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Constant Propagation

Constant Propagation. Harry Xu CS 142 (b) 02/19/2013. Dataflow Analysis. A static technique for gathering information about the possible set of values calculated at various points in a program ( wikipedia ) Widely used in modern compilers Performed on top of a control flow graph

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Constant Propagation

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  1. Constant Propagation Harry Xu CS 142 (b) 02/19/2013

  2. Dataflow Analysis • A static technique for gathering information about the possible set of values calculated at various points in a program (wikipedia) • Widely used in modern compilers • Performed on top of a control flow graph • Iterate over the statements of a function to solve dataflow equations • Liveness analysis is a type of dataflow analysis

  3. Constant Propagation • If the result of an expression is known at compile time, we do not need to execute it a = 123; b = a – 12; c = a + b; d = c * b + a; • a = 123; • b = 111; • c = 234; • d = 26097;

  4. How to Compute Values for Expressions • At each statement, maintain a set C of values for each variable • C is a singleton set for constant propagation • C contains either a constant value v, or a symbol ⊥(bottom), or a symbol ⊤ (top) • Meanings of the values • v: the variable must have this constant value during execution • ⊥:the initial (known) value of each variable • ⊤: the variable may have different values during execution

  5. Transfer Function and Join • Transfer function defines how to update dataflow facts at each statement • C[s: a = b + c] = valuea [s] • valuea [s] = {valueb[s] + valuec[s]} if they are both values {⊤} otherwise • Join operation defines what happens when different control flow paths merge • valuea[s] = join s1,s2 ∊prec(s)(valuea[s1], valuea[s2] ) join s1,s2 ∊prec(s)(valueb[s1], valueb[s2] ) = valueb[s1] if valueb[s1] = valueb[s2] = {⊤} otherwise

  6. Constant Propagation Analysis • C1 = {⊥} • C2 = {⊥} • C3 = {⊥} • C4 = {⊥} • C5 = {⊥} • C6 = {⊥} • C7 = {⊥} • C8 = {⊥} • C9 = {⊥} • C10 = {⊥} L1: a = 3; L2: b = 5; L3: d = 4; L4: x = 100; L5: if a > b then L6: c = a + b; L7: d = 2; L8: endif L9: c = 4; L10:return b * d + c; C[s: a = b + c] = valuea [s] valueb[s] = join s1,s2 ∊prec(s)(valueb[s1], valueb[s2] ) • Worklist = {L1}

  7. Constant Propagation Analysis • C1 = {3} • C2 = {⊥} • C3 = {⊥} • C4 = {⊥} • C5 = {⊥} • C6 = {⊥} • C7 = {⊥} • C8 = {⊥} • C9 = {⊥} • C10 = {⊥} L1: a = 3; L2: b = 5; L3: d = 4; L4: x = 100; L5: if a > b then L6: c = a + b; L7: d = 2; L8: endif L9: c = 4; L10:return b * d + c; • valuea[L1]= {3} • Valueb[L1]= {⊥} • Valued[L1]= {⊥} • valuex[L1] = {⊥} • valuec[L1] = {⊥} • Worklist = {L2} C[s: a = b + c] = valuea [s] valueb[s] = join s1,s2 ∊prec(s)(valueb[s1], valueb[s2] )

  8. Constant Propagation Analysis • C1 = {3} • C2 = {5} • C3 = {⊥} • C4 = {⊥} • C5 = {⊥} • C6 = {⊥} • C7 = {⊥} • C8 = {⊥} • C9 = {⊥} • C10 = {⊥} L1: a = 3; L2: b = 5; L3: d = 4; L4: x = 100; L5: if a > b then L6: c = a + b; L7: d = 2; L8: endif L9: c = 4; L10:return b * d + c; • valuea[L2]= {3} • valueb[L2]= {5} • valued[L2]= {⊥} • valuex[L2]= {⊥} • valuec[L2]= {⊥} • Worklist = {L3} C[s: a = b + c] = valuea [s] valueb[s] = join s1,s2 ∊prec(s)(valueb[s1], valueb[s2] )

  9. Constant Propagation Analysis • C1 = {3} • C2 = {5} • C3 = {4} • C4 = {⊥} • C5 = {⊥} • C6 = {⊥} • C7 = {⊥} • C8 = {⊥} • C9 = {⊥} • C10 = {⊥} L1: a = 3; L2: b = 5; L3: d = 4; L4: x = 100; L5: if a > b then L6: c = a + b; L7: d = 2; L8: endif L9: c = 4; L10:return b * d + c; • valuea[L3] = {3} • valueb[L3] = {5} • valued[L3] = {4} • valuex[L3] = {⊥} • valuec[L3] = {⊥} • Worklist = {L4} C[s: a = b + c] = valuea [s] valueb[s] = join s1,s2 ∊prec(s)(valueb[s1], valueb[s2] )

  10. Constant Propagation Analysis • C1 = {3} • C2 = {5} • C3 = {4} • C4 = {100} • C5 = {⊥} • C6 = {⊥} • C7 = {⊥} • C8 = {⊥} • C9 = {⊥} • C10 = {⊥} L1: a = 3; L2: b = 5; L3: d = 4; L4: x = 100; L5: if a > b then L6: c = a + b; L7: d = 2; L8: endif L9: c = 4; L10:return b * d + c; • valuea[L4] = {3} • valueb[L4] = {5} • valued[L4] = {4} • valuex[L4] = {100} • valuec[L4] = {⊥} • Worklist = {L5} C[s: a = b + c] = valuea [s] valueb[s] = join s1,s2 ∊prec(s)(valueb[s1], valueb[s2] )

