Implement TR29124 C++ special Math Functions.

2016-01-14  Edward Smith-Rowland  <3dw4rd@verizon.net>
	    Jonathan Wakely  <jwakely@redhat.com>
	    Florian Goth <CaptainSifff@gmx.de>

	Implement TR29124 C++ special Math Functions.
	* include/Makefile.am: Add new headers.
	* include/Makefile.in: Regenerate.
	* include/bits/specfun.h: New.
	* include/c_global/cmath: Adjust for both tr1 and tr29124 maths.
	* include/tr1/bessel_function.tcc: Ditto.
	* include/tr1/beta_function.tcc: Ditto.
	* include/tr1/cmath: Ditto.
	* include/tr1/ell_integral.tcc: Ditto.
	* include/tr1/exp_integral.tcc: Ditto.
	* include/tr1/gamma.tcc: Ditto.
	* include/tr1/hypergeometric.tcc: Ditto.
	* include/tr1/legendre_function.tcc: Ditto.
	* include/tr1/modified_bessel_func.tcc: Ditto.
	* include/tr1/poly_hermite.tcc: Ditto.
	* include/tr1/poly_laguerre.tcc: Ditto.
	* include/tr1/riemann_zeta.tcc: Ditto.
	* include/tr1/special_function_util.h: Ditto.
	* testsuite/ext/special_functions/conf_hyperg: New.
	* testsuite/ext/special_functions/conf_hyperg/check_nan.cc: New.
	* testsuite/ext/special_functions/conf_hyperg/check_value.cc: New.
	* testsuite/ext/special_functions/conf_hyperg/compile.cc: New.
	* testsuite/ext/special_functions/hyperg: New.
	* testsuite/ext/special_functions/hyperg/check_nan.cc: New.
	* testsuite/ext/special_functions/hyperg/check_value.cc: New.
	* testsuite/ext/special_functions/hyperg/compile.cc: New.
	* testsuite/libstdc++-dg/conformance.exp: Add special_functions directory.
	* testsuite/special_functions/01_assoc_laguerre/check_nan.cc: New.
	* testsuite/special_functions/01_assoc_laguerre/check_value.cc: New.
	* testsuite/special_functions/01_assoc_laguerre/compile.cc: New.
	* testsuite/special_functions/01_assoc_laguerre/compile_2.cc: New.
	* testsuite/special_functions/02_assoc_legendre/check_nan.cc: New.
	* testsuite/special_functions/02_assoc_legendre/check_value.cc: New.
	* testsuite/special_functions/02_assoc_legendre/compile.cc: New.
	* testsuite/special_functions/02_assoc_legendre/compile_2.cc: New.
	* testsuite/special_functions/03_beta/check_nan.cc: New.
	* testsuite/special_functions/03_beta/check_value.cc: New.
	* testsuite/special_functions/03_beta/compile.cc: New.
	* testsuite/special_functions/03_beta/compile_2.cc: New.
	* testsuite/special_functions/04_comp_ellint_1/check_nan.cc: New.
	* testsuite/special_functions/04_comp_ellint_1/check_value.cc: New.
	* testsuite/special_functions/04_comp_ellint_1/compile.cc: New.
	* testsuite/special_functions/04_comp_ellint_1/compile_2.cc: New.
	* testsuite/special_functions/05_comp_ellint_2/check_nan.cc: New.
	* testsuite/special_functions/05_comp_ellint_2/check_value.cc: New.
	* testsuite/special_functions/05_comp_ellint_2/compile.cc: New.
	* testsuite/special_functions/05_comp_ellint_2/compile_2.cc: New.
	* testsuite/special_functions/06_comp_ellint_3/check_nan.cc: New.
	* testsuite/special_functions/06_comp_ellint_3/check_value.cc: New.
	* testsuite/special_functions/06_comp_ellint_3/compile.cc: New.
	* testsuite/special_functions/06_comp_ellint_3/compile_2.cc: New.
	* testsuite/special_functions/07_cyl_bessel_i/check_nan.cc: New.
	* testsuite/special_functions/07_cyl_bessel_i/check_value.cc: New.
	* testsuite/special_functions/07_cyl_bessel_i/compile.cc: New.
