time-to-botec

Benchmark sampling in different programming languages
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gapxsumkbn2.js (2329B)

      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 a second-order iterative Kahan–Babuška algorithm.
     30 *
     31 * ## Method
     32 *
     33 * -   This implementation uses a second-order iterative Kahan–Babuška algorithm, as described by Klein (2005).
     34 *
     35 * ## References
     36 *
     37 * -   Klein, Andreas. 2005. "A Generalized Kahan-Babuška-Summation-Algorithm." _Computing_ 76 (3): 279–93. doi:[10.1007/s00607-005-0139-x](https://doi.org/10.1007/s00607-005-0139-x).
     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 = gapxsumkbn2( N, 5.0, x, 1 );
     50 * // returns 16.0
     51 */
     52 function gapxsumkbn2( N, alpha, x, stride ) {
     53 	var sum;
     54 	var ccs;
     55 	var ix;
     56 	var cs;
     57 	var cc;
     58 	var v;
     59 	var t;
     60 	var c;
     61 	var i;
     62 
     63 	if ( N <= 0 ) {
     64 		return 0.0;
     65 	}
     66 	if ( N === 1 || stride === 0 ) {
     67 		return alpha + x[ 0 ];
     68 	}
     69 	if ( stride < 0 ) {
     70 		ix = (1-N) * stride;
     71 	} else {
     72 		ix = 0;
     73 	}
     74 	sum = 0.0;
     75 	ccs = 0.0; // second order correction term for lost low order bits
     76 	cs = 0.0; // first order correction term for lost low order bits
     77 	for ( i = 0; i < N; i++ ) {
     78 		v = alpha + x[ ix ];
     79 		t = sum + v;
     80 		if ( abs( sum ) >= abs( v ) ) {
     81 			c = (sum-t) + v;
     82 		} else {
     83 			c = (v-t) + sum;
     84 		}
     85 		sum = t;
     86 		t = cs + c;
     87 		if ( abs( cs ) >= abs( c ) ) {
     88 			cc = (cs-t) + c;
     89 		} else {
     90 			cc = (c-t) + cs;
     91 		}
     92 		cs = t;
     93 		ccs += cc;
     94 		ix += stride;
     95 	}
     96 	return sum + cs + ccs;
     97 }
     98 
     99 
    100 // EXPORTS //
    101 
    102 module.exports = gapxsumkbn2;