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gapxsumpw
Add a constant to each strided array element and compute the sum using pairwise summation.
Installation
npm install @stdlib/blasextbasegapxsumpw
Usage
var gapxsumpw = require( '@stdlib/blasextbasegapxsumpw' );
gapxsumpw( N, alpha, x, stride )
Adds a constant to each strided array element and computes the sum using pairwise summation.
var x = [ 1.0, 2.0, 2.0 ];
var N = x.length;
var v = gapxsumpw( N, 5.0, x, 1 );
// returns 16.0
The function has the following parameters:
 N: number of indexed elements.

x: input
Array
ortyped array
. 
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
,
var floor = require( '@stdlib/mathbasespecialfloor' );
var x = [ 1.0, 2.0, 2.0, 7.0, 2.0, 3.0, 4.0, 2.0 ];
var N = floor( x.length / 2 );
var v = gapxsumpw( N, 5.0, x, 2 );
// returns 25.0
Note that indexing is relative to the first index. To introduce an offset, use typed array
views.
var Float64Array = require( '@stdlib/arrayfloat64' );
var floor = require( '@stdlib/mathbasespecialfloor' );
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 N = floor( x0.length / 2 );
var v = gapxsumpw( N, 5.0, x1, 2 );
// returns 25.0
gapxsumpw.ndarray( N, alpha, x, stride, offset )
Adds a constant to each strided array element and computes the sum using pairwise summation and alternative indexing semantics.
var x = [ 1.0, 2.0, 2.0 ];
var N = x.length;
var v = gapxsumpw.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
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
var floor = require( '@stdlib/mathbasespecialfloor' );
var x = [ 2.0, 1.0, 2.0, 2.0, 2.0, 2.0, 3.0, 4.0 ];
var N = floor( x.length / 2 );
var v = gapxsumpw.ndarray( N, 5.0, x, 2, 1 );
// returns 25.0
Notes
 If
N <= 0
, both functions return0.0
.  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–BabuškaNeumaier 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.
 Depending on the environment, the typed versions (
dapxsumpw
,sapxsumpw
, etc.) are likely to be significantly more performant.
Examples
var randu = require( '@stdlib/randombaserandu' );
var round = require( '@stdlib/mathbasespecialround' );
var Float64Array = require( '@stdlib/arrayfloat64' );
var gapxsumpw = require( '@stdlib/blasextbasegapxsumpw' );
var x;
var i;
x = new Float64Array( 10 );
for ( i = 0; i < x.length; i++ ) {
x[ i ] = round( randu()*100.0 );
}
console.log( x );
var v = gapxsumpw( 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.
See Also

@stdlib/blasext/base/dapxsumpw
: adds a constant to each doubleprecision floatingpoint strided array element and computes the sum using pairwise summation. 
@stdlib/blasext/base/gapxsum
: adds a constant to each strided array element and computes the sum. 
@stdlib/blasext/base/gsumpw
: calculate the sum of strided array elements using pairwise summation. 
@stdlib/blasext/base/sapxsumpw
: adds a constant to each singleprecision floatingpoint strided array element and computes the sum using pairwise summation.
Notice
This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.
For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.
Community
License
See LICENSE.
Copyright
Copyright © 20162024. The Stdlib Authors.