diff --git a/libstdc++-v3/ChangeLog b/libstdc++-v3/ChangeLog index 94f08c22a4f..93935ab9787 100644 --- a/libstdc++-v3/ChangeLog +++ b/libstdc++-v3/ChangeLog @@ -1,9 +1,3 @@ -2018-05-07 Edward Smith-Rowland <3dw4rd@verizon.net> - - Moar PR libstdc++/80506 - * include/bits/random.tcc (gamma_distribution::__generate_impl()): - Fix magic number used in loop condition. - 2018-05-04 Jonathan Wakely PR libstdc++/85642 fix is_nothrow_default_constructible> diff --git a/libstdc++-v3/include/bits/random.tcc b/libstdc++-v3/include/bits/random.tcc index 6db900cc0cd..f398150d416 100644 --- a/libstdc++-v3/include/bits/random.tcc +++ b/libstdc++-v3/include/bits/random.tcc @@ -2408,7 +2408,7 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION __v = __v * __v * __v; __u = __aurng(); } - while (__u > result_type(1.0) - 0.331 * __n * __n * __n * __n + while (__u > result_type(1.0) - 0.0331 * __n * __n * __n * __n && (std::log(__u) > (0.5 * __n * __n + __a1 * (1.0 - __v + std::log(__v))))); @@ -2429,7 +2429,7 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION __v = __v * __v * __v; __u = __aurng(); } - while (__u > result_type(1.0) - 0.331 * __n * __n * __n * __n + while (__u > result_type(1.0) - 0.0331 * __n * __n * __n * __n && (std::log(__u) > (0.5 * __n * __n + __a1 * (1.0 - __v + std::log(__v))))); diff --git a/libstdc++-v3/include/std/complex b/libstdc++-v3/include/std/complex index 2e2c2c06560..54f2b9db898 100644 --- a/libstdc++-v3/include/std/complex +++ b/libstdc++-v3/include/std/complex @@ -70,7 +70,7 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION /// Return phase angle of @a z. template _Tp arg(const complex<_Tp>&); /// Return @a z magnitude squared. - template _Tp norm(const complex<_Tp>&); + template _Tp _GLIBCXX_CONSTEXPR norm(const complex<_Tp>&); /// Return complex conjugate of @a z. template complex<_Tp> conj(const complex<_Tp>&); @@ -322,7 +322,7 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION //@{ /// Return new complex value @a x plus @a y. template - inline complex<_Tp> + _GLIBCXX_CONSTEXPR inline complex<_Tp> operator+(const complex<_Tp>& __x, const complex<_Tp>& __y) { complex<_Tp> __r = __x; @@ -331,7 +331,7 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION } template - inline complex<_Tp> + _GLIBCXX_CONSTEXPR inline complex<_Tp> operator+(const complex<_Tp>& __x, const _Tp& __y) { complex<_Tp> __r = __x; @@ -340,7 +340,7 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION } template - inline complex<_Tp> + _GLIBCXX_CONSTEXPR inline complex<_Tp> operator+(const _Tp& __x, const complex<_Tp>& __y) { complex<_Tp> __r = __y; @@ -352,7 +352,7 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION //@{ /// Return new complex value @a x minus @a y. template - inline complex<_Tp> + _GLIBCXX_CONSTEXPR inline complex<_Tp> operator-(const complex<_Tp>& __x, const complex<_Tp>& __y) { complex<_Tp> __r = __x; @@ -361,7 +361,7 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION } template - inline complex<_Tp> + _GLIBCXX_CONSTEXPR inline complex<_Tp> operator-(const complex<_Tp>& __x, const _Tp& __y) { complex<_Tp> __r = __x; @@ -370,7 +370,7 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION } template - inline complex<_Tp> + _GLIBCXX_CONSTEXPR inline complex<_Tp> operator-(const _Tp& __x, const complex<_Tp>& __y) { complex<_Tp> __r(__x, -__y.imag()); @@ -382,7 +382,7 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION //@{ /// Return new complex value @a x times @a y. template - inline complex<_Tp> + _GLIBCXX_CONSTEXPR inline complex<_Tp> operator*(const complex<_Tp>& __x, const complex<_Tp>& __y) { complex<_Tp> __r = __x; @@ -391,7 +391,7 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION } template - inline complex<_Tp> + inline _GLIBCXX_CONSTEXPR complex<_Tp> operator*(const complex<_Tp>& __x, const _Tp& __y) { complex<_Tp> __r = __x; @@ -400,7 +400,7 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION } template - inline complex<_Tp> + _GLIBCXX_CONSTEXPR inline complex<_Tp> operator*(const _Tp& __x, const complex<_Tp>& __y) { complex<_Tp> __r = __y; @@ -412,7 +412,7 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION //@{ /// Return new complex value @a x divided by @a y. template - inline complex<_Tp> + _GLIBCXX_CONSTEXPR inline complex<_Tp> operator/(const complex<_Tp>& __x, const complex<_Tp>& __y) { complex<_Tp> __r = __x; @@ -421,7 +421,7 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION } template - inline complex<_Tp> + _GLIBCXX_CONSTEXPR inline complex<_Tp> operator/(const complex<_Tp>& __x, const _Tp& __y) { complex<_Tp> __r = __x; @@ -430,7 +430,7 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION } template - inline complex<_Tp> + _GLIBCXX_CONSTEXPR inline complex<_Tp> operator/(const _Tp& __x, const complex<_Tp>& __y) { complex<_Tp> __r = __x; @@ -441,30 +441,30 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION /// Return @a x. template - inline complex<_Tp> + _GLIBCXX_CONSTEXPR inline complex<_Tp> operator+(const complex<_Tp>& __x) { return __x; } /// Return complex negation of @a x. template - inline complex<_Tp> + _GLIBCXX_CONSTEXPR inline complex<_Tp> operator-(const complex<_Tp>& __x) { return complex<_Tp>(-__x.real(), -__x.imag()); } //@{ /// Return true if @a x is equal to @a y. template - inline _GLIBCXX_CONSTEXPR bool + _GLIBCXX_CONSTEXPR inline bool operator==(const complex<_Tp>& __x, const complex<_Tp>& __y) { return __x.real() == __y.real() && __x.imag() == __y.imag(); } template - inline _GLIBCXX_CONSTEXPR bool + _GLIBCXX_CONSTEXPR inline bool operator==(const complex<_Tp>& __x, const _Tp& __y) { return __x.real() == __y && __x.imag() == _Tp(); } template - inline _GLIBCXX_CONSTEXPR bool + _GLIBCXX_CONSTEXPR inline bool operator==(const _Tp& __x, const complex<_Tp>& __y) { return __x == __y.real() && _Tp() == __y.imag(); } //@} @@ -472,17 +472,17 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION //@{ /// Return false if @a x is equal to @a y. template - inline _GLIBCXX_CONSTEXPR bool + _GLIBCXX_CONSTEXPR inline bool operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y) { return __x.real() != __y.real() || __x.imag() != __y.imag(); } template - inline _GLIBCXX_CONSTEXPR bool + _GLIBCXX_CONSTEXPR inline bool operator!=(const complex<_Tp>& __x, const _Tp& __y) { return __x.real() != __y || __x.imag() != _Tp(); } template - inline _GLIBCXX_CONSTEXPR bool + _GLIBCXX_CONSTEXPR inline bool operator!=(const _Tp& __x, const complex<_Tp>& __y) { return __x != __y.real() || _Tp() != __y.imag(); } //@} @@ -658,7 +658,7 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION struct _Norm_helper { template - static inline _Tp _S_do_it(const complex<_Tp>& __z) + static _GLIBCXX_CONSTEXPR inline _Tp _S_do_it(const complex<_Tp>& __z) { const _Tp __x = __z.real(); const _Tp __y = __z.imag(); @@ -670,7 +670,7 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION struct _Norm_helper { template - static inline _Tp _S_do_it(const complex<_Tp>& __z) + static _GLIBCXX_CONSTEXPR inline _Tp _S_do_it(const complex<_Tp>& __z) { _Tp __res = std::abs(__z); return __res * __res; @@ -678,7 +678,7 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION }; template - inline _Tp + _GLIBCXX_CONSTEXPR inline _Tp norm(const complex<_Tp>& __z) { return _Norm_helper<__is_floating<_Tp>::__value @@ -1866,7 +1866,7 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION { return _Tp(); } template - inline typename __gnu_cxx::__promote<_Tp>::__type + _GLIBCXX_CONSTEXPR inline typename __gnu_cxx::__promote<_Tp>::__type norm(_Tp __x) { typedef typename __gnu_cxx::__promote<_Tp>::__type __type; @@ -1905,10 +1905,11 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION // Forward declarations. // DR 781. - template std::complex<_Tp> proj(const std::complex<_Tp>&); + template + _GLIBCXX_CONSTEXPR std::complex<_Tp> proj(const std::complex<_Tp>&); template - std::complex<_Tp> + _GLIBCXX_CONSTEXPR std::complex<_Tp> __complex_proj(const std::complex<_Tp>& __z) { const _Tp __den = (__z.real() * __z.real() @@ -1919,25 +1920,25 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION } #if _GLIBCXX_USE_C99_COMPLEX - inline __complex__ float + _GLIBCXX_CONSTEXPR inline __complex__ float __complex_proj(__complex__ float __z) { return __builtin_cprojf(__z); } - inline __complex__ double + _GLIBCXX_CONSTEXPR inline __complex__ double __complex_proj(__complex__ double __z) { return __builtin_cproj(__z); } - inline __complex__ long double + _GLIBCXX_CONSTEXPR inline __complex__ long double __complex_proj(const __complex__ long double& __z) { return __builtin_cprojl(__z); } template - inline std::complex<_Tp> + _GLIBCXX_CONSTEXPR inline std::complex<_Tp> proj(const std::complex<_Tp>& __z) { return __complex_proj(__z.__rep()); } #else template - inline std::complex<_Tp> + _GLIBCXX_CONSTEXPR inline std::complex<_Tp> proj(const std::complex<_Tp>& __z) { return __complex_proj(__z); } #endif diff --git a/libstdc++-v3/include/tr1/bessel_function.tcc b/libstdc++-v3/include/tr1/bessel_function.tcc index 26c66cabe29..1ae88a3c952 100644 --- a/libstdc++-v3/include/tr1/bessel_function.tcc +++ b/libstdc++-v3/include/tr1/bessel_function.tcc @@ -353,21 +353,47 @@ namespace tr1 * @param __x The argument of the Bessel functions. * @param __Jnu The output Bessel function of the first kind. * @param __Nnu The output Neumann function (Bessel function of the second kind). + * + * Adapted for libstdc++ from GNU GSL version 2.4 specfunc/bessel_j.c + * Copyright (C) 1996,1997,1998,1999,2000,2001,2002,2003 Gerard Jungman */ template void __cyl_bessel_jn_asymp(_Tp __nu, _Tp __x, _Tp & __Jnu, _Tp & __Nnu) { const _Tp __mu = _Tp(4) * __nu * __nu; - const _Tp __mum1 = __mu - _Tp(1); - const _Tp __mum9 = __mu - _Tp(9); - const _Tp __mum25 = __mu - _Tp(25); - const _Tp __mum49 = __mu - _Tp(49); - const _Tp __xx = _Tp(64) * __x * __x; - const _Tp __P = _Tp(1) - __mum1 * __mum9 / (_Tp(2) * __xx) - * (_Tp(1) - __mum25 * __mum49 / (_Tp(12) * __xx)); - const _Tp __Q = __mum1 / (_Tp(8) * __x) - * (_Tp(1) - __mum9 * __mum25 / (_Tp(6) * __xx)); + const _Tp __8x = _Tp(8) * __x; + + _Tp __P = _Tp(0); + _Tp __Q = _Tp(0); + + _Tp k = _Tp(0); + _Tp __term = _Tp(1); + + int __epsP = 0; + int __epsQ = 0; + + _Tp __eps = std::numeric_limits<_Tp>::epsilon(); + + do + { + __term *= (k == 0) ? _Tp(1) : -(__mu - (2 * k - 1) * (2 * k - 1)) / (k * __8x); + __epsP = std::abs(__term) < std::abs(__eps * __P); + __P += __term; + + k++; + + __term *= (__mu - (2 * k - 1) * (2 * k - 1)) / (k * __8x); + __epsQ = std::abs(__term) < std::abs(__eps * __Q); + __Q += __term; + + if (__epsP && __epsQ && k > __nu / 2.) + break; + + k++; + } + while (k < 1000); + const _Tp __chi = __x - (__nu + _Tp(0.5L)) * __numeric_constants<_Tp>::__pi_2(); diff --git a/libstdc++-v3/include/tr1/legendre_function.tcc b/libstdc++-v3/include/tr1/legendre_function.tcc index a07d83a0bb1..e2d1880ecb0 100644 --- a/libstdc++-v3/include/tr1/legendre_function.tcc +++ b/libstdc++-v3/include/tr1/legendre_function.tcc @@ -65,7 +65,7 @@ namespace tr1 namespace __detail { /** - * @brief Return the Legendre polynomial by recursion on degree + * @brief Return the Legendre polynomial by recursion on order * @f$ l @f$. * * The Legendre function of @f$ l @f$ and @f$ x @f$, @@ -74,7 +74,7 @@ namespace tr1 * P_l(x) = \frac{1}{2^l l!}\frac{d^l}{dx^l}(x^2 - 1)^{l} * @f] * - * @param l The degree of the Legendre polynomial. @f$l >= 0@f$. + * @param l The order of the Legendre polynomial. @f$l >= 0@f$. * @param x The argument of the Legendre polynomial. @f$|x| <= 1@f$. */ template @@ -127,19 +127,16 @@ namespace tr1 * P_l^m(x) = (1 - x^2)^{m/2}\frac{d^m}{dx^m}P_l(x) * @f] * - * @param l The degree of the associated Legendre function. + * @param l The order of the associated Legendre function. * @f$ l >= 0 @f$. * @param m The order of the associated Legendre function. * @f$ m <= l @f$. * @param x The argument of the associated Legendre function. * @f$ |x| <= 1 @f$. - * @param phase The phase of the associated Legendre function. - * Use -1 for the Condon-Shortley phase convention. */ template _Tp - __assoc_legendre_p(unsigned int __l, unsigned int __m, _Tp __x, - _Tp __phase = _Tp{+1}) + __assoc_legendre_p(unsigned int __l, unsigned int __m, _Tp __x) { if (__x < _Tp(-1) || __x > _Tp(+1)) @@ -163,7 +160,7 @@ namespace tr1 _Tp __fact = _Tp(1); for (unsigned int __i = 1; __i <= __m; ++__i) { - __p_mm *= __phase * __fact * __root; + __p_mm *= -__fact * __root; __fact += _Tp(2); } } @@ -208,10 +205,8 @@ namespace tr1 * but this factor is rather large for large @f$ l @f$ and @f$ m @f$ * and so this function is stable for larger differences of @f$ l @f$ * and @f$ m @f$. - * @note Unlike the case for __assoc_legendre_p the Condon-Shortley - * phase factor @f$ (-1)^m @f$ is present here. * - * @param l The degree of the spherical associated Legendre function. + * @param l The order of the spherical associated Legendre function. * @f$ l >= 0 @f$. * @param m The order of the spherical associated Legendre function. * @f$ m <= l @f$. @@ -270,15 +265,19 @@ namespace tr1 const _Tp __lnpre_val = -_Tp(0.25L) * __numeric_constants<_Tp>::__lnpi() + _Tp(0.5L) * (__lnpoch + __m * __lncirc); - const _Tp __sr = std::sqrt((_Tp(2) + _Tp(1) / __m) - / (_Tp(4) * __numeric_constants<_Tp>::__pi())); + _Tp __sr = std::sqrt((_Tp(2) + _Tp(1) / __m) + / (_Tp(4) * __numeric_constants<_Tp>::__pi())); _Tp __y_mm = __sgn * __sr * std::exp(__lnpre_val); _Tp __y_mp1m = __y_mp1m_factor * __y_mm; if (__l == __m) - return __y_mm; + { + return __y_mm; + } else if (__l == __m + 1) - return __y_mp1m; + { + return __y_mp1m; + } else { _Tp __y_lm = _Tp(0); diff --git a/libstdc++-v3/testsuite/special_functions/02_assoc_legendre/check_value.cc b/libstdc++-v3/testsuite/special_functions/02_assoc_legendre/check_value.cc index d99d31e6c9a..e393b4aa183 100644 --- a/libstdc++-v3/testsuite/special_functions/02_assoc_legendre/check_value.cc +++ b/libstdc++-v3/testsuite/special_functions/02_assoc_legendre/check_value.cc @@ -1,6 +1,6 @@ // { dg-do run { target c++11 } } -// { dg-options "-D__STDCPP_WANT_MATH_SPEC_FUNCS__ -ffp-contract=off" } - +// { dg-options "-D__STDCPP_WANT_MATH_SPEC_FUNCS__" } +// // Copyright (C) 2016-2018 Free Software Foundation, Inc. // // This file is part of the GNU ISO C++ Library. This library is free @@ -30,7 +30,7 @@ { \ std::cout << "line " << __LINE__ \ << " max_abs_frac = " << max_abs_frac \ - << '\n'; \ + << std::endl; \ } #else # include @@ -148,53 +148,53 @@ const double toler002 = 2.5000000000000020e-13; // Test data for l=1, m=1. // max(|f - f_GSL|): 2.2204460492503131e-16 at index 12 // max(|f - f_GSL| / |f_GSL|): 2.4227052612512390e-16 -// mean(f - f_GSL): -1.0573552615477681e-17 +// mean(f - f_GSL): 1.0573552615477681e-17 // variance(f - f_GSL): 5.8695007828944331e-36 // stddev(f - f_GSL): 2.4227052612512388e-18 const testcase_assoc_legendre data003[21] = { - { 0.0000000000000000, 1, 1, + { -0.0000000000000000, 