npm package: @stdlib/blas-ext-base-sapxsumkbn
Description: Add a scalar constant to each single-precision floating-point strided array element and compute the sum using an improved Kahan–Babuška algorithm.
Author: The Stdlib Authors
Latest version: 0.3.1

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# sapxsumkbn

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> Add a scalar constant to each single-precision floating-point strided array element and compute the sum using an improved Kahan–Babuška algorithm.

<section class="intro">

</section>

<!-- /.intro -->

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

#### sapxsumkbn( N, alpha, x, strideX )

Adds a scalar constant to each single-precision floating-point strided array element and computes the sum using an improved Kahan–Babuška algorithm.

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

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

var v = sapxsumkbn( x.length, 5.0, x, 1 );
// returns 16.0
```

The function has the following parameters:

-   **N**: number of indexed elements.
-   **alpha**: scalar constant.
-   **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 access every other element in the strided array:

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

#### sapxsumkbn.ndarray( N, alpha, x, strideX, offsetX )

Adds a scalar constant to each single-precision floating-point strided array element and computes the sum using an improved Kahan–Babuška algorithm and alternative indexing semantics.

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

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

var v = sapxsumkbn.ndarray( x.length, 5.0, x, 1, 0 );
// returns 16.0
```

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 access 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 = sapxsumkbn.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-array-discrete-uniform' );
var sapxsumkbn = require( '@stdlib/blas-ext-base-sapxsumkbn' );

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

var v = sapxsumkbn( x.length, 5.0, 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/sapxsumkbn.h"
```

#### stdlib_strided_sapxsumkbn( N, alpha, \*X, strideX )

Adds a scalar constant to each single-precision floating-point strided array element and computes the sum using an improved Kahan–Babuška algorithm.

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

float v = stdlib_strided_sapxsumkbn( 4, 5.0f, x, 1 );
// returns 30.0f
```

The function accepts the following arguments:

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

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

#### stdlib_strided_sapxsumkbn_ndarray( N, alpha, \*X, strideX, offsetX )

Adds a scalar constant to each single-precision floating-point strided array element and computes the sum using an improved Kahan–Babuška algorithm and alternative indexing semantics.

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

float v = stdlib_strided_sapxsumkbn_ndarray( 4, 5.0f, x, 1, 0 );
// returns 30.0f
```

The function accepts the following arguments:

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

```c
float stdlib_strided_sapxsumkbn_ndarray( const CBLAS_INT N, const float alpha, 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/sapxsumkbn.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_sapxsumkbn( N, 5.0f, x, strideX );

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

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

<section class="references">

## References

-   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].

</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/dapxsumkbn`][@stdlib/blas/ext/base/dapxsumkbn]</span><span class="delimiter">: </span><span class="description">add a constant to each double-precision floating-point strided array element and compute the sum using an improved Kahan–Babuška algorithm.</span>
-   <span class="package-name">[`@stdlib/blas-ext/base/gapxsumkbn`][@stdlib/blas/ext/base/gapxsumkbn]</span><span class="delimiter">: </span><span class="description">add a scalar constant to each strided array element and compute the sum using an improved Kahan–Babuška algorithm.</span>
-   <span class="package-name">[`@stdlib/blas-ext/base/sapxsum`][@stdlib/blas/ext/base/sapxsum]</span><span class="delimiter">: </span><span class="description">add a constant to each single-precision floating-point strided array element and compute the sum.</span>
-   <span class="package-name">[`@stdlib/blas-ext/base/ssumkbn`][@stdlib/blas/ext/base/ssumkbn]</span><span class="delimiter">: </span><span class="description">calculate the sum of single-precision floating-point strided array elements using an improved Kahan–Babuška algorithm.</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>

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[umd]: https://github.com/umdjs/umd
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[@neumaier:1974a]: https://doi.org/10.1002/zamm.19740540106

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

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

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

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

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

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