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CS 201 Compiler Construction. Lecture 9 Static Single Assignment Form. Program Representations. Why develop Advanced Program Representations? To develop faster algorithms To develop more powerful algorithms Superior representation for Data Flow Static Single Assignment Form (SSA Form)
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CS 201Compiler Construction Lecture 9 Static Single Assignment Form
Program Representations Why develop Advanced Program Representations? • To develop faster algorithms • To develop more powerful algorithms Superior representation for Data Flow Static Single Assignment Form (SSA Form) superior to def-use chains Superior representation for Control Flow Control Dependence Graph superior to control flow graph
SSA-Form A program in SSA-form satisfies the following two properties: • A use of a variable is reached by exactly one definition of that variable. • The program is augmented with ϕ–nodes that distinguish values of variables transmitted on distinct incoming control flow edges.
Example K11 L11 Repeat K2ϕ(K1,K5) L2ϕ(L1,L6) if (P) then if (Q) then L32 else L43 L5ϕ(L3,L4) K3K2+1 else K4K2+2 K5ϕ(K3,K4) L6ϕ(L2,L5) Until (T) K 1 L 1 Repeat if (P) then if (Q) then L2 else L3 KK+1 else KK+2 Until (T)
SSA-Form Observations: • SSA-form has def-use information textually embedded in it. Given a use, we know where the definition comes from. • SSA-form is more compact representation of def-use chains. • Def-use chains: #defs x #uses – O(n2) • SSA-form: 2 x #defs or #uses – O(n)
Constructing SSA-Form Step 1: Introduce functions at certain points in the program -- v ϕ (v,v,….) where of operands equals number of control predecessors and ith operand corresponds to ith predecessor.
Contd.. Step 2: Each variable v is given several new names v1, v2, …. Such that every name appears exactly once on the left hand side of an assignment.
Step 1: Introducing ϕ-functions Node Z needs a ϕ-function for variable V if Z is the first node common to two non-null paths that originate at two different nodes each containing: an assignment to V; or a ϕ-function for V.
Step 1 Contd.. Definition: X strictly dominates Y ≅ X dominates Y & X != Y. Definition: Immediate dominator of a node is its closest strict dominator. Notation: X = idom(Y). Definition: Dominance Frontier DF(X) = {Y: there exists P εpred(Y) such that X dominates P & X does not strictly dominate Y} ϕ-functions are placed at nodes in DF nodes of nodes with assignments.
Step 1 Contd.. Y ε DF(X) Strict Domination Does Not Strictly Domination Dominate
Step 1 Contd.. Observation: if Y εDF(X) then there may or may not be a direct edge from X to Y.
Step 1 Contd.. Computing Dominance Frontier: for each Y εsucc(X) do if idom(Y) != X then DF(X) = DF(X) U {Y} for each Z εChidren(X) in the dominator tree do for each Y εDF(Z) do if idom(Y) != X then DF(X) = DF(X) U {Y} Compute bottom-up order According to dominator tree
Step 1 Contd.. Dominator Tree
Step 1 Contd.. Dominance Frontier of a Set of Nodes S DF(S) = DF(X) Iterated Dominance Frontier DF+(S): DF1 = DF(S) DFi+1 = DF(S U DFi) S – set of nodes which assign to variable V DF+(S) – set of nodes including those where ϕ-functions must be placed.
Step 2: Rename the Variables Step 2: For each variable v rename its left hand side occurrences as v1, v2, …. Perform reaching definition analysis to identify names to use in the right hand side occurrences of v.