118 lines
3.3 KiB
C++
118 lines
3.3 KiB
C++
/* Translated into C++ by SciPy developers in 2024.
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* Original header with Copyright information appears below.
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*/
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/* ellpk.c
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*
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* Complete elliptic integral of the first kind
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*
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*
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*
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* SYNOPSIS:
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*
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* double m1, y, ellpk();
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*
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* y = ellpk( m1 );
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*
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*
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*
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* DESCRIPTION:
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*
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* Approximates the integral
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*
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*
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*
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* pi/2
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* -
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* | |
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* | dt
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* K(m) = | ------------------
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* | 2
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* | | sqrt( 1 - m sin t )
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* -
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* 0
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*
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* where m = 1 - m1, using the approximation
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*
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* P(x) - log x Q(x).
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*
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* The argument m1 is used internally rather than m so that the logarithmic
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* singularity at m = 1 will be shifted to the origin; this
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* preserves maximum accuracy.
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*
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* K(0) = pi/2.
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*
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* ACCURACY:
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*
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* Relative error:
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* arithmetic domain # trials peak rms
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* IEEE 0,1 30000 2.5e-16 6.8e-17
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*
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* ERROR MESSAGES:
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*
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* message condition value returned
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* ellpk domain x<0, x>1 0.0
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*
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*/
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/* ellpk.c */
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/*
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* Cephes Math Library, Release 2.0: April, 1987
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* Copyright 1984, 1987 by Stephen L. Moshier
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* Direct inquiries to 30 Frost Street, Cambridge, MA 02140
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*/
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#pragma once
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#include "../config.h"
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#include "../error.h"
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#include "const.h"
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#include "polevl.h"
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namespace xsf {
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namespace cephes {
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namespace detail {
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constexpr double ellpk_P[] = {1.37982864606273237150E-4, 2.28025724005875567385E-3, 7.97404013220415179367E-3,
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9.85821379021226008714E-3, 6.87489687449949877925E-3, 6.18901033637687613229E-3,
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8.79078273952743772254E-3, 1.49380448916805252718E-2, 3.08851465246711995998E-2,
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9.65735902811690126535E-2, 1.38629436111989062502E0};
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constexpr double ellpk_Q[] = {2.94078955048598507511E-5, 9.14184723865917226571E-4, 5.94058303753167793257E-3,
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1.54850516649762399335E-2, 2.39089602715924892727E-2, 3.01204715227604046988E-2,
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3.73774314173823228969E-2, 4.88280347570998239232E-2, 7.03124996963957469739E-2,
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1.24999999999870820058E-1, 4.99999999999999999821E-1};
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constexpr double ellpk_C1 = 1.3862943611198906188E0; /* log(4) */
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} // namespace detail
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XSF_HOST_DEVICE inline double ellpk(double x) {
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if (x < 0.0) {
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set_error("ellpk", SF_ERROR_DOMAIN, NULL);
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return (std::numeric_limits<double>::quiet_NaN());
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}
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if (x > 1.0) {
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if (std::isinf(x)) {
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return 0.0;
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}
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return ellpk(1 / x) / std::sqrt(x);
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}
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if (x > detail::MACHEP) {
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return (polevl(x, detail::ellpk_P, 10) - std::log(x) * polevl(x, detail::ellpk_Q, 10));
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} else {
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if (x == 0.0) {
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set_error("ellpk", SF_ERROR_SINGULAR, NULL);
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return (std::numeric_limits<double>::infinity());
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} else {
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return (detail::ellpk_C1 - 0.5 * std::log(x));
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}
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}
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}
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} // namespace cephes
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} // namespace xsf
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