Slides on Dataflow Analysis - Fall 2005 | EECS 583, Study notes of Electrical and Electronics Engineering

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Reading Material^ Y^ Today’s class^ »^ Compilers: Principles, Techniques, and Tools

A. Aho, R. Sethi, and J. Ullman, Addison-Wesley, 1988. (Sections: 10.5, 10.6, 10.9, 10.10) Y Material for the next lecture » “Analysis Techniques for Predicated Code”, R. Johnson and M. Schlansker, MICRO-29, 1996

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Dataflow Analysis Introduction

Dataflow analysis^ – Collection of information that summarizes the creation/destruction of r1 = r2 + r3 values in a program. Used to identify legal r6 = r4 – r5 optimization opportunities.Pick an arbitrary point in the program^ Which VRs contain usefuldata values? (liveness or upward r4 = 4exposed uses) r6 = 8Which definitions may reachthis point? (reaching defns)Which definitions are guaranteed r6 = r2 + r3to reach this point? (available defns) r7 = r4 – r5Which uses below are exposed?(downward exposed uses)

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Live Variable (Liveness) Analysis^ Y^ Defn: For each point p in a program and each variable y,determine whether y can be used before being redefinedstarting at p^ Y^ Algorithm sketch^ »^ For each BB, y is live if it is used before defined in the BB or it islive leaving the block^ »^ Backward dataflow analysis as propagation occurs from usesupwards to defs^ Y^ 4 sets^ »^ GEN = set of external variables consumed in the BB^ »^ KILL = set of external variable uses killed by the BB^ y^ equivalent to set of variables defined by the BB^ »^ IN = set of variables that are live at the entry point of a BB^ »^ OUT = set of variables that are live at the exit point of a BB

• EECS 583 – Class 7 Dataflow Analysis University of Michigan January 31,
• Example - GEN/KILL Computation BB1 r1 = MEM[r2+0] r2 = r2 + 1 r3 = r1 * r
• GEN(1) = r2,r4 KILL(1) = r1,r
• GEN(2) = r1,r5 r1 = r1 + 5 r3 = r5 – r1 r7 = r3 *
• BB3 r2 = 0 r7 = 23 r1 =
• KILL(2) = r3,r7 BB
• GEN(3) = 0 KILL(3) = r1, r2, r
• BB4 r3 = r3 + r7 GEN(4.3) = r3,r7,r8 r1 = r3 – r8 r3 = r1 *
• KILL(4.3) = r1 GEN(4.2) = r3,r8 KILL(4.2) = r1 GEN(4.1) = r1 KILL(4.1) = r

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Compute IN/OUT Sets for all BBs^ initialize IN(X) to 0 for all basic blocks X^ change = 1^ while^ (change) do^ change = 0^ for^ each basic block in procedure, X, do^ old_IN = IN(X)^ OUT(X) = Union(IN(Y)) for all successors Y of X^ IN(X) = GEN(X) + (OUT(X) – KILL(X))^ if^ (old_IN != IN(X)) then^ change = 1^ endif^ endfor^ endfor

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Liveness in Elcor^ Y^ Calculating the info^ »^ delete_local_analysis_info_for_all_hbs_bbs(Region);^ »^ create_local_analysis_info_for_all_hbs_bbs(Region);^ y^ Analysis/pred_analysis.cpp^ y^ Calculates intra-BB info (i.e., GEN/KILL)^ »^ el_flow_compute_liveness(Region, ANALYZE_ALLREG);^ y^ Analysis/flow_analysis_solver.cpp^ y^ Applies meet/transfer functions to compute IN/OUT^ »^ Generally liveness always done on a Procedure^ Y^ Accessing the info^ »^ Stored as an attribute on Control edges from branches^ »^ Liveness_info live = get_liveness_info(Edge*);^ »^ Liveness_info^ Æ

List » Iterate over it, check for membership, etc.

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Class Problem

Compute liveness^ Calculate GEN/KILL for each BB r1 = 3^ Calculate IN/OUT for each BB r2 = r3 r3 = r r1 = r1 + 1 r7 = r1 * r2 r4 = r4 + 1 r4 = r3 + r2^ r8 = 8^ r9 = r7 + r

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Rdefs (2)^ Y^ Algorithm sketch^ » Forward dataflow analysis as propagation occurs fromdefs downwards^ » (Liveness was backwards!)^ Y^ 4 sets^ » GEN = set of definitions generated in the BB^ » KILL = set of definitions killed in the BB^ » IN = set of definitions reaching the BB entry^ » OUT = set of definitions reaching the BB exit

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Compute Rdef GEN/KILL Sets for each BB^ GEN = set of definitions created by an operation^ KILL = set of definitions destroyed by an operation^ - Assume each operation only has 1 destination for simplicity^ so just keep track of “ops”..^ for^ each basic block in the procedure, X, do^ GEN(X) = 0^ KILL(X) = 0^ for^ each operation in sequential order in X, op, do^ for^ each destination operand of op, dest, do^ G = op^ K = {all ops which define dest – op}^ GEN(X) = G + (GEN(X) – K)^ KILL(X) = K + (KILL(X) – G)^ endfor^ endfor^ endfor

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Compute Rdef IN/OUT Sets for all BBs^ IN = set of definitions reaching the entry of BB^ OUT = set of definitions leaving BB^ initialize IN(X) = 0 for all basic blocks X^ initialize OUT(X) = GEN(X) for all basic blocks X^ change = 1^ while^ (change) do^ change = 0^ for^ each basic block in procedure, X, do^ old_OUT = OUT(X)^ IN(X) = Union(OUT(Y)) for all predecessors Y of X^ OUT(X) = GEN(X) + (IN(X) – KILL(X))^ if^ (old_OUT != OUT(X)) then^ change = 1^ endif^ endfor^ endfor

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Example Rdef IN/OUT Calculation^ r1 = MEM[r2+0]^ r2 = r2 + 1^ r3 = r1 * r4^ r1 = r1 + 5^ r3 = r5 – r1^ r7 = r3 * 2

r2 = 0 r7 = 23 r1 = 4 r8 = r7 + 5 r1 = r3 – r8 r3 = r1 * 2

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DU/UD Chains^ Y^ Convenient way to access/use reaching defs info^ Y^ Def-Use chains^ » Given a def, what are all the possible consumers of theoperand produced^ » Maybe consumer^ Y^ Use-Def chains^ » Given a use, what are all the possible producers of theoperand consumed^ » Maybe producer

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Example – DU/UD Chains^ r1 = 3^ r2 = r3^ r3 = r4^ r1 = r1 + 1^ r7 = r1 * r2^ r4 = r4 + 1^

r4 = r3 r8 = 8 r9 = r7 + r