Revert 20001.

From-SVN: r260002

diff --git a/libstdc++-v3/ChangeLog b/libstdc++-v3/ChangeLog
index 94f08c22a4f6d52fafe3a3ecacd81f010e75dfe4..93935ab9787870db7c538bee3a0c45d97469bfb4 100644 (file)
--- 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  <jwakely@redhat.com>
 
        PR libstdc++/85642 fix is_nothrow_default_constructible<optional<T>>

diff --git a/libstdc++-v3/include/bits/random.tcc b/libstdc++-v3/include/bits/random.tcc
index 6db900cc0cd94fa31289f3354d4d5af3755cbc6f..f398150d41605bad62c8b0c75f2f1feaec89450f 100644 (file)
--- 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 2e2c2c06560680b288cb2617ffce7a53e264ac81..54f2b9db898d91e66353cbb01e0798c560f5430e 100644 (file)
--- 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<typename _Tp> _Tp arg(const complex<_Tp>&);
   ///  Return @a z magnitude squared.
-  template<typename _Tp> _Tp norm(const complex<_Tp>&);
+  template<typename _Tp> _Tp _GLIBCXX_CONSTEXPR norm(const complex<_Tp>&);
 
   ///  Return complex conjugate of @a z.
   template<typename _Tp> complex<_Tp> conj(const complex<_Tp>&);
@@ -322,7 +322,7 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION
   //@{
   ///  Return new complex value @a x plus @a y.
   template<typename _Tp>
-    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<typename _Tp>
-    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<typename _Tp>
-    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<typename _Tp>
-    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<typename _Tp>
-    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<typename _Tp>
-    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<typename _Tp>
-    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<typename _Tp>
-    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<typename _Tp>
-    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<typename _Tp>
-    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<typename _Tp>
-    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<typename _Tp>
-    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<typename _Tp>
-    inline complex<_Tp>
+    _GLIBCXX_CONSTEXPR inline complex<_Tp>
     operator+(const complex<_Tp>& __x)
     { return __x; }
 
   ///  Return complex negation of @a x.
   template<typename _Tp>
-    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<typename _Tp>
-    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<typename _Tp>
-    inline _GLIBCXX_CONSTEXPR bool
+    _GLIBCXX_CONSTEXPR inline bool
     operator==(const complex<_Tp>& __x, const _Tp& __y)
     { return __x.real() == __y && __x.imag() == _Tp(); }
 
   template<typename _Tp>
-    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<typename _Tp>
-    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<typename _Tp>
-    inline _GLIBCXX_CONSTEXPR bool
+    _GLIBCXX_CONSTEXPR inline bool
     operator!=(const complex<_Tp>& __x, const _Tp& __y)
     { return __x.real() != __y || __x.imag() != _Tp(); }
 
   template<typename _Tp>
-    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<typename _Tp>
-        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<true>
     {
       template<typename _Tp>
-        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<typename _Tp>
-    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<typename _Tp>
-    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<typename _Tp> std::complex<_Tp> proj(const std::complex<_Tp>&);
+  template<typename _Tp>
+    _GLIBCXX_CONSTEXPR std::complex<_Tp> proj(const std::complex<_Tp>&);
 
   template<typename _Tp>
-    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<typename _Tp>
-    inline std::complex<_Tp>
+    _GLIBCXX_CONSTEXPR inline std::complex<_Tp>
     proj(const std::complex<_Tp>& __z)
     { return __complex_proj(__z.__rep()); }
 #else
   template<typename _Tp>
-    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 26c66cabe29e13bd0c8275a3402963c193a4cfad..1ae88a3c95228fd878112c2b7f64bb4cd4bf00ef 100644 (file)
--- 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 <typename _Tp>
     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 a07d83a0bb1eba4d33d6058c64d78d04d622e16c..e2d1880ecb003b4d9ddc6a8b4fbbd5904f98a16b 100644 (file)
--- 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$.
