2007-03-16 Benjamin Kosnik <bkoz@redhat.com>

	
	* testsuite/lib/dg-options.exp (dg-require-c-std): New.
	* testsuite/lib/libstdc++.exp (check_v3_target_c_std): New. Check to
	see if _GLIBCXX_USE_C99_MATH is active. 
	* testsuite/tr1/5_numerical_facilities/special_functions/
	08_cyl_bessel_i/check_nan.cc: Use dg-require-c-std.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	17_hyperg/check_nan.cc: Same.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	13_ellint_2/check_nan.cc: Same.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	20_riemann_zeta/check_nan.cc: Same.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	01_assoc_laguerre/check_nan.cc: Same.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	02_assoc_legendre/check_nan.cc: Same.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	22_sph_legendre/check_nan.cc: Same.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	10_cyl_bessel_k/check_nan.cc: Same.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	09_cyl_bessel_j/check_nan.cc: Same.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	21_sph_bessel/check_nan.cc: Same.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	07_conf_hyperg/check_nan.cc: Same.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	16_hermite/check_nan.cc: Same.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	12_ellint_1/check_nan.cc: Same.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	05_comp_ellint_2/check_nan.cc: Same.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	18_laguerre/check_nan.cc: Same.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	14_ellint_3/check_nan.cc: Same.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	04_comp_ellint_1/check_nan.cc: Same.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	06_comp_ellint_3/check_nan.cc: Same.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	19_legendre/check_nan.cc: Same.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	03_beta/check_nan.cc: Same.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	11_cyl_neumann/check_nan.cc: Same.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	15_expint/check_nan.cc: Same.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	23_sph_neumann/check_nan.cc: Same.

	* include/tr1/poly_laguerre.tcc (__poly_laguerre): Don't check if
	unsigned int can be a NaN.

2007-03-16  Edward M. Smith-Rowland  <3dw4rd@verizon.net>

	* docs/html/ext/tr1.html : Marked tr1 math special functions done.
	* docs/html/faq/index.html : Ditto.
	* include/Makefile.in : Added new special function header files.
	* include/Makefile.am : Ditto.	
	* include/tr1/common.h : Added type promotion routines for three
	and four args.

	* include/tr1/special_function_util.h: New.
	* include/tr1/bessel_function.tcc: New.
	* include/tr1/beta_function.tcc: New.
	* include/tr1/ell_integral.tcc: New.
	* include/tr1/exp_integral.tcc: New.
	* include/tr1/gamma.tcc: New.
	* include/tr1/hypergeometric.tcc: New.
	* include/tr1/legendre_function.tcc: New.
	* include/tr1/modified_bessel_func.tcc: New.
	* include/tr1/poly_hermite.tcc: New.
	* include/tr1/poly_laguerre.tcc: New.
	* include/tr1/riemann_zeta.tcc: New.
	* include/tr1/cmath : Included tr1 math special functions.
	* include/tr1/math.h : Ditto.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	testcase.h: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	01_assoc_laguerre/compile.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	01_assoc_laguerre/check_nan.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	01_assoc_laguerre/check_value.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	01_assoc_laguerre/compile_2.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	02_assoc_legendre/compile.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	02_assoc_legendre/check_nan.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	02_assoc_legendre/check_value.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	02_assoc_legendre/compile_2.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/03_beta/
	compile.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/03_beta/
	check_nan.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/03_beta/
	check_value.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/03_beta/
	compile_2.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	04_comp_ellint_1/compile.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	04_comp_ellint_1/check_nan.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	04_comp_ellint_1/check_value.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	04_comp_ellint_1/compile_2.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	05_comp_ellint_2/compile.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	05_comp_ellint_2/check_nan.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	05_comp_ellint_2/check_value.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	05_comp_ellint_2/compile_2.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	06_comp_ellint_3/compile.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	06_comp_ellint_3/check_nan.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	06_comp_ellint_3/check_value.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	06_comp_ellint_3/compile_2.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	07_conf_hyperg/compile.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	07_conf_hyperg/check_nan.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	07_conf_hyperg/check_value.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	07_conf_hyperg/compile_2.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	08_cyl_bessel_i/compile.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	08_cyl_bessel_i/check_nan.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	08_cyl_bessel_i/check_value.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	08_cyl_bessel_i/compile_2.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	09_cyl_bessel_j/compile.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	09_cyl_bessel_j/check_nan.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	09_cyl_bessel_j/check_value.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	09_cyl_bessel_j/compile_2.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	10_cyl_bessel_k/compile.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	10_cyl_bessel_k/check_nan.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	10_cyl_bessel_k/check_value.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	10_cyl_bessel_k/compile_2.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	11_cyl_neumann/compile.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	11_cyl_neumann/check_nan.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	11_cyl_neumann/check_value.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	11_cyl_neumann/compile_2.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/12_ellint_1/
