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Add strided interface to add a constant and compute the sum using an improved Kahan-Babuska algorithm
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‎lib/node_modules/@stdlib/blas/ext/base/gapxsumkbn/README.md

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<!--
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@license Apache-2.0
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Copyright (c) 2020 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# gapxsumkbn
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> Add a constant to each strided array element and compute the sum using improved Kahan–Babuška algorithm.
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<section class="intro">
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</section>
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<!-- /.intro -->
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<section class="usage">
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## Usage
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```javascript
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var gapxsumkbn = require( '@stdlib/blas/ext/base/gapxsumkbn' );
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```
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#### gapxsumkbn( N, alpha, x, stride )
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Adds a constant to each strided array element and computes the sum using improved Kahan–Babuška algorithm.
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```javascript
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var x = [ 1.0, -2.0, 2.0 ];
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var N = x.length;
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var v = gapxsumkbn( N, 5.0, x, 1 );
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// returns 16.0
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```
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The function has the following parameters:
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- **N**: number of indexed elements.
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- **x**: input [`Array`][mdn-array] or [`typed array`][mdn-typed-array].
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- **stride**: index increment for `x`.
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The `N` and `stride` parameters determine which elements in `x` are accessed at runtime. For example, to access every other element in `x`,
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```javascript
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var floor = require( '@stdlib/math/base/special/floor' );
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var x = [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ];
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var N = floor( x.length / 2 );
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var v = gapxsumkbn( N, 5.0, x, 2 );
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// returns 25.0
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```
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Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
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<!-- eslint-disable stdlib/capitalized-comments -->
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var floor = require( '@stdlib/math/base/special/floor' );
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var x0 = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
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var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
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var N = floor( x0.length / 2 );
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var v = gapxsumkbn( N, 5.0, x1, 2 );
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// returns 25.0
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```
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#### gapxsumkbn.ndarray( N, alpha, x, stride, offset )
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Adds a constant to each strided array element and computes the sum using improved Kahan–Babuška algorithm and alternative indexing semantics.
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```javascript
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var x = [ 1.0, -2.0, 2.0 ];
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var N = x.length;
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var v = gapxsumkbn.ndarray( N, 5.0, x, 1, 0 );
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// returns 16.0
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```
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The function has the following additional parameters:
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- **offset**: starting index for `x`.
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While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying `buffer`, the `offset` parameter supports indexing semantics based on a starting index. For example, to access every other value in `x` starting from the second value
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```javascript
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var floor = require( '@stdlib/math/base/special/floor' );
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var x = [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ];
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var N = floor( x.length / 2 );
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var v = gapxsumkbn.ndarray( N, 5.0, x, 2, 1 );
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// returns 25.0
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```
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</section>
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<!-- /.usage -->
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<section class="notes">
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## Notes
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- If `N <= 0`, both functions return `0.0`.
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- Depending on the environment, the typed versions ([`dapxsum`][@stdlib/blas/ext/base/dapxsum], [`sapxsum`][@stdlib/blas/ext/base/sapxsum], etc.) are likely to be significantly more performant.
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</section>
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<!-- /.notes -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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```javascript
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var randu = require( '@stdlib/random/base/randu' );
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var round = require( '@stdlib/math/base/special/round' );
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var Float64Array = require( '@stdlib/array/float64' );
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var gapxsumkbn = require( '@stdlib/blas/ext/base/gapxsumkbn' );
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var x;
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var i;
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x = new Float64Array( 10 );
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for ( i = 0; i < x.length; i++ ) {
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x[ i ] = round( randu()*100.0 );
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}
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console.log( x );
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var v = gapxsumkbn( x.length, 5.0, x, 1 );
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console.log( v );
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```
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</section>
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<!-- /.examples -->
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* * *
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<section class="references">
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## References
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- 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][@neumaier:1974a].
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</section>
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<!-- /.references -->
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<section class="links">
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[mdn-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array
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[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
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[@stdlib/blas/ext/base/dapxsum]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/blas/ext/base/dapxsum
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[@stdlib/blas/ext/base/sapxsum]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/blas/ext/base/sapxsum
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[@neumaier:1974a]: https://doi.org/10.1002/zamm.19740540106
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</section>
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<!-- /.links -->

‎lib/node_modules/@stdlib/blas/ext/base/gapxsumkbn/benchmark/benchmark.js

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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2020 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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'use strict';
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// MODULES //
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var bench = require( '@stdlib/bench' );
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var randu = require( '@stdlib/random/base/randu' );
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var isnan = require( '@stdlib/math/base/assert/is-nan' );
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var pow = require( '@stdlib/math/base/special/pow' );
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var pkg = require( './../package.json' ).name;
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var gapxsumkbn = require( './../lib/gapxsumkbn.js' );
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// FUNCTIONS //
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/**
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* Creates a benchmark function.
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*
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* @private
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* @param {PositiveInteger} len - array length
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* @returns {Function} benchmark function
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*/
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function createBenchmark( len ) {
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var x;
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var i;
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x = [];
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for ( i = 0; i < len; i++ ) {
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x.push( ( randu()*20.0 ) - 10.0 );
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}
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return benchmark;
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function benchmark( b ) {
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var v;
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var i;
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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v = gapxsumkbn( x.length, 5.0, x, 1 );
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if ( isnan( v ) ) {
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b.fail( 'should not return NaN' );
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}
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}
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b.toc();
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if ( isnan( v ) ) {
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b.fail( 'should not return NaN' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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}
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}
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// MAIN //
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/**
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* Main execution sequence.
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*
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* @private
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*/
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function main() {
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var len;
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var min;
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var max;
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var f;
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var i;
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min = 1; // 10^min
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max = 6; // 10^max
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for ( i = min; i <= max; i++ ) {
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len = pow( 10, i );
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f = createBenchmark( len );
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bench( pkg+':len='+len, f );
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}
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}
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main();

‎lib/node_modules/@stdlib/blas/ext/base/gapxsumkbn/benchmark/benchmark.ndarray.js

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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2020 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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'use strict';
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// MODULES //
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var bench = require( '@stdlib/bench' );
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var randu = require( '@stdlib/random/base/randu' );
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var isnan = require( '@stdlib/math/base/assert/is-nan' );
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var pow = require( '@stdlib/math/base/special/pow' );
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var pkg = require( './../package.json' ).name;
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var gapxsumkbn = require( './../lib/ndarray.js' );
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// FUNCTIONS //
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/**
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* Creates a benchmark function.
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*
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* @private
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* @param {PositiveInteger} len - array length
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* @returns {Function} benchmark function
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*/
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function createBenchmark( len ) {
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var x;
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var i;
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x = [];
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for ( i = 0; i < len; i++ ) {
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x.push( ( randu()*20.0 ) - 10.0 );
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}
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return benchmark;
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function benchmark( b ) {
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var v;
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var i;
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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v = gapxsumkbn( x.length, 5.0, x, 1, 0 );
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if ( isnan( v ) ) {
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b.fail( 'should not return NaN' );
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}
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}
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b.toc();
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if ( isnan( v ) ) {
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b.fail( 'should not return NaN' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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}
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}
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// MAIN //
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/**
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* Main execution sequence.
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*
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* @private
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*/
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function main() {
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var len;
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var min;
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var max;
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var f;
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var i;
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min = 1; // 10^min
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max = 6; // 10^max
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for ( i = min; i <= max; i++ ) {
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len = pow( 10, i );
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f = createBenchmark( len );
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bench( pkg+':ndarray:len='+len, f );
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}
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}
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main();

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