time-to-botec

Benchmark sampling in different programming languages
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dapxsumkbn2.js (2440B)

      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 double-precision floating-point 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 {Float64Array} x - input array
     42 * @param {integer} stride - stride length
     43 * @returns {number} sum
     44 *
     45 * @example
     46 * var Float64Array = require( '@stdlib/array/float64' );
     47 *
     48 * var x = new Float64Array( [ 1.0, -2.0, 2.0 ] );
     49 * var N = x.length;
     50 *
     51 * var v = dapxsumkbn2( N, 5.0, x, 1 );
     52 * // returns 16.0
     53 */
     54 function dapxsumkbn2( N, alpha, x, stride ) {
     55 	var sum;
     56 	var ccs;
     57 	var ix;
     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 0.0;
     67 	}
     68 	if ( N === 1 || stride === 0 ) {
     69 		return alpha + x[ 0 ];
     70 	}
     71 	if ( stride < 0 ) {
     72 		ix = (1-N) * stride;
     73 	} else {
     74 		ix = 0;
     75 	}
     76 	sum = 0.0;
     77 	ccs = 0.0; // second order correction term for lost low order bits
     78 	cs = 0.0; // first order correction term for lost low order bits
     79 	for ( i = 0; i < N; i++ ) {
     80 		v = alpha + x[ ix ];
     81 		t = sum + v;
     82 		if ( abs( sum ) >= abs( v ) ) {
     83 			c = (sum-t) + v;
     84 		} else {
     85 			c = (v-t) + sum;
     86 		}
     87 		sum = t;
     88 		t = cs + c;
     89 		if ( abs( cs ) >= abs( c ) ) {
     90 			cc = (cs-t) + c;
     91 		} else {
     92 			cc = (c-t) + cs;
     93 		}
     94 		cs = t;
     95 		ccs += cc;
     96 		ix += stride;
     97 	}
     98 	return sum + cs + ccs;
     99 }
    100 
    101 
    102 // EXPORTS //
    103 
    104 module.exports = dapxsumkbn2;