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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 isnan = require( '@stdlib/math/base/assert/is-nan' );
var abs = require( '@stdlib/math/base/special/abs' );
// MAIN //
/**
* Computes the sum of double-precision floating-point strided array elements, ignoring `NaN` values and 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 - input array
* @param {integer} strideX - stride length for `x`
* @param {NonNegativeInteger} offsetX - starting index for `x`
* @param {Float64Array} out - output array
* @param {integer} strideOut - stride length for `out`
* @param {NonNegativeInteger} offsetOut - starting index for `out`
* @returns {Float64Array} output array
*
* @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, NaN, NaN ] );
* var out = new Float64Array( 2 );
*
* var v = dnannsumkbn( 5, x, 2, 1, out, 1, 0 );
* // returns <Float64Array>[ 5.0, 4 ]
*/
function dnannsumkbn( N, x, strideX, offsetX, out, strideOut, offsetOut ) {
var sum;
var flg;
var ix;
var io;
var v;
var t;
var c;
var n;
var i;
io = offsetOut;
if ( N <= 0 ) {
out[ io ] = 0.0;
out[ io+strideOut ] = 0;
return out;
}
ix = offsetX;
if ( strideX === 0 ) {
if ( isnan( x[ ix ] ) ) {
out[ io ] = 0.0;
out[ io+strideOut ] = 0;
return out;
}
out[ io ] = x[ ix ] * N;
out[ io+strideOut ] = N;
return out;
}
// Find the first non-NaN element...
for ( i = 0; i < N; i++ ) {
v = x[ ix ];
if ( isnan( v ) === false ) {
break;
}
ix += strideX;
}
if ( i === N ) {
out[ io ] = 0.0;
out[ io+strideOut ] = 0;
return out;
}
n = 1;
sum = v;
ix += strideX;
i += 1;
// 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 < N; i++ ) {
v = x[ ix ];
if ( isnan( v ) === false ) {
if ( v !== 0.0 ) {
flg = true;
break;
}
sum += v;
n += 1;
}
ix += strideX;
}
} else {
flg = true;
}
c = 0.0;
for ( ; i < N; i++ ) {
v = x[ ix ];
if ( isnan( v ) === false ) {
t = sum + v;
if ( abs( sum ) >= abs( v ) ) {
c += (sum-t) + v;
} else {
c += (v-t) + sum;
}
sum = t;
n += 1;
}
ix += strideX;
}
out[ io ] = ( flg ) ? sum+c : sum;
out[ io+strideOut ] = n;
return out;
}
// EXPORTS //
module.exports = dnannsumkbn;
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