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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 1985, 1987, 1989, 2000 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 isnan = require( './../../../../base/assert/is-nan' );
var ln = require( './../../../../base/special/ln' );
var PI_SQUARED = require( '@stdlib/constants/float64/pi-squared' );
var polyvalA = require( './polyval_a.js' );
var polyvalB = require( './polyval_b.js' );
// MAIN //
/**
* Evaluates Spence’s function, which is also known as the dilogarithm.
*
* ## Method
*
* - A rational approximation gives the integral in the interval (0.5, 1.5).
* - Transformation formulas for \\( \tfrac{1}{x} \\) and \\( 1 - x \\) are employed outside the basic expansion range.
*
* ## Notes
*
* - Relative error:
*
* | arithmetic | domain | # trials | peak | rms |
* |:----------:|:-----------:|:--------:|:-------:|:-------:|
* | IEEE | 0,4 | 30000 | 3.9e-15 | 5.4e-16 |
*
*
* @param {NonNegativeNumber} x - input value
* @returns {number} function value
*
* @example
* var v = spence( 3.0 );
* // returns ~-1.437
*
* @example
* var v = spence( 0.0 );
* // returns ~1.645
*
* @example
* var v = spence( -9.0 );
* // returns NaN
*
* @example
* var v = spence( NaN );
* // returns NaN
*/
function spence( x ) {
var flg;
var w;
var y;
var z;
if ( isnan( x ) || x < 0.0 ) {
return NaN;
}
if ( x === 1.0 ) {
return 0.0;
}
if ( x === 0.0 ) {
return ( PI_SQUARED / 6.0 );
}
flg = 0;
if ( x > 2.0 ) {
x = 1.0 / x;
flg |= 2;
}
if ( x > 1.5 ) {
w = (1.0 / x) - 1.0;
flg |= 2;
}
else if ( x < 0.5 ) {
w = -x;
flg |= 1;
}
else {
w = x - 1.0;
}
y = -w * polyvalA( w ) / polyvalB( w );
if ( flg & 1 ) {
y = ( PI_SQUARED/6.0 ) - ( ln( x ) * ln( 1.0-x ) ) - y;
}
if ( flg & 2 ) {
z = ln( x );
y = -( 0.5 * z * z ) - y;
}
return y;
}
// EXPORTS //
module.exports = spence;
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