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/**
* @license Apache-2.0
*
* Copyright (c) 2018 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 [Boost library]{@link https://github.com/boostorg/math/blob/develop/include/boost/math/special_functions/detail/bessel_j0.hpp}. The implementation has been modified for JavaScript.
*
* ```text
* Copyright Xiaogang Zhang, 2006.
*
* Use, modification and distribution are subject to the
* Boost Software License, Version 1.0. (See accompanying file
* LICENSE or copy at http://www.boost.org/LICENSE_1_0.txt)
* ```
*/
'use strict';
// MODULES //
var sqrt = require( './../../../../base/special/sqrt' );
var sincos = require( './../../../../base/special/sincos' );
var PINF = require( '@stdlib/constants/float64/pinf' );
var poly1 = require( './rational_p1q1.js' );
var poly2 = require( './rational_p2q2.js' );
var polyC = require( './rational_pcqc.js' );
var polyS = require( './rational_psqs.js' );
// VARIABLES //
var ONE_DIV_SQRT_PI = 0.5641895835477563;
var x1 = 2.4048255576957727686e+00;
var x2 = 5.5200781102863106496e+00;
var x11 = 6.160e+02;
var x12 = -1.42444230422723137837e-03;
var x21 = 1.4130e+03;
var x22 = 5.46860286310649596604e-04;
// `sincos` workspace:
var sc = [ 0.0, 0.0 ]; // WARNING: not thread safe
// MAIN //
/**
* Computes the Bessel function of the first kind of order zero.
*
* @param {number} x - input value
* @returns {number} evaluated Bessel function
*
* @example
* var v = j0( 0.0 );
* // returns 1.0
*
* v = j0( 1.0 );
* // returns ~0.765
*
* v = j0( Infinity );
* // returns 0.0
*
* v = j0( -Infinity );
* // returns 0.0
*
* v = j0( NaN );
* // returns NaN
*/
function j0( x ) {
var rc;
var rs;
var y2;
var r;
var y;
var f;
if ( x < 0 ) {
x = -x;
}
if ( x === PINF ) {
return 0.0;
}
if ( x === 0 ) {
return 1.0;
}
if ( x <= 4.0 ) {
y = x * x;
r = poly1( y );
f = ( x+x1 ) * ( (x - (x11/256.0)) - x12 );
return f * r;
}
if ( x <= 8.0 ) {
y = 1.0 - ( ( x*x )/64.0 );
r = poly2( y );
f = ( x+x2 ) * ( (x - (x21/256.0)) - x22 );
return f * r;
}
y = 8.0 / x;
y2 = y * y;
rc = polyC( y2 );
rs = polyS( y2 );
f = ONE_DIV_SQRT_PI / sqrt(x);
/*
* What follows is really just:
*
* ```
* var z = x - pi/4;
* return f * (rc * cos(z) - y * rs * sin(z));
* ```
*
* But using the addition formulae for sin and cos, plus the special values for sin/cos of `π/4`.
*/
sincos( sc, x );
return f * ( ( rc * (sc[1]+sc[0]) ) - ( (y*rs) * (sc[0]-sc[1]) ) );
}
// EXPORTS //
module.exports = j0;
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