Press n or j to go to the next uncovered block, b, p or k for the previous block.
| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 | 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x | /**
* @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/12.2.0/lib/msun/src/e_atanh.c?view=markup}. The implementation follows the original, but has been modified according to project conventions.
*
* ```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 SIGN_MASK = require( '@stdlib/constants/float64/high-word-sign-mask' );
var ABS_MASK = require( '@stdlib/constants/float64/high-word-abs-mask' );
var getHighWord = require( '@stdlib/number/float64/base/get-high-word' );
var setHighWord = require( '@stdlib/number/float64/base/set-high-word' );
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var log1p = require( '@stdlib/math/base/special/log1p' );
var PINF = require( '@stdlib/constants/float64/pinf' );
var NINF = require( '@stdlib/constants/float64/ninf' );
// VARIABLES //
// 2^0 = 1 => 0 01111111111 00000000000000000000 => 0x3ff00000 = 1072693248
var HIGH_BIASED_EXP_0 = 0x3ff00000|0; // asm type annotation
// 2^-1 = 0.5 => 0 01111111110 00000000000000000000 => 0x3fe00000 = 1071644672
var HIGH_BIASED_EXP_NEG_1 = 0x3fe00000|0; // asm type annotation
// 2^-28 = 3.725290298461914e-9 => 0 01111100011 00000000000000000000 => 0x3e300000 = 1043333120
var HIGH_BIASED_EXP_NEG_28 = 0x3e300000|0; // asm type annotation
// MAIN //
/**
* Computes the hyperbolic arctangent of a double-precision floating-point number.
*
* ## Method
*
* 1. Reduce \\( x \\) to positive by \\( \operatorname{atanh}(-x) = -\operatorname{atanh}(x) \\)
*
* 2. For \\( x \ge 0.5 \\), we calculate
*
* ```tex
* \operatorname{atanh}(x) = \frac{1}{2} \cdot \log\left( 1 + \tfrac{2x}{1-x} \right) = \frac{1}{2} \cdot \operatorname{log1p}\left( 2 \tfrac{x}{1-x} \right)
* ```
*
* For \\( x < 0.5 \\), we have
*
* ```tex
* \operatorname{atanh}(x) = \frac{1}{2} \cdot \operatorname{log1p}\left( 2x + \tfrac{2x^2}{1-x} \right)
* ```
*
* ## Special Cases
*
* ```tex
* \begin{align*}
* \operatorname{atanh}(\mathrm{NaN}) &= \mathrm{NaN}\\
* \operatorname{atanh}(1.0) &= \infty \\
* \operatorname{atanh}(-1.0) &= -\infty \\
* \end{align*}
* ```
*
* @param {number} x - input value
* @returns {number} hyperbolic arctangent
*
* @example
* var v = atanh( 0.0 );
* // returns 0.0
*
* @example
* var v = atanh( 0.9 );
* // returns ~1.472
*
* @example
* var v = atanh( 1.0 );
* // returns Infinity
*
* @example
* var v = atanh( -1.0 );
* // returns -Infinity
*
* @example
* var v = atanh( NaN );
* // returns NaN
*/
function atanh( x ) {
var sgn;
var ax;
var hx;
var ix;
var t;
if ( isnan( x ) || x < -1.0 || x > 1.0 ) {
return NaN;
}
// Extract the higher order word from `x`:
hx = getHighWord( x );
// Isolate the sign bit:
sgn = (hx & SIGN_MASK)>>>0;
// Turn off the sign bit:
ix = (hx & ABS_MASK)|0; // asm type annotation
// Case: |x| == 1
if ( ix === HIGH_BIASED_EXP_0 ) {
return ( sgn === 0 ) ? PINF : NINF;
}
// Case: |x| < 2**-28
if ( ix < HIGH_BIASED_EXP_NEG_28 ) {
return x;
}
// Compute `|x|` by setting the high word of `x` to the high word with the sign bit turned off:
ax = setHighWord( x, ix );
// Case: |x| < 0.5
if ( ix < HIGH_BIASED_EXP_NEG_1 ) {
t = ax + ax;
t = 0.5 * log1p( t + ( t*ax/(1.0-ax) ) );
} else {
t = 0.5 * log1p( (ax+ax) / (1.0-ax) );
}
return ( sgn === 0 ) ? t : -t;
}
// EXPORTS //
module.exports = atanh;
|