      */
     template<typename _Tp>
@@ -127,19 +127,16 @@ namespace tr1
      *     P_l^m(x) = (1 - x^2)^{m/2}\frac{d^m}{dx^m}P_l(x)
      *   @f]
      * 
-     *   @param  l  The degree of the associated Legendre function.
+     *   @param  l  The order of the associated Legendre function.
      *              @f$ 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<typename _Tp>
     _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 d99d31e6c9a0f08fd1d31167b52b2915daeba071..e393b4aa18347df2d5a0c3fb579e5c4b4e1eb46c 100644 (file)
--- 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 <testsuite_hooks.h>
@@ -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<double>
 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<double>
 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, 
+  { 1.4399999999999999, 2, 1, 
          -0.80000000000000004, 0.0 },
-  { -1.4996999699939983, 2, 1, 
+  { 1.4996999699939983, 2, 1, 
          -0.69999999999999996, 0.0 },
-  { -1.4399999999999999, 2, 1, 
+  { 1.4399999999999999, 2, 1, 
          -0.59999999999999998, 0.0 },
-  { -1.2990381056766580, 2, 1, 
+  { 1.2990381056766580, 2, 1, 
          -0.50000000000000000, 0.0 },
-  { -1.0998181667894014, 2, 1, 
+  { 1.0998181667894014, 2, 1, 
          -0.39999999999999991, 0.0 },
-  { -0.85854528127525076, 2, 1, 
+  { 0.85854528127525076, 2, 1, 
          -0.29999999999999993, 0.0 },
-  { -0.58787753826796263, 2, 1, 
+  { 0.58787753826796263, 2, 1, 
          -0.19999999999999996, 0.0 },
-  { -0.29849623113198592, 2, 1, 
+  { 0.29849623113198592, 2, 1, 
          -0.099999999999999978, 0.0 },
-  { 0.0000000000000000, 2, 1, 
+  { -0.0000000000000000, 2, 1, 
          0.0000000000000000, 0.0 },
-  { 0.29849623113198626, 2, 1, 
+  { -0.29849623113198626, 2, 1, 
          0.10000000000000009, 0.0 },
-  { 0.58787753826796330, 2, 1, 
+  { -0.58787753826796330, 2, 1, 
          0.20000000000000018, 0.0 },
-  { 0.85854528127525132, 2, 1, 
+  { -0.85854528127525132, 2, 1, 
          0.30000000000000004, 0.0 },
-  { 1.0998181667894018, 2, 1, 
+  { -1.0998181667894018, 2, 1, 
          0.40000000000000013, 0.0 },
-  { 1.2990381056766580, 2, 1, 
+  { -1.2990381056766580, 2, 1, 
          0.50000000000000000, 0.0 },
-  { 1.4400000000000002, 2, 1, 
+  { -1.4400000000000002, 2, 1, 
          0.60000000000000009, 0.0 },
-  { 1.4996999699939983, 2, 1, 
+  { -1.4996999699939983, 2, 1, 
          0.70000000000000018, 0.0 },
-  { 1.4399999999999999, 2, 1, 
+  { -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<double>
 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<double>
 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<double>
 data012[21] =
 {
-  { 0.0000000000000000, 10, 1, 
+  { -0.0000000000000000, 10, 1, 
          -1.0000000000000000, 0.0 },
-  { 3.0438748781479039, 10, 1, 
+  { -3.0438748781479039, 10, 1, 
          -0.90000000000000002, 0.0 },
-  { 0.87614260800000254, 10, 1, 
+  { -0.87614260800000254, 10, 1, 
          -0.80000000000000004, 0.0 },
-  { -2.9685359952934527, 10, 1, 
+  { 2.9685359952934527, 10, 1, 
          -0.69999999999999996, 0.0 },
-  { -1.2511825919999997, 10, 1, 
+  { 1.2511825919999997, 10, 1, 
          -0.59999999999999998, 0.0 },
-  { 2.0066877394361260, 10, 1, 
+  { -2.0066877394361260, 10, 1, 
          -0.50000000000000000, 0.0 },
-  { 2.4822196173476647, 10, 1, 
