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@stdlib/blas-ext-base-gcusumpw

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Calculate the cumulative sum of strided array elements using pairwise summation.

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/** * @license Apache-2.0 * * Copyright (c) 2020 The Stdlib Authors. * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ 'use strict'; // MODULES // var floor = require( '@stdlib/math-base-special-floor' ); // VARIABLES // // Blocksize for pairwise summation: var BLOCKSIZE = 128; // MAIN // /** * Computes the cumulative sum of strided array elements using pairwise summation. * * ## Method * * - This implementation uses pairwise summation, which accrues rounding error `O(log2 N)` instead of `O(N)`. The recursion depth is also `O(log2 N)`. * * ## References * * - 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). * * @param {PositiveInteger} N - number of indexed elements * @param {number} sum - initial sum * @param {NumericArray} x - input array * @param {integer} strideX - `x` stride length * @param {NonNegativeInteger} offsetX - starting index for `x` * @param {NumericArray} y - output array * @param {integer} strideY - `y` stride length * @param {NonNegativeInteger} offsetY - starting index for `y` * @returns {NumericArray} output array * * @example * var floor = require( '@stdlib/math-base-special-floor' ); * * var x = [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ]; * var y = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ]; * var N = floor( x.length / 2 ); * * gcusumpw( N, 0.0, x, 2, 1, y, 1, 0 ); * // y => [ 1.0, -1.0, 1.0, 5.0, 0.0, 0.0, 0.0, 0.0 ] */ function gcusumpw( N, sum, x, strideX, offsetX, y, strideY, offsetY ) { var ix; var iy; var s; var n; var i; if ( N <= 0 ) { return y; } ix = offsetX; iy = offsetY; if ( N <= BLOCKSIZE ) { s = 0.0; for ( i = 0; i < N; i++ ) { s += x[ ix ]; y[ iy ] = sum + s; ix += strideX; iy += strideY; } return y; } n = floor( N/2 ); gcusumpw( n, sum, x, strideX, ix, y, strideY, iy ); iy += (n-1) * strideY; gcusumpw( N-n, y[ iy ], x, strideX, ix+(n*strideX), y, strideY, iy+strideY ); // eslint-disable-line max-len return y; } // EXPORTS // module.exports = gcusumpw;