1, 1, -1.0000000000000000, 0.0 }, - { 0.43588989435406728, 1, 1, + { -0.43588989435406728, 1, 1, -0.90000000000000002, 0.0 }, - { 0.59999999999999987, 1, 1, + { -0.59999999999999987, 1, 1, -0.80000000000000004, 0.0 }, - { 0.71414284285428509, 1, 1, + { -0.71414284285428509, 1, 1, -0.69999999999999996, 0.0 }, - { 0.80000000000000004, 1, 1, + { -0.80000000000000004, 1, 1, -0.59999999999999998, 0.0 }, - { 0.86602540378443860, 1, 1, + { -0.86602540378443860, 1, 1, -0.50000000000000000, 0.0 }, - { 0.91651513899116799, 1, 1, + { -0.91651513899116799, 1, 1, -0.39999999999999991, 0.0 }, - { 0.95393920141694555, 1, 1, + { -0.95393920141694555, 1, 1, -0.29999999999999993, 0.0 }, - { 0.97979589711327120, 1, 1, + { -0.97979589711327120, 1, 1, -0.19999999999999996, 0.0 }, - { 0.99498743710661997, 1, 1, + { -0.99498743710661997, 1, 1, -0.099999999999999978, 0.0 }, - { 1.0000000000000000, 1, 1, + { -1.0000000000000000, 1, 1, 0.0000000000000000, 0.0 }, - { 0.99498743710661997, 1, 1, + { -0.99498743710661997, 1, 1, 0.10000000000000009, 0.0 }, - { 0.97979589711327120, 1, 1, + { -0.97979589711327120, 1, 1, 0.20000000000000018, 0.0 }, - { 0.95393920141694577, 1, 1, + { -0.95393920141694577, 1, 1, 0.30000000000000004, 0.0 }, - { 0.91651513899116788, 1, 1, + { -0.91651513899116788, 1, 1, 0.40000000000000013, 0.0 }, - { 0.86602540378443860, 1, 1, + { -0.86602540378443860, 1, 1, 0.50000000000000000, 0.0 }, - { 0.79999999999999993, 1, 1, + { -0.79999999999999993, 1, 1, 0.60000000000000009, 0.0 }, - { 0.71414284285428475, 1, 1, + { -0.71414284285428475, 1, 1, 0.70000000000000018, 0.0 }, - { 0.59999999999999987, 1, 1, + { -0.59999999999999987, 1, 1, 0.80000000000000004, 0.0 }, - { 0.43588989435406711, 1, 1, + { -0.43588989435406711, 1, 1, 0.90000000000000013, 0.0 }, - { 0.0000000000000000, 1, 1, + { -0.0000000000000000, 1, 1, 1.0000000000000000, 0.0 }, }; const double toler003 = 2.5000000000000020e-13; @@ -256,53 +256,53 @@ const double toler004 = 2.5000000000000020e-13; // Test data for l=2, m=1. // max(|f - f_GSL|): 2.2204460492503131e-16 at index 3 // max(|f - f_GSL| / |f_GSL|): 3.7770554319736585e-16 -// mean(f - f_GSL): 1.0573552615477681e-17 +// mean(f - f_GSL): -1.0573552615477681e-17 // variance(f - f_GSL): 5.8695007828944331e-36 // stddev(f - f_GSL): 2.4227052612512388e-18 const testcase_assoc_legendre data005[21] = { - { -0.0000000000000000, 2, 1, + { 0.0000000000000000, 2, 1, -1.0000000000000000, 0.0 }, - { -1.1769027147559816, 2, 1, + { 1.1769027147559816, 2, 1, -0.90000000000000002, 0.0 }, - { -1.4399999999999999, 2, 1, - -0.80000000000000004, 0.0 }, - { -1.4996999699939983, 2, 1, - -0.69999999999999996, 0.0 }, - { -1.4399999999999999, 2, 1, - -0.59999999999999998, 0.0 }, - { -1.2990381056766580, 2, 1, - -0.50000000000000000, 0.0 }, - { -1.0998181667894014, 2, 1, - -0.39999999999999991, 0.0 }, - { -0.85854528127525076, 2, 1, - -0.29999999999999993, 0.0 }, - { -0.58787753826796263, 2, 1, - -0.19999999999999996, 0.0 }, - { -0.29849623113198592, 2, 1, - -0.099999999999999978, 0.0 }, - { 0.0000000000000000, 2, 1, - 0.0000000000000000, 0.0 }, - { 0.29849623113198626, 2, 1, - 0.10000000000000009, 0.0 }, - { 0.58787753826796330, 2, 1, - 0.20000000000000018, 0.0 }, - { 0.85854528127525132, 2, 1, - 0.30000000000000004, 0.0 }, - { 1.0998181667894018, 2, 1, - 0.40000000000000013, 0.0 }, - { 1.2990381056766580, 2, 1, - 0.50000000000000000, 0.0 }, - { 1.4400000000000002, 2, 1, - 0.60000000000000009, 0.0 }, - { 1.4996999699939983, 2, 1, - 0.70000000000000018, 0.0 }, { 1.4399999999999999, 2, 1, + -0.80000000000000004, 0.0 }, + { 1.4996999699939983, 2, 1, + -0.69999999999999996, 0.0 }, + { 1.4399999999999999, 2, 1, + -0.59999999999999998, 0.0 }, + { 1.2990381056766580, 2, 1, + -0.50000000000000000, 0.0 }, + { 1.0998181667894014, 2, 1, + -0.39999999999999991, 0.0 }, + { 0.85854528127525076, 2, 1, + -0.29999999999999993, 0.0 }, + { 0.58787753826796263, 2, 1, + -0.19999999999999996, 0.0 }, + { 0.29849623113198592, 2, 1, + -0.099999999999999978, 0.0 }, + { -0.0000000000000000, 2, 1, + 0.0000000000000000, 0.0 }, + { -0.29849623113198626, 2, 1, + 0.10000000000000009, 0.0 }, + { -0.58787753826796330, 2, 1, + 0.20000000000000018, 0.0 }, + { -0.85854528127525132, 2, 1, + 0.30000000000000004, 0.0 }, + { -1.0998181667894018, 2, 1, + 0.40000000000000013, 0.0 }, + { -1.2990381056766580, 2, 1, + 0.50000000000000000, 0.0 }, + { -1.4400000000000002, 2, 1, + 0.60000000000000009, 0.0 }, + { -1.4996999699939983, 2, 1, + 0.70000000000000018, 0.0 }, + { -1.4399999999999999, 2, 1, 0.80000000000000004, 0.0 }, - { 1.1769027147559812, 2, 1, + { -1.1769027147559812, 2, 1, 0.90000000000000013, 0.0 }, - { 0.0000000000000000, 2, 1, + { -0.0000000000000000, 2, 1, 1.0000000000000000, 0.0 }, }; const double toler005 = 2.5000000000000020e-13; @@ -418,53 +418,53 @@ const double toler007 = 2.5000000000000020e-13; // Test data for l=5, m=1. // max(|f - f_GSL|): 6.6613381477509392e-16 at index 14 // max(|f - f_GSL| / |f_GSL|): 5.5186908001167120e-16 -// mean(f - f_GSL): 1.0573552615477681e-17 +// mean(f - f_GSL): -1.0573552615477681e-17 // variance(f - f_GSL): 5.8695007828944331e-36 // stddev(f - f_GSL): 2.4227052612512388e-18 const testcase_assoc_legendre data008[21] = { - { -0.0000000000000000, 5, 1, + { 0.0000000000000000, 5, 1, -1.0000000000000000, 0.0 }, - { 2.8099369608350981, 5, 1, + { -2.8099369608350981, 5, 1, -0.90000000000000002, 0.0 }, - { 0.72180000000000089, 5, 1, + { -0.72180000000000089, 5, 1, -0.80000000000000004, 0.0 }, - { -1.0951826834447254, 5, 1, + { 1.0951826834447254, 5, 1, -0.69999999999999996, 0.0 }, - { -1.9775999999999998, 5, 1, + { 1.9775999999999998, 5, 1, -0.59999999999999998, 0.0 }, - { -1.9282596881137892, 5, 1, + { 1.9282596881137892, 5, 1, -0.50000000000000000, 0.0 }, - { -1.2070504380513671, 5, 1, + { 1.2070504380513671, 5, 1, -0.39999999999999991, 0.0 }, - { -0.16079837663884300, 5, 1, + { 0.16079837663884300, 5, 1, -0.29999999999999993, 0.0 }, - { 0.87005875663658538, 5, 1, + { -0.87005875663658538, 5, 1, -0.19999999999999996, 0.0 }, - { 1.6083350053680323, 5, 1, + { -1.6083350053680323, 5, 1, -0.099999999999999978, 0.0 }, - { 1.8750000000000000, 5, 1, + { -1.8750000000000000, 5, 1, 0.0000000000000000, 0.0 }, - { 1.6083350053680314, 5, 1, + { -1.6083350053680314, 5, 1, 0.10000000000000009, 0.0 }, - { 0.87005875663658327, 5, 1, + { -0.87005875663658327, 5, 1, 0.20000000000000018, 0.0 }, - { -0.16079837663884422, 5, 1, + { 0.16079837663884422, 5, 1, 0.30000000000000004, 0.0 }, - { -1.2070504380513694, 5, 1, + { 1.2070504380513694, 5, 1, 0.40000000000000013, 0.0 }, - { -1.9282596881137892, 5, 1, + { 1.9282596881137892, 5, 1, 0.50000000000000000, 0.0 }, - { -1.9775999999999998, 5, 1, + { 1.9775999999999998, 5, 1, 0.60000000000000009, 0.0 }, - { -1.0951826834447216, 5, 1, + { 1.0951826834447216, 5, 1, 0.70000000000000018, 0.0 }, - { 0.72180000000000089, 5, 1, + { -0.72180000000000089, 5, 1, 0.80000000000000004, 0.0 }, - { 2.8099369608350999, 5, 1, + { -2.8099369608350999, 5, 1, 0.90000000000000013, 0.0 }, - { -0.0000000000000000, 5, 1, + { 0.0000000000000000, 5, 1, 1.0000000000000000, 0.0 }, }; const double toler008 = 2.5000000000000020e-13; @@ -526,53 +526,53 @@ const double toler009 = 2.5000000000000020e-13; // Test data for l=5, m=5. // max(|f - f_GSL|): 1.0231815394945443e-12 at index 12 // max(|f - f_GSL| / |f_GSL|): 1.1990652164995755e-15 -// mean(f - f_GSL): -3.1128538899966297e-14 +// mean(f - f_GSL): 3.1128538899966297e-14 // variance(f - f_GSL): 5.0871761537452526e-29 // stddev(f - f_GSL): 7.1324442891236469e-15 const testcase_assoc_legendre data010[21] = { - { 0.0000000000000000, 5, 5, + { -0.0000000000000000, 5, 5, -1.0000000000000000, 0.0 }, - { 14.870165800941818, 5, 5, + { -14.870165800941818, 5, 5, -0.90000000000000002, 0.0 }, - { 73.483199999999925, 5, 5, + { -73.483199999999925, 5, 5, -0.80000000000000004, 0.0 }, - { 175.53238298794764, 5, 5, + { -175.53238298794764, 5, 5, -0.69999999999999996, 0.0 }, - { 309.65760000000006, 5, 5, + { -309.65760000000006, 5, 5, -0.59999999999999998, 0.0 }, - { 460.34662869916559, 5, 5, + { -460.34662869916559, 5, 5, -0.50000000000000000, 0.0 }, - { 611.12496255819883, 5, 5, + { -611.12496255819883, 5, 5, -0.39999999999999991, 0.0 }, - { 746.50941479523703, 5, 5, + { -746.50941479523703, 5, 5, -0.29999999999999993, 0.0 }, - { 853.31600434671316, 5, 5, + { -853.31600434671316, 5, 5, -0.19999999999999996, 0.0 }, - { 921.55189181724734, 5, 5, + { -921.55189181724734, 5, 5, -0.099999999999999978, 0.0 }, - { 945.00000000000000, 5, 5, + { -945.00000000000000, 5, 5, 0.0000000000000000, 0.0 }, - { 921.55189181724734, 5, 5, + { -921.55189181724734, 5, 5, 0.10000000000000009, 0.0 }, - { 853.31600434671316, 5, 5, + { -853.31600434671316, 5, 5, 0.20000000000000018, 0.0 }, - { 746.50941479523760, 5, 5, + { -746.50941479523760, 5, 5, 0.30000000000000004, 0.0 }, - { 611.12496255819838, 5, 5, + { -611.12496255819838, 5, 5, 0.40000000000000013, 0.0 }, - { 460.34662869916559, 5, 5, + { -460.34662869916559, 5, 5, 0.50000000000000000, 0.0 }, - { 309.65759999999989, 5, 5, + { -309.65759999999989, 5, 5, 0.60000000000000009, 0.0 }, - { 175.53238298794724, 5, 5, + { -175.53238298794724, 5, 5, 0.70000000000000018, 0.0 }, - { 73.483199999999925, 5, 5, + { -73.483199999999925, 5, 5, 0.80000000000000004, 0.0 }, - { 14.870165800941789, 5, 5, + { -14.870165800941789, 5, 5, 0.90000000000000013, 0.0 }, - { 0.0000000000000000, 5, 5, + { -0.0000000000000000, 5, 5, 1.0000000000000000, 0.0 }, }; const double toler010 = 2.5000000000000020e-13; @@ -634,53 +634,53 @@ const double toler011 = 2.5000000000000020e-13; // Test data for l=10, m=1. // max(|f - f_GSL|): 1.3322676295501878e-15 at index 14 // max(|f - f_GSL| / |f_GSL|): 5.3672431731635395e-16 -// mean(f - f_GSL): -6.3441315692866085e-17 +// mean(f - f_GSL): 6.3441315692866085e-17 // variance(f - f_GSL): 2.1130202818419960e-34 // stddev(f - f_GSL): 1.4536231567507432e-17 const testcase_assoc_legendre data012[21] = { - { 0.0000000000000000, 10, 1, - -1.0000000000000000, 0.0 }, - { 3.0438748781479039, 10, 1, - -0.90000000000000002, 0.0 }, - { 0.87614260800000254, 10, 1, - -0.80000000000000004, 0.0 }, - { -2.9685359952934527, 10, 1, - -0.69999999999999996, 0.0 }, - { -1.2511825919999997, 10, 1, - -0.59999999999999998, 0.0 }, - { 2.0066877394361260, 10, 1, - -0.50000000000000000, 0.0 }, - { 2.4822196173476647, 10, 1, - -0.39999999999999991, 0.0 }, - { 0.12309508907433593, 10, 1, - -0.29999999999999993, 0.0 }, - { -2.2468221751958413, 10, 1, - -0.19999999999999996, 0.0 }, - { -2.2472659777983512, 10, 1, - -0.099999999999999978, 0.0 }, - { 0.0000000000000000, 10, 1, - 0.0000000000000000, 0.0 }, - { 2.2472659777983535, 10, 1, - 0.10000000000000009, 0.0 }, - { 2.2468221751958377, 10, 1, - 0.20000000000000018, 0.0 }, - { -0.12309508907433910, 10, 1, - 0.30000000000000004, 0.0 }, - { -2.4822196173476669, 10, 1, - 0.40000000000000013, 0.0 }, - { -2.0066877394361260, 10, 1, - 0.50000000000000000, 0.0 }, - { 1.2511825920000037, 10, 1, - 0.60000000000000009, 0.0 }, - { 2.9685359952934505, 10, 1, - 0.70000000000000018, 0.0 }, - { -0.87614260800000254, 10, 1, - 0.80000000000000004, 0.0 }, - { -3.0438748781478981, 10, 1, - 0.90000000000000013, 0.0 }, { -0.0000000000000000, 10, 1, + -1.0000000000000000, 0.0 }, + { -3.0438748781479039, 10, 1, + -0.90000000000000002, 0.0 }, + { -0.87614260800000254, 10, 1, + -0.80000000000000004, 0.0 }, + { 2.9685359952934527, 10, 1, + -0.69999999999999996, 0.0 }, + { 1.2511825919999997, 10, 1, + -0.59999999999999998, 0.0 }, + { -2.0066877394361260, 10, 1, + -0.50000000000000000, 0.0 }, + { -2.4822196173476647, 10, 1, + -0.39999999999999991, 0.0 }, + { -0.12309508907433593, 10, 1, + -0.29999999999999993, 0.0 }, + { 2.2468221751958413, 10, 1, + -0.19999999999999996, 0.0 }, + { 2.2472659777983512, 10, 1, + -0.099999999999999978, 0.0 }, + { -0.0000000000000000, 10, 1, + 0.0000000000000000, 0.0 }, + { -2.2472659777983535, 10, 1, + 0.10000000000000009, 0.0 }, + { -2.2468221751958377, 10, 1, + 0.20000000000000018, 0.0 }, + { 0.12309508907433910, 10, 1, + 0.30000000000000004, 0.0 }, + { 2.4822196173476669, 10, 1, + 0.40000000000000013, 0.0 }, + { 2.0066877394361260, 10, 1, + 0.50000000000000000, 0.0 }, + { -1.2511825920000037, 10, 1, + 0.60000000000000009, 0.0 }, + { -2.9685359952934505, 10, 1, + 0.70000000000000018, 0.0 }, + { 0.87614260800000254, 10, 1, + 0.80000000000000004, 0.0 }, + { 3.0438748781478981, 10, 1, + 0.90000000000000013, 0.0 }, + { 0.0000000000000000, 10, 1, 1.0000000000000000, 0.0 }, }; const double toler012 = 2.5000000000000020e-13; @@ -742,53 +742,53 @@ const double toler013 = 2.5000000000000020e-13; // Test data for l=10, m=5. // max(|f - f_GSL|): 2.9103830456733704e-11 at index 12 // max(|f - f_GSL| / |f_GSL|): 1.4825078449301893e-15 -// mean(f - f_GSL): -2.4253192047278085e-12 +// mean(f - f_GSL): 2.4253192047278085e-12 // variance(f - f_GSL): 3.0881409535313035e-25 // stddev(f - f_GSL): 5.5571044200476413e-13 const testcase_assoc_legendre data014[21] = { - { -0.0000000000000000, 10, 5, - -1.0000000000000000, 0.0 }, - { -21343.618518164680, 10, 5, - -0.90000000000000002, 0.0 }, - { -40457.016407807983, 10, 5, - -0.80000000000000004, 0.0 }, - { -20321.279317331315, 10, 5, - -0.69999999999999996, 0.0 }, - { 14410.820616192004, 10, 5, - -0.59999999999999998, 0.0 }, - { 30086.169706116176, 10, 5, - -0.50000000000000000, 0.0 }, - { 17177.549337582834, 10, 5, - -0.39999999999999991, 0.0 }, - { -9272.5119495412546, 10, 5, - -0.29999999999999993, 0.0 }, - { -26591.511184414714, 10, 5, - -0.19999999999999996, 0.0 }, - { -21961.951238504211, 10, 5, - -0.099999999999999978, 0.0 }, { 0.0000000000000000, 10, 5, - 0.0000000000000000, 0.0 }, - { 21961.951238504229, 10, 5, - 0.10000000000000009, 0.0 }, - { 26591.511184414703, 10, 5, - 0.20000000000000018, 0.0 }, - { 9272.5119495412364, 10, 5, - 0.30000000000000004, 0.0 }, - { -17177.549337582877, 10, 5, - 0.40000000000000013, 0.0 }, - { -30086.169706116176, 10, 5, - 0.50000000000000000, 0.0 }, - { -14410.820616191972, 10, 5, - 0.60000000000000009, 0.0 }, - { 20321.279317331391, 10, 5, - 0.70000000000000018, 0.0 }, + -1.0000000000000000, 0.0 }, + { 21343.618518164680, 10, 5, + -0.90000000000000002, 0.0 }, { 40457.016407807983, 10, 5, - 0.80000000000000004, 0.0 }, - { 21343.618518164636, 10, 5, - 0.90000000000000013, 0.0 }, + -0.80000000000000004, 0.0 }, + { 20321.279317331315, 10, 5, + -0.69999999999999996, 0.0 }, + { -14410.820616192004, 10, 5, + -0.59999999999999998, 0.0 }, + { -30086.169706116176, 10, 5, + -0.50000000000000000, 0.0 }, + { -17177.549337582834, 10, 5, + -0.39999999999999991, 0.0 }, + { 9272.5119495412546, 10, 5, + -0.29999999999999993, 0.0 }, + { 26591.511184414714, 10, 5, + -0.19999999999999996, 0.0 }, + { 21961.951238504211, 10, 5, + -0.099999999999999978, 0.0 }, { -0.0000000000000000, 10, 5, + 0.0000000000000000, 0.0 }, + { -21961.951238504229, 10, 5, + 0.10000000000000009, 0.0 }, + { -26591.511184414703, 10, 5, + 