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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 following copyright, license, and long comment were part of the original implementation available as part of [FreeBSD]{@link https://svnweb.freebsd.org/base/release/12.2.0/lib/msun/src/e_acoshf.c?view=markup}. The implementation follows the original, but has been modified for JavaScript.
*
* ```text
* Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ```
*/
'use strict';
// MODULES //
var isnanf = require( '@stdlib/math/base/assert/is-nanf' );
var log1pf = require( '@stdlib/math/base/special/log1pf' );
var sqrtf = require( '@stdlib/math/base/special/sqrtf' );
var FLOAT32_LN2 = require( '@stdlib/constants/float32/ln-two' );
var lnf = require( '@stdlib/math/base/special/lnf' );
var f32 = require( '@stdlib/number/float64/base/to-float32' );
// VARIABLES //
var HUGE = f32( 1 << 28 ); // 2**28
var ZERO = f32( 0.0 );
var ONE = f32( 1.0 );
var TWO = f32( 2.0 );
// MAIN //
/**
* Computes the hyperbolic arccosine of a single-precision floating-point number.
*
* ## Method
*
* Based on
*
* ```tex
* \operatorname{acoshf}(x) = \logf \left[ x + \sqrtf{ x^2 - 1 } \right]
* ```
*
* we have
*
* ```tex
* \operatorname{acoshf}(x) = \begin{cases}
* \logf(x) + \tfrac{\ln}{2} & \text{ if x is large } \\
* \logf \left( 2x-\tfrac{1}{\sqrtf{x^2-1}+x} \right) & \text{ if } x > 2 \\
* \operatorname{log1pf}\left( x - 1 + \sqrtf{ 2 \cdot (x-1) + (x-1)^2 } \right) & \text{ otherwise }
* \end{cases}
* ```
*
* ## Special Cases
*
* ```tex
* \begin{align*}
* \operatorname{acoshf}(x) &= \mathrm{NaN}\ \text{ if } x < 1 \\
* \end{align*}
* ```
*
* @param {number} x - input value
* @returns {number} hyperbolic arccosine
*
* @example
* var v = acoshf( 1.0 );
* // returns 0.0
*
* @example
* var v = acoshf( 2.0 );
* // returns ~1.317
*
* @example
* var v = acoshf( NaN );
* // returns NaN
*/
function acoshf( x ) {
var t;
var s;
x = f32( x );
if ( isnanf( x ) || x < ONE ) {
return NaN;
}
if ( x === ONE ) {
return ZERO;
}
if ( x >= HUGE ) {
return f32( lnf( x ) + FLOAT32_LN2 );
}
if ( x > TWO ) {
t = f32( x*x );
s = f32( t - ONE );
return lnf( f32( f32( TWO*x ) - f32( ONE / f32( x + sqrtf( s ) ) ) ) );
}
// Case: 2 >= x > 1
t = f32( x - ONE );
return log1pf( f32( t + sqrtf( f32( f32( TWO*t ) + f32( t*t ) ) ) ) );
}
// EXPORTS //
module.exports = acoshf;
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