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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, long comment, copyright, license, and constants are from [Cephes]{@link http://www.netlib.org/cephes}. The implementation follows the original, but has been modified for JavaScript.
*
* ```text
* Copyright 1984, 1987, 1989 by Stephen L. Moshier
*
* Some software in this archive may be from the book _Methods and Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster International, 1989) or from the Cephes Mathematical Library, a commercial product. In either event, it is copyrighted by the author. What you see here may be used freely but it comes with no support or guarantee.
*
* Stephen L. Moshier
* moshier@na-net.ornl.gov
* ```
*/
'use strict';
// MODULES //
var isInfinitef = require( '@stdlib/math/base/assert/is-infinitef' );
var isnanf = require( '@stdlib/math/base/assert/is-nanf' );
var cosf = require( '@stdlib/math/base/special/cosf' );
var sinf = require( '@stdlib/math/base/special/sinf' );
var lnf = require( '@stdlib/math/base/special/lnf' );
var f32 = require( '@stdlib/number/float64/base/to-float32' );
var HALF_PI = require( '@stdlib/constants/float32/half-pi' );
var GAMMA = require( '@stdlib/constants/float32/eulergamma' );
var NINF = require( '@stdlib/constants/float32/ninf' );
var polyvalFN4 = require( './polyval_fn4.js' );
var polyvalFD4 = require( './polyval_fd4.js' );
var polyvalFN8 = require( './polyval_fn8.js' );
var polyvalFD8 = require( './polyval_fd8.js' );
var polyvalGN4 = require( './polyval_gn4.js' );
var polyvalGD4 = require( './polyval_gd4.js' );
var polyvalGN8 = require( './polyval_gn8.js' );
var polyvalGD8 = require( './polyval_gd8.js' );
var polyvalSN = require( './polyval_sn.js' );
var polyvalSD = require( './polyval_sd.js' );
var polyvalCN = require( './polyval_cn.js' );
var polyvalCD = require( './polyval_cd.js' );
// VARIABLES //
var ZERO = f32( 0.0 );
var ONE = f32( 1.0 );
var FOUR = f32( 4.0 );
var EIGHT = f32( 8.0 );
var HUGE = f32( 1.0e9 );
// MAIN //
/**
* Computes the sine and cosine integrals in single-precision floating-point format and assigns results to a provided output array.
*
* ## Method
*
* - The integrals are approximated by rational functions.
*
* - For \\( x > 8 \\), auxiliary functions \\( f(x) \\) and \\( g(x) \\) are employed such that
*
* ```tex
* \operatorname{Ci}(x) = f(x) \sin(x) - g(x) \cos(x) \\
* \operatorname{Si}(x) = \pi/2 - f(x) \cos(x) - g(x) \sin(x)
* ```
*
* ## Notes
*
* - Absolute error on test interval \\( \[0,50\] \\), except relative when greater than \\( 1 \\):
*
* | arithmetic | function | # trials | peak | rms |
* |:----------:|:-----------:|:--------:|:-------:|:-------:|
* | IEEE | Si | 30000 | 2.1e-7 | 4.3e-8 |
* | IEEE | Ci | 30000 | 3.9e-7 | 2.2e-8 |
*
* @private
* @param {number} x - input value
* @param {Collection} out - output array
* @param {integer} stride - output array stride
* @param {NonNegativeInteger} offset - output array index offset
* @returns {Collection} output array
*
* @example
* var v = sicif( 3.0, [ 0.0, 0.0 ], 1, 0 );
* // returns [ ~1.849, ~0.12 ]
*
* @example
* var v = sicif( 0.0, [ 0.0, 0.0 ], 1, 0 );
* // returns [ 0.0, -Infinity ]
*
* @example
* var v = sicif( -9.0, [ 0.0, 0.0 ], 1, 0 );
* // returns [ ~-1.665, ~0.055 ]
*
* @example
* var v = sicif( NaN, [ 0.0, 0.0 ], 1, 0 );
* // returns [ NaN, NaN ]
*/
function sicif( x, out, stride, offset ) {
var sgn;
var si;
var ci;
var c;
var f;
var g;
var s;
var z;
x = f32( x );
if ( isnanf( x ) ) {
out[ offset ] = NaN;
out[ offset + stride ] = NaN;
return out;
}
if ( x < ZERO ) {
sgn = -1;
x = f32( -x );
} else {
sgn = 0;
}
if ( x === ZERO ) {
out[ offset ] = ZERO;
out[ offset + stride ] = NINF;
return out;
}
if ( x > HUGE ) {
if ( isInfinitef( x ) ) {
if ( sgn === -1 ) {
si = f32( -HALF_PI );
ci = NaN;
} else {
si = f32( HALF_PI );
ci = ZERO;
}
out[ offset ] = si;
out[ offset + stride ] = ci;
return out;
}
si = f32( HALF_PI - f32( cosf( x ) / x ) );
ci = f32( sinf( x ) / x );
}
if ( x > FOUR ) {
s = sinf( x );
c = cosf( x );
z = f32( ONE / f32( x*x ) );
if ( x < EIGHT ) {
f = f32( polyvalFN4( z ) / f32( x * polyvalFD4( z ) ) );
g = f32( f32( z * polyvalGN4( z ) ) / polyvalGD4( z ) );
} else {
f = f32( polyvalFN8( z ) / f32( x * polyvalFD8( z ) ) );
g = f32( f32( z * polyvalGN8( z ) ) / polyvalGD8( z ) );
}
si = f32( f32( HALF_PI - f32( f*c ) ) - f32( g*s ) );
if ( sgn ) {
si = f32( -si );
}
ci = f32( f32( f*s ) - f32( g*c ) );
out[ offset ] = si;
out[ offset + stride ] = ci;
return out;
}
z = f32( x * x );
s = f32( f32( x * polyvalSN( z ) ) / polyvalSD( z ) );
c = f32( f32( z * polyvalCN( z ) ) / polyvalCD( z ) );
if ( sgn ) {
s = f32( -s );
}
si = s;
ci = f32( f32( GAMMA + lnf( x ) ) + c ); // real part if x < 0
out[ offset ] = si;
out[ offset + stride ] = ci;
return out;
}
// EXPORTS //
module.exports = sicif;
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