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

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

/*                                                     airy.c
 *
 *     Airy function
 *
 *
 *
 * SYNOPSIS:
 *
 * double x, ai, aip, bi, bip;
 * int airy();
 *
 * airy( x, _&ai, _&aip, _&bi, _&bip );
 *
 *
 *
 * DESCRIPTION:
 *
 * Solution of the differential equation
 *
 *     y"(x) = xy.
 *
 * The function returns the two independent solutions Ai, Bi
 * and their first derivatives Ai'(x), Bi'(x).
 *
 * Evaluation is by power series summation for small x,
 * by rational minimax approximations for large x.
 *
 *
 *
 * ACCURACY:
 * Error criterion is absolute when function <= 1, relative
 * when function > 1, except * denotes relative error criterion.
 * For large negative x, the absolute error increases as x^1.5.
 * For large positive x, the relative error increases as x^1.5.
 *
 * Arithmetic  domain   function  # trials      peak         rms
 * IEEE        -10, 0     Ai        10000       1.6e-15     2.7e-16
 * IEEE          0, 10    Ai        10000       2.3e-14*    1.8e-15*
 * IEEE        -10, 0     Ai'       10000       4.6e-15     7.6e-16
 * IEEE          0, 10    Ai'       10000       1.8e-14*    1.5e-15*
 * IEEE        -10, 10    Bi        30000       4.2e-15     5.3e-16
 * IEEE        -10, 10    Bi'       30000       4.9e-15     7.3e-16
 *
 */
/*							airy.c */

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

#include "../config.h"
#include "const.h"
#include "polevl.h"

namespace xsf {
namespace cephes {

    namespace detail {

        constexpr double airy_c1 = 0.35502805388781723926;
        constexpr double airy_c2 = 0.258819403792806798405;
        constexpr double MAXAIRY = 103.892;

        constexpr double airy_AN[8] = {
            3.46538101525629032477E-1, 1.20075952739645805542E1, 7.62796053615234516538E1, 1.68089224934630576269E2,
            1.59756391350164413639E2,  7.05360906840444183113E1, 1.40264691163389668864E1, 9.99999999999999995305E-1,
        };

        constexpr double airy_AD[8] = {
            5.67594532638770212846E-1, 1.47562562584847203173E1, 8.45138970141474626562E1, 1.77318088145400459522E2,
            1.64234692871529701831E2,  7.14778400825575695274E1, 1.40959135607834029598E1, 1.00000000000000000470E0,
        };

        constexpr double airy_APN[8] = {
            6.13759184814035759225E-1, 1.47454670787755323881E1, 8.20584123476060982430E1, 1.71184781360976385540E2,
            1.59317847137141783523E2,  6.99778599330103016170E1, 1.39470856980481566958E1, 1.00000000000000000550E0,
        };

        constexpr double airy_APD[8] = {
            3.34203677749736953049E-1, 1.11810297306158156705E1, 7.11727352147859965283E1, 1.58778084372838313640E2,
            1.53206427475809220834E2,  6.86752304592780337944E1, 1.38498634758259442477E1, 9.99999999999999994502E-1,
        };

        constexpr double airy_BN16[5] = {
            -2.53240795869364152689E-1, 5.75285167332467384228E-1,  -3.29907036873225371650E-1,
            6.44404068948199951727E-2,  -3.82519546641336734394E-3,
        };

        constexpr double airy_BD16[5] = {
            /* 1.00000000000000000000E0, */
            -7.15685095054035237902E0, 1.06039580715664694291E1,   -5.23246636471251500874E0,
            9.57395864378383833152E-1, -5.50828147163549611107E-2,
        };

        constexpr double airy_BPPN[5] = {
            4.65461162774651610328E-1,  -1.08992173800493920734E0, 6.38800117371827987759E-1,
            -1.26844349553102907034E-1, 7.62487844342109852105E-3,
        };

        constexpr double airy_BPPD[5] = {
            /* 1.00000000000000000000E0, */
            -8.70622787633159124240E0, 1.38993162704553213172E1,   -7.14116144616431159572E0,
            1.34008595960680518666E0,  -7.84273211323341930448E-2,
        };