	* testsuite/special_functions/07_cyl_bessel_i/compile_2.cc: New.
	* testsuite/special_functions/07_cyl_bessel_i/pr56216.cc: New.
	* testsuite/special_functions/08_cyl_bessel_j/check_nan.cc: New.
	* testsuite/special_functions/08_cyl_bessel_j/check_value.cc: New.
	* testsuite/special_functions/08_cyl_bessel_j/compile.cc: New.
	* testsuite/special_functions/08_cyl_bessel_j/compile_2.cc: New.
	* testsuite/special_functions/09_cyl_bessel_k/check_nan.cc: New.
	* testsuite/special_functions/09_cyl_bessel_k/check_value.cc: New.
	* testsuite/special_functions/09_cyl_bessel_k/compile.cc: New.
	* testsuite/special_functions/09_cyl_bessel_k/compile_2.cc: New.
	* testsuite/special_functions/10_cyl_neumann/check_nan.cc: New.
	* testsuite/special_functions/10_cyl_neumann/check_value.cc: New.
	* testsuite/special_functions/10_cyl_neumann/compile.cc: New.
	* testsuite/special_functions/10_cyl_neumann/compile_2.cc: New.
	* testsuite/special_functions/11_ellint_1/check_nan.cc: New.
	* testsuite/special_functions/11_ellint_1/check_value.cc: New.
	* testsuite/special_functions/11_ellint_1/compile.cc: New.
	* testsuite/special_functions/11_ellint_1/compile_2.cc: New.
	* testsuite/special_functions/12_ellint_2/check_nan.cc: New.
	* testsuite/special_functions/12_ellint_2/check_value.cc: New.
	* testsuite/special_functions/12_ellint_2/compile.cc: New.
	* testsuite/special_functions/12_ellint_2/compile_2.cc: New.
	* testsuite/special_functions/13_ellint_3/check_nan.cc: New.
	* testsuite/special_functions/13_ellint_3/check_value.cc: New.
	* testsuite/special_functions/13_ellint_3/compile.cc: New.
	* testsuite/special_functions/13_ellint_3/compile_2.cc: New.
	* testsuite/special_functions/14_expint/check_nan.cc: New.
	* testsuite/special_functions/14_expint/check_value.cc: New.
	* testsuite/special_functions/14_expint/compile.cc: New.
	* testsuite/special_functions/14_expint/compile_2.cc: New.
	* testsuite/special_functions/15_hermite/check_nan.cc: New.
	* testsuite/special_functions/15_hermite/check_value.cc: New.
	* testsuite/special_functions/15_hermite/compile.cc: New.
	* testsuite/special_functions/15_hermite/compile_2.cc: New.
	* testsuite/special_functions/16_laguerre/check_nan.cc: New.
	* testsuite/special_functions/16_laguerre/check_value.cc: New.
	* testsuite/special_functions/16_laguerre/compile.cc: New.
	* testsuite/special_functions/16_laguerre/compile_2.cc: New.
	* testsuite/special_functions/17_legendre/check_nan.cc: New.
	* testsuite/special_functions/17_legendre/check_value.cc: New.
	* testsuite/special_functions/17_legendre/compile.cc: New.
	* testsuite/special_functions/17_legendre/compile_2.cc: New.
	* testsuite/special_functions/18_riemann_zeta/check_nan.cc: New.
	* testsuite/special_functions/18_riemann_zeta/check_value.cc: New.
	* testsuite/special_functions/18_riemann_zeta/compile.cc: New.
	* testsuite/special_functions/18_riemann_zeta/compile_2.cc: New.
	* testsuite/special_functions/19_sph_bessel/check_nan.cc: New.
	* testsuite/special_functions/19_sph_bessel/check_value.cc: New.
	* testsuite/special_functions/19_sph_bessel/compile.cc: New.
	* testsuite/special_functions/19_sph_bessel/compile_2.cc: New.
	* testsuite/special_functions/20_sph_legendre/check_nan.cc: New.
	* testsuite/special_functions/20_sph_legendre/check_value.cc: New.
	* testsuite/special_functions/20_sph_legendre/compile.cc: New.
