# dsapxsumpw
> Add a constant to each single-precision floating-point strided array element and compute the sum using pairwise summation with extended accumulation and returning an extended precision result.
## Usage
```javascript
var dsapxsumpw = require( '@stdlib/blas/ext/base/dsapxsumpw' );
```
#### dsapxsumpw( N, alpha, x, stride )
Adds a constant to each single-precision floating-point strided array element and computes the sum using pairwise summation with extended accumulation and returning an extended precision result.
```javascript
var Float32Array = require( '@stdlib/array/float32' );
var x = new Float32Array( [ 1.0, -2.0, 2.0 ] );
var N = x.length;
var v = dsapxsumpw( N, 5.0, x, 1 );
// returns 16.0
```
The function has the following parameters:
- **N**: number of indexed elements.
- **x**: input [`Float32Array`][@stdlib/array/float32].
- **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 Float32Array = require( '@stdlib/array/float32' );
var floor = require( '@stdlib/math/base/special/floor' );
var x = new Float32Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] );
var N = floor( x.length / 2 );
var v = dsapxsumpw( 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.
```javascript
var Float32Array = require( '@stdlib/array/float32' );
var floor = require( '@stdlib/math/base/special/floor' );
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 N = floor( x0.length / 2 );
var v = dsapxsumpw( N, 5.0, x1, 2 );
// returns 25.0
```
#### dsapxsumpw.ndarray( N, alpha, x, stride, offset )
Adds a constant to each single-precision floating-point strided array element and computes the sum using pairwise summation with extended accumulation and alternative indexing semantics and returning an extended precision result.
```javascript
var Float32Array = require( '@stdlib/array/float32' );
var x = new Float32Array( [ 1.0, -2.0, 2.0 ] );
var N = x.length;
var v = dsapxsumpw.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 Float32Array = require( '@stdlib/array/float32' );
var floor = require( '@stdlib/math/base/special/floor' );
var x = new Float32Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
var N = floor( x.length / 2 );
var v = dsapxsumpw.ndarray( N, 5.0, x, 2, 1 );
// returns 25.0
```
## Notes
- If `N <= 0`, both functions return `0.0`.
- Accumulated intermediate values are stored as double-precision floating-point numbers.
## Examples
```javascript
var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var Float32Array = require( '@stdlib/array/float32' );
var dsapxsumpw = require( '@stdlib/blas/ext/base/dsapxsumpw' );
var x;
var i;
x = new Float32Array( 10 );
for ( i = 0; i < x.length; i++ ) {
x[ i ] = round( randu()*100.0 );
}
console.log( x );
var v = dsapxsumpw( x.length, 5.0, x, 1 );
console.log( v );
```
* * *
## References
- Higham, Nicholas J. 1993. "The Accuracy of Floating Point Summation." _SIAM Journal on Scientific Computing_ 14 (4): 783–99. doi:[10.1137/0914050][@higham:1993a].
[@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
[@higham:1993a]: https://doi.org/10.1137/0914050