        constexpr double airy_AFN[9] = {
            -1.31696323418331795333E-1, -6.26456544431912369773E-1, -6.93158036036933542233E-1,
            -2.79779981545119124951E-1, -4.91900132609500318020E-2, -4.06265923594885404393E-3,
            -1.59276496239262096340E-4, -2.77649108155232920844E-6, -1.67787698489114633780E-8,
        };

        constexpr double airy_AFD[9] = {
            /* 1.00000000000000000000E0, */
            1.33560420706553243746E1,  3.26825032795224613948E1,  2.67367040941499554804E1,
            9.18707402907259625840E0,  1.47529146771666414581E0,  1.15687173795188044134E-1,
            4.40291641615211203805E-3, 7.54720348287414296618E-5, 4.51850092970580378464E-7,
        };

        constexpr double airy_AGN[11] = {
            1.97339932091685679179E-2, 3.91103029615688277255E-1, 1.06579897599595591108E0,   9.39169229816650230044E-1,
            3.51465656105547619242E-1, 6.33888919628925490927E-2, 5.85804113048388458567E-3,  2.82851600836737019778E-4,
            6.98793669997260967291E-6, 8.11789239554389293311E-8, 3.41551784765923618484E-10,
        };

        constexpr double airy_AGD[10] = {
            /*  1.00000000000000000000E0, */
            9.30892908077441974853E0,  1.98352928718312140417E1,  1.55646628932864612953E1,  5.47686069422975497931E0,
            9.54293611618961883998E-1, 8.64580826352392193095E-2, 4.12656523824222607191E-3, 1.01259085116509135510E-4,
            1.17166733214413521882E-6, 4.91834570062930015649E-9,
        };

        constexpr double airy_APFN[9] = {
            1.85365624022535566142E-1, 8.86712188052584095637E-1, 9.87391981747398547272E-1,
            4.01241082318003734092E-1, 7.10304926289631174579E-2, 5.90618657995661810071E-3,
            2.33051409401776799569E-4, 4.08718778289035454598E-6, 2.48379932900442457853E-8,
        };

        constexpr double airy_APFD[9] = {
            /*  1.00000000000000000000E0, */
            1.47345854687502542552E1,  3.75423933435489594466E1,  3.14657751203046424330E1,
            1.09969125207298778536E1,  1.78885054766999417817E0,  1.41733275753662636873E-1,
            5.44066067017226003627E-3, 9.39421290654511171663E-5, 5.65978713036027009243E-7,
        };

        constexpr double airy_APGN[11] = {
            -3.55615429033082288335E-2, -6.37311518129435504426E-1,  -1.70856738884312371053E0,
            -1.50221872117316635393E0,  -5.63606665822102676611E-1,  -1.02101031120216891789E-1,
            -9.48396695961445269093E-3, -4.60325307486780994357E-4,  -1.14300836484517375919E-5,
            -1.33415518685547420648E-7, -5.63803833958893494476E-10,
        };

        constexpr double airy_APGD[11] = {
            /*  1.00000000000000000000E0, */
            9.85865801696130355144E0,  2.16401867356585941885E1,  1.73130776389749389525E1,  6.17872175280828766327E0,
            1.08848694396321495475E0,  9.95005543440888479402E-2, 4.78468199683886610842E-3, 1.18159633322838625562E-4,
            1.37480673554219441465E-6, 5.79912514929147598821E-9,
        };

    } // namespace detail

    XSF_HOST_DEVICE inline int airy(double x, double *ai, double *aip, double *bi, double *bip) {
        double z, zz, t, f, g, uf, ug, k, zeta, theta;
        int domflg;

        domflg = 0;
        if (x > detail::MAXAIRY) {
            *ai = 0;
            *aip = 0;
            *bi = std::numeric_limits<double>::infinity();
            *bip = std::numeric_limits<double>::infinity();
            return (-1);
        }

