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

Calculate the sum of double-precision floating-point strided array elements using pairwise summation.

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# dsumpw

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> Calculate the sum of double-precision floating-point strided array elements using pairwise summation.

<section class="intro">

</section>

<!-- /.intro -->

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

#### dsumpw( N, x, stride )

Computes the sum of double-precision floating-point strided array elements 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 = dsumpw( N, x, 1 );
// returns 1.0
```

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 compute the sum of 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 = dsumpw( 4, x, 2 );
// returns 5.0
```

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 = dsumpw( 4, x1, 2 );
// returns 5.0
```

#### dsumpw.ndarray( N, x, stride, offset )

Computes the sum of double-precision floating-point strided array elements 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 = dsumpw.ndarray( N, x, 1, 0 );
// returns 1.0
```

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 calculate the sum of 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 = dsumpw.ndarray( 4, x, 2, 1 );
// returns 5.0
```

</section>

<!-- /.usage -->

<section class="notes">

## 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.

</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 dsumpw = require( '@stdlib/blas-ext-base-dsumpw' );

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

var v = dsumpw( x.length, 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/dnansumpw`][@stdlib/blas/ext/base/dnansumpw]</span><span class="delimiter">: </span><span class="description">calculate the sum of double-precision floating-point strided array elements, ignoring NaN values and using pairwise summation.</span>
-   <span class="package-name">[`@stdlib/blas-ext/base/dsum`][@stdlib/blas/ext/base/dsum]</span><span class="delimiter">: </span><span class="description">calculate the sum of double-precision floating-point strided array elements.</span>
-   <span class="package-name">[`@stdlib/blas-ext/base/dsumkbn2`][@stdlib/blas/ext/base/dsumkbn2]</span><span class="delimiter">: </span><span class="description">calculate the sum of double-precision floating-point strided array elements using a second-order iterative Kahan–Babuška algorithm.</span>
-   <span class="package-name">[`@stdlib/blas-ext/base/dsumors`][@stdlib/blas/ext/base/dsumors]</span><span class="delimiter">: </span><span class="description">calculate the sum of double-precision floating-point strided array elements using ordinary recursive summation.</span>
-   <span class="package-name">[`@stdlib/blas-ext/base/gsumpw`][@stdlib/blas/ext/base/gsumpw]</span><span class="delimiter">: </span><span class="description">calculate the sum of strided array elements using pairwise summation.</span>
-   <span class="package-name">[`@stdlib/blas-ext/base/ssumpw`][@stdlib/blas/ext/base/ssumpw]</span><span class="delimiter">: </span><span class="description">calculate the sum of single-precision floating-point strided array elements using pairwise summation.</span>

</section>

<!-- /.related -->

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* * *

## 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].

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

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

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

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

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