This document discusses partial redundancy elimination, which aims to minimize redundant expression evaluations by identifying partially redundant expressions and inserting computations to make them fully redundant so they can be eliminated. It describes partial redundancy as occurring when an expression is evaluated along at least one path to a program point but not all paths. The document outlines the key steps of partial redundancy elimination as inserting computations to make partially redundant expressions fully redundant, then eliminating the redundant expressions. It also discusses some challenges around identifying candidate expressions and safe insertion points.

1. PARTIAL
REDUNDANCY
ELIMINATION
BY
M.LAVANYA,M.SC(CS)
NADAR SARASWATHI COLLEGE
OF ARTS AND SCIENCE ,THENI.

2. PARTIAL REDUNDANCY ELIMINATION
Partial-Redundancy Elimination Minimize the number of
expression evaluations By moving around the places where
an expression.
Global code motion optimization
• Remove partially redundant expressions
• Loop invariant code motion
• Can be extended to do Strength Reduction
• No loop analysis needed
• Bidirectional flow problem C

3. PARTIAL REDUNDANCY ELIMINATION
 Global code motion optimization
• Remove partially redundant expressions
• Loop invariant code motion
• Can be extended to do Strength Reduction
 No loop analysis needed
 Bidirectional flow problem C

4. REDUNDANCY
• A Common Sub expression is a Redundant Computation
t1= a + b t2= a + b
t3 =a + b

5. REDUNDANCY
• Occurrence of expression E at P is redundant if E is
available there: – E is evaluated along every path to P, with
no operands redefined since.
• Redundant expression can be eliminated

6. PARTIAL REDUNDANCY
 Partially Redundant Computation:
t1 = a + b
t2 = a + b

7. PARTIAL REDUNDANCY
 Occurrence of expression E at P is partially redundant if E
is partially available there:
• E is evaluated along atleast one path t P to P, with no operands
redefined since.
 Partially redundant expression can be eliminated if we
can insert computations to make it fully redundant .

8. LOOP INVARIANTS ARE PARTIAL
REDUNDANCIES
 Loop invariant expression is partially redundant:
A = …
t1 = a + b

9. LOOP INVARIANTS ARE PARTIAL
REDUNDANCIES
 As before, partially redundant computation can be
eliminated if we insert computations to make it fully
redundant.
 Remaining copies can be eliminated through copy
propagation or more complex analysis of partially
redundant assignments.

10. PARTIAL REDUNDANCY METHODS
1. Insert Computations to make partially redundant
expression(s) fully redundant.
2. Eliminate redundant expression(s).

11. PARTIAL REDUNDANCY ISSUES
1. What expression occurrences are candidates for
elimination?
2. Where can we safely insert computations?
3. Where do we want to insert them?
• For this lecture, we assume one expression of interest, a
+ b. – In practice, with some restrictions, can do many
expressions in parallel.

12. WHICH OCCURANCE MIGHT BE
ELIMINATED
 In CSE,
• E is available at P if it is previously evaluate along every path
to P, with no subsequent re definitions of operands.
• If so, we can eliminate computation at P.
 In PRE,
• E is partially available at P if it is previously evaluated along at
least one path to P, with no subsequent redefinitions of operands.

13. WHICH OCCURANCE MIGHT BE
ELIMINATED
• If so, we might be able to eliminate computation at P, if we can
insert computations to make it fully redundant.
 Occurrences of E where E is partially available are
candidates for elimination.

14. FINDING PARTIALLY AVAILABLE
EXPRESSIONS
 Forward flow problem
• Lattice = { 0, 1 }, meet is union ( ), Top = 0 (not PAVAIL), entry = 0
• PAVOUT[i] = (PAVIN[i] – KILL[i]) AVLOC[i]
•PAVIN[i] = 0 i = entry PAVOUT[p] otherwise
 For a block,
• Expression is locally available (AVLOC) if downwards exposed.
• Expression is killed (KILL) if any assignments to operands.

15. FINDING PARTIALLY AVAILABLE
EXPRESSIONS
A = …
… = a + b
… = a + b
a = …