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# gapxsumkbn2

> Add a scalar constant to each strided array element and compute the sum using a second-order iterative Kahan–Babuška algorithm.

<section class="intro">

</section>

<!-- /.intro -->

<section class="usage">

## Usage

```javascript
var gapxsumkbn2 = require( '@stdlib/blas/ext/base/gapxsumkbn2' );
```

#### gapxsumkbn2( N, alpha, x, strideX )

Adds a scalar constant to each strided array element and computes the sum using a second-order iterative Kahan–Babuška algorithm.

```javascript
var x = [ 1.0, -2.0, 2.0 ];

var v = gapxsumkbn2( 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 [`Array`][mdn-array] or [`typed array`][mdn-typed-array].
-   **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:

```javascript
var x = [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ];

var v = gapxsumkbn2( 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 = gapxsumkbn2( 4, 5.0, x1, 2 );
// returns 25.0
```

#### gapxsumkbn2.ndarray( N, alpha, x, strideX, offsetX )

Adds a scalar constant to each strided array element and computes the sum using a second-order iterative Kahan–Babuška algorithm and alternative indexing semantics.

```javascript
var x = [ 1.0, -2.0, 2.0 ];

var v = gapxsumkbn2.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 x = [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ];

var v = gapxsumkbn2.ndarray( 4, 5.0, x, 2, 1 );
// returns 25.0
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   If `N <= 0`, both functions return `0.0`.
-   Both functions support array-like objects having getter and setter accessors for array element access (e.g., [`@stdlib/array/base/accessor`][@stdlib/array/base/accessor]).
-   Depending on the environment, the typed versions ([`dapxsumkbn2`][@stdlib/blas/ext/base/dapxsumkbn2], [`sapxsumkbn2`][@stdlib/blas/ext/base/sapxsumkbn2], etc.) are likely to be significantly more performant.

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

```javascript
var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
var gapxsumkbn2 = require( '@stdlib/blas/ext/base/gapxsumkbn2' );

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

var v = gapxsumkbn2( x.length, 5.0, x, 1 );
console.log( v );
```

</section>

<!-- /.examples -->

* * *

<section class="references">

## References

-   Klein, Andreas. 2005. "A Generalized Kahan-Babuška-Summation-Algorithm." _Computing_ 76 (3): 279–93. doi:[10.1007/s00607-005-0139-x][@klein:2005a].

</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/dapxsumkbn2`][@stdlib/blas/ext/base/dapxsumkbn2]</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 using a second-order iterative Kahan–Babuška algorithm.</span>
-   <span class="package-name">[`@stdlib/blas/ext/base/gapxsum`][@stdlib/blas/ext/base/gapxsum]</span><span class="delimiter">: </span><span class="description">add a scalar constant to each strided array element and compute the sum.</span>
-   <span class="package-name">[`@stdlib/blas/ext/base/gsumkbn2`][@stdlib/blas/ext/base/gsumkbn2]</span><span class="delimiter">: </span><span class="description">calculate the sum of strided array elements using a second-order iterative Kahan–Babuška algorithm.</span>
-   <span class="package-name">[`@stdlib/blas/ext/base/sapxsumkbn2`][@stdlib/blas/ext/base/sapxsumkbn2]</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 a second-order iterative Kahan–Babuška algorithm.</span>

</section>

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

<section class="links">

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

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

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

[@klein:2005a]: https://doi.org/10.1007/s00607-005-0139-x

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

[@stdlib/blas/ext/base/dapxsumkbn2]: https://github.com/stdlib-js/blas/tree/main/ext/base/dapxsumkbn2

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

[@stdlib/blas/ext/base/gsumkbn2]: https://github.com/stdlib-js/blas/tree/main/ext/base/gsumkbn2

[@stdlib/blas/ext/base/sapxsumkbn2]: https://github.com/stdlib-js/blas/tree/main/ext/base/sapxsumkbn2

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

</section>

<!-- /.links -->
