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* @license Apache-2.0
*
* Copyright (c) 2025 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 isnan = require( '@stdlib/math/base/assert/is-nan' );
var abs = require( '@stdlib/math/base/special/abs' );
// MAIN //
/**
* Computes the sum of strided array elements, ignoring `NaN` values and using an improved Kahan–Babuška algorithm.
*
* ## Method
*
* - This implementation uses an "improved Kahan–Babuška algorithm", as described by Neumaier (1974).
*
* ## References
*
* - Neumaier, Arnold. 1974. "Rounding Error Analysis of Some Methods for Summing Finite Sums." _Zeitschrift Für Angewandte Mathematik Und Mechanik_ 54 (1): 39–51. doi:[10.1002/zamm.19740540106](https://doi.org/10.1002/zamm.19740540106).
*
* @private
* @param {PositiveInteger} N - number of indexed elements
* @param {Object} x - input array object
* @param {Collection} x.data - input array data
* @param {Array<Function>} x.accessors - array element accessors
* @param {integer} strideX - stride length for `x`
* @param {NonNegativeInteger} offsetX - starting index for `x`
* @param {Object} out - output array object
* @param {Collection} out.data - output array data
* @param {Array<Function>} out.accessors - array element accessors
* @param {integer} strideOut - stride length for `out`
* @param {NonNegativeInteger} offsetOut - starting index for `out`
* @returns {Object} output array object
*
* @example
* var toAccessorArray = require( '@stdlib/array/base/to-accessor-array' );
* var arraylike2object = require( '@stdlib/array/base/arraylike2object' );
*
* var x = toAccessorArray( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0, NaN, NaN ] );
* var out = toAccessorArray( [ 0.0, 0 ] );
*
* var v = gnannsumkbn( 5, arraylike2object( x ), 2, 1, arraylike2object( out ), 1, 0 );
* // returns {...}
*/
function gnannsumkbn( N, x, strideX, offsetX, out, strideOut, offsetOut ) {
var obuf;
var xbuf;
var xget;
var oset;
var sum;
var ix;
var v;
var t;
var c;
var n;
var i;
// Cache reference to array data:
xbuf = x.data;
obuf = out.data;
// Cache reference to the element accessors:
xget = x.accessors[ 0 ];
oset = out.accessors[ 1 ];
sum = 0.0;
ix = offsetX;
if ( strideX === 0 ) {
v = xget( xbuf, ix );
if ( isnan( v ) ) {
oset( obuf, offsetOut, sum );
oset( obuf, offsetOut+strideOut, 0 );
return out;
}
oset( obuf, offsetOut, v * N );
oset( obuf, offsetOut+strideOut, N );
return out;
}
c = 0.0;
n = 0;
for ( i = 0; i < N; i++ ) {
v = xget( xbuf, ix );
if ( isnan( v ) === false ) {
t = sum + v;
if ( abs( sum ) >= abs( v ) ) {
c += (sum-t) + v;
} else {
c += (v-t) + sum;
}
sum = t;
n += 1;
}
ix += strideX;
}
oset( obuf, offsetOut, sum + c );
oset( obuf, offsetOut+strideOut, n );
return out;
}
// EXPORTS //
module.exports = gnannsumkbn;
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