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About stdlib...

We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.

The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.

When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.

To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!

scusumpw

NPM version Build Status Coverage Status

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

Usage

To use in Observable,

scusumpw = require( 'https://cdn.jsdelivr.net/gh/stdlib-js/blas-ext-base-scusumpw@umd/browser.js' )

To vendor stdlib functionality and avoid installing dependency trees for Node.js, you can use the UMD server build:

var scusumpw = require( 'path/to/vendor/umd/blas-ext-base-scusumpw/index.js' )

To include the bundle in a webpage,

<script type="text/javascript" src="https://cdn.jsdelivr.net/gh/stdlib-js/blas-ext-base-scusumpw@umd/browser.js"></script>

If no recognized module system is present, access bundle contents via the global scope:

<script type="text/javascript">
(function () {
    window.scusumpw;
})();
</script>

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: index increment for x.
  • y: output Float32Array.
  • strideY: index increment 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 in x,

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, offsetX and offsetY parameters support indexing semantics based on a starting indices. For example, to calculate the cumulative sum of every other value in x starting from the second value 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

<!DOCTYPE html>
<html lang="en">
<body>
<script type="text/javascript" src="https://cdn.jsdelivr.net/gh/stdlib-js/random-base-discrete-uniform@umd/browser.js"></script>
<script type="text/javascript">
(function () {.factory;
var filledarrayBy = require( '@stdlib/array-filled-by' );
var Float32Array = require( '@stdlib/array-float32' );
var scusumpw = require( '@stdlib/blas-ext-base-scusumpw' );

var x = filledarrayBy( 10, 'float32', discreteUniform( 0, 100 ) );
var y = new Float32Array( x.length );

console.log( x );
console.log( y );

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

})();
</script>
</body>
</html>

References

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

See Also

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

Copyright © 2016-2024. The Stdlib Authors.