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diff --git a/gcc-4.4.3/libstdc++-v3/include/tr1/ell_integral.tcc b/gcc-4.4.3/libstdc++-v3/include/tr1/ell_integral.tcc deleted file mode 100644 index 09bda9aa9..000000000 --- a/gcc-4.4.3/libstdc++-v3/include/tr1/ell_integral.tcc +++ /dev/null @@ -1,750 +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/ell_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) B. C. Carlson Numer. Math. 33, 1 (1979) -// (2) B. C. Carlson, Special Functions of Applied Mathematics (1977) -// (3) The Gnu Scientific Library, http://www.gnu.org/software/gsl -// (4) Numerical Recipes in C, 2nd ed, by W. H. Press, S. A. Teukolsky, -// W. T. Vetterling, B. P. Flannery, Cambridge University Press -// (1992), pp. 261-269 - -#ifndef _GLIBCXX_TR1_ELL_INTEGRAL_TCC -#define _GLIBCXX_TR1_ELL_INTEGRAL_TCC 1 - -namespace std -{ -namespace tr1 -{ - - // [5.2] Special functions - - // Implementation-space details. - namespace __detail - { - - /** - * @brief Return the Carlson elliptic function @f$ R_F(x,y,z) @f$ - * of the first kind. - * - * The Carlson elliptic function of the first kind is defined by: - * @f[ - * R_F(x,y,z) = \frac{1}{2} \int_0^\infty - * \frac{dt}{(t + x)^{1/2}(t + y)^{1/2}(t + z)^{1/2}} - * @f] - * - * @param __x The first of three symmetric arguments. - * @param __y The second of three symmetric arguments. - * @param __z The third of three symmetric arguments. - * @return The Carlson elliptic function of the first kind. - */ - template<typename _Tp> - _Tp - __ellint_rf(const _Tp __x, const _Tp __y, const _Tp __z) - { - const _Tp __min = std::numeric_limits<_Tp>::min(); - const _Tp __max = std::numeric_limits<_Tp>::max(); - const _Tp __lolim = _Tp(5) * __min; - const _Tp __uplim = __max / _Tp(5); - - if (__x < _Tp(0) || __y < _Tp(0) || __z < _Tp(0)) - std::__throw_domain_error(__N("Argument less than zero " - "in __ellint_rf.")); - else if (__x + __y < __lolim || __x + __z < __lolim - || __y + __z < __lolim) - std::__throw_domain_error(__N("Argument too small in __ellint_rf")); - else - { - const _Tp __c0 = _Tp(1) / _Tp(4); - const _Tp __c1 = _Tp(1) / _Tp(24); - const _Tp __c2 = _Tp(1) / _Tp(10); - const _Tp __c3 = _Tp(3) / _Tp(44); - const _Tp __c4 = _Tp(1) / _Tp(14); - - _Tp __xn = __x; - _Tp __yn = __y; - _Tp __zn = __z; - - const _Tp __eps = std::numeric_limits<_Tp>::epsilon(); - const _Tp __errtol = std::pow(__eps, _Tp(1) / _Tp(6)); - _Tp __mu; - _Tp __xndev, __yndev, __zndev; - - const unsigned int __max_iter = 100; - for (unsigned int __iter = 0; __iter < __max_iter; ++__iter) - { - __mu = (__xn + __yn + __zn) / _Tp(3); - __xndev = 2 - (__mu + __xn) / __mu; - __yndev = 2 - (__mu + __yn) / __mu; - __zndev = 2 - (__mu + __zn) / __mu; - _Tp __epsilon = std::max(std::abs(__xndev), std::abs(__yndev)); - __epsilon = std::max(__epsilon, std::abs(__zndev)); - if (__epsilon < __errtol) - break; - const _Tp __xnroot = std::sqrt(__xn); - const _Tp __ynroot = std::sqrt(__yn); - const _Tp __znroot = std::sqrt(__zn); - const _Tp __lambda = __xnroot * (__ynroot + __znroot) - + __ynroot * __znroot; - __xn = __c0 * (__xn + __lambda); - __yn = __c0 * (__yn + __lambda); - __zn = __c0 * (__zn + __lambda); - } - - const _Tp __e2 = __xndev * __yndev - __zndev * __zndev; - const _Tp __e3 = __xndev * __yndev * __zndev; - const _Tp __s = _Tp(1) + (__c1 * __e2 - __c2 - __c3 * __e3) * __e2 - + __c4 * __e3; - - return __s / std::sqrt(__mu); - } - } - - - /** - * @brief Return the complete elliptic integral of the first kind - * @f$ K(k) @f$ by series expansion. - * - * The complete elliptic integral of the first kind is defined as - * @f[ - * K(k) = F(k,\pi/2) = \int_0^{\pi/2}\frac{d\theta} - * {\sqrt{1 - k^2sin^2\theta}} - * @f] - * - * This routine is not bad as long as |k| is somewhat smaller than 1 - * but is not is good as the Carlson elliptic integral formulation. - * - * @param __k The argument of the complete elliptic function. - * @return The complete elliptic function of the first kind. - */ - template<typename _Tp> - _Tp - __comp_ellint_1_series(const _Tp __k) - { - - const _Tp __kk = __k * __k; - - _Tp __term = __kk / _Tp(4); - _Tp __sum = _Tp(1) + __term; - - const unsigned int __max_iter = 1000; - for (unsigned int __i = 2; __i < __max_iter; ++__i) - { - __term *= (2 * __i - 1) * __kk / (2 * __i); - if (__term < std::numeric_limits<_Tp>::epsilon()) - break; - __sum += __term; - } - - return __numeric_constants<_Tp>::__pi_2() * __sum; - } - - - /** - * @brief Return the complete elliptic integral of the first kind - * @f$ K(k) @f$ using the Carlson formulation. - * - * The complete elliptic integral of the first kind is defined as - * @f[ - * K(k) = F(k,\pi/2) = \int_0^{\pi/2}\frac{d\theta} - * {\sqrt{1 - k^2 sin^2\theta}} - * @f] - * where @f$ F(k,\phi) @f$ is the incomplete elliptic integral of the - * first kind. - * - * @param __k The argument of the complete elliptic function. - * @return The complete elliptic function of the first kind. - */ - template<typename _Tp> - _Tp - __comp_ellint_1(const _Tp __k) - { - - if (__isnan(__k)) - return std::numeric_limits<_Tp>::quiet_NaN(); - else if (std::abs(__k) >= _Tp(1)) - return std::numeric_limits<_Tp>::quiet_NaN(); - else - return __ellint_rf(_Tp(0), _Tp(1) - __k * __k, _Tp(1)); - } - - - /** - * @brief Return the incomplete elliptic integral of the first kind - * @f$ F(k,\phi) @f$ using the Carlson formulation. - * - * The incomplete elliptic integral of the first kind is defined as - * @f[ - * F(k,\phi) = \int_0^{\phi}\frac{d\theta} - * {\sqrt{1 - k^2 sin^2\theta}} - * @f] - * - * @param __k The argument of the elliptic function. - * @param __phi The integral limit argument of the elliptic function. - * @return The elliptic function of the first kind. - */ - template<typename _Tp> - _Tp - __ellint_1(const _Tp __k, const _Tp __phi) - { - - if (__isnan(__k) || __isnan(__phi)) - return std::numeric_limits<_Tp>::quiet_NaN(); - else if (std::abs(__k) > _Tp(1)) - std::__throw_domain_error(__N("Bad argument in __ellint_1.")); - else - { - // Reduce phi to -pi/2 < phi < +pi/2. - const int __n = std::floor(__phi / __numeric_constants<_Tp>::__pi() - + _Tp(0.5L)); - const _Tp __phi_red = __phi - - __n * __numeric_constants<_Tp>::__pi(); - - const _Tp __s = std::sin(__phi_red); - const _Tp __c = std::cos(__phi_red); - - const _Tp __F = __s - * __ellint_rf(__c * __c, - _Tp(1) - __k * __k * __s * __s, _Tp(1)); - - if (__n == 0) - return __F; - else - return __F + _Tp(2) * __n * __comp_ellint_1(__k); - } - } - - - /** - * @brief Return the complete elliptic integral of the second kind - * @f$ E(k) @f$ by series expansion. - * - * The complete elliptic integral of the second kind is defined as - * @f[ - * E(k,\pi/2) = \int_0^{\pi/2}\sqrt{1 - k^2 sin^2\theta} - * @f] - * - * This routine is not bad as long as |k| is somewhat smaller than 1 - * but is not is good as the Carlson elliptic integral formulation. - * - * @param __k The argument of the complete elliptic function. - * @return The complete elliptic function of the second kind. - */ - template<typename _Tp> - _Tp - __comp_ellint_2_series(const _Tp __k) - { - - const _Tp __kk = __k * __k; - - _Tp __term = __kk; - _Tp __sum = __term; - - const unsigned int __max_iter = 1000; - for (unsigned int __i = 2; __i < __max_iter; ++__i) - { - const _Tp __i2m = 2 * __i - 1; - const _Tp __i2 = 2 * __i; - __term *= __i2m * __i2m * __kk / (__i2 * __i2); - if (__term < std::numeric_limits<_Tp>::epsilon()) - break; - __sum += __term / __i2m; - } - - return __numeric_constants<_Tp>::__pi_2() * (_Tp(1) - __sum); - } - - - /** - * @brief Return the Carlson elliptic function of the second kind - * @f$ R_D(x,y,z) = R_J(x,y,z,z) @f$ where - * @f$ R_J(x,y,z,p) @f$ is the Carlson elliptic function - * of the third kind. - * - * The Carlson elliptic function of the second kind is defined by: - * @f[ - * R_D(x,y,z) = \frac{3}{2} \int_0^\infty - * \frac{dt}{(t + x)^{1/2}(t + y)^{1/2}(t + z)^{3/2}} - * @f] - * - * Based on Carlson's algorithms: - * - B. C. Carlson Numer. Math. 33, 1 (1979) - * - B. C. Carlson, Special Functions of Applied Mathematics (1977) - * - Numerical Recipes in C, 2nd ed, pp. 261-269, - * by Press, Teukolsky, Vetterling, Flannery (1992) - * - * @param __x The first of two symmetric arguments. - * @param __y The second of two symmetric arguments. - * @param __z The third argument. - * @return The Carlson elliptic function of the second kind. - */ - template<typename _Tp> - _Tp - __ellint_rd(const _Tp __x, const _Tp __y, const _Tp __z) - { - const _Tp __eps = std::numeric_limits<_Tp>::epsilon(); - const _Tp __errtol = std::pow(__eps / _Tp(8), _Tp(1) / _Tp(6)); - const _Tp __min = std::numeric_limits<_Tp>::min(); - const _Tp __max = std::numeric_limits<_Tp>::max(); - const _Tp __lolim = _Tp(2) / std::pow(__max, _Tp(2) / _Tp(3)); - const _Tp __uplim = std::pow(_Tp(0.1L) * __errtol / __min, _Tp(2) / _Tp(3)); - - if (__x < _Tp(0) || __y < _Tp(0)) - std::__throw_domain_error(__N("Argument less than zero " - "in __ellint_rd.")); - else if (__x + __y < __lolim || __z < __lolim) - std::__throw_domain_error(__N("Argument too small " - "in __ellint_rd.")); - else - { - const _Tp __c0 = _Tp(1) / _Tp(4); - const _Tp __c1 = _Tp(3) / _Tp(14); - const _Tp __c2 = _Tp(1) / _Tp(6); - const _Tp __c3 = _Tp(9) / _Tp(22); - const _Tp __c4 = _Tp(3) / _Tp(26); - - _Tp __xn = __x; - _Tp __yn = __y; - _Tp __zn = __z; - _Tp __sigma = _Tp(0); - _Tp __power4 = _Tp(1); - - _Tp __mu; - _Tp __xndev, __yndev, __zndev; - - const unsigned int __max_iter = 100; - for (unsigned int __iter = 0; __iter < __max_iter; ++__iter) - { - __mu = (__xn + __yn + _Tp(3) * __zn) / _Tp(5); - __xndev = (__mu - __xn) / __mu; - __yndev = (__mu - __yn) / __mu; - __zndev = (__mu - __zn) / __mu; - _Tp __epsilon = std::max(std::abs(__xndev), std::abs(__yndev)); - __epsilon = std::max(__epsilon, std::abs(__zndev)); - if (__epsilon < __errtol) - break; - _Tp __xnroot = std::sqrt(__xn); - _Tp __ynroot = std::sqrt(__yn); - _Tp __znroot = std::sqrt(__zn); - _Tp __lambda = __xnroot * (__ynroot + __znroot) - + __ynroot * __znroot; - __sigma += __power4 / (__znroot * (__zn + __lambda)); - __power4 *= __c0; - __xn = __c0 * (__xn + __lambda); - __yn = __c0 * (__yn + __lambda); - __zn = __c0 * (__zn + __lambda); - } - - // Note: __ea is an SPU badname. - _Tp __eaa = __xndev * __yndev; - _Tp __eb = __zndev * __zndev; - _Tp __ec = __eaa - __eb; - _Tp __ed = __eaa - _Tp(6) * __eb; - _Tp __ef = __ed + __ec + __ec; - _Tp __s1 = __ed * (-__c1 + __c3 * __ed - / _Tp(3) - _Tp(3) * __c4 * __zndev * __ef - / _Tp(2)); - _Tp __s2 = __zndev - * (__c2 * __ef - + __zndev * (-__c3 * __ec - __zndev * __c4 - __eaa)); - - return _Tp(3) * __sigma + __power4 * (_Tp(1) + __s1 + __s2) - / (__mu * std::sqrt(__mu)); - } - } - - - /** - * @brief Return the complete elliptic integral of the second kind - * @f$ E(k) @f$ using the Carlson formulation. - * - * The complete elliptic integral of the second kind is defined as - * @f[ - * E(k,\pi/2) = \int_0^{\pi/2}\sqrt{1 - k^2 sin^2\theta} - * @f] - * - * @param __k The argument of the complete elliptic function. - * @return The complete elliptic function of the second kind. - */ - template<typename _Tp> - _Tp - __comp_ellint_2(const _Tp __k) - { - - if (__isnan(__k)) - return std::numeric_limits<_Tp>::quiet_NaN(); - else if (std::abs(__k) == 1) - return _Tp(1); - else if (std::abs(__k) > _Tp(1)) - std::__throw_domain_error(__N("Bad argument in __comp_ellint_2.")); - else - { - const _Tp __kk = __k * __k; - - return __ellint_rf(_Tp(0), _Tp(1) - __kk, _Tp(1)) - - __kk * __ellint_rd(_Tp(0), _Tp(1) - __kk, _Tp(1)) / _Tp(3); - } - } - - - /** - * @brief Return the incomplete elliptic integral of the second kind - * @f$ E(k,\phi) @f$ using the Carlson formulation. - * - * The incomplete elliptic integral of the second kind is defined as - * @f[ - * E(k,\phi) = \int_0^{\phi} \sqrt{1 - k^2 sin^2\theta} - * @f] - * - * @param __k The argument of the elliptic function. - * @param __phi The integral limit argument of the elliptic function. - * @return The elliptic function of the second kind. - */ - template<typename _Tp> - _Tp - __ellint_2(const _Tp __k, const _Tp __phi) - { - - if (__isnan(__k) || __isnan(__phi)) - return std::numeric_limits<_Tp>::quiet_NaN(); - else if (std::abs(__k) > _Tp(1)) - std::__throw_domain_error(__N("Bad