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* @license Apache-2.0
*
* Copyright (c) 2025 The Stdlib Authors.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*
*
* ## Notice
*
* The original C code and copyright notice are from the [xsf library]{@link https://github.com/scipy/xsf/blob/main/include/xsf/airy.h}. The implementation has been modified for JavaScript.
*
* ```text
* Copyright 2024, SciPy
*
* Use, modification and distribution are subject to the
* BSD 3-Clause License (See accompanying file LICENSE or copy at
* https://github.com/scipy/xsf/blob/main/LICENSE)
* ```
*/
/* eslint-disable max-statements */
'use strict';
// MODULES //
var SQRT3 = require( '@stdlib/constants/float64/sqrt-three' );
var floor = require( '@stdlib/math/base/special/floor' );
var PINF = require( '@stdlib/constants/float64/pinf' );
var sqrt = require( '@stdlib/math/base/special/sqrt' );
var sin = require( '@stdlib/math/base/special/sin' );
var cos = require( '@stdlib/math/base/special/cos' );
var exp = require( '@stdlib/math/base/special/exp' );
var abs = require( '@stdlib/math/base/special/abs' );
var PI = require( '@stdlib/constants/float64/pi' );
// VARIABLES //
var C1 = 0.355028053887817;
var C2 = 0.258819403792807;
var EPS = 1.0e-15;
var ck = new Array( 52 ); // eslint-disable-line stdlib/no-new-array
var dk = new Array( 52 ); // eslint-disable-line stdlib/no-new-array
/**
* Evaluates the Airy functions of the first and second kind, Ai(x) and Bi(x), and their first derivatives, Ai'(x) and Bi'(x), and assigns to a provided output array.
*
* @param {number} x - input value
* @param {Array} out - output array
* @param {integer} stride - output array stride
* @param {NonNegativeInteger} offset - output array index offset
* @returns {Array} array containing Ai(x), Ai'(x), Bi(x), and Bi'(x)
*/
function airy(x, out, stride, offset) { // @eslint-disable-line max-statements
var kmax;
var km2;
var sai;
var sad;
var sbi;
var sbd;
var xp1;
var xr2;
var xar;
var xr1;
var xcs;
var xss;
var ssa;
var sda;
var ssb;
var sdb;
var xa;
var xq;
var xm;
var xf;
var rp;
var xe;
var gx;
var df;
var dg;
var fx;
var km;
var r;
var k;
if ( x === PINF ) {
out[offset] = 0.0;
out[offset + stride] = 0.0;
out[offset + (2 * stride)] = PINF;
out[offset + (3 * stride)] = PINF;
return out;
}
km2 = 0;
xa = abs(x);
xq = sqrt(xa);
xm = 8.0;
if (x > 0.0) {
xm = 5.0;
}
if (x === 0.0) {
out[offset] = C1;
out[offset + stride] = -C2;
out[offset + (2 * stride)] = SQRT3 * C1;
out[offset + (3 * stride)] = SQRT3 * C2;
return out;
}
if (xa <= xm) {
fx = 1.0;
r = 1.0;
for (k = 1; k <= 40; k++) {
r = r * x / (3.0 * k) * x / ((3.0 * k) - 1.0) * x;
fx += r;
if (abs(r) < abs(fx) * EPS) {
break;
}
}
gx = x;
r = x;
for (k = 1; k <= 40; k++) {
r = r * x / (3.0 * k) * x / ((3.0 * k) + 1.0) * x;
gx += r;
if (abs(r) < abs(gx) * EPS) {
break;
}
}
out[offset] = (C1 * fx) - (C2 * gx);
out[offset + (2 * stride)] = SQRT3 * ((C1 * fx) + (C2 * gx));
df = 0.5 * x * x;
r = df;
for (k = 1; k <= 40; k++) {
r = r * x / (3.0 * k) * x / ((3.0 * k) + 2.0) * x;
df += r;
if (abs(r) < abs(df) * EPS) {
break;
}
}
dg = 1.0;
r = 1.0;
for (k = 1; k <= 40; k++) {
r = r * x / (3.0 * k) * x / ((3.0 * k) - 2.0) * x;
dg += r;
if (abs(r) < abs(dg) * EPS) {
break;
}
}
out[offset + stride] = (C1 * df) - (C2 * dg);
out[offset + (3 * stride)] = SQRT3 * ((C1 * df) + (C2 * dg));
} else {
km = floor(24.5 - xa);
if (xa < 6.0) {
km = 14;
}
if (xa > 15.0) {
km = 10;
}
if (x > 0.0) {
kmax = km;
} else {
/* Choose cutoffs so that the remainder term in asymptotic
expansion is epsilon size. The X<0 branch needs to be fast
in order to make AIRYZO efficient */
if (xa > 70.0) {
km = 3;
}
if (xa > 500.0) {
km = 2;
}
if (xa > 1000.0) {
km = 1;
}
km2 = km;
if (xa > 150.0) {
km2 = 1;
}
if (xa > 3000.0) {
km2 = 0;
}
kmax = (2 * km) + 1;
}
xe = xa * xq / 1.5;
xr1 = 1.0 / xe;
xar = 1.0 / xq;
xf = sqrt(xar);
rp = 0.5641895835477563;
r = 1.0;
for (k = 1; k <= kmax; k++) {
r = r * ((6.0 * k) - 1.0) / 216.0 * ((6.0 * k) - 3.0) / k;
r *= ((6.0 * k) - 5.0) / ((2.0 * k) - 1.0);
ck[k - 1] = r;
dk[k - 1] = -((6.0 * k) + 1.0) / ((6.0 * k) - 1.0) * r;
}
if (x > 0.0) {
sai = 1.0;
sad = 1.0;
r = 1.0;
for (k = 1; k <= km; k++) {
r *= -xr1;
sai += ck[k - 1] * r;
sad += dk[k - 1] * r;
}
sbi = 1.0;
sbd = 1.0;
r = 1.0;
for (k = 1; k <= km; k++) {
r *= xr1;
sbi += ck[k - 1] * r;
sbd += dk[k - 1] * r;
}
xp1 = exp(-xe);
out[offset] = 0.5 * rp * xf * xp1 * sai;
out[offset + stride] = -0.5 * rp / xf * xp1 * sad;
out[offset + (2*stride)] = rp * xf / xp1 * sbi;
out[offset + (3*stride)] = rp / xf / xp1 * sbd;
} else {
xcs = cos(xe + (PI / 4.0));
xss = sin(xe + (PI / 4.0));
ssa = 1.0;
sda = 1.0;
r = 1.0;
xr2 = 1.0 / (xe * xe);
for (k = 1; k <= km; k++) {
r *= -xr2;
ssa += ck[(2 * k) - 1] * r;
sda += dk[(2 * k) - 1] * r;
}
ssb = ck[0] * xr1;
sdb = dk[0] * xr1;
r = xr1;
for (k = 1; k <= km2; k++) {
r *= -xr2;
ssb += ck[2 * k] * r;
sdb += dk[2 * k] * r;
}
out[offset] = rp * xf * ((xss * ssa) - (xcs * ssb));
out[offset + stride] = -rp / xf * ((xcs * sda) + (xss * sdb));
out[offset + (2*stride)] = rp * xf * ((xcs * ssa) + (xss * ssb));
out[offset + (3*stride)] = rp / xf * ((xss * sda) - (xcs * sdb));
}
}
return out;
}
module.exports = airy;
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