	compile.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/12_ellint_1/
	check_nan.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/12_ellint_1/
	check_value.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/12_ellint_1/
	compile_2.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/13_ellint_2/
	compile.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/13_ellint_2/
	check_nan.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/13_ellint_2/
	check_value.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/13_ellint_2/
	compile_2.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/14_ellint_3/
	compile.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/14_ellint_3/
	check_nan.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/14_ellint_3/
	check_value.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/14_ellint_3/
	compile_2.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/15_expint/
	check_value_neg.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/15_expint/
	compile.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/15_expint/
	check_nan.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/15_expint/
	compile_2.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/15_expint/
	check_value_pos.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/16_hermite/
	compile.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/16_hermite/
	check_nan.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/16_hermite/
	compile_2.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/17_hyperg/
	compile.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/17_hyperg/
	check_nan.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/17_hyperg/
	check_value.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/17_hyperg/
	compile_2.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/18_laguerre/
	compile.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/18_laguerre/
	check_nan.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/18_laguerre/
	check_value.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/18_laguerre/
	compile_2.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/19_legendre/
	compile.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/19_legendre/
	check_nan.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/19_legendre/
	check_value.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/19_legendre/
	compile_2.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	20_riemann_zeta/check_value_neg.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	20_riemann_zeta/compile.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	20_riemann_zeta/check_nan.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	20_riemann_zeta/compile_2.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	20_riemann_zeta/check_value_pos.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	21_sph_bessel/compile.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	21_sph_bessel/check_nan.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	21_sph_bessel/check_value.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	21_sph_bessel/compile_2.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	22_sph_legendre/compile.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	22_sph_legendre/check_nan.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	22_sph_legendre/check_value.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	22_sph_legendre/compile_2.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	23_sph_neumann/compile.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	23_sph_neumann/check_nan.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	23_sph_neumann/check_value.cc: New.
	* testsuite/tr1/5_numerical_facilities/special_functions/
	23_sph_neumann/ compile_2.cc: New.
	


git-svn-id: svn+ssh://gcc.gnu.org/svn/gcc/trunk@122986 138bc75d-0d04-0410-961f-82ee72b054a4

1 files changed, 342 insertions, 0 deletions

diff --git a/libstdc++-v3/include/tr1/poly_laguerre.tcc b/libstdc++-v3/include/tr1/poly_laguerre.tcc
new file mode 100644
index 00000000000..5200cab79c0
--- /dev/null
+++ b/libstdc++-v3/include/tr1/poly_laguerre.tcc
@@ -0,0 +1,342 @@
+// Special functions -*- C++ -*-
+
+// Copyright (C) 2006-2007
+// 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 2, 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 COPYING.  If not, write to the Free
+// Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301,
+// USA.
+//
+// As a special exception, you may use this file as part of a free software
+// library without restriction.  Specifically, if other files instantiate
+// templates or use macros or inline functions from this file, or you compile
+// this file and link it with other files to produce an executable, this
+// file does not by itself cause the resulting executable to be covered by
+// the GNU General Public License.  This exception does not however
+// invalidate any other reasons why the executable file might be covered by
+// the GNU General Public License.
+
+/** @file tr1/poly_laguerre.tcc
+ *  This is an internal header file, included by other library headers.
+ *  You should not attempt to use it directly.
+ */
+
+//
+// ISO C++ 14882 TR1: 5.2  Special functions
+//
+
+// Written by Edward Smith-Rowland based on:
+//   (1) Handbook of Mathematical Functions,
+//       Ed. Milton Abramowitz and Irene A. Stegun,
+//       Dover Publications,
+//       Section 13, pp. 509-510, Section 22 pp. 773-802
+//   (2) The Gnu Scientific Library, http://www.gnu.org/software/gsl
+
+#ifndef _TR1_POLY_LAGUERRE_TCC
+#define _TR1_POLY_LAGUERRE_TCC 1
+
+namespace std
+{
+_GLIBCXX_BEGIN_NAMESPACE(_GLIBCXX_TR1)
+
+  // [5.2] Special functions
+
+  /**
+   * @ingroup tr1_math_spec_func
+   * @{
+   */
+
+  //
+  // Implementation-space details.
