FM / tr1

/usr/include/c++/4.4.4/tr1/

/usr/include/c++/4.4.4/tr1

Name	Size	Mode	Actions
array	1802	0644	edit dl rm
bessel_function.tcc	22103	0644	edit dl rm
beta_function.tcc	5510	0644	edit dl rm
ccomplex	1256	0644	edit dl rm
cctype	1670	0644	edit dl rm
cfenv	1729	0644	edit dl rm
cfloat	1387	0644	edit dl rm
cinttypes	2006	0644	edit dl rm
climits	1467	0644	edit dl rm
cmath	16362	0644	edit dl rm
complex	2689	0644	edit dl rm
complex.h	1262	0644	edit dl rm
cstdarg	1253	0644	edit dl rm
cstdbool	1351	0644	edit dl rm
cstdint	2355	0644	edit dl rm
cstdio	1767	0644	edit dl rm
cstdlib	1775	0644	edit dl rm
ctgmath	1255	0644	edit dl rm
ctime	1241	0644	edit dl rm
ctype.h	1210	0644	edit dl rm
cwchar	1773	0644	edit dl rm
cwctype	1781	0644	edit dl rm
ell_integral.tcc	27553	0644	edit dl rm
exp_integral.tcc	15728	0644	edit dl rm
fenv.h	1205	0644	edit dl rm
float.h	1210	0644	edit dl rm
functional	2034	0644	edit dl rm
functional_hash.h	1912	0644	edit dl rm
gamma.tcc	14296	0644	edit dl rm
hashtable.h	1866	0644	edit dl rm
hypergeometric.tcc	27804	0644	edit dl rm
inttypes.h	1274	0644	edit dl rm
legendre_function.tcc	10561	0644	edit dl rm
limits.h	1215	0644	edit dl rm
math.h	4560	0644	edit dl rm
memory	2265	0644	edit dl rm
modified_bessel_func.tcc	15686	0644	edit dl rm
poly_hermite.tcc	3628	0644	edit dl rm
poly_laguerre.tcc	11481	0644	edit dl rm
random	2045	0644	edit dl rm
regex	1984	0644	edit dl rm
riemann_zeta.tcc	13633	0644	edit dl rm
shared_ptr.h	29180	0644	edit dl rm
special_function_util.h	4771	0644	edit dl rm
stdarg.h	1215	0644	edit dl rm
stdbool.h	1220	0644	edit dl rm
stdint.h	1215	0644	edit dl rm
stdio.h	1210	0644	edit dl rm
stdlib.h	1487	0644	edit dl rm
tgmath.h	1262	0644	edit dl rm
tuple	12049	0644	edit dl rm
type_traits	7236	0644	edit dl rm
unordered_map	2069	0644	edit dl rm
unordered_set	2069	0644	edit dl rm
utility	1858	0644	edit dl rm
wchar.h	1256	0644	edit dl rm
wctype.h	1262	0644	edit dl rm

Edit: /usr/include/c++/4.4.4/tr1/exp_integral.tcc (15728B)

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

// Copyright (C) 2006, 2007, 2008, 2009
// 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
// <http://www.gnu.org/licenses/>.

/** @file tr1/exp_integral.tcc
 *  This is an internal header file, included by other library headers.
 *  You should not attempt to use it directly.
 */

//
// ISO C++ 14882 TR1: 5.2  Special functions
//

//  Written by Edward Smith-Rowland based on:
//
//   (1) Handbook of Mathematical Functions,
//       Ed. by Milton Abramowitz and Irene A. Stegun,
//       Dover Publications, New-York, Section 5, pp. 228-251.
//   (2) The Gnu Scientific Library, http://www.gnu.org/software/gsl
//   (3) Numerical Recipes in C, by W. H. Press, S. A. Teukolsky,
//       W. T. Vetterling, B. P. Flannery, Cambridge University Press (1992),
//       2nd ed, pp. 222-225.
//

#ifndef _GLIBCXX_TR1_EXP_INTEGRAL_TCC
#define _GLIBCXX_TR1_EXP_INTEGRAL_TCC 1

#include "special_function_util.h"

