1. CS 614: Theory and Construction of Compilers Lecture 17 Fall 2003 Department of Computer Science University of Alabama Joel Jones

2. Lecture 17©2003 Joel Jones2 Overview Lattices and Flow Functions Taxonomy of DataFlow Problems and Solution Methods Iterative Data-Flow Analysis Reading for Next Time

3. Lecture 17©2003 Joel Jones3 Lattices and Flow Functions Lattice – an algebraic structure that has associated with it elements and functions that map from one element of the lattice to the other. (these are necessary but not sufficient conditions).

4. Lecture 17©2003 Joel Jones4 Lattice Preliminaries See handout

5. Lecture 17©2003 Joel Jones5 Lattice properties A lattice consists of a set of values and two operations called meet and join Meet – forms greatest lower bound Join - forms least upper bound Properties of meet and join See handout

6. Lecture 17©2003 Joel Jones6 Properties of Common Lattices in Compilers Elements are bit vectors Meet and Join are bit-wise and and or, respectively Bottom element is all zeros and Top element is all ones Pair Up: What would the lattice for booleans look like?, factors of 12 ordered by divisibility?

7. Lecture 17©2003 Joel Jones7 Taxonomy of Data-Flow Problems and Solution Methods How characterize? Information provided Relational or independent Types of lattices, meanings, and functions Direction: forward, backward, both

8. Lecture 17©2003 Joel Jones8 Data-flow Problems Reaching DefinitionsIbit-vectorFWhich definitions reach which program points Available ExpressionsIbit-vectorFWhich expressions reach which program points Live VariablesIbit-vectorBWhich variables have a use between program point and exit Upwards Exposed Uses Ibit-vectorBWhat use of variables at program point are reached by which definitions Copy-propagationIbit-vectorFWhich program points a copy expression reaches (x  y) Constant-propagationIICP n F Which constant assignments (x  const) reach which points with same constant value Partial-redundancyIbit-vectorBiWhich computations are performed >1 times without modification

9. Lecture 17©2003 Joel Jones9 Iterative Data-Flow Analysis See handout Worklist_Iterate(N:set of Node; entry:Node, F: Node x L  L, dfin: Node  L, init: L) dfin(entry) := init; Worklist: set of Node := N - {entry} for each B: Node  N do dfin(B) := top od repeat B :=   ; Worklist -= {B}; totaleffect := top for each P  Pred(B) do effect := F(P, dfin(P)) totaleffect meetAssign effect od if dfin(B) ≠ totaleffect then dfin(B) := totaleffect; Worklist  Succ(B) fi Until Worklist = ø end

10. Lecture 17©2003 Joel Jones10 Readings for Next Time Sections 8.2–8.4 of the textbook