+  { -2.4822196173476647, 10, 1, 
          -0.39999999999999991, 0.0 },
-  { 0.12309508907433593, 10, 1, 
+  { -0.12309508907433593, 10, 1, 
          -0.29999999999999993, 0.0 },
-  { -2.2468221751958413, 10, 1, 
+  { 2.2468221751958413, 10, 1, 
          -0.19999999999999996, 0.0 },
-  { -2.2472659777983512, 10, 1, 
+  { 2.2472659777983512, 10, 1, 
          -0.099999999999999978, 0.0 },
-  { 0.0000000000000000, 10, 1, 
+  { -0.0000000000000000, 10, 1, 
          0.0000000000000000, 0.0 },
-  { 2.2472659777983535, 10, 1, 
+  { -2.2472659777983535, 10, 1, 
          0.10000000000000009, 0.0 },
-  { 2.2468221751958377, 10, 1, 
+  { -2.2468221751958377, 10, 1, 
          0.20000000000000018, 0.0 },
-  { -0.12309508907433910, 10, 1, 
+  { 0.12309508907433910, 10, 1, 
          0.30000000000000004, 0.0 },
-  { -2.4822196173476669, 10, 1, 
+  { 2.4822196173476669, 10, 1, 
          0.40000000000000013, 0.0 },
-  { -2.0066877394361260, 10, 1, 
+  { 2.0066877394361260, 10, 1, 
          0.50000000000000000, 0.0 },
-  { 1.2511825920000037, 10, 1, 
+  { -1.2511825920000037, 10, 1, 
          0.60000000000000009, 0.0 },
-  { 2.9685359952934505, 10, 1, 
+  { -2.9685359952934505, 10, 1, 
          0.70000000000000018, 0.0 },
-  { -0.87614260800000254, 10, 1, 
+  { 0.87614260800000254, 10, 1, 
          0.80000000000000004, 0.0 },
-  { -3.0438748781478981, 10, 1, 
+  { 3.0438748781478981, 10, 1, 
          0.90000000000000013, 0.0 },
-  { -0.0000000000000000, 10, 1, 
+  { 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<double>
 data014[21] =
 {
-  { -0.0000000000000000, 10, 5, 
+  { 0.0000000000000000, 10, 5, 
          -1.0000000000000000, 0.0 },
-  { -21343.618518164680, 10, 5, 
+  { 21343.618518164680, 10, 5, 
          -0.90000000000000002, 0.0 },
-  { -40457.016407807983, 10, 5, 
+  { 40457.016407807983, 10, 5, 
          -0.80000000000000004, 0.0 },
-  { -20321.279317331315, 10, 5, 
+  { 20321.279317331315, 10, 5, 
          -0.69999999999999996, 0.0 },
-  { 14410.820616192004, 10, 5, 
+  { -14410.820616192004, 10, 5, 
          -0.59999999999999998, 0.0 },
-  { 30086.169706116176, 10, 5, 
+  { -30086.169706116176, 10, 5, 
          -0.50000000000000000, 0.0 },
-  { 17177.549337582834, 10, 5, 
+  { -17177.549337582834, 10, 5, 
          -0.39999999999999991, 0.0 },
-  { -9272.5119495412546, 10, 5, 
+  { 9272.5119495412546, 10, 5, 
          -0.29999999999999993, 0.0 },
-  { -26591.511184414714, 10, 5, 
+  { 26591.511184414714, 10, 5, 
          -0.19999999999999996, 0.0 },
-  { -21961.951238504211, 10, 5, 
+  { 21961.951238504211, 10, 5, 
          -0.099999999999999978, 0.0 },
-  { 0.0000000000000000, 10, 5, 
+  { -0.0000000000000000, 10, 5, 
          0.0000000000000000, 0.0 },
-  { 21961.951238504229, 10, 5, 
+  { -21961.951238504229, 10, 5, 
          0.10000000000000009, 0.0 },
-  { 26591.511184414703, 10, 5, 
+  { -26591.511184414703, 10, 5, 
          0.20000000000000018, 0.0 },
-  { 9272.5119495412364, 10, 5, 
+  { -9272.5119495412364, 10, 5, 
          0.30000000000000004, 0.0 },
-  { -17177.549337582877, 10, 5, 
+  { 17177.549337582877, 10, 5, 
          0.40000000000000013, 0.0 },
-  { -30086.169706116176, 10, 5, 
+  { 30086.169706116176, 10, 5, 
          0.50000000000000000, 0.0 },
-  { -14410.820616191972, 10, 5, 
+  { 14410.820616191972, 10, 5, 
          0.60000000000000009, 0.0 },
