Tiling Examples for X86 ISA

Tiling Examples for X86 ISASlides Selected from Radu Rugina’sCS412/413 Lecture on InstructionSelection at Cornell

Instruction Selection• Translate 3‐address code to DAG• Cover DAG with tiles– Disjoint i set of tiles cover DAG– Algorithm:• Greedy maximal munch• Dynamic programming

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

Example• a = a + i where a is a local variable and i is aa = a + i where a is a local variable and i is aparameter passed in from a caller

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

More Tile Examples

Conditional Branches

Load Effective Address

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

Greedy Tiling

ADD Expression and Statement

Designing Tiles• Only add tiles that are useful to compiler• Many instructions will be too hard to useeffectively or will offer no advantage• Need tiles for all single‐node trees toguarantee that every tree can be tiled

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

Matching Tiles

Finding globally optimum tiling• Goal: find minimum total cost tiling of DAG• Algorithm: for every node, find minimum totalcost tiling of that node and subgraph below it• Lemma: Given minimum cost tiling of allnodes in subgraph, we can find minimum costtiling of the node by trying out all possibletiles matching the node• Therefore: start from leaves, work upward totop node

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

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 ischosen.• To compute for node n– Consider every tile t’ that matches rooted at n, andcompute total cost c’ = cost of tile t’ + sum of the costs oftiling the subgraphs rooted at the leaves of t’ (which costscan be computed recursively and memoized)–Store lowest‐cost tile t’ and its total cost c’• To emit code, traverse least‐cost tiles recursively and emitcode in postorder