# gnannsumkbn
> Calculate the sum of strided array elements, ignoring `NaN` values and using an improved Kahan–Babuška algorithm.
## Usage
```javascript
var gnannsumkbn = require( '@stdlib/blas/ext/base/gnannsumkbn' );
```
#### gnannsumkbn( N, x, strideX, out, strideOut )
Computes the sum of strided array elements, ignoring `NaN` values and using an improved Kahan–Babuška algorithm.
```javascript
var x = [ 1.0, -2.0, NaN, 2.0 ];
var out = [ 0.0, 0 ];
var v = gnannsumkbn( x.length, x, 1, out, 1 );
// returns [ 1.0, 3 ]
```
The function has the following parameters:
- **N**: number of indexed elements.
- **x**: input [`Array`][mdn-array] or [`typed array`][mdn-typed-array].
- **strideX**: index increment for `x`.
- **out**: output [`Array`][mdn-array] or [`typed array`][mdn-typed-array] whose first element is the sum and whose second element is the number of non-NaN elements.
- **strideOut**: index increment for `out`.
The `N` and `stride` parameters determine which elements are accessed at runtime. For example, to compute the sum of every other element in `x`,
```javascript
var floor = require( '@stdlib/math/base/special/floor' );
var x = [ 1.0, 2.0, NaN, -7.0, NaN, 3.0, 4.0, 2.0 ];
var out = [ 0.0, 0 ];
var N = floor( x.length / 2 );
var v = gnannsumkbn( N, x, 2, out, 1 );
// returns [ 5.0, 2 ]
```
Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
```javascript
var Float64Array = require( '@stdlib/array/float64' );
var floor = require( '@stdlib/math/base/special/floor' );
var x0 = new Float64Array( [ 2.0, 1.0, NaN, -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 out0 = new Float64Array( 4 );
var out1 = new Float64Array( out0.buffer, out0.BYTES_PER_ELEMENT*2 ); // start at 3rd element
var N = floor( x0.length / 2 );
var v = gnannsumkbn( N, x1, 2, out1, 1 );
// returns [ 5.0, 4 ]
```
#### gnannsumkbn.ndarray( N, x, strideX, offsetX, out, strideOut, offsetOut )
Computes the sum of strided array elements, ignoring `NaN` values and using an improved Kahan–Babuška algorithm and alternative indexing semantics.
```javascript
var x = [ 1.0, -2.0, NaN, 2.0 ];
var out = [ 0.0, 0 ];
var v = gnannsumkbn.ndarray( x.length, x, 1, 0, out, 1, 0 );
// returns [ 1.0, 3 ]
```
The function has the following additional parameters:
- **offsetX**: starting index for `x`.
- **offsetOut**: starting index for `out`.
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 value in `x` starting from the second value
```javascript
var floor = require( '@stdlib/math/base/special/floor' );
var x = [ 2.0, 1.0, NaN, -2.0, -2.0, 2.0, 3.0, 4.0 ];
var out = [ 0.0, 0.0, 0.0, 0 ];
var N = floor( x.length / 2 );
var v = gnannsumkbn.ndarray( N, x, 2, 1, out, 2, 1 );
// returns [ 0.0, 5.0, 0.0, 4 ]
```
## Notes
- If `N <= 0`, both functions return a sum equal to `0.0`.
## Examples
```javascript
var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var Float64Array = require( '@stdlib/array/float64' );
var gnannsumkbn = require( '@stdlib/blas/ext/base/gnannsumkbn' );
var x;
var i;
x = new Float64Array( 10 );
for ( i = 0; i < x.length; i++ ) {
if ( randu() < 0.2 ) {
x[ i ] = NaN;
} else {
x[ i ] = round( randu()*100.0 );
}
}
console.log( x );
var out = new Float64Array( 2 );
gnannsumkbn( x.length, x, 1, out, 1 );
console.log( out );
```
* * *
## 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].
[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
[@neumaier:1974a]: https://doi.org/10.1002/zamm.19740540106