namespace std
{
namespace tr1
{

// [5.2] Special functions

// Implementation-space details.
  namespace __detail
  {

/**
     *   @brief Return the exponential integral @f$ E_1(x) @f$
     *          by series summation.  This should be good
     *          for @f$ x < 1 @f$.
     * 
     *   The exponential integral is given by
     *          \f[
     *            E_1(x) = \int_{1}^{\infty} \frac{e^{-xt}}{t} dt
     *          \f]
     * 
     *   @param  __x  The argument of the exponential integral function.
     *   @return  The exponential integral.
     */
    template<typename _Tp>
    _Tp
    __expint_E1_series(const _Tp __x)
    {
      const _Tp __eps = std::numeric_limits<_Tp>::epsilon();
      _Tp __term = _Tp(1);
      _Tp __esum = _Tp(0);
      _Tp __osum = _Tp(0);
      const unsigned int __max_iter = 100;
      for (unsigned int __i = 1; __i < __max_iter; ++__i)
        {
          __term *= - __x / __i;
          if (std::abs(__term) < __eps)
            break;
          if (__term >= _Tp(0))
            __esum += __term / __i;
          else
            __osum += __term / __i;
        }

return - __esum - __osum
             - __numeric_constants<_Tp>::__gamma_e() - std::log(__x);
    }

/**
     *   @brief Return the exponential integral @f$ E_1(x) @f$
     *          by asymptotic expansion.
     * 
     *   The exponential integral is given by
     *          \f[
     *            E_1(x) = \int_{1}^\infty \frac{e^{-xt}}{t} dt
     *          \f]
     * 
     *   @param  __x  The argument of the exponential integral function.
     *   @return  The exponential integral.
     */
    template<typename _Tp>
    _Tp
    __expint_E1_asymp(const _Tp __x)
    {
      _Tp __term = _Tp(1);
      _Tp __esum = _Tp(1);
      _Tp __osum = _Tp(0);
      const unsigned int __max_iter = 1000;
      for (unsigned int __i = 1; __i < __max_iter; ++__i)
        {
          _Tp __prev = __term;
          __term *= - __i / __x;
          if (std::abs(__term) > std::abs(__prev))
            break;
          if (__term >= _Tp(0))
            __esum += __term;
          else
            __osum += __term;
        }

return std::exp(- __x) * (__esum + __osum) / __x;
    }

/**
     *   @brief Return the exponential integral @f$ E_n(x) @f$
     *          by series summation.
     * 
     *   The exponential integral is given by
     *          \f[
     *            E_n(x) = \int_{1}^\infty \frac{e^{-xt}}{t^n} dt
     *          \f]
     * 
     *   @param  __n  The order of the exponential integral function.
     *   @param  __x  The argument of the exponential integral function.
     *   @return  The exponential integral.
     */
    template<typename _Tp>
    _Tp
    __expint_En_series(const unsigned int __n, const _Tp __x)
    {
      const unsigned int __max_iter = 100;
      const _Tp __eps = std::numeric_limits<_Tp>::epsilon();
      const int __nm1 = __n - 1;
      _Tp __ans = (__nm1 != 0
                ? _Tp(1) / __nm1 : -std::log(__x)
                                   - __numeric_constants<_Tp>::__gamma_e());
      _Tp __fact = _Tp(1);
      for (int __i = 1; __i <= __max_iter; ++__i)
        {
          __fact *= -__x / _Tp(__i);
          _Tp __del;
          if ( __i != __nm1 )
            __del = -__fact / _Tp(__i - __nm1);
          else
            {
              _Tp __psi = -_TR1_GAMMA_TCC;
              for (int __ii = 1; __ii <= __nm1; ++__ii)
                __psi += _Tp(1) / _Tp(__ii);
              __del = __fact * (__psi - std::log(__x)); 
            }
          __ans += __del;
          if (std::abs(__del) < __eps * std::abs(__ans))
            return __ans;
        }
      std::__throw_runtime_error(__N("Series summation failed "
                                     "in __expint_En_series."));
    }

/**
     *   @brief Return the exponential integral @f$ E_n(x) @f$
     *          by continued fractions.
     * 
     *   The exponential integral is given by
     *          \f[
     *            E_n(x) = \int_{1}^\infty \frac{e^{-xt}}{t^n} dt
     *          \f]
     * 
     *   @param  __n  The order of the exponential integral function.
     *   @param  __x  The argument of the exponential integral function.
     *   @return  The exponential integral.
     */
    template<typename _Tp>
    _Tp
    __expint_En_cont_frac(const unsigned int __n, const _Tp __x)
    {
      const unsigned int __max_iter = 100;
      const _Tp __eps = std::numeric_limits<_Tp>::epsilon();
      const _Tp __fp_min = std::numeric_limits<_Tp>::min();
      const int __nm1 = __n - 1;
      _Tp __b = __x + _Tp(__n);
      _Tp __c = _Tp(1) / __fp_min;
      _Tp __d = _Tp(1) / __b;
      _Tp __h = __d;
      for ( unsigned int __i = 1; __i <= __max_iter; ++__i )
        {
          _Tp __a = -_Tp(__i * (__nm1 + __i));
          __b += _Tp(2);
          __d = _Tp(1) / (__a * __d + __b);
          __c = __b + __a / __c;
          const _Tp __del = __c * __d;
          __h *= __del;
          if (std::abs(__del - _Tp(1)) < __eps)
            {
              const _Tp __ans = __h * std::exp(-__x);
              return __ans;
            }
        }
      std::__throw_runtime_error(__N("Continued fraction failed "
                                     "in __expint_En_cont_frac."));
    }

