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

   1 // Special functions -*- C++ -*-
   2
   3 // Copyright (C) 2006, 2007, 2008
   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 2, 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 // You should have received a copy of the GNU General Public License along
  18 // with this library; see the file COPYING.  If not, write to the Free
  19 // Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301,
  20 // USA.
  21 //
  22 // As a special exception, you may use this file as part of a free software
  23 // library without restriction.  Specifically, if other files instantiate
  24 // templates or use macros or inline functions from this file, or you compile
  25 // this file and link it with other files to produce an executable, this
  26 // file does not by itself cause the resulting executable to be covered by
  27 // the GNU General Public License.  This exception does not however
  28 // invalidate any other reasons why the executable file might be covered by
  29 // the GNU General Public License.
  30
  31 /** @file tr1/poly_hermite.tcc
  32  *  This is an internal header file, included by other library headers.
  33  *  You should not attempt to use it directly.
  34  */
  35
  36 //
  37 // ISO C++ 14882 TR1: 5.2  Special functions
  38 //
  39
  40 // Written by Edward Smith-Rowland based on:
  41 //   (1) Handbook of Mathematical Functions,
  42 //       Ed. Milton Abramowitz and Irene A. Stegun,
  43 //       Dover Publications, Section 22 pp. 773-802
  44
  45 #ifndef _GLIBCXX_TR1_POLY_HERMITE_TCC
  46 #define _GLIBCXX_TR1_POLY_HERMITE_TCC 1
  47
  48 namespace std
  49 {
  50 namespace tr1
  51 {
  52
  53   // [5.2] Special functions
  54
  55   // Implementation-space details.
  56   namespace __detail
  57   {
  58
  59     /**
  60      *   @brief This routine returns the Hermite polynomial
  61      *          of order n: \f$ H_n(x) \f$ by recursion on n.
  62      *
  63      *   The Hermite polynomial is defined by:
  64      *   @f[
  65      *     H_n(x) = (-1)^n e^{x^2} \frac{d^n}{dx^n} e^{-x^2}
  66      *   @f]
  67      *
  68      *   @param __n The order of the Hermite polynomial.
  69      *   @param __x The argument of the Hermite polynomial.
  70      *   @return The value of the Hermite polynomial of order n
  71      *           and argument x.
  72      */
  73     template<typename _Tp>
  74     _Tp
  75     __poly_hermite_recursion(const unsigned int __n, const _Tp __x)
  76     {
  77       //  Compute H_0.
  78       _Tp __H_0 = 1;
  79       if (__n == 0)
  80         return __H_0;
  81
  82       //  Compute H_1.
  83       _Tp __H_1 = 2 * __x;
  84       if (__n == 1)
  85         return __H_1;
  86
  87       //  Compute H_n.
  88       _Tp __H_n, __H_nm1, __H_nm2;
  89       unsigned int __i;
  90       for  (__H_nm2 = __H_0, __H_nm1 = __H_1, __i = 2; __i <= __n; ++__i)
  91         {
  92           __H_n = 2 * (__x * __H_nm1 + (__i - 1) * __H_nm2);
  93           __H_nm2 = __H_nm1;
  94           __H_nm1 = __H_n;
  95         }
  96
  97       return __H_n;
  98     }
  99
 100
 101     /**
 102      *   @brief This routine returns the Hermite polynomial
 103      *          of order n: \f$ H_n(x) \f$.
 104      *
 105      *   The Hermite polynomial is defined by:
 106      *   @f[
 107      *     H_n(x) = (-1)^n e^{x^2} \frac{d^n}{dx^n} e^{-x^2}
 108      *   @f]
 109      *
 110      *   @param __n The order of the Hermite polynomial.
 111      *   @param __x The argument of the Hermite polynomial.
 112      *   @return The value of the Hermite polynomial of order n
 113      *           and argument x.
 114      */
 115     template<typename _Tp>
 116     inline _Tp
 117     __poly_hermite(const unsigned int __n, const _Tp __x)
 118     {
 119       if (__isnan(__x))
 120         return std::numeric_limits<_Tp>::quiet_NaN();
 121       else
 122         return __poly_hermite_recursion(__n, __x);
 123     }
 124
 125   } // namespace std::tr1::__detail
 126 }
 127 }
 128
 129 #endif // _GLIBCXX_TR1_POLY_HERMITE_TCC