npm package: @stdlib/blas-ext-base-dapxsumkbn
Description: Add a constant to each double-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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# dapxsumkbn

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> Add a scalar constant to each double-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-dapxsumkbn
```

</section>

<section class="usage">

## Usage

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

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

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

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

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

var v = dapxsumkbn( 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 [`Float64Array`][@stdlib/array/float64].
-   **strideX**: stride length for `x`.

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

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

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

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

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

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

var v = dapxsumkbn.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 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 = dapxsumkbn.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 dapxsumkbn = require( '@stdlib/blas-ext-base-dapxsumkbn' );

var x = discreteUniform( 10, -100, 100, {
    'dtype': 'float64'
});
console.log( x );

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

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

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

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

double v = stdlib_strided_dapxsumkbn( 4, 5.0, x, 1 );
// returns 30.0
```

The function accepts the following arguments:

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

```c
double stdlib_strided_dapxsumkbn( const CBLAS_INT N, const double alpha, const double *X, const CBLAS_INT strideX );
```

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

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

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

double v = stdlib_strided_dapxsumkbn_ndarray( 4, 5.0, x, 1, 0 );
// returns 30.0
```

The function accepts the following arguments:

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

```c
double stdlib_strided_dapxsumkbn_ndarray( const CBLAS_INT N, const double alpha, const double *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/dapxsumkbn.h"
#include <stdio.h>

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

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

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

    // Compute the sum:
    double v = stdlib_strided_dapxsumkbn( N, 5.0, x, strideX );

    // Print the result:
    printf( "Sum: %lf\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/dapxsum`][@stdlib/blas/ext/base/dapxsum]</span><span class="delimiter">: </span><span class="description">add a scalar constant to each double-precision floating-point strided array element and compute the sum.</span>
-   <span class="package-name">[`@stdlib/blas-ext/base/dsumkbn`][@stdlib/blas/ext/base/dsumkbn]</span><span class="delimiter">: </span><span class="description">calculate the sum of double-precision floating-point strided array elements 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/sapxsumkbn`][@stdlib/blas/ext/base/sapxsumkbn]</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 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

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---

## License

See [LICENSE][stdlib-license].


## Copyright

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

</section>

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[@neumaier:1974a]: https://doi.org/10.1002/zamm.19740540106

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

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

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

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

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

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