	* testsuite/special_functions/20_sph_legendre/compile_2.cc: New.
	* testsuite/special_functions/21_sph_neumann/check_nan.cc: New.
	* testsuite/special_functions/21_sph_neumann/check_value.cc: New.
	* testsuite/special_functions/21_sph_neumann/compile.cc: New.
	* testsuite/special_functions/21_sph_neumann/compile_2.cc: New.
	* testsuite/util/specfun_testcase.h: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/08_cyl_bessel_i/check_value.cc: More testcases.
	* testsuite/tr1/5_numerical_facilities/special_functions/09_cyl_bessel_j/check_value.cc: Ditto.
	* testsuite/tr1/5_numerical_facilities/special_functions/10_cyl_bessel_k/check_value.cc: Ditto.
	* testsuite/tr1/5_numerical_facilities/special_functions/11_cyl_neumann/check_value.cc: Ditto.
	* testsuite/tr1/5_numerical_facilities/special_functions/21_sph_bessel/check_value.cc: Ditto.
	* testsuite/tr1/5_numerical_facilities/special_functions/23_sph_neumann/check_value.cc: Ditto.
	* testsuite/tr1/5_numerical_facilities/special_functions/16_hermite/check_value.cc: New.


Co-Authored-By: Florian Goth <CaptainSifff@gmx.de>
Co-Authored-By: Jonathan Wakely <jwakely@redhat.com>

From-SVN: r232377

4 files changed, 462 insertions, 0 deletions

diff --git a/libstdc++-v3/testsuite/special_functions/17_legendre/check_nan.cc b/libstdc++-v3/testsuite/special_functions/17_legendre/check_nan.cc
new file mode 100644
index 00000000000..98a9a30741c
--- /dev/null
+++ b/libstdc++-v3/testsuite/special_functions/17_legendre/check_nan.cc
@@ -0,0 +1,59 @@
+// { dg-require-c-std "" }
+// { dg-add-options ieee }
+// { dg-options "-D__STDCPP_WANT_MATH_SPEC_FUNCS__" }
+
+// Copyright (C) 2016 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/>.
+
+// 8.1.17 legendre
+
+#include <cmath>
+#include <testsuite_hooks.h>
+
+void
+test01()
+{
+
+  float xf = std::numeric_limits<float>::quiet_NaN();
+  double xd = std::numeric_limits<double>::quiet_NaN();
+  long double xl = std::numeric_limits<long double>::quiet_NaN();
+
+  unsigned int l = 2;
+
+  float a = std::legendre(l, xf);
+  float b = std::legendref(l, xf);
+  double c = std::legendre(l, xd);
+  long double d = std::legendre(l, xl);
+  long double e = std::legendrel(l, xl);
+
+  bool test [[gnu::unused]] = true;
+  VERIFY(std::isnan(a));
+  VERIFY(std::isnan(b));
+  VERIFY(std::isnan(c));
+  VERIFY(std::isnan(d));
+  VERIFY(std::isnan(e));
+
+  return;
+}
+
+int
+main()
+{
+  test01();
+  return 0;
+}
+
diff --git a/libstdc++-v3/testsuite/special_functions/17_legendre/check_value.cc b/libstdc++-v3/testsuite/special_functions/17_legendre/check_value.cc
new file mode 100644
index 00000000000..58944783928
--- /dev/null
+++ b/libstdc++-v3/testsuite/special_functions/17_legendre/check_value.cc
@@ -0,0 +1,319 @@
+// { dg-options "-D__STDCPP_WANT_MATH_SPEC_FUNCS__" }
+//
+// Copyright (C) 2016 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/>.
+
+//  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 <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.
