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/* Translated into C++ by SciPy developers in 2024.
* Original header with Copyright information appears below.
*/
/* sici.c
*
* Sine and cosine integrals
*
*
*
* SYNOPSIS:
*
* double x, Ci, Si, sici();
*
* sici( x, &Si, &Ci );
*
*
* DESCRIPTION:
*
* Evaluates the integrals
*
* x
* -
* | cos t - 1
* Ci(x) = eul + ln x + | --------- dt,
* | t
* -
* 0
* x
* -
* | sin t
* Si(x) = | ----- dt
* | t
* -
* 0
*
* where eul = 0.57721566490153286061 is Euler's constant.
* The integrals are approximated by rational functions.
* For x > 8 auxiliary functions f(x) and g(x) are employed
* such that
*
* Ci(x) = f(x) sin(x) - g(x) cos(x)
* Si(x) = pi/2 - f(x) cos(x) - g(x) sin(x)
*
*
* ACCURACY:
* Test interval = [0,50].
* Absolute error, except relative when > 1:
* arithmetic function # trials peak rms
* IEEE Si 30000 4.4e-16 7.3e-17
* IEEE Ci 30000 6.9e-16 5.1e-17
*/
/*
* Cephes Math Library Release 2.1: January, 1989
* Copyright 1984, 1987, 1989 by Stephen L. Moshier
* Direct inquiries to 30 Frost Street, Cambridge, MA 02140
*/
#pragma once
#include "../config.h"
#include "const.h"
#include "polevl.h"
namespace xsf {
namespace cephes {
namespace detail {
constexpr double sici_SN[] = {
-8.39167827910303881427E-11, 4.62591714427012837309E-8, -9.75759303843632795789E-6,
9.76945438170435310816E-4, -4.13470316229406538752E-2, 1.00000000000000000302E0,
};
constexpr double sici_SD[] = {
2.03269266195951942049E-12, 1.27997891179943299903E-9, 4.41827842801218905784E-7,
9.96412122043875552487E-5, 1.42085239326149893930E-2, 9.99999999999999996984E-1,
};
constexpr double sici_CN[] = {
2.02524002389102268789E-11, -1.35249504915790756375E-8, 3.59325051419993077021E-6,
-4.74007206873407909465E-4, 2.89159652607555242092E-2, -1.00000000000000000080E0,
};
constexpr double sici_CD[] = {
4.07746040061880559506E-12, 3.06780997581887812692E-9, 1.23210355685883423679E-6,
3.17442024775032769882E-4, 5.10028056236446052392E-2, 4.00000000000000000080E0,
};
constexpr double sici_FN4[] = {
4.23612862892216586994E0, 5.45937717161812843388E0, 1.62083287701538329132E0, 1.67006611831323023771E-1,
6.81020132472518137426E-3, 1.08936580650328664411E-4, 5.48900223421373614008E-7,
};
constexpr double sici_FD4[] = {
/* 1.00000000000000000000E0, */
8.16496634205391016773E0, 7.30828822505564552187E0, 1.86792257950184183883E0, 1.78792052963149907262E-1,
7.01710668322789753610E-3, 1.10034357153915731354E-4, 5.48900252756255700982E-7,
};
constexpr double sici_FN8[] = {
4.55880873470465315206E-1, 7.13715274100146711374E-1, 1.60300158222319456320E-1,
1.16064229408124407915E-2, 3.49556442447859055605E-4, 4.86215430826454749482E-6,
3.20092790091004902806E-8, 9.41779576128512936592E-11, 9.70507110881952024631E-14,
};
constexpr double sici_FD8[] = {
/* 1.00000000000000000000E0, */
9.17463611873684053703E-1, 1.78685545332074536321E-1, 1.22253594771971293032E-2,
3.58696481881851580297E-4, 4.92435064317881464393E-6, 3.21956939101046018377E-8,
9.43720590350276732376E-11, 9.70507110881952025725E-14,
};
constexpr double sici_GN4[] = {
8.71001698973114191777E-2, 6.11379109952219284151E-1, 3.97180296392337498885E-1, 7.48527737628469092119E-2,
5.38868681462177273157E-3, 1.61999794598934024525E-4, 1.97963874140963632189E-6, 7.82579040744090311069E-9,
};
constexpr double sici_GD4[] = {
/* 1.00000000000000000000E0, */
1.64402202413355338886E0, 6.66296701268987968381E-1, 9.88771761277688796203E-2, 6.22396345441768420760E-3,
1.73221081474177119497E-4, 2.02659182086343991969E-6, 7.82579218933534490868E-9,
};
constexpr double sici_GN8[] = {
6.97359953443276214934E-1, 3.30410979305632063225E-1, 3.84878767649974295920E-2,
1.71718239052347903558E-3, 3.48941165502279436777E-5, 3.47131167084116673800E-7,
1.70404452782044526189E-9, 3.85945925430276600453E-12, 3.14040098946363334640E-15,
};
constexpr double sici_GD8[] = {
/* 1.00000000000000000000E0, */
1.68548898811011640017E0, 4.87852258695304967486E-1, 4.67913194259625806320E-2,
1.90284426674399523638E-3, 3.68475504442561108162E-5, 3.57043223443740838771E-7,
1.72693748966316146736E-9, 3.87830166023954706752E-12, 3.14040098946363335242E-15,
};
} // namespace detail
XSF_HOST_DEVICE inline int sici(double x, double *si, double *ci) {
double z, c, s, f, g;
short sign;
if (x < 0.0) {
sign = -1;
x = -x;
} else {
sign = 0;
}
if (x == 0.0) {
*si = 0.0;
*ci = -std::numeric_limits<double>::infinity();
return (0);
}
if (x > 1.0e9) {
if (std::isinf(x)) {
if (sign == -1) {
*si = -M_PI_2;
*ci = std::numeric_limits<double>::quiet_NaN();
} else {
*si = M_PI_2;
*ci = 0;
}
return 0;
}
*si = M_PI_2 - std::cos(x) / x;
*ci = std::sin(x) / x;
}
if (x > 4.0) {
goto asympt;
}
z = x * x;
s = x * polevl(z, detail::sici_SN, 5) / polevl(z, detail::sici_SD, 5);
c = z * polevl(z, detail::sici_CN, 5) / polevl(z, detail::sici_CD, 5);
if (sign) {
s = -s;
}
*si = s;
*ci = detail::SCIPY_EULER + std::log(x) + c; /* real part if x < 0 */
return (0);
/* The auxiliary functions are:
*
*
* *si = *si - M_PI_2;
* c = cos(x);
* s = sin(x);
*
* t = *ci * s - *si * c;
* a = *ci * c + *si * s;
*
* *si = t;
* *ci = -a;
*/
asympt:
s = std::sin(x);
c = std::cos(x);
z = 1.0 / (x * x);
if (x < 8.0) {
f = polevl(z, detail::sici_FN4, 6) / (x * p1evl(z, detail::sici_FD4, 7));
g = z * polevl(z, detail::sici_GN4, 7) / p1evl(z, detail::sici_GD4, 7);
} else {
f = polevl(z, detail::sici_FN8, 8) / (x * p1evl(z, detail::sici_FD8, 8));
g = z * polevl(z, detail::sici_GN8, 8) / p1evl(z, detail::sici_GD8, 9);
}
*si = M_PI_2 - f * c - g * s;
if (sign) {
*si = -(*si);
}
*ci = f * s - g * c;
return (0);
}
} // namespace cephes
} // namespace xsf
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