time-to-botec

Benchmark sampling in different programming languages
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gsumkbn2.js (2232B)

      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 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 {NumericArray} x - input array
     41 * @param {integer} stride - stride length
     42 * @returns {number} sum
     43 *
     44 * @example
     45 * var x = [ 1.0, -2.0, 2.0 ];
     46 * var N = x.length;
     47 *
     48 * var v = gsumkbn2( N, x, 1 );
     49 * // returns 1.0
     50 */
     51 function gsumkbn2( N, x, stride ) {
     52 	var sum;
     53 	var ccs;
     54 	var ix;
     55 	var cs;
     56 	var cc;
     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[ 0 ];
     67 	}
     68 	if ( stride < 0 ) {
     69 		ix = (1-N) * stride;
     70 	} else {
     71 		ix = 0;
     72 	}
     73 	sum = 0.0;
     74 	ccs = 0.0; // second order correction term for lost low order bits
     75 	cs = 0.0; // first order correction term for lost low order bits
     76 	for ( i = 0; i < N; i++ ) {
     77 		v = x[ ix ];
     78 		t = sum + v;
     79 		if ( abs( sum ) >= abs( v ) ) {
     80 			c = (sum-t) + v;
     81 		} else {
     82 			c = (v-t) + sum;
     83 		}
     84 		sum = t;
     85 		t = cs + c;
     86 		if ( abs( cs ) >= abs( c ) ) {
     87 			cc = (cs-t) + c;
     88 		} else {
     89 			cc = (c-t) + cs;
     90 		}
     91 		cs = t;
     92 		ccs += cc;
     93 		ix += stride;
     94 	}
     95 	return sum + cs + ccs;
     96 }
     97 
     98 
     99 // EXPORTS //
    100 
    101 module.exports = gsumkbn2;