/**
     *   @brief Return the exponential integral @f$ E_n(x) @f$
     *          by recursion.  Use upward recursion for @f$ x < n @f$
     *          and downward recursion (Miller's algorithm) otherwise.
     * 
     *   The exponential integral is given by
     *          \f[
     *            E_n(x) = \int_{1}^\infty \frac{e^{-xt}}{t^n} dt
     *          \f]
     * 
     *   @param  __n  The order of the exponential integral function.
     *   @param  __x  The argument of the exponential integral function.
     *   @return  The exponential integral.
     */
    template<typename _Tp>
    _Tp
    __expint_En_recursion(const unsigned int __n, const _Tp __x)
    {
      _Tp __En;
      _Tp __E1 = __expint_E1(__x);
      if (__x < _Tp(__n))
        {
          //  Forward recursion is stable only for n < x.
          __En = __E1;
          for (unsigned int __j = 2; __j < __n; ++__j)
            __En = (std::exp(-__x) - __x * __En) / _Tp(__j - 1);
        }
      else
        {
          //  Backward recursion is stable only for n >= x.
          __En = _Tp(1);
          const int __N = __n + 20;  //  TODO: Check this starting number.
          _Tp __save = _Tp(0);
          for (int __j = __N; __j > 0; --__j)
            {
              __En = (std::exp(-__x) - __j * __En) / __x;
              if (__j == __n)
                __save = __En;
            }
            _Tp __norm = __En / __E1;
            __En /= __norm;
        }

return __En;
    }

/**
     *   @brief Return the exponential integral @f$ Ei(x) @f$
     *          by series summation.
     * 
     *   The exponential integral is given by
     *          \f[
     *            Ei(x) = -\int_{-x}^\infty \frac{e^t}{t} dt
     *          \f]
     * 
     *   @param  __x  The argument of the exponential integral function.
     *   @return  The exponential integral.
     */
    template<typename _Tp>
    _Tp
    __expint_Ei_series(const _Tp __x)
    {
      _Tp __term = _Tp(1);
      _Tp __sum = _Tp(0);
      const unsigned int __max_iter = 1000;
      for (unsigned int __i = 1; __i < __max_iter; ++__i)
        {
          __term *= __x / __i;
          __sum += __term / __i;
          if (__term < std::numeric_limits<_Tp>::epsilon() * __sum)
            break;
        }

return __numeric_constants<_Tp>::__gamma_e() + __sum + std::log(__x);
    }

/**
     *   @brief Return the exponential integral @f$ Ei(x) @f$
     *          by asymptotic expansion.
     * 
     *   The exponential integral is given by
     *          \f[
     *            Ei(x) = -\int_{-x}^\infty \frac{e^t}{t} dt
     *          \f]
     * 
     *   @param  __x  The argument of the exponential integral function.
     *   @return  The exponential integral.
     */
    template<typename _Tp>
    _Tp
    __expint_Ei_asymp(const _Tp __x)
    {
      _Tp __term = _Tp(1);
      _Tp __sum = _Tp(1);
      const unsigned int __max_iter = 1000;
      for (unsigned int __i = 1; __i < __max_iter; ++__i)
        {
          _Tp __prev = __term;
          __term *= __i / __x;
          if (__term < std::numeric_limits<_Tp>::epsilon())
            break;
          if (__term >= __prev)
            break;
          __sum += __term;
        }

return std::exp(__x) * __sum / __x;
    }

/**
     *   @brief Return the exponential integral @f$ Ei(x) @f$.
     * 
     *   The exponential integral is given by
     *          \f[
     *            Ei(x) = -\int_{-x}^\infty \frac{e^t}{t} dt
     *          \f]
     * 
     *   @param  __x  The argument of the exponential integral function.
     *   @return  The exponential integral.
     */
    template<typename _Tp>
    _Tp
    __expint_Ei(const _Tp __x)
    {
      if (__x < _Tp(0))
        return -__expint_E1(-__x);
      else if (__x < -std::log(std::numeric_limits<_Tp>::epsilon()))
        return __expint_Ei_series(__x);
      else
        return __expint_Ei_asymp(__x);
    }

