time-to-botec

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

gapxsumkbn.js (2079B)

      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 * Adds a constant to each strided array element and computes the sum 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} alpha - constant
     41 * @param {NumericArray} x - input array
     42 * @param {integer} stride - stride length
     43 * @returns {number} sum
     44 *
     45 * @example
     46 * var x = [ 1.0, -2.0, 2.0 ];
     47 * var N = x.length;
     48 *
     49 * var v = gapxsumkbn( N, 5.0, x, 1 );
     50 * // returns 16.0
     51 */
     52 function gapxsumkbn( N, alpha, x, stride ) {
     53 	var sum;
     54 	var ix;
     55 	var v;
     56 	var t;
     57 	var c;
     58 	var i;
     59 
     60 	if ( N <= 0 ) {
     61 		return 0.0;
     62 	}
     63 	if ( N === 1 || stride === 0 ) {
     64 		return alpha + x[ 0 ];
     65 	}
     66 	if ( stride < 0 ) {
     67 		ix = (1-N) * stride;
     68 	} else {
     69 		ix = 0;
     70 	}
     71 	sum = 0.0;
     72 	c = 0.0;
     73 	for ( i = 0; i < N; i++ ) {
     74 		v = alpha + x[ ix ];
     75 		t = sum + v;
     76 		if ( abs( sum ) >= abs( v ) ) {
     77 			c += (sum-t) + v;
     78 		} else {
     79 			c += (v-t) + sum;
     80 		}
     81 		sum = t;
     82 		ix += stride;
     83 	}
     84 	return sum + c;
     85 }
     86 
     87 
     88 // EXPORTS //
     89 
     90 module.exports = gapxsumkbn;