[TIR] Update symbolic index term order in loop fusion
This change just keep stride terms order the same with fused loop order in fuse primitive. In symbolic circumstances, previous form suffer from simplification issues and would make the expression tree much complex in following lowering steps.
Take [M, N] tiling as an example, the previous binding form after
i, j = sch.get_loops(block_b)
i0, i1 = sch.split(i, factors=[None, 64])
j0, j1 = sch.split(j, factors=[None, 16])
sch.reorder(i0, j0, i1, j1)
sch.fuse(i0, j0)
would be like (i_0_j_0_fused in [0, ceildiv(M, 64) * ceildiv(N, 16)]
vi = T.axis.spatial(M, i_0_j_0_fused % ((N + 15) // 16 * ((M + 63) // 64)) // ((N + 15) // 16) * 64 + i_1)
instead of more simple version
vi = T.axis.spatial(M, i_0_j_0_fused // ((N + 15) // 16) * 64 + i_1)
This is because unfortunately we do not know ceildiv(N, 16) * ceildiv(M, 64) == ceildiv(M, 64) * ceildiv(N, 16) in rule based simplifications. And then certain analysis (for example, region estimation) may fail to give concise estimations, due to complex dynamic expression trees.
Summary of Changes
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This pull request refines the symbolic index term ordering within the loop fusion mechanism of the TIR schedule. The adjustment aims to simplify generated expressions, particularly in symbolic contexts, which previously led to complex expression trees and hindered analysis like region estimation. By ensuring that stride terms maintain an order consistent with the fused loops, the change improves the efficiency and clarity of the intermediate representation, making subsequent lowering steps more robust.
Highlights
- Symbolic Index Term Order: The pull request updates the order of symbolic index terms within the loop fusion primitive to ensure consistency with the fused loop order.
- Expression Simplification: This change addresses previous issues where symbolic expressions became overly complex, hindering simplification and analysis (e.g., region estimation).
-
Code Logic Adjustment: The core logic in
loop_transformation.ccwas modified to reorder multiplication terms infloormodandlowerupdates, and thefused_extentcalculation loop direction was reversed. -
New Test Case: A new test,
test_fused_symbolic_2D_tiling, has been added to validate the improved symbolic index term ordering after loop fusion with 2D tiling.
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