/**
     *   @brief Return the exponential integral @f$ E_1(x) @f$.
     * 
     *   The exponential integral is given by
     *          \f[
     *            E_1(x) = \int_{1}^\infty \frac{e^{-xt}}{t} dt
     *          \f]
     * 
     *   @param  __x  The argument of the exponential integral function.
     *   @return  The exponential integral.
     */
    template<typename _Tp>
    _Tp
    __expint_E1(const _Tp __x)
    {
      if (__x < _Tp(0))
        return -__expint_Ei(-__x);
      else if (__x < _Tp(1))
        return __expint_E1_series(__x);
      else if (__x < _Tp(100))  //  TODO: Find a good asymptotic switch point.
        return __expint_En_cont_frac(1, __x);
      else
        return __expint_E1_asymp(__x);
    }

/**
     *   @brief Return the exponential integral @f$ E_n(x) @f$
     *          for large argument.
     * 
     *   The exponential integral is given by
     *          \f[
     *            E_n(x) = \int_{1}^\infty \frac{e^{-xt}}{t^n} dt
     *          \f]
     * 
     *   This is something of an extension.
     * 
     *   @param  __n  The order of the exponential integral function.
     *   @param  __x  The argument of the exponential integral function.
     *   @return  The exponential integral.
     */
    template<typename _Tp>
    _Tp
    __expint_asymp(const unsigned int __n, const _Tp __x)
    {
      _Tp __term = _Tp(1);
      _Tp __sum = _Tp(1);
      for (unsigned int __i = 1; __i <= __n; ++__i)
        {
          _Tp __prev = __term;
          __term *= -(__n - __i + 1) / __x;
          if (std::abs(__term) > std::abs(__prev))
            break;
          __sum += __term;
        }

return std::exp(-__x) * __sum / __x;
    }

/**
     *   @brief Return the exponential integral @f$ E_n(x) @f$
     *          for large order.
     * 
     *   The exponential integral is given by
     *          \f[
     *            E_n(x) = \int_{1}^\infty \frac{e^{-xt}}{t^n} dt
     *          \f]
     *        
     *   This is something of an extension.
     * 
     *   @param  __n  The order of the exponential integral function.
     *   @param  __x  The argument of the exponential integral function.
     *   @return  The exponential integral.
     */
    template<typename _Tp>
    _Tp
    __expint_large_n(const unsigned int __n, const _Tp __x)
    {
      const _Tp __xpn = __x + __n;
      const _Tp __xpn2 = __xpn * __xpn;
      _Tp __term = _Tp(1);
      _Tp __sum = _Tp(1);
      for (unsigned int __i = 1; __i <= __n; ++__i)
        {
          _Tp __prev = __term;
          __term *= (__n - 2 * (__i - 1) * __x) / __xpn2;
          if (std::abs(__term) < std::numeric_limits<_Tp>::epsilon())
            break;
          __sum += __term;
        }

return std::exp(-__x) * __sum / __xpn;
    }

/**
     *   @brief Return the exponential integral @f$ E_n(x) @f$.
     * 
     *   The exponential integral is given by
     *          \f[
     *            E_n(x) = \int_{1}^\infty \frac{e^{-xt}}{t^n} dt
     *          \f]
     *   This is something of an extension.
     * 
     *   @param  __n  The order of the exponential integral function.
     *   @param  __x  The argument of the exponential integral function.
     *   @return  The exponential integral.
     */
    template<typename _Tp>
    _Tp
    __expint(const unsigned int __n, const _Tp __x)
    {
      //  Return NaN on NaN input.
      if (__isnan(__x))
        return std::numeric_limits<_Tp>::quiet_NaN();
      else if (__n <= 1 && __x == _Tp(0))
        return std::numeric_limits<_Tp>::infinity();
      else
        {
          _Tp __E0 = std::exp(__x) / __x;
          if (__n == 0)
            return __E0;

_Tp __E1 = __expint_E1(__x);
          if (__n == 1)
            return __E1;

if (__x == _Tp(0))
            return _Tp(1) / static_cast<_Tp>(__n - 1);

_Tp __En = __expint_En_recursion(__n, __x);

return __En;
        }
    }

/**
     *   @brief Return the exponential integral @f$ Ei(x) @f$.
     * 
     *   The exponential integral is given by
     *   \f[
     *     Ei(x) = -\int_{-x}^\infty \frac{e^t}{t} dt
     *   \f]
     * 
     *   @param  __x  The argument of the exponential integral function.
     *   @return  The exponential integral.
     */
    template<typename _Tp>
    inline _Tp
    __expint(const _Tp __x)
    {
      if (__isnan(__x))
        return std::numeric_limits<_Tp>::quiet_NaN();
      else
        return __expint_Ei(__x);
    }

} // namespace std::tr1::__detail
}
}

#endif // _GLIBCXX_TR1_EXP_INTEGRAL_TCC

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