        if (x < -2.09) {
            domflg = 15;
            t = std::sqrt(-x);
            zeta = -2.0 * x * t / 3.0;
            t = std::sqrt(t);
            k = detail::SQRT1OPI / t;
            z = 1.0 / zeta;
            zz = z * z;
            uf = 1.0 + zz * polevl(zz, detail::airy_AFN, 8) / p1evl(zz, detail::airy_AFD, 9);
            ug = z * polevl(zz, detail::airy_AGN, 10) / p1evl(zz, detail::airy_AGD, 10);
            theta = zeta + 0.25 * M_PI;
            f = std::sin(theta);
            g = std::cos(theta);
            *ai = k * (f * uf - g * ug);
            *bi = k * (g * uf + f * ug);
            uf = 1.0 + zz * polevl(zz, detail::airy_APFN, 8) / p1evl(zz, detail::airy_APFD, 9);
            ug = z * polevl(zz, detail::airy_APGN, 10) / p1evl(zz, detail::airy_APGD, 10);
            k = detail::SQRT1OPI * t;
            *aip = -k * (g * uf + f * ug);
            *bip = k * (f * uf - g * ug);
            return (0);
        }

        if (x >= 2.09) { /* cbrt(9) */
            domflg = 5;
            t = std::sqrt(x);
            zeta = 2.0 * x * t / 3.0;
            g = std::exp(zeta);
            t = std::sqrt(t);
            k = 2.0 * t * g;
            z = 1.0 / zeta;
            f = polevl(z, detail::airy_AN, 7) / polevl(z, detail::airy_AD, 7);
            *ai = detail::SQRT1OPI * f / k;
            k = -0.5 * detail::SQRT1OPI * t / g;
            f = polevl(z, detail::airy_APN, 7) / polevl(z, detail::airy_APD, 7);
            *aip = f * k;

            if (x > 8.3203353) { /* zeta > 16 */
                f = z * polevl(z, detail::airy_BN16, 4) / p1evl(z, detail::airy_BD16, 5);
                k = detail::SQRT1OPI * g;
                *bi = k * (1.0 + f) / t;
                f = z * polevl(z, detail::airy_BPPN, 4) / p1evl(z, detail::airy_BPPD, 5);
                *bip = k * t * (1.0 + f);
                return (0);
            }
        }

        f = 1.0;
        g = x;
        t = 1.0;
        uf = 1.0;
        ug = x;
        k = 1.0;
        z = x * x * x;
        while (t > detail::MACHEP) {
            uf *= z;
            k += 1.0;
            uf /= k;
            ug *= z;
            k += 1.0;
            ug /= k;
            uf /= k;
            f += uf;
            k += 1.0;
            ug /= k;
            g += ug;
            t = std::abs(uf / f);
        }
        uf = detail::airy_c1 * f;
        ug = detail::airy_c2 * g;
        if ((domflg & 1) == 0) {
            *ai = uf - ug;
        }
        if ((domflg & 2) == 0) {
            *bi = detail::SQRT3 * (uf + ug);
        }

        /* the deriviative of ai */
        k = 4.0;
        uf = x * x / 2.0;
        ug = z / 3.0;
        f = uf;
        g = 1.0 + ug;
        uf /= 3.0;
        t = 1.0;

        while (t > detail::MACHEP) {
            uf *= z;
            ug /= k;
            k += 1.0;
            ug *= z;
            uf /= k;
            f += uf;
            k += 1.0;
            ug /= k;
            uf /= k;
            g += ug;
            k += 1.0;
            t = std::abs(ug / g);
        }

        uf = detail::airy_c1 * f;
        ug = detail::airy_c2 * g;
        if ((domflg & 4) == 0) {
            *aip = uf - ug;
        }
        if ((domflg & 8) == 0) {
            *bip = detail::SQRT3 * (uf + ug);
        };
        return (0);
    }

    inline int airy(float xf, float *aif, float *aipf, float *bif, float *bipf) {
        double ai;
        double aip;
        double bi;
        double bip;
        int res = cephes::airy(xf, &ai, &aip, &bi, &bip);

        *aif = ai;
        *aipf = aip;
        *bif = bi;
        *bipf = bip;
        return res;
    }

} // namespace cephes
} // namespace xsf