libstdc++-v3/include/tr1/poly_hermite.tcc

   1 // Special functions -*- C++ -*-
   2
   3 // Copyright (C) 2006, 2007, 2008, 2009, 2010, 2011
   4 // Free Software Foundation, Inc.
   5 //
   6 // This file is part of the GNU ISO C++ Library.  This library is free
   7 // software; you can redistribute it and/or modify it under the
   8 // terms of the GNU General Public License as published by the
   9 // Free Software Foundation; either version 3, or (at your option)
  10 // any later version.
  11 //
  12 // This library is distributed in the hope that it will be useful,
  13 // but WITHOUT ANY WARRANTY; without even the implied warranty of
  14 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  15 // GNU General Public License for more details.
  16 //
  17 // Under Section 7 of GPL version 3, you are granted additional
  18 // permissions described in the GCC Runtime Library Exception, version
  19 // 3.1, as published by the Free Software Foundation.
  20
  21 // You should have received a copy of the GNU General Public License and
  22 // a copy of the GCC Runtime Library Exception along with this program;
  23 // see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
  24 // <http://www.gnu.org/licenses/>.
  25
  26 /** @file tr1/poly_hermite.tcc
  27  *  This is an internal header file, included by other library headers.
  28  *  Do not attempt to use it directly. @headername{tr1/cmath}
  29  */
  30
  31 //
  32 // ISO C++ 14882 TR1: 5.2  Special functions
  33 //
  34
  35 // Written by Edward Smith-Rowland based on:
  36 //   (1) Handbook of Mathematical Functions,
  37 //       Ed. Milton Abramowitz and Irene A. Stegun,
  38 //       Dover Publications, Section 22 pp. 773-802
  39
  40 #ifndef _GLIBCXX_TR1_POLY_HERMITE_TCC
  41 #define _GLIBCXX_TR1_POLY_HERMITE_TCC 1
  42
  43 namespace std _GLIBCXX_VISIBILITY(default)
  44 {
  45 namespace tr1
  46 {
  47   // [5.2] Special functions
  48
  49   // Implementation-space details.
  50   namespace __detail
  51   {
  52   _GLIBCXX_BEGIN_NAMESPACE_VERSION
  53
  54     /**
  55      *   @brief This routine returns the Hermite polynomial
  56      *          of order n: \f$ H_n(x) \f$ by recursion on n.
  57      *
  58      *   The Hermite polynomial is defined by:
  59      *   @f[
  60      *     H_n(x) = (-1)^n e^{x^2} \frac{d^n}{dx^n} e^{-x^2}
  61      *   @f]
  62      *
  63      *   @param __n The order of the Hermite polynomial.
  64      *   @param __x The argument of the Hermite polynomial.
  65      *   @return The value of the Hermite polynomial of order n
  66      *           and argument x.
  67      */
  68     template<typename _Tp>
  69     _Tp
  70     __poly_hermite_recursion(const unsigned int __n, const _Tp __x)
  71     {
  72       //  Compute H_0.
  73       _Tp __H_0 = 1;
  74       if (__n == 0)
  75         return __H_0;
  76
  77       //  Compute H_1.
  78       _Tp __H_1 = 2 * __x;
  79       if (__n == 1)
  80         return __H_1;
  81
  82       //  Compute H_n.
  83       _Tp __H_n, __H_nm1, __H_nm2;
  84       unsigned int __i;
  85       for  (__H_nm2 = __H_0, __H_nm1 = __H_1, __i = 2; __i <= __n; ++__i)
  86         {
  87           __H_n = 2 * (__x * __H_nm1 - (__i - 1) * __H_nm2);
  88           __H_nm2 = __H_nm1;
  89           __H_nm1 = __H_n;
  90         }
  91
  92       return __H_n;
  93     }
  94
  95
  96     /**
  97      *   @brief This routine returns the Hermite polynomial
  98      *          of order n: \f$ H_n(x) \f$.
  99      *
 100      *   The Hermite polynomial is defined by:
 101      *   @f[
 102      *     H_n(x) = (-1)^n e^{x^2} \frac{d^n}{dx^n} e^{-x^2}
 103      *   @f]
 104      *
 105      *   @param __n The order of the Hermite polynomial.
 106      *   @param __x The argument of the Hermite polynomial.
 107      *   @return The value of the Hermite polynomial of order n
 108      *           and argument x.
 109      */
 110     template<typename _Tp>
 111     inline _Tp
 112     __poly_hermite(const unsigned int __n, const _Tp __x)
 113     {
 114       if (__isnan(__x))
 115         return std::numeric_limits<_Tp>::quiet_NaN();
 116       else
 117         return __poly_hermite_recursion(__n, __x);
 118     }
 119
 120   _GLIBCXX_END_NAMESPACE_VERSION
 121   } // namespace std::tr1::__detail
 122 }
 123 }
 124
 125 #endif // _GLIBCXX_TR1_POLY_HERMITE_TCC