time-to-botec

Benchmark sampling in different programming languages
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dcusumkbn.js (2393B)

      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 double-precision floating-point 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 {Float64Array} x - input array
     42 * @param {integer} strideX - `x` stride length
     43 * @param {Float64Array} y - output array
     44 * @param {integer} strideY - `y` stride length
     45 * @returns {Float64Array} output array
     46 *
     47 * @example
     48 * var Float64Array = require( '@stdlib/array/float64' );
     49 *
     50 * var x = new Float64Array( [ 1.0, -2.0, 2.0 ] );
     51 * var y = new Float64Array( x.length );
     52 * var N = x.length;
     53 *
     54 * var v = dcusumkbn( N, 0.0, x, 1, y, 1 );
     55 * // returns <Float64Array>[ 1.0, -1.0, 1.0 ]
     56 */
     57 function dcusumkbn( N, sum, x, strideX, y, strideY ) {
     58 	var ix;
     59 	var iy;
     60 	var s;
     61 	var v;
     62 	var t;
     63 	var c;
     64 	var i;
     65 
     66 	if ( N <= 0 ) {
     67 		return y;
     68 	}
     69 	if ( strideX < 0 ) {
     70 		ix = (1-N) * strideX;
     71 	} else {
     72 		ix = 0;
     73 	}
     74 	if ( strideY < 0 ) {
     75 		iy = (1-N) * strideY;
     76 	} else {
     77 		iy = 0;
     78 	}
     79 	s = sum;
     80 	c = 0.0;
     81 	for ( i = 0; i < N; i++ ) {
     82 		v = x[ ix ];
     83 		t = s + v;
     84 		if ( abs( s ) >= abs( v ) ) {
     85 			c += (s-t) + v;
     86 		} else {
     87 			c += (v-t) + s;
     88 		}
     89 		s = t;
     90 		y[ iy ] = s + c;
     91 		ix += strideX;
     92 		iy += strideY;
     93 	}
     94 	return y;
     95 }
     96 
     97 
     98 // EXPORTS //
     99 
    100 module.exports = dcusumkbn;