# scusumkbn
> Calculate the cumulative sum of single-precision floating-point strided array elements using an improved Kahan–Babuška algorithm.
## 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 => [ 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 => [ 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**: index increment for `x`.
- **y**: output [`Float32Array`][@stdlib/array/float32].
- **strideY**: index increment 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 in `x`,
```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 => [ 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.
```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 => [ 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 => [ 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`, offset parameters support indexing semantics based on a starting indices. For example, to calculate the cumulative sum of every other value in `x` starting from the second value 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 => [ 0.0, 0.0, 0.0, 0.0, 5.0, 1.0, -1.0, 1.0 ]
```
## Notes
- If `N <= 0`, both functions return `y` unchanged.
## Examples
```javascript
var discreteUniform = require( '@stdlib/random/base/discrete-uniform' ).factory;
var filledarrayBy = require( '@stdlib/array/filled-by' );
var scusumkbn = require( '@stdlib/blas/ext/base/scusumkbn' );
var x = filledarrayBy( 10, 'float32', discreteUniform( 0, 100 ) );
console.log( x );
var y = filledarrayBy( x.length, 'float32', discreteUniform( 0, 10 ) );
console.log( y );
scusumkbn( x.length, 0.0, x, 1, y, -1 );
console.log( y );
```
* * *
## 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/dcusumkbn]: https://github.com/stdlib-js/blas/tree/main/ext/base/dcusumkbn
[@stdlib/blas/ext/base/gcusumkbn]: https://github.com/stdlib-js/blas/tree/main/ext/base/gcusumkbn
[@stdlib/blas/ext/base/scusum]: https://github.com/stdlib-js/blas/tree/main/ext/base/scusum
[@stdlib/blas/ext/base/scusumkbn2]: https://github.com/stdlib-js/blas/tree/main/ext/base/scusumkbn2