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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 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 isnan = require( './../../../../base/assert/is-nan' );
var PINF = require( '@stdlib/constants/float64/pinf' );
var PIO2 = require( '@stdlib/constants/float64/half-pi' );
var PIO4 = require( '@stdlib/constants/float64/fourth-pi' );
var NINF = require( '@stdlib/constants/float64/ninf' );
var polyvalP = require( './polyval_p.js' );
var polyvalQ = require( './polyval_q.js' );
// VARIABLES //
var MOREBITS = 6.123233995736765886130e-17; // pi/2 = PIO2 + MOREBITS.
var T3P8 = 2.41421356237309504880; // tan( 3*pi/8 )
// MAIN //
/**
* Computes the arctangent of a number.
*
* ## Method
*
* - Range reduction is from three intervals into the interval from 0 to 0.66. The approximant uses a rational function of degree 4/5 of the form
*
* ```tex
* x + x^3 \frac{P(x)}{Q(x)}
* ```
*
* ## Notes
*
* - Relative error:
*
* | arithmetic | domain | # trials | peak | rms |
* |:-----------|:--------|:---------|:--------|:--------|
* | DEC | -10, 10 | 50000 | 2.4e-17 | 8.3e-18 |
* | IEEE | -10, 10 | 10^6 | 1.8e-16 | 5.0e-17 |
*
* @param {number} x - input value
* @returns {number} arctangent (in radians)
*
* @example
* var v = atan( 0.0 );
* // returns ~0.0
*
* @example
* var PI = require( '@stdlib/constants/float64/pi' );
*
* var v = atan( -PI/4.0 );
* // returns ~-0.666
*
* @example
* var PI = require( '@stdlib/constants/float64/pi' );
*
* var v = atan( PI/4.0 );
* // returns ~0.666
*
* @example
* var v = atan( NaN );
* // returns NaN
*/
function atan( x ) {
var flg;
var sgn;
var y;
var z;
if ( isnan( x ) || x === 0.0 ) {
return x;
}
if ( x === PINF ) {
return PIO2;
}
if ( x === NINF ) {
return -PIO2;
}
if ( x < 0.0 ) {
sgn = true;
x = -x;
}
// Range reduction:
flg = 0;
if ( x > T3P8 ) {
y = PIO2;
flg = 1;
x = -( 1.0/x );
}
else if ( x <= 0.66 ) {
y = 0.0;
}
else {
y = PIO4;
flg = 2;
x = (x-1.0) / (x+1.0);
}
z = x * x;
z = z*polyvalP( z ) / polyvalQ( z );
z = ( x*z ) + x;
if ( flg === 2 ) {
z += 0.5 * MOREBITS;
}
else if ( flg === 1 ) {
z += MOREBITS;
}
y += z;
return ( sgn ) ? -y : y;
}
// EXPORTS //
module.exports = atan;
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