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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 abs = require( '@stdlib/math/base/special/abs' );
// MAIN //
/**
* Computes the sum of double-precision floating-point strided array elements 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).
*
* @param {PositiveInteger} N - number of indexed elements
* @param {Float64Array} x - input array
* @param {integer} strideX - stride length
* @param {NonNegativeInteger} offsetX - starting index
* @returns {number} sum
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var x = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
*
* var v = dsumkbn2( 4, x, 2, 1 );
* // returns 5.0
*/
function dsumkbn2( N, x, strideX, offsetX ) {
var sum;
var ccs;
var flg;
var ix;
var cs;
var cc;
var v;
var t;
var c;
var i;
if ( N <= 0 ) {
return 0.0;
}
ix = offsetX;
if ( strideX === 0 ) {
return 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 += v;
ix += strideX;
}
} else {
flg = true;
i = 1;
}
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 < N; i++ ) {
v = x[ ix ];
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 ( flg ) ? sum+cs+ccs : sum;
}
// EXPORTS //
module.exports = dsumkbn2;
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