time-to-botec

Benchmark sampling in different programming languages
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ndarray.js (2852B)

      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 floor = require( '@stdlib/math/base/special/floor' );
     25 
     26 
     27 // VARIABLES //
     28 
     29 // Blocksize for pairwise summation:
     30 var BLOCKSIZE = 128;
     31 
     32 
     33 // MAIN //
     34 
     35 /**
     36 * Computes the cumulative sum of single-precision floating-point strided array elements using pairwise summation.
     37 *
     38 * ## Method
     39 *
     40 * -   This implementation uses pairwise summation, which accrues rounding error `O(log2 N)` instead of `O(N)`. The recursion depth is also `O(log2 N)`.
     41 *
     42 * ## References
     43 *
     44 * -   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).
     45 *
     46 * @param {PositiveInteger} N - number of indexed elements
     47 * @param {number} sum - initial sum
     48 * @param {Float32Array} x - input array
     49 * @param {integer} strideX - `x` stride length
     50 * @param {NonNegativeInteger} offsetX - starting index for `x`
     51 * @param {Float32Array} y - output array
     52 * @param {integer} strideY - `y` stride length
     53 * @param {NonNegativeInteger} offsetY - starting index for `y`
     54 * @returns {Float32Array} output array
     55 *
     56 * @example
     57 * var Float32Array = require( '@stdlib/array/float32' );
     58 * var floor = require( '@stdlib/math/base/special/floor' );
     59 *
     60 * var x = new Float32Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
     61 * var y = new Float32Array( x.length );
     62 * var N = floor( x.length / 2 );
     63 *
     64 * var v = scusumpw( N, 0.0, x, 2, 1, y, 1, 0 );
     65 * // returns <Float32Array>[ 1.0, -1.0, 1.0, 5.0, 0.0, 0.0, 0.0, 0.0 ]
     66 */
     67 function scusumpw( N, sum, x, strideX, offsetX, y, strideY, offsetY ) {
     68 	var ix;
     69 	var iy;
     70 	var s;
     71 	var n;
     72 	var i;
     73 
     74 	if ( N <= 0 ) {
     75 		return y;
     76 	}
     77 	ix = offsetX;
     78 	iy = offsetY;
     79 	if ( N <= BLOCKSIZE ) {
     80 		s = 0.0;
     81 		for ( i = 0; i < N; i++ ) {
     82 			s = float64ToFloat32( s + x[ ix ] );
     83 			y[ iy ] = float64ToFloat32( sum + s );
     84 			ix += strideX;
     85 			iy += strideY;
     86 		}
     87 		return y;
     88 	}
     89 	n = floor( N/2 );
     90 	scusumpw( n, sum, x, strideX, ix, y, strideY, iy );
     91 	iy += (n-1) * strideY;
     92 	scusumpw( N-n, y[ iy ], x, strideX, ix+(n*strideX), y, strideY, iy+strideY ); // eslint-disable-line max-len
     93 	return y;
     94 }
     95 
     96 
     97 // EXPORTS //
     98 
     99 module.exports = scusumpw;