time-to-botec

Benchmark sampling in different programming languages
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gcusumkbn2.js (2489B)

      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 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 {number} sum - initial sum
     41 * @param {NumericArray} x - input array
     42 * @param {integer} strideX - `x` stride length
     43 * @param {NumericArray} y - output array
     44 * @param {integer} strideY - `y` stride length
     45 * @returns {NumericArray} output array
     46 *
     47 * @example
     48 * var x = [ 1.0, -2.0, 2.0 ];
     49 * var y = [ 0.0, 0.0, 0.0 ];
     50 *
     51 * var v = gcusumkbn2( x.length, 0.0, x, 1, y, 1 );
     52 * // returns [ 1.0, -1.0, 1.0 ]
     53 */
     54 function gcusumkbn2( N, sum, x, strideX, y, strideY ) {
     55 	var ccs;
     56 	var ix;
     57 	var iy;
     58 	var cs;
     59 	var cc;
     60 	var v;
     61 	var t;
     62 	var c;
     63 	var i;
     64 
     65 	if ( N <= 0 ) {
     66 		return y;
     67 	}
     68 	if ( strideX < 0 ) {
     69 		ix = (1-N) * strideX;
     70 	} else {
     71 		ix = 0;
     72 	}
     73 	if ( strideY < 0 ) {
     74 		iy = (1-N) * strideY;
     75 	} else {
     76 		iy = 0;
     77 	}
     78 	ccs = 0.0; // second order correction term for lost low order bits
     79 	cs = 0.0; // first order correction term for lost low order bits
     80 	for ( i = 0; i < N; i++ ) {
     81 		v = x[ ix ];
     82 		t = sum + v;
     83 		if ( abs( sum ) >= abs( v ) ) {
     84 			c = (sum-t) + v;
     85 		} else {
     86 			c = (v-t) + sum;
     87 		}
     88 		sum = t;
     89 		t = cs + c;
     90 		if ( abs( cs ) >= abs( c ) ) {
     91 			cc = (cs-t) + c;
     92 		} else {
     93 			cc = (c-t) + cs;
     94 		}
     95 		cs = t;
     96 		ccs += cc;
     97 
     98 		y[ iy ] = sum + cs + ccs;
     99 		ix += strideX;
    100 		iy += strideY;
    101 	}
    102 	return y;
    103 }
    104 
    105 
    106 // EXPORTS //
    107 
    108 module.exports = gcusumkbn2;