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# dapxsumkbn2

> Add a constant to each double-precision floating-point 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 dapxsumkbn2 = require( '@stdlib/blas/ext/base/dapxsumkbn2' );
```

#### dapxsumkbn2( N, alpha, x, stride )

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

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

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

var v = dapxsumkbn2( N, 5.0, x, 1 );
// returns 16.0
```

The function has the following parameters:

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

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

```javascript
var Float64Array = require( '@stdlib/array/float64' );
var floor = require( '@stdlib/math/base/special/floor' );

var x = new Float64Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] );
var N = floor( x.length / 2 );

var v = dapxsumkbn2( N, 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 floor = require( '@stdlib/math/base/special/floor' );

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 N = floor( x0.length / 2 );

var v = dapxsumkbn2( N, 5.0, x1, 2 );
// returns 25.0
```

#### dapxsumkbn2.ndarray( N, alpha, x, stride, offset )

Adds a constant to each double-precision floating-point strided array element and computes the sum using a second-order iterative 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 N = x.length;

var v = dapxsumkbn2.ndarray( N, 5.0, x, 1, 0 );
// returns 16.0
```

The function has the following additional parameters:

-   **offset**: 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 value in `x` starting from the second value

```javascript
var Float64Array = require( '@stdlib/array/float64' );
var floor = require( '@stdlib/math/base/special/floor' );

var x = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
var N = floor( x.length / 2 );

var v = dapxsumkbn2.ndarray( N, 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 randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var Float64Array = require( '@stdlib/array/float64' );
var dapxsumkbn2 = require( '@stdlib/blas/ext/base/dapxsumkbn2' );

var x;
var i;

x = new Float64Array( 10 );
for ( i = 0; i < x.length; i++ ) {
    x[ i ] = round( randu()*100.0 );
}
console.log( x );

var v = dapxsumkbn2( 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 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

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

</section>

<!-- /.links -->