dsumkbn

Calculate the sum of double-precision floating-point strided array elements using an improved Kahan–Babuška algorithm.

Usage

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

dsumkbn( N, x, stride )

Computes the sum of double-precision floating-point strided array elements using an improved Kahan–Babuška algorithm.

var Float64Array = require( '@stdlib/array/float64' );

var x = new Float64Array( [ 1.0, -2.0, 2.0 ] );
var N = x.length;

var v = dsumkbn( N, x, 1 );
// returns 1.0

The function has the following parameters:

N: number of indexed elements.
x: input Float64Array.
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 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 = dsumkbn( 4, x, 2 );
// returns 5.0

Note that indexing is relative to the first index. To introduce an offset, use typed array views.

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 = dsumkbn( 4, x1, 2 );
// returns 5.0

dsumkbn.ndarray( N, x, stride, offset )

Computes the sum of double-precision floating-point strided array elements using an improved Kahan–Babuška algorithm and alternative indexing semantics.

var Float64Array = require( '@stdlib/array/float64' );

var x = new Float64Array( [ 1.0, -2.0, 2.0 ] );

var v = dsumkbn.ndarray( 3, x, 1, 0 );
// returns 1.0

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 calculate the sum of every other value in the strided array starting from the second value

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 = dsumkbn.ndarray( 4, x, 2, 1 );
// returns 5.0

Notes

If N <= 0, both functions return 0.0.

Examples

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

var x = filledarrayBy( 10, 'float64', discreteUniform( 0, 100 ) );
console.log( x );

var v = dsumkbn( x.length, x, 1 );
console.log( v );

References

Neumaier, Arnold. 1974. "Rounding Error Analysis of Some Methods for Summing Finite Sums." Zeitschrift Für Angewandte Mathematik Und Mechanik 54 (1): 39–51. doi:10.1002/zamm.19740540106.