@stdlib/blas-ext-base-dapxsumpw/README.md

Adds a constant to each double-precision floating-point strided array element and computes the sum using pairwise summation.

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# dapxsumpw

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

> Add a constant to each double-precision floating-point strided array element and compute the sum using pairwise summation.

<section class="intro">

</section>

<!-- /.intro -->

<section class="installation">

## Installation

```bash
npm install @stdlib/blas-ext-base-dapxsumpw
```

</section>

<section class="usage">

## Usage

```javascript
var dapxsumpw = require( '@stdlib/blas-ext-base-dapxsumpw' );
```

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

Adds a constant to each double-precision floating-point strided array element and computes the sum using pairwise summation.

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

var x = new Float64Array( [ 1.0, -2.0, 2.0 ] );
var N = x.length;

var v = dapxsumpw( N, 5.0, x, 1 );
// returns 16.0
```

The function has the following parameters:

-   **N**: number of indexed elements.
-   **x**: input [`Float64Array`][@stdlib/array/float64].
-   **stride**: index increment for `x`.

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

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

var x = new Float64Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] );

var v = dapxsumpw( 4, 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.

<!-- eslint-disable stdlib/capitalized-comments -->

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

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 v = dapxsumpw( 4, 5.0, x1, 2 );
// returns 25.0
```

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

Adds a constant to each double-precision floating-point strided array element and computes the sum using pairwise summation and alternative indexing semantics.

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

var x = new Float64Array( [ 1.0, -2.0, 2.0 ] );
var N = x.length;

var v = dapxsumpw.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 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 = dapxsumpw.ndarray( 4, 5.0, x, 2, 1 );
// returns 25.0
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

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

</section>

<!-- /.notes -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var discreteUniform = require( '@stdlib/random-base-discrete-uniform' ).factory;
var filledarrayBy = require( '@stdlib/array-filled-by' );
var dapxsumpw = require( '@stdlib/blas-ext-base-dapxsumpw' );

var x = filledarrayBy( 10, 'float64', discreteUniform( 0, 100 ) );
console.log( x );

var v = dapxsumpw( x.length, 5.0, x, 1 );
console.log( v );
```

</section>

<!-- /.examples -->

* * *

<section class="references">

## 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].

</section>

<!-- /.references -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

* * *

## See Also

-   <span class="package-name">[`@stdlib/blas-ext/base/dapxsum`][@stdlib/blas/ext/base/dapxsum]</span><span class="delimiter">: </span><span class="description">adds a constant to each double-precision floating-point strided array element and computes the sum.</span>
-   <span class="package-name">[`@stdlib/blas-ext/base/dsumpw`][@stdlib/blas/ext/base/dsumpw]</span><span class="delimiter">: </span><span class="description">calculate the sum of double-precision floating-point strided array elements using pairwise summation.</span>
-   <span class="package-name">[`@stdlib/blas-ext/base/gapxsumpw`][@stdlib/blas/ext/base/gapxsumpw]</span><span class="delimiter">: </span><span class="description">adds a constant to each strided array element and computes the sum using pairwise summation.</span>
-   <span class="package-name">[`@stdlib/blas-ext/base/sapxsumpw`][@stdlib/blas/ext/base/sapxsumpw]</span><span class="delimiter">: </span><span class="description">adds a constant to each single-precision floating-point strided array element and computes the sum using pairwise summation.</span>

</section>

<!-- /.related -->

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<section class="main-repo" >

* * *

## 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

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---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2024. The Stdlib [Authors][stdlib-authors].

</section>

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[@stdlib/array/float64]: https://www.npmjs.com/package/@stdlib/array-float64

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

<!-- <related-links> -->

[@stdlib/blas/ext/base/dapxsum]: https://www.npmjs.com/package/@stdlib/blas-ext-base-dapxsum

[@stdlib/blas/ext/base/dsumpw]: https://www.npmjs.com/package/@stdlib/blas-ext-base-dsumpw

[@stdlib/blas/ext/base/gapxsumpw]: https://www.npmjs.com/package/@stdlib/blas-ext-base-gapxsumpw

[@stdlib/blas/ext/base/sapxsumpw]: https://www.npmjs.com/package/@stdlib/blas-ext-base-sapxsumpw

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