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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 following copyright, license, and long comment were part of the original implementation available as part of [FreeBSD]{@link https://svnweb.freebsd.org/base/release/9.3.0/lib/msun/src/s_tan.c}. The implementation follows the original, but has been modified for JavaScript.
*
* ```text
* Copyright (C) 1993 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 getHighWord = require( '@stdlib/number/float64/base/get-high-word' );
var kernelTan = require( '@stdlib/math/base/special/kernel-tan' );
var rempio2 = require( '@stdlib/math/base/special/rempio2' );
var HIGH_WORD_ABS_MASK = require( '@stdlib/constants/float64/high-word-abs-mask' );
var HIGH_WORD_EXPONENT_MASK = require( '@stdlib/constants/float64/high-word-exponent-mask' );
// VARIABLES //
// Scratch buffer:
var buffer = [ 0.0, 0.0 ]; // WARNING: not thread safe
// High word for pi/4: 0x3fe921fb => 00111111111010010010000111111011
var HIGH_WORD_PIO4 = 0x3fe921fb|0; // asm type annotation
// High word for a small value: 2^-27 = 7.450580596923828e-9 => high word => 0x3e400000 => 00111110010000000000000000000000
var HIGH_WORD_TWO_NEG_27 = 0x3e400000|0; // asm type annotation
// MAIN //
/**
* Evaluates the tangent of a number.
*
* ## Method
*
* - Let \\(S\\), \\(C\\), and \\(T\\) denote the \\(\sin\\), \\(\cos\\), and \\(\tan\\), respectively, on \\(\[-\pi/4, +\pi/4\]\\).
*
* - Reduce the argument \\(x\\) to \\(y1+y2 = x-k\pi/2\\) in \\(\[-\pi/4, +\pi/4\]\\), and let \\(n = k \mod 4\\).
*
* - We have
*
* | n | sin(x) | cos(x) | tan(x) |
* | - | ------ | ------ | ------ |
* | 0 | S | C | T |
* | 1 | C | -S | -1/T |
* | 2 | -S | -C | T |
* | 3 | -C | S | -1/T |
*
* @param {number} x - input value (in radians)
* @returns {number} tangent
*
* @example
* var v = tan( 0.0 );
* // returns ~0.0
*
* @example
* var v = tan( -3.141592653589793/4.0 );
* // returns ~-1.0
*
* @example
* var v = tan( 3.141592653589793/4.0 );
* // returns ~1.0
*
* @example
* var v = tan( NaN );
* // returns NaN
*/
function tan( x ) {
var ix;
var n;
ix = getHighWord( x );
ix &= HIGH_WORD_ABS_MASK;
// Case: |x| ~< π/4
if ( ix <= HIGH_WORD_PIO4 ) {
// Case: |x| < 2**-27
if ( ix < HIGH_WORD_TWO_NEG_27 ) {
return x;
}
return kernelTan( x, 0.0, 1 );
}
// Case: tan(Inf or NaN) is NaN
if ( ix >= HIGH_WORD_EXPONENT_MASK ) {
return NaN;
}
// Argument reduction needed...
n = rempio2( x, buffer );
return kernelTan( buffer[ 0 ], buffer[ 1 ], 1-((n&1)<<1) );
}
// EXPORTS //
module.exports = tan;
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