# sasumpw
> Calculate the sum of absolute values ([_L1_ norm][l1norm]) of single-precision floating-point strided array elements using pairwise summation.
The [_L1_ norm][l1norm] is defined as
## Usage
```javascript
var sasumpw = require( '@stdlib/blas/ext/base/sasumpw' );
```
#### sasumpw( N, x, stride )
Computes the sum of absolute values ([_L1_ norm][l1norm]) of single-precision floating-point strided array elements using pairwise summation.
```javascript
var Float32Array = require( '@stdlib/array/float32' );
var x = new Float32Array( [ 1.0, -2.0, 2.0 ] );
var N = x.length;
var v = sasumpw( N, x, 1 );
// returns 5.0
```
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 compute the sum of absolute values of 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 = sasumpw( N, x, 2 );
// returns 9.0
```
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 = sasumpw( N, x1, 2 );
// returns 9.0
```
#### sasumpw.ndarray( N, x, stride, offset )
Computes the sum of absolute values ([_L1_ norm][l1norm]) of single-precision floating-point strided array elements using pairwise summation and alternative indexing semantics.
```javascript
var Float32Array = require( '@stdlib/array/float32' );
var x = new Float32Array( [ 1.0, -2.0, 2.0 ] );
var N = x.length;
var v = sasumpw.ndarray( N, x, 1, 0 );
// returns 5.0
```
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 calculate the sum of absolute values of 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 = sasumpw.ndarray( N, x, 2, 1 );
// returns 9.0
```
## Notes
- If `N <= 0`, both functions return `0.0`.
- In general, pairwise summation is more numerically stable than ordinary recursive summation (i.e., "simple" summation), with slightly worse performance. While not the most numerically stable summation technique (e.g., compensated summation techniques such as the Kahan–Babuška-Neumaier algorithm are generally more numerically stable), pairwise summation strikes a reasonable balance between numerical stability and performance. If either numerical stability or performance is more desirable for your use case, consider alternative summation techniques.
## Examples
```javascript
var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var Float32Array = require( '@stdlib/array/float32' );
var sasumpw = require( '@stdlib/blas/ext/base/sasumpw' );
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 = sasumpw( x.length, 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
[l1norm]: http://en.wikipedia.org/wiki/Norm_%28mathematics%29
[@higham:1993a]: https://doi.org/10.1137/0914050