-  { 20321.279317331391, 10, 5, 
+  { -20321.279317331391, 10, 5, 
          0.70000000000000018, 0.0 },
-  { 40457.016407807983, 10, 5, 
+  { -40457.016407807983, 10, 5, 
          0.80000000000000004, 0.0 },
-  { 21343.618518164636, 10, 5, 
+  { -21343.618518164636, 10, 5, 
          0.90000000000000013, 0.0 },
-  { -0.0000000000000000, 10, 5, 
+  { 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<double>
 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, 
+  { -0.63138296146340844, 20, 1, 
          -0.80000000000000004, 0.0 },
-  { -0.72274871413391395, 20, 1, 
+  { 0.72274871413391395, 20, 1, 
          -0.69999999999999996, 0.0 },
-  { 2.3203528743824910, 20, 1, 
+  { -2.3203528743824910, 20, 1, 
          -0.59999999999999998, 0.0 },
-  { -3.7399919228791405, 20, 1, 
+  { 3.7399919228791405, 20, 1, 
          -0.50000000000000000, 0.0 },
-  { 3.1692202279270085, 20, 1, 
+  { -3.1692202279270085, 20, 1, 
          -0.39999999999999991, 0.0 },
-  { -0.15804468835345031, 20, 1, 
+  { 0.15804468835345031, 20, 1, 
          -0.29999999999999993, 0.0 },
-  { -3.0366182393271171, 20, 1, 
+  { 3.0366182393271171, 20, 1, 
          -0.19999999999999996, 0.0 },
-  { 3.2115523815580209, 20, 1, 
+  { -3.2115523815580209, 20, 1, 
          -0.099999999999999978, 0.0 },
-  { -0.0000000000000000, 20, 1, 
+  { 0.0000000000000000, 20, 1, 
          0.0000000000000000, 0.0 },
-  { -3.2115523815580169, 20, 1, 
+  { 3.2115523815580169, 20, 1, 
          0.10000000000000009, 0.0 },
-  { 3.0366182393271259, 20, 1, 
+  { -3.0366182393271259, 20, 1, 
          0.20000000000000018, 0.0 },
-  { 0.15804468835344135, 20, 1, 
+  { -0.15804468835344135, 20, 1, 
          0.30000000000000004, 0.0 },
-  { -3.1692202279269970, 20, 1, 
+  { 3.1692202279269970, 20, 1, 
          0.40000000000000013, 0.0 },
-  { 3.7399919228791405, 20, 1, 
+  { -3.7399919228791405, 20, 1, 
          0.50000000000000000, 0.0 },
-  { -2.3203528743824995, 20, 1, 
+  { 2.3203528743824995, 20, 1, 
          0.60000000000000009, 0.0 },
-  { 0.72274871413393793, 20, 1, 
+  { -0.72274871413393793, 20, 1, 
          0.70000000000000018, 0.0 },
-  { -0.63138296146340844, 20, 1, 
+  { 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<double>
 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, 
+  { 503060.91484852589, 20, 5, 
          -0.80000000000000004, 0.0 },
-  { 298127.28360361955, 20, 5, 
+  { -298127.28360361955, 20, 5, 
          -0.69999999999999996, 0.0 },
-  { 114444.61447464029, 20, 5, 
+  { -114444.61447464029, 20, 5, 
          -0.59999999999999998, 0.0 },
-  { -543428.40914592845, 20, 5, 
+  { 543428.40914592845, 20, 5, 
          -0.50000000000000000, 0.0 },
-  { 613842.07728185481, 20, 5, 
+  { -613842.07728185481, 20, 5, 
          -0.39999999999999991, 0.0 },
-  { -143765.42411271061, 20, 5, 
+  { 143765.42411271061, 20, 5, 
          -0.29999999999999993, 0.0 },
-  { -472600.45321372285, 20, 5, 
+  { 472600.45321372285, 20, 5, 
          -0.19999999999999996, 0.0 },
-  { 563861.76771496492, 20, 5, 
+  { -563861.76771496492, 20, 5, 
          -0.099999999999999978, 0.0 },
-  { -0.0000000000000000, 20, 5, 
+  { 0.0000000000000000, 20, 5, 
          0.0000000000000000, 0.0 },
-  { -563861.76771496458, 20, 5, 
+  { 563861.76771496458, 20, 5, 
          0.10000000000000009, 0.0 },
-  { 472600.45321372483, 20, 5, 
+  { -472600.45321372483, 20, 5, 
