Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
SSA Destruction after Register Allocation Tutorial on Register