binaryLoopOrder

Reorder ndarray dimensions and associated strides for loop interchange.

Usage

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

binaryLoopOrder( shape, stridesX, stridesY, stridesZ )

Reorders ndarray dimensions and associated strides for loop interchange.

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

// Define the strides for the input arrays:
var stridesX = [ 2, 1 ]; // row-major
var stridesY = [ 4, 2 ]; // row-major

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

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

The function returns an object having the following properties:

sh: ordered dimensions.
sx: first input array strides sorted in loop order.
sy: second input array strides sorted in loop order.
sz: output array strides 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.
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 most common layout order. Accordingly, if the output ndarray has a different layout order (e.g., if the input ndarrays are 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/binary-loop-interchange-order' );

// Create ndarrays:
var x = array( [ [ 1, 2 ], [ 3, 4 ] ] );
var y = array( [ [ 5, 6 ], [ 7, 8 ] ] );
var z = array( [ [ 0, 0 ], [ 0, 0 ] ] );

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

console.log( o );