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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 abs = require( '@stdlib/math/base/special/abs' );
// MAIN //
/**
* Computes the sum of strided array elements 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
* @param {NonNegativeInteger} offsetX - starting index
* @returns {number} sum
*
* @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 ] );
*
* var v = gsumkbn( 4, arraylike2object( x ), 2, 1 );
* // returns 5.0
*/
function gsumkbn( N, x, strideX, offsetX ) {
var xbuf;
var get;
var sum;
var flg;
var ix;
var v;
var t;
var c;
var i;
// Cache reference to array data:
xbuf = x.data;
// Cache a reference to the element accessor:
get = x.accessors[ 0 ];
ix = offsetX;
if ( strideX === 0 ) {
return N * get( xbuf, ix );
}
v = get( xbuf, ix );
ix += strideX;
sum = v;
// In order to preserve the sign of zero which can be lost during compensated summation below, find the first non-zero element...
if ( sum === 0.0 ) {
for ( i = 1; i < N; i++ ) {
v = get( xbuf, ix );
if ( v !== 0.0 ) {
flg = true;
break;
}
sum += v;
ix += strideX;
}
} else {
flg = true;
i = 1;
}
c = 0.0;
for ( ; i < N; i++ ) {
v = get( xbuf, ix );
t = sum + v;
if ( abs( sum ) >= abs( v ) ) {
c += (sum-t) + v;
} else {
c += (v-t) + sum;
}
sum = t;
ix += strideX;
}
return ( flg ) ? sum+c : sum;
}
// EXPORTS //
module.exports = gsumkbn;
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