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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 reinterpret = require( '@stdlib/strided/base/reinterpret-complex64' );
var Complex64 = require( '@stdlib/complex/float32/ctor' );
var absf = require( '@stdlib/math/base/special/absf' );
// MAIN //
/**
* Computes the sum of single-precision complex floating-point 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).
*
* @param {PositiveInteger} N - number of indexed elements
* @param {Complex64Array} x - input array
* @param {integer} strideX - stride length
* @param {NonNegativeInteger} offsetX - starting index
* @returns {Complex64} sum
*
* @example
* var Complex64Array = require( '@stdlib/array/complex64' );
*
* var x = new Complex64Array( [ 1.0, -2.0, 2.0, 3.0 ] );
*
* var v = csumkbn( x.length, x, 1, 0 );
* // returns <Complex64>[ 3.0, 1.0 ]
*/
function csumkbn( N, x, strideX, offsetX ) {
var rsum;
var isum;
var sx;
var ix;
var vr;
var vi;
var tr;
var ti;
var cr;
var ci;
var i;
var j;
var k;
if ( N <= 0 ) {
return new Complex64( 0.0, 0.0 );
}
x = reinterpret( x, 0 );
ix = offsetX * 2;
if ( strideX === 0 ) {
return new Complex64( N * x[ ix ], N * x[ ix+1 ] );
}
sx = strideX * 2;
vr = x[ ix ];
vi = x[ ix+1 ];
rsum = vr;
isum = vi;
// In order to preserve the sign of zero which can be lost during compensated summation below, find the first non-zero components...
if ( vr === 0.0 || vi === 0.0 ) {
j = -1;
k = -1;
for ( i = 0; i < N; i++ ) {
if ( j < 0 ) {
vr = x[ ix ];
if ( vr === 0.0 ) {
rsum += vr;
} else {
j = i;
}
}
if ( k < 0 ) {
vi = x[ ix+1 ];
if ( vi === 0.0 ) {
isum += vi;
} else {
k = i;
}
}
if ( j >= 0 && k >= 0 ) {
break;
}
ix += sx;
}
} else {
j = 0;
k = 0;
}
// Reset the pointer:
ix = ( offsetX * 2 ) + sx;
// Initialize correction terms:
cr = 0.0;
ci = 0.0;
for ( i = 1; i < N; i++ ) {
if ( i >= j ) {
vr = x[ ix ];
tr = rsum + vr;
if ( absf( rsum ) >= absf( vr ) ) {
cr += (rsum-tr) + vr;
} else {
cr += (vr-tr) + rsum;
}
rsum = tr;
}
if ( i >= k ) {
vi = x[ ix+1 ];
ti = isum + vi;
if ( absf( isum ) >= absf( vi ) ) {
ci += (isum-ti) + vi;
} else {
ci += (vi-ti) + isum;
}
isum = ti;
}
ix += sx;
}
if ( j >= 0 ) {
rsum += cr;
}
if ( k >= 0 ) {
isum += ci;
}
return new Complex64( rsum, isum );
}
// EXPORTS //
module.exports = csumkbn;
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