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https://github.com/stdlib-js/blas-ext-base-gapxsumpw

Adds a constant to each strided array element and computes the sum using pairwise summation.
https://github.com/stdlib-js/blas-ext-base-gapxsumpw

array blas extended javascript math mathematics node node-js nodejs pairwise pw statistics stats stdlib strided strided-array sum summation total typed

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Adds a constant to each strided array element and computes the sum using pairwise summation.

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README 

        



  

    About stdlib...

  

  
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# gapxsumpw



[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] 



> Add a constant to each strided array element and compute the sum using pairwise summation.



## Installation



```bash

npm install @stdlib/blas-ext-base-gapxsumpw

```



Alternatively,



-   To load the package in a website via a `script` tag without installation and bundlers, use the [ES Module][es-module] available on the [`esm`][esm-url] branch (see [README][esm-readme]).

-   If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions).

-   For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [`umd`][umd-url] branch (see [README][umd-readme]).



The [branches.md][branches-url] file summarizes the available branches and displays a diagram illustrating their relationships.



To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.



## Usage



```javascript

var gapxsumpw = require( '@stdlib/blas-ext-base-gapxsumpw' );

```



#### gapxsumpw( N, alpha, x, stride )



Adds a constant to each strided array element and computes the sum using pairwise summation.



```javascript

var x = [ 1.0, -2.0, 2.0 ];

var N = x.length;



var v = gapxsumpw( N, 5.0, x, 1 );

// returns 16.0

```



The function has the following parameters:



-   **N**: number of indexed elements.

-   **x**: input [`Array`][mdn-array] or [`typed array`][mdn-typed-array].

-   **stride**: index increment for `x`.



The `N` and `stride` parameters determine which elements in `x` are accessed at runtime. For example, to access every other element in `x`,



```javascript

var floor = require( '@stdlib/math-base-special-floor' );



var x = [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ];

var N = floor( x.length / 2 );



var v = gapxsumpw( N, 5.0, x, 2 );

// returns 25.0

```



Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.



```javascript

var Float64Array = require( '@stdlib/array-float64' );

var floor = require( '@stdlib/math-base-special-floor' );



var x0 = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );

var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element



var N = floor( x0.length / 2 );



var v = gapxsumpw( N, 5.0, x1, 2 );

// returns 25.0

```



#### gapxsumpw.ndarray( N, alpha, x, stride, offset )



Adds a constant to each strided array element and computes the sum using pairwise summation and alternative indexing semantics.



```javascript

var x = [ 1.0, -2.0, 2.0 ];

var N = x.length;



var v = gapxsumpw.ndarray( N, 5.0, x, 1, 0 );

// returns 16.0

```



The function has the following additional parameters:



-   **offset**: starting index for `x`.



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



```javascript

var floor = require( '@stdlib/math-base-special-floor' );



var x = [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ];

var N = floor( x.length / 2 );



var v = gapxsumpw.ndarray( N, 5.0, x, 2, 1 );

// returns 25.0

```



## Notes



-   If `N <= 0`, both functions return `0.0`.

-   In general, pairwise summation is more numerically stable than ordinary recursive summation (i.e., "simple" summation), with slightly worse performance. While not the most numerically stable summation technique (e.g., compensated summation techniques such as the Kahan–Babuška-Neumaier algorithm are generally more numerically stable), pairwise summation strikes a reasonable balance between numerical stability and performance. If either numerical stability or performance is more desirable for your use case, consider alternative summation techniques.

-   Depending on the environment, the typed versions ([`dapxsumpw`][@stdlib/blas/ext/base/dapxsumpw], [`sapxsumpw`][@stdlib/blas/ext/base/sapxsumpw], etc.) are likely to be significantly more performant.



