npm package: @stdlib/blas-ext-base-sasumpw
Description: Calculate the sum of absolute values (L1 norm) of single-precision floating-point strided array elements using pairwise summation.
Author: The Stdlib Authors
Latest version: 0.3.1

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# sasumpw

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> Calculate the sum of absolute values ([_L1_ norm][l1norm]) of single-precision floating-point strided array elements using pairwise summation.

<section class="intro">

The [_L1_ norm][l1norm] is defined as

<!-- <equation class="equation" label="eq:l1norm" align="center" raw="\|\mathbf{x}\|_1 = \sum_{i=0}^{n-1} \vert x_i \vert" alt="L1 norm definition."> -->

<div class="equation" align="center" data-raw-text="\|\mathbf{x}\|_1 = \sum_{i=0}^{n-1} \vert x_i \vert" data-equation="eq:l1norm">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@a230d54328acdaee1e2e456106e5b5c1cfd62b18/lib/node_modules/@stdlib/blas/ext/base/sasumpw/docs/img/equation_l1norm.svg" alt="L1 norm definition.">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

#### sasumpw( N, x, strideX )

Computes the sum of absolute values ([_L1_ norm][l1norm]) of single-precision floating-point strided array elements using pairwise summation.

```javascript
var Float32Array = require( '@stdlib/array-float32' );

var x = new Float32Array( [ 1.0, -2.0, 2.0 ] );

var v = sasumpw( x.length, x, 1 );
// returns 5.0
```

The function has the following parameters:

-   **N**: number of indexed elements.
-   **x**: input [`Float32Array`][@stdlib/array/float32].
-   **strideX**: stride length.

The `N` and stride parameters determine which elements in the strided array are accessed at runtime. For example, to compute the sum of absolute values of every other element:

```javascript
var Float32Array = require( '@stdlib/array-float32' );

var x = new Float32Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] );

var v = sasumpw( 4, x, 2 );
// returns 9.0
```

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 Float32Array = require( '@stdlib/array-float32' );

var x0 = new Float32Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
var x1 = new Float32Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

var v = sasumpw( 4, x1, 2 );
// returns 9.0
```

#### sasumpw.ndarray( N, x, strideX, offsetX )

Computes the sum of absolute values ([_L1_ norm][l1norm]) of single-precision floating-point strided array elements using pairwise summation and alternative indexing semantics.

```javascript
var Float32Array = require( '@stdlib/array-float32' );

var x = new Float32Array( [ 1.0, -2.0, 2.0 ] );

var v = sasumpw.ndarray( x.length, x, 1, 0 );
// returns 5.0
```

The function has the following additional parameters:

-   **offsetX**: starting index.

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 absolute values of every other element starting from the second element:

```javascript
var Float32Array = require( '@stdlib/array-float32' );

var x = new Float32Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );

var v = sasumpw.ndarray( 4, x, 2, 1 );
// returns 9.0
```

</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-array-discrete-uniform' );
var sasumpw = require( '@stdlib/blas-ext-base-sasumpw' );

var x = discreteUniform( 10, -100, 100, {
    'dtype': 'float32'
});
console.log( x );

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

</section>

<!-- /.examples -->

<!-- C interface documentation. -->

* * *

<section class="c">

## C APIs

<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->

<section class="intro">

</section>

<!-- /.intro -->

<!-- C usage documentation. -->

<section class="usage">

### Usage

```c
#include "stdlib/blas/ext/base/sasumpw.h"
```

#### stdlib_strided_sasumpw( N, \*X, strideX )

Computes the sum of absolute values ([_L1_ norm][l1norm]) of single-precision floating-point strided array elements using pairwise summation.

```c
const float x[] = { 1.0f, 2.0f, 3.0f, 4.0f };

float v = stdlib_strided_sasumpw( 4, x, 1 );
// returns 10.0f
```

The function accepts the following arguments:

-   **N**: `[in] CBLAS_INT` number of indexed elements.
-   **X**: `[in] float*` input array.
-   **strideX**: `[in] CBLAS_INT` stride length.

```c
float stdlib_strided_sasumpw( const CBLAS_INT N, const float *X, const CBLAS_INT strideX );
```

#### stdlib_strided_sasumpw_ndarray( N, \*X, strideX, offsetX )

Computes the sum of absolute values ([_L1_ norm][l1norm]) of single-precision floating-point strided array elements using pairwise summation and alternative indexing semantics.

```c
const float x[] = { 1.0f, 2.0f, 3.0f, 4.0f };

float v = stdlib_strided_sasumpw_ndarray( 4, x, 1, 0 );
// returns 10.0f
```

The function accepts the following arguments:

-   **N**: `[in] CBLAS_INT` number of indexed elements.
-   **X**: `[in] float*` input array.
-   **strideX**: `[in] CBLAS_INT` stride length.
-   **offsetX**: `[in] CBLAS_INT` starting index.

```c
float stdlib_strided_sasumpw_ndarray( const CBLAS_INT N, const float *X, const CBLAS_INT strideX, const CBLAS_INT offsetX );
```

</section>

<!-- /.usage -->

<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="notes">

</section>

<!-- /.notes -->

<!-- C API usage examples. -->

<section class="examples">

### Examples

```c
#include "stdlib/blas/ext/base/sasumpw.h"
#include <stdio.h>

int main( void ) {
    // Create a strided array:
    const float x[] = { 1.0f, -2.0f, 3.0f, -4.0f, 5.0f, -6.0f, 7.0f, -8.0f };

    // Specify the number of indexed elements:
    const int N = 8;

    // Specify a stride:
    const int strideX = 1;

    // Compute the sum:
    float v = stdlib_strided_sasumpw( N, x, strideX );

    // Print the result:
    printf( "sumabs: %f\n", v );
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

<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-base/sasum`][@stdlib/blas/base/sasum]</span><span class="delimiter">: </span><span class="description">compute the sum of absolute values (L1 norm).</span>
-   <span class="package-name">[`@stdlib/blas-ext/base/dasumpw`][@stdlib/blas/ext/base/dasumpw]</span><span class="delimiter">: </span><span class="description">calculate the sum of absolute values (L1 norm) of double-precision floating-point strided array elements using pairwise summation.</span>
-   <span class="package-name">[`@stdlib/blas-ext/base/gasumpw`][@stdlib/blas/ext/base/gasumpw]</span><span class="delimiter">: </span><span class="description">calculate the sum of absolute values (L1 norm) 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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<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

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

---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

</section>

<!-- /.stdlib -->

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

[@stdlib/array/float32]: https://www.npmjs.com/package/@stdlib/array-float32

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[l1norm]: https://en.wikipedia.org/wiki/Norm_%28mathematics%29

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

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

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