0.20000000000000018, 0.0 }, + { -9272.5119495412364, 10, 5, + 0.30000000000000004, 0.0 }, + { 17177.549337582877, 10, 5, + 0.40000000000000013, 0.0 }, + { 30086.169706116176, 10, 5, + 0.50000000000000000, 0.0 }, + { 14410.820616191972, 10, 5, + 0.60000000000000009, 0.0 }, + { -20321.279317331391, 10, 5, + 0.70000000000000018, 0.0 }, + { -40457.016407807983, 10, 5, + 0.80000000000000004, 0.0 }, + { -21343.618518164636, 10, 5, + 0.90000000000000013, 0.0 }, + { 0.0000000000000000, 10, 5, 1.0000000000000000, 0.0 }, }; const double toler014 = 2.5000000000000020e-13; @@ -904,53 +904,53 @@ const double toler016 = 2.5000000000000020e-13; // Test data for l=20, m=1. // max(|f - f_GSL|): 1.3322676295501878e-15 at index 12 // max(|f - f_GSL| / |f_GSL|): 1.0752784502271902e-15 -// mean(f - f_GSL): -1.4274296030894871e-16 +// mean(f - f_GSL): 1.4274296030894871e-16 // variance(f - f_GSL): 1.0697165176825104e-33 // stddev(f - f_GSL): 3.2706521026891724e-17 const testcase_assoc_legendre data017[21] = { - { -0.0000000000000000, 20, 1, + { 0.0000000000000000, 20, 1, -1.0000000000000000, 0.0 }, - { -4.3838334818220499, 20, 1, + { 4.3838334818220499, 20, 1, -0.90000000000000002, 0.0 }, - { 0.63138296146340844, 20, 1, - -0.80000000000000004, 0.0 }, - { -0.72274871413391395, 20, 1, - -0.69999999999999996, 0.0 }, - { 2.3203528743824910, 20, 1, - -0.59999999999999998, 0.0 }, - { -3.7399919228791405, 20, 1, - -0.50000000000000000, 0.0 }, - { 3.1692202279270085, 20, 1, - -0.39999999999999991, 0.0 }, - { -0.15804468835345031, 20, 1, - -0.29999999999999993, 0.0 }, - { -3.0366182393271171, 20, 1, - -0.19999999999999996, 0.0 }, - { 3.2115523815580209, 20, 1, - -0.099999999999999978, 0.0 }, - { -0.0000000000000000, 20, 1, - 0.0000000000000000, 0.0 }, - { -3.2115523815580169, 20, 1, - 0.10000000000000009, 0.0 }, - { 3.0366182393271259, 20, 1, - 0.20000000000000018, 0.0 }, - { 0.15804468835344135, 20, 1, - 0.30000000000000004, 0.0 }, - { -3.1692202279269970, 20, 1, - 0.40000000000000013, 0.0 }, - { 3.7399919228791405, 20, 1, - 0.50000000000000000, 0.0 }, - { -2.3203528743824995, 20, 1, - 0.60000000000000009, 0.0 }, - { 0.72274871413393793, 20, 1, - 0.70000000000000018, 0.0 }, { -0.63138296146340844, 20, 1, + -0.80000000000000004, 0.0 }, + { 0.72274871413391395, 20, 1, + -0.69999999999999996, 0.0 }, + { -2.3203528743824910, 20, 1, + -0.59999999999999998, 0.0 }, + { 3.7399919228791405, 20, 1, + -0.50000000000000000, 0.0 }, + { -3.1692202279270085, 20, 1, + -0.39999999999999991, 0.0 }, + { 0.15804468835345031, 20, 1, + -0.29999999999999993, 0.0 }, + { 3.0366182393271171, 20, 1, + -0.19999999999999996, 0.0 }, + { -3.2115523815580209, 20, 1, + -0.099999999999999978, 0.0 }, + { 0.0000000000000000, 20, 1, + 0.0000000000000000, 0.0 }, + { 3.2115523815580169, 20, 1, + 0.10000000000000009, 0.0 }, + { -3.0366182393271259, 20, 1, + 0.20000000000000018, 0.0 }, + { -0.15804468835344135, 20, 1, + 0.30000000000000004, 0.0 }, + { 3.1692202279269970, 20, 1, + 0.40000000000000013, 0.0 }, + { -3.7399919228791405, 20, 1, + 0.50000000000000000, 0.0 }, + { 2.3203528743824995, 20, 1, + 0.60000000000000009, 0.0 }, + { -0.72274871413393793, 20, 1, + 0.70000000000000018, 0.0 }, + { 0.63138296146340844, 20, 1, 0.80000000000000004, 0.0 }, - { 4.3838334818220686, 20, 1, + { -4.3838334818220686, 20, 1, 0.90000000000000013, 0.0 }, - { -0.0000000000000000, 20, 1, + { 0.0000000000000000, 20, 1, 1.0000000000000000, 0.0 }, }; const double toler017 = 2.5000000000000020e-13; @@ -1012,53 +1012,53 @@ const double toler018 = 2.5000000000000020e-13; // Test data for l=20, m=5. // max(|f - f_GSL|): 1.2805685400962830e-09 at index 14 // max(|f - f_GSL| / |f_GSL|): 2.0861530799041223e-15 -// mean(f - f_GSL): -1.1641532182693481e-10 +// mean(f - f_GSL): 1.1641532182693481e-10 // variance(f - f_GSL): 7.1150767569361226e-22 // stddev(f - f_GSL): 2.6674101216228678e-11 const testcase_assoc_legendre data019[21] = { - { 0.0000000000000000, 20, 5, + { -0.0000000000000000, 20, 5, -1.0000000000000000, 0.0 }, - { 315702.32715134218, 20, 5, + { -315702.32715134218, 20, 5, -0.90000000000000002, 0.0 }, - { -503060.91484852589, 20, 5, - -0.80000000000000004, 0.0 }, - { 298127.28360361955, 20, 5, - -0.69999999999999996, 0.0 }, - { 114444.61447464029, 20, 5, - -0.59999999999999998, 0.0 }, - { -543428.40914592845, 20, 5, - -0.50000000000000000, 0.0 }, - { 613842.07728185481, 20, 5, - -0.39999999999999991, 0.0 }, - { -143765.42411271061, 20, 5, - -0.29999999999999993, 0.0 }, - { -472600.45321372285, 20, 5, - -0.19999999999999996, 0.0 }, - { 563861.76771496492, 20, 5, - -0.099999999999999978, 0.0 }, - { -0.0000000000000000, 20, 5, - 0.0000000000000000, 0.0 }, - { -563861.76771496458, 20, 5, - 0.10000000000000009, 0.0 }, - { 472600.45321372483, 20, 5, - 0.20000000000000018, 0.0 }, - { 143765.42411270936, 20, 5, - 0.30000000000000004, 0.0 }, - { -613842.07728185353, 20, 5, - 0.40000000000000013, 0.0 }, - { 543428.40914592845, 20, 5, - 0.50000000000000000, 0.0 }, - { -114444.61447464178, 20, 5, - 0.60000000000000009, 0.0 }, - { -298127.28360361519, 20, 5, - 0.70000000000000018, 0.0 }, { 503060.91484852589, 20, 5, + -0.80000000000000004, 0.0 }, + { -298127.28360361955, 20, 5, + -0.69999999999999996, 0.0 }, + { -114444.61447464029, 20, 5, + -0.59999999999999998, 0.0 }, + { 543428.40914592845, 20, 5, + -0.50000000000000000, 0.0 }, + { -613842.07728185481, 20, 5, + -0.39999999999999991, 0.0 }, + { 143765.42411271061, 20, 5, + -0.29999999999999993, 0.0 }, + { 472600.45321372285, 20, 5, + -0.19999999999999996, 0.0 }, + { -563861.76771496492, 20, 5, + -0.099999999999999978, 0.0 }, + { 0.0000000000000000, 20, 5, + 0.0000000000000000, 0.0 }, + { 563861.76771496458, 20, 5, + 0.10000000000000009, 0.0 }, + { -472600.45321372483, 20, 5, + 0.20000000000000018, 0.0 }, + { -143765.42411270936, 20, 5, + 0.30000000000000004, 0.0 }, + { 613842.07728185353, 20, 5, + 0.40000000000000013, 0.0 }, + { -543428.40914592845, 20, 5, + 0.50000000000000000, 0.0 }, + { 114444.61447464178, 20, 5, + 0.60000000000000009, 0.0 }, + { 298127.28360361519, 20, 5, + 0.70000000000000018, 0.0 }, + { -503060.91484852589, 20, 5, 0.80000000000000004, 0.0 }, - { -315702.32715133618, 20, 5, + { 315702.32715133618, 20, 5, 0.90000000000000013, 0.0 }, - { -0.0000000000000000, 20, 5, + { 0.0000000000000000, 20, 5, 1.0000000000000000, 0.0 }, }; const double toler019 = 2.5000000000000020e-13; @@ -1228,53 +1228,53 @@ const double toler022 = 2.5000000000000020e-13; // Test data for l=50, m=1. // max(|f - f_GSL|): 4.4408920985006262e-15 at index 3 // max(|f - f_GSL| / |f_GSL|): 6.6657627150738456e-16 -// mean(f - f_GSL): -6.3441315692866085e-17 +// mean(f - f_GSL): 6.3441315692866085e-17 // variance(f - f_GSL): 2.1130202818419960e-34 // stddev(f - f_GSL): 1.4536231567507432e-17 const testcase_assoc_legendre data023[21] = { - { -0.0000000000000000, 50, 1, - -1.0000000000000000, 0.0 }, - { 0.13424149984449490, 50, 1, - -0.90000000000000002, 0.0 }, - { -2.2011219672413018, 50, 1, - -0.80000000000000004, 0.0 }, - { -6.6622414993232004, 50, 1, - -0.69999999999999996, 0.0 }, - { -5.5772846936919249, 50, 1, - -0.59999999999999998, 0.0 }, - { -5.8787148815607608, 50, 1, - -0.50000000000000000, 0.0 }, - { -5.5473459458634080, 50, 1, - -0.39999999999999991, 0.0 }, - { -1.8444956647620248, 50, 1, - -0.29999999999999993, 0.0 }, - { 3.8722014306642127, 50, 1, - -0.19999999999999996, 0.0 }, - { 5.3488751322285628, 50, 1, - -0.099999999999999978, 0.0 }, { 0.0000000000000000, 50, 1, - 0.0000000000000000, 0.0 }, - { -5.3488751322285522, 50, 1, - 0.10000000000000009, 0.0 }, - { -3.8722014306642620, 50, 1, - 0.20000000000000018, 0.0 }, - { 1.8444956647619930, 50, 1, - 0.30000000000000004, 0.0 }, - { 5.5473459458633814, 50, 1, - 0.40000000000000013, 0.0 }, - { 5.8787148815607608, 50, 1, - 0.50000000000000000, 0.0 }, - { 5.5772846936919453, 50, 1, - 0.60000000000000009, 0.0 }, - { 6.6622414993232182, 50, 1, - 0.70000000000000018, 0.0 }, + -1.0000000000000000, 0.0 }, + { -0.13424149984449490, 50, 1, + -0.90000000000000002, 0.0 }, { 2.2011219672413018, 50, 1, - 0.80000000000000004, 0.0 }, - { -0.13424149984438935, 50, 1, - 0.90000000000000013, 0.0 }, + -0.80000000000000004, 0.0 }, + { 6.6622414993232004, 50, 1, + -0.69999999999999996, 0.0 }, + { 5.5772846936919249, 50, 1, + -0.59999999999999998, 0.0 }, + { 5.8787148815607608, 50, 1, + -0.50000000000000000, 0.0 }, + { 5.5473459458634080, 50, 1, + -0.39999999999999991, 0.0 }, + { 1.8444956647620248, 50, 1, + -0.29999999999999993, 0.0 }, + { -3.8722014306642127, 50, 1, + -0.19999999999999996, 0.0 }, + { -5.3488751322285628, 50, 1, + -0.099999999999999978, 0.0 }, { -0.0000000000000000, 50, 1, + 0.0000000000000000, 0.0 }, + { 5.3488751322285522, 50, 1, + 0.10000000000000009, 0.0 }, + { 3.8722014306642620, 50, 1, + 0.20000000000000018, 0.0 }, + { -1.8444956647619930, 50, 1, + 0.30000000000000004, 0.0 }, + { -5.5473459458633814, 50, 1, + 0.40000000000000013, 0.0 }, + { -5.8787148815607608, 50, 1, + 0.50000000000000000, 0.0 }, + { -5.5772846936919453, 50, 1, + 0.60000000000000009, 0.0 }, + { -6.6622414993232182, 50, 1, + 0.70000000000000018, 0.0 }, + { -2.2011219672413018, 50, 1, + 0.80000000000000004, 0.0 }, + { 0.13424149984438935, 50, 1, + 0.90000000000000013, 0.0 }, + { 0.0000000000000000, 50, 1, 1.0000000000000000, 0.0 }, }; const double toler023 = 2.5000000000000020e-13; @@ -1336,53 +1336,53 @@ const double toler024 = 5.0000000000000039e-13; // Test data for l=50, m=5. // max(|f - f_GSL|): 7.4505805969238281e-08 at index 14 // max(|f - f_GSL| / |f_GSL|): 2.0088060426072767e-15 -// mean(f - f_GSL): 6.3862119402204238e-09 +// mean(f - f_GSL): -6.3862119402204238e-09 // variance(f - f_GSL): 2.1411444046342303e-18 // stddev(f - f_GSL): 1.4632649810045447e-09 const testcase_assoc_legendre data025[21] = { - { 0.0000000000000000, 50, 5, - -1.0000000000000000, 0.0 }, - { 27340473.952132829, 50, 5, - -0.90000000000000002, 0.0 }, - { -27753716.768532373, 50, 5, - -0.80000000000000004, 0.0 }, - { -40808153.913493633, 50, 5, - -0.69999999999999996, 0.0 }, - { -32071189.035790090, 50, 5, - -0.59999999999999998, 0.0 }, - { -36265736.218529105, 50, 5, - -0.50000000000000000, 0.0 }, - { -37089596.700204931, 50, 5, - -0.39999999999999991, 0.0 }, - { -14562029.629244687, 50, 5, - -0.29999999999999993, 0.0 }, - { 23686895.217517190, 50, 5, - -0.19999999999999996, 0.0 }, - { 34878992.965676002, 50, 5, - -0.099999999999999978, 0.0 }, - { 0.0000000000000000, 50, 5, - 0.0000000000000000, 0.0 }, - { -34878992.965675958, 50, 5, - 0.10000000000000009, 0.0 }, - { -23686895.217517529, 50, 5, - 0.20000000000000018, 0.0 }, - { 14562029.629244499, 50, 5, - 0.30000000000000004, 0.0 }, - { 37089596.700204782, 50, 5, - 0.40000000000000013, 0.0 }, - { 36265736.218529105, 50, 5, - 0.50000000000000000, 0.0 }, - { 32071189.035790242, 50, 5, - 0.60000000000000009, 0.0 }, - { 40808153.913493834, 50, 5, - 0.70000000000000018, 0.0 }, - { 27753716.768532373, 50, 5, - 0.80000000000000004, 0.0 }, - { -27340473.952132136, 50, 5, - 0.90000000000000013, 0.0 }, { -0.0000000000000000, 50, 5, + -1.0000000000000000, 0.0 }, + { -27340473.952132829, 50, 5, + -0.90000000000000002, 0.0 }, + { 27753716.768532373, 50, 5, + -0.80000000000000004, 0.0 }, + { 40808153.913493633, 50, 5, + -0.69999999999999996, 0.0 }, + { 32071189.035790090, 50, 5, + -0.59999999999999998, 0.0 }, + { 36265736.218529105, 50, 5, + -0.50000000000000000, 0.0 }, + { 37089596.700204931, 50, 5, + -0.39999999999999991, 0.0 }, + { 14562029.629244687, 50, 5, + -0.29999999999999993, 0.0 }, + { -23686895.217517190, 50, 5, + -0.19999999999999996, 0.0 }, + { -34878992.965676002, 50, 5, + -0.099999999999999978, 0.0 }, + { -0.0000000000000000, 50, 5, + 0.0000000000000000, 0.0 }, + { 34878992.965675958, 50, 5, + 0.10000000000000009, 0.0 }, + { 23686895.217517529, 50, 5, + 0.20000000000000018, 0.0 }, + { -14562029.629244499, 50, 5, + 0.30000000000000004, 0.0 }, + { -37089596.700204782, 50, 5, + 0.40000000000000013, 0.0 }, + { -36265736.218529105, 50, 5, + 0.50000000000000000, 0.0 }, + { -32071189.035790242, 50, 5, + 0.60000000000000009, 0.0 }, + { -40808153.913493834, 50, 5, + 0.70000000000000018, 0.0 }, + { -27753716.768532373, 50, 5, + 0.80000000000000004, 0.0 }, + { 27340473.952132136, 50, 5, + 0.90000000000000013, 0.0 }, + { 0.0000000000000000, 50, 5, 1.0000000000000000, 0.0 }, }; const double toler025 = 2.5000000000000020e-13; @@ -1606,53 +1606,53 @@ const double toler029 = 5.0000000000000039e-13; // Test data for l=100, m=1. // max(|f - f_GSL|): 1.1546319456101628e-14 at index 3 // max(|f - f_GSL| / |f_GSL|): 2.1111954004946762e-15 -// mean(f - f_GSL): 8.0358999877630379e-16 +// mean(f - f_GSL): -8.0358999877630379e-16 // variance(f - f_GSL): 3.3902236521998243e-32 // stddev(f - f_GSL): 1.8412559985509414e-16 const testcase_assoc_legendre data030[21] = { - { 0.0000000000000000, 100, 1, + { -0.0000000000000000, 100, 1, -1.0000000000000000, 0.0 }, - { -6.5200167187780345, 100, 1, + { 6.5200167187780345, 100, 1, -0.90000000000000002, 0.0 }, - { -9.0065170007027486, 100, 1, - -0.80000000000000004, 0.0 }, - { 5.4690908541180976, 100, 1, - -0.69999999999999996, 0.0 }, - { 8.6275439170430790, 100, 1, - -0.59999999999999998, 0.0 }, - { 6.0909031663448454, 100, 1, - -0.50000000000000000, 0.0 }, - { -4.1160338699560395, 100, 1, - -0.39999999999999991, 0.0 }, - { -5.8491043010758634, 100, 1, - -0.29999999999999993, 0.0 }, - { 7.9435138723089826, 100, 1, - -0.19999999999999996, 0.0 }, - { -4.7996285823989355, 100, 1, - -0.099999999999999978, 0.0 }, - { -0.0000000000000000, 100, 1, - 0.0000000000000000, 0.0 }, - { 4.7996285823990101, 100, 1, - 0.10000000000000009, 0.0 }, - { -7.9435138723090155, 100, 1, - 0.20000000000000018, 0.0 }, - { 5.8491043010758013, 100, 1, - 0.30000000000000004, 0.0 }, - { 4.1160338699562162, 100, 1, - 0.40000000000000013, 0.0 }, - { -6.0909031663448454, 100, 1, - 0.50000000000000000, 0.0 }, - { -8.6275439170430470, 100, 1, - 0.60000000000000009, 0.0 }, - { -5.4690908541178693, 100, 1, - 0.70000000000000018, 0.0 }, { 9.0065170007027486, 100, 1, + -0.80000000000000004, 0.0 }, + { -5.4690908541180976, 100, 1, + -0.69999999999999996, 0.0 }, + { -8.6275439170430790, 100, 1, + -0.59999999999999998, 0.0 }, + { -6.0909031663448454, 100, 1, + -0.50000000000000000, 0.0 }, + { 4.1160338699560395, 100, 1, + -0.39999999999999991, 0.0 }, + { 5.8491043010758634, 100, 1, + -0.29999999999999993, 0.0 }, + { -7.9435138723089826, 100, 1, + -0.19999999999999996, 0.0 }, + { 4.7996285823989355, 100, 1, + -0.099999999999999978, 0.0 }, + { 0.0000000000000000, 100, 1, + 0.0000000000000000, 0.0 }, + { -4.7996285823990101, 100, 1, + 0.10000000000000009, 0.0 }, + { 7.9435138723090155, 100, 1, + 0.20000000000000018, 0.0 }, + { -5.8491043010758013, 100, 1, + 0.30000000000000004, 0.0 }, + { -4.1160338699562162, 100, 1, + 0.40000000000000013, 0.0 }, + { 6.0909031663448454, 100, 1, + 0.50000000000000000, 0.0 }, + { 8.6275439170430470, 100, 1, + 0.60000000000000009, 0.0 }, + { 5.4690908541178693, 100, 