Advanced Compilers CMPSCI 710 Spring 2003 Using SSA

Advanced Compilers CMPSCI 710 Spring 2003 Using SSA form Emery Berger University of Massachusetts, Amherst UNIVERSITY OF MASSACHUSETTS, AMHERST • DEPARTMENT OF COMPUTER SCIENCE

Topics n Last time n n Computing SSA form This time n Optimizations using SSA form n n Constant propagation & dead code elimination Loop invariant code motion UNIVERSITY OF MASSACHUSETTS, AMHERST • DEPARTMENT OF COMPUTER SCIENCE 2

Constant Propagation n Lattice for integer addition, multiplication, mod, etc. > false … -1 0 1 … true ? UNIVERSITY OF MASSACHUSETTS, AMHERST • DEPARTMENT OF COMPUTER SCIENCE 3

Boolean Lattices, AND n meet functions example: true AND ? , false AND > UNIVERSITY OF MASSACHUSETTS, AMHERST • DEPARTMENT OF COMPUTER SCIENCE 4

Boolean Lattices, OR n meet functions example: true OR ? , false OR > UNIVERSITY OF MASSACHUSETTS, AMHERST • DEPARTMENT OF COMPUTER SCIENCE 5

Lattice for -Nodes n To propagate constants: if constant appears in conditional Ø Insert assignment on true branch UNIVERSITY OF MASSACHUSETTS, AMHERST • DEPARTMENT OF COMPUTER SCIENCE 6

Constant Propagation Using SSA Form n n Initialize all expressions to > Two work lists: n CFG edges = (entry, x) n n n x = first reachable node SSA edges = Pick edge from either list until empty n n Propagate constants when visiting either edge When we visit a node: n n -node: meet lattice values others: add SSA successors, CFG successors UNIVERSITY OF MASSACHUSETTS, AMHERST • DEPARTMENT OF COMPUTER SCIENCE 7

Sparse Conditional Constant Propagation Example entry a 1 Ã 2 B 1 b 1 Ã 3 B 2 n if a 1 < b 1 B 3 n Initialize all expressions to > Two work lists: n B 4 c 1 Ã 4 c 2 Ã 5 B 5 n n Pick edge from either list until empty n c 3 Ã 6(c 1, c 2) B 6 exit CFG edges = (entry, x) SSA edges = n Propagate constants when visiting either edge When we visit a node: n n -node: meet lattice values others: add SSA successors, CFG successors UNIVERSITY OF MASSACHUSETTS, AMHERST • DEPARTMENT OF COMPUTER SCIENCE 8

Loop Optimizations n Why optimize loops? Ø Loops = frequently-accessed code n n Ø n regular patterns – can simplify optimizations rule of thumb: loop bodies execute 10 depth times optimizations pay off But why do we care if we aren’t using FORTRAN? n Loops aren’t just over arrays! n n Pointer-based data structures Text processing… UNIVERSITY OF MASSACHUSETTS, AMHERST • DEPARTMENT OF COMPUTER SCIENCE 9

Loop Invariant Code Motion n Classical loop optimization n avoids unnecessary computation while (z < 1000) t = a + b z += t t=a+b while (z < 1000) z += t UNIVERSITY OF MASSACHUSETTS, AMHERST • DEPARTMENT OF COMPUTER SCIENCE 10

Removing Loop Invariant Code n n Build SSA graph Simple test: n n no operands in statement are defined by node or have definition inside loop if match: n n assign computation new temporary name and move to loop pre-header, and add assignment to temp e. g. , l = r 1 op r 2 becomes t 1 = r 1 op r 2; l = t 1 UNIVERSITY OF MASSACHUSETTS, AMHERST • DEPARTMENT OF COMPUTER SCIENCE 11

Loop Invariant Code Motion Example n a 1 Ã 2 b 1 Ã 3 n Build SSA graph Simple test: n n no operands in statement are defined by node or have definition inside loop if match: n n assign computation new temporary name and move to loop pre-header, and add assignment to temp e. g. , l = r 1 op r 2 becomes t 1 = r 1 op r 2; l = t 1 x = a 1 + b 1 y=x+y UNIVERSITY OF MASSACHUSETTS, AMHERST • DEPARTMENT OF COMPUTER SCIENCE 12

Finding More Invariants n n Build SSA graph If operands point to definition inside loop and definition is function of invariants (recursively) Ø replace as before UNIVERSITY OF MASSACHUSETTS, AMHERST • DEPARTMENT OF COMPUTER SCIENCE 13

Loop Invariant Code Motion Example II a 1 Ã 2 xÃq b 1 Ã 3 yÃr n n Build SSA graph If operands point to definition inside loop and definition is function of invariants (recursively) n replace as before x = a 1 + b 1 y=x+y z = x + a 1 UNIVERSITY OF MASSACHUSETTS, AMHERST • DEPARTMENT OF COMPUTER SCIENCE 14

Loop Induction Variables n Loop induction variable: increases or decreases by constant amount inside loop n n e. g. , for (i = 0; i < 100; i++) Opportunity for: n strength reduction n n e. g. , j = 2 * i becomes j = j + 2 identifying stride of accesses for prefetching n e. g. : array accesses UNIVERSITY OF MASSACHUSETTS, AMHERST • DEPARTMENT OF COMPUTER SCIENCE 15

Easy Detection of Loop Induction Variables n Pattern match & check: n n n Search for “i = i + b” in loop i is induction variable if no other assignment to i in loop Pros & Cons: Easy! - Does not catch all loop induction variables e. g. , “i = a * c + 2” + UNIVERSITY OF MASSACHUSETTS, AMHERST • DEPARTMENT OF COMPUTER SCIENCE 16

Next Time n n n Finding loop induction variables Strength reduction Read ACDI ch. 12, pp 333 -342 Project Design documents due March 13: project presentations n n 5 -10 minutes 3 slides UNIVERSITY OF MASSACHUSETTS, AMHERST • DEPARTMENT OF COMPUTER SCIENCE 17

Taxonomy of Induction Variables n basic induction variable: n n only definition in loop is assignment j : = j § c, where c is loop invariant mutual induction variable: n definition is linear function of other induction variable i ‘: n n n i = c 1 * i‘ § c 2 i = i‘ / c 1 § c 2 family of basic induction variable j = set of induction variables i such that i always assigned linear function of j UNIVERSITY OF MASSACHUSETTS, AMHERST • DEPARTMENT OF COMPUTER SCIENCE 18