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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 a second-order iterative Kahan–Babuška algorithm.
*
* ## Method
*
* - This implementation uses a second-order iterative Kahan–Babuška algorithm, as described by Klein (2005).
*
* ## References
*
* - Klein, Andreas. 2005. "A Generalized Kahan-Babuška-Summation-Algorithm." _Computing_ 76 (3): 279–93. doi:[10.1007/s00607-005-0139-x](https://doi.org/10.1007/s00607-005-0139-x).
*
* @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`
* @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 = gnansumkbn2( 4, arraylike2object( x ), 2, 1 );
* // returns 5.0
*/
function gnansumkbn2( N, x, strideX, offsetX ) {
var xbuf;
var xget;
var sum;
var ccs;
var cs;
var cc;
var ix;
var v;
var t;
var c;
var i;
// Cache reference to array data:
xbuf = x.data;
// Cache reference to the element accessors:
xget = x.accessors[ 0 ];
ix = offsetX;
if ( strideX === 0 ) {
if ( isnan( xget( xbuf, ix ) ) ) {
return 0.0;
}
return N * xget( xbuf, ix );
}
sum = 0.0;
ccs = 0.0; // second order correction term for lost low order bits
cs = 0.0; // first order correction term for lost low order bits
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;
t = cs + c;
if ( abs( cs ) >= abs( c ) ) {
cc = (cs-t) + c;
} else {
cc = (c-t) + cs;
}
cs = t;
ccs += cc;
}
ix += strideX;
}
return sum + cs + ccs;
}
// EXPORTS //
module.exports = gnansumkbn2;
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