1 CS 201 Compiler Construction Lecture 5 Code Optimizations: Copy Propagation & Elimination

2 Global Code Optimizations –Copy Propagation & Elimination: copy assignments are eliminated by replacing lhs variable with rhs variable. –Constant Folding & Propagation: constant assignments are exploited by substituting constant values for variables; if all operands of an expression are found to be constants, the expression can be computed at compile time. –Strength Reduction: replaces expensive operations with cheaper ones – multiplaction  addition; exponentiation  multiplication.

3 Global Code Optimizations –Partial Redundancy Elimination: eliminating repeated evaluation of the same expression. Loop Invariant Code Motion (full redundancy) Common Sub-Expression Elimination (full redundancy) The idea applies to expressions, loads, and even conditional branches. –Partial Dead Code Elimination: avoiding execution of statements whose results are not used. Dead Code Elimination The idea applies to expressions and stores.

4 Copy Propagation & Elimination 1. Uses of A replaced by uses of B. 2. A=B is eliminated because no more uses of A are left.

Contd.. Conditions under which optimization can be performed: Copy A=B is the only definition of A that reaches each use of A in def-use chain of A=B, i.e. no definition of A is encountered along the way. There is no definition of B on any path from d to any use u including paths through u that do not pass through d again. 5

Data Flow Equations 6 GEN[B]: Copies in B that reach the end of the block, i.e., no redefinitions of variables used in the copy statement. KILL[B]: Copies not in B whose variables (lhs or rhs) are defined in B. IN[B]: Copies that reach B’s entry. OUT[B]: Copies that reach B’s exit.

Data Flow Analysis The analysis propagates copies such that a copy reaches its use only if it can be propagated to the use. However, the copy can only be eliminated if it can be propagated to all of its uses. 7

Code Transformation Algorithm for each copy S: X=Y do OK = true for each use u on def-use(X,S) do if (s is in IN[B] where B contains a use of X) and (there is no redinifition of X or Y in B prior to u) then /* can propagate */ else OK = false endif /* cannot propagate */ endfor if Ok then replace all uses u of X in def-use(X,S) by use of Y; remove S endif endfor 8

9 Example Eliminated: D=A Not Eliminated: A=B Y=D W=A A=B X=A+2 W=A D=A A=3*M Y=D Z=D+2 W=D+3 Assume W,A,X,Y,Z Are live A=B X=B+2 A=3*M Y=B Z=B+2 W=B+3 W=B