MDRange iteration order transformation

[cwpearson]

Note

Work in progress
I'll squash / tidy this up once it's ready to go.

Improves memory access locality for GPUs.

• The Cost of a memref is modeled as its reuse distance scaled by loop trip count and whether it's a load or store
• The reuse distance of a memref is the partial derivative of it's offset w.r.t the right-most induction variable of the enclosing scf.parallel
  1. Compute d(offset)/d(memref index variable) for all of the memref's index variables
  2. Compute d(memref index variable)/d(scf.parallel induction variable) for all of the memref's index variables
     • may not be computable
  3. Sum up all quantities from (1) and (2) to get the desired partial derivative d(offset)/d(scf.parallel induction variable)
     • may not be computable due to (2)
  4. The resulting Cost will usually include unknown memref extents and loop trip counts
     • or may not be computable due to (2)

• Phase 1: walk the modules and compute a map of (scf.parallel) -> trip count
• Phase 2: walk the module and compute a map of (memref, induction variable) -> Cost, to refer to in phase 2
  • incorporate reuse distance
  • incorporate load vs store
  • incorporate loop trip count
• Phase 3: consider all possible choices for right-most induction variable for all scf.parallel
  • iterate all choices of right-most induction variable
  • Add up the evaluated cost model for all memrefs
  • Evaluate the cost model with Monte-Carlo method for unknowns
    • principled "sampling" method?
      • log random
    • principled "aggregation" method?
      • median
• Phase 3: generate a new module
  • clone original module
  • modify scf.parallel things
• Phase 4: does it work?