scusumpw

Calculate the cumulative sum of single-precision floating-point strided array elements using pairwise summation.

Usage

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

scusumpw( N, sum, x, strideX, y, strideY )

Computes the cumulative sum of single-precision floating-point strided array elements using pairwise summation.

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

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

scusumpw( x.length, 0.0, x, 1, y, 1 );
// y => <Float32Array>[ 1.0, -1.0, 1.0 ]

x = new Float32Array( [ 1.0, -2.0, 2.0 ] );
y = new Float32Array( x.length );

scusumpw( x.length, 10.0, x, 1, y, 1 );
// y => <Float32Array>[ 11.0, 9.0, 11.0 ]

The function has the following parameters:

• N: number of indexed elements.
• sum: initial sum.
• x: input Float32Array.
• strideX: stride length for x.
• y: output Float32Array.
• strideY: stride length for y.

The N and stride parameters determine which elements in the strided arrays are accessed at runtime. For example, to compute the cumulative 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 y = new Float32Array( x.length );

var v = scusumpw( 4, 0.0, x, 2, y, 1 );
// y => <Float32Array>[ 1.0, 3.0, 1.0, 5.0, 0.0, 0.0, 0.0, 0.0 ]

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

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

// Initial arrays...
var x0 = new Float32Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
var y0 = new Float32Array( x0.length );

// Create offset views...
var x1 = new Float32Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var y1 = new Float32Array( y0.buffer, y0.BYTES_PER_ELEMENT*3 ); // start at 4th element

scusumpw( 4, 0.0, x1, -2, y1, 1 );
// y0 => <Float32Array>[ 0.0, 0.0, 0.0, 4.0, 6.0, 4.0, 5.0, 0.0 ]

scusumpw.ndarray( N, sum, x, strideX, offsetX, y, strideY, offsetY )

Computes the cumulative sum of single-precision floating-point strided array elements using pairwise summation and alternative indexing semantics.

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

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

scusumpw.ndarray( x.length, 0.0, x, 1, 0, y, 1, 0 );
// y => <Float32Array>[ 1.0, -1.0, 1.0 ]

The function has the following additional parameters:

• offsetX: starting index for x.
• offsetY: starting index for y.

While typed array views mandate a view offset based on the underlying buffer, the offset parameters support indexing semantics based on starting indices. For example, to calculate the cumulative sum of every other element starting from the second element and to store in the last N elements of y starting from the last 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 y = new Float32Array( x.length );

scusumpw.ndarray( 4, 0.0, x, 2, 1, y, -1, y.length-1 );
// y => <Float32Array>[ 0.0, 0.0, 0.0, 0.0, 5.0, 1.0, -1.0, 1.0 ]

Notes

• If N <= 0, both functions return y unchanged.
• 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–Babuška-Neumaier 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.

Examples

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

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

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

scusumpw( x.length, 0.0, x, 1, y, -1 );
console.log( y );

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C APIs

Usage

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

stdlib_strided_scusumpw( N, sum, *X, strideX, *Y, strideY )

Computes the cumulative sum of single-precision floating-point strided array elements using pairwise summation.

const float x[] = { 1.0f, 2.0f, 3.0f, 4.0f }
float y[] = { 0.0f, 0.0f, 0.0f, 0.0f }

stdlib_strided_scusumpw( 4, 0.0f, x, 1, y, 1 );

The function accepts the following arguments:

• N: [in] CBLAS_INT number of indexed elements.
• sum: [in] float initial sum.
• X: [in] float* input array.
• strideX: [in] CBLAS_INT stride length for X.
• Y: [out] float* output array.
• strideY: [in] CBLAS_INT stride length for Y.

void stdlib_strided_scusumpw( const CBLAS_INT N, const float sum, const float *X, const CBLAS_INT strideX, float *Y, const CBLAS_INT strideY );

stdlib_strided_scusumpw_ndarray( N, sum, *X, strideX, offsetX, *Y, strideY, offsetY )

Computes the cumulative sum of single-precision floating-point strided array elements using pairwise summation and alternative indexing semantics.

const float x[] = { 1.0f, 2.0f, 3.0f, 4.0f }
float y[] = { 0.0f, 0.0f, 0.0f, 0.0f }

stdlib_strided_scusumpw_ndarray( 4, 0.0f, x, 1, 0, y, 1, 0 );

The function accepts the following arguments:

• N: [in] CBLAS_INT number of indexed elements.
• sum: [in] float initial sum.
• X: [in] float* input array.
• strideX: [in] CBLAS_INT stride length for X.
• offsetX: [in] CBLAS_INT starting index for X.
• Y: [out] float* output array.
• strideY: [in] CBLAS_INT stride length for Y.
• offsetY: [in] CBLAS_INT starting index for Y.

void stdlib_strided_scusumpw_ndarray( const CBLAS_INT N, const float sum, const float *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, float *Y, const CBLAS_INT strideY, const CBLAS_INT offsetY );

Examples

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

int main( void ) {
    // Create strided arrays:
    const float x[] = { 1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f, 8.0f };
    float y[] = { 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f };

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

    // Specify stride lengths:
    const int strideX = 2;
    const int strideY = -2;

    // Compute the cumulative sum:
    stdlib_strided_scusumpw( N, 0.0f, x, strideX, y, strideY );

    // Print the result:
    for ( int i = 0; i < 8; i++ ) {
        printf( "y[ %d ] = %f\n", i, y[ i ] );
    }
}

References

• Higham, Nicholas J. 1993. "The Accuracy of Floating Point Summation." SIAM Journal on Scientific Computing 14 (4): 783–99. doi:10.1137/0914050.

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See Also

• @stdlib/blas/ext/base/dcusumpw: calculate the cumulative sum of double-precision floating-point strided array elements using pairwise summation.
• @stdlib/blas/ext/base/gcusumpw: calculate the cumulative sum of strided array elements using pairwise summation.
• @stdlib/blas/ext/base/scusum: calculate the cumulative sum of single-precision floating-point strided array elements.