          0.20000000000000018, 0.0 },
-  { 143765.42411270936, 20, 5, 
+  { -143765.42411270936, 20, 5, 
          0.30000000000000004, 0.0 },
-  { -613842.07728185353, 20, 5, 
+  { 613842.07728185353, 20, 5, 
          0.40000000000000013, 0.0 },
-  { 543428.40914592845, 20, 5, 
+  { -543428.40914592845, 20, 5, 
          0.50000000000000000, 0.0 },
-  { -114444.61447464178, 20, 5, 
+  { 114444.61447464178, 20, 5, 
          0.60000000000000009, 0.0 },
-  { -298127.28360361519, 20, 5, 
+  { 298127.28360361519, 20, 5, 
          0.70000000000000018, 0.0 },
-  { 503060.91484852589, 20, 5, 
+  { -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<double>
 data023[21] =
 {
-  { -0.0000000000000000, 50, 1, 
+  { 0.0000000000000000, 50, 1, 
          -1.0000000000000000, 0.0 },
-  { 0.13424149984449490, 50, 1, 
+  { -0.13424149984449490, 50, 1, 
          -0.90000000000000002, 0.0 },
-  { -2.2011219672413018, 50, 1, 
+  { 2.2011219672413018, 50, 1, 
          -0.80000000000000004, 0.0 },
-  { -6.6622414993232004, 50, 1, 
+  { 6.6622414993232004, 50, 1, 
          -0.69999999999999996, 0.0 },
-  { -5.5772846936919249, 50, 1, 
+  { 5.5772846936919249, 50, 1, 
          -0.59999999999999998, 0.0 },
-  { -5.8787148815607608, 50, 1, 
+  { 5.8787148815607608, 50, 1, 
          -0.50000000000000000, 0.0 },
-  { -5.5473459458634080, 50, 1, 
+  { 5.5473459458634080, 50, 1, 
          -0.39999999999999991, 0.0 },
-  { -1.8444956647620248, 50, 1, 
+  { 1.8444956647620248, 50, 1, 
          -0.29999999999999993, 0.0 },
-  { 3.8722014306642127, 50, 1, 
+  { -3.8722014306642127, 50, 1, 
          -0.19999999999999996, 0.0 },
-  { 5.3488751322285628, 50, 1, 
+  { -5.3488751322285628, 50, 1, 
          -0.099999999999999978, 0.0 },
-  { 0.0000000000000000, 50, 1, 
+  { -0.0000000000000000, 50, 1, 
          0.0000000000000000, 0.0 },
-  { -5.3488751322285522, 50, 1, 
+  { 5.3488751322285522, 50, 1, 
          0.10000000000000009, 0.0 },
-  { -3.8722014306642620, 50, 1, 
+  { 3.8722014306642620, 50, 1, 
          0.20000000000000018, 0.0 },
-  { 1.8444956647619930, 50, 1, 
+  { -1.8444956647619930, 50, 1, 
          0.30000000000000004, 0.0 },
-  { 5.5473459458633814, 50, 1, 
+  { -5.5473459458633814, 50, 1, 
          0.40000000000000013, 0.0 },
-  { 5.8787148815607608, 50, 1, 
+  { -5.8787148815607608, 50, 1, 
          0.50000000000000000, 0.0 },
-  { 5.5772846936919453, 50, 1, 
+  { -5.5772846936919453, 50, 1, 
          0.60000000000000009, 0.0 },
-  { 6.6622414993232182, 50, 1, 
+  { -6.6622414993232182, 50, 1, 
          0.70000000000000018, 0.0 },
-  { 2.2011219672413018, 50, 1, 
+  { -2.2011219672413018, 50, 1, 
          0.80000000000000004, 0.0 },
-  { -0.13424149984438935, 50, 1, 
+  { 0.13424149984438935, 50, 1, 
          0.90000000000000013, 0.0 },
-  { -0.0000000000000000, 50, 1, 
+  { 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<double>
 data025[21] =
 {
-  { 0.0000000000000000, 50, 5, 
+  { -0.0000000000000000, 50, 5, 
          -1.0000000000000000, 0.0 },
-  { 27340473.952132829, 50, 5, 
+  { -27340473.952132829, 50, 5, 
          -0.90000000000000002, 0.0 },
-  { -27753716.768532373, 50, 5, 
+  { 27753716.768532373, 50, 5, 
          -0.80000000000000004, 0.0 },
-  { -40808153.913493633, 50, 5, 
+  { 40808153.913493633, 50, 5, 
          -0.69999999999999996, 0.0 },
-  { -32071189.035790090, 50, 5, 
