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Tiling Examples for X86 ISA

Tiling Examples for X86 ISA. Slides Selected from Radu Rugina’s CS412/413 Lecture on Instruction Selection at Cornell. Instruction Selection. Translate 3-address code to DAG Cover DAG with tiles Disjoint set of tiles cover DAG Algorithm: Greedy maximal munch Dynamic programming. Tiling.

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Tiling Examples for X86 ISA

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  1. Tiling Examples for X86 ISA Slides Selected from RaduRugina’s CS412/413 Lecture on Instruction Selection at Cornell

  2. Instruction Selection • Translate 3-address code to DAG • Cover DAG with tiles • Disjoint set of tiles cover DAG • Algorithm: • Greedy maximal munch • Dynamic programming

  3. Tiling • Assume abstract assembly • Infinite registers • Temporary and/or local variables stored in registers • Array, struct, parameter passing use memory accesses • Translation process from IR: • Convert 3-address code IR to abstract assembly • Build DAG • Perform tiling

  4. Example • a = a + i where a is a local variable and i is a parameter passed in from a caller

  5. Pentium ISA • Two-address CISC • Multiple addressing modes • Immediate: $imm • Register: reg • Indirect: (reg), (reg + imm) • Indexed: (reg + reg’), (reg + imm*reg’)

  6. More Tile Examples

  7. Conditional Branches

  8. Load Effective Address

  9. Maximal Munch Algorithm • A greedy algorithm • Start from top of tree (or DAG) • Find largest tile that matches top node • Tile the sub-trees recursively

  10. Non-Greedy Tiling

  11. Greedy Tiling

  12. ADD Expression and Statement

  13. Designing Tiles • Only add tiles that are useful to compiler • Many instructions will be too hard to use effectively or will offer no advantage • Need tiles for all single-node trees to guarantee that every tree can be tiled

  14. Implementation • Maximal Munch: start from top node • Find largest tile matching top node and all of the children nodes • Invoke recursively on all children of tile • Generate code for this tile • Code for children will have been generated already in recursive calls

  15. Matching Tiles

  16. Finding globally optimum tiling • Goal: find minimum total cost tiling of DAG • Algorithm: for every node, find minimum total cost tiling of that node and subgraph below it • Lemma: Given minimum cost tiling of all nodes in subgraph, we can find minimum cost tiling of the node by trying out all possible tiles matching the node • Therefore: start from leaves, work upward to top node

  17. Timing Cost Model • Idea: associate cost with each tile (say proportional to number of cycles to execute) • May not be a good metric on modern architectures • Total execution time is sum of costs of all tiles

  18. Dynamic Progamming • Traverse DAG recursively, and for each node n, record <t,c>, where – t is the best tile to use for subgraph rooted at n, – c is the total cost of tiling the subgraph rooted at n if t is chosen. • To compute <t,c> for node n – Consider every tile t’ that matches rooted at n, and compute total cost c’ = cost of tile t’ + sum of the costs of tiling the subgraphs rooted at the leaves of t’ (which costs can be computed recursively and memoized) – Store lowest-cost tile t’ and its total cost c’ • To emit code, traverse least-cost tiles recursively and emit code in postorder

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