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* @license Apache-2.0
*
* Copyright (c) 2026 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://www.boost.org/doc/libs/1_92_0/boost/math/special_functions/detail/bessel_j1.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 sqrtf = require( '@stdlib/math/base/special/sqrtf' );
var absf = require( '@stdlib/math/base/special/absf' );
var sincosf = require( '@stdlib/math/base/special/sincosf' ).assign;
var f32 = require( '@stdlib/number/float64/base/to-float32' );
var PINF = require( '@stdlib/constants/float32/pinf' );
var FLOAT32_SQRT_PI = require( '@stdlib/constants/float32/sqrt-pi' );
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 x1 = f32( 3.8317059702075123156e+00 );
var x2 = f32( 7.0155866698156187535e+00 );
var x11 = f32( 9.810e+02 );
var x12 = f32( -3.2527979248768438556e-04 );
var x21 = f32( 1.7960e+03 );
var x22 = f32( -3.8330184381246462950e-05 );
// `sincosf` workspace:
var sc = [ 0.0, 0.0 ];
// MAIN //
/**
* Computes the Bessel function of the first kind of order one for a single-precision floating-point number.
*
* @param {number} x - input value
* @returns {number} evaluated Bessel function
*
* @example
* var v = besselj1f( 0.0 );
* // returns 0.0
*
* @example
* var v = besselj1f( 1.0 );
* // returns ~0.440
*
* @example
* var v = besselj1f( Infinity );
* // returns 0.0
*
* @example
* var v = besselj1f( -Infinity );
* // returns 0.0
*
* @example
* var v = besselj1f( NaN );
* // returns NaN
*/
function besselj1f( x ) {
var value;
var rc;
var rs;
var y2;
var r;
var y;
var f;
var w;
x = f32( x );
w = absf( x );
if ( x === 0.0 ) {
return 0.0;
}
if ( w === PINF ) {
return 0.0;
}
if ( w <= 4.0 ) {
y = f32( x * x );
r = f32( poly1( y ) );
f = f32( f32( w * f32( w + x1 ) ) * f32( f32( w - f32( x11 / 256.0 ) ) - x12 ) ); // eslint-disable-line max-len
value = f32( f * r );
} else if ( w <= 8.0 ) {
y = f32( x * x );
r = f32( poly2( y ) );
f = f32( f32( w * f32( w + x2 ) ) * f32( f32( w - f32( x21 / 256.0 ) ) - x22 ) ); // eslint-disable-line max-len
value = f32( f * r );
} else {
y = f32( 8.0 / w );
y2 = f32( y * y );
rc = f32( polyC( y2 ) );
rs = f32( polyS( y2 ) );
f = f32( 1.0 / f32( sqrtf( w ) * FLOAT32_SQRT_PI ) );
/*
* What follows is really just:
*
* ```
* z = w - 0.75 * pi;
* value = f * ( rc * cos( z ) - y * rs * sin( z ) );
* ```
*
* but using the sin/cos addition rules plus constants for the values of sin/cos of `3π/4` which then cancel out with corresponding terms in "f".
*/
sincosf( w, sc, 1, 0 );
value = f32( f * f32( f32( rc * f32( sc[0] - sc[1] ) ) + f32( f32( y * rs ) * f32( sc[0] + sc[1] ) ) ) ); // eslint-disable-line max-len
}
if ( x < 0.0 ) {
value = f32( -value );
}
return value;
}
// EXPORTS //
module.exports = besselj1f;
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