0.75), static_cast<T>(2.25)), static_cast<T>(0.1757594233240278196989039119899901986211L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(39, 15, static_cast<T>(-0.75), static_cast<T>(2.25)), static_cast<T>(-0.1837126108841860058078729532035715580790L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(39, 15, static_cast<T>(-0.75), static_cast<T>(-2.25)), static_cast<T>(0.1757594233240278196989039119899901986211L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(39, 15, static_cast<T>(-0.75), static_cast<T>(-2.25)), static_cast<T>(0.1837126108841860058078729532035715580790L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(39, 15, static_cast<T>(0.75), static_cast<T>(-2.25)), static_cast<T>(-0.1757594233240278196989039119899901986211L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(39, 15, static_cast<T>(0.75), static_cast<T>(-2.25)), static_cast<T>(-0.1837126108841860058078729532035715580790L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(39, 15, static_cast<T>(0.75), static_cast<T>(2.25)), static_cast<T>(-0.1757594233240278196989039119899901986211L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(39, 15, static_cast<T>(0.75), static_cast<T>(2.25)), static_cast<T>(0.1837126108841860058078729532035715580790L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(19, 14, static_cast<T>(-0.75), static_cast<T>(2.25)), static_cast<T>(0.2341701030303444033808969389588343934828L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(19, 14, static_cast<T>(-0.75), static_cast<T>(2.25)), static_cast<T>(0.0197340092863212879172432610952871202640L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(19, 14, static_cast<T>(-0.75), static_cast<T>(-2.25)), static_cast<T>(0.2341701030303444033808969389588343934828L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(19, 14, static_cast<T>(-0.75), static_cast<T>(-2.25)), static_cast<T>(-0.0197340092863212879172432610952871202640L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(19, 14, static_cast<T>(0.75), static_cast<T>(-2.25)), static_cast<T>(0.2341701030303444033808969389588343934828L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(19, 14, static_cast<T>(0.75), static_cast<T>(-2.25)), static_cast<T>(-0.0197340092863212879172432610952871202640L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(19, 14, static_cast<T>(0.75), static_cast<T>(2.25)), static_cast<T>(0.2341701030303444033808969389588343934828L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(19, 14, static_cast<T>(0.75), static_cast<T>(2.25)), static_cast<T>(0.0197340092863212879172432610952871202640L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(40, -15, static_cast<T>(-0.75), static_cast<T>(2.25)), static_cast<T>(-0.2806904825045745687343492963236868973484L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(40, -15, static_cast<T>(-0.75), static_cast<T>(2.25)), static_cast<T>(-0.2933918444656603582282372590387544902135L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(40, -15, static_cast<T>(-0.75), static_cast<T>(-2.25)), static_cast<T>(-0.2806904825045745687343492963236868973484L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(40, -15, static_cast<T>(-0.75), static_cast<T>(-2.25)), static_cast<T>(0.2933918444656603582282372590387544902135L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(40, -15, static_cast<T>(0.75), static_cast<T>(-2.25)), static_cast<T>(0.2806904825045745687343492963236868973484L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(40, -15, static_cast<T>(0.75), static_cast<T>(-2.25)), static_cast<T>(-0.2933918444656603582282372590387544902135L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(40, -15, static_cast<T>(0.75), static_cast<T>(2.25)), static_cast<T>(0.2806904825045745687343492963236868973484L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(40, -15, static_cast<T>(0.75), static_cast<T>(2.25)), static_cast<T>(0.2933918444656603582282372590387544902135L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(20, -14, static_cast<T>(-0.75), static_cast<T>(2.25)), static_cast<T>(0.3479218186133435466692822481919867452442L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(20, -14, static_cast<T>(-0.75), static_cast<T>(2.25)), static_cast<T>(-0.0293201066685263879566422194539567289974L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(20, -14, static_cast<T>(-0.75), static_cast<T>(-2.25)), static_cast<T>(0.3479218186133435466692822481919867452442L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(20, -14, static_cast<T>(-0.75), static_cast<T>(-2.25)), static_cast<T>(0.0293201066685263879566422194539567289974L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(20, -14, static_cast<T>(0.75), static_cast<T>(-2.25)), static_cast<T>(0.3479218186133435466692822481919867452442L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(20, -14, static_cast<T>(0.75), static_cast<T>(-2.25)), static_cast<T>(0.0293201066685263879566422194539567289974L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(20, -14, static_cast<T>(0.75), static_cast<T>(2.25)), static_cast<T>(0.3479218186133435466692822481919867452442L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(20, -14, static_cast<T>(0.75), static_cast<T>(2.25)), static_cast<T>(-0.0293201066685263879566422194539567289974L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(20, 14, static_cast<T>(-4), static_cast<T>(2.25)), static_cast<T>(0.5253373768014719124617844890495875474590L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(20, 14, static_cast<T>(-4), static_cast<T>(2.25)), static_cast<T>(0.0442712905622650144694916590407495495699L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(20, 14, static_cast<T>(-4), static_cast<T>(-2.25)), static_cast<T>(0.5253373768014719124617844890495875474590L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(20, 14, static_cast<T>(-4), static_cast<T>(-2.25)), static_cast<T>(-0.0442712905622650144694916590407495495699L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(20, 14, static_cast<T>(4), static_cast<T>(-2.25)), static_cast<T>(0.5253373768014719124617844890495875474590L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(20, 14, static_cast<T>(4), static_cast<T>(-2.25)), static_cast<T>(-0.0442712905622650144694916590407495495699L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(20, 14, static_cast<T>(4), static_cast<T>(2.25)), static_cast<T>(0.5253373768014719124617844890495875474590L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(20, 14, static_cast<T>(4), static_cast<T>(2.25)), static_cast<T>(0.0442712905622650144694916590407495495699L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(20, 15, static_cast<T>(-4), static_cast<T>(2.25)), static_cast<T>(-0.2991140325667575801827063718821420263438L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(20, 15, static_cast<T>(-4), static_cast<T>(2.25)), static_cast<T>(0.3126490678888350710506307405826667514065L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(20, 15, static_cast<T>(-4), static_cast<T>(-2.25)), static_cast<T>(-0.2991140325667575801827063718821420263438L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(20, 15, static_cast<T>(-4), static_cast<T>(-2.25)), static_cast<T>(-0.3126490678888350710506307405826667514065L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(20, 15, static_cast<T>(4), static_cast<T>(-2.25)), static_cast<T>(0.2991140325667575801827063718821420263438L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(20, 15, static_cast<T>(4), static_cast<T>(-2.25)), static_cast<T>(0.3126490678888350710506307405826667514065L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(20, 15, static_cast<T>(4), static_cast<T>(2.25)), static_cast<T>(0.2991140325667575801827063718821420263438L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(20, 15, static_cast<T>(4), static_cast<T>(2.25)), static_cast<T>(-0.3126490678888350710506307405826667514065L), tolerance);
BOOST_CHECK_EQUAL(::boost::math::spherical_harmonic_r(10, 15, static_cast<T>(-0.75), static_cast<T>(2.25)), static_cast<T>(0));
BOOST_CHECK_EQUAL(::boost::math::spherical_harmonic_i(10, 15, static_cast<T>(-0.75), static_cast<T>(2.25)), static_cast<T>(0));
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_r(53, 42, static_cast<T>(-8.75), static_cast<T>(-2.25)), static_cast<T>(-0.0008147976618889536159592309471859037113647L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(::boost::math::spherical_harmonic_i(53, 42, static_cast<T>(-8.75), static_cast<T>(-2.25)), static_cast<T>(0.0002099802242493057018193798824353982612756L), tolerance);
}