npm package: @stdlib/blas-ext-base-scusumkbn
Description: Calculate the cumulative sum of single-precision floating-point strided array elements using an improved Kahan–Babuška algorithm.
Author: The Stdlib Authors
Latest version: 0.3.1

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# scusumkbn

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> Calculate the cumulative sum of single-precision floating-point strided array elements using an improved Kahan–Babuška algorithm.

<section class="intro">

</section>

<!-- /.intro -->

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

#### scusumkbn( N, sum, x, strideX, y, strideY )

Computes the cumulative sum of single-precision floating-point strided array elements using an improved Kahan–Babuška algorithm.

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

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

scusumkbn( x.length, 0.0, x, 1, y, 1 );
// y => <Float32Array>[ 1.0, -1.0, 1.0 ]

x = new Float32Array( [ 1.0, -2.0, 2.0 ] );
y = new Float32Array( x.length );

scusumkbn( x.length, 10.0, x, 1, y, 1 );
// y => <Float32Array>[ 11.0, 9.0, 11.0 ]
```

The function has the following parameters:

-   **N**: number of indexed elements.
-   **sum**: initial sum.
-   **x**: input [`Float32Array`][@stdlib/array/float32].
-   **strideX**: stride length for `x`.
-   **y**: output [`Float32Array`][@stdlib/array/float32].
-   **strideY**: stride length for `y`.

The `N` and stride parameters determine which elements in the strided arrays are accessed at runtime. For example, to compute the cumulative 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 y = new Float32Array( x.length );

var v = scusumkbn( 4, 0.0, x, 2, y, 1 );
// y => <Float32Array>[ 1.0, 3.0, 1.0, 5.0, 0.0, 0.0, 0.0, 0.0 ]
```

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' );

// Initial arrays...
var x0 = new Float32Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
var y0 = new Float32Array( x0.length );

// Create offset views...
var x1 = new Float32Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var y1 = new Float32Array( y0.buffer, y0.BYTES_PER_ELEMENT*3 ); // start at 4th element

scusumkbn( 4, 0.0, x1, -2, y1, 1 );
// y0 => <Float32Array>[ 0.0, 0.0, 0.0, 4.0, 6.0, 4.0, 5.0, 0.0 ]
```

#### scusumkbn.ndarray( N, sum, x, strideX, offsetX, y, strideY, offsetY )

Computes the cumulative sum of single-precision floating-point strided array elements 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 y = new Float32Array( 3 );

scusumkbn.ndarray( 3, 0.0, x, 1, 0, y, 1, 0 );
// y => <Float32Array>[ 1.0, -1.0, 1.0 ]
```

The function has the following additional parameters:

-   **offsetX**: starting index for `x`.
-   **offsetY**: starting index for `y`.

While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying buffer, the offset parameters support indexing semantics based on starting indices. For example, to calculate the cumulative sum of every other element starting from the second element and to store in the last `N` elements of `y` starting from the last 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 y = new Float32Array( x.length );

scusumkbn.ndarray( 4, 0.0, x, 2, 1, y, -1, y.length-1 );
// y => <Float32Array>[ 0.0, 0.0, 0.0, 0.0, 5.0, 1.0, -1.0, 1.0 ]
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   If `N <= 0`, both functions return `y` unchanged.

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

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

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

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

scusumkbn( x.length, 0.0, x, 1, y, -1 );
console.log( y );
```

</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/scusumkbn.h"
```

#### stdlib_strided_scusumkbn( N, sum, \*X, strideX, \*Y, strideY )

Computes the cumulative sum of single-precision floating-point strided array elements using an improved Kahan–Babuška algorithm.

```c
const float x[] = { 1.0f, 2.0f, 3.0f, 4.0f };
float y[] = { 0.0f, 0.0f, 0.0f, 0.0f };

stdlib_strided_scusumkbn( 4, 0.0f, x, 1, y, 1 );
```

The function accepts the following arguments:

-   **N**: `[in] CBLAS_INT` number of indexed elements.
-   **sum**: `[in] float` initial sum.
-   **X**: `[in] float*` input array.
-   **strideX**: `[in] CBLAS_INT` stride length for `X`.
-   **Y**: `[out] float*` output array.
-   **strideY**: `[in] CBLAS_INT` stride length for `Y`.

```c
void stdlib_strided_scusumkbn( const CBLAS_INT N, const float sum, const float *X, const CBLAS_INT strideX, float *Y, const CBLAS_INT strideY );
```

<!-- lint disable maximum-heading-length -->

#### stdlib_strided_scusumkbn_ndarray( N, sum, \*X, strideX, offsetX, \*Y, strideY, offsetY )

<!-- lint enable maximum-heading-length -->

Computes the cumulative sum of single-precision floating-point strided array elements using an improved Kahan–Babuška algorithm and alternative indexing semantics.

```c
const float x[] = { 1.0f, 2.0f, 3.0f, 4.0f };
float y[] = { 0.0f, 0.0f, 0.0f, 0.0f };

stdlib_strided_scusumkbn_ndarray( 4, 0.0f, x, 1, 0, y, 1, 0 );
```

The function accepts the following arguments:

-   **N**: `[in] CBLAS_INT` number of indexed elements.
-   **sum**: `[in] float` initial sum.
-   **X**: `[in] float*` input array.
-   **strideX**: `[in] CBLAS_INT` stride length for `X`.
-   **offsetX**: `[in] CBLAS_INT` starting index for `X`.
-   **Y**: `[out] float*` output array.
-   **strideY**: `[in] CBLAS_INT` stride length for `Y`.
-   **offsetY**: `[in] CBLAS_INT` starting index for `Y`.

```c
void stdlib_strided_scusumkbn_ndarray( const CBLAS_INT N, const float sum, const float *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, float *Y, const CBLAS_INT strideY, const CBLAS_INT offsetY );
```

</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/scusumkbn.h"
#include <stdio.h>

int main( void ) {
    // Create strided arrays:
    const float x[] = { 1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f, 8.0f };
    float y[] = { 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f };

    // Specify the number of elements:
    const int N = 4;

    // Specify stride lengths:
    const int strideX = 2;
    const int strideY = -2;

    // Compute the cumulative sum:
    stdlib_strided_scusumkbn( N, 0.0f, x, strideX, y, strideY );

    // Print the result:
    for ( int i = 0; i < 8; i++ ) {
        printf( "y[ %d ] = %f\n", i, y[ i ] );
    }
}
```

</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/dcusumkbn`][@stdlib/blas/ext/base/dcusumkbn]</span><span class="delimiter">: </span><span class="description">calculate the cumulative sum of double-precision floating-point strided array elements using an improved Kahan–Babuška algorithm.</span>
-   <span class="package-name">[`@stdlib/blas-ext/base/gcusumkbn`][@stdlib/blas/ext/base/gcusumkbn]</span><span class="delimiter">: </span><span class="description">calculate the cumulative sum of strided array elements using an improved Kahan–Babuška algorithm.</span>
-   <span class="package-name">[`@stdlib/blas-ext/base/scusum`][@stdlib/blas/ext/base/scusum]</span><span class="delimiter">: </span><span class="description">calculate the cumulative sum of single-precision floating-point strided array elements.</span>
-   <span class="package-name">[`@stdlib/blas-ext/base/scusumkbn2`][@stdlib/blas/ext/base/scusumkbn2]</span><span class="delimiter">: </span><span class="description">calculate the cumulative sum of single-precision floating-point strided array elements using a second-order iterative Kahan–Babuška algorithm.</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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[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/blas-ext-base-scusumkbn/main/LICENSE

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

[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray

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

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

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