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 | 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 8025x 8025x 8025x 1238x 1238x 8025x 1238x 1238x 5549x 8025x 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.
*/
'use strict';
// MODULES //
var atanh = require( '@stdlib/math/base/special/atanh' );
var log1p = require( '@stdlib/math/base/special/log1p' );
// MAIN //
/**
* Computes the inverse hyperbolic cotangent of a double-precision floating-point number.
*
* @param {number} x - input value
* @returns {number} inverse hyperbolic cotangent
*
* @example
* var v = acoth( 2.0 );
* // returns ~0.5493
*
* @example
* var v = acoth( 0.0 );
* // returns NaN
*
* @example
* var v = acoth( 0.5 );
* // returns NaN
*
* @example
* var v = acoth( 1.0 );
* // returns Infinity
*
* @example
* var v = acoth( NaN );
* // returns NaN
*/
function acoth( x ) {
// Near `|x| = 1`, `atanh( 1/x )` loses the low bits of `1-|1/x|` to the rounding of `1/x`. Use `acoth(x) = log( (x+1)/(x-1) )/2 = log1p( 2/(x-1) )/2` instead, where `x-1` is exact for `1 <= x <= 2`:
if ( x >= 1.0 && x <= 2.0 ) {
return 0.5 * log1p( 2.0 / ( x - 1.0 ) );
}
if ( x <= -1.0 && x >= -2.0 ) {
return -0.5 * log1p( 2.0 / ( -x - 1.0 ) );
}
return atanh( 1.0/x );
}
// EXPORTS //
module.exports = acoth;
|