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# 06 - Program Representation Dominator Relationships Last...

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Program Representation Last Time Live variable analysis Constant propagation leads us to SSA and how to connect uses and def Today Finish constants Goal: understand control flow more deeply to build SSA Dominator relationships DOM, IDOM, DOM - 1 , DOM!, post-dominators Control Dependence CS 380C Lecture 6 1 Program Representation Dominator Relationships Dominators x dominates y , x DOM y , in a CFG if paths from Entry to y include x . DOM ( v ) = the set of all vertices that dominate v . All vertices dominate themselves, v DOM ( v ) . Entry dominates every vertex in the graph, v Entry DOM ( v ) . DOM is reflexive, antisymmetric, and transitive. Strict Dominators DOM! ( v ) = DOM ( v ) - { v } , strictly dominates v antisymmetric and transitive Immediate Dominator IDOM ( v ) = the closest, strict dominator of v . d IDOM v if d DOM! v and ( w w DOM! v ) [ w DOM d ] antisymmetric CS 380C Lecture 6 2 Program Representation

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Dominator Example B C D E F A - entry G - exit v DOM ( v ) DOM! (Strict) IDOM(v) A B C D E F G CS 380C Lecture 6 3
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