time-to-botec

Benchmark sampling in different programming languages
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gcusumkbn.js (2244B)

      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 {NumericArray} y - output array
     44 * @param {integer} strideY - `y` stride length
     45 * @returns {NumericArray} output array
     46 *
     47 * @example
     48 * var x = [ 1.0, -2.0, 2.0 ];
     49 * var y = [ 0.0, 0.0, 0.0 ];
     50 *
     51 * var v = gcusumkbn( x.length, 0.0, x, 1, y, 1 );
     52 * // returns [ 1.0, -1.0, 1.0 ]
     53 */
     54 function gcusumkbn( N, sum, x, strideX, y, strideY ) {
     55 	var ix;
     56 	var iy;
     57 	var s;
     58 	var v;
     59 	var t;
     60 	var c;
     61 	var i;
     62 
     63 	if ( N <= 0 ) {
     64 		return y;
     65 	}
     66 	if ( strideX < 0 ) {
     67 		ix = (1-N) * strideX;
     68 	} else {
     69 		ix = 0;
     70 	}
     71 	if ( strideY < 0 ) {
     72 		iy = (1-N) * strideY;
     73 	} else {
     74 		iy = 0;
     75 	}
     76 	s = sum;
     77 	c = 0.0;
     78 	for ( i = 0; i < N; i++ ) {
     79 		v = x[ ix ];
     80 		t = s + v;
     81 		if ( abs( s ) >= abs( v ) ) {
     82 			c += (s-t) + v;
     83 		} else {
     84 			c += (v-t) + s;
     85 		}
     86 		s = t;
     87 		y[ iy ] = s + c;
     88 		ix += strideX;
     89 		iy += strideY;
     90 	}
     91 	return y;
     92 }
     93 
     94 
     95 // EXPORTS //
     96 
     97 module.exports = gcusumkbn;