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

   1 // Special functions -*- C++ -*-
   2
   3 // Copyright (C) 2006-2013 Free Software Foundation, Inc.
   4 //
   5 // This file is part of the GNU ISO C++ Library.  This library is free
   6 // software; you can redistribute it and/or modify it under the
   7 // terms of the GNU General Public License as published by the
   8 // Free Software Foundation; either version 3, or (at your option)
   9 // any later version.
  10 //
  11 // This library is distributed in the hope that it will be useful,
  12 // but WITHOUT ANY WARRANTY; without even the implied warranty of
  13 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  14 // GNU General Public License for more details.
  15 //
  16 // Under Section 7 of GPL version 3, you are granted additional
  17 // permissions described in the GCC Runtime Library Exception, version
  18 // 3.1, as published by the Free Software Foundation.
  19
  20 // You should have received a copy of the GNU General Public License and
  21 // a copy of the GCC Runtime Library Exception along with this program;
  22 // see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
  23 // <http://www.gnu.org/licenses/>.
  24
  25 /** @file tr1/poly_hermite.tcc
  26  *  This is an internal header file, included by other library headers.
  27  *  Do not attempt to use it directly. @headername{tr1/cmath}
  28  */
  29
  30 //
  31 // ISO C++ 14882 TR1: 5.2  Special functions
  32 //
  33
  34 // Written by Edward Smith-Rowland based on:
  35 //   (1) Handbook of Mathematical Functions,
  36 //       Ed. Milton Abramowitz and Irene A. Stegun,
  37 //       Dover Publications, Section 22 pp. 773-802
  38
  39 #ifndef _GLIBCXX_TR1_POLY_HERMITE_TCC
  40 #define _GLIBCXX_TR1_POLY_HERMITE_TCC 1
  41
  42 namespace std _GLIBCXX_VISIBILITY(default)
  43 {
  44 namespace tr1
  45 {
  46   // [5.2] Special functions
  47
  48   // Implementation-space details.
  49   namespace __detail
  50   {
  51   _GLIBCXX_BEGIN_NAMESPACE_VERSION
  52
  53     /**
  54      *   @brief This routine returns the Hermite polynomial
  55      *          of order n: \f$ H_n(x) \f$ by recursion on n.
  56      *
  57      *   The Hermite polynomial is defined by:
  58      *   @f[
  59      *     H_n(x) = (-1)^n e^{x^2} \frac{d^n}{dx^n} e^{-x^2}
  60      *   @f]
  61      *
  62      *   @param __n The order of the Hermite polynomial.
  63      *   @param __x The argument of the Hermite polynomial.
  64      *   @return The value of the Hermite polynomial of order n
  65      *           and argument x.
  66      */
  67     template<typename _Tp>
  68     _Tp
  69     __poly_hermite_recursion(unsigned int __n, _Tp __x)
  70     {
  71       //  Compute H_0.
  72       _Tp __H_0 = 1;
  73       if (__n == 0)
  74         return __H_0;
  75
  76       //  Compute H_1.
  77       _Tp __H_1 = 2 * __x;
  78       if (__n == 1)
  79         return __H_1;
  80
  81       //  Compute H_n.
  82       _Tp __H_n, __H_nm1, __H_nm2;
  83       unsigned int __i;
  84       for  (__H_nm2 = __H_0, __H_nm1 = __H_1, __i = 2; __i <= __n; ++__i)
  85         {
  86           __H_n = 2 * (__x * __H_nm1 - (__i - 1) * __H_nm2);
  87           __H_nm2 = __H_nm1;
  88           __H_nm1 = __H_n;
  89         }
  90
  91       return __H_n;
  92     }
  93
  94
  95     /**
  96      *   @brief This routine returns the Hermite polynomial
  97      *          of order n: \f$ H_n(x) \f$.
  98      *
  99      *   The Hermite polynomial is defined by:
 100      *   @f[
 101      *     H_n(x) = (-1)^n e^{x^2} \frac{d^n}{dx^n} e^{-x^2}
 102      *   @f]
 103      *
 104      *   @param __n The order of the Hermite polynomial.
 105      *   @param __x The argument of the Hermite polynomial.
 106      *   @return The value of the Hermite polynomial of order n
 107      *           and argument x.
 108      */
 109     template<typename _Tp>
 110     inline _Tp
 111     __poly_hermite(unsigned int __n, _Tp __x)
 112     {
 113       if (__isnan(__x))
 114         return std::numeric_limits<_Tp>::quiet_NaN();
 115       else
 116         return __poly_hermite_recursion(__n, __x);
 117     }
 118
 119   _GLIBCXX_END_NAMESPACE_VERSION
 120   } // namespace std::tr1::__detail
 121 }
 122 }
 123
 124 #endif // _GLIBCXX_TR1_POLY_HERMITE_TCC