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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 gsumpw = require( '@stdlib/blas/ext/base/gsumpw' ).ndarray;
// MAIN //
/**
* Adds a scalar constant to each strided array element and computes the sum 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} alpha - scalar constant
* @param {NumericArray} x - input array
* @param {integer} strideX - stride length
* @param {NonNegativeInteger} offsetX - starting index
* @returns {number} sum
*
* @example
* var x = [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ];
*
* var v = gapxsumpw( 4, 5.0, x, 2, 1 );
* // returns 25.0
*/
function gapxsumpw( N, alpha, x, strideX, offsetX ) {
if ( N <= 0 ) {
return 0.0;
}
return ( N * alpha ) + gsumpw( N, x, strideX, offsetX );
}
// EXPORTS //
module.exports = gapxsumpw;
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