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ssumkbn

README.md

ssumkbn

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

Usage

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

ssumkbn( N, x, strideX )

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

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

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

var v = ssumkbn( x.length, x, 1 );
// returns 1.0

The function has the following parameters:

  • N: number of indexed elements.
  • x: input Float32Array.
  • strideX: stride length.

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:

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 = ssumkbn( 4, x, 2 );
// returns 5.0

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

ssumkbn.ndarray( N, x, strideX, offsetX )

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

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

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

var v = ssumkbn.ndarray( x.length, x, 1, 0 );
// returns 1.0

The function has the following additional parameters:

  • offsetX: starting index.

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 element starting from the second element:

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

Notes

  • If N <= 0, both functions return 0.0.

Examples

var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
var ssumkbn = require( '@stdlib/blas/ext/base/ssumkbn' );

var x = discreteUniform( 10, -100, 100, {
    'dtype': 'float32'
});
console.log( x );

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

C APIs

Usage

#include "stdlib/blas/ext/base/ssumkbn.h"

stdlib_strided_ssumkbn( N, *X, strideX )

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

const float x[] = { 1.0f, 2.0f, 3.0f, 4.0f };

float v = stdlib_strided_ssumkbn( 4, x, 1 );
// returns 10.0f

The function accepts the following arguments:

  • N: [in] CBLAS_INT number of indexed elements.
  • X: [in] float* input array.
  • strideX: [in] CBLAS_INT stride length.
float stdlib_strided_ssumkbn( const CBLAS_INT N, const float *X, const CBLAS_INT strideX );

stdlib_strided_ssumkbn_ndarray( N, *X, strideX, offsetX )

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

const float x[] = { 1.0f, 2.0f, 3.0f, 4.0f };

float v = stdlib_strided_ssumkbn_ndarray( 4, x, 1, 0 );
// returns 10.0f

The function accepts the following arguments:

  • N: [in] CBLAS_INT number of indexed elements.
  • X: [in] float* input array.
  • strideX: [in] CBLAS_INT stride length.
  • offsetX: [in] CBLAS_INT starting index.
float stdlib_strided_ssumkbn_ndarray( const CBLAS_INT N, const float *X, const CBLAS_INT strideX, const CBLAS_INT offsetX );

Examples

#include "stdlib/blas/ext/base/ssumkbn.h"
#include <stdio.h>

int main( void ) {
    // Create a strided array:
    const float x[] = { 1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f, 8.0f };

    // Specify the number of elements:
    const int N = 4;

    // Specify the stride length:
    const int strideX = 2;

    // Compute the sum:
    float v = stdlib_strided_ssumkbn( N, x, strideX );

    // Print the result:
    printf( "Sum: %f\n", 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.

See Also