File size: 3,392 Bytes
7885a28 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 |
/* Translated into C++ by SciPy developers in 2024.
* Original header with Copyright information appears below.
*/
/* ellpk.c
*
* Complete elliptic integral of the first kind
*
*
*
* SYNOPSIS:
*
* double m1, y, ellpk();
*
* y = ellpk( m1 );
*
*
*
* DESCRIPTION:
*
* Approximates the integral
*
*
*
* pi/2
* -
* | |
* | dt
* K(m) = | ------------------
* | 2
* | | sqrt( 1 - m sin t )
* -
* 0
*
* where m = 1 - m1, using the approximation
*
* P(x) - log x Q(x).
*
* The argument m1 is used internally rather than m so that the logarithmic
* singularity at m = 1 will be shifted to the origin; this
* preserves maximum accuracy.
*
* K(0) = pi/2.
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE 0,1 30000 2.5e-16 6.8e-17
*
* ERROR MESSAGES:
*
* message condition value returned
* ellpk domain x<0, x>1 0.0
*
*/
/* ellpk.c */
/*
* Cephes Math Library, Release 2.0: April, 1987
* Copyright 1984, 1987 by Stephen L. Moshier
* Direct inquiries to 30 Frost Street, Cambridge, MA 02140
*/
#pragma once
#include "../config.h"
#include "../error.h"
#include "const.h"
#include "polevl.h"
namespace xsf {
namespace cephes {
namespace detail {
constexpr double ellpk_P[] = {1.37982864606273237150E-4, 2.28025724005875567385E-3, 7.97404013220415179367E-3,
9.85821379021226008714E-3, 6.87489687449949877925E-3, 6.18901033637687613229E-3,
8.79078273952743772254E-3, 1.49380448916805252718E-2, 3.08851465246711995998E-2,
9.65735902811690126535E-2, 1.38629436111989062502E0};
constexpr double ellpk_Q[] = {2.94078955048598507511E-5, 9.14184723865917226571E-4, 5.94058303753167793257E-3,
1.54850516649762399335E-2, 2.39089602715924892727E-2, 3.01204715227604046988E-2,
3.73774314173823228969E-2, 4.88280347570998239232E-2, 7.03124996963957469739E-2,
1.24999999999870820058E-1, 4.99999999999999999821E-1};
constexpr double ellpk_C1 = 1.3862943611198906188E0; /* log(4) */
} // namespace detail
XSF_HOST_DEVICE inline double ellpk(double x) {
if (x < 0.0) {
set_error("ellpk", SF_ERROR_DOMAIN, NULL);
return (std::numeric_limits<double>::quiet_NaN());
}
if (x > 1.0) {
if (std::isinf(x)) {
return 0.0;
}
return ellpk(1 / x) / std::sqrt(x);
}
if (x > detail::MACHEP) {
return (polevl(x, detail::ellpk_P, 10) - std::log(x) * polevl(x, detail::ellpk_Q, 10));
} else {
if (x == 0.0) {
set_error("ellpk", SF_ERROR_SINGULAR, NULL);
return (std::numeric_limits<double>::infinity());
} else {
return (detail::ellpk_C1 - 0.5 * std::log(x));
}
}
}
} // namespace cephes
} // namespace xsf
|