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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 double-precision floating-point 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 {Float64Array} x - input array
* @param {integer} strideX - stride length for `x`
* @param {NonNegativeInteger} offsetX - starting index for `x`
* @param {Float64Array} y - output array
* @param {integer} strideY - stride length for `y`
* @param {NonNegativeInteger} offsetY - starting index for `y`
* @returns {Float64Array} output array
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var x = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
* var y = new Float64Array( x.length );
*
* var v = dcusumpw( 4, 0.0, x, 2, 1, y, 1, 0 );
* // returns <Float64Array>[ 1.0, -1.0, 1.0, 5.0, 0.0, 0.0, 0.0, 0.0 ]
*/
function dcusumpw( 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 = x[ ix ];
y[ iy ] = sum + s;
ix += strideX;
iy += strideY;
for ( i = 1; i < N; i++ ) {
s += x[ ix ];
y[ iy ] = sum + s;
ix += strideX;
iy += strideY;
}
return y;
}
n = floor( N/2 );
dcusumpw( n, sum, x, strideX, ix, y, strideY, iy );
iy += (n-1) * strideY;
dcusumpw( N-n, y[ iy ], x, strideX, ix+(n*strideX), y, strideY, iy+strideY ); // eslint-disable-line max-len
return y;
}
// EXPORTS //
module.exports = dcusumpw;
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