+// max(|f - f_GSL|): 0.0000000000000000
+// max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
+const testcase_legendre<double>
+data001[21] =
+{
+  { 1.0000000000000000, 0, -1.0000000000000000 },
+  { 1.0000000000000000, 0, -0.90000000000000002 },
+  { 1.0000000000000000, 0, -0.80000000000000004 },
+  { 1.0000000000000000, 0, -0.69999999999999996 },
+  { 1.0000000000000000, 0, -0.59999999999999998 },
+  { 1.0000000000000000, 0, -0.50000000000000000 },
+  { 1.0000000000000000, 0, -0.40000000000000002 },
+  { 1.0000000000000000, 0, -0.30000000000000004 },
+  { 1.0000000000000000, 0, -0.19999999999999996 },
+  { 1.0000000000000000, 0, -0.099999999999999978 },
+  { 1.0000000000000000, 0, 0.0000000000000000 },
+  { 1.0000000000000000, 0, 0.10000000000000009 },
+  { 1.0000000000000000, 0, 0.19999999999999996 },
+  { 1.0000000000000000, 0, 0.30000000000000004 },
+  { 1.0000000000000000, 0, 0.39999999999999991 },
+  { 1.0000000000000000, 0, 0.50000000000000000 },
+  { 1.0000000000000000, 0, 0.60000000000000009 },
+  { 1.0000000000000000, 0, 0.69999999999999996 },
+  { 1.0000000000000000, 0, 0.80000000000000004 },
+  { 1.0000000000000000, 0, 0.89999999999999991 },
+  { 1.0000000000000000, 0, 1.0000000000000000 },
+};
+const double toler001 = 2.5000000000000020e-13;
+
+// Test data for l=1.
+// max(|f - f_GSL|): 0.0000000000000000
+// max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
+const testcase_legendre<double>
+data002[21] =
+{
+  { -1.0000000000000000, 1, -1.0000000000000000 },
+  { -0.90000000000000002, 1, -0.90000000000000002 },
+  { -0.80000000000000004, 1, -0.80000000000000004 },
+  { -0.69999999999999996, 1, -0.69999999999999996 },
+  { -0.59999999999999998, 1, -0.59999999999999998 },
+  { -0.50000000000000000, 1, -0.50000000000000000 },
+  { -0.40000000000000002, 1, -0.40000000000000002 },
+  { -0.30000000000000004, 1, -0.30000000000000004 },
+  { -0.19999999999999996, 1, -0.19999999999999996 },
+  { -0.099999999999999978, 1, -0.099999999999999978 },
+  { 0.0000000000000000, 1, 0.0000000000000000 },
+  { 0.10000000000000009, 1, 0.10000000000000009 },
+  { 0.19999999999999996, 1, 0.19999999999999996 },
+  { 0.30000000000000004, 1, 0.30000000000000004 },
+  { 0.39999999999999991, 1, 0.39999999999999991 },
+  { 0.50000000000000000, 1, 0.50000000000000000 },
+  { 0.60000000000000009, 1, 0.60000000000000009 },
+  { 0.69999999999999996, 1, 0.69999999999999996 },
+  { 0.80000000000000004, 1, 0.80000000000000004 },
+  { 0.89999999999999991, 1, 0.89999999999999991 },
+  { 1.0000000000000000, 1, 1.0000000000000000 },
+};
+const double toler002 = 2.5000000000000020e-13;
+
+// Test data for l=2.
+// max(|f - f_GSL|): 1.1102230246251565e-16
+// max(|f - f_GSL| / |f_GSL|): 1.3877787807814482e-15
+const testcase_legendre<double>
+data003[21] =
+{
+  { 1.0000000000000000, 2, -1.0000000000000000 },
+  { 0.71500000000000008, 2, -0.90000000000000002 },
+  { 0.46000000000000019, 2, -0.80000000000000004 },
+  { 0.23499999999999988, 2, -0.69999999999999996 },
+  { 0.039999999999999925, 2, -0.59999999999999998 },
+  { -0.12500000000000000, 2, -0.50000000000000000 },
+  { -0.25999999999999995, 2, -0.40000000000000002 },
+  { -0.36499999999999999, 2, -0.30000000000000004 },
+  { -0.44000000000000006, 2, -0.19999999999999996 },
+  { -0.48499999999999999, 2, -0.099999999999999978 },
+  { -0.50000000000000000, 2, 0.0000000000000000 },
+  { -0.48499999999999999, 2, 0.10000000000000009 },
+  { -0.44000000000000006, 2, 0.19999999999999996 },
+  { -0.36499999999999999, 2, 0.30000000000000004 },
+  { -0.26000000000000012, 2, 0.39999999999999991 },
+  { -0.12500000000000000, 2, 0.50000000000000000 },
+  { 0.040000000000000147, 2, 0.60000000000000009 },
+  { 0.23499999999999988, 2, 0.69999999999999996 },
+  { 0.46000000000000019, 2, 0.80000000000000004 },
+  { 0.71499999999999986, 2, 0.89999999999999991 },
+  { 1.0000000000000000, 2, 1.0000000000000000 },
+};
+const double toler003 = 2.5000000000000020e-13;
+
+// Test data for l=5.
