time-to-botec

Benchmark sampling in different programming languages
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ndarray.js (2439B)

      1 /**
      2 * @license Apache-2.0
      3 *
      4 * Copyright (c) 2020 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 abs = require( '@stdlib/math/base/special/abs' );
     24 
     25 
     26 // MAIN //
     27 
     28 /**
     29 * Computes the cumulative sum of strided array elements using an improved Kahan–Babuška algorithm.
     30 *
     31 * ## Method
     32 *
     33 * -   This implementation uses an "improved Kahan–Babuška algorithm", as described by Neumaier (1974).
     34 *
     35 * ## References
     36 *
     37 * -   Neumaier, Arnold. 1974. "Rounding Error Analysis of Some Methods for Summing Finite Sums." _Zeitschrift Für Angewandte Mathematik Und Mechanik_ 54 (1): 39–51. doi:[10.1002/zamm.19740540106](https://doi.org/10.1002/zamm.19740540106).
     38 *
     39 * @param {PositiveInteger} N - number of indexed elements
     40 * @param {number} sum - initial sum
     41 * @param {NumericArray} x - input array
     42 * @param {integer} strideX - `x` stride length
     43 * @param {NonNegativeInteger} offsetX - starting index for `x`
     44 * @param {NumericArray} y - output array
     45 * @param {integer} strideY - `y` stride length
     46 * @param {NonNegativeInteger} offsetY - starting index for `y`
     47 * @returns {NumericArray} output array
     48 *
     49 * @example
     50 * var floor = require( '@stdlib/math/base/special/floor' );
     51 *
     52 * var x = [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ];
     53 * var y = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
     54 * var N = floor( x.length / 2 );
     55 *
     56 * gcusumkbn( N, 0.0, x, 2, 1, y, 1, 0 );
     57 * // y => [ 1.0, -1.0, 1.0, 5.0, 0.0, 0.0, 0.0, 0.0 ]
     58 */
     59 function gcusumkbn( N, sum, x, strideX, offsetX, y, strideY, offsetY ) {
     60 	var ix;
     61 	var iy;
     62 	var s;
     63 	var v;
     64 	var t;
     65 	var c;
     66 	var i;
     67 
     68 	if ( N <= 0 ) {
     69 		return y;
     70 	}
     71 	ix = offsetX;
     72 	iy = offsetY;
     73 	s = sum;
     74 	c = 0.0;
     75 	for ( i = 0; i < N; i++ ) {
     76 		v = x[ ix ];
     77 		t = s + v;
     78 		if ( abs( s ) >= abs( v ) ) {
     79 			c += (s-t) + v;
     80 		} else {
     81 			c += (v-t) + s;
     82 		}
     83 		s = t;
     84 		y[ iy ] = s + c;
     85 		ix += strideX;
     86 		iy += strideY;
     87 	}
     88 	return y;
     89 }
     90 
     91 
     92 // EXPORTS //
     93 
     94 module.exports = gcusumkbn;