+  //
+  namespace __detail
+  {
+
+
+    /**
+     *   @brief This routine returns the associated Laguerre polynomial 
+     *          of order @f$ n @f$, degree @f$ \alpha @f$ for large n.
+     *   Abramowitz & Stegun, 13.5.21
+     *
+     *   @param __n The order of the Laguerre function.
+     *   @param __alpha The degree of the Laguerre function.
+     *   @param __x The argument of the Laguerre function.
+     *   @return The value of the Laguerre function of order n,
+     *           degree @f$ \alpha @f$, and argument x.
+     *
+     *  This is from the GNU Scientific Library.
+     */
+    template<typename _Tpa, typename _Tp>
+    _Tp
+    __poly_laguerre_large_n(const unsigned __n, const _Tpa __alpha,
+                            const _Tp __x)
+    {
+      const _Tp __a = -_Tp(__n);
+      const _Tp __b = _Tp(__alpha) + _Tp(1);
+      const _Tp __eta = _Tp(2) * __b - _Tp(4) * __a;
+      const _Tp __cos2th = __x / __eta;
+      const _Tp __sin2th = _Tp(1) - __cos2th;
+      const _Tp __th = std::acos(std::sqrt(__cos2th));
+      const _Tp __pre_h = __numeric_constants<_Tp>::__pi_2()
+                        * __numeric_constants<_Tp>::__pi_2()
+                        * __eta * __eta * __cos2th * __sin2th;
+
+#if _GLIBCXX_USE_C99_MATH_TR1
+      const _Tp __lg_b = std::_GLIBCXX_TR1::lgamma(_Tp(__n) + __b);
+      const _Tp __lnfact = std::_GLIBCXX_TR1::lgamma(_Tp(__n + 1));
+#else
+      const _Tp __lg_b = __log_gamma(_Tp(__n) + __b);
+      const _Tp __lnfact = __log_gamma(_Tp(__n + 1));
+#endif
+
+      _Tp __pre_term1 = _Tp(0.5L) * (_Tp(1) - __b)
+                      * std::log(_Tp(0.25L) * __x * __eta);
+      _Tp __pre_term2 = _Tp(0.25L) * std::log(__pre_h);
+      _Tp __lnpre = __lg_b - __lnfact + _Tp(0.5L) * __x
+                      + __pre_term1 - __pre_term2;
+      _Tp __ser_term1 = std::sin(__a * __numeric_constants<_Tp>::__pi());
+      _Tp __ser_term2 = std::sin(_Tp(0.25L) * __eta
+                              * (_Tp(2) * __th
+                               - std::sin(_Tp(2) * __th))
+                               + __numeric_constants<_Tp>::__pi_4());
+      _Tp __ser = __ser_term1 + __ser_term2;
+
+      return std::exp(__lnpre) * __ser;
+    }
+
+
+    /**
+     *  @brief  Evaluate the polynomial based on the confluent hypergeometric
+     *          function in a safe way, with no restriction on the arguments.
+     *
+     *   The associated Laguerre function is defined by
+     *   @f[
+     *       L_n^\alpha(x) = \frac{(\alpha + 1)_n}{n!}
+     *                       _1F_1(-n; \alpha + 1; x)
+     *   @f]
+     *   where @f$ (\alpha)_n @f$ is the Pochhammer symbol and
+     *   @f$ _1F_1(a; c; x) @f$ is the confluent hypergeometric function.
+     *
+     *  This function assumes x != 0.
+     *
+     *  This is from the GNU Scientific Library.
+     */
+    template<typename _Tpa, typename _Tp>
+    _Tp
+    __poly_laguerre_hyperg(const unsigned int __n, const _Tpa __alpha, const _Tp __x)
+    {
+      const _Tp __b = _Tp(__alpha) + _Tp(1);
+      const _Tp __mx = -__x;
+      const _Tp __tc_sgn = (__x < _Tp(0) ? _Tp(1)
+                         : ((__n % 2 == 1) ? -_Tp(1) : _Tp(1)));
+      //  Get |x|^n/n!
