nullaryLoopOrder

Reorder ndarray dimensions and associated strides for loop interchange.

Usage

var nullaryLoopOrder = require( '@stdlib/ndarray/base/nullary-loop-interchange-order' );

nullaryLoopOrder( shape, stridesX )

Reorders ndarray dimensions and associated strides for loop interchange.

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

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

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

The function returns an object having the following properties:

sh: ordered dimensions.
sx: 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 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.

Examples

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

// Create an ndarray:
var x = array( [ [ 1, 2 ], [ 3, 4 ] ] );

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

console.log( o );