time-to-botec

Benchmark sampling in different programming languages
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gsumpw.js (1862B)

      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 sum = require( './ndarray.js' );
     24 
     25 
     26 // MAIN //
     27 
     28 /**
     29 * Computes the sum of strided array elements using pairwise summation.
     30 *
     31 * ## Method
     32 *
     33 * -   This implementation uses pairwise summation, which accrues rounding error `O(log2 N)` instead of `O(N)`. The recursion depth is also `O(log2 N)`.
     34 *
     35 * ## References
     36 *
     37 * -   Higham, Nicholas J. 1993. "The Accuracy of Floating Point Summation." _SIAM Journal on Scientific Computing_ 14 (4): 783–99. doi:[10.1137/0914050](https://doi.org/10.1137/0914050).
     38 *
     39 * @param {PositiveInteger} N - number of indexed elements
     40 * @param {NumericArray} x - input array
     41 * @param {integer} stride - stride length
     42 * @returns {number} sum
     43 *
     44 * @example
     45 * var x = [ 1.0, -2.0, 2.0 ];
     46 * var N = x.length;
     47 *
     48 * var v = gsumpw( N, x, 1 );
     49 * // returns 1.0
     50 */
     51 function gsumpw( N, x, stride ) {
     52 	var ix;
     53 	var s;
     54 	var i;
     55 
     56 	if ( N <= 0 ) {
     57 		return 0.0;
     58 	}
     59 	if ( N === 1 || stride === 0 ) {
     60 		return x[ 0 ];
     61 	}
     62 	if ( stride < 0 ) {
     63 		ix = (1-N) * stride;
     64 	} else {
     65 		ix = 0;
     66 	}
     67 	if ( N < 8 ) {
     68 		// Use simple summation...
     69 		s = 0.0;
     70 		for ( i = 0; i < N; i++ ) {
     71 			s += x[ ix ];
     72 			ix += stride;
     73 		}
     74 		return s;
     75 	}
     76 	return sum( N, x, stride, ix );
     77 }
     78 
     79 
     80 // EXPORTS //
     81 
     82 module.exports = gsumpw;