1. Examples of SSA based optimizers: Global Value Numbering

2. Global Value Numbering (GVN): Common Sub-expression Elimination that does not depend on variable names. –Assume that there is a table as a set of projections from variables/expressions to their value numbers, such as { a -> 1, b -> 2, ( ⊕, 1, 2) -> 3 }, where each expression is represented as a tuple with an operator and value numbers of operands –The uses of the same definition have the same value number. –The left and right hand sides of a copy assignment such as a = b have the same value number. –Handling a statement x = a ⊕ b: 1.Search the value numbers of a and b in the table, where let a and b be 1 and 2 respectively. 2.If ( ⊕, 1, 2) is found in the table, its value number is assigned to x; otherwise, the new value number is assigned to ( ⊕, 1, 2) and x.

3. An example of GVN GVN based on dominance relation ： copy propagation + redundancy elimination b1=x1+s1 a1=x1+t1 p1=a1*5 q1=b1*5 s1=5 t1=5

4. An example of GVN GVN based on dominance relation ： copy propagation + redundancy elimination b1=x1+s1 a1=x1+t1 p1=a1*5 q1=b1*5 s1=5 t1=5 a1=x1+5

5. t1=5 a1=x1+5 An example of GVN GVN based on dominance relation ： copy propagation + redundancy elimination b1=x1+s1 a1=x1+5 p1=a1*5 q1=b1*5 s1=5 t1=5 a1=x1+5 s1=5

6. An example of GVN GVN based on dominance relation ： copy propagation + redundancy elimination b1=x1+s1 a1=x1+5 p1=a1*5 q1=b1*5 t1=5 a1=x1+5 s1=5 b1=x1+5 b1=a1 t1=5 a1=x1+5 s1=5 b1=a1

7. An example of GVN GVN based on dominance relation ： copy propagation + redundancy elimination a1=x1+5 p1=a1*5 q1=b1*5 t1=5 a1=x1+5 s1=5 b1=a1 q1=a1*5 t1=5 a1=x1+5 s1=5 b1=a1 q1=a1*5

8. An example of GVN GVN based on dominance relation ： copy propagation + redundancy elimination a1=x1+5 p1=a1*5 q1=b1*5q1=a1*5 t1=5 a1=x1+5 s1=5 b1=a1 q1=a1*5 p1=q1 t1=5 a1=x1+5 s1=5 b1=a1 q1=a1*5 p1=q1