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Computer Science 313 – Advanced Programming Topics

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Static Single Assignment Ignores local variables programmer wrote Programmers are stupid Creates lots of variables on its own Each variable is assigned exactly once (def) Variable use tied to definition at the assignment

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Examples of SSA Form a = 2; b = a + 1; a = 3; b = a + 1; a 1 = 2; b 1 = a 1 + 1; a 2 = 3; b 2 = a 2 + 1; if (…) { a = 2; } else { a = 3; } b = a + 1; if (…) { a 1 = 2; } else { a 2 = 3; } a 3 = Φ(a 1, a 2 ); b = a 3 + 1;

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Control Flow Graph Common technique showing program structure Visualizes different ways method can be run Also referred to as the flow of a program’s control Basic blocks are vertices in this graph Basic block is code that must be executed together Edges represent transfer of flow between blocks Normally result from start & end of loops or branches

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Example of a CFG a 1 = 2; b 1 = a 1 + 1; a 2 = 3; b 2 = a 2 + 1; if (b 2 > 20) { System.out.println(“Woot”); } else { System.err.print(“Doh”); foo(a 2 ); } b 3 = a 2 + b 2

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Example of a CFG a 1 = 2; b 1 = a 1 + 1; a 2 = 3; b 2 = a 2 + 1; if (b 2 > 20) System.err.print(“Woot”); System.err.print(“Doh”); foo(a 2 ); T F b 3 = a 2 + b 2 ;

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Ф Functions Are Fun! SSA could have problem with basic blocks What happens when variable defined in if & else Uses Ф function to merge variable definitions Ф function has one input per merged block Variables have exactly one definition with function Function does not really exist Keeps value from the basic block executed Keeps books properly balanced

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Examples of SSA Form a 1 = 2; b 1 = a 1 + 1; a 2 = 3; b 2 = a 2 + 1; if (b 2 > 20) b 3 = 21 foo(a 2 ); T F b 4 = Ф (b 3, b 2 ); b 5 = a 2 + b 4 ;

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Dominators X dominates Y if and only if X on all paths from method start to Y Used to help convert code to SSA form Excuse for explaining –trix suffix Domination both reflexive & transitive dom(Y) defines dominators of Y Set of definitions which reach a given block Will create need to add Ф for Y using dom(Y)

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Dominator Tree Example START a b c d END START CFG DT

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Dominator Tree Example START a b c d END START CFG DT a

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Dominator Tree Example START a b c d END START CFG DT a b c

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Dominator Tree Example START a b c d END START CFG DT a b c d

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Dominator Tree Example START a b c d END START CFG DT a b c d END

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Next Step for SSA Form Dominance frontier for node X in CFG Defines set of nodes such that each node Y in set X dominates predecessor of Y, but X does not dominate Y and X != Y

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DF Computation Algorithm to compute dominance frontier for (Vertex b : CFG.vertices()) if ( CFG.countInEdges( b ) ≥ 2) for (Vertex p : CFG.adjacentVertices( b )) runner p while ( runner != dominatorTree. parent (b)) // Add b to runner ’s dominance frontier runner dominatorTree. parent (b)

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DF Example START a b c d END START a d END b c CFG DT DF(c) = ?

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DF Example START a b c d END START a d END b c CFG DT DF(c) = {d} c dominates c, but not d

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DF(a) = {END} a dominates b,c,&d, but not END DF Example START a b c d END START a d END b c CFG DT DF(c) = {d}

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DF Computation Algorithm to compute dominance frontier for (Vertex b : CFG.vertices()) if ( CFG.countInEdges( b ) ≥ 2) for (Vertex p : CFG.adacentVertices( b )) runner p while ( runner != dominatorTree. parent (b)) // Add b to runner ’s dominance frontier runner dominatorTree. parent (b)

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Placing Φ Nodes If basic block, x, defines variable named a Need Φ function for a at start of all blocks where Block is in x ’s dominance frontier –or– In dominance frontier of block in x ’s dominance frontier Repeat algorithm however long as needed Must be computed iteratively

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For Next Class Lab #6 available on Angel Will start to look at how SSA can be used

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