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unaryLoopOrder

Reorder ndarray dimensions and associated strides for loop interchange.

Installation

npm install @stdlib/ndarray-base-unary-loop-interchange-order

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 unaryLoopOrder = require( '@stdlib/ndarray-base-unary-loop-interchange-order' );

unaryLoopOrder( shape, stridesX, stridesY )

Reorders ndarray dimensions and associated strides for loop interchange.

// Define an array shape:
var shape = [ 2, 2 ];

// Define the strides for the input array:
var stridesX = [ 2, 1 ]; // row-major

// Define the strides for the output array:
var stridesY = [ 1, 2 ]; // column-major

// Resolve the loop interchange order:
var o = unaryLoopOrder( shape, stridesX, stridesY );
// returns {...}

The function returns an object having the following properties:

• sh: ordered dimensions.
• sx: input array strides sorted in loop order.
• sy: output array strides sorted in loop order.
• idx: dimension indices sorted in loop order.

For all returned arrays, the first element corresponds to the innermost loop, and the last element corresponds to the outermost loop.

Notes

• When iterating over the elements of a multi-dimensional array, accessing elements which are closer in memory can improve performance. To this end, loop interchange is a technique used in loop nest optimization to improve locality of reference and take advantage of CPU cache.

  The purpose of this function is to order ndarray dimensions according to the magnitude of input array strides. By using the ordered dimensions and associated strides, one can construct nested loops (one for each dimension) such that the innermost loop iterates over the dimension in which array elements are closest in memory and the outermost loop iterates over the dimension in which array elements are farthest apart in memory. As a consequence, element iteration is optimized to minimize cache misses and ensure locality of reference.

• Cache performance may be degraded if the layout order (i.e., row-major or column-major) differs for the input and output ndarrays. This function is intended to optimize cache performance for the input ndarray. If the output ndarray has a different layout order (e.g., if the input ndarray is row-major and the output ndarray is column-major), cache misses are likely for the output ndarray. In general, to ensure best performance, input and output ndarrays should have the same layout order.

• The function assumes that the input and output ndarrays have the same shape. Hence, loop interchange order should only be determined after broadcasting.

Examples

var array = require( '@stdlib/ndarray-array' );
var loopOrder = require( '@stdlib/ndarray-base-unary-loop-interchange-order' );

// Create ndarrays:
var x = array( [ [ 1, 2 ], [ 3, 4 ] ] );
var y = array( [ [ 0, 0 ], [ 0, 0 ] ] );

// Resolve loop interchange data:
var o = loopOrder( x.shape, x.strides, y.strides );
// returns {...}

console.log( o );

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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

Copyright © 2016-2024. The Stdlib Authors.