Press n or j to go to the next uncovered block, b, p or k for the previous block.
| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 | 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x | /**
* @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' );
var arraylike2object = require( '@stdlib/array/base/arraylike2object' );
var accessors = require( './accessors.js' );
// MAIN //
/**
* Computes the sum of 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 {NumericArray} x - input array
* @param {integer} strideX - stride length
* @param {NonNegativeInteger} offsetX - starting index
* @returns {number} sum
*
* @example
* var x = [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ];
*
* var v = gsumkbn( 4, x, 2, 1 );
* // returns 5.0
*/
function gsumkbn( N, x, strideX, offsetX ) {
var sum;
var flg;
var ix;
var o;
var v;
var t;
var c;
var i;
if ( N <= 0 ) {
return 0.0;
}
o = arraylike2object( x );
if ( o.accessorProtocol ) {
return accessors( N, o, strideX, offsetX );
}
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;
}
c = 0.0;
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;
ix += strideX;
}
return ( flg ) ? sum+c : sum;
}
// EXPORTS //
module.exports = gsumkbn;
|