## Examples



```javascript

var randu = require( '@stdlib/random-base-randu' );

var round = require( '@stdlib/math-base-special-round' );

var Float64Array = require( '@stdlib/array-float64' );

var gapxsumpw = require( '@stdlib/blas-ext-base-gapxsumpw' );



var x;

var i;



x = new Float64Array( 10 );

for ( i = 0; i < x.length; i++ ) {

    x[ i ] = round( randu()*100.0 );

}

console.log( x );



var v = gapxsumpw( x.length, 5.0, x, 1 );

console.log( v );

```



* * *



## References



-   Higham, Nicholas J. 1993. "The Accuracy of Floating Point Summation." _SIAM Journal on Scientific Computing_ 14 (4): 783–99. doi:[10.1137/0914050][@higham:1993a].



* * *



## See Also



-   [`@stdlib/blas-ext/base/dapxsumpw`][@stdlib/blas/ext/base/dapxsumpw]: adds a constant to each double-precision floating-point strided array element and computes the sum using pairwise summation.

-   [`@stdlib/blas-ext/base/gapxsum`][@stdlib/blas/ext/base/gapxsum]: adds a constant to each strided array element and computes the sum.

-   [`@stdlib/blas-ext/base/gsumpw`][@stdlib/blas/ext/base/gsumpw]: calculate the sum of strided array elements using pairwise summation.

-   [`@stdlib/blas-ext/base/sapxsumpw`][@stdlib/blas/ext/base/sapxsumpw]: adds a constant to each single-precision floating-point strided array element and computes the sum using pairwise summation.



* * *



## Notice



This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.



For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].



#### Community



[![Chat][chat-image]][chat-url]



---



## License



See [LICENSE][stdlib-license].



## Copyright



Copyright © 2016-2024. The Stdlib [Authors][stdlib-authors].



[npm-image]: http://img.shields.io/npm/v/@stdlib/blas-ext-base-gapxsumpw.svg

[npm-url]: https://npmjs.org/package/@stdlib/blas-ext-base-gapxsumpw



[test-image]: https://github.com/stdlib-js/blas-ext-base-gapxsumpw/actions/workflows/test.yml/badge.svg?branch=main

[test-url]: https://github.com/stdlib-js/blas-ext-base-gapxsumpw/actions/workflows/test.yml?query=branch:main



[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/blas-ext-base-gapxsumpw/main.svg

[coverage-url]: https://codecov.io/github/stdlib-js/blas-ext-base-gapxsumpw?branch=main



[chat-image]: https://img.shields.io/gitter/room/stdlib-js/stdlib.svg

[chat-url]: https://app.gitter.im/#/room/#stdlib-js_stdlib:gitter.im



[stdlib]: https://github.com/stdlib-js/stdlib



[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors



[umd]: https://github.com/umdjs/umd

[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules



[deno-url]: https://github.com/stdlib-js/blas-ext-base-gapxsumpw/tree/deno

[deno-readme]: https://github.com/stdlib-js/blas-ext-base-gapxsumpw/blob/deno/README.md

[umd-url]: https://github.com/stdlib-js/blas-ext-base-gapxsumpw/tree/umd

[umd-readme]: https://github.com/stdlib-js/blas-ext-base-gapxsumpw/blob/umd/README.md

[esm-url]: https://github.com/stdlib-js/blas-ext-base-gapxsumpw/tree/esm

[esm-readme]: https://github.com/stdlib-js/blas-ext-base-gapxsumpw/blob/esm/README.md

[branches-url]: https://github.com/stdlib-js/blas-ext-base-gapxsumpw/blob/main/branches.md



[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/blas-ext-base-gapxsumpw/main/LICENSE



[mdn-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array



[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray



[@higham:1993a]: https://doi.org/10.1137/0914050



[@stdlib/blas/ext/base/dapxsumpw]: https://github.com/stdlib-js/blas-ext-base-dapxsumpw



[@stdlib/blas/ext/base/gapxsum]: https://github.com/stdlib-js/blas-ext-base-gapxsum



[@stdlib/blas/ext/base/gsumpw]: https://github.com/stdlib-js/blas-ext-base-gsumpw



[@stdlib/blas/ext/base/sapxsumpw]: https://github.com/stdlib-js/blas-ext-base-sapxsumpw