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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 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 isnanf = require( '@stdlib/math/base/assert/is-nanf' );
var lnf = require( '@stdlib/math/base/special/lnf' );
var f32 = require( '@stdlib/number/float64/base/to-float32' );
var polyvalA = require( './polyval_a.js' );
var polyvalB = require( './polyval_b.js' );
// VARIABLES //
var PI2O6 = f32( 1.64493406684822643647 ); // π^2 / 6
// MAIN //
/**
* Evaluates Spence's function (the dilogarithm) for a single-precision floating-point number.
*
* ## 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 | 4.4e-7 | 6.3e-8 |
*
* @param {NonNegativeNumber} x - input value
* @returns {number} function value
*
* @example
* var v = spencef( 3.0 );
* // returns ~-1.437
*
* @example
* var v = spencef( 0.0 );
* // returns ~1.645
*
* @example
* var v = spencef( -9.0 );
* // returns NaN
*
* @example
* var v = spencef( NaN );
* // returns NaN
*/
function spencef( x ) {
var flg;
var w;
var y;
var z;
if ( isnanf( x ) || x < 0.0 ) {
return NaN;
}
if ( x === 1.0 ) {
return 0.0;
}
if ( x === 0.0 ) {
return PI2O6;
}
flg = 0;
if ( x > 2.0 ) {
x = f32( 1.0 / f32( x ) );
flg |= 2;
}
if ( x > 1.5 ) {
w = f32( 1.0 / f32( x ) ) - 1.0;
flg |= 2;
} else if ( x < 0.5 ) {
w = f32( -x );
flg |= 1;
} else {
w = f32( x ) - 1.0;
}
y = f32( -w * f32( f32( polyvalA(w) ) / f32( polyvalB(w) ) ) );
if ( flg & 1 ) {
y = f32( PI2O6 - f32( lnf( x )*lnf( 1.0-x ) ) - y );
}
if ( flg & 2 ) {
z = lnf( x );
y = -f32( f32( 0.5*z*z ) + y );
}
return y;
}
// EXPORTS //
module.exports = spencef;
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