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* @license Apache-2.0
*
* Copyright (c) 2026 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, 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 absf = require( '@stdlib/math/base/special/absf' );
var expf = require( '@stdlib/math/base/special/expf' );
var f32 = require( '@stdlib/number/float64/base/to-float32' );
var MAXLOGF = require( '@stdlib/constants/float32/max-ln' );
var polyvalP = require( './polyval_p.js' );
// VARIABLES //
var ZERO = f32( 0.0 );
var ONE = f32( 1.0 );
var TWO = f32( 2.0 );
// MAIN //
/**
* Computes the hyperbolic tangent of a single-precision floating-point number.
*
* ## Method
*
* For \\( |x| < 0.625 \\), we use a polynomial approximation of the form
*
* ```tex
* x + x^3 \mathrm{P}(x)
* ```
*
* Otherwise,
*
* ```tex
* \begin{align*}
* \operatorname{tanhf}(x) &= \frac{\operatorname{sinhf}(x)}{\operatorname{coshf}(x)} \\
* &= 1 - \frac{2}{e^{2x} + 1}
* \end{align*}
* ```
*
* @param {number} x - input value
* @returns {number} hyperbolic tangent
*
* @example
* var v = tanhf( 0.0 );
* // returns 0.0
*
* @example
* var v = tanhf( 2.0 );
* // returns ~0.964
*
* @example
* var v = tanhf( -2.0 );
* // returns ~-0.964
*
* @example
* var v = tanhf( NaN );
* // returns NaN
*/
function tanhf( x ) {
var s;
var z;
x = f32( x );
z = absf( x );
if ( z > f32( 0.5 * MAXLOGF ) ) {
return ( x < ZERO ) ? -ONE : ONE;
}
if ( z >= f32( 0.625 ) ) {
s = expf( f32( TWO * z ) );
z = f32( ONE - f32( TWO / f32( s + ONE ) ) );
if ( x < ZERO ) {
z = -z;
}
} else {
if ( x === ZERO ) {
return x; // Handle `+-0`
}
s = f32( x * x );
z = f32( x + f32( f32( x * s ) * polyvalP( s ) ) );
}
return z;
}
// EXPORTS //
module.exports = tanhf;
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