time-to-botec

Benchmark sampling in different programming languages
Log | Files | Refs | README

ndarray.js (2100B)

      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 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 {NumericArray} x - input array
     41 * @param {integer} stride - stride length
     42 * @param {NonNegativeInteger} offset - starting index
     43 * @returns {number} sum
     44 *
     45 * @example
     46 * var floor = require( '@stdlib/math/base/special/floor' );
     47 *
     48 * var x = [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ];
     49 * var N = floor( x.length / 2 );
     50 *
     51 * var v = gsumkbn( N, x, 2, 1 );
     52 * // returns 5.0
     53 */
     54 function gsumkbn( N, x, stride, offset ) {
     55 	var sum;
     56 	var ix;
     57 	var v;
     58 	var t;
     59 	var c;
     60 	var i;
     61 
     62 	if ( N <= 0 ) {
     63 		return 0.0;
     64 	}
     65 	if ( N === 1 || stride === 0 ) {
     66 		return x[ offset ];
     67 	}
     68 	ix = offset;
     69 	sum = 0.0;
     70 	c = 0.0;
     71 	for ( i = 0; i < N; i++ ) {
     72 		v = x[ ix ];
     73 		t = sum + v;
     74 		if ( abs( sum ) >= abs( v ) ) {
     75 			c += (sum-t) + v;
     76 		} else {
     77 			c += (v-t) + sum;
     78 		}
     79 		sum = t;
     80 		ix += stride;
     81 	}
     82 	return sum + c;
     83 }
     84 
     85 
     86 // EXPORTS //
     87 
     88 module.exports = gsumkbn;