+  { 32071189.035790090, 50, 5, 
          -0.59999999999999998, 0.0 },
-  { -36265736.218529105, 50, 5, 
+  { 36265736.218529105, 50, 5, 
          -0.50000000000000000, 0.0 },
-  { -37089596.700204931, 50, 5, 
+  { 37089596.700204931, 50, 5, 
          -0.39999999999999991, 0.0 },
-  { -14562029.629244687, 50, 5, 
+  { 14562029.629244687, 50, 5, 
          -0.29999999999999993, 0.0 },
-  { 23686895.217517190, 50, 5, 
+  { -23686895.217517190, 50, 5, 
          -0.19999999999999996, 0.0 },
-  { 34878992.965676002, 50, 5, 
+  { -34878992.965676002, 50, 5, 
          -0.099999999999999978, 0.0 },
-  { 0.0000000000000000, 50, 5, 
+  { -0.0000000000000000, 50, 5, 
          0.0000000000000000, 0.0 },
-  { -34878992.965675958, 50, 5, 
+  { 34878992.965675958, 50, 5, 
          0.10000000000000009, 0.0 },
-  { -23686895.217517529, 50, 5, 
+  { 23686895.217517529, 50, 5, 
          0.20000000000000018, 0.0 },
-  { 14562029.629244499, 50, 5, 
+  { -14562029.629244499, 50, 5, 
          0.30000000000000004, 0.0 },
-  { 37089596.700204782, 50, 5, 
+  { -37089596.700204782, 50, 5, 
          0.40000000000000013, 0.0 },
-  { 36265736.218529105, 50, 5, 
+  { -36265736.218529105, 50, 5, 
          0.50000000000000000, 0.0 },
-  { 32071189.035790242, 50, 5, 
+  { -32071189.035790242, 50, 5, 
          0.60000000000000009, 0.0 },
-  { 40808153.913493834, 50, 5, 
+  { -40808153.913493834, 50, 5, 
          0.70000000000000018, 0.0 },
-  { 27753716.768532373, 50, 5, 
+  { -27753716.768532373, 50, 5, 
          0.80000000000000004, 0.0 },
-  { -27340473.952132136, 50, 5, 
+  { 27340473.952132136, 50, 5, 
          0.90000000000000013, 0.0 },
-  { -0.0000000000000000, 50, 5, 
+  { 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<double>
 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, 
+  { 9.0065170007027486, 100, 1, 
          -0.80000000000000004, 0.0 },
-  { 5.4690908541180976, 100, 1, 
+  { -5.4690908541180976, 100, 1, 
          -0.69999999999999996, 0.0 },
-  { 8.6275439170430790, 100, 1, 
+  { -8.6275439170430790, 100, 1, 
          -0.59999999999999998, 0.0 },
-  { 6.0909031663448454, 100, 1, 
+  { -6.0909031663448454, 100, 1, 
          -0.50000000000000000, 0.0 },
-  { -4.1160338699560395, 100, 1, 
+  { 4.1160338699560395, 100, 1, 
          -0.39999999999999991, 0.0 },
-  { -5.8491043010758634, 100, 1, 
+  { 5.8491043010758634, 100, 1, 
          -0.29999999999999993, 0.0 },
-  { 7.9435138723089826, 100, 1, 
+  { -7.9435138723089826, 100, 1, 
          -0.19999999999999996, 0.0 },
-  { -4.7996285823989355, 100, 1, 
+  { 4.7996285823989355, 100, 1, 
          -0.099999999999999978, 0.0 },
-  { -0.0000000000000000, 100, 1, 
+  { 0.0000000000000000, 100, 1, 
          0.0000000000000000, 0.0 },
-  { 4.7996285823990101, 100, 1, 
+  { -4.7996285823990101, 100, 1, 
          0.10000000000000009, 0.0 },
-  { -7.9435138723090155, 100, 1, 
+  { 7.9435138723090155, 100, 1, 
          0.20000000000000018, 0.0 },
-  { 5.8491043010758013, 100, 1, 
+  { -5.8491043010758013, 100, 1, 
          0.30000000000000004, 0.0 },
-  { 4.1160338699562162, 100, 1, 
+  { -4.1160338699562162, 100, 1, 
          0.40000000000000013, 0.0 },
-  { -6.0909031663448454, 100, 1, 
+  { 6.0909031663448454, 100, 1, 
          0.50000000000000000, 0.0 },
-  { -8.6275439170430470, 100, 1, 
+  { 8.6275439170430470, 100, 1, 
