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ssumpw

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

Installation

npm install @stdlib/blas-ext-base-ssumpw

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

Usage

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

ssumpw( N, x, strideX )

Computes the 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 v = ssumpw( x.length, x, 1 );
// returns 1.0

The function has the following parameters:

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

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

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

Computes the 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 v = ssumpw.ndarray( x.length, x, 1, 0 );
// returns 1.0

The function has the following additional parameters:

• offsetX: 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 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 = ssumpw.ndarray( 4, x, 2, 1 );
// returns 5.0

Notes

• If N <= 0, both functions return 0.0.
• 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–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-base-discrete-uniform' ).factory;
var filledarrayBy = require( '@stdlib/array-filled-by' );
var ssumpw = require( '@stdlib/blas-ext-base-ssumpw' );

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

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

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C APIs

Usage

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

stdlib_strided_ssumpw( N, *X, strideX )

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

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

float v = stdlib_strided_ssumpw( 3, x, 1 );
// returns 1.0f

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 for X.

float stdlib_strided_ssumpw( const CBLAS_INT N, const float *X, const CBLAS_INT strideX );

stdlib_strided_ssumpw_ndarray( N, *X, strideX, offsetX )

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

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

float v = stdlib_strided_ssumpw_ndarray( 3, x, 1, 0 );
// returns 1.0f

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 for X.
• offsetX: [in] CBLAS_INT starting index for X.

float stdlib_strided_ssumpw_ndarray( const CBLAS_INT N, const float *X, const CBLAS_INT strideX, const CBLAS_INT offsetX );

Examples

#include "stdlib/blas/ext/base/ssumpw.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_ssumpw( N, x, strideX );

    // Print the result:
    printf( "sum: %f\n", v );
}

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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/dsumpw: calculate the sum of double-precision floating-point strided array elements using pairwise summation.
• @stdlib/blas-ext/base/gsumpw: calculate the sum of strided array elements using pairwise summation.
• @stdlib/blas-ext/base/snansumpw: calculate the sum of single-precision floating-point strided array elements, ignoring NaN values and using pairwise summation.
• @stdlib/blas-ext/base/ssum: calculate the sum of single-precision floating-point strided array elements.
• @stdlib/blas-ext/base/ssumkbn2: calculate the sum of single-precision floating-point strided array elements using a second-order iterative Kahan–Babuška algorithm.
• @stdlib/blas-ext/base/ssumors: calculate the sum of single-precision floating-point strided array elements using ordinary recursive summation.

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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

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License

See LICENSE.

Copyright

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