+// max(|f - f_GSL|): 2.0122792321330962e-16
+// max(|f - f_GSL| / |f_GSL|): 4.8911475274404243e-15
+const testcase_legendre<double>
+data004[21] =
+{
+  { -1.0000000000000000, 5, -1.0000000000000000 },
+  { 0.041141250000000087, 5, -0.90000000000000002 },
+  { 0.39951999999999993, 5, -0.80000000000000004 },
+  { 0.36519874999999991, 5, -0.69999999999999996 },
+  { 0.15263999999999994, 5, -0.59999999999999998 },
+  { -0.089843750000000000, 5, -0.50000000000000000 },
+  { -0.27063999999999994, 5, -0.40000000000000002 },
+  { -0.34538625000000001, 5, -0.30000000000000004 },
+  { -0.30751999999999996, 5, -0.19999999999999996 },
+  { -0.17882874999999995, 5, -0.099999999999999978 },
+  { 0.0000000000000000, 5, 0.0000000000000000 },
+  { 0.17882875000000015, 5, 0.10000000000000009 },
+  { 0.30751999999999996, 5, 0.19999999999999996 },
+  { 0.34538625000000001, 5, 0.30000000000000004 },
+  { 0.27064000000000010, 5, 0.39999999999999991 },
+  { 0.089843750000000000, 5, 0.50000000000000000 },
+  { -0.15264000000000016, 5, 0.60000000000000009 },
+  { -0.36519874999999991, 5, 0.69999999999999996 },
+  { -0.39951999999999993, 5, 0.80000000000000004 },
+  { -0.041141250000000261, 5, 0.89999999999999991 },
+  { 1.0000000000000000, 5, 1.0000000000000000 },
+};
+const double toler004 = 2.5000000000000020e-13;
+
+// Test data for l=10.
+// max(|f - f_GSL|): 2.7755575615628914e-16
+// max(|f - f_GSL| / |f_GSL|): 1.0547610802636413e-15
+const testcase_legendre<double>
+data005[21] =
+{
+  { 1.0000000000000000, 10, -1.0000000000000000 },
+  { -0.26314561785585960, 10, -0.90000000000000002 },
+  { 0.30052979560000004, 10, -0.80000000000000004 },
+  { 0.085805795531640333, 10, -0.69999999999999996 },
+  { -0.24366274560000001, 10, -0.59999999999999998 },
+  { -0.18822860717773438, 10, -0.50000000000000000 },
+  { 0.096839064399999925, 10, -0.40000000000000002 },
+  { 0.25147634951601561, 10, -0.30000000000000004 },
+  { 0.12907202559999983, 10, -0.19999999999999996 },
+  { -0.12212499738710943, 10, -0.099999999999999978 },
+  { -0.24609375000000000, 10, 0.0000000000000000 },
+  { -0.12212499738710922, 10, 0.10000000000000009 },
+  { 0.12907202559999983, 10, 0.19999999999999996 },
+  { 0.25147634951601561, 10, 0.30000000000000004 },
+  { 0.096839064400000258, 10, 0.39999999999999991 },
+  { -0.18822860717773438, 10, 0.50000000000000000 },
+  { -0.24366274559999984, 10, 0.60000000000000009 },
+  { 0.085805795531640333, 10, 0.69999999999999996 },
+  { 0.30052979560000004, 10, 0.80000000000000004 },
+  { -0.26314561785585899, 10, 0.89999999999999991 },
+  { 1.0000000000000000, 10, 1.0000000000000000 },
+};
+const double toler005 = 2.5000000000000020e-13;
+
+// Test data for l=20.
