Advanced Control Flow Analysis for Optimizing Compilers

1. Optimizing CompilersCISC 673Spring 2009Control Flow John Cavazos University of Delaware

2. Control-Flow Analysis • Motivating example: identifying loops • majority of runtime • focus optimization on loop bodies! • remove redundant code, replace expensive operations ) speed up program • Finding loops: • easy… i = 1; j = 1; k = 1; A1: if i > 1000 goto L1; A2: if j > 1000 goto L2; A3: if k > 1000 goto L3; do something k = k + 1; goto A3; L3: j = j + 1; goto A2; L2: i = i + 1; goto A1; L1: halt for i = 1 to 1000 for j = 1 to 1000 for k = 1 to 1000 do something • or harder(GOTOs)

3. Steps to Finding Loops • Identify basic blocks • Build control-flow graph • Analyze CFG to find loops

4. Control-Flow Graphs • Control-flow graph: • Node: an instruction or sequence of instructions (a basic block) • Two instructions i, j in same basic blockiff execution of i guarantees execution of j • Directed edge: potential flow of control • Distinguished start node Entry • First instruction in program

5. Identifying Basic Blocks • Input: sequence of instructions instr(i) • Identify leaders:first instruction of basic block • Iterate: add subsequent instructions to basic block until we reach another leader

6. Basic Block Partition Algorithm leaders = instr(1) // first instruction for i = 1 to |n| // iterate thru all instrs if instr(i) is a branch leaders = leaders ∪ targets of instr(i) leaders = leaders ∪ instr(i+1) // instr after branch worklist = leaders While worklist notempty x = first instruction in worklist worklist = worklist – {x} block(x) = {x} for (i = x + 1; i <= |n| && i notin leaders; i++) block(x) = block(x) ∪ {i}

7. Class Example leaders = instr(1) for i = 1 to |n| if instr(i) is a branch leaders = leaders ∪ targets of instr(i) leaders = leaders ∪ instr(i+1) worklist = leaders While worklist notempty x = first instruction in worklist worklist = worklist – {x} block(x) = {x} for (i = x + 1; i <= |n| && i notin leaders; i++) block(x) = block(x) ∪ {i} A = 4 t1 = A * B L1: t2 = t1/C if t2 < W goto L2 M = t1 * k t3 = M + I L2: H = I M = t3 – H if t3 >= 0 goto L4 L3: goto L1 L4: goto L3

8. Basic Block Example • A = 4 • t1 = A * B • L1: t2 = t1/C • if t2 < W goto L2 • M = t1 * k • t3 = M + I • L2: H = I • M = t3 – H • if t3 >= 0 goto L4 • L3: goto L1 • L4: goto L3 Leaders Basic blocks

9. Control-Flow Edges • Basic blocks = nodes • Edges: • Add directed edge between B1 and B2 if: • BRANCH from last statement of B1 to first statement of B2 (B2 is a leader), or • B2 immediately follows B1 in program order and B1 does NOT end with unconditional branch (goto)

10. Control-Flow Edge Algorithm Input: block(i), sequence of basic blocks Output: CFG where nodes are basic blocks for i = 1 to the number of blocks x = last instruction of block(i) if instr(x) is a branch for each target y of instr(x), create edge block i to block y if instr(x) is not unconditional branch, create edge block i to block i+1

11. CFG Edge Example A • A = 4 • t1 = A * B • L1: t2 = t1/C • if t2 < W goto L2 • M = t1 * k • t3 = M + I • L2: H = I • M = t3 – H • if t3 >= 0 goto L4 • L3: goto L1 • L4: goto L3 Leaders B Basic blocks C D E F

12. Steps to Finding Loops • Identify basic blocks • Build control-flow graph • Analyze CFG to find loops • Spanning trees, depth-first spanning trees • Reducibility • Dominators • Dominator tree • Strongly-connected components

13. Spanning Tree • Build a tree containing every node and some edges from CFG A procedure Span (v) for w in Succ(v) if not InTree(w) add w, v→ w to ST InTree(w) = true Span(w) for v in V do inTree = false InTree(root) = true Span(root) B C D E F

14. CFG Edge Classification Tree edge: in CFG & ST Advancing edge: (v,w) not tree edge but w is descendant of v in ST Back edge: (v,w): v=w or w is proper ancestor of v in ST Cross edge: (v,w): w neither ancestor nor descendant of v in ST A B C loop D E F

15. Depth-first spanning tree procedure DFST (v) pre(v) = vnum++ InStack(v) = true for w in Succ(v) if not InTree(w) add v→w to TreeEdges InTree(w) = true DFST(w) else if pre(v) < pre(w) add v→w to AdvancingEdges else if InStack(w) add v→w to BackEdges else add v→w to CrossEdges InStack(v) = false for v in V do inTree(v) = false vnum = 0 InTree(root) DFST(root) A 1 B 2 C 3 D 4 E F 5 6

16. Class Problem: Identify Edges procedure DFST (v) pre(v) = vnum++ InStack(v) = true for w in Succ(v) if not InTree(w) add v→w to TreeEdges InTree(w) = true DFST(w) else if pre(v) < pre(w) add v→w to AdvancingEdges else if InStack(w) add v→w to BackEdges else add v→w to CrossEdges InStack(v) = false for v in V do inTree(v) = false vnum = 0 InTree(root) DFST(root)

17. Compiler Optimizations I • Unrolling and other loop optimizations for improving instruction level parallelism (ILP) IDEA 1: Predict Best Unrolling Factor IDEA 2: Implement Different Loop Opt Reversal, Interchange, Fusion, Fission

18. Compiler Optimizations II • Policies for method inlining Question 1: What Method Characteristics are most important for Inlining? Question 2: What is the impact of Inlining to Register Allocation?

19. Compiler Optimizations III • Escape analysis IDEA 1 : Move object access that do not “escape” method into registers. IDEA 2: Allocate objects that do not “escape” on the stack.

20. Compiler Optimizations IV • Improving virtual memory behavior IDEA 1: Performance study of optimizations on virtual memory and/or parts of memory hierarchy (e.g., L3 cache). Use tool to analyze memory behavior.

21. Compiler Optimizations V • Class analysis for safe object inlining • Policies for object inlining IDEA 1: Implement object inlining optimization.

22. Compiler Optimizations VI • Field Reordering • Graph Coloring RA • Porting of old code • Instruction Scheduling for X86 • Porting PowerPC version to X86 • Autotuning Java applications • Interesting!

23. Next Time • Reducibility • Dominance • Wikipedia: Dominator (graph_theory) • Some Dataflow • T.J. Marlowe and B.G. Ryder Properties of Data Flow Frameworks, pp. 121-163, ACTA Informatica, 28, 1990.