venv/lib/python3.11/site-packages/scipy/special/xsf/cephes/sici.h

/* 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