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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, 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 isInfinite = require( './../../../../base/assert/is-infinite' );
var isnan = require( './../../../../base/assert/is-nan' );
var cos = require( './../../../../base/special/cos' );
var sin = require( './../../../../base/special/sin' );
var ln = require( './../../../../base/special/ln' );
var HALF_PI = require( '@stdlib/constants/float64/half-pi' );
var GAMMA = require( '@stdlib/constants/float64/eulergamma' );
var NINF = require( '@stdlib/constants/float64/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' );
// MAIN //
/**
* Computes the sine and cosine integrals.
*
* ## 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 | 4.4e-16 | 7.3e-17 |
* | IEEE | Ci | 30000 | 6.9e-16 | 5.1e-17 |
*
*
* @private
* @param {(Array|TypedArray|Object)} out - output array
* @param {number} x - input value
* @returns {(Array|TypedArray|Object)} output array
*
* @example
* var v = sici( [ 0.0, 0.0 ], 3.0 );
* // returns [ ~1.849, ~0.12 ]
*
* @example
* var v = sici( [ 0.0, 0.0 ], 0.0 );
* // returns [ 0.0, -Infinity ]
*
* @example
* var v = sici( [ 0.0, 0.0 ], -9.0 );
* // returns [ ~-1.665, ~0.055 ]
*
* @example
* var v = sici( [ 0.0, 0.0 ], NaN );
* // returns [ NaN, NaN ]
*/
function sici( out, x ) {
var sgn;
var si;
var ci;
var c;
var f;
var g;
var s;
var z;
if ( isnan( x ) ) {
out[ 0 ] = NaN;
out[ 1 ] = NaN;
return out;
}
if ( x < 0.0 ) {
sgn = -1;
x = -x;
} else {
sgn = 0;
}
if ( x === 0.0 ) {
out[ 0 ] = 0.0;
out[ 1 ] = NINF;
return out;
}
if ( x > 1.0e9 ) {
if ( isInfinite( x ) ) {
if ( sgn === -1 ) {
si = -HALF_PI;
ci = NaN;
} else {
si = HALF_PI;
ci = 0.0;
}
out[ 0 ] = si;
out[ 1 ] = ci;
return out;
}
si = HALF_PI - ( cos( x ) / x );
ci = sin( x ) / x;
}
if ( x > 4.0 ) {
s = sin( x );
c = cos( x );
z = 1.0 / ( x*x );
if ( x < 8.0 ) {
f = polyvalFN4( z ) / ( x * polyvalFD4( z ) );
g = z * polyvalGN4( z ) / polyvalGD4( z );
} else {
f = polyvalFN8( z ) / ( x * polyvalFD8( z ) );
g = z * polyvalGN8( z ) / polyvalGD8( z );
}
si = HALF_PI - ( f*c ) - ( g*s );
if ( sgn ) {
si = -si;
}
ci = ( f*s ) - ( g*c );
out[ 0 ] = si;
out[ 1 ] = ci;
return out;
}
z = x * x;
s = x * polyvalSN( z ) / polyvalSD( z );
c = z * polyvalCN( z ) / polyvalCD( z );
if ( sgn ) {
s = -s;
}
si = s;
ci = GAMMA + ln( x ) + c; // real part if x < 0
out[ 0 ] = si;
out[ 1 ] = ci;
return out;
}
// EXPORTS //
module.exports = sici;
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