+// max(|f - f_GSL|): 3.3306690738754696e-16
+// max(|f - f_GSL| / |f_GSL|): 2.2307336678138069e-15
+const testcase_legendre<double>
+data006[21] =
+{
+  { 1.0000000000000000, 20, -1.0000000000000000 },
+  { -0.14930823530984835, 20, -0.90000000000000002 },
+  { 0.22420460541741347, 20, -0.80000000000000004 },
+  { -0.20457394463834172, 20, -0.69999999999999996 },
+  { 0.15916752910098109, 20, -0.59999999999999998 },
+  { -0.048358381067373557, 20, -0.50000000000000000 },
+  { -0.10159261558628156, 20, -0.40000000000000002 },
+  { 0.18028715947998042, 20, -0.30000000000000004 },
+  { -0.098042194344594796, 20, -0.19999999999999996 },
+  { -0.082077130944527663, 20, -0.099999999999999978 },
+  { 0.17619705200195312, 20, 0.0000000000000000 },
+  { -0.082077130944528023, 20, 0.10000000000000009 },
+  { -0.098042194344594796, 20, 0.19999999999999996 },
+  { 0.18028715947998042, 20, 0.30000000000000004 },
+  { -0.10159261558628112, 20, 0.39999999999999991 },
+  { -0.048358381067373557, 20, 0.50000000000000000 },
+  { 0.15916752910098075, 20, 0.60000000000000009 },
+  { -0.20457394463834172, 20, 0.69999999999999996 },
+  { 0.22420460541741347, 20, 0.80000000000000004 },
+  { -0.14930823530984924, 20, 0.89999999999999991 },
+  { 1.0000000000000000, 20, 1.0000000000000000 },
+};
+const double toler006 = 2.5000000000000020e-13;
+
+// Test data for l=50.
+// max(|f - f_GSL|): 3.6082248300317588e-16
+// max(|f - f_GSL| / |f_GSL|): 2.1700196856209138e-15
+const testcase_legendre<double>
+data007[21] =
+{
+  { 1.0000000000000000, 50, -1.0000000000000000 },
+  { -0.17003765994383671, 50, -0.90000000000000002 },
+  { 0.13879737345093113, 50, -0.80000000000000004 },
+  { -0.014572731645892852, 50, -0.69999999999999996 },
+  { -0.058860798844002096, 50, -0.59999999999999998 },
+  { -0.031059099239609811, 50, -0.50000000000000000 },
+  { 0.041569033381825375, 50, -0.40000000000000002 },
+  { 0.10911051574714797, 50, -0.30000000000000004 },
+  { 0.083432272204197494, 50, -0.19999999999999996 },
+  { -0.038205812661313600, 50, -0.099999999999999978 },
+  { -0.11227517265921705, 50, 0.0000000000000000 },
+  { -0.038205812661314155, 50, 0.10000000000000009 },
+  { 0.083432272204197494, 50, 0.19999999999999996 },
+  { 0.10911051574714797, 50, 0.30000000000000004 },
+  { 0.041569033381824674, 50, 0.39999999999999991 },
+  { -0.031059099239609811, 50, 0.50000000000000000 },
+  { -0.058860798844001430, 50, 0.60000000000000009 },
+  { -0.014572731645892852, 50, 0.69999999999999996 },
+  { 0.13879737345093113, 50, 0.80000000000000004 },
+  { -0.17003765994383657, 50, 0.89999999999999991 },
+  { 1.0000000000000000, 50, 1.0000000000000000 },
+};
+const double toler007 = 2.5000000000000020e-13;
+
+// Test data for l=100.
