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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, 1995, 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( '@stdlib/math/base/assert/is-nan' );
var exp = require( '@stdlib/math/base/special/exp' );
// MAIN //
/**
* Computes the hyperbolic cosine of a double-precision floating-point number.
*
* ## Method
*
* ```tex
* \operatorname{cosh}(x) = \frac{ \exp(x) + \exp(-x) }{2}
* ```
*
* ## Notes
*
* - Relative error:
*
* | arithmetic | domain | # trials | peak | rms |
* |:----------:|:--------:|:--------:|:-------:|:-------:|
* | DEC | +- 88 | 50000 | 4.0e-17 | 7.7e-18 |
* | IEEE | +-MAXLOG | 30000 | 2.6e-16 | 5.7e-17 |
*
* @param {number} x - input value
* @returns {number} hyperbolic cosine
*
* @example
* var v = cosh( 0.0 );
* // returns 1.0
*
* @example
* var v = cosh( 2.0 );
* // returns ~3.762
*
* @example
* var v = cosh( -2.0 );
* // returns ~3.762
*
* @example
* var v = cosh( NaN );
* // returns NaN
*/
function cosh( x ) {
if ( isnan( x ) ) {
return x;
}
if ( x < 0.0 ) {
x = -x;
}
if ( x > 21.0 ) {
return exp( x ) / 2.0;
}
return ( exp(x) + exp(-x) ) / 2.0;
}
// EXPORTS //
module.exports = cosh;
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