1, + 0.70000000000000018, 0.0 }, + { -9.0065170007027486, 100, 1, 0.80000000000000004, 0.0 }, - { 6.5200167187777787, 100, 1, + { -6.5200167187777787, 100, 1, 0.90000000000000013, 0.0 }, - { -0.0000000000000000, 100, 1, + { 0.0000000000000000, 100, 1, 1.0000000000000000, 0.0 }, }; const double toler030 = 2.5000000000000020e-13; @@ -1714,53 +1714,53 @@ const double toler031 = 2.5000000000000020e-13; // Test data for l=100, m=5. // max(|f - f_GSL|): 1.4305114746093750e-06 at index 14 // max(|f - f_GSL| / |f_GSL|): 3.7628882298853693e-15 -// mean(f - f_GSL): 5.1089695521763390e-08 +// mean(f - f_GSL): -5.1089695521763390e-08 // variance(f - f_GSL): 1.3703324189659077e-16 // stddev(f - f_GSL): 1.1706119848036358e-08 const testcase_assoc_legendre data032[21] = { - { -0.0000000000000000, 100, 5, + { 0.0000000000000000, 100, 5, -1.0000000000000000, 0.0 }, - { -900551126.09653807, 100, 5, + { 900551126.09653807, 100, 5, -0.90000000000000002, 0.0 }, - { -988567431.55756140, 100, 5, - -0.80000000000000004, 0.0 }, - { 645646451.90344620, 100, 5, - -0.69999999999999996, 0.0 }, - { 897114585.29920685, 100, 5, - -0.59999999999999998, 0.0 }, - { 661710744.42483854, 100, 5, - -0.50000000000000000, 0.0 }, - { -380163158.51424754, 100, 5, - -0.39999999999999991, 0.0 }, - { -617391071.36633193, 100, 5, - -0.29999999999999993, 0.0 }, - { 805288801.85509109, 100, 5, - -0.19999999999999996, 0.0 }, - { -481041740.16728652, 100, 5, - -0.099999999999999978, 0.0 }, - { -0.0000000000000000, 100, 5, - 0.0000000000000000, 0.0 }, - { 481041740.16729391, 100, 5, - 0.10000000000000009, 0.0 }, - { -805288801.85509515, 100, 5, - 0.20000000000000018, 0.0 }, - { 617391071.36632574, 100, 5, - 0.30000000000000004, 0.0 }, - { 380163158.51426536, 100, 5, - 0.40000000000000013, 0.0 }, - { -661710744.42483854, 100, 5, - 0.50000000000000000, 0.0 }, - { -897114585.29920483, 100, 5, - 0.60000000000000009, 0.0 }, - { -645646451.90342283, 100, 5, - 0.70000000000000018, 0.0 }, { 988567431.55756140, 100, 5, + -0.80000000000000004, 0.0 }, + { -645646451.90344620, 100, 5, + -0.69999999999999996, 0.0 }, + { -897114585.29920685, 100, 5, + -0.59999999999999998, 0.0 }, + { -661710744.42483854, 100, 5, + -0.50000000000000000, 0.0 }, + { 380163158.51424754, 100, 5, + -0.39999999999999991, 0.0 }, + { 617391071.36633193, 100, 5, + -0.29999999999999993, 0.0 }, + { -805288801.85509109, 100, 5, + -0.19999999999999996, 0.0 }, + { 481041740.16728652, 100, 5, + -0.099999999999999978, 0.0 }, + { 0.0000000000000000, 100, 5, + 0.0000000000000000, 0.0 }, + { -481041740.16729391, 100, 5, + 0.10000000000000009, 0.0 }, + { 805288801.85509515, 100, 5, + 0.20000000000000018, 0.0 }, + { -617391071.36632574, 100, 5, + 0.30000000000000004, 0.0 }, + { -380163158.51426536, 100, 5, + 0.40000000000000013, 0.0 }, + { 661710744.42483854, 100, 5, + 0.50000000000000000, 0.0 }, + { 897114585.29920483, 100, 5, + 0.60000000000000009, 0.0 }, + { 645646451.90342283, 100, 5, + 0.70000000000000018, 0.0 }, + { -988567431.55756140, 100, 5, 0.80000000000000004, 0.0 }, - { 900551126.09651637, 100, 5, + { -900551126.09651637, 100, 5, 0.90000000000000013, 0.0 }, - { -0.0000000000000000, 100, 5, + { 0.0000000000000000, 100, 5, 1.0000000000000000, 0.0 }, }; const double toler032 = 2.5000000000000020e-13; diff --git a/libstdc++-v3/testsuite/special_functions/08_cyl_bessel_j/check_value.cc b/libstdc++-v3/testsuite/special_functions/08_cyl_bessel_j/check_value.cc index 475c6dcaa4a..74c08d021dc 100644 --- a/libstdc++-v3/testsuite/special_functions/08_cyl_bessel_j/check_value.cc +++ b/libstdc++-v3/testsuite/special_functions/08_cyl_bessel_j/check_value.cc @@ -698,6 +698,26 @@ data026[21] = }; const double toler026 = 1.0000000000000006e-11; +// Test data for nu=100.00000000000000. +// max(|f - f_GSL|): 2.5857788132910287e-14 +// max(|f - f_GSL| / |f_GSL|): 1.6767662425535933e-11 +const testcase_cyl_bessel_j +data027[11] = +{ + { 0.0116761350077845, 100.0000000000000000, 1000.0000000000000000, 0.0 }, + {-0.0116998547780258, 100.0000000000000000, 1100.0000000000000000, 0.0 }, + {-0.0228014834050837, 100.0000000000000000, 1200.0000000000000000, 0.0 }, + {-0.0169735007873739, 100.0000000000000000, 1300.0000000000000000, 0.0 }, + {-0.0014154528803530, 100.0000000000000000, 1400.0000000000000000, 0.0 }, + { 0.0133337265844988, 100.0000000000000000, 1500.0000000000000000, 0.0 }, + { 0.0198025620201474, 100.0000000000000000, 1600.0000000000000000, 0.0 }, + { 0.0161297712798388, 100.0000000000000000, 1700.0000000000000000, 0.0 }, + { 0.0053753369281577, 100.0000000000000000, 1800.0000000000000000, 0.0 }, + {-0.0069238868725646, 100.0000000000000000, 1900.0000000000000000, 0.0 }, + {-0.0154878717200738, 100.0000000000000000, 2000.0000000000000000, 0.0 }, +}; +const double toler027 = 1.0000000000000006e-10; + template void test(const testcase_cyl_bessel_j (&data)[Num], Ret toler) @@ -748,5 +768,6 @@ main() test(data024, toler024); test(data025, toler025); test(data026, toler026); + test(data027, toler027); return 0; } diff --git a/libstdc++-v3/testsuite/special_functions/10_cyl_neumann/check_value.cc b/libstdc++-v3/testsuite/special_functions/10_cyl_neumann/check_value.cc index da1250278d5..cde8cf611f9 100644 --- a/libstdc++-v3/testsuite/special_functions/10_cyl_neumann/check_value.cc +++ b/libstdc++-v3/testsuite/special_functions/10_cyl_neumann/check_value.cc @@ -742,6 +742,26 @@ data028[20] = }; const double toler028 = 1.0000000000000006e-11; +// Test data for nu=100.00000000000000. +// max(|f - f_GSL|): 3.1049815496508870e-14 +// max(|f - f_GSL| / |f_GSL|): 8.4272302674970308e-12 +const testcase_cyl_neumann +data029[11] = +{ + {-0.0224386882577326, 100.0000000000000000, 1000.0000000000000000, 0.0 }, + {-0.0210775951598200, 100.0000000000000000, 1100.0000000000000000, 0.0 }, + {-0.0035299439206693, 100.0000000000000000, 1200.0000000000000000, 0.0 }, + { 0.0142500193265366, 100.0000000000000000, 1300.0000000000000000, 0.0 }, + { 0.0213046790897353, 100.0000000000000000, 1400.0000000000000000, 0.0 }, + { 0.0157343950779022, 100.0000000000000000, 1500.0000000000000000, 0.0 }, + { 0.0025544633636228, 100.0000000000000000, 1600.0000000000000000, 0.0 }, + {-0.0107220455248494, 100.0000000000000000, 1700.0000000000000000, 0.0 }, + {-0.0180369192432256, 100.0000000000000000, 1800.0000000000000000, 0.0 }, + {-0.0169584155930798, 100.0000000000000000, 1900.0000000000000000, 0.0 }, + {-0.0088788704566206, 100.0000000000000000, 2000.0000000000000000, 0.0 }, +}; +const double toler029 = 1.0000000000000006e-11; + template void test(const testcase_cyl_neumann (&data)[Num], Ret toler) @@ -794,5 +814,6 @@ main() test(data026, toler026); test(data027, toler027); test(data028, toler028); + test(data029, toler029); return 0; } diff --git a/libstdc++-v3/testsuite/tr1/5_numerical_facilities/special_functions/02_assoc_legendre/check_value.cc b/libstdc++-v3/testsuite/tr1/5_numerical_facilities/special_functions/02_assoc_legendre/check_value.cc new file mode 100644 index 00000000000..782894cb94d --- /dev/null +++ b/libstdc++-v3/testsuite/tr1/5_numerical_facilities/special_functions/02_assoc_legendre/check_value.cc @@ -0,0 +1,2052 @@ +// { dg-do run { target c++11 } } +// { dg-options "-D__STDCPP_WANT_MATH_SPEC_FUNCS__" } +// +// Copyright (C) 2016-2018 Free Software Foundation, Inc. +// +// This file is part of the GNU ISO C++ Library. This library is free +// software; you can redistribute it and/or modify it under the +// terms of the GNU General Public License as published by the +// Free Software Foundation; either version 3, or (at your option) +// any later version. +// +// This library is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// +// You should have received a copy of the GNU General Public License along +// with this library; see the file COPYING3. If not see +// . + +// assoc_legendre +// Compare against values generated by the GNU Scientific Library. +// The GSL can be found on the web: http://www.gnu.org/software/gsl/ +#include +#include +#if defined(__TEST_DEBUG) +# include +# define VERIFY(A) \ + if (!(A)) \ + { \ + std::cout << "line " << __LINE__ \ + << " max_abs_frac = " << max_abs_frac \ + << std::endl; \ + } +#else +# include +#endif +#include + +// Test data for l=0, m=0. +// max(|f - f_GSL|): 0.0000000000000000 at index 0 +// max(|f - f_GSL| / |f_GSL|): 0.0000000000000000 +// mean(f - f_GSL): 0.0000000000000000 +// variance(f - f_GSL): 0.0000000000000000 +// stddev(f - f_GSL): 0.0000000000000000 +const testcase_assoc_legendre +data001[21] = +{ + { 1.0000000000000000, 0, 0, + -1.0000000000000000, 0.0 }, + { 1.0000000000000000, 0, 0, + -0.90000000000000002, 0.0 }, + { 1.0000000000000000, 0, 0, + -0.80000000000000004, 0.0 }, + { 1.0000000000000000, 0, 0, + -0.69999999999999996, 0.0 }, + { 1.0000000000000000, 0, 0, + -0.59999999999999998, 0.0 }, + { 1.0000000000000000, 0, 0, + -0.50000000000000000, 0.0 }, + { 1.0000000000000000, 0, 0, + -0.39999999999999991, 0.0 }, + { 1.0000000000000000, 0, 0, + -0.29999999999999993, 0.0 }, + { 1.0000000000000000, 0, 0, + -0.19999999999999996, 0.0 }, + { 1.0000000000000000, 0, 0, + -0.099999999999999978, 0.0 }, + { 1.0000000000000000, 0, 0, + 0.0000000000000000, 0.0 }, + { 1.0000000000000000, 0, 0, + 0.10000000000000009, 0.0 }, + { 1.0000000000000000, 0, 0, + 0.20000000000000018, 0.0 }, + { 1.0000000000000000, 0, 0, + 0.30000000000000004, 0.0 }, + { 1.0000000000000000, 0, 0, + 0.40000000000000013, 0.0 }, + { 1.0000000000000000, 0, 0, + 0.50000000000000000, 0.0 }, + { 1.0000000000000000, 0, 0, + 0.60000000000000009, 0.0 }, + { 1.0000000000000000, 0, 0, + 0.70000000000000018, 0.0 }, + { 1.0000000000000000, 0, 0, + 0.80000000000000004, 0.0 }, + { 1.0000000000000000, 0, 0, + 0.90000000000000013, 0.0 }, + { 1.0000000000000000, 0, 0, + 1.0000000000000000, 0.0 }, +}; +const double toler001 = 2.5000000000000020e-13; + +// Test data for l=1, m=0. +// max(|f - f_GSL|): 0.0000000000000000 at index 0 +// max(|f - f_GSL| / |f_GSL|): 0.0000000000000000 +// mean(f - f_GSL): 0.0000000000000000 +// variance(f - f_GSL): 0.0000000000000000 +// stddev(f - f_GSL): 0.0000000000000000 +const testcase_assoc_legendre +data002[21] = +{ + { -1.0000000000000000, 1, 0, + -1.0000000000000000, 0.0 }, + { -0.90000000000000002, 1, 0, + -0.90000000000000002, 0.0 }, + { -0.80000000000000004, 1, 0, + -0.80000000000000004, 0.0 }, + { -0.69999999999999996, 1, 0, + -0.69999999999999996, 0.0 }, + { -0.59999999999999998, 1, 0, + -0.59999999999999998, 0.0 }, + { -0.50000000000000000, 1, 0, + -0.50000000000000000, 0.0 }, + { -0.39999999999999991, 1, 0, + -0.39999999999999991, 0.0 }, + { -0.29999999999999993, 1, 0, + -0.29999999999999993, 0.0 }, + { -0.19999999999999996, 1, 0, + -0.19999999999999996, 0.0 }, + { -0.099999999999999978, 1, 0, + -0.099999999999999978, 0.0 }, + { 0.0000000000000000, 1, 0, + 0.0000000000000000, 0.0 }, + { 0.10000000000000009, 1, 0, + 0.10000000000000009, 0.0 }, + { 0.20000000000000018, 1, 0, + 0.20000000000000018, 0.0 }, + { 0.30000000000000004, 1, 0, + 0.30000000000000004, 0.0 }, + { 0.40000000000000013, 1, 0, + 0.40000000000000013, 0.0 }, + { 0.50000000000000000, 1, 0, + 0.50000000000000000, 0.0 }, + { 0.60000000000000009, 1, 0, + 0.60000000000000009, 0.0 }, + { 0.70000000000000018, 1, 0, + 0.70000000000000018, 0.0 }, + { 0.80000000000000004, 1, 0, + 0.80000000000000004, 0.0 }, + { 0.90000000000000013, 1, 0, + 0.90000000000000013, 0.0 }, + { 1.0000000000000000, 1, 0, + 1.0000000000000000, 0.0 }, +}; +const double toler002 = 2.5000000000000020e-13; + +// Test data for l=1, m=1. +// max(|f - f_GSL|): 2.2204460492503131e-16 at index 12 +// max(|f - f_GSL| / |f_GSL|): 2.4227052612512390e-16 +// mean(f - f_GSL): 1.0573552615477681e-17 +// variance(f - f_GSL): 5.8695007828944331e-36 +// stddev(f - f_GSL): 2.4227052612512388e-18 +const testcase_assoc_legendre +data003[21] = +{ + { -0.0000000000000000, 1, 1, + -1.0000000000000000, 0.0 }, + { -0.43588989435406728, 1, 1, + -0.90000000000000002, 0.0 }, + { -0.59999999999999987, 1, 1, + -0.80000000000000004, 0.0 }, + { -0.71414284285428509, 1, 1, + -0.69999999999999996, 0.0 }, + { -0.80000000000000004, 1, 1, + -0.59999999999999998, 0.0 }, + { -0.86602540378443860, 1, 1, + -0.50000000000000000, 0.0 }, + { -0.91651513899116799, 1, 1, + -0.39999999999999991, 0.0 }, + { -0.95393920141694555, 1, 1, + -0.29999999999999993, 0.0 }, + { -0.97979589711327120, 1, 1, + -0.19999999999999996, 0.0 }, + { -0.99498743710661997, 1, 1, + -0.099999999999999978, 0.0 }, + { -1.0000000000000000, 1, 1, + 0.0000000000000000, 0.0 }, + { -0.99498743710661997, 1, 1, + 0.10000000000000009, 0.0 }, + { -0.97979589711327120, 1, 1, + 0.20000000000000018, 0.0 }, + { -0.95393920141694577, 1, 1, + 0.30000000000000004, 0.0 }, + { -0.91651513899116788, 1, 1, + 0.40000000000000013, 0.0 }, + { -0.86602540378443860, 1, 1, + 0.50000000000000000, 0.0 }, + { -0.79999999999999993, 1, 1, + 0.60000000000000009, 0.0 }, + { -0.71414284285428475, 1, 1, + 0.70000000000000018, 0.0 }, + { -0.59999999999999987, 1, 1, + 0.80000000000000004, 0.0 }, + { -0.43588989435406711, 1, 1, + 0.90000000000000013, 0.0 }, + { -0.0000000000000000, 1, 1, + 1.0000000000000000, 0.0 }, +}; +const double toler003 = 2.5000000000000020e-13; + +// Test data for l=2, m=0. +// max(|f - f_GSL|): 1.1102230246251565e-16 at index 17 +// max(|f - f_GSL| / |f_GSL|): 1.3877787807814482e-15 +// mean(f - f_GSL): 1.8503717077085941e-17 +// variance(f - f_GSL): 1.7975346147614202e-35 +// stddev(f - f_GSL): 4.2397342071896678e-18 +const testcase_assoc_legendre +data004[21] = +{ + { 1.0000000000000000, 2, 0, + -1.0000000000000000, 0.0 }, + { 0.71500000000000008, 2, 0, + -0.90000000000000002, 0.0 }, + { 0.46000000000000019, 2, 0, + -0.80000000000000004, 0.0 }, + { 0.23499999999999988, 2, 0, + -0.69999999999999996, 0.0 }, + { 0.039999999999999925, 2, 0, + -0.59999999999999998, 0.0 }, + { -0.12500000000000000, 2, 0, + -0.50000000000000000, 0.0 }, + { -0.26000000000000012, 2, 0, + -0.39999999999999991, 0.0 }, + { -0.36500000000000005, 2, 0, + -0.29999999999999993, 0.0 }, + { -0.44000000000000006, 2, 0, + -0.19999999999999996, 0.0 }, + { -0.48499999999999999, 2, 0, + -0.099999999999999978, 0.0 }, + { -0.50000000000000000, 2, 0, + 0.0000000000000000, 0.0 }, + { -0.48499999999999999, 2, 0, + 0.10000000000000009, 0.0 }, + { -0.43999999999999989, 2, 0, + 0.20000000000000018, 0.0 }, + { -0.36499999999999999, 2, 0, + 0.30000000000000004, 0.0 }, + { -0.25999999999999984, 2, 0, + 0.40000000000000013, 0.0 }, + { -0.12500000000000000, 2, 0, + 0.50000000000000000, 0.0 }, + { 0.040000000000000147, 2, 0, + 0.60000000000000009, 0.0 }, + { 0.23500000000000032, 2, 0, + 0.70000000000000018, 0.0 }, + { 0.46000000000000019, 2, 0, + 0.80000000000000004, 0.0 }, + { 0.71500000000000030, 2, 0, + 0.90000000000000013, 0.0 }, + { 1.0000000000000000, 2, 0, + 1.0000000000000000, 0.0 }, +}; +const double toler004 = 2.5000000000000020e-13; + +// Test data for l=2, m=1. +// max(|f - f_GSL|): 2.2204460492503131e-16 at index 3 +// max(|f - f_GSL| / |f_GSL|): 3.7770554319736585e-16 +// mean(f - f_GSL): -1.0573552615477681e-17 +// variance(f - f_GSL): 5.8695007828944331e-36 +// stddev(f - f_GSL): 2.4227052612512388e-18 +const testcase_assoc_legendre +data005[21] = +{ + { 0.0000000000000000, 2, 1, + -1.0000000000000000, 0.0 }, + { 1.1769027147559816, 2, 1, + -0.90000000000000002, 0.0 }, + { 1.4399999999999999, 2, 1, + -0.80000000000000004, 0.0 }, + { 1.4996999699939983, 2, 1, + -0.69999999999999996, 0.0 }, + { 1.4399999999999999, 2, 1, + -0.59999999999999998, 0.0 }, + { 1.2990381056766580, 2, 1, + -0.50000000000000000, 0.0 }, + { 1.0998181667894014, 2, 1, + -0.39999999999999991, 0.0 }, + { 0.85854528127525076, 2, 1, + -0.29999999999999993, 0.0 }, + { 0.58787753826796263, 2, 1, + -0.19999999999999996, 0.0 }, + { 0.29849623113198592, 2, 1, + -0.099999999999999978, 0.0 }, + { -0.0000000000000000, 2, 1, + 0.0000000000000000, 0.0 }, + { -0.29849623113198626, 2, 1, + 0.10000000000000009, 0.0 }, + { -0.58787753826796330, 2, 1, + 0.20000000000000018, 0.0 }, + { -0.85854528127525132, 2, 1, + 0.30000000000000004, 0.0 }, + { -1.0998181667894018, 2, 1, + 0.40000000000000013, 0.0 }, + { -1.2990381056766580, 2, 1, + 0.50000000000000000, 0.0 }, + { -1.4400000000000002, 2, 1, + 0.60000000000000009, 0.0 }, + { -1.4996999699939983, 2, 1, + 0.70000000000000018, 0.0 }, + { -1.4399999999999999, 2, 1, + 0.80000000000000004, 0.0 }, + { -1.1769027147559812, 2, 1, + 0.90000000000000013, 0.0 }, + { -0.0000000000000000, 2, 1, + 1.0000000000000000, 0.0 }, +}; +const double toler005 = 2.5000000000000020e-13; + +// Test data for l=2, m=2. +// max(|f - f_GSL|): 1.3322676295501878e-15 at index 12 +// max(|f - f_GSL| / |f_GSL|): 5.2867763077388426e-16 +// mean(f - f_GSL): -8.4588420923821446e-17 +// variance(f - f_GSL): 3.7564805010524372e-34 +// stddev(f - f_GSL): 1.9381642090009910e-17 +const testcase_assoc_legendre +data006[21] = +{ + { 0.0000000000000000, 2, 2, + -1.0000000000000000, 0.0 }, + { 0.56999999999999984, 2, 2, + -0.90000000000000002, 0.0 }, + { 1.0799999999999996, 2, 2, + -0.80000000000000004, 0.0 }, + { 1.5300000000000005, 2, 2, + -0.69999999999999996, 0.0 }, + { 1.9200000000000004, 2, 2, + -0.59999999999999998, 0.0 }, + { 2.2500000000000000, 2, 2, + -0.50000000000000000, 0.0 }, + { 2.5200000000000000, 2, 2, + -0.39999999999999991, 0.0 }, + { 2.7299999999999995, 2, 2, + -0.29999999999999993, 0.0 }, + { 2.8799999999999999, 2, 2, + -0.19999999999999996, 0.0 }, + { 2.9700000000000002, 2, 2, + -0.099999999999999978, 0.0 }, + { 3.0000000000000000, 2, 2, + 0.0000000000000000, 0.0 }, + { 2.9700000000000002, 2, 2, + 0.10000000000000009, 0.0 }, + { 2.8799999999999999, 2, 2, + 0.20000000000000018, 0.0 }, + { 2.7300000000000004, 2, 2, + 0.30000000000000004, 0.0 }, + { 2.5199999999999991, 2, 2, + 0.40000000000000013, 0.0 }, + { 2.2500000000000000, 2, 2, + 0.50000000000000000, 0.0 }, + { 1.9199999999999997, 2, 2, + 0.60000000000000009, 0.0 }, + { 1.5299999999999989, 2, 2, + 0.70000000000000018, 0.0 }, + { 1.0799999999999996, 2, 2, + 0.80000000000000004, 0.0 }, + { 0.56999999999999929, 2, 2, + 0.90000000000000013, 0.0 }, + { 0.0000000000000000, 2, 2, + 1.0000000000000000, 0.0 }, +}; +const double toler006 = 2.5000000000000020e-13; + +// Test data for l=5, m=0. +// max(|f - f_GSL|): 2.0122792321330962e-16 at index 19 +// max(|f - f_GSL| / |f_GSL|): 4.8911475274405560e-15 +// mean(f - f_GSL): -2.3129646346357427e-18 +// variance(f - f_GSL): 2.8086478355647191e-37 +// stddev(f - f_GSL): 5.2996677589870847e-19 +const testcase_assoc_legendre +data007[21] = +{ + { -1.0000000000000000, 5, 0, + -1.0000000000000000, 0.0 }, + { 0.041141250000000087, 5, 0, + -0.90000000000000002, 0.0 }, + { 0.39951999999999993, 5, 0, + -0.80000000000000004, 0.0 }, + { 0.36519874999999991, 5, 0, + -0.69999999999999996, 0.0 }, + { 0.15263999999999994, 5, 0, + -0.59999999999999998, 0.0 }, + { -0.089843750000000000, 5, 0, + -0.50000000000000000, 0.0 }, + { -0.27064000000000010, 5, 0, + -0.39999999999999991, 0.0 }, + { -0.34538624999999995, 5, 0, + -0.29999999999999993, 0.0 }, + { -0.30751999999999996, 5, 0, + -0.19999999999999996, 0.0 }, + { -0.17882874999999995, 5, 0, + -0.099999999999999978, 0.0 }, + { 0.0000000000000000, 5, 0, + 0.0000000000000000, 0.0 }, + { 0.17882875000000015, 5, 0, + 0.10000000000000009, 0.0 }, + { 0.30752000000000013, 5, 0, + 0.20000000000000018, 0.0 }, + { 0.34538625000000001, 5, 0, + 0.30000000000000004, 0.0 }, + { 0.27063999999999988, 5, 0, + 0.40000000000000013, 0.0 }, + { 0.089843750000000000, 5, 0, + 0.50000000000000000, 0.0 }, + { -0.15264000000000016, 5, 0, + 0.60000000000000009, 0.0 }, + { -0.36519875000000024, 5, 0, + 0.70000000000000018, 0.0 }, + { -0.39951999999999993, 5, 0, + 0.80000000000000004, 0.0 }, + { -0.041141249999999151, 5, 0, + 0.90000000000000013, 0.0 }, + { 1.0000000000000000, 5, 0, + 1.0000000000000000, 0.0 }, +}; +const double toler007 = 2.5000000000000020e-13; + +// Test data for l=5, m=1. +// max(|f - f_GSL|): 6.6613381477509392e-16 at index 14 +// max(|f - f_GSL| / |f_GSL|): 5.5186908001167120e-16 +// mean(f - f_GSL): -1.0573552615477681e-17 +// variance(f - f_GSL): 5.8695007828944331e-36 +// stddev(f - f_GSL): 2.4227052612512388e-18 +const testcase_assoc_legendre +data008[21] = +{ + { 0.0000000000000000, 5, 1, + -1.0000000000000000, 0.0 }, + { -2.8099369608350981, 5, 1, + -0.90000000000000002, 0.0 }, + { -0.72180000000000089, 5, 1, + -0.80000000000000004, 0.0 }, + { 1.0951826834447254, 5, 1, + -0.69999999999999996, 0.0 }, + { 1.9775999999999998, 5, 1, + -0.59999999999999998, 0.0 }, + { 1.9282596881137892, 5, 1, + -0.50000000000000000, 0.0 }, + { 1.2070504380513671, 5, 1, + -0.39999999999999991, 0.0 }, + { 0.16079837663884300, 5, 1, + -0.29999999999999993, 0.0 }, + { -0.87005875663658538, 5, 1, + -0.19999999999999996, 0.0 }, + { -1.6083350053680323, 5, 1, + -0.099999999999999978, 0.0 }, + { -1.8750000000000000, 5, 1, + 0.0000000000000000, 0.0 }, + { -1.6083350053680314, 5, 1, + 0.10000000000000009, 0.0 }, + { -0.87005875663658327, 5, 1, + 0.20000000000000018, 0.0 }, + { 0.16079837663884422, 5, 1, + 0.30000000000000004, 0.0 }, + { 1.2070504380513694, 5, 1, + 0.40000000000000013, 0.0 }, + { 1.9282596881137892, 5, 1, + 0.50000000000000000, 0.0 }, + { 1.9775999999999998, 5, 1, + 0.60000000000000009, 0.0 }, + { 1.0951826834447216, 5, 1, + 0.70000000000000018, 0.0 }, + { -0.72180000000000089, 5, 1, + 0.80000000000000004, 0.0 }, + { -2.8099369608350999, 5, 1, + 0.90000000000000013, 0.0 }, + { 0.0000000000000000, 5, 1, + 1.0000000000000000, 0.0 }, +}; +const double toler008 = 2.5000000000000020e-13; + +// Test data for l=5, m=2. +// max(|f - f_GSL|): 3.5527136788005009e-15 at index 12 +// max(|f - f_GSL| / |f_GSL|): 5.4136589391245733e-16 +// mean(f - f_GSL): 0.0000000000000000 +// variance(f - f_GSL): 0.0000000000000000 +// stddev(f - f_GSL): 0.0000000000000000 +const testcase_assoc_legendre +data009[21] = +{ + { 0.0000000000000000, 5, 2, + -1.0000000000000000, 0.0 }, + { -12.837825000000000, 5, 2, + -0.90000000000000002, 0.0 }, + { -13.910400000000001, 5, 2, + -0.80000000000000004, 0.0 }, + { -8.8089749999999967, 5, 2, + -0.69999999999999996, 0.0 }, + { -1.6128000000000000, 5, 2, + -0.59999999999999998, 0.0 }, + { 4.9218750000000000, 5, 2, + -0.50000000000000000, 0.0 }, + { 9.1728000000000005, 5, 2, + -0.39999999999999991, 0.0 }, + { 10.462724999999997, 5, 2, + -0.29999999999999993, 0.0 }, + { 8.8703999999999983, 5, 2, + -0.19999999999999996, 0.0 }, + { 5.0415749999999990, 5, 2, + -0.099999999999999978, 0.0 }, + { -0.0000000000000000, 5, 2, + 0.0000000000000000, 0.0 }, + { -5.0415750000000044, 5, 2, + 0.10000000000000009, 0.0 }, + { -8.8704000000000054, 5, 2, + 0.20000000000000018, 0.0 }, + { -10.462725000000001, 5, 2, + 0.30000000000000004, 0.0 }, + { -9.1727999999999970, 5, 2, + 0.40000000000000013, 0.0 }, + { -4.9218750000000000, 5, 2, + 0.50000000000000000, 0.0 }, + { 1.6128000000000047, 5, 2, + 0.60000000000000009, 0.0 }, + { 8.8089750000000109, 5, 2, + 0.70000000000000018, 0.0 }, + { 13.910400000000001, 5, 2, + 0.80000000000000004, 0.0 }, + { 12.837824999999990, 5, 2, + 0.90000000000000013, 0.0 }, + { 0.0000000000000000, 5, 2, + 1.0000000000000000, 0.0 }, +}; +const double toler009 = 2.5000000000000020e-13; + +// Test data for l=5, m=5. +// max(|f - f_GSL|): 1.0231815394945443e-12 at index 12 +// max(|f - f_GSL| / |f_GSL|): 1.1990652164995755e-15 +// mean(f - f_GSL): 3.1128538899966297e-14 +// variance(f - f_GSL): 5.0871761537452526e-29 +// stddev(f - f_GSL): 7.1324442891236469e-15 +const testcase_assoc_legendre +data010[21] = +{ + { -0.0000000000000000, 5, 5, + -1.0000000000000000, 0.0 }, + { -14.870165800941818, 5, 5, + -0.90000000000000002, 0.0 }, + { -73.483199999999925, 5, 5, + -0.80000000000000004, 0.0 }, + { -175.53238298794764, 5, 5, + -0.69999999999999996, 0.0 }, + { -309.65760000000006, 5, 5, + -0.59999999999999998, 0.0 }, + { -460.34662869916559, 5, 5, + -0.50000000000000000, 0.0 }, + { -611.12496255819883, 5, 5, + -0.39999999999999991, 0.0 }, + { -746.50941479523703, 5, 5, + -0.29999999999999993, 0.0 }, + { -853.31600434671316, 5, 5, + -0.19999999999999996, 0.0 }, + { -921.55189181724734, 5, 5, + -0.099999999999999978, 0.0 }, + { -945.00000000000000, 5, 5, + 0.0000000000000000, 0.0 }, + { -921.55189181724734, 5, 5, + 0.10000000000000009, 0.0 }, + { -853.31600434671316, 5, 5, + 0.20000000000000018, 0.0 }, + { -746.50941479523760, 5, 5, + 0.30000000000000004, 0.0 }, + { -611.12496255819838, 5, 5, + 0.40000000000000013, 0.0 }, + { -460.34662869916559, 5, 5, + 0.50000000000000000, 0.0 }, + { -309.65759999999989, 5, 5, + 0.60000000000000009, 0.0 }, + { -175.53238298794724, 5, 5, + 0.70000000000000018, 0.0 }, + { -73.483199999999925, 5, 5, + 0.80000000000000004, 0.0 }, + { -14.870165800941789, 5, 5, + 0.90000000000000013, 0.0 }, + { -0.0000000000000000, 5, 5, + 1.0000000000000000, 0.0 }, +}; +const double toler010 = 2.5000000000000020e-13; + +// Test data for l=10, m=0. +// max(|f - f_GSL|): 3.8857805861880479e-16 at index 19 +// max(|f - f_GSL| / |f_GSL|): 1.4766655123690915e-15 +// mean(f - f_GSL): -2.5112187461759493e-17 +// variance(f - f_GSL): 3.3107652853513909e-35 +// stddev(f - f_GSL): 5.7539249954716919e-18 +const testcase_assoc_legendre +data011[21] = +{ + { 1.0000000000000000, 10, 0, + -1.0000000000000000, 0.0 }, + { -0.26314561785585960, 10, 0, + -0.90000000000000002, 0.0 }, + { 0.30052979560000004, 10, 0, + -0.80000000000000004, 0.0 }, + { 0.085805795531640333, 10, 0, + -0.69999999999999996, 0.0 }, + { -0.24366274560000001, 10, 0, + -0.59999999999999998, 0.0 }, + { -0.18822860717773438, 10, 0, + -0.50000000000000000, 0.0 }, + { 0.096839064400000258, 10, 0, + -0.39999999999999991, 0.0 }, + { 0.25147634951601561, 10, 0, + -0.29999999999999993, 0.0 }, + { 0.12907202559999983, 10, 0, + -0.19999999999999996, 0.0 }, + { -0.12212499738710943, 10, 0, + -0.099999999999999978, 0.0 }, + { -0.24609375000000000, 10, 0, + 0.0000000000000000, 0.0 }, + { -0.12212499738710922, 10, 0, + 0.10000000000000009, 0.0 }, + { 0.12907202560000042, 10, 0, + 0.20000000000000018, 0.0 }, + { 0.25147634951601561, 10, 0, + 0.30000000000000004, 0.0 }, + { 0.096839064399999633, 10, 0, + 0.40000000000000013, 0.0 }, + { -0.18822860717773438, 10, 0, + 0.50000000000000000, 0.0 }, + { -0.24366274559999984, 10, 0, + 0.60000000000000009, 0.0 }, + { 0.085805795531641277, 10, 0, + 0.70000000000000018, 0.0 }, + { 0.30052979560000004, 10, 0, + 0.80000000000000004, 0.0 }, + { -0.26314561785586010, 10, 0, + 0.90000000000000013, 0.0 }, + { 1.0000000000000000, 10, 0, + 1.0000000000000000, 0.0 }, +}; +const double toler011 = 2.5000000000000020e-13; + +// Test data for l=10, m=1. +// max(|f - f_GSL|): 1.3322676295501878e-15 at index 14 +// max(|f - f_GSL| / |f_GSL|): 5.3672431731635395e-16 +// mean(f - f_GSL): 6.3441315692866085e-17 +// variance(f - f_GSL): 2.1130202818419960e-34 +// stddev(f - f_GSL): 1.4536231567507432e-17 +const testcase_assoc_legendre +data012[21] = +{ + { -0.0000000000000000, 10, 1, + -1.0000000000000000, 0.0 }, + { -3.0438748781479039, 10, 1, + -0.90000000000000002, 0.0 }, + { -0.87614260800000254, 10, 1, + -0.80000000000000004, 0.0 }, + { 2.9685359952934527, 10, 1, + -0.69999999999999996, 0.0 }, + { 1.2511825919999997, 10, 1, + -0.59999999999999998, 0.0 }, + { -2.0066877394361260, 10, 1, + -0.50000000000000000, 0.0 }, + { -2.4822196173476647, 10, 1, + -0.39999999999999991, 0.0 }, + { -0.12309508907433593, 10, 1, + -0.29999999999999993, 0.0 }, + { 2.2468221751958413, 10, 1, + -0.19999999999999996, 0.0 }, + { 2.2472659777983512, 10, 1, + -0.099999999999999978, 0.0 }, + { -0.0000000000000000, 10, 1, + 0.0000000000000000, 0.0 }, + { -2.2472659777983535, 10, 1, + 0.10000000000000009, 0.0 }, + { -2.2468221751958377, 10, 1, + 0.20000000000000018, 0.0 }, + { 0.12309508907433910, 10, 1, + 0.30000000000000004, 0.0 }, + { 2.4822196173476669, 10, 1, + 0.40000000000000013, 0.0 }, + { 2.0066877394361260, 10, 1, + 0.50000000000000000, 0.0 }, + { -1.2511825920000037, 10, 1, + 0.60000000000000009, 0.0 }, + { -2.9685359952934505, 10, 1, + 0.70000000000000018, 0.0 }, + { 0.87614260800000254, 10, 1, + 0.80000000000000004, 0.0 }, + { 3.0438748781478981, 10, 1, + 0.90000000000000013, 0.0 }, + { 0.0000000000000000, 10, 1, + 1.0000000000000000, 0.0 }, +}; +const double toler012 = 2.5000000000000020e-13; + +// Test data for l=10, m=2. +// max(|f - f_GSL|): 1.2434497875801753e-14 at index 12 +// max(|f - f_GSL| / |f_GSL|): 1.9632900580960751e-15 +// mean(f - f_GSL): -8.4588420923821446e-17 +// variance(f - f_GSL): 3.7564805010524372e-34 +// stddev(f - f_GSL): 1.9381642090009910e-17 +const testcase_assoc_legendre +data013[21] = +{ + { 0.0000000000000000, 10, 2, + -1.0000000000000000, 0.0 }, + { 16.376387762496137, 10, 2, + -0.90000000000000002, 0.0 }, + { -35.394657804000005, 10, 2, + -0.80000000000000004, 0.0 }, + { -3.6191429423788648, 10, 2, + -0.69999999999999996, 0.0 }, + { 28.679675904000014, 10, 2, + -0.59999999999999998, 0.0 }, + { 18.388023376464844, 10, 2, + -0.50000000000000000, 0.0 }, + { -12.818955996000021, 10, 2, + -0.39999999999999991, 0.0 }, + { -27.739821675972646, 10, 2, + -0.29999999999999993, 0.0 }, + { -13.280661503999987, 10, 2, + -0.19999999999999996, 0.0 }, + { 13.885467170308601, 10, 2, + -0.099999999999999978, 0.0 }, + { 27.070312500000000, 10, 2, + 0.0000000000000000, 0.0 }, + { 13.885467170308573, 10, 2, + 0.10000000000000009, 0.0 }, + { -13.280661504000051, 10, 2, + 0.20000000000000018, 0.0 }, + { -27.739821675972664, 10, 2, + 0.30000000000000004, 0.0 }, + { -12.818955995999961, 10, 2, + 0.40000000000000013, 0.0 }, + { 18.388023376464844, 10, 2, + 0.50000000000000000, 0.0 }, + { 28.679675904000000, 10, 2, + 0.60000000000000009, 0.0 }, + { -3.6191429423789856, 10, 2, + 0.70000000000000018, 0.0 }, + { -35.394657804000005, 10, 2, + 0.80000000000000004, 0.0 }, + { 16.376387762496201, 10, 2, + 0.90000000000000013, 0.0 }, + { 0.0000000000000000, 10, 2, + 1.0000000000000000, 0.0 }, +}; +const double