  11. Constant Propagation Analysis • C1 = {3} • C2 = {5} • C3 = {4} • C4 = {100} • C5 = {⊥} • C6 = {⊥} • C7 = {⊥} • C8 = {⊥} • C9 = {⊥} • C10 = {⊥} L1: a = 3; L2: b = 5; L3: d = 4; L4: x = 100; L5: if a > b then L6: c = a + b; L7: d = 2; L8: endif L9: c = 4; L10:return b * d + c; • valuea[L5] = {3} • valueb[L5] = {5} • valued[L5] = {4} • valuex[L5] = {100} • valuec[L5] = {⊥} • Worklist = {L6} C[s: a = b + c] = valuea [s] valueb[s] = join s1,s2 ∊prec(s)(valueb[s1], valueb[s2] )

  12. Constant Propagation Analysis • C1 = {3} • C2 = {5} • C3 = {4} • C4 = {100} • C5 = {⊥} • C6 = {8} • C7 = {⊥} • C8 = {⊥} • C9 = {⊥} • C10 = {⊥} L1: a = 3; L2: b = 5; L3: d = 4; L4: x = 100; L5: if a > b then L6: c = a + b; L7: d = 2; L8: endif L9: c = 4; L10:return b * d + c; • valuea[L6] = {3} • valueb[L6] = {5} • valued[L6] = {4} • valuex[L6] = {100} • valuec[L6] = {8} • Worklist = {L7} C[s: a = b + c] = valuea [s] valueb[s] = join s1,s2 ∊prec(s)(valueb[s1], valueb[s2] )

  13. Constant Propagation Analysis • C1 = {3} • C2 = {5} • C3 = {4} • C4 = {100} • C5 = {⊥} • C6 = {8} • C7 = {2} • C8 = {⊥} • C9 = {⊥} • C10 = {⊥} L1: a = 3; L2: b = 5; L3: d = 4; L4: x = 100; L5: if a > b then L6: c = a + b; L7: d = 2; L8: endif L9: c = 4; L10:return b * d + c; • valuea[L7] = {3} • valueb[L7] = {5} • valued[L7] = {2} • valuex[L7] = {100} • valuec[L7] = {8} • Worklist = {L8} C[s: a = b + c] = valuea [s] valueb[s] = join s1,s2 ∊prec(s)(valueb[s1], valueb[s2] )

  14. Constant Propagation Analysis • C1 = {3} • C2 = {5} • C3 = {4} • C4 = {100} • C5 = {⊥} • C6 = {8} • C7 = {2} • C8 = {⊥} • C9 = {⊥} • C10 = {⊥} L1: a = 3; L2: b = 5; L3: d = 4; L4: x = 100; L5: if a > b then L6: c = a + b; L7: d = 2; L8: endif L9: c = 4; L10:return b * d + c; • valuea[L8] = {3} • valueb[L8] = {5} • valued[L8] = {2} • valuex[L8] = {100} • valuec[L8] = {8} • Worklist = {L9} C[s: a = b + c] = valuea [s] valueb[s] = join s1,s2 ∊prec(s)(valueb[s1], valueb[s2] )

  15. Constant Propagation Analysis • C1 = {3} • C2 = {5} • C3 = {4} • C4 = {100} • C5 = {⊥} • C6 = {8} • C7 = {2} • C8 = {⊥} • C9 = {4} • C10 = {⊥} L1: a = 3; L2: b = 5; L3: d = 4; L4: x = 100; L5: if a > b then L6: c = a + b; L7: d = 2; L8: endif L9: c = 4; L10:return b * d + c; • valuea[L9] = {3} • valueb[L9] = {5} • valued[L9] = {⊤} • valuex[L9] = {100} • valuec[L9] = {4} • Worklist = {L10} C[s: a = b + c] = valuea [s] valueb[s] = join s1,s2 ∊prec(s)(valueb[s1], valueb[s2] )

  16. Constant Propagation Analysis • C1 = {3} • C2 = {5} • C3 = {4} • C4 = {100} • C5 = {⊥} • C6 = {8} • C7 = {2} • C8 = {⊥} • C9 = {4} • C10 = {⊤} L1: a = 3; L2: b = 5; L3: d = 4; L4: x = 100; L5: if a > b then L6: c = a + b; L7: d = 2; L8: endif L9: c = 4; L10:return b * d + c; • valuea[L10] = {3} • valueb[L10] = {5} • valued[L10] = {⊤} • valuex[L10] = {100} • valuec[L10] = {4} • Worklist = {} C[s: a = b + c] = valuea [s] valueb[s] = join s1,s2 ∊prec(s)(valueb[s1], valueb[s2] )

  17. Handling of Loop • A fixed-point computation is needed • Keep performing join at loop merge points until the value sets no longer change • If a statement s: a = … has a constant value set CS ={v}, it should be replaced with a new statement a = v;

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