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Diffstat (limited to 'gcc-4.4.3/libstdc++-v3/include/tr1/exp_integral.tcc')
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diff --git a/gcc-4.4.3/libstdc++-v3/include/tr1/exp_integral.tcc b/gcc-4.4.3/libstdc++-v3/include/tr1/exp_integral.tcc deleted file mode 100644 index 5b3af5d8e..000000000 --- a/gcc-4.4.3/libstdc++-v3/include/tr1/exp_integral.tcc +++ /dev/null @@ -1,524 +0,0 @@ -// 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 |