time-to-botec

Benchmark sampling in different programming languages
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dcusumkbn2.js (2638B)

      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 double-precision floating-point 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 {Float64Array} x - input array
     42 * @param {integer} strideX - `x` stride length
     43 * @param {Float64Array} y - output array
     44 * @param {integer} strideY - `y` stride length
     45 * @returns {Float64Array} output array
     46 *
     47 * @example
     48 * var Float64Array = require( '@stdlib/array/float64' );
     49 *
     50 * var x = new Float64Array( [ 1.0, -2.0, 2.0 ] );
     51 * var y = new Float64Array( x.length );
     52 * var N = x.length;
     53 *
     54 * var v = dcusumkbn2( N, 0.0, x, 1, y, 1 );
     55 * // returns <Float64Array>[ 1.0, -1.0, 1.0 ]
     56 */
     57 function dcusumkbn2( N, sum, x, strideX, y, strideY ) {
     58 	var ccs;
     59 	var ix;
     60 	var iy;
     61 	var cs;
     62 	var cc;
     63 	var v;
     64 	var t;
     65 	var c;
     66 	var i;
     67 
     68 	if ( N <= 0 ) {
     69 		return y;
     70 	}
     71 	if ( strideX < 0 ) {
     72 		ix = (1-N) * strideX;
     73 	} else {
     74 		ix = 0;
     75 	}
     76 	if ( strideY < 0 ) {
     77 		iy = (1-N) * strideY;
     78 	} else {
     79 		iy = 0;
     80 	}
     81 	ccs = 0.0; // second order correction term for lost low order bits
     82 	cs = 0.0; // first order correction term for lost low order bits
     83 	for ( i = 0; i < N; i++ ) {
     84 		v = x[ ix ];
     85 		t = sum + v;
     86 		if ( abs( sum ) >= abs( v ) ) {
     87 			c = (sum-t) + v;
     88 		} else {
     89 			c = (v-t) + sum;
     90 		}
     91 		sum = t;
     92 		t = cs + c;
     93 		if ( abs( cs ) >= abs( c ) ) {
     94 			cc = (cs-t) + c;
     95 		} else {
     96 			cc = (c-t) + cs;
     97 		}
     98 		cs = t;
     99 		ccs += cc;
    100 
    101 		y[ iy ] = sum + cs + ccs;
    102 		ix += strideX;
    103 		iy += strideY;
    104 	}
    105 	return y;
    106 }
    107 
    108 
    109 // EXPORTS //
    110 
    111 module.exports = dcusumkbn2;