Static Single Assignment Form (SSA)

1
Static Single Assignment Form (SSA)

• Andrew McCreight
• (based on Prof. Shaos slides)
• CS421
• 11/18/05

2
Improving Compiler Efficiency

• Many optimization passes
• Lots of time spent optimizing
• Worth it to have new IR for opt.
• translation to/from new IR (cost)
• easier/faster opt. (benefit)
• so lets extend the basic CFG

3
Static Single Assignment

• Main idea each assignment has a unique name

v 4 z v 5 v 6 y v 7 if P then v
4 else v 6 u v y
v1 4 z v1 5 v2 6 y v2 7 if
P then v3 4 else v4 6 v5 F(v3,v4) u
v5 y
SSA transformation
4
F-Functions

• To support this special F-functions are added to
  each branch join point
• F(v1, v2, ) is equal to vi, if we take the i-th
  predecessor to get to it

if P then v3 4 else v4 6 v5
F(v3,v4) u v5 y
if P then v 4 else v 6 u v y
SSA transformation
5
Dominance

• Also a def must dominate all of its uses
• Statement a dominates statement b if along all
  valid paths from the entry to the exit, you reach
  a before you reach b.

v1 4 z v1 5 v2 6 y v2 7 if P then
v3 4 else v4 6 v5 F(v3,v4) u v5 y
6
What it buys us

• Easy to determine def of each use theres only
  one!
• Less need for data flow analysis

v 4 z v 5 v 6 y v 7 if P then v
4 else v 6 u v y
v1 4 z v1 5 v2 6 y v2 7 if
P then v3 4 else v4 6 v5 F(v3,v4) u
v5 y
SSA transformation
use-def chains are much simpler
7
More efficiency

• Weve basically pre-computed some dataflow
  information, which allows us to avoid redoing it
  with multiple passes
• Before, there were a quadratic number of use-def
  chains (in terms of edges)
• Now, there are a linear number of them
• Asymptotic efficiency improvement

8
Whats the catch?

• More variables
• Increase in code size due to F-functions
• But only linearly (in practice, SSA is 0.6-2.4
  times larger)
• Some optimizations are more annoying (things that
  copy blocks)
• But on the whole, a win for compilers

9
Sparse Analysis

• Some properties are global
• v1 is always 4, everywhere in the program
• Dont have to track the value of v at each point
• This means it is sparse

v1 4 z v1 5 v2 6 y v2 7 if
P then v3 4 else v4 6 v5 F(v3,v4) u
v5 y
10
Sparse Constant Prop

• Keep a global table of things that are const
• At each instruction, check each use to see if it
  is constant.
• If you dont know yet, find out, save the answer.
• Only have to examine each def once.
• At phi, only const if all args are same const

v1 4 z v1 5 v2 6 y v2 7 if
P then v3 4 else v4 6 v5 F(v3,v4) u
v5 y
11
Sparse conditional const prop

• We can be more clever, by evaluating branches.
  Track which blocks are run.
• First, assume only first block is run
• Ignore vals from unrun blocks
• If ends with a jump, add next block, check it
• If ends with a branch, see if we can figure out
  result of test.
• If we can, only do taken branch next.
• If we cant, do both branches
• Repeat, until no more blocks to examine.

12
Construction

• First, decide what variables need F-functions,
  and where
• Next, rename the variables
• First step is harder
• For second, just give each assignment a unique
  name, do a reaching definitions kind of analysis

13
Placing F Functions

• Need a F function at every join point where two
  different defs of the same variable reach
• Want to minimize the number of them
• Can be computed efficiently (see Appel ch. 19)

14
De-SSA

• Eventually, we want to leave SSA
• Drop all subscripts
• Simplest way convert all phi statements to move
  instructions (in predecessor block)
• Many of these moves can be eliminated if you are
  more clever, or through later optimization