npm package: @stdlib/blas-ext-base-sdsapxsumpw
Description: Add a constant to each single-precision floating-point strided array element and compute the sum using pairwise summation with extended accumulation.
Author: The Stdlib Authors
Latest version: 0.3.1

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# sdsapxsumpw

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> Add a scalar constant to each single-precision floating-point strided array element and compute the sum using pairwise summation with extended accumulation.

<section class="intro">

</section>

<!-- /.intro -->

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

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

Adds a scalar constant to each single-precision floating-point strided array element and computes the sum using pairwise summation with extended accumulation.

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

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

var v = sdsapxsumpw( 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 compute the sum 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 = sdsapxsumpw( 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 = sdsapxsumpw( 4, 5.0, x1, 2 );
// returns 25.0
```

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

Adds a scalar constant to each single-precision floating-point strided array element and computes the sum using pairwise summation with extended accumulation and alternative indexing semantics.

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

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

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

The function has the following additional parameters:

-   **offsetX**: 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 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 = sdsapxsumpw.ndarray( 4, 5.0, x, 2, 1 );
// returns 25.0
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   If `N <= 0`, both functions return `0.0`.
-   Accumulated intermediate values are stored as double-precision floating-point numbers.

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

```javascript
var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var sdsapxsumpw = require( '@stdlib/blas-ext-base-sdsapxsumpw' );

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

var v = sdsapxsumpw( 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/sdsapxsumpw.h"
```

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

Adds a scalar constant to each single-precision floating-point strided array element and computes the sum using pairwise summation with extended accumulation.

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

float v = stdlib_strided_sdsapxsumpw( 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_sdsapxsumpw( const CBLAS_INT N, const float alpha, const float *X, const CBLAS_INT strideX );
```

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

Adds a scalar constant to each single-precision floating-point strided array element and computes the sum using pairwise summation with extended accumulation and alternative indexing semantics.

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

float v = stdlib_strided_sdsapxsumpw_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_sdsapxsumpw_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/sdsapxsumpw.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_sdsapxsumpw( N, 5.0f, x, strideX );

    // Print the result:
    printf( "Sum: %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-ext/base/dsapxsumpw`][@stdlib/blas/ext/base/dsapxsumpw]</span><span class="delimiter">: </span><span class="description">add a constant to each single-precision floating-point strided array element and compute the sum using pairwise summation with extended accumulation and returning an extended precision result.</span>
-   <span class="package-name">[`@stdlib/blas-ext/base/sapxsumpw`][@stdlib/blas/ext/base/sapxsumpw]</span><span class="delimiter">: </span><span class="description">add a scalar constant to each single-precision floating-point strided array element and compute the sum using pairwise summation.</span>
-   <span class="package-name">[`@stdlib/blas-ext/base/sdsapxsum`][@stdlib/blas/ext/base/sdsapxsum]</span><span class="delimiter">: </span><span class="description">add a scalar constant to each single-precision floating-point strided array element and compute the sum using extended accumulation.</span>
-   <span class="package-name">[`@stdlib/blas-ext/base/sdssumpw`][@stdlib/blas/ext/base/sdssumpw]</span><span class="delimiter">: </span><span class="description">calculate the sum of single-precision floating-point strided array elements using pairwise summation with extended accumulation.</span>

</section>

<!-- /.related -->

<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->


<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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