What does "most" and "least" significant dimension mean?

Question

I am reading a book on C++ AMP and don't really understand some of the terminology:

Always choose your tile size so that the number of threads in the least significant dimension is at least 16, and use 32 or even 64 if you can.

I had seen similar terminology used in the Eigen documentation, so I suspect this is quite common usage.

So let's suppose I have a 2D index, array, whatever:

// construct it:
ArrayType my2DArray(rows,columns);

// now index it:
float element = my2DArray[rowIdx,colIdx];

Forgetting for a moment the type of ArrayType, and thinking more about the terminology, which would be the most and least significant dimension of that array?

Answer 1

When allocating threads logically in multiple dimensions, there is generally a mapping from that N-dimensional space to a linear space. The dimension that varies the linear space least is the least significant dimension.

As an example, mapping a 2-dimensional (X,Y) coordinate to linear space might be determined using the expression (Y * width + X). Here, X is the least significant dimension and Y is the most significant dimension. Likewise, for a 3-dimensional (X,Y,Z) space, the expression might be (Z * width * height + Y * width + X). Here, X is still the least significant, but Z is the most significant. Your layout may not necessarily be the same, for example you may choose to map linear space to (Z * width * height + X * height + Y), in which case Y is the least significant dimension.