+      _Tp __tc = _Tp(1);
+      const _Tp __ax = std::abs(__x);
+      for (unsigned int __k = 1; __k <= __n; ++__k)
+        __tc *= (__ax / __k);
+
+      _Tp __term = __tc * __tc_sgn;
+      _Tp __sum = __term;
+      for (int __k = int(__n) - 1; __k >= 0; --__k)
+        {
+          __term *= ((__b + _Tp(__k)) / _Tp(int(__n) - __k))
+                  * _Tp(__k + 1) / __mx;
+          __sum += __term;
+        }
+
+      return __sum;
+    }
+
+
+    /**
+     *   @brief This routine returns the associated Laguerre polynomial 
+     *          of order @f$ n @f$, degree @f$ \alpha @f$: @f$ L_n^\alpha(x) @f$
+     *          by recursion.
+     *
+     *   The associated Laguerre function is defined by
+     *   @f[
+     *       L_n^\alpha(x) = \frac{(\alpha + 1)_n}{n!}
+     *                       _1F_1(-n; \alpha + 1; x)
+     *   @f]
+     *   where @f$ (\alpha)_n @f$ is the Pochhammer symbol and
+     *   @f$ _1F_1(a; c; x) @f$ is the confluent hypergeometric function.
+     *
+     *   The associated Laguerre polynomial is defined for integral
+     *   @f$ \alpha = m @f$ by:
+     *   @f[
+     *       L_n^m(x) = (-1)^m \frac{d^m}{dx^m} L_{n + m}(x)
+     *   @f]
+     *   where the Laguerre polynomial is defined by:
+     *   @f[
+     *       L_n(x) = \frac{e^x}{n!} \frac{d^n}{dx^n} (x^ne^{-x})
+     *   @f]
+     *
+     *   @param __n The order of the Laguerre function.
+     *   @param __alpha The degree of the Laguerre function.
+     *   @param __x The argument of the Laguerre function.
+     *   @return The value of the Laguerre function of order n,
+     *           degree @f$ \alpha @f$, and argument x.
+     */
+    template<typename _Tpa, typename _Tp>
+    _Tp
+    __poly_laguerre_recursion(const unsigned int __n,
+                              const _Tpa __alpha, const _Tp __x)
+    {
+      //   Compute l_0.
+      _Tp __l_0 = _Tp(1);
+      if  (__n == 0)
+        return __l_0;
+
+      //  Compute l_1^alpha.
+      _Tp __l_1 = -__x + _Tp(1) + _Tp(__alpha);
+      if  (__n == 1)
+        return __l_1;
+
+      //  Compute l_n^alpha by recursion on n.
+      _Tp __l_n2 = __l_0;
+      _Tp __l_n1 = __l_1;
+      _Tp __l_n = _Tp(0);
+      for  (unsigned int __nn = 2; __nn <= __n; ++__nn)
+        {
+            __l_n = (_Tp(2 * __nn - 1) + _Tp(__alpha) - __x)
+                  * __l_n1 / _Tp(__nn)
+                  - (_Tp(__nn - 1) + _Tp(__alpha)) * __l_n2 / _Tp(__nn);
+            __l_n2 = __l_n1;
+            __l_n1 = __l_n;
+        }
+
+      return __l_n;
+    }
+
+
+    /**
+     *   @brief This routine returns the associated Laguerre polynomial
+     *          of order n, degree @f$ \alpha @f$: @f$ L_n^alpha(x) @f$.
+     *
+     *   The associated Laguerre function is defined by
+     *   @f[
+     *       L_n^\alpha(x) = \frac{(\alpha + 1)_n}{n!}
+     *                       _1F_1(-n; \alpha + 1; x)
+     *   @f]
+     *   where @f$ (\alpha)_n @f$ is the Pochhammer symbol and
+     *   @f$ _1F_1(a; c; x) @f$ is the confluent hypergeometric function.
