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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 sumpw = require( './sumpw.js' );
// MAIN //
/**
* Computes the sum of double-precision floating-point strided array elements, ignoring `NaN` values and 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 {Float64Array} x - input array
* @param {integer} strideX - stride length for `x`
* @param {NonNegativeInteger} offsetX - starting index for `x`
* @param {Float64Array} out - output array
* @param {integer} strideOut - stride length for `out`
* @param {NonNegativeInteger} offsetOut - starting index for `out`
* @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, NaN, NaN ] );
* var out = new Float64Array( 2 );
*
* var v = dnannsumpw( 5, x, 2, 1, out, 1, 0 );
* // returns <Float64Array>[ 5.0, 4 ]
*/
function dnannsumpw( N, x, strideX, offsetX, out, strideOut, offsetOut ) {
var io = offsetOut;
// Initialize output values:
out[ io ] = -0.0; // note: initialize to negative zero to allow preservation of negative zero for the edge case of an input array containing only negative zeros
out[ io+strideOut ] = 0;
// Perform pairwise summation:
sumpw( N, x, strideX, offsetX, out, strideOut, io );
// If all elements were `NaN`, the default sum is positive zero...
if ( out[ io+strideOut ] === 0 ) {
out[ io ] = 0.0;
}
return out;
}
// EXPORTS //
module.exports = dnannsumpw;
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