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* @license Apache-2.0
*
* Copyright (c) 2026 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 residual sum of squares of two double-precision floating-point strided arrays 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).
*
* @param {PositiveInteger} N - number of indexed elements
* @param {Float64Array} x - first input array
* @param {integer} strideX - stride length of `x`
* @param {NonNegativeInteger} offsetX - starting index of `x`
* @param {Float64Array} y - second input array
* @param {integer} strideY - stride length of `y`
* @param {NonNegativeInteger} offsetY - starting index of `y`
* @returns {number} residual sum of squares
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var x = new Float64Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] );
* var y = new Float64Array( [ 2.0, 1.0, 2.0, 1.0, -2.0, 2.0, 3.0, 4.0 ] );
*
* var z = drsskbn( x.length, x, 1, 0, y, 1, 0 );
* // returns 72.0
*/
function drsskbn( N, x, strideX, offsetX, y, strideY, offsetY ) {
var sum;
var ix;
var iy;
var r;
var v;
var t;
var c;
var i;
if ( N <= 0 ) {
return 0.0;
}
ix = offsetX;
iy = offsetY;
sum = 0.0;
c = 0.0;
for ( i = 0; i < N; i++ ) {
r = x[ ix ] - y[ iy ];
v = r * r;
t = sum + v;
if ( abs( sum ) >= abs( v ) ) {
c += ( sum - t ) + v;
} else {
c += ( v - t ) + sum;
}
sum = t;
ix += strideX;
iy += strideY;
}
return sum + c;
}
// EXPORTS //
module.exports = drsskbn;
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