Data Flow Analysis 2 - Lecture Slides | CMSC 430, Study notes of Computer Science

Download Data Flow Analysis 2 - Lecture Slides | CMSC 430 and more Study notes Computer Science in PDF only on Docsity! 1 Dataflow Analysis 2 CS430 2 Data-flow Analysis • Algorithm 1. Find basic blocks, build CFG 2. Find propagation functions for basic blocks 3. Propagate information around CFG 4. Propagate information into basic blocks • Example Code Control flow graph (CFG) CS430 3 Live Variables LV(B) = ∪ ( GEN(Bi) ∪ [ LV(Bi) - KILL(Bi) ] ) Bi ε SUCC(B) GEN(Bi) : All uses in Bi that are not killed by preceding definitions in Bi KILL(Bi): All uses of variables x that are defined in Bi A use of a variable x is a statement where the value of x may be read. A use of variable x is killed if x is reassigned a value; the “killing” definition must occur. CS430 4 Live Variables • Universe of facts? → All possible subsets of variables in the program • GEN and KILL sets for each basic block? → GEN = variables used in basic block AND not killed before reaching beginning of basic block → KILL = variables defined in basic block • Initial values of LV(B) before propagation starts? → All variables in the program
Assumes variable is live until proven otherwise
The conservative assumption CS430 5 Live Variables Example = x B2: B3: B4: B1: = x B4 B3 B2 B1 KILLGEN Basic Block LV(B) = ∪ ( GEN(Bi) ∪ [LV(Bi) - KILL(Bi) ] ) Bi ε SUCC(B) x = x = CS430 6 Available Expressions An expression e is defined if its value is computed. An expression e is killed if the values of any of its operands may have been changed. AVAIL(B) = ∩ ( GEN(Bi) ∪ [ AVAIL(Bi) - KILL(Bi) ] ) Bi ε PRED(B) GEN(Bi) : All definitions of expressions in Bi that are not subsequently killed in Bi KILL(Bi): All expressions with operand variables defined in Bi 2 CS430 7 Available Expressions • Universe of facts? → All possible subsets of expressions in the program • GEN and KILL sets for each basic block? → GEN = expressions defined in basic block AND operands not defined before reaching end of basic block → KILL = expressions whose operands are defined in basic block • Initial values of AVAIL(B) before propagation starts? → ∅
Assumes expression is not available until proven otherwise
The conservative assumption CS430 8 Available Expressions Example • Control flow graph • Solution • Local information CS430 9 Very Busy Expressions An expression e is defined if its value is used before any definition of its operands. An expression e is killed if the values of any of its operands may have been changed before it is used VBE(B) = ∩ ( GEN(Bi) ∪ [ VBE(Bi) - KILL(Bi) ] ) Bi ε SUCC(B) GEN(Bi) : All definitions of expressions in Bi that are used before they are killed in Bi KILL(Bi): All expressions with operand variables defined in Bi CS430 10 Very Busy Expressions • Universe of facts? → All possible subsets of expressions in the program • GEN and KILL sets for each basic block? → GEN = expressions used in basic block AND operands not defined before reaching beginning of basic block → KILL = expressions whose operands are defined in basic block • Initial values of VBE(B) before propagation starts? → ∅
Assumes expression is not busy until proven otherwise
The conservative assumption CS430 11 Very Busy Expressions Example = a+b B2: B3: B4: B1: b = B4 B3 B2 B1 KILLGEN Basic Block VBE(B) = ∩ ( GEN(Bi) ∪ [VBE(Bi) - KILL(Bi) ] ) Bi ε SUCC(B) = a+b a = CS430 12 Implementation Issues: Bit-vector Problems The set of facts (universe of facts) can often be expressed as finite subsets of a finite base set. Such sets can be represented as bit-vectors. Example: RD - { B1: a:=2, B2: c := d+2, B3: d := a-5 } B1:a B2:c B3:d B1:a, B2:c B1:a, B3:d B2:c, B3:d B1:a, B2:c, B3:d =