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* @license Apache-2.0
*
* Copyright (c) 2024 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 isnanf = require( '@stdlib/math/base/assert/is-nanf' );
var sqrtf = require( '@stdlib/math/base/special/sqrtf' );
var float64ToFloat32 = require( '@stdlib/number/float64/base/to-float32' );
var PI02F = require( '@stdlib/constants/float32/half-pi' );
var polyp = require( './poly_p.js' );
// MAIN //
/**
* Computes the arcsine of a single-precision floating-point number.
*
* ## Method
*
* - A polynomial of the form
*
* ```tex
* x + x^3 P(x^2)
* ```
*
* is used for \\(\|x\|\\) in the interval \\(\[0, 0.5\]\\). If \\(\|x\| > 0.5\\), it is transformed by the identity
*
* ```tex
* \operatorname{asinf}(x) = \frac{\pi}{2} - 2 \operatorname{asinf}( \sqrt{ (1-x)/2 } )
* ```
*
* ## Notes
*
* - Relative error:
*
* | arithmetic | domain | # trials | peak | rms |
* |:-----------|:-------|:---------|:--------|:--------|
* | IEEE | -1, 1 | 10^5 | 2.5e-7 | 5.0e-8 |
*
* @param {number} x - input value
* @returns {number} arcsine (in radians)
*
* @example
* var v = asinf( 0.0 );
* // returns 0.0
*
* @example
* var v = asinf( 3.14/4.0 );
* // returns ~0.903
*
* @example
* var v = asinf( -3.14/6.0 );
* // returns ~-0.551
*
* @example
* var v = asinf( NaN );
* // returns NaN
*/
function asinf( x ) {
var flag;
var sgn;
var ax;
var z;
if ( isnanf( x ) ) {
return NaN;
}
x = float64ToFloat32( x );
if ( x > 0.0 ) {
sgn = 1;
ax = x;
} else {
sgn = -1;
ax = -x;
}
if ( ax > 1.0 ) {
return NaN;
}
if ( ax < 1.0e-4 ) {
return x;
}
if ( ax > 0.5 ) {
z = float64ToFloat32( 0.5 * float64ToFloat32( 1.0 - ax ) );
ax = sqrtf( z );
flag = 1;
} else {
z = float64ToFloat32( ax * ax );
flag = 0;
}
z = float64ToFloat32( float64ToFloat32( float64ToFloat32( polyp( z ) * z ) * ax ) + ax ); // eslint-disable-line max-len
if ( flag !== 0 ) {
z = float64ToFloat32( z + z );
z = float64ToFloat32( PI02F - z );
}
if ( sgn < 0 ) {
z = -z;
}
return z;
}
// EXPORTS //
module.exports = asinf;
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