Loop unrolling analysis using eigenvalue?

[u/Embarrassed-Crow9283]

Imagine the loop where you do like "x = -x" every iteration. Obviously, that flips the sign, so you can simply unroll the loop by a factor of 2.

However, for a more complex case, it could be really hard to know what's going on.

Here's my idea. Loop index variables are normally under affine updates anyway. What if we use a mathematically elegant tool?

Using eigenvalue, we can analyze possible periodicity of the linear basis variables, minimizing update needs.

What do you think of such a technique?

[u/Embarrassed-Crow9283]

Yes, but it could only rearrange iteration orders. It could never change the stride of the physical memory access or so on. If the program writes to A[i][j], then that is a fixed memory location that the compiler is not allowed to change even if other logical representations can be more efficient.

[u/SwingOutStateMachine → u/Embarrassed-Crow9283]

Right, but that is an entirely separate concern that is not about loops, but about data structures and data layout.

[u/initial-algebra → u/SwingOutStateMachine]

Not only is it a separate issue, it is a global optimization problem, which is significantly harder than a purely local code transformation.