argument in __ellint_2.")); - else - { - // Reduce phi to -pi/2 < phi < +pi/2. - const int __n = std::floor(__phi / __numeric_constants<_Tp>::__pi() - + _Tp(0.5L)); - const _Tp __phi_red = __phi - - __n * __numeric_constants<_Tp>::__pi(); - - const _Tp __kk = __k * __k; - const _Tp __s = std::sin(__phi_red); - const _Tp __ss = __s * __s; - const _Tp __sss = __ss * __s; - const _Tp __c = std::cos(__phi_red); - const _Tp __cc = __c * __c; - - const _Tp __E = __s - * __ellint_rf(__cc, _Tp(1) - __kk * __ss, _Tp(1)) - - __kk * __sss - * __ellint_rd(__cc, _Tp(1) - __kk * __ss, _Tp(1)) - / _Tp(3); - - if (__n == 0) - return __E; - else - return __E + _Tp(2) * __n * __comp_ellint_2(__k); - } - } - - - /** - * @brief Return the Carlson elliptic function - * @f$ R_C(x,y) = R_F(x,y,y) @f$ where @f$ R_F(x,y,z) @f$ - * is the Carlson elliptic function of the first kind. - * - * The Carlson elliptic function is defined by: - * @f[ - * R_C(x,y) = \frac{1}{2} \int_0^\infty - * \frac{dt}{(t + x)^{1/2}(t + y)} - * @f] - * - * Based on Carlson's algorithms: - * - B. C. Carlson Numer. Math. 33, 1 (1979) - * - B. C. Carlson, Special Functions of Applied Mathematics (1977) - * - Numerical Recipes in C, 2nd ed, pp. 261-269, - * by Press, Teukolsky, Vetterling, Flannery (1992) - * - * @param __x The first argument. - * @param __y The second argument. - * @return The Carlson elliptic function. - */ - template<typename _Tp> - _Tp - __ellint_rc(const _Tp __x, const _Tp __y) - { - const _Tp __min = std::numeric_limits<_Tp>::min(); - const _Tp __max = std::numeric_limits<_Tp>::max(); - const _Tp __lolim = _Tp(5) * __min; - const _Tp __uplim = __max / _Tp(5); - - if (__x < _Tp(0) || __y < _Tp(0) || __x + __y < __lolim) - std::__throw_domain_error(__N("Argument less than zero " - "in __ellint_rc.")); - else - { - const _Tp __c0 = _Tp(1) / _Tp(4); - const _Tp __c1 = _Tp(1) / _Tp(7); - const _Tp __c2 = _Tp(9) / _Tp(22); - const _Tp __c3 = _Tp(3) / _Tp(10); - const _Tp __c4 = _Tp(3) / _Tp(8); - - _Tp __xn = __x; - _Tp __yn = __y; - - const _Tp __eps = std::numeric_limits<_Tp>::epsilon(); - const _Tp __errtol = std::pow(__eps / _Tp(30), _Tp(1) / _Tp(6)); - _Tp __mu; - _Tp __sn; - - const unsigned int __max_iter = 100; - for (unsigned int __iter = 0; __iter < __max_iter; ++__iter) - { - __mu = (__xn + _Tp(2) * __yn) / _Tp(3); - __sn = (__yn + __mu) / __mu - _Tp(2); - if (std::abs(__sn) < __errtol) - break; - const _Tp __lambda = _Tp(2) * std::sqrt(__xn) * std::sqrt(__yn) - + __yn; - __xn = __c0 * (__xn + __lambda); - __yn = __c0 * (__yn + __lambda); - } - - _Tp __s = __sn * __sn - * (__c3 + __sn*(__c1 + __sn * (__c4 + __sn * __c2))); - - return (_Tp(1) + __s) / std::sqrt(__mu); - } - } - - - /** - * @brief Return the Carlson elliptic function @f$ R_J(x,y,z,p) @f$ - * of the third kind. - * - * The Carlson elliptic function of the third kind is defined by: - * @f[ - * R_J(x,y,z,p) = \frac{3}{2} \int_0^\infty - * \frac{dt}{(t + x)^{1/2}(t + y)^{1/2}(t + z)^{1/2}(t + p)} - * @f] - * - * Based on Carlson's algorithms: - * - B. C. Carlson Numer. Math. 33, 1 (1979) - * - B. C. Carlson, Special Functions of Applied Mathematics (1977) - * - Numerical Recipes in C, 2nd ed, pp. 261-269, - * by Press, Teukolsky, Vetterling, Flannery (1992) - * - * @param __x The first of three symmetric arguments. - * @param __y The second of three symmetric arguments. - * @param __z The third of three symmetric arguments. - * @param __p The fourth argument. - * @return The Carlson elliptic function of the fourth kind. - */ - template<typename _Tp> - _Tp - __ellint_rj(const _Tp __x, const _Tp __y, const _Tp __z, const _Tp __p) - { - const _Tp __min = std::numeric_limits<_Tp>::min(); - const _Tp __max = std::numeric_limits<_Tp>::max(); - const _Tp __lolim = std::pow(_Tp(5) * __min, _Tp(1)/_Tp(3)); - const _Tp __uplim = _Tp(0.3L) - * std::pow(_Tp(0.2L) * __max, _Tp(1)/_Tp(3)); - - if (__x < _Tp(0) || __y < _Tp(0) || __z < _Tp(0)) - std::__throw_domain_error(__N("Argument less than zero " - "in __ellint_rj.")); - else if (__x + __y < __lolim || __x + __z < __lolim - || __y + __z < __lolim || __p < __lolim) - std::__throw_domain_error(__N("Argument too small " - "in __ellint_rj")); - else - { - const _Tp __c0 = _Tp(1) / _Tp(4); - const _Tp __c1 = _Tp(3) / _Tp(14); - const _Tp __c2 = _Tp(1) / _Tp(3); - const _Tp __c3 = _Tp(3) / _Tp(22); - const _Tp __c4 = _Tp(3) / _Tp(26); - - _Tp __xn = __x; - _Tp __yn = __y; - _Tp __zn = __z; - _Tp __pn = __p; - _Tp __sigma = _Tp(0); - _Tp __power4 = _Tp(1); - - const _Tp __eps = std::numeric_limits<_Tp>::epsilon(); - const _Tp __errtol = std::pow(__eps / _Tp(8), _Tp(1) / _Tp(6)); - - _Tp __lambda, __mu; - _Tp __xndev, __yndev, __zndev, __pndev; - - const unsigned int __max_iter = 100; - for (unsigned int __iter = 0; __iter < __max_iter; ++__iter) - { - __mu = (__xn + __yn + __zn + _Tp(2) * __pn) / _Tp(5); - __xndev = (__mu - __xn) / __mu; - __yndev = (__mu - __yn) / __mu; - __zndev = (__mu - __zn) / __mu; - __pndev = (__mu - __pn) / __mu; - _Tp __epsilon = std::max(std::abs(__xndev), std::abs(__yndev)); - __epsilon = std::max(__epsilon, std::abs(__zndev)); - __epsilon = std::max(__epsilon, std::abs(__pndev)); - if (__epsilon < __errtol) - break; - const _Tp __xnroot = std::sqrt(__xn); - const _Tp __ynroot = std::sqrt(__yn); - const _Tp __znroot = std::sqrt(__zn); - const _Tp __lambda = __xnroot * (__ynroot + __znroot) - + __ynroot * __znroot; - const _Tp __alpha1 = __pn * (__xnroot + __ynroot + __znroot) - + __xnroot * __ynroot * __znroot; - const _Tp __alpha2 = __alpha1 * __alpha1; - const _Tp __beta = __pn * (__pn + __lambda) - * (__pn + __lambda); - __sigma += __power4 * __ellint_rc(__alpha2, __beta); - __power4 *= __c0; - __xn = __c0 * (__xn + __lambda); - __yn = __c0 * (__yn + __lambda); - __zn = __c0 * (__zn + __lambda); - __pn = __c0 * (__pn + __lambda); - } - - // Note: __ea is an SPU badname. - _Tp __eaa = __xndev * (__yndev + __zndev) + __yndev * __zndev; - _Tp __eb = __xndev * __yndev * __zndev; - _Tp __ec = __pndev * __pndev; - _Tp __e2 = __eaa - _Tp(3) * __ec; - _Tp __e3 = __eb + _Tp(2) * __pndev * (__eaa - __ec); - _Tp __s1 = _Tp(1) + __e2 * (-__c1 + _Tp(3) * __c3 * __e2 / _Tp(4) - - _Tp(3) * __c4 * __e3 / _Tp(2)); - _Tp __s2 = __eb * (__c2 / _Tp(2) - + __pndev * (-__c3 - __c3 + __pndev * __c4)); - _Tp __s3 = __pndev * __eaa * (__c2 - __pndev * __c3) - - __c2 * __pndev * __ec; - - return _Tp(3) * __sigma + __power4 * (__s1 + __s2 + __s3) - / (__mu * std::sqrt(__mu)); - } - } - - - /** - * @brief Return the complete elliptic integral of the third kind - * @f$ \Pi(k,\nu) = \Pi(k,\nu,\pi/2) @f$ using the - * Carlson formulation. - * - * The complete elliptic integral of the third kind is defined as - * @f[ - * \Pi(k,\nu) = \int_0^{\pi/2} - * \frac{d\theta} - * {(1 - \nu \sin^2\theta)\sqrt{1 - k^2 \sin^2\theta}} - * @f] - * - * @param __k The argument of the elliptic function. - * @param __nu The second argument of the elliptic function. - * @return The complete elliptic function of the third kind. - */ - template<typename _Tp> - _Tp - __comp_ellint_3(const _Tp __k, const _Tp __nu) - { - - if (__isnan(__k) || __isnan(__nu)) - return std::numeric_limits<_Tp>::quiet_NaN(); - else if (__nu == _Tp(1)) - return std::numeric_limits<_Tp>::infinity(); - else if (std::abs(__k) > _Tp(1)) - std::__throw_domain_error(__N("Bad argument in __comp_ellint_3.")); - else - { - const _Tp __kk = __k * __k; - - return __ellint_rf(_Tp(0), _Tp(1) - __kk, _Tp(1)) - - __nu - * __ellint_rj(_Tp(0), _Tp(1) - __kk, _Tp(1), _Tp(1) + __nu) - / _Tp(3); - } - } - - - /** - * @brief Return the incomplete elliptic integral of the third kind - * @f$ \Pi(k,\nu,\phi) @f$ using the Carlson formulation. - * - * The incomplete elliptic integral of the third kind is defined as - * @f[ - * \Pi(k,\nu,\phi) = \int_0^{\phi} - * \frac{d\theta} - * {(1 - \nu \sin^2\theta) - * \sqrt{1 - k^2 \sin^2\theta}} - * @f] - * - * @param __k The argument of the elliptic function. - * @param __nu The second argument of the elliptic function. - * @param __phi The integral limit argument of the elliptic function. - * @return The elliptic function of the third kind. - */ - template<typename _Tp> - _Tp - __ellint_3(const _Tp __k, const _Tp __nu, const _Tp __phi) - { - - if (__isnan(__k) || __isnan(__nu) || __isnan(__phi)) - return std::numeric_limits<_Tp>::quiet_NaN(); - else if (std::abs(__k) > _Tp(1)) - std::__throw_domain_error(__N("Bad argument in __ellint_3.")); - else - { - // Reduce phi to -pi/2 < phi < +pi/2. - const int __n = std::floor(__phi / __numeric_constants<_Tp>::__pi() - + _Tp(0.5L)); - const _Tp __phi_red = __phi - - __n * __numeric_constants<_Tp>::__pi(); - - const _Tp __kk = __k * __k; - const _Tp __s = std::sin(__phi_red); - const _Tp __ss = __s * __s; - const _Tp __sss = __ss * __s; - const _Tp __c = std::cos(__phi_red); - const _Tp __cc = __c * __c; - - const _Tp __Pi = __s - * __ellint_rf(__cc, _Tp(1) - __kk * __ss, _Tp(1)) - - __nu * __sss - * __ellint_rj(__cc, _Tp(1) - __kk * __ss, _Tp(1), - _Tp(1) + __nu * __ss) / _Tp(3); - - if (__n == 0) - return __Pi; - else - return __Pi + _Tp(2) * __n * __comp_ellint_3(__k, __nu); - } - } - - } // namespace std::tr1::__detail -} -} - -#endif // _GLIBCXX_TR1_ELL_INTEGRAL_TCC - |