poly_hermite.tcc File Reference

Macros
#define	_GLIBCXX_TR1_POLY_HERMITE_TCC   1

Functions
namespace std	_GLIBCXX_VISIBILITY (default)

Detailed Description

This is an internal header file, included by other library headers. Do not attempt to use it directly. {tr1/cmath}

Macro Definition Documentation

#define _GLIBCXX_TR1_POLY_HERMITE_TCC   1

Function Documentation

namespace std _GLIBCXX_VISIBILITY

(

default

)

This routine returns the Hermite polynomial of order n: by recursion on n.

The Hermite polynomial is defined by:

Parameters

__n	The order of the Hermite polynomial.
__x	The argument of the Hermite polynomial.

Returns

The value of the Hermite polynomial of order n and argument x.

This routine returns the Hermite polynomial of order n: .

The Hermite polynomial is defined by:

Parameters

__n	The order of the Hermite polynomial.
__x	The argument of the Hermite polynomial.

Returns

The value of the Hermite polynomial of order n and argument x.

{
namespace tr1
{
  // [5.2] Special functions

  // Implementation-space details.
  namespace __detail
  {
  _GLIBCXX_BEGIN_NAMESPACE_VERSION

    template<typename _Tp>
    _Tp
    __poly_hermite_recursion(unsigned int __n, _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;
    }


    template<typename _Tp>
    inline _Tp
    __poly_hermite(unsigned int __n, _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
}
}