# sapxsumkbn
> Add a constant to each single-precision floating-point strided array element and compute the sum using an improved Kahan–Babuška algorithm.
## Usage
```javascript
var sapxsumkbn = require( '@stdlib/blas/ext/base/sapxsumkbn' );
```
#### sapxsumkbn( N, alpha, x, stride )
Adds a constant to each single-precision floating-point strided array element and computes the sum using an improved Kahan–Babuška algorithm.
```javascript
var Float32Array = require( '@stdlib/array/float32' );
var x = new Float32Array( [ 1.0, -2.0, 2.0 ] );
var v = sapxsumkbn( 3, 5.0, x, 1 );
// returns 16.0
```
The function has the following parameters:
- **N**: number of indexed elements.
- **alpha**: scalar constant.
- **x**: input [`Float32Array`][@stdlib/array/float32].
- **stride**: index increment for `x`.
The `N` and `stride` parameters determine which elements in the strided array are accessed at runtime. For example, to access every other element in the strided array,
```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 v = sapxsumkbn( 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.
```javascript
var Float32Array = require( '@stdlib/array/float32' );
var x0 = new Float32Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
var x1 = new Float32Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var v = sapxsumkbn( 4, 5.0, x1, 2 );
// returns 25.0
```
#### sapxsumkbn.ndarray( N, alpha, x, stride, offset )
Adds a constant to each single-precision floating-point strided array element and computes the sum 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 v = sapxsumkbn.ndarray( 3, 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 the strided array starting from the second value
```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 v = sapxsumkbn.ndarray( 4, 5.0, x, 2, 1 );
// returns 25.0
```
## Notes
- If `N <= 0`, both functions return `0.0`.
## Examples
```javascript
var discreteUniform = require( '@stdlib/random/base/discrete-uniform' ).factory;
var filledarrayBy = require( '@stdlib/array/filled-by' );
var sapxsumkbn = require( '@stdlib/blas/ext/base/sapxsumkbn' );
var x = filledarrayBy( 10, 'float32', discreteUniform( 0, 100 ) );
console.log( x );
var v = sapxsumkbn( x.length, 5.0, x, 1 );
console.log( v );
```
* * *
## 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].
[@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
[@stdlib/blas/ext/base/dapxsumkbn]: https://github.com/stdlib-js/blas/tree/main/ext/base/dapxsumkbn
[@stdlib/blas/ext/base/gapxsumkbn]: https://github.com/stdlib-js/blas/tree/main/ext/base/gapxsumkbn
[@stdlib/blas/ext/base/sapxsum]: https://github.com/stdlib-js/blas/tree/main/ext/base/sapxsum
[@stdlib/blas/ext/base/ssumkbn]: https://github.com/stdlib-js/blas/tree/main/ext/base/ssumkbn