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* @license Apache-2.0
*
* Copyright (c) 2020 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 f32 = require( '@stdlib/number/float64/base/to-float32' );
var absf = require( '@stdlib/math/base/special/absf' );
// MAIN //
/**
* Computes the sum of single-precision 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 {Float32Array} x - input array
* @param {integer} strideX - stride length
* @param {NonNegativeInteger} offsetX - starting index
* @returns {number} sum
*
* @example
* var Float32Array = require( '@stdlib/array/float32' );
*
* var x = new Float32Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
*
* var v = ssumkbn( 4, x, 2, 1 );
* // returns 5.0
*/
function ssumkbn( N, x, strideX, offsetX ) {
var sum;
var flg;
var ix;
var v;
var t;
var c;
var i;
if ( N <= 0 ) {
return 0.0;
}
ix = offsetX;
if ( strideX === 0 ) {
return f32( N * x[ ix ] );
}
v = x[ 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 = x[ ix ];
if ( v !== 0.0 ) {
flg = true;
break;
}
sum = f32( sum + v );
ix += strideX;
}
} else {
flg = true;
i = 1;
}
c = 0.0;
for ( ; i < N; i++ ) {
v = x[ ix ];
t = f32( sum + v );
if ( absf( sum ) >= absf( v ) ) {
c = f32( c + f32( f32( sum-t ) + v ) );
} else {
c = f32( c + f32( f32( v-t ) + sum ) );
}
sum = t;
ix += strideX;
}
return ( flg ) ? f32( sum+c ) : sum;
}
// EXPORTS //
module.exports = ssumkbn;
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