# dapxsumpw
> Add a scalar constant to each double-precision floating-point strided array element and compute the sum using pairwise summation.
## Usage
```javascript
var dapxsumpw = require( '@stdlib/blas/ext/base/dapxsumpw' );
```
#### dapxsumpw( N, alpha, x, strideX )
Adds a scalar constant to each double-precision floating-point strided array element and computes the sum using pairwise summation.
```javascript
var Float64Array = require( '@stdlib/array/float64' );
var x = new Float64Array( [ 1.0, -2.0, 2.0 ] );
var N = x.length;
var v = dapxsumpw( N, 5.0, x, 1 );
// returns 16.0
```
The function has the following parameters:
- **N**: number of indexed elements.
- **x**: input [`Float64Array`][@stdlib/array/float64].
- **strideX**: 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 `x`,
```javascript
var Float64Array = require( '@stdlib/array/float64' );
var x = new Float64Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] );
var v = dapxsumpw( 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 Float64Array = require( '@stdlib/array/float64' );
var x0 = new Float64Array( [ 2.0, 1.0, 2.0, -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 v = dapxsumpw( 4, 5.0, x1, 2 );
// returns 25.0
```
#### dapxsumpw.ndarray( N, alpha, x, strideX, offsetX )
Adds a scalar constant to each double-precision floating-point strided array element and computes the sum using pairwise summation and alternative indexing semantics.
```javascript
var Float64Array = require( '@stdlib/array/float64' );
var x = new Float64Array( [ 1.0, -2.0, 2.0 ] );
var N = x.length;
var v = dapxsumpw.ndarray( N, 5.0, x, 1, 0 );
// returns 16.0
```
The function has the following additional parameters:
- **offsetX**: 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 Float64Array = require( '@stdlib/array/float64' );
var x = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
var v = dapxsumpw.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/array/discrete-uniform' );
var dapxsumpw = require( '@stdlib/blas/ext/base/dapxsumpw' );
var x = discreteUniform( 10, -100, 100, {
'dtype': 'float64'
});
console.log( x );
var v = dapxsumpw( x.length, 5.0, x, 1 );
console.log( v );
```
* * *
## C APIs
### Usage
```c
#include "stdlib/blas/ext/base/dapxsumpw.h"
```
#### stdlib_strided_dapxsumpw( N, alpha, \*X, strideX )
Adds a scalar constant to each double-precision floating-point strided array element and computes the sum using pairwise summation.
```c
const double x[] = { 1.0, 2.0, 3.0, 4.0 };
double v = stdlib_strided_dapxsumpw( 4, 5.0, x, 1 );
// returns 30.0
```
The function accepts the following arguments:
- **N**: `[in] CBLAS_INT` number of indexed elements.
- **alpha**: `[in] double` scalar constant.
- **X**: `[in] double*` input array.
- **strideX**: `[in] CBLAS_INT` index increment for `X`.
```c
double stdlib_strided_dapxsumpw( const CBLAS_INT N, const double alpha, const double *X, const CBLAS_INT strideX );
```
#### stdlib_strided_dapxsumpw_ndarray( N, alpha, \*X, strideX, offsetX )
Adds a scalar constant to each double-precision floating-point strided array element and computes the sum using pairwise summation and alternative indexing semantics.
```c
const double x[] = { 1.0, 2.0, 3.0, 4.0 };
double v = stdlib_strided_dapxsumpw_ndarray( 4, 5.0, x, 1, 0 );
// returns 30.0
```
The function accepts the following arguments:
- **N**: `[in] CBLAS_INT` number of indexed elements.
- **alpha**: `[in] double` scalar constant.
- **X**: `[in] double*` input array.
- **strideX**: `[in] CBLAS_INT` index increment for `X`.
- **offsetX**: `[in] CBLAS_INT` starting index for `X`.
```c
double stdlib_strided_dapxsumpw_ndarray( const CBLAS_INT N, const double alpha, const double *X, const CBLAS_INT strideX, const CBLAS_INT offsetX );
```
### Examples
```c
#include "stdlib/blas/ext/base/dapxsumpw.h"
#include
int main( void ) {
// Create a strided array:
const double x[] = { 1.0, -2.0, 3.0, -4.0, 5.0, -6.0, 7.0, -8.0 };
// Specify the number of indexed elements:
const int N = 8;
// Specify a stride:
const int strideX = 1;
// Compute the sum:
double v = stdlib_strided_dapxsumpw( N, 5.0, x, strideX );
// Print the result:
printf( "Sum: %lf\n", sum );
}
```
## 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/float64]: https://www.npmjs.com/package/@stdlib/array-float64
[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
[@higham:1993a]: https://doi.org/10.1137/0914050
[@stdlib/blas/ext/base/dapxsum]: https://github.com/stdlib-js/blas/tree/main/ext/base/dapxsum
[@stdlib/blas/ext/base/dsumpw]: https://github.com/stdlib-js/blas/tree/main/ext/base/dsumpw
[@stdlib/blas/ext/base/gapxsumpw]: https://github.com/stdlib-js/blas/tree/main/ext/base/gapxsumpw
[@stdlib/blas/ext/base/sapxsumpw]: https://github.com/stdlib-js/blas/tree/main/ext/base/sapxsumpw