+// max(|f - f_GSL|): 3.4694469519536142e-16
+// max(|f - f_GSL| / |f_GSL|): 6.8214063779431592e-15
+const testcase_legendre<double>
+data008[21] =
+{
+  { 1.0000000000000000, 100, -1.0000000000000000 },
+  { 0.10226582055871893, 100, -0.90000000000000002 },
+  { 0.050861167913584228, 100, -0.80000000000000004 },
+  { -0.077132507199778641, 100, -0.69999999999999996 },
+  { -0.023747023905133141, 100, -0.59999999999999998 },
+  { -0.060518025961861198, 100, -0.50000000000000000 },
+  { -0.072258202125684470, 100, -0.40000000000000002 },
+  { 0.057127392202801566, 100, -0.30000000000000004 },
+  { 0.014681835355659706, 100, -0.19999999999999996 },
+  { -0.063895098434750205, 100, -0.099999999999999978 },
+  { 0.079589237387178727, 100, 0.0000000000000000 },
+  { -0.063895098434749761, 100, 0.10000000000000009 },
+  { 0.014681835355659706, 100, 0.19999999999999996 },
+  { 0.057127392202801566, 100, 0.30000000000000004 },
+  { -0.072258202125685025, 100, 0.39999999999999991 },
+  { -0.060518025961861198, 100, 0.50000000000000000 },
+  { -0.023747023905134217, 100, 0.60000000000000009 },
+  { -0.077132507199778641, 100, 0.69999999999999996 },
+  { 0.050861167913584228, 100, 0.80000000000000004 },
+  { 0.10226582055871711, 100, 0.89999999999999991 },
+  { 1.0000000000000000, 100, 1.0000000000000000 },
+};
+const double toler008 = 5.0000000000000039e-13;
+
+template<typename Tp, unsigned int Num>
+  void
+  test(const testcase_legendre<Tp> (&data)[Num], Tp toler)
+  {
+    bool test __attribute__((unused)) = true;
+    const Tp eps = std::numeric_limits<Tp>::epsilon();
+    Tp max_abs_diff = -Tp(1);
+    Tp max_abs_frac = -Tp(1);
+    unsigned int num_datum = Num;
+    for (unsigned int i = 0; i < num_datum; ++i)
+      {
+	const Tp f = std::legendre(data[i].l, data[i].x);
+	const Tp f0 = data[i].f0;
+	const Tp diff = f - f0;
+	if (std::abs(diff) > max_abs_diff)
+	  max_abs_diff = std::abs(diff);
+	if (std::abs(f0) > Tp(10) * eps
+	 && std::abs(f) > Tp(10) * eps)
+	  {
+	    const Tp 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);
+  return 0;
+}
diff --git a/libstdc++-v3/testsuite/special_functions/17_legendre/compile.cc b/libstdc++-v3/testsuite/special_functions/17_legendre/compile.cc
new file mode 100644
index 00000000000..820293a1ba1
--- /dev/null
+++ b/libstdc++-v3/testsuite/special_functions/17_legendre/compile.cc
@@ -0,0 +1,42 @@
+// { dg-do compile }
+// { dg-options "-D__STDCPP_WANT_MATH_SPEC_FUNCS__" }
+
+// Copyright (C) 2016 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/>.
+
+// 8.1.17 legendre
+
+#include <cmath>
+
+void
+test01()
+{
+  float xf = 0.5F;
+  double xd = 0.5;
+  long double xl = 0.5L;
+
+  unsigned int l = 2;
+
+  std::legendre(l, xf);
+  std::legendref(l, xf);
+  std::legendre(l, xd);
+  std::legendre(l, xl);
+  std::legendrel(l, xl);
+
+  return;
+}
+
diff --git a/libstdc++-v3/testsuite/special_functions/17_legendre/compile_2.cc b/libstdc++-v3/testsuite/special_functions/17_legendre/compile_2.cc
new file mode 100644
index 00000000000..4c69f9ae07a
--- /dev/null
+++ b/libstdc++-v3/testsuite/special_functions/17_legendre/compile_2.cc
@@ -0,0 +1,42 @@
+// { dg-do compile { xfail *-*-* } }
+// { dg-excess-errors "" }
+// { dg-options "-D__STDCPP_WANT_MATH_SPEC_FUNCS__" }
+
+// Copyright (C) 2016 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/>.
+
+// 8.1.17 legendre
+
+#include <math.h>
+
+void
+test01()
+{
+  float xf = 0.5F;
+  double xd = 0.5;
+  long double xl = 0.5L;
+  unsigned int l = 2;
+
+  legendre(l, xf);
+  legendref(l, xf);
+  legendre(l, xd);
+  legendre(l, xl);
+  legendrel(l, xl);
+
+  return;
+}
+