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Global Common Subexpression Elimination

Global Common Subexpression Elimination. Available Expression Analysis Eliminating CSEs Dragon : pp. 627- 631, 633 - 636. add t1 = x, y add t2 = c, d. ldc t3 = 0 cpy x = t3 add t4 = x, y cpy m = t4. sub t5 = a, b ldc t6 = -1 cpy c = t6. sub t7 = a, b cpy m = t7 add t8 = x, y

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Global Common Subexpression Elimination

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  1. Global Common Subexpression Elimination Available Expression Analysis Eliminating CSEs Dragon : pp. 627- 631, 633 - 636

  2. add t1 = x, y add t2 = c, d ldc t3 = 0 cpy x = t3 add t4 = x, y cpy m = t4 sub t5 = a, b ldc t6 = -1 cpy c = t6 sub t7 = a, b cpy m = t7 add t8 = x, y add t9 = c, d Global Common Subexpression

  3. Availability of an expression E at point P • Definition : Along every path to P in the flow graph : • E must be evaluated at least once • No variables in E redefined after the last evaluation • Observations : E may have different values on different paths : variables holding value may have been overwritten

  4. Formulating the Problem • Domain : A bit vector, a bit for each lexically unique expression in the program • Forward or Backward ? • Lattice elements ? • Meet operator ? (check commutative, idempotent, associative) • Partial ordering • Top ? Bottom ? • Initialization for iterative algorithm

  5. Transfer Functions • Can use the same equation as reaching definitions • out[b] = gen[b] ∪(in[b] - kill[b]) • Start with the transfer function for a single instruction • When does the instruction generate an expression ? • When does it kill an expression ? • Calculate transfer function for complete basic blocks • Compose individual instruction transfer functions

  6. in1 out1 = gen1 ∪ (in1 - kill1) out2 = gen2 ∪ (in2 - kill2) Composing Transfer Functions Derive the transfer function for an entire block • Since out1 = in2, we can simplify : • out2 = gen2 ∪ ((gen1 ∪ (in1 - kill1)) - kill2) out2 = gen2 ∪ (gen1 - kill2) ∪ (in1 - (kill1 ∪ kill2)) • Result • gen = gen2 ∪ (gen1 - kill2) • kill = kill1 ∪ kill2

  7. Eliminating CSEs • Available expressions (across basic blocks) • Provide the set of expressions available at the start of a block • Value numbering (within basic block) • Initialize Value table with available expressions • If CSE is an “available expression”, transform the code • Original target register may be : • a temporary register • overwritten • different from the variables on other paths • A solution : Copy the expression to a new variable at each evaluation reaching the redundant use

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