time-to-botec

Benchmark sampling in different programming languages
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main.js (3071B)

      1 /**
      2 * @license Apache-2.0
      3 *
      4 * Copyright (c) 2018 The Stdlib Authors.
      5 *
      6 * Licensed under the Apache License, Version 2.0 (the "License");
      7 * you may not use this file except in compliance with the License.
      8 * You may obtain a copy of the License at
      9 *
     10 *    http://www.apache.org/licenses/LICENSE-2.0
     11 *
     12 * Unless required by applicable law or agreed to in writing, software
     13 * distributed under the License is distributed on an "AS IS" BASIS,
     14 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
     15 * See the License for the specific language governing permissions and
     16 * limitations under the License.
     17 */
     18 
     19 'use strict';
     20 
     21 // MODULES //
     22 
     23 var log1p = require( './../../../../base/special/log1p' );
     24 var abs = require( './../../../../base/special/abs' );
     25 var expm1 = require( './../../../../base/special/expm1' );
     26 var isnan = require( './../../../../base/assert/is-nan' );
     27 var NINF = require( '@stdlib/constants/float64/ninf' );
     28 
     29 
     30 // MAIN //
     31 
     32 /**
     33 * Computes a one-parameter Box-Cox transformation of `1+x`.
     34 *
     35 * ## Method
     36 *
     37 * When computing a one-parameter Box-Cox transformation
     38 *
     39 * -   If \\( \lambda << 1 \\) and \\( \ln( x ) < 1.0 \\), then the product \\( \lambda \cdot \ln(x) \\) can lose precision, and, furthermore, \\( \operatorname{expm1}(x) = x \\) for \\( x < \epsilon \\).
     40 * -   For double-precision floating-point numbers, the range of the natural log is \\( \[-744.44, 709.78\] and \\( \epsilon \\) is the smallest value produced.
     41 * -   The value range means that we will have \\( |\lambda \cdot \ln(x)| < \epsilon \\) whenever \\( |\lambda| \leq \frac{\epsilon}{-\ln(d) \\), where \\( d \\) is the minimum double-precision floating-point number, thus corresponding to the value \\( \approx 2.98 \times 10^{-19} \\).
     42 *
     43 * For small `x` values, the same method described above applies with the modification that the smallest value returned by \\( \operatorname{log1p}(x) \\) is the minimum representable value, not \\( \epsilon \\). Furthermore, we need to guard against underflow when \\( \operatorname{log1p}(x) < \epsilon \\).
     44 *
     45 * @param {number} x - input value
     46 * @param {number} lambda - power parameter
     47 * @returns {number} Box-Cox transformation of `1+x`
     48 *
     49 * @example
     50 * var v = boxcox1p( 1.0, 2.5 );
     51 * // returns ~1.8627
     52 *
     53 * @example
     54 * var v = boxcox1p( 4.0, 2.5 );
     55 * // returns ~21.9607
     56 *
     57 * @example
     58 * var v = boxcox1p( 10.0, 2.5 );
     59 * // returns ~160.1246
     60 *
     61 * @example
     62 * var v = boxcox1p( 2.0, 0.0 );
     63 * // returns ~1.0986
     64 *
     65 * @example
     66 * var v = boxcox1p( -1.0, 2.5 );
     67 * // returns -0.4
     68 *
     69 * @example
     70 * var v = boxcox1p( 0.0, -1.0 );
     71 * // returns 0.0
     72 *
     73 * @example
     74 * var v = boxcox1p( -1.0, -1.0 );
     75 * // returns -Infinity
     76 */
     77 function boxcox1p( x, lambda ) {
     78 	var lgx;
     79 	if ( isnan( x ) || isnan( lambda ) || x < -1.0 ) {
     80 		return NaN;
     81 	}
     82 	if ( x === -1.0 && lambda < 0.0 ) {
     83 		return NINF;
     84 	}
     85 	lgx = log1p( x );
     86 	if (
     87 		abs( lambda ) < 1.0e-19 ||
     88 
     89 		// Guard against underflow...
     90 		(
     91 			abs( lgx ) < 1.0e-289 &&
     92 			abs( lambda ) < 1.0e273
     93 		)
     94 	) {
     95 		return lgx;
     96 	}
     97 	return expm1( lambda*lgx ) / lambda;
     98 }
     99 
    100 
    101 // EXPORTS //
    102 
    103 module.exports = boxcox1p;