          0.60000000000000009, 0.0 },
-  { -5.4690908541178693, 100, 1, 
+  { 5.4690908541178693, 100, 1, 
          0.70000000000000018, 0.0 },
-  { 9.0065170007027486, 100, 1, 
+  { -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<double>
 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, 
+  { 988567431.55756140, 100, 5, 
          -0.80000000000000004, 0.0 },
-  { 645646451.90344620, 100, 5, 
+  { -645646451.90344620, 100, 5, 
          -0.69999999999999996, 0.0 },
-  { 897114585.29920685, 100, 5, 
+  { -897114585.29920685, 100, 5, 
          -0.59999999999999998, 0.0 },
-  { 661710744.42483854, 100, 5, 
+  { -661710744.42483854, 100, 5, 
          -0.50000000000000000, 0.0 },
-  { -380163158.51424754, 100, 5, 
+  { 380163158.51424754, 100, 5, 
          -0.39999999999999991, 0.0 },
-  { -617391071.36633193, 100, 5, 
+  { 617391071.36633193, 100, 5, 
          -0.29999999999999993, 0.0 },
-  { 805288801.85509109, 100, 5, 
+  { -805288801.85509109, 100, 5, 
          -0.19999999999999996, 0.0 },
-  { -481041740.16728652, 100, 5, 
+  { 481041740.16728652, 100, 5, 
          -0.099999999999999978, 0.0 },
-  { -0.0000000000000000, 100, 5, 
+  { 0.0000000000000000, 100, 5, 
          0.0000000000000000, 0.0 },
-  { 481041740.16729391, 100, 5, 
+  { -481041740.16729391, 100, 5, 
          0.10000000000000009, 0.0 },
-  { -805288801.85509515, 100, 5, 
+  { 805288801.85509515, 100, 5, 
          0.20000000000000018, 0.0 },
-  { 617391071.36632574, 100, 5, 
+  { -617391071.36632574, 100, 5, 
          0.30000000000000004, 0.0 },
-  { 380163158.51426536, 100, 5, 
+  { -380163158.51426536, 100, 5, 
          0.40000000000000013, 0.0 },
-  { -661710744.42483854, 100, 5, 
+  { 661710744.42483854, 100, 5, 
          0.50000000000000000, 0.0 },
-  { -897114585.29920483, 100, 5, 
+  { 897114585.29920483, 100, 5, 
          0.60000000000000009, 0.0 },
-  { -645646451.90342283, 100, 5, 
+  { 645646451.90342283, 100, 5, 
          0.70000000000000018, 0.0 },
-  { 988567431.55756140, 100, 5, 
+  { -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 475c6dcaa4a777b008ba0006846784f21aec9d1a..74c08d021dc86aab89d7a17ba2e5811bee32b2e9 100644 (file)
--- 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<double>
+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<typename Ret, unsigned int Num>
   void
   test(const testcase_cyl_bessel_j<Ret> (&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 da1250278d55860f025d41c1b8f110b8fccdba81..cde8cf611f9fd6afd5ca4c9b20db2842c5a8d430 100644 (file)
--- 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<double>
+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<typename Ret, unsigned int Num>
   void
   test(const testcase_cyl_neumann<Ret> (&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 (file)
index 0000000..782894c
--- /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
+// <http://www.gnu.org/licenses/>.
+
+//  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 <limits>
+#include <tr1/cmath>
+#if defined(__TEST_DEBUG)
+#  include <iostream>
+#  define VERIFY(A) \
+  if (!(A)) \
+    { \
+      std::cout << "line " << __LINE__ \
+       << "  max_abs_frac = " << max_abs_frac \
+       << std::endl; \
+    }
+#else
+#  include <testsuite_hooks.h>
+#endif
+#include <specfun_testcase.h>
+
+// 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<double>
