venv/lib/python3.11/site-packages/scipy/special/xsf/cephes/j1.h

/* Translated into C++ by SciPy developers in 2024.
 * Original header with Copyright information appears below.
 */

/*                                                     j1.c
 *
 *     Bessel function of order one
 *
 *
 *
 * SYNOPSIS:
 *
 * double x, y, j1();
 *
 * y = j1( x );
 *
 *
 *
 * DESCRIPTION:
 *
 * Returns Bessel function of order one of the argument.
 *
 * The domain is divided into the intervals [0, 8] and
 * (8, infinity). In the first interval a 24 term Chebyshev
 * expansion is used. In the second, the asymptotic
 * trigonometric representation is employed using two
 * rational functions of degree 5/5.
 *
 *
 *
 * ACCURACY:
 *
 *                      Absolute error:
 * arithmetic   domain      # trials      peak         rms
 *    IEEE      0, 30       30000       2.6e-16     1.1e-16
 *
 *
 */
/*							y1.c
 *
 *	Bessel function of second kind of order one
 *
 *
 *
 * SYNOPSIS:
 *
 * double x, y, y1();
 *
 * y = y1( x );
 *
 *
 *
 * DESCRIPTION:
 *
 * Returns Bessel function of the second kind of order one
 * of the argument.
 *
 * The domain is divided into the intervals [0, 8] and
 * (8, infinity). In the first interval a 25 term Chebyshev
 * expansion is used, and a call to j1() is required.
 * In the second, the asymptotic trigonometric representation
 * is employed using two rational functions of degree 5/5.
 *
 *
 *
 * ACCURACY:
 *
 *                      Absolute error:
 * arithmetic   domain      # trials      peak         rms
 *    IEEE      0, 30       30000       1.0e-15     1.3e-16
 *
 * (error criterion relative when |y1| > 1).
 *
 */

/*
 * Cephes Math Library Release 2.8:  June, 2000
 * Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier
 */

/*
 * #define PIO4 .78539816339744830962
 * #define THPIO4 2.35619449019234492885
 * #define SQ2OPI .79788456080286535588
 */
#pragma once

#include "../config.h"
#include "../error.h"

#include "const.h"
#include "polevl.h"

namespace xsf {
namespace cephes {

    namespace detail {
        constexpr double j1_RP[4] = {
            -8.99971225705559398224E8,
            4.52228297998194034323E11,
            -7.27494245221818276015E13,
            3.68295732863852883286E15,
        };

        constexpr double j1_RQ[8] = {
            /* 1.00000000000000000000E0, */
            6.20836478118054335476E2,  2.56987256757748830383E5,  8.35146791431949253037E7,  2.21511595479792499675E10,
            4.74914122079991414898E12, 7.84369607876235854894E14, 8.95222336184627338078E16, 5.32278620332680085395E18,
        };

        constexpr double j1_PP[7] = {
            7.62125616208173112003E-4, 7.31397056940917570436E-2, 1.12719608129684925192E0, 5.11207951146807644818E0,
            8.42404590141772420927E0,  5.21451598682361504063E0,  1.00000000000000000254E0,
        };

        constexpr double j1_PQ[7] = {
            5.71323128072548699714E-4, 6.88455908754495404082E-2, 1.10514232634061696926E0,  5.07386386128601488557E0,
            8.39985554327604159757E0,  5.20982848682361821619E0,  9.99999999999999997461E-1,
        };

        constexpr double j1_QP[8] = {
            5.10862594750176621635E-2, 4.98213872951233449420E0, 7.58238284132545283818E1, 3.66779609360150777800E2,
            7.10856304998926107277E2,  5.97489612400613639965E2, 2.11688757100572135698E2, 2.52070205858023719784E1,
        };

        constexpr double j1_QQ[7] = {
            /* 1.00000000000000000000E0, */
            7.42373277035675149943E1, 1.05644886038262816351E3, 4.98641058337653607651E3, 9.56231892404756170795E3,
            7.99704160447350683650E3, 2.82619278517639096600E3, 3.36093607810698293419E2,
        };

        constexpr double j1_YP[6] = {
            1.26320474790178026440E9,   -6.47355876379160291031E11, 1.14509511541823727583E14,
            -8.12770255501325109621E15, 2.02439475713594898196E17,  -7.78877196265950026825E17,
        };

        constexpr double j1_YQ[8] = {
            /* 1.00000000000000000000E0, */
            5.94301592346128195359E2,  2.35564092943068577943E5,  7.34811944459721705660E7,  1.87601316108706159478E10,
            3.88231277496238566008E12, 6.20557727146953693363E14, 6.87141087355300489866E16, 3.97270608116560655612E18,
        };

        constexpr double j1_Z1 = 1.46819706421238932572E1;
        constexpr double j1_Z2 = 4.92184563216946036703E1;

    } // namespace detail

    XSF_HOST_DEVICE inline double j1(double x) {
        double w, z, p, q, xn;

        w = x;
        if (x < 0) {
            return -j1(-x);
        }

        if (w <= 5.0) {
            z = x * x;
            w = polevl(z, detail::j1_RP, 3) / p1evl(z, detail::j1_RQ, 8);
            w = w * x * (z - detail::j1_Z1) * (z - detail::j1_Z2);
            return (w);
        }

        w = 5.0 / x;
        z = w * w;
        p = polevl(z, detail::j1_PP, 6) / polevl(z, detail::j1_PQ, 6);
        q = polevl(z, detail::j1_QP, 7) / p1evl(z, detail::j1_QQ, 7);
        xn = x - detail::THPIO4;
        p = p * std::cos(xn) - w * q * std::sin(xn);
        return (p * detail::SQRT2OPI / std::sqrt(x));
    }

    XSF_HOST_DEVICE inline double y1(double x) {
        double w, z, p, q, xn;

        if (x <= 5.0) {
            if (x == 0.0) {
                set_error("y1", SF_ERROR_SINGULAR, NULL);
                return -std::numeric_limits<double>::infinity();
            } else if (x <= 0.0) {
                set_error("y1", SF_ERROR_DOMAIN, NULL);
                return std::numeric_limits<double>::quiet_NaN();
            }
            z = x * x;
            w = x * (polevl(z, detail::j1_YP, 5) / p1evl(z, detail::j1_YQ, 8));
            w += M_2_PI * (j1(x) * std::log(x) - 1.0 / x);
            return (w);
        }

        w = 5.0 / x;
        z = w * w;
        p = polevl(z, detail::j1_PP, 6) / polevl(z, detail::j1_PQ, 6);
        q = polevl(z, detail::j1_QP, 7) / p1evl(z, detail::j1_QQ, 7);
        xn = x - detail::THPIO4;
        p = p * std::sin(xn) + w * q * std::cos(xn);
        return (p * detail::SQRT2OPI / std::sqrt(x));
    }
} // namespace cephes
} // namespace xsf