FM / tr1

/usr/include/c++/4.4.4/tr1/

/usr/include/c++/4.4.4/tr1

Name	Size	Mode	Actions
array	1802	0644	edit dl rm
bessel_function.tcc	22103	0644	edit dl rm
beta_function.tcc	5510	0644	edit dl rm
ccomplex	1256	0644	edit dl rm
cctype	1670	0644	edit dl rm
cfenv	1729	0644	edit dl rm
cfloat	1387	0644	edit dl rm
cinttypes	2006	0644	edit dl rm
climits	1467	0644	edit dl rm
cmath	16362	0644	edit dl rm
complex	2689	0644	edit dl rm
complex.h	1262	0644	edit dl rm
cstdarg	1253	0644	edit dl rm
cstdbool	1351	0644	edit dl rm
cstdint	2355	0644	edit dl rm
cstdio	1767	0644	edit dl rm
cstdlib	1775	0644	edit dl rm
ctgmath	1255	0644	edit dl rm
ctime	1241	0644	edit dl rm
ctype.h	1210	0644	edit dl rm
cwchar	1773	0644	edit dl rm
cwctype	1781	0644	edit dl rm
ell_integral.tcc	27553	0644	edit dl rm
exp_integral.tcc	15728	0644	edit dl rm
fenv.h	1205	0644	edit dl rm
float.h	1210	0644	edit dl rm
functional	2034	0644	edit dl rm
functional_hash.h	1912	0644	edit dl rm
gamma.tcc	14296	0644	edit dl rm
hashtable.h	1866	0644	edit dl rm
hypergeometric.tcc	27804	0644	edit dl rm
inttypes.h	1274	0644	edit dl rm
legendre_function.tcc	10561	0644	edit dl rm
limits.h	1215	0644	edit dl rm
math.h	4560	0644	edit dl rm
memory	2265	0644	edit dl rm
modified_bessel_func.tcc	15686	0644	edit dl rm
poly_hermite.tcc	3628	0644	edit dl rm
poly_laguerre.tcc	11481	0644	edit dl rm
random	2045	0644	edit dl rm
regex	1984	0644	edit dl rm
riemann_zeta.tcc	13633	0644	edit dl rm
shared_ptr.h	29180	0644	edit dl rm
special_function_util.h	4771	0644	edit dl rm
stdarg.h	1215	0644	edit dl rm
stdbool.h	1220	0644	edit dl rm
stdint.h	1215	0644	edit dl rm
stdio.h	1210	0644	edit dl rm
stdlib.h	1487	0644	edit dl rm
tgmath.h	1262	0644	edit dl rm
tuple	12049	0644	edit dl rm
type_traits	7236	0644	edit dl rm
unordered_map	2069	0644	edit dl rm
unordered_set	2069	0644	edit dl rm
utility	1858	0644	edit dl rm
wchar.h	1256	0644	edit dl rm
wctype.h	1262	0644	edit dl rm

Edit: /usr/include/c++/4.4.4/tr1/poly_laguerre.tcc (11481B)

// Special functions -*- C++ -*-

// Copyright (C) 2006, 2007, 2008, 2009
// 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.
//
// Under Section 7 of GPL version 3, you are granted additional
// permissions described in the GCC Runtime Library Exception, version
// 3.1, as published by the Free Software Foundation.

// You should have received a copy of the GNU General Public License and
// a copy of the GCC Runtime Library Exception along with this program;
// see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
// <http://www.gnu.org/licenses/>.

/** @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 _GLIBCXX_TR1_POLY_LAGUERRE_TCC
#define _GLIBCXX_TR1_POLY_LAGUERRE_TCC 1

namespace std
{
namespace tr1
{

// [5.2] Special functions

// 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 __alpha1,
                            const _Tp __x)
    {
      const _Tp __a = -_Tp(__n);
      const _Tp __b = _Tp(__alpha1) + _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::tr1::lgamma(_Tp(__n) + __b);
      const _Tp __lnfact = std::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 __alpha1,
			   const _Tp __x)
    {
      const _Tp __b = _Tp(__alpha1) + _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 __alpha1, 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(__alpha1);
      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(__alpha1) - __x)
                  * __l_n1 / _Tp(__nn)
                  - (_Tp(__nn - 1) + _Tp(__alpha1)) * __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 __alpha1,
                    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(__alpha1) - __x;
      else if (__x == _Tp(0))
        {
          _Tp __prod = _Tp(__alpha1) + _Tp(1);
          for (unsigned int __k = 2; __k <= __n; ++__k)
            __prod *= (_Tp(__alpha1) + _Tp(__k)) / _Tp(__k);
          return __prod;
        }
      else if (__n > 10000000 && _Tp(__alpha1) > -_Tp(1)
            && __x < _Tp(2) * (_Tp(__alpha1) + _Tp(1)) + _Tp(4 * __n))
        return __poly_laguerre_large_n(__n, __alpha1, __x);
      else if (_Tp(__alpha1) >= _Tp(0)
           || (__x > _Tp(0) && _Tp(__alpha1) < -_Tp(__n + 1)))
        return __poly_laguerre_recursion(__n, __alpha1, __x);
      else
        return __poly_laguerre_hyperg(__n, __alpha1, __x);
    }

/**
     *   @brief This routine returns the associated Laguerre polynomial
     *          of order n, degree m: @f$ L_n^m(x) @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 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
}
}

#endif // _GLIBCXX_TR1_POLY_LAGUERRE_TCC

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