toler013 = 2.5000000000000020e-13; + +// Test data for l=10, m=5. +// max(|f - f_GSL|): 2.9103830456733704e-11 at index 12 +// max(|f - f_GSL| / |f_GSL|): 1.4825078449301893e-15 +// mean(f - f_GSL): 2.4253192047278085e-12 +// variance(f - f_GSL): 3.0881409535313035e-25 +// stddev(f - f_GSL): 5.5571044200476413e-13 +const testcase_assoc_legendre +data014[21] = +{ + { 0.0000000000000000, 10, 5, + -1.0000000000000000, 0.0 }, + { 21343.618518164680, 10, 5, + -0.90000000000000002, 0.0 }, + { 40457.016407807983, 10, 5, + -0.80000000000000004, 0.0 }, + { 20321.279317331315, 10, 5, + -0.69999999999999996, 0.0 }, + { -14410.820616192004, 10, 5, + -0.59999999999999998, 0.0 }, + { -30086.169706116176, 10, 5, + -0.50000000000000000, 0.0 }, + { -17177.549337582834, 10, 5, + -0.39999999999999991, 0.0 }, + { 9272.5119495412546, 10, 5, + -0.29999999999999993, 0.0 }, + { 26591.511184414714, 10, 5, + -0.19999999999999996, 0.0 }, + { 21961.951238504211, 10, 5, + -0.099999999999999978, 0.0 }, + { -0.0000000000000000, 10, 5, + 0.0000000000000000, 0.0 }, + { -21961.951238504229, 10, 5, + 0.10000000000000009, 0.0 }, + { -26591.511184414703, 10, 5, + 0.20000000000000018, 0.0 }, + { -9272.5119495412364, 10, 5, + 0.30000000000000004, 0.0 }, + { 17177.549337582877, 10, 5, + 0.40000000000000013, 0.0 }, + { 30086.169706116176, 10, 5, + 0.50000000000000000, 0.0 }, + { 14410.820616191972, 10, 5, + 0.60000000000000009, 0.0 }, + { -20321.279317331391, 10, 5, + 0.70000000000000018, 0.0 }, + { -40457.016407807983, 10, 5, + 0.80000000000000004, 0.0 }, + { -21343.618518164636, 10, 5, + 0.90000000000000013, 0.0 }, + { 0.0000000000000000, 10, 5, + 1.0000000000000000, 0.0 }, +}; +const double toler014 = 2.5000000000000020e-13; + +// Test data for l=10, m=10. +// max(|f - f_GSL|): 1.1920928955078125e-06 at index 12 +// max(|f - f_GSL| / |f_GSL|): 2.3944993944674592e-15 +// mean(f - f_GSL): -1.5610740298316593e-08 +// variance(f - f_GSL): 1.2793998664727994e-17 +// stddev(f - f_GSL): 3.5768699535666649e-09 +const testcase_assoc_legendre +data015[21] = +{ + { 0.0000000000000000, 10, 10, + -1.0000000000000000, 0.0 }, + { 162117.40078784220, 10, 10, + -0.90000000000000002, 0.0 }, + { 3958896.3481267113, 10, 10, + -0.80000000000000004, 0.0 }, + { 22589806.343887307, 10, 10, + -0.69999999999999996, 0.0 }, + { 70300999.121633321, 10, 10, + -0.59999999999999998, 0.0 }, + { 155370278.54003900, 10, 10, + -0.50000000000000000, 0.0 }, + { 273815518.20150518, 10, 10, + -0.39999999999999991, 0.0 }, + { 408571989.13158852, 10, 10, + -0.29999999999999993, 0.0 }, + { 533848212.07990247, 10, 10, + -0.19999999999999996, 0.0 }, + { 622640835.70523083, 10, 10, + -0.099999999999999978, 0.0 }, + { 654729075.00000000, 10, 10, + 0.0000000000000000, 0.0 }, + { 622640835.70523083, 10, 10, + 0.10000000000000009, 0.0 }, + { 533848212.07990247, 10, 10, + 0.20000000000000018, 0.0 }, + { 408571989.13158917, 10, 10, + 0.30000000000000004, 0.0 }, + { 273815518.20150483, 10, 10, + 0.40000000000000013, 0.0 }, + { 155370278.54003900, 10, 10, + 0.50000000000000000, 0.0 }, + { 70300999.121633217, 10, 10, + 0.60000000000000009, 0.0 }, + { 22589806.343887202, 10, 10, + 0.70000000000000018, 0.0 }, + { 3958896.3481267113, 10, 10, + 0.80000000000000004, 0.0 }, + { 162117.40078784159, 10, 10, + 0.90000000000000013, 0.0 }, + { 0.0000000000000000, 10, 10, + 1.0000000000000000, 0.0 }, +}; +const double toler015 = 2.5000000000000020e-13; + +// Test data for l=20, m=0. +// max(|f - f_GSL|): 3.6082248300317588e-16 at index 19 +// max(|f - f_GSL| / |f_GSL|): 2.4166281401316513e-15 +// mean(f - f_GSL): 0.0000000000000000 +// variance(f - f_GSL): 4.9424644697959907e-65 +// stddev(f - f_GSL): 7.0302663319365015e-33 +const testcase_assoc_legendre +data016[21] = +{ + { 1.0000000000000000, 20, 0, + -1.0000000000000000, 0.0 }, + { -0.14930823530984835, 20, 0, + -0.90000000000000002, 0.0 }, + { 0.22420460541741347, 20, 0, + -0.80000000000000004, 0.0 }, + { -0.20457394463834172, 20, 0, + -0.69999999999999996, 0.0 }, + { 0.15916752910098109, 20, 0, + -0.59999999999999998, 0.0 }, + { -0.048358381067373557, 20, 0, + -0.50000000000000000, 0.0 }, + { -0.10159261558628112, 20, 0, + -0.39999999999999991, 0.0 }, + { 0.18028715947998047, 20, 0, + -0.29999999999999993, 0.0 }, + { -0.098042194344594796, 20, 0, + -0.19999999999999996, 0.0 }, + { -0.082077130944527663, 20, 0, + -0.099999999999999978, 0.0 }, + { 0.17619705200195312, 20, 0, + 0.0000000000000000, 0.0 }, + { -0.082077130944528023, 20, 0, + 0.10000000000000009, 0.0 }, + { -0.098042194344594089, 20, 0, + 0.20000000000000018, 0.0 }, + { 0.18028715947998042, 20, 0, + 0.30000000000000004, 0.0 }, + { -0.10159261558628192, 20, 0, + 0.40000000000000013, 0.0 }, + { -0.048358381067373557, 20, 0, + 0.50000000000000000, 0.0 }, + { 0.15916752910098075, 20, 0, + 0.60000000000000009, 0.0 }, + { -0.20457394463834136, 20, 0, + 0.70000000000000018, 0.0 }, + { 0.22420460541741347, 20, 0, + 0.80000000000000004, 0.0 }, + { -0.14930823530984758, 20, 0, + 0.90000000000000013, 0.0 }, + { 1.0000000000000000, 20, 0, + 1.0000000000000000, 0.0 }, +}; +const double toler016 = 2.5000000000000020e-13; + +// Test data for l=20, m=1. +// max(|f - f_GSL|): 1.3322676295501878e-15 at index 12 +// max(|f - f_GSL| / |f_GSL|): 1.0752784502271902e-15 +// mean(f - f_GSL): 1.4274296030894871e-16 +// variance(f - f_GSL): 1.0697165176825104e-33 +// stddev(f - f_GSL): 3.2706521026891724e-17 +const testcase_assoc_legendre +data017[21] = +{ + { 0.0000000000000000, 20, 1, + -1.0000000000000000, 0.0 }, + { 4.3838334818220499, 20, 1, + -0.90000000000000002, 0.0 }, + { -0.63138296146340844, 20, 1, + -0.80000000000000004, 0.0 }, + { 0.72274871413391395, 20, 1, + -0.69999999999999996, 0.0 }, + { -2.3203528743824910, 20, 1, + -0.59999999999999998, 0.0 }, + { 3.7399919228791405, 20, 1, + -0.50000000000000000, 0.0 }, + { -3.1692202279270085, 20, 1, + -0.39999999999999991, 0.0 }, + { 0.15804468835345031, 20, 1, + -0.29999999999999993, 0.0 }, + { 3.0366182393271171, 20, 1, + -0.19999999999999996, 0.0 }, + { -3.2115523815580209, 20, 1, + -0.099999999999999978, 0.0 }, + { 0.0000000000000000, 20, 1, + 0.0000000000000000, 0.0 }, + { 3.2115523815580169, 20, 1, + 0.10000000000000009, 0.0 }, + { -3.0366182393271259, 20, 1, + 0.20000000000000018, 0.0 }, + { -0.15804468835344135, 20, 1, + 0.30000000000000004, 0.0 }, + { 3.1692202279269970, 20, 1, + 0.40000000000000013, 0.0 }, + { -3.7399919228791405, 20, 1, + 0.50000000000000000, 0.0 }, + { 2.3203528743824995, 20, 1, + 0.60000000000000009, 0.0 }, + { -0.72274871413393793, 20, 1, + 0.70000000000000018, 0.0 }, + { 0.63138296146340844, 20, 1, + 0.80000000000000004, 0.0 }, + { -4.3838334818220686, 20, 1, + 0.90000000000000013, 0.0 }, + { 0.0000000000000000, 20, 1, + 1.0000000000000000, 0.0 }, +}; +const double toler017 = 2.5000000000000020e-13; + +// Test data for l=20, m=2. +// max(|f - f_GSL|): 2.4868995751603507e-14 at index 5 +// max(|f - f_GSL| / |f_GSL|): 1.0097407175524082e-15 +// mean(f - f_GSL): -2.0301221021717147e-15 +// variance(f - f_GSL): 2.1637327686062039e-31 +// stddev(f - f_GSL): 4.6515941016023782e-16 +const testcase_assoc_legendre +data018[21] = +{ + { 0.0000000000000000, 20, 2, + -1.0000000000000000, 0.0 }, + { 80.812425587310102, 20, 2, + -0.90000000000000002, 0.0 }, + { -95.849622172549374, 20, 2, + -0.80000000000000004, 0.0 }, + { 87.337927630325510, 20, 2, + -0.69999999999999996, 0.0 }, + { -70.330891533985834, 20, 2, + -0.59999999999999998, 0.0 }, + { 24.629090735179489, 20, 2, + -0.50000000000000000, 0.0 }, + { 39.902576338912247, 20, 2, + -0.39999999999999991, 0.0 }, + { -75.621201471396546, 20, 2, + -0.29999999999999993, 0.0 }, + { 42.417415829726494, 20, 2, + -0.19999999999999996, 0.0 }, + { 33.826848678871293, 20, 2, + -0.099999999999999978, 0.0 }, + { -74.002761840820312, 20, 2, + 0.0000000000000000, 0.0 }, + { 33.826848678871464, 20, 2, + 0.10000000000000009, 0.0 }, + { 42.417415829726188, 20, 2, + 0.20000000000000018, 0.0 }, + { -75.621201471396603, 20, 2, + 0.30000000000000004, 0.0 }, + { 39.902576338912553, 20, 2, + 0.40000000000000013, 0.0 }, + { 24.629090735179489, 20, 2, + 0.50000000000000000, 0.0 }, + { -70.330891533985721, 20, 2, + 0.60000000000000009, 0.0 }, + { 87.337927630325453, 20, 2, + 0.70000000000000018, 0.0 }, + { -95.849622172549374, 20, 2, + 0.80000000000000004, 0.0 }, + { 80.812425587309747, 20, 2, + 0.90000000000000013, 0.0 }, + { 0.0000000000000000, 20, 2, + 1.0000000000000000, 0.0 }, +}; +const double toler018 = 2.5000000000000020e-13; + +// Test data for l=20, m=5. +// max(|f - f_GSL|): 1.2805685400962830e-09 at index 14 +// max(|f - f_GSL| / |f_GSL|): 2.0861530799041223e-15 +// mean(f - f_GSL): 1.1641532182693481e-10 +// variance(f - f_GSL): 7.1150767569361226e-22 +// stddev(f - f_GSL): 2.6674101216228678e-11 +const testcase_assoc_legendre +data019[21] = +{ + { -0.0000000000000000, 20, 5, + -1.0000000000000000, 0.0 }, + { -315702.32715134218, 20, 5, + -0.90000000000000002, 0.0 }, + { 503060.91484852589, 20, 5, + -0.80000000000000004, 0.0 }, + { -298127.28360361955, 20, 5, + -0.69999999999999996, 0.0 }, + { -114444.61447464029, 20, 5, + -0.59999999999999998, 0.0 }, + { 543428.40914592845, 20, 5, + -0.50000000000000000, 0.0 }, + { -613842.07728185481, 20, 5, + -0.39999999999999991, 0.0 }, + { 143765.42411271061, 20, 5, + -0.29999999999999993, 0.0 }, + { 472600.45321372285, 20, 5, + -0.19999999999999996, 0.0 }, + { -563861.76771496492, 20, 5, + -0.099999999999999978, 0.0 }, + { 0.0000000000000000, 20, 5, + 0.0000000000000000, 0.0 }, + { 563861.76771496458, 20, 5, + 0.10000000000000009, 0.0 }, + { -472600.45321372483, 20, 5, + 0.20000000000000018, 0.0 }, + { -143765.42411270936, 20, 5, + 0.30000000000000004, 0.0 }, + { 613842.07728185353, 20, 5, + 0.40000000000000013, 0.0 }, + { -543428.40914592845, 20, 5, + 0.50000000000000000, 0.0 }, + { 114444.61447464178, 20, 5, + 0.60000000000000009, 0.0 }, + { 298127.28360361519, 20, 5, + 0.70000000000000018, 0.0 }, + { -503060.91484852589, 20, 5, + 0.80000000000000004, 0.0 }, + { 315702.32715133618, 20, 5, + 0.90000000000000013, 0.0 }, + { 0.0000000000000000, 20, 5, + 1.0000000000000000, 0.0 }, +}; +const double toler019 = 2.5000000000000020e-13; + +// Test data for l=20, m=10. +// max(|f - f_GSL|): 0.0039062500000000000 at index 12 +// max(|f - f_GSL| / |f_GSL|): 2.6634565089260680e-15 +// mean(f - f_GSL): -0.00043596540178571431 +// variance(f - f_GSL): 9.9784562846311215e-09 +// stddev(f - f_GSL): 9.9892223344117843e-05 +const testcase_assoc_legendre +data020[21] = +{ + { -0.0000000000000000, 20, 10, + -1.0000000000000000, 0.0 }, + { 990017476694.99084, 20, 10, + -0.90000000000000002, 0.0 }, + { 2392757933281.0498, 20, 10, + -0.80000000000000004, 0.0 }, + { -1548364524949.5808, 20, 10, + -0.69999999999999996, 0.0 }, + { -424471915195.05627, 20, 10, + -0.59999999999999998, 0.0 }, + { 1744502295946.2073, 20, 10, + -0.50000000000000000, 0.0 }, + { -899973487310.55530, 20, 10, + -0.39999999999999991, 0.0 }, + { -1092420454297.7119, 20, 10, + -0.29999999999999993, 0.0 }, + { 1466609267659.8816, 20, 10, + -0.19999999999999996, 0.0 }, + { 356041756390.71674, 20, 10, + -0.099999999999999978, 0.0 }, + { -1612052956674.3164, 20, 10, + 0.0000000000000000, 0.0 }, + { 356041756390.71985, 20, 10, + 0.10000000000000009, 0.0 }, + { 1466609267659.8796, 20, 10, + 0.20000000000000018, 0.0 }, + { -1092420454297.7161, 20, 10, + 0.30000000000000004, 0.0 }, + { -899973487310.54810, 20, 10, + 0.40000000000000013, 0.0 }, + { 1744502295946.2073, 20, 10, + 0.50000000000000000, 0.0 }, + { -424471915195.05896, 20, 10, + 0.60000000000000009, 0.0 }, + { -1548364524949.5730, 20, 10, + 0.70000000000000018, 0.0 }, + { 2392757933281.0498, 20, 10, + 0.80000000000000004, 0.0 }, + { 990017476694.98828, 20, 10, + 0.90000000000000013, 0.0 }, + { 0.0000000000000000, 20, 10, + 1.0000000000000000, 0.0 }, +}; +const double toler020 = 2.5000000000000020e-13; + +// Test data for l=20, m=20. +// max(|f - f_GSL|): 838860800.00000000 at index 12 +// max(|f - f_GSL| / |f_GSL|): 4.3488507135833189e-15 +// mean(f - f_GSL): -2855497.1428571427 +// variance(f - f_GSL): inf +// stddev(f - f_GSL): inf +const testcase_assoc_legendre +data021[21] = +{ + { 0.0000000000000000, 20, 20, + -1.0000000000000000, 0.0 }, + { 19609049712023808., 20, 20, + -0.90000000000000002, 0.0 }, + { 1.1693527616833221e+19, 20, 20, + -0.80000000000000004, 0.0 }, + { 3.8073455880620691e+20, 20, 20, + -0.69999999999999996, 0.0 }, + { 3.6874002249007927e+21, 20, 20, + -0.59999999999999998, 0.0 }, + { 1.8010806978179592e+22, 20, 20, + -0.50000000000000000, 0.0 }, + { 5.5938832584012466e+22, 20, 20, + -0.39999999999999991, 0.0 }, + { 1.2454734132297759e+23, 20, 20, + -0.29999999999999993, 0.0 }, + { 2.1263407800797497e+23, 20, 20, + -0.19999999999999996, 0.0 }, + { 2.8924941146976873e+23, 20, 20, + -0.099999999999999978, 0.0 }, + { 3.1983098677287775e+23, 20, 20, + 0.0000000000000000, 0.0 }, + { 2.8924941146976873e+23, 20, 20, + 0.10000000000000009, 0.0 }, + { 2.1263407800797497e+23, 20, 20, + 0.20000000000000018, 0.0 }, + { 1.2454734132297811e+23, 20, 20, + 0.30000000000000004, 0.0 }, + { 5.5938832584012366e+22, 20, 20, + 0.40000000000000013, 0.0 }, + { 1.8010806978179592e+22, 20, 20, + 0.50000000000000000, 0.0 }, + { 3.6874002249007807e+21, 20, 20, + 0.60000000000000009, 0.0 }, + { 3.8073455880620343e+20, 20, 20, + 0.70000000000000018, 0.0 }, + { 1.1693527616833221e+19, 20, 20, + 0.80000000000000004, 0.0 }, + { 19609049712023672., 20, 20, + 0.90000000000000013, 0.0 }, + { 0.0000000000000000, 20, 20, + 1.0000000000000000, 0.0 }, +}; +const double toler021 = 2.5000000000000020e-13; + +// Test data for l=50, m=0. +// max(|f - f_GSL|): 1.6653345369377348e-16 at index 2 +// max(|f - f_GSL| / |f_GSL|): 1.6665460706897444e-15 +// mean(f - f_GSL): -8.0953762212251003e-18 +// variance(f - f_GSL): 3.4405935985667807e-36 +// stddev(f - f_GSL): 1.8548837156454796e-18 +const testcase_assoc_legendre +data022[21] = +{ + { 1.0000000000000000, 50, 0, + -1.0000000000000000, 0.0 }, + { -0.17003765994383671, 50, 0, + -0.90000000000000002, 0.0 }, + { 0.13879737345093113, 50, 0, + -0.80000000000000004, 0.0 }, + { -0.014572731645892852, 50, 0, + -0.69999999999999996, 0.0 }, + { -0.058860798844002096, 50, 0, + -0.59999999999999998, 0.0 }, + { -0.031059099239609811, 50, 0, + -0.50000000000000000, 0.0 }, + { 0.041569033381824674, 50, 0, + -0.39999999999999991, 0.0 }, + { 0.10911051574714790, 50, 0, + -0.29999999999999993, 0.0 }, + { 0.083432272204197494, 50, 0, + -0.19999999999999996, 0.0 }, + { -0.038205812661313600, 50, 0, + -0.099999999999999978, 0.0 }, + { -0.11227517265921705, 50, 0, + 0.0000000000000000, 0.0 }, + { -0.038205812661314155, 50, 0, + 0.10000000000000009, 0.0 }, + { 0.083432272204196564, 50, 0, + 0.20000000000000018, 0.0 }, + { 0.10911051574714797, 50, 0, + 0.30000000000000004, 0.0 }, + { 0.041569033381826007, 50, 0, + 0.40000000000000013, 0.0 }, + { -0.031059099239609811, 50, 0, + 0.50000000000000000, 0.0 }, + { -0.058860798844001430, 50, 0, + 0.60000000000000009, 0.0 }, + { -0.014572731645890737, 50, 0, + 0.70000000000000018, 0.0 }, + { 0.13879737345093113, 50, 0, + 0.80000000000000004, 0.0 }, + { -0.17003765994383679, 50, 0, + 0.90000000000000013, 0.0 }, + { 1.0000000000000000, 50, 0, + 1.0000000000000000, 0.0 }, +}; +const double toler022 = 2.5000000000000020e-13; + +// Test data for l=50, m=1. +// max(|f - f_GSL|): 4.4408920985006262e-15 at index 3 +// max(|f - f_GSL| / |f_GSL|): 6.6657627150738456e-16 +// mean(f - f_GSL): 6.3441315692866085e-17 +// variance(f - f_GSL): 2.1130202818419960e-34 +// stddev(f - f_GSL): 1.4536231567507432e-17 +const testcase_assoc_legendre +data023[21] = +{ + { 0.0000000000000000, 50, 1, + -1.0000000000000000, 0.0 }, + { -0.13424149984449490, 50, 1, + -0.90000000000000002, 0.0 }, + { 2.2011219672413018, 50, 1, + -0.80000000000000004, 0.0 }, + { 6.6622414993232004, 50, 1, + -0.69999999999999996, 0.0 }, + { 5.5772846936919249, 50, 1, + -0.59999999999999998, 0.0 }, + { 5.8787148815607608, 50, 1, + -0.50000000000000000, 0.0 }, + { 5.5473459458634080, 50, 1, + -0.39999999999999991, 0.0 }, + { 1.8444956647620248, 50, 1, + -0.29999999999999993, 0.0 }, + { -3.8722014306642127, 50, 1, + -0.19999999999999996, 0.0 }, + { -5.3488751322285628, 50, 1, + -0.099999999999999978, 0.0 }, + { -0.0000000000000000, 50, 1, + 0.0000000000000000, 0.0 }, + { 5.3488751322285522, 50, 1, + 0.10000000000000009, 0.0 }, + { 3.8722014306642620, 50, 1, + 0.20000000000000018, 0.0 }, + { -1.8444956647619930, 50, 1, + 0.30000000000000004, 0.0 }, + { -5.5473459458633814, 50, 1, + 0.40000000000000013, 0.0 }, + { -5.8787148815607608, 50, 1, + 0.50000000000000000, 0.0 }, + { -5.5772846936919453, 50, 1, + 0.60000000000000009, 0.0 }, + { -6.6622414993232182, 50, 1, + 0.70000000000000018, 0.0 }, + { -2.2011219672413018, 50, 1, + 0.80000000000000004, 0.0 }, + { 0.13424149984438935, 50, 1, + 0.90000000000000013, 0.0 }, + { 0.0000000000000000, 50, 1, + 1.0000000000000000, 0.0 }, +}; +const double toler023 = 2.5000000000000020e-13; + +// Test data for l=50, m=2. +// max(|f - f_GSL|): 3.0553337637684308e-13 at index 3 +// max(|f - f_GSL| / |f_GSL|): 6.0837685805857877e-15 +// mean(f - f_GSL): -3.3835368369528578e-16 +// variance(f - f_GSL): 6.0103688016838995e-33 +// stddev(f - f_GSL): 7.7526568360039641e-17 +const testcase_assoc_legendre +data024[21] = +{ + { 0.0000000000000000, 50, 2, + -1.0000000000000000, 0.0 }, + { 433.04168483713511, 50, 2, + -0.90000000000000002, 0.0 }, + { -348.06364372056424, 50, 2, + -0.80000000000000004, 0.0 }, + { 50.221071418108444, 50, 2, + -0.69999999999999996, 0.0 }, + { 158.46096409274352, 50, 2, + -0.59999999999999998, 0.0 }, + { 85.988858299721457, 50, 2, + -0.50000000000000000, 0.0 }, + { -101.15891460879088, 50, 2, + -0.39999999999999991, 0.0 }, + { -277.07168105316526, 50, 2, + -0.29999999999999993, 0.0 }, + { -214.33311373510401, 50, 2, + -0.19999999999999996, 0.0 }, + { 96.349657930951665, 50, 2, + -0.099999999999999978, 0.0 }, + { 286.30169028100346, 50, 2, + 0.0000000000000000, 0.0 }, + { 96.349657930953242, 50, 2, + 0.10000000000000009, 0.0 }, + { -214.33311373510165, 50, 2, + 0.20000000000000018, 0.0 }, + { -277.07168105316617, 50, 2, + 0.30000000000000004, 0.0 }, + { -101.15891460879435, 50, 2, + 0.40000000000000013, 0.0 }, + { 85.988858299721457, 50, 2, + 0.50000000000000000, 0.0 }, + { 158.46096409274153, 50, 2, + 0.60000000000000009, 0.0 }, + { 50.221071418103143, 50, 2, + 0.70000000000000018, 0.0 }, + { -348.06364372056424, 50, 2, + 0.80000000000000004, 0.0 }, + { 433.04168483713596, 50, 2, + 0.90000000000000013, 0.0 }, + { 0.0000000000000000, 50, 2, + 1.0000000000000000, 0.0 }, +}; +const double toler024 = 5.0000000000000039e-13; + +// Test data for l=50, m=5. +// max(|f - f_GSL|): 7.4505805969238281e-08 at index 14 +// max(|f - f_GSL| / |f_GSL|): 2.0088060426072767e-15 +// mean(f - f_GSL): -6.3862119402204238e-09 +// variance(f - f_GSL): 2.1411444046342303e-18 +// stddev(f - f_GSL): 1.4632649810045447e-09 +const testcase_assoc_legendre +data025[21] = +{ + { -0.0000000000000000, 50, 5, + -1.0000000000000000, 0.0 }, + { -27340473.952132829, 50, 5, + -0.90000000000000002, 0.0 }, + { 27753716.768532373, 50, 5, + -0.80000000000000004, 0.0 }, + { 40808153.913493633, 50, 5, + -0.69999999999999996, 0.0 }, + { 32071189.035790090, 50, 5, + -0.59999999999999998, 0.0 }, + { 36265736.218529105, 50, 5, + -0.50000000000000000, 0.0 }, + { 37089596.700204931, 50, 5, + -0.39999999999999991, 0.0 }, + { 14562029.629244687, 50, 5, + -0.29999999999999993, 0.0 }, + { -23686895.217517190, 50, 5, + -0.19999999999999996, 0.0 }, + { -34878992.965676002, 50, 5, + -0.099999999999999978, 0.0 }, + { -0.0000000000000000, 50, 5, + 0.0000000000000000, 0.0 }, + { 34878992.965675958, 50, 5, + 0.10000000000000009, 0.0 }, + { 23686895.217517529, 50, 5, + 0.20000000000000018, 0.0 }, + { -14562029.629244499, 50, 5, + 0.30000000000000004, 0.0 }, + { -37089596.700204782, 50, 5, + 0.40000000000000013, 0.0 }, + { -36265736.218529105, 50, 5, + 0.50000000000000000, 0.0 }, + { -32071189.035790242, 50, 5, + 0.60000000000000009, 0.0 }, + { -40808153.913493834, 50, 5, + 0.70000000000000018, 0.0 }, + { -27753716.768532373, 50, 5, + 0.80000000000000004, 0.0 }, + { 27340473.952132136, 50, 5, + 0.90000000000000013, 0.0 }, + { 0.0000000000000000, 50, 5, + 1.0000000000000000, 0.0 }, +}; +const double toler025 = 2.5000000000000020e-13; + +// Test data for l=50, m=10. +// max(|f - f_GSL|): 22.000000000000000 at index 3 +// max(|f - f_GSL| / |f_GSL|): 2.2163032493360465e-15 +// mean(f - f_GSL): -1.9821428571428572 +// variance(f - f_GSL): inf +// stddev(f - f_GSL): inf +const testcase_assoc_legendre +data026[21] = +{ + { -0.0000000000000000, 50, 10, + -1.0000000000000000, 0.0 }, + { -8994661710093155.0, 50, 10, + -0.90000000000000002, 0.0 }, + { 932311375306569.62, 50, 10, + -0.80000000000000004, 0.0 }, + { 12153535011507012., 50, 10, + -0.69999999999999996, 0.0 }, + { 12176690755542240., 50, 10, + -0.59999999999999998, 0.0 }, + { 9180035388465754.0, 50, 10, + -0.50000000000000000, 0.0 }, + { 889201701866984.00, 50, 10, + -0.39999999999999991, 0.0 }, + { -9451384032851544.0, 50, 10, + -0.29999999999999993, 0.0 }, + { -9926439446673564.0, 50, 10, + -0.19999999999999996, 0.0 }, + { 2794368162749970.5, 50, 10, + -0.099999999999999978, 0.0 }, + { 11452238249246346., 50, 10, + 0.0000000000000000, 0.0 }, + { 2794368162750031.0, 50, 10, + 0.10000000000000009, 0.0 }, + { -9926439446673506.0, 50, 10, + 0.20000000000000018, 0.0 }, + { -9451384032851604.0, 50, 10, + 0.30000000000000004, 0.0 }, + { 889201701866835.25, 50, 10, + 0.40000000000000013, 0.0 }, + { 9180035388465754.0, 50, 10, + 0.50000000000000000, 0.0 }, + { 12176690755542214., 50, 10, + 0.60000000000000009, 0.0 }, + { 12153535011506908., 50, 10, + 0.70000000000000018, 0.0 }, + { 932311375306569.62, 50, 10, + 0.80000000000000004, 0.0 }, + { -8994661710093013.0, 50, 10, + 0.90000000000000013, 0.0 }, + { 0.0000000000000000, 50, 10, + 1.0000000000000000, 0.0 }, +}; +const double toler026 = 2.5000000000000020e-13; + +// Test data for l=50, m=20. +// max(|f - f_GSL|): 3.6028797018963968e+18 at index 14 +// max(|f - f_GSL| / |f_GSL|): 5.0227025739283085e-15 +// mean(f - f_GSL): -1.8529095609752899e+17 +// variance(f - f_GSL): inf +// stddev(f - f_GSL): inf +const testcase_assoc_legendre +data027[21] = +{ + { 0.0000000000000000, 50, 20, + -1.0000000000000000, 0.0 }, + { 1.6630925158645501e+33, 50, 20, + -0.90000000000000002, 0.0 }, + { 1.0622676657892052e+33, 50, 20, + -0.80000000000000004, 0.0 }, + { 8.6022521164717112e+32, 50, 20, + -0.69999999999999996, 0.0 }, + { 4.0860128756808466e+32, 50, 20, + -0.59999999999999998, 0.0 }, + { -4.0169860814274459e+32, 50, 20, + -0.50000000000000000, 0.0 }, + { -8.2324325279773994e+32, 50, 20, + -0.39999999999999991, 0.0 }, + { -4.0054067236247267e+31, 50, 20, + -0.29999999999999993, 0.0 }, + { 7.9309266056434309e+32, 50, 20, + -0.19999999999999996, 0.0 }, + { 5.4151358290898977e+31, 50, 20, + -0.099999999999999978, 0.0 }, + { -7.8735935697332210e+32, 50, 20, + 0.0000000000000000, 0.0 }, + { 5.4151358290894924e+31, 50, 20, + 0.10000000000000009, 0.0 }, + { 7.9309266056434453e+32, 50, 20, + 0.20000000000000018, 0.0 }, + { -4.0054067236243731e+31, 50, 20, + 0.30000000000000004, 0.0 }, + { -8.2324325279773893e+32, 50, 20, + 0.40000000000000013, 0.0 }, + { -4.0169860814274459e+32, 50, 20, + 0.50000000000000000, 0.0 }, + { 4.0860128756807846e+32, 50, 20, + 0.60000000000000009, 0.0 }, + { 8.6022521164716291e+32, 50, 20, + 0.70000000000000018, 0.0 }, + { 1.0622676657892052e+33, 50, 20, + 0.80000000000000004, 0.0 }, + { 1.6630925158645541e+33, 50, 20, + 0.90000000000000013, 0.0 }, + { 0.0000000000000000, 50, 20, + 1.0000000000000000, 0.0 }, +}; +const double toler027 = 5.0000000000000039e-13; + +// Test data for l=50, m=50. +// max(|f - f_GSL|): 1.0695779622587839e+64 at index 12 +// max(|f - f_GSL| / |f_GSL|): 1.1061123055945194e-14 +// mean(f - f_GSL): -2.0817504896587826e+62 +// variance(f - f_GSL): inf +// stddev(f - f_GSL): inf +const testcase_assoc_legendre +data028[21] = +{ + { 0.0000000000000000, 50, 50, + -1.0000000000000000, 0.0 }, + { 2.5366994974431341e+60, 50, 50, + -0.90000000000000002, 0.0 }, + { 2.2028834403101213e+67, 50, 50, + -0.80000000000000004, 0.0 }, + { 1.3325496559566651e+71, 50, 50, + -0.69999999999999996, 0.0 }, + { 3.8898096431781969e+73, 50, 50, + -0.59999999999999998, 0.0 }, + { 2.0509760257037188e+75, 50, 50, + -0.50000000000000000, 0.0 }, + { 3.4866724533443283e+76, 50, 50, + -0.39999999999999991, 0.0 }, + { 2.5790740224149893e+77, 50, 50, + -0.29999999999999993, 0.0 }, + { 9.8222237931680989e+77, 50, 50, + -0.19999999999999996, 0.0 }, + { 2.1198682190366617e+78, 50, 50, + -0.099999999999999978, 0.0 }, + { 2.7253921397507295e+78, 50, 50, + 0.0000000000000000, 0.0 }, + { 2.1198682190366617e+78, 50, 50, + 0.10000000000000009, 0.0 }, + { 9.8222237931680989e+77, 50, 50, + 0.20000000000000018, 0.0 }, + { 2.5790740224150207e+77, 50, 50, + 0.30000000000000004, 0.0 }, + { 3.4866724533443123e+76, 50, 50, + 0.40000000000000013, 0.0 }, + { 2.0509760257037188e+75, 50, 50, + 0.50000000000000000, 0.0 }, + { 3.8898096431781724e+73, 50, 50, + 0.60000000000000009, 0.0 }, + { 1.3325496559566344e+71, 50, 50, + 0.70000000000000018, 0.0 }, + { 2.2028834403101213e+67, 50, 50, + 0.80000000000000004, 0.0 }, + { 2.5366994974430855e+60, 50, 50, + 0.90000000000000013, 0.0 }, + { 0.0000000000000000, 50, 50, + 1.0000000000000000, 0.0 }, +}; +const double toler028 = 1.0000000000000008e-12; + +// Test data for l=100, m=0. +// max(|f - f_GSL|): 3.4694469519536142e-16 at index 2 +// max(|f - f_GSL| / |f_GSL|): 6.8214063779431592e-15 +// mean(f - f_GSL): -4.1385545784018113e-17 +// variance(f - f_GSL): 8.9920078491655612e-35 +// stddev(f - f_GSL): 9.4826198116161765e-18 +const testcase_assoc_legendre +data029[21] = +{ + { 1.0000000000000000, 100, 0, + -1.0000000000000000, 0.0 }, + { 0.10226582055871893, 100, 0, + -0.90000000000000002, 0.0 }, + { 0.050861167913584228, 100, 0, + -0.80000000000000004, 0.0 }, + { -0.077132507199778641, 100, 0, + -0.69999999999999996, 0.0 }, + { -0.023747023905133141, 100, 0, + -0.59999999999999998, 0.0 }, + { -0.060518025961861198, 100, 0, + -0.50000000000000000, 0.0 }, + { -0.072258202125685025, 100, 0, + -0.39999999999999991, 0.0 }, + { 0.057127392202801046, 100, 0, + -0.29999999999999993, 0.0 }, + { 0.014681835355659706, 100, 0, + -0.19999999999999996, 0.0 }, + { -0.063895098434750205, 100, 0, + -0.099999999999999978, 0.0 }, + { 0.079589237387178727, 100, 0, + 0.0000000000000000, 0.0 }, + { -0.063895098434749761, 100, 0, + 0.10000000000000009, 0.0 }, + { 0.014681835355657875, 100, 0, + 0.20000000000000018, 0.0 }, + { 0.057127392202801566, 100, 0, + 0.30000000000000004, 0.0 }, + { -0.072258202125684082, 100, 0, + 0.40000000000000013, 0.0 }, + { -0.060518025961861198, 100, 0, + 0.50000000000000000, 0.0 }, + { -0.023747023905134217, 100, 0, + 0.60000000000000009, 0.0 }, + { -0.077132507199780501, 100, 0, + 0.70000000000000018, 0.0 }, + { 0.050861167913584228, 100, 0, + 0.80000000000000004, 0.0 }, + { 0.10226582055872063, 100, 0, + 0.90000000000000013, 0.0 }, + { 1.0000000000000000, 100, 0, + 1.0000000000000000, 0.0 }, +}; +const double toler029 = 5.0000000000000039e-13; + +// Test data for l=100, m=1. +// max(|f - f_GSL|): 1.1546319456101628e-14 at index 3 +// max(|f - f_GSL| / |f_GSL|): 2.1111954004946762e-15 +// mean(f - f_GSL): -8.0358999877630379e-16 +// variance(f - f_GSL): 3.3902236521998243e-32 +// stddev(f - f_GSL): 1.8412559985509414e-16 +const testcase_assoc_legendre +data030[21] = +{ + { -0.0000000000000000, 100, 1, + -1.0000000000000000, 0.0 }, + { 6.5200167187780345, 100, 1, + -0.90000000000000002, 0.0 }, + { 9.0065170007027486, 100, 1, + -0.80000000000000004, 0.0 }, + { -5.4690908541180976, 100, 1, + -0.69999999999999996, 0.0 }, + { -8.6275439170430790, 100, 1, + -0.59999999999999998, 0.0 }, + { -6.0909031663448454, 100, 1, + -0.50000000000000000, 0.0 }, + { 4.1160338699560395, 100, 1, + -0.39999999999999991, 0.0 }, + { 5.8491043010758634, 100, 1, + -0.29999999999999993, 0.0 }, + { -7.9435138723089826, 100, 1, + -0.19999999999999996, 0.0 }, + { 4.7996285823989355, 100, 1, + -0.099999999999999978, 0.0 }, + { 0.0000000000000000, 100, 1, + 0.0000000000000000, 0.0 }, + { -4.7996285823990101, 100, 1, + 0.10000000000000009, 0.0 }, + { 7.9435138723090155, 100, 1, + 0.20000000000000018, 0.0 }, + { -5.8491043010758013, 100, 1, + 0.30000000000000004, 0.0 }, + { -4.1160338699562162, 100, 1, + 0.40000000000000013, 0.0 }, + { 6.0909031663448454, 100, 1, + 0.50000000000000000, 0.0 }, + { 8.6275439170430470, 100, 1, + 0.60000000000000009, 0.0 }, + { 5.4690908541178693, 100, 1, + 0.70000000000000018, 0.0 }, + { -9.0065170007027486, 100, 1, + 0.80000000000000004, 0.0 }, + { -6.5200167187777787, 100, 1, + 0.90000000000000013, 0.0 }, + { 0.0000000000000000, 100, 1, + 1.0000000000000000, 0.0 }, +}; +const double toler030 = 2.5000000000000020e-13; + +// Test data for l=100, m=2. +// max(|f - f_GSL|): 6.8212102632969618e-13 at index 5 +// max(|f - f_GSL| / |f_GSL|): 2.0632212207447263e-15 +// mean(f - f_GSL): 8.2558298821649733e-14 +// variance(f - f_GSL): 3.5783331697705263e-28 +// stddev(f - f_GSL): 1.8916482679849673e-14 +const testcase_assoc_legendre +data031[21] = +{ + { 0.0000000000000000, 100, 2, + -1.0000000000000000, 0.0 }, + { -1005.9604880761002, 100, 2, + -0.90000000000000002, 0.0 }, + { -489.68041725865947, 100, 2, + -0.80000000000000004, 0.0 }, + { 768.31676011669924, 100, 2, + -0.69999999999999996, 0.0 }, + { 226.90362556627937, 100, 2, + -0.59999999999999998, 0.0 }, + { 604.19889304940341, 100, 2, + -0.50000000000000000, 0.0 }, + { 733.40061037838518, 100, 2, + -0.39999999999999991, 0.0 }, + { -573.30774483995629, 100, 2, + -0.29999999999999993, 0.0 }, + { -151.52946305080880, 100, 2, + -0.19999999999999996, 0.0 }, + { 646.30525583587985, 100, 2, + -0.099999999999999978, 0.0 }, + { -803.85129761050518, 100, 2, + 0.0000000000000000, 0.0 }, + { 646.30525583587439, 100, 2, + 0.10000000000000009, 0.0 }, + { -151.52946305079013, 100, 2, + 0.20000000000000018, 0.0 }, + { -573.30774483996390, 100, 2, + 0.30000000000000004, 0.0 }, + { 733.40061037837552, 100, 2, + 0.40000000000000013, 0.0 }, + { 604.19889304940341, 100, 2, + 0.50000000000000000, 0.0 }, + { 226.90362556629168, 100, 2, + 0.60000000000000009, 0.0 }, + { 768.31676011671766, 100, 2, + 0.70000000000000018, 0.0 }, + { -489.68041725865947, 100, 2, + 0.80000000000000004, 0.0 }, + { -1005.9604880761161, 100, 2, + 0.90000000000000013, 0.0 }, + { 0.0000000000000000, 100, 2, + 1.0000000000000000, 0.0 }, +}; +const double toler031 = 2.5000000000000020e-13; + +// Test data for l=100, m=5. +// max(|f - f_GSL|): 1.4305114746093750e-06 at index 14 +// max(|f - f_GSL| / |f_GSL|): 3.7628882298853693e-15 +// mean(f - f_GSL): -5.1089695521763390e-08 +// variance(f - f_GSL): 1.3703324189659077e-16 +// stddev(f - f_GSL): 1.1706119848036358e-08 +const testcase_assoc_legendre +data032[21] = +{ + { 0.0000000000000000, 100, 5, + -1.0000000000000000, 0.0 }, + { 900551126.09653807, 100, 5, + -0.90000000000000002, 0.0 }, + { 988567431.55756140, 100, 5, + -0.80000000000000004, 0.0 }, + { -645646451.90344620, 100, 5, + -0.69999999999999996, 0.0 }, + { -897114585.29920685, 100, 5, + -0.59999999999999998, 0.0 }, + { -661710744.42483854, 100, 5, + -0.50000000000000000, 0.0 }, + { 380163158.51424754, 100, 5, + -0.39999999999999991, 0.0 }, + { 617391071.36633193, 100, 5, + -0.29999999999999993, 0.0 }, + { -805288801.85509109, 100, 5, + -0.19999999999999996, 0.0 }, + { 481041740.16728652, 100, 5, + -0.099999999999999978, 0.0 }, + { 0.0000000000000000, 100, 5, + 0.0000000000000000, 0.0 }, + { -481041740.16729391, 100, 5, + 0.10000000000000009, 0.0 }, + { 805288801.85509515, 100, 5, + 0.20000000000000018, 0.0 }, + { -617391071.36632574, 100, 5, + 0.30000000000000004, 0.0 }, + { -380163158.51426536, 100, 5, + 0.40000000000000013, 0.0 }, + { 661710744.42483854, 100, 5, + 0.50000000000000000, 0.0 }, + { 897114585.29920483, 100, 5, + 0.60000000000000009, 0.0 }, + { 645646451.90342283, 100, 5, + 0.70000000000000018, 0.0 }, + { -988567431.55756140, 100, 5, + 0.80000000000000004, 0.0 }, + { -900551126.09651637, 100, 5, + 0.90000000000000013, 0.0 }, + { 0.0000000000000000, 100, 5, + 1.0000000000000000, 0.0 }, +}; +const double toler032 = 2.5000000000000020e-13; + +// Test data for l=100, m=10. +// max(|f - f_GSL|): 14336.000000000000 at index 14 +// max(|f - f_GSL| / |f_GSL|): 3.4905902237930355e-15 +// mean(f - f_GSL): 341.33333333333331 +// variance(f - f_GSL): inf +// stddev(f - f_GSL): inf +const testcase_assoc_legendre +data033[21] = +{ + { 0.0000000000000000, 100, 10, + -1.0000000000000000, 0.0 }, + { 2.5643395957658602e+17, 100, 10, + -0.90000000000000002, 0.0 }, + { 1.5778673545673485e+18, 100, 10, + -0.80000000000000004, 0.0 }, + { 4.4355048487496801e+18, 100, 10, + -0.69999999999999996, 0.0 }, + { -9.5936111659124288e+17, 100, 10, + -0.59999999999999998, 0.0 }, + { 4.2387123021963438e+18, 100, 10, + -0.50000000000000000, 0.0 }, + { 8.2370834618426767e+18, 100, 10, + -0.39999999999999991, 0.0 }, + { -4.9089358388051978e+18, 100, 10, + -0.29999999999999993, 0.0 }, + { -2.3468810358091274e+18, 100, 10, + -0.19999999999999996, 0.0 }, + { 6.8627855225034568e+18, 100, 10, + -0.099999999999999978, 0.0 }, + { -8.2494597181670380e+18, 100, 10, + 0.0000000000000000, 0.0 }, + { 6.8627855225034056e+18, 100, 10, + 0.10000000000000009, 0.0 }, + { -2.3468810358089518e+18, 100, 10, + 0.20000000000000018, 0.0 }, + { -4.9089358388052941e+18, 100, 10, + 0.30000000000000004, 0.0 }, + { 8.2370834618426112e+18, 100, 10, + 0.40000000000000013, 0.0 }, + { 4.2387123021963438e+18, 100, 10, + 0.50000000000000000, 0.0 }, + { -9.5936111659112640e+17, 100, 10, + 0.60000000000000009, 0.0 }, + { 4.4355048487499668e+18, 100, 10, + 0.70000000000000018, 0.0 }, + { 1.5778673545673485e+18, 100, 10, + 0.80000000000000004, 0.0 }, + { 2.5643395957630058e+17, 100, 10, + 0.90000000000000013, 0.0 }, + { 0.0000000000000000, 100, 10, + 1.0000000000000000, 0.0 }, +}; +const double toler033 = 2.5000000000000020e-13; + +// Test data for l=100, m=20. +// max(|f - f_GSL|): 3.9290089137475448e+24 at index 14 +// max(|f - f_GSL| / |f_GSL|): 5.1615589395022552e-15 +// mean(f - f_GSL): -5.0371909150609551e+23 +// variance(f - f_GSL): inf +// stddev(f - f_GSL): inf +const testcase_assoc_legendre +data034[21] = +{ + { 0.0000000000000000, 100, 20, + -1.0000000000000000, 0.0 }, + { 7.1604344878780134e+37, 100, 20, + -0.90000000000000002, 0.0 }, + { -8.3963895116962231e+38, 100, 20, + -0.80000000000000004, 0.0 }, + { 7.9022236853110145e+38, 100, 20, + -0.69999999999999996, 0.0 }, + { 8.2680005574121013e+38, 100, 20, + -0.59999999999999998, 0.0 }, + { 3.0750497039999552e+38, 100, 20, + -0.50000000000000000, 0.0 }, + { -7.6120586043843556e+38, 100, 20, + -0.39999999999999991, 0.0 }, + { 1.1474496891900921e+38, 100, 20, + -0.29999999999999993, 0.0 }, + { 4.3966251307444241e+38, 100, 20, + -0.19999999999999996, 0.0 }, + { -7.0503266451702591e+38, 100, 20, + -0.099999999999999978, 0.0 }, + { 7.7727439836159581e+38, 100, 20, + 0.0000000000000000, 0.0 }, + { -7.0503266451702213e+38, 100, 20, + 0.10000000000000009, 0.0 }, + { 4.3966251307442783e+38, 100, 20, + 0.20000000000000018, 0.0 }, + { 1.1474496891901797e+38, 100, 20, + 0.30000000000000004, 0.0 }, + { -7.6120586043844176e+38, 100, 20, + 0.40000000000000013, 0.0 }, + { 3.0750497039999552e+38, 100, 20, + 0.50000000000000000, 0.0 }, + { 8.2680005574120394e+38, 100, 20, + 0.60000000000000009, 0.0 }, + { 7.9022236853108422e+38, 100, 20, + 0.70000000000000018, 0.0 }, + { -8.3963895116962231e+38, 100, 20, + 0.80000000000000004, 0.0 }, + { 7.1604344878751847e+37, 100, 20, + 0.90000000000000013, 0.0 }, + { 0.0000000000000000, 100, 20, + 1.0000000000000000, 0.0 }, +}; +const double toler034 = 5.0000000000000039e-13; + +// Test data for l=100, m=50. +// max(|f - f_GSL|): 6.8296953242310788e+83 at index 14 +// max(|f - f_GSL| / |f_GSL|): 2.0345950516284159e-14 +// mean(f - f_GSL): 7.0103750947133818e+82 +// variance(f - f_GSL): inf +// stddev(f - f_GSL): inf +const testcase_assoc_legendre +data035[21] = +{ + { 0.0000000000000000, 100, 50, + -1.0000000000000000, 0.0 }, + { 9.3231278516893716e+96, 100, 50, + -0.90000000000000002, 0.0 }, + { -1.1029797977454281e+98, 100, 50, + -0.80000000000000004, 0.0 }, + { 1.8089333903465606e+97, 100, 50, + -0.69999999999999996, 0.0 }, + { 5.9364045925669405e+97, 100, 50, + -0.59999999999999998, 0.0 }, + { -8.2252620339727118e+97, 100, 50, + -0.50000000000000000, 0.0 }, + { 7.1431385093740728e+97, 100, 50, + -0.39999999999999991, 0.0 }, + { -3.3520602067479935e+97, 100, 50, + -0.29999999999999993, 0.0 }, + { -2.7791149588121382e+97, 100, 50, + -0.19999999999999996, 0.0 }, + { 9.0119338550180417e+97, 100, 50, + -0.099999999999999978, 0.0 }, + { -1.1712145031578381e+98, 100, 50, + 0.0000000000000000, 0.0 }, + { 9.0119338550181207e+97, 100, 50, + 0.10000000000000009, 0.0 }, + { -2.7791149588123644e+97, 100, 50, + 0.20000000000000018, 0.0 }, + { -3.3520602067479344e+97, 100, 50, + 0.30000000000000004, 0.0 }, + { 7.1431385093738816e+97, 100, 50, + 0.40000000000000013, 0.0 }, + { -8.2252620339727118e+97, 100, 50, + 0.50000000000000000, 0.0 }, + { 5.9364045925668024e+97, 100, 50, + 0.60000000000000009, 0.0 }, + { 1.8089333903469005e+97, 100, 50, + 0.70000000000000018, 0.0 }, + { -1.1029797977454281e+98, 100, 50, + 0.80000000000000004, 0.0 }, + { 9.3231278516892938e+96, 100, 50, + 0.90000000000000013, 0.0 }, + { 0.0000000000000000, 100, 50, + 1.0000000000000000, 0.0 }, +}; +const double toler035 = 2.5000000000000015e-12; + +// Test data for l=100, m=100. +// max(|f - f_GSL|): 1.9201920817492002e+172 at index 12 +// max(|f - f_GSL| / |f_GSL|): 2.3348104188683898e-14 +// mean(f - f_GSL): -4.0709851490379341e+170 +// variance(f - f_GSL): inf +// stddev(f - f_GSL): inf +const testcase_assoc_legendre +data036[21] = +{ + { 0.0000000000000000, 100, 100, + -1.0000000000000000, 0.0 }, + { 5.7751792255758316e+150, 100, 100, + -0.90000000000000002, 0.0 }, + { 4.3552236041585515e+164, 100, 100, + -0.80000000000000004, 0.0 }, + { 1.5936546850595123e+172, 100, 100, + -0.69999999999999996, 0.0 }, + { 1.3579510590289176e+177, 100, 100, + -0.59999999999999998, 0.0 }, + { 3.7752749682889513e+180, 100, 100, + -0.50000000000000000, 0.0 }, + { 1.0910627330458913e+183, 100, 100, + -0.39999999999999991, 0.0 }, + { 5.9697347526821064e+184, 100, 100, + -0.29999999999999993, 0.0 }, + { 8.6585879147526714e+185, 100, 100, + -0.19999999999999996, 0.0 }, + { 4.0331571908057011e+186, 100, 100, + -0.099999999999999978, 0.0 }, + { 6.6663086700729543e+186, 100, 100, + 0.0000000000000000, 0.0 }, + { 4.0331571908057011e+186, 100, 100, + 0.10000000000000009, 0.0 }, + { 8.6585879147526714e+185, 100, 100, + 0.20000000000000018, 0.0 }, + { 5.9697347526822483e+184, 100, 100, + 0.30000000000000004, 0.0 }, + { 1.0910627330458797e+183, 100, 100, + 0.40000000000000013, 0.0 }, + { 3.7752749682889513e+180, 100, 100, + 0.50000000000000000, 0.0 }, + { 1.3579510590289000e+177, 100, 100, + 0.60000000000000009, 0.0 }, + { 1.5936546850594382e+172, 100, 100, + 0.70000000000000018, 0.0 }, + { 4.3552236041585515e+164, 100, 100, + 0.80000000000000004, 0.0 }, + { 5.7751792255756128e+150, 100, 100, + 0.90000000000000013, 0.0 }, + { 0.0000000000000000, 100, 100, + 1.0000000000000000, 0.0 }, +}; +const double toler036 = 2.5000000000000015e-12; + +template + void + test(const testcase_assoc_legendre (&data)[Num], Ret toler) + { + bool test __attribute__((unused)) = true; + const Ret eps = std::numeric_limits::epsilon(); + Ret max_abs_diff = -Ret(1); + Ret max_abs_frac = -Ret(1); + unsigned int num_datum = Num; + for (unsigned int i = 0; i < num_datum; ++i) + { + const Ret f = std::tr1::assoc_legendre(data[i].l, data[i].m, + data[i].x); + const Ret f0 = data[i].f0; + const Ret diff = f - f0; + if (std::abs(diff) > max_abs_diff) + max_abs_diff = std::abs(diff); + if (std::abs(f0) > Ret(10) * eps + && std::abs(f) > Ret(10) * eps) + { + const Ret frac = diff / f0; + if (std::abs(frac) > max_abs_frac) + max_abs_frac = std::abs(frac); + } + } + VERIFY(max_abs_frac < toler); + } + +int +main() +{ + test(data001, toler001); + test(data002, toler002); + test(data003, toler003); + test(data004, toler004); + test(data005, toler005); + test(data006, toler006); + test(data007, toler007); + test(data008, toler008); + test(data009, toler009); + test(data010, toler010); + test(data011, toler011); + test(data012, toler012); + test(data013, toler013); + test(data014, toler014); + test(data015, toler015); + test(data016, toler016); + test(data017, toler017); + test(data018, toler018); + test(data019, toler019); + test(data020, toler020); + test(data021, toler021); + test(data022, toler022); + test(data023, toler023); + test(data024, toler024); + test(data025, toler025); + test(data026, toler026); + test(data027, toler027); + test(data028, toler028); + test(data029, toler029); + test(data030, toler030); + test(data031, toler031); + test(data032, toler032); + test(data033, toler033); + test(data034, toler034); + test(data035, toler035); + test(data036, toler036); + return 0; +} diff --git a/libstdc++-v3/testsuite/tr1/5_numerical_facilities/special_functions/09_cyl_bessel_j/check_value.cc b/libstdc++-v3/testsuite/tr1/5_numerical_facilities/special_functions/09_cyl_bessel_j/check_value.cc index 06a2d192df0..82141c89ee9 100644 --- a/libstdc++-v3/testsuite/tr1/5_numerical_facilities/special_functions/09_cyl_bessel_j/check_value.cc +++ b/libstdc++-v3/testsuite/tr1/5_numerical_facilities/special_functions/09_cyl_bessel_j/check_value.cc @@ -698,6 +698,26 @@ data026[21] = }; const double toler026 = 1.0000000000000006e-11; +// Test data for nu=100.00000000000000. +// max(|f - f_GSL|): 2.5857788132910287e-14 +// max(|f - f_GSL| / |f_GSL|): 1.6767662425535933e-11 +const testcase_cyl_bessel_j +data027[11] = +{ + { 0.0116761350077845, 100.0000000000000000, 1000.0000000000000000, 0.0 }, + {-0.0116998547780258, 100.0000000000000000, 1100.0000000000000000, 0.0 }, + {-0.0228014834050837, 100.0000000000000000, 1200.0000000000000000, 0.0 }, + {-0.0169735007873739, 100.0000000000000000, 1300.0000000000000000, 0.0 }, + {-0.0014154528803530, 100.0000000000000000, 1400.0000000000000000, 0.0 }, + { 0.0133337265844988, 100.0000000000000000, 1500.0000000000000000, 0.0 }, + { 0.0198025620201474, 100.0000000000000000, 1600.0000000000000000, 0.0 }, + { 0.0161297712798388, 100.0000000000000000, 1700.0000000000000000, 0.0 }, + { 0.0053753369281577, 100.0000000000000000, 1800.0000000000000000, 0.0 }, + {-0.0069238868725646, 100.0000000000000000, 1900.0000000000000000, 0.0 }, + {-0.0154878717200738, 100.0000000000000000, 2000.0000000000000000, 0.0 }, +}; +const double toler027 = 1.0000000000000006e-10; + template void test(const testcase_cyl_bessel_j (&data)[Num], Ret toler) @@ -748,5 +768,6 @@ main() test(data024, toler024); test(data025, toler025); test(data026, toler026); + test(data027, toler027); return 0; } diff --git a/libstdc++-v3/testsuite/tr1/5_numerical_facilities/special_functions/11_cyl_neumann/check_value.cc b/libstdc++-v3/testsuite/tr1/5_numerical_facilities/special_functions/11_cyl_neumann/check_value.cc index 3c0cbe7b977..86678be73e1 100644 --- a/libstdc++-v3/testsuite/tr1/5_numerical_facilities/special_functions/11_cyl_neumann/check_value.cc +++ b/libstdc++-v3/testsuite/tr1/5_numerical_facilities/special_functions/11_cyl_neumann/check_value.cc @@ -742,6 +742,26 @@ data028[20] = }; const double toler028 = 1.0000000000000006e-11; +// Test data for nu=100.00000000000000. +// max(|f - f_GSL|): 3.1049815496508870e-14 +// max(|f - f_GSL| / |f_GSL|): 8.4272302674970308e-12 +const testcase_cyl_neumann +data029[11] = +{ + {-0.0224386882577326, 100.0000000000000000, 1000.0000000000000000, 0.0 }, + {-0.0210775951598200, 100.0000000000000000, 1100.0000000000000000, 0.0 }, + {-0.0035299439206693, 100.0000000000000000, 1200.0000000000000000, 0.0 }, + { 0.0142500193265366, 100.0000000000000000, 1300.0000000000000000, 0.0 }, + { 0.0213046790897353, 100.0000000000000000, 1400.0000000000000000, 0.0 }, + { 0.0157343950779022, 100.0000000000000000, 1500.0000000000000000, 0.0 }, + { 0.0025544633636228, 100.0000000000000000, 1600.0000000000000000, 0.0 }, + {-0.0107220455248494, 100.0000000000000000, 1700.0000000000000000, 0.0 }, + {-0.0180369192432256, 100.0000000000000000, 1800.0000000000000000, 0.0 }, + {-0.0169584155930798, 100.0000000000000000, 1900.0000000000000000, 0.0 }, + {-0.0088788704566206, 100.0000000000000000, 2000.0000000000000000, 0.0 }, +}; +const double toler029 = 1.0000000000000006e-11; + template void test(const testcase_cyl_neumann (&data)[Num], Ret toler) @@ -794,5 +814,6 @@ main() test(data026, toler026); test(data027, toler027); test(data028, toler028); + test(data029, toler029); return 0; }