+     *
+     *   The associated Laguerre polynomial is defined for integral
+     *   @f$ \alpha = m @f$ by:
+     *   @f[
+     *       L_n^m(x) = (-1)^m \frac{d^m}{dx^m} L_{n + m}(x)
+     *   @f]
+     *   where the Laguerre polynomial is defined by:
+     *   @f[
+     *       L_n(x) = \frac{e^x}{n!} \frac{d^n}{dx^n} (x^ne^{-x})
+     *   @f]
+     *
+     *   @param __n The order of the Laguerre function.
+     *   @param __alpha The degree of the Laguerre function.
+     *   @param __x The argument of the Laguerre function.
+     *   @return The value of the Laguerre function of order n,
+     *           degree @f$ \alpha @f$, and argument x.
+     */
+    template<typename _Tpa, typename _Tp>
+    inline _Tp
+    __poly_laguerre(const unsigned int __n, const _Tpa __alpha,
+                    const _Tp __x)
+    {
+      if (__x < _Tp(0))
+        std::__throw_domain_error(__N("Negative argument "
+                                      "in __poly_laguerre."));
+      //  Return NaN on NaN input.
+      else if (__isnan(__x))
+        return std::numeric_limits<_Tp>::quiet_NaN();
+      else if (__n == 0)
+        return _Tp(1);
+      else if (__n == 1)
+        return _Tp(1) + _Tp(__alpha) - __x;
+      else if (__x == _Tp(0))
+        {
+          _Tp __prod = _Tp(__alpha) + _Tp(1);
+          for (unsigned int __k = 2; __k <= __n; ++__k)
+            __prod *= (_Tp(__alpha) + _Tp(__k)) / _Tp(__k);
+          return __prod;
+        }
+      else if (__n > 10000000 && _Tp(__alpha) > -_Tp(1)
+            && __x < _Tp(2) * (_Tp(__alpha) + _Tp(1)) + _Tp(4 * __n))
+        return __poly_laguerre_large_n(__n, __alpha, __x);
+      else if (_Tp(__alpha) >= _Tp(0)
+           || (__x > _Tp(0) && _Tp(__alpha) < -_Tp(__n + 1)))
+        return __poly_laguerre_recursion(__n, __alpha, __x);
+      else
+        return __poly_laguerre_hyperg(__n, __alpha, __x);
+    }
+
+
+    /**
+     *   @brief This routine returns the associated Laguerre polynomial
+     *          of order n, degree m: @f$ L_n^m @f$.
+     *
+     *   The associated Laguerre polynomial is defined for integral
+     *   @f$ \alpha = m @f$ by:
+     *   @f[
+     *       L_n^m(x) = (-1)^m \frac{d^m}{dx^m} L_{n + m}(x)
+     *   @f]
+     *   where the Laguerre polynomial is defined by:
+     *   @f[
+     *       L_n(x) = \frac{e^x}{n!} \frac{d^n}{dx^n} (x^ne^{-x})
+     *   @f]
+     *
+     *   @param __n The order of the Laguerre polynomial.
+     *   @param __m The degree of the Laguerre polynomial.
+     *   @param __x The argument of the Laguerre polynomial.
+     *   @return The value of the associated Laguerre polynomial of order n,
+     *           degree m, and argument x.
+     */
+    template<typename _Tp>
+    inline _Tp
+    __assoc_laguerre(const unsigned int __n, const unsigned int __m,
+                     const _Tp __x)
+    {
+      return __poly_laguerre<unsigned int, _Tp>(__n, __m, __x);
+    }
+
+
+    /**
+     *   @brief This routine returns the associated Laguerre polynomial
+     *          of order n: @f$ L_n(x) @f$.
+     *
+     *   The Laguerre polynomial is defined by:
+     *   @f[
+     *       L_n(x) = \frac{e^x}{n!} \frac{d^n}{dx^n} (x^ne^{-x})
+     *   @f]
+     *
+     *   @param __n The order of the Laguerre polynomial.
+     *   @param __x The argument of the Laguerre polynomial.
+     *   @return The value of the Laguerre polynomial of order n
+     *           and argument x.
+     */
+    template<typename _Tp>
+    inline _Tp
+    __laguerre(const unsigned int __n, const _Tp __x)
+    {
+      return __poly_laguerre<unsigned int, _Tp>(__n, 0, __x);
+    }
+
+  } // namespace std::tr1::__detail
+
+  /* @} */ // group tr1_math_spec_func
+
+_GLIBCXX_END_NAMESPACE
+}
+
+#endif // _TR1_POLY_LAGUERRE_TCC