1. Tiling Examples for X86 ISA Slides Selected from Radu Ruginas 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, 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 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