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

// Copyright (C) 2006, 2007, 2008, 2009, 2010, 2011

// 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

// .

/** @file tr1/poly_hermite.tcc

 *  This is an internal header file, included by other library headers.

 *  Do not attempt to use it directly. @headername{tr1/cmath}

 */

//

// 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 22 pp. 773-802

#ifndef _GLIBCXX_TR1_POLY_HERMITE_TCC

#define _GLIBCXX_TR1_POLY_HERMITE_TCC 1

namespace std _GLIBCXX_VISIBILITY(default)

{

namespace tr1

{

  // [5.2] Special functions

  // Implementation-space details.

  namespace __detail

  {

  _GLIBCXX_BEGIN_NAMESPACE_VERSION

    /**

     *   @brief This routine returns the Hermite polynomial

     *          of order n: \f$ H_n(x) \f$ by recursion on n.

     *

     *   The Hermite polynomial is defined by:

     *   @f[

     *     H_n(x) = (-1)^n e^{x^2} \frac{d^n}{dx^n} e^{-x^2}

     *   @f]

     *

     *   @param __n The order of the Hermite polynomial.

     *   @param __x The argument of the Hermite polynomial.

     *   @return The value of the Hermite polynomial of order n

     *           and argument x.

     */

    template

    _Tp

    __poly_hermite_recursion(const unsigned int __n, const _Tp __x)

    {

      //  Compute H_0.

      _Tp __H_0 = 1;

      if (__n == 0)

        return __H_0;

      //  Compute H_1.

      _Tp __H_1 = 2 * __x;

      if (__n == 1)

        return __H_1;

      //  Compute H_n.

      _Tp __H_n, __H_nm1, __H_nm2;

      unsigned int __i;

      for  (__H_nm2 = __H_0, __H_nm1 = __H_1, __i = 2; __i <= __n; ++__i)

        {

          __H_n = 2 * (__x * __H_nm1 - (__i - 1) * __H_nm2);

          __H_nm2 = __H_nm1;

          __H_nm1 = __H_n;

        }

      return __H_n;

    }

    /**

     *   @brief This routine returns the Hermite polynomial

     *          of order n: \f$ H_n(x) \f$.

     *

     *   The Hermite polynomial is defined by:

     *   @f[

     *     H_n(x) = (-1)^n e^{x^2} \frac{d^n}{dx^n} e^{-x^2}

     *   @f]

     *

     *   @param __n The order of the Hermite polynomial.

     *   @param __x The argument of the Hermite polynomial.

     *   @return The value of the Hermite polynomial of order n

     *           and argument x.

     */

    template

    inline _Tp

    __poly_hermite(const unsigned int __n, const _Tp __x)

    {

      if (__isnan(__x))

        return std::numeric_limits<_Tp>::quiet_NaN();

      else

        return __poly_hermite_recursion(__n, __x);

    }

  _GLIBCXX_END_NAMESPACE_VERSION

  } // namespace std::tr1::__detail

}

}

#endif // _GLIBCXX_TR1_POLY_HERMITE_TCC