225 lines
7.2 KiB
C++
225 lines
7.2 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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/* sici.c
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*
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* Sine and cosine integrals
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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 x, Ci, Si, sici();
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*
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* sici( x, &Si, &Ci );
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*
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*
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* DESCRIPTION:
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*
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* Evaluates the integrals
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*
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* x
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* -
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* | cos t - 1
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* Ci(x) = eul + ln x + | --------- dt,
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* | t
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* -
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* 0
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* x
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* -
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* | sin t
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* Si(x) = | ----- dt
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* | t
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* -
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* 0
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*
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* where eul = 0.57721566490153286061 is Euler's constant.
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* The integrals are approximated by rational functions.
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* For x > 8 auxiliary functions f(x) and g(x) are employed
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* such that
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*
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* Ci(x) = f(x) sin(x) - g(x) cos(x)
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* Si(x) = pi/2 - f(x) cos(x) - g(x) sin(x)
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*
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*
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* ACCURACY:
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* Test interval = [0,50].
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* Absolute error, except relative when > 1:
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* arithmetic function # trials peak rms
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* IEEE Si 30000 4.4e-16 7.3e-17
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* IEEE Ci 30000 6.9e-16 5.1e-17
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*/
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/*
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* Cephes Math Library Release 2.1: January, 1989
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* Copyright 1984, 1987, 1989 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 "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 sici_SN[] = {
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-8.39167827910303881427E-11, 4.62591714427012837309E-8, -9.75759303843632795789E-6,
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9.76945438170435310816E-4, -4.13470316229406538752E-2, 1.00000000000000000302E0,
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};
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constexpr double sici_SD[] = {
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2.03269266195951942049E-12, 1.27997891179943299903E-9, 4.41827842801218905784E-7,
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9.96412122043875552487E-5, 1.42085239326149893930E-2, 9.99999999999999996984E-1,
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};
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constexpr double sici_CN[] = {
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2.02524002389102268789E-11, -1.35249504915790756375E-8, 3.59325051419993077021E-6,
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-4.74007206873407909465E-4, 2.89159652607555242092E-2, -1.00000000000000000080E0,
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};
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constexpr double sici_CD[] = {
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4.07746040061880559506E-12, 3.06780997581887812692E-9, 1.23210355685883423679E-6,
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3.17442024775032769882E-4, 5.10028056236446052392E-2, 4.00000000000000000080E0,
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};
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constexpr double sici_FN4[] = {
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4.23612862892216586994E0, 5.45937717161812843388E0, 1.62083287701538329132E0, 1.67006611831323023771E-1,
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6.81020132472518137426E-3, 1.08936580650328664411E-4, 5.48900223421373614008E-7,
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};
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constexpr double sici_FD4[] = {
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/* 1.00000000000000000000E0, */
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8.16496634205391016773E0, 7.30828822505564552187E0, 1.86792257950184183883E0, 1.78792052963149907262E-1,
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7.01710668322789753610E-3, 1.10034357153915731354E-4, 5.48900252756255700982E-7,
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};
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constexpr double sici_FN8[] = {
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4.55880873470465315206E-1, 7.13715274100146711374E-1, 1.60300158222319456320E-1,
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1.16064229408124407915E-2, 3.49556442447859055605E-4, 4.86215430826454749482E-6,
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3.20092790091004902806E-8, 9.41779576128512936592E-11, 9.70507110881952024631E-14,
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};
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constexpr double sici_FD8[] = {
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/* 1.00000000000000000000E0, */
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9.17463611873684053703E-1, 1.78685545332074536321E-1, 1.22253594771971293032E-2,
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3.58696481881851580297E-4, 4.92435064317881464393E-6, 3.21956939101046018377E-8,
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9.43720590350276732376E-11, 9.70507110881952025725E-14,
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};
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constexpr double sici_GN4[] = {
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8.71001698973114191777E-2, 6.11379109952219284151E-1, 3.97180296392337498885E-1, 7.48527737628469092119E-2,
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5.38868681462177273157E-3, 1.61999794598934024525E-4, 1.97963874140963632189E-6, 7.82579040744090311069E-9,
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};
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constexpr double sici_GD4[] = {
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/* 1.00000000000000000000E0, */
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1.64402202413355338886E0, 6.66296701268987968381E-1, 9.88771761277688796203E-2, 6.22396345441768420760E-3,
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1.73221081474177119497E-4, 2.02659182086343991969E-6, 7.82579218933534490868E-9,
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};
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constexpr double sici_GN8[] = {
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6.97359953443276214934E-1, 3.30410979305632063225E-1, 3.84878767649974295920E-2,
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1.71718239052347903558E-3, 3.48941165502279436777E-5, 3.47131167084116673800E-7,
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1.70404452782044526189E-9, 3.85945925430276600453E-12, 3.14040098946363334640E-15,
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};
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constexpr double sici_GD8[] = {
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/* 1.00000000000000000000E0, */
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1.68548898811011640017E0, 4.87852258695304967486E-1, 4.67913194259625806320E-2,
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1.90284426674399523638E-3, 3.68475504442561108162E-5, 3.57043223443740838771E-7,
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1.72693748966316146736E-9, 3.87830166023954706752E-12, 3.14040098946363335242E-15,
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};
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} // namespace detail
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XSF_HOST_DEVICE inline int sici(double x, double *si, double *ci) {
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double z, c, s, f, g;
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short sign;
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if (x < 0.0) {
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sign = -1;
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x = -x;
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} else {
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sign = 0;
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}
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if (x == 0.0) {
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*si = 0.0;
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*ci = -std::numeric_limits<double>::infinity();
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return (0);
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}
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if (x > 1.0e9) {
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if (std::isinf(x)) {
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if (sign == -1) {
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*si = -M_PI_2;
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*ci = std::numeric_limits<double>::quiet_NaN();
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} else {
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*si = M_PI_2;
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*ci = 0;
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}
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return 0;
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}
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*si = M_PI_2 - std::cos(x) / x;
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*ci = std::sin(x) / x;
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}
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if (x > 4.0) {
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goto asympt;
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}
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z = x * x;
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s = x * polevl(z, detail::sici_SN, 5) / polevl(z, detail::sici_SD, 5);
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c = z * polevl(z, detail::sici_CN, 5) / polevl(z, detail::sici_CD, 5);
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if (sign) {
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s = -s;
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}
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*si = s;
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*ci = detail::SCIPY_EULER + std::log(x) + c; /* real part if x < 0 */
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return (0);
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/* The auxiliary functions are:
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*
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*
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* *si = *si - M_PI_2;
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* c = cos(x);
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* s = sin(x);
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*
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* t = *ci * s - *si * c;
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* a = *ci * c + *si * s;
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*
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* *si = t;
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* *ci = -a;
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*/
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asympt:
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s = std::sin(x);
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c = std::cos(x);
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z = 1.0 / (x * x);
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if (x < 8.0) {
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f = polevl(z, detail::sici_FN4, 6) / (x * p1evl(z, detail::sici_FD4, 7));
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g = z * polevl(z, detail::sici_GN4, 7) / p1evl(z, detail::sici_GD4, 7);
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} else {
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f = polevl(z, detail::sici_FN8, 8) / (x * p1evl(z, detail::sici_FD8, 8));
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g = z * polevl(z, detail::sici_GN8, 8) / p1evl(z, detail::sici_GD8, 9);
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}
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*si = M_PI_2 - f * c - g * s;
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if (sign) {
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*si = -(*si);
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}
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*ci = f * s - g * c;
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return (0);
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}
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} // namespace cephes
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} // namespace xsf
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