venv/lib/python3.11/site-packages/scipy/special/xsf/cephes/i0.h

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

/*                                                     i0.c
 *
 *     Modified Bessel function of order zero
 *
 *
 *
 * SYNOPSIS:
 *
 * double x, y, i0();
 *
 * y = i0( x );
 *
 *
 *
 * DESCRIPTION:
 *
 * Returns modified Bessel function of order zero of the
 * argument.
 *
 * The function is defined as i0(x) = j0( ix ).
 *
 * The range is partitioned into the two intervals [0,8] and
 * (8, infinity).  Chebyshev polynomial expansions are employed
 * in each interval.
 *
 *
 *
 * ACCURACY:
 *
 *                      Relative error:
 * arithmetic   domain     # trials      peak         rms
 *    IEEE      0,30        30000       5.8e-16     1.4e-16
 *
 */
/*							i0e.c
 *
 *	Modified Bessel function of order zero,
 *	exponentially scaled
 *
 *
 *
 * SYNOPSIS:
 *
 * double x, y, i0e();
 *
 * y = i0e( x );
 *
 *
 *
 * DESCRIPTION:
 *
 * Returns exponentially scaled modified Bessel function
 * of order zero of the argument.
 *
 * The function is defined as i0e(x) = exp(-|x|) j0( ix ).
 *
 *
 *
 * ACCURACY:
 *
 *                      Relative error:
 * arithmetic   domain     # trials      peak         rms
 *    IEEE      0,30        30000       5.4e-16     1.2e-16
 * See i0().
 *
 */

/*                                                     i0.c            */

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

#include "../config.h"
#include "chbevl.h"

namespace xsf {
namespace cephes {

    namespace detail {

        /* Chebyshev coefficients for exp(-x) I0(x)
         * in the interval [0,8].
         *
         * lim(x->0){ exp(-x) I0(x) } = 1.
         */
        constexpr double i0_A[] = {
            -4.41534164647933937950E-18, 3.33079451882223809783E-17,  -2.43127984654795469359E-16,
            1.71539128555513303061E-15,  -1.16853328779934516808E-14, 7.67618549860493561688E-14,
            -4.85644678311192946090E-13, 2.95505266312963983461E-12,  -1.72682629144155570723E-11,
            9.67580903537323691224E-11,  -5.18979560163526290666E-10, 2.65982372468238665035E-9,
            -1.30002500998624804212E-8,  6.04699502254191894932E-8,   -2.67079385394061173391E-7,
            1.11738753912010371815E-6,   -4.41673835845875056359E-6,  1.64484480707288970893E-5,
            -5.75419501008210370398E-5,  1.88502885095841655729E-4,   -5.76375574538582365885E-4,
            1.63947561694133579842E-3,   -4.32430999505057594430E-3,  1.05464603945949983183E-2,
            -2.37374148058994688156E-2,  4.93052842396707084878E-2,   -9.49010970480476444210E-2,
            1.71620901522208775349E-1,   -3.04682672343198398683E-1,  6.76795274409476084995E-1};

        /* Chebyshev coefficients for exp(-x) sqrt(x) I0(x)
         * in the inverted interval [8,infinity].
         *
         * lim(x->inf){ exp(-x) sqrt(x) I0(x) } = 1/sqrt(2pi).
         */
        constexpr double i0_B[] = {
            -7.23318048787475395456E-18, -4.83050448594418207126E-18, 4.46562142029675999901E-17,
            3.46122286769746109310E-17,  -2.82762398051658348494E-16, -3.42548561967721913462E-16,
            1.77256013305652638360E-15,  3.81168066935262242075E-15,  -9.55484669882830764870E-15,
            -4.15056934728722208663E-14, 1.54008621752140982691E-14,  3.85277838274214270114E-13,
            7.18012445138366623367E-13,  -1.79417853150680611778E-12, -1.32158118404477131188E-11,
            -3.14991652796324136454E-11, 1.18891471078464383424E-11,  4.94060238822496958910E-10,
            3.39623202570838634515E-9,   2.26666899049817806459E-8,   2.04891858946906374183E-7,
            2.89137052083475648297E-6,   6.88975834691682398426E-5,   3.36911647825569408990E-3,
            8.04490411014108831608E-1};
    } // namespace detail

    XSF_HOST_DEVICE inline double i0(double x) {
        double y;

        if (x < 0)
            x = -x;
        if (x <= 8.0) {
            y = (x / 2.0) - 2.0;
            return (std::exp(x) * chbevl(y, detail::i0_A, 30));
        }

        return (std::exp(x) * chbevl(32.0 / x - 2.0, detail::i0_B, 25) / sqrt(x));
    }

    XSF_HOST_DEVICE inline double i0e(double x) {
        double y;

        if (x < 0)
            x = -x;
        if (x <= 8.0) {
            y = (x / 2.0) - 2.0;
            return (chbevl(y, detail::i0_A, 30));
        }

        return (chbevl(32.0 / x - 2.0, detail::i0_B, 25) / std::sqrt(x));
    }

} // namespace cephes
} // namespace xsf