When a Loop Becomes an Integer Problem: Presburger Reasoning in MLIR Affine

Mon, 27 Jul 2026 00:00:00 +0300

Suppose I want to parallelize this loop:

affine.for %i = 0 to %N {
 %x = affine.load %A[2 * %i] : memref<?xf32>
 affine.store %x, %A[2 * %i + 1] : memref<?xf32>
}

Assume %A has room for $2N$ elements. Every iteration reads an even address and writes the following odd address. Because both accesses use the same memref and one of them writes, dependence analysis must ask whether two distinct, ordered iterations can touch the same element.

To compare two executions of the loop, call the earlier iteration $p$ and the later iteration $q$ . They are two possible values of the loop variable %i. For any iteration $t$ , the read and write addresses are

Programming on onur.one

When a Loop Becomes an Integer Problem: Presburger Reasoning in MLIR Affine