sdsapxsumpw

Add a constant to each single-precision floating-point strided array element and compute the sum using pairwise summation with extended accumulation.

Usage

var sdsapxsumpw = require( '@stdlib/blas/ext/base/sdsapxsumpw' );

sdsapxsumpw( 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.

var Float32Array = require( '@stdlib/array/float32' );

var x = new Float32Array( [ 1.0, -2.0, 2.0 ] );

var v = sdsapxsumpw( 3, 5.0, x, 1 );
// returns 16.0

The function has the following parameters:

N: number of indexed elements.
alpha: scalar constant.
x: input Float32Array.
stride: index increment for x.

The N and stride parameters determine which elements in the strided array are accessed at runtime. For example, to compute the sum of every other element in the strided array,

var Float32Array = require( '@stdlib/array/float32' );

var x = new Float32Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] );

var v = sdsapxsumpw( 4, 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 Float32Array = require( '@stdlib/array/float32' );

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 v = sdsapxsumpw( 4, 5.0, x1, 2 );
// returns 25.0

sdsapxsumpw.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.

var Float32Array = require( '@stdlib/array/float32' );

var x = new Float32Array( [ 1.0, -2.0, 2.0 ] );

var v = sdsapxsumpw.ndarray( 3, 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 the strided array starting from the second value

var Float32Array = require( '@stdlib/array/float32' );

var x = new Float32Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );

var v = sdsapxsumpw.ndarray( 4, 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

var discreteUniform = require( '@stdlib/random/base/discrete-uniform' ).factory;
var filledarrayBy = require( '@stdlib/array/filled-by' );
var sdsapxsumpw = require( '@stdlib/blas/ext/base/sdsapxsumpw' );

var x = filledarrayBy( 10, 'float32', discreteUniform( 0, 100 ) );
console.log( x );

var v = sdsapxsumpw( 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.