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Really Basic Stuff

This technical report introduces key code optimization techniques including flow graphs, constant folding, global common subexpressions, and induction variables reduction.

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Really Basic Stuff

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  1. Really Basic Stuff Flow Graphs Constant Folding Global Common Subexpressions Induction Variables/Reduction in Strength

  2. Dawn of Code Optimization • A never-published Stanford technical report by Fran Allen in 1968. • Flow graphs of intermediate code. • Key things worth doing.

  3. Intermediate Code for (i=0; i<n; i++) A[i] = 1; • Intermediate code exposes optimizable constructs we cannot see at source-code level. • Make flow explicit by breaking into basic blocks = sequences of steps with entry at beginning, exit at end.

  4. i = 0 if i>=n goto … t1 = 8*i A[t1] = 1 i = i+1 Basic Blocks

  5. Induction Variables • x is an induction variable in a loop if it takes on a linear sequence of values each time through the loop. • Common case: loop index like i and computed array index like t1. • Eliminate “superfluous” induction variables. • Replace multiplication by addition (reduction in strength ).

  6. i = 0 if i>=n goto … t1 = 8*i A[t1] = 1 i = i+1 Example t1 = 0 n1 = 8*n if t1>=n1 goto … A[t1] = 1 t1 = t1+8

  7. Loop-Invariant Code Motion • Sometimes, a computation is done each time around a loop. • Move it before the loop to save n-1 computations. • Be careful: could n=0? I.e., the loop is typically executed 0 times.

  8. Example i = 0 i = 0 t1 = y+z if i>=n goto … if i>=n goto … t1 = y+z x = x+t1 i = i+1 x = x+t1 i = i+1

  9. Constant Folding • Sometimes a variable has a known constant value at a point. • If so, replacing the variable by the constant simplifies and speeds-up the code. • Easy within a basic block; harder across blocks.

  10. i = 0 n = 100 if i>=n goto … t1 = 8*i A[t1] = 1 i = i+1 Example t1 = 0 if t1>=800 goto … A[t1] = 1 t1 = t1+8

  11. Global Common Subexpressions • Suppose block B has a computation of x+y. • Suppose we are sure that when we reach this computation, we are sure to have: • Computed x+y, and • Not subsequently reassigned x or y. • Then we can hold the value of x+y and use it in B.

  12. a = x+y t = x+y a = t b = x+y t = x+y b = t c = x+y c = t Example

  13. t = x+y a = t t = x+y b = t c = t Example --- Even Better t = x+y a = t b = t t = x+y b = t c = t

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