time-to-botec

Benchmark sampling in different programming languages
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gapxsumpw.js (1966B)

      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 * Adds a constant to each strided array element and computes the sum 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 {number} alpha - constant
     41 * @param {NumericArray} x - input array
     42 * @param {integer} stride - stride length
     43 * @returns {number} sum
     44 *
     45 * @example
     46 * var x = [ 1.0, -2.0, 2.0 ];
     47 * var N = x.length;
     48 *
     49 * var v = gapxsumpw( N, 5.0, x, 1 );
     50 * // returns 16.0
     51 */
     52 function gapxsumpw( N, alpha, x, stride ) {
     53 	var ix;
     54 	var s;
     55 	var i;
     56 
     57 	if ( N <= 0 ) {
     58 		return 0.0;
     59 	}
     60 	if ( N === 1 || stride === 0 ) {
     61 		return alpha + x[ 0 ];
     62 	}
     63 	if ( stride < 0 ) {
     64 		ix = (1-N) * stride;
     65 	} else {
     66 		ix = 0;
     67 	}
     68 	if ( N < 8 ) {
     69 		// Use simple summation...
     70 		s = 0.0;
     71 		for ( i = 0; i < N; i++ ) {
     72 			s += alpha + x[ ix ];
     73 			ix += stride;
     74 		}
     75 		return s;
     76 	}
     77 	return sum( N, alpha, x, stride, ix );
     78 }
     79 
     80 
     81 // EXPORTS //
     82 
     83 module.exports = gapxsumpw;