time-to-botec

Benchmark sampling in different programming languages
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sapxsumkbn2.js (2805B)

      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 a second-order iterative Kahan–Babuška algorithm.
     31 *
     32 * ## Method
     33 *
     34 * -   This implementation uses a second-order iterative Kahan–Babuška algorithm, as described by Klein (2005).
     35 *
     36 * ## References
     37 *
     38 * -   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).
     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 = sapxsumkbn2( N, 5.0, x, 1 );
     53 * // returns 16.0
     54 */
     55 function sapxsumkbn2( N, alpha, x, stride ) {
     56 	var sum;
     57 	var ccs;
     58 	var ix;
     59 	var cs;
     60 	var cc;
     61 	var v;
     62 	var t;
     63 	var c;
     64 	var i;
     65 
     66 	if ( N <= 0 ) {
     67 		return 0.0;
     68 	}
     69 	if ( N === 1 || stride === 0 ) {
     70 		return float64ToFloat32( alpha + x[ 0 ] );
     71 	}
     72 	if ( stride < 0 ) {
     73 		ix = (1-N) * stride;
     74 	} else {
     75 		ix = 0;
     76 	}
     77 	sum = 0.0;
     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 = float64ToFloat32( alpha + x[ ix ] );
     82 		t = float64ToFloat32( sum+v );
     83 		if ( abs( sum ) >= abs( v ) ) {
     84 			c = float64ToFloat32( float64ToFloat32( sum-t ) + v );
     85 		} else {
     86 			c = float64ToFloat32( float64ToFloat32( v-t ) + sum );
     87 		}
     88 		sum = t;
     89 		t = float64ToFloat32( cs+c );
     90 		if ( abs( cs ) >= abs( c ) ) {
     91 			cc = float64ToFloat32( float64ToFloat32( cs-t ) + c );
     92 		} else {
     93 			cc = float64ToFloat32( float64ToFloat32( c-t ) + cs );
     94 		}
     95 		cs = t;
     96 		ccs = float64ToFloat32( ccs+cc );
     97 		ix += stride;
     98 	}
     99 	return float64ToFloat32( sum + float64ToFloat32( cs+ccs ) );
    100 }
    101 
    102 
    103 // EXPORTS //
    104 
    105 module.exports = sapxsumkbn2;