+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<double>
+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<double>
+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<double>
+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<double>
+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<double>
+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<double>
+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<double>
+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<double>
+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<double>
+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<double>
+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<double>
+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<double>
+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<double>
+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<double>
+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<double>
+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<double>
+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<double>
+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<double>
+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<double>
+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<double>
+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<double>
+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<double>
+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<double>
+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<double>
+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<double>
+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<double>
+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<double>
+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<double>
+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<double>
+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<double>
+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<double>
+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<double>
+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<double>
+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<double>
+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<double>
+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<typename Ret, unsigned int Num>
+  void
+  test(const testcase_assoc_legendre<Ret> (&data)[Num], Ret toler)
+  {
+    bool test __attribute__((unused)) = true;
+    const Ret eps = std::numeric_limits<Ret>::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 06a2d192df0b1e7a67d5c36178fd1dcf852769e4..82141c89ee9d790d4c5ec7fa7cf0e577f00da395 100644 (file)
--- 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<double>
+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<typename Ret, unsigned int Num>
   void
   test(const testcase_cyl_bessel_j<Ret> (&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 3c0cbe7b977093bfb4761fc1e446ad26d5e1f9f0..86678be73e1e3bb4a9886e19554baa3343081321 100644 (file)
--- 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<double>
+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<typename Ret, unsigned int Num>
   void
   test(const testcase_cyl_neumann<Ret> (&data)[Num], Ret toler)
@@ -794,5 +814,6 @@ main()
   test(data026, toler026);
   test(data027, toler027);
   test(data028, toler028);
+  test(data029, toler029);
   return 0;
 }