time-to-botec

Benchmark sampling in different programming languages
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sapxsumkbn.js (2530B)

      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 float64ToFloat32 = require( '@stdlib/number/float64/base/to-float32' );
     24 var abs = require( '@stdlib/math/base/special/abs' );
     25 
     26 
     27 // MAIN //
     28 
     29 /**
     30 * Adds a constant to each single-precision floating-point strided array element and computes the sum using an improved Kahan–Babuška algorithm.
     31 *
     32 * ## Method
     33 *
     34 * -   This implementation uses an "improved Kahan–Babuška algorithm", as described by Neumaier (1974).
     35 *
     36 * ## References
     37 *
     38 * -   Neumaier, Arnold. 1974. "Rounding Error Analysis of Some Methods for Summing Finite Sums." _Zeitschrift Für Angewandte Mathematik Und Mechanik_ 54 (1): 39–51. doi:[10.1002/zamm.19740540106](https://doi.org/10.1002/zamm.19740540106).
     39 *
     40 * @param {PositiveInteger} N - number of indexed elements
     41 * @param {number} alpha - constant
     42 * @param {Float32Array} x - input array
     43 * @param {integer} stride - stride length
     44 * @returns {number} sum
     45 *
     46 * @example
     47 * var Float32Array = require( '@stdlib/array/float32' );
     48 *
     49 * var x = new Float32Array( [ 1.0, -2.0, 2.0 ] );
     50 * var N = x.length;
     51 *
     52 * var v = sapxsumkbn( N, 5.0, x, 1 );
     53 * // returns 16.0
     54 */
     55 function sapxsumkbn( N, alpha, x, stride ) {
     56 	var sum;
     57 	var ix;
     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 float64ToFloat32( alpha + x[ 0 ] );
     68 	}
     69 	if ( stride < 0 ) {
     70 		ix = (1-N) * stride;
     71 	} else {
     72 		ix = 0;
     73 	}
     74 	sum = 0.0;
     75 	c = 0.0;
     76 	for ( i = 0; i < N; i++ ) {
     77 		v = float64ToFloat32( alpha + x[ ix ] );
     78 		t = float64ToFloat32( sum + v );
     79 		if ( abs( sum ) >= abs( v ) ) {
     80 			c = float64ToFloat32( c + float64ToFloat32( float64ToFloat32( sum-t ) + v ) ); // eslint-disable-line max-len
     81 		} else {
     82 			c = float64ToFloat32( c + float64ToFloat32( float64ToFloat32( v-t ) + sum ) ); // eslint-disable-line max-len
     83 		}
     84 		sum = t;
     85 		ix += stride;
     86 	}
     87 	return float64ToFloat32( sum + c );
     88 }
     89 
     90 
     91 // EXPORTS //
     92 
     93 module.exports = sapxsumkbn;