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# dsumkbn

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

<section class="intro">

</section>

<!-- /.intro -->

<section class="usage">

## Usage

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

#### dsumkbn( N, x, strideX )

Computes the sum of double-precision floating-point strided array elements 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 = dsumkbn( x.length, x, 1 );
// returns 1.0
```

The function has the following parameters:

-   **N**: number of indexed elements.
-   **x**: input [`Float64Array`][@stdlib/array/float64].
-   **strideX**: stride length for `x`.

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 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 = dsumkbn( 4, x, 2 );
// returns 5.0
```

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

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

Computes the sum of double-precision floating-point strided array elements 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 = dsumkbn.ndarray( 3, x, 1, 0 );
// returns 1.0
```

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 calculate the sum of 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 = dsumkbn.ndarray( 4, x, 2, 1 );
// returns 5.0
```

</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 dsumkbn = require( '@stdlib/blas/ext/base/dsumkbn' );

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

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

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

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

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

double v = stdlib_strided_dsumkbn( 4, x, 1 );
// returns 10.0
```

The function accepts the following arguments:

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

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

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

Computes the sum of double-precision floating-point strided array elements 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_dsumkbn_ndarray( 4, x, 1, 0 );
// returns 10.0
```

The function accepts the following arguments:

-   **N**: `[in] CBLAS_INT` number of indexed elements.
-   **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_dsumkbn_ndarray( const CBLAS_INT N, 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/dsumkbn.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 elements:
    const int N = 4;

    // Specify the stride length:
    const int strideX = 2;

    // Compute the sum:
    double v = stdlib_strided_dsumkbn( N, 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/dnansumkbn`][@stdlib/blas/ext/base/dnansumkbn]</span><span class="delimiter">: </span><span class="description">calculate the sum of double-precision floating-point strided array elements, ignoring NaN values and using an improved Kahan–Babuška algorithm.</span>
-   <span class="package-name">[`@stdlib/blas/ext/base/dsum`][@stdlib/blas/ext/base/dsum]</span><span class="delimiter">: </span><span class="description">calculate the sum of double-precision floating-point strided array elements.</span>
-   <span class="package-name">[`@stdlib/blas/ext/base/dsumkbn2`][@stdlib/blas/ext/base/dsumkbn2]</span><span class="delimiter">: </span><span class="description">calculate the sum of double-precision floating-point strided array elements using a second-order iterative Kahan–Babuška algorithm.</span>
-   <span class="package-name">[`@stdlib/blas/ext/base/dsumors`][@stdlib/blas/ext/base/dsumors]</span><span class="delimiter">: </span><span class="description">calculate the sum of double-precision floating-point strided array elements using ordinary recursive summation.</span>
-   <span class="package-name">[`@stdlib/blas/ext/base/dsumpw`][@stdlib/blas/ext/base/dsumpw]</span><span class="delimiter">: </span><span class="description">calculate the sum of double-precision floating-point strided array elements using pairwise summation.</span>
-   <span class="package-name">[`@stdlib/blas/ext/base/gsumkbn`][@stdlib/blas/ext/base/gsumkbn]</span><span class="delimiter">: </span><span class="description">calculate the sum of strided array elements using an improved Kahan–Babuška algorithm.</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 -->

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

<section class="links">

[@stdlib/array/float64]: https://www.npmjs.com/package/@stdlib/array-float64

[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

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

[@stdlib/blas/ext/base/dnansumkbn]: https://github.com/stdlib-js/blas/tree/main/ext/base/dnansumkbn

[@stdlib/blas/ext/base/dsum]: https://github.com/stdlib-js/blas/tree/main/ext/base/dsum

[@stdlib/blas/ext/base/dsumkbn2]: https://github.com/stdlib-js/blas/tree/main/ext/base/dsumkbn2

[@stdlib/blas/ext/base/dsumors]: https://github.com/stdlib-js/blas/tree/main/ext/base/dsumors

[@stdlib/blas/ext/base/dsumpw]: https://github.com/stdlib-js/blas/tree/main/ext/base/dsumpw

[@stdlib/blas/ext/base/gsumkbn]: https://github.com/stdlib-js/blas/tree/main/ext/base/gsumkbn

[@stdlib/blas/ext/base/ssumkbn]: https://github.com/stdlib-js/blas/tree/main/ext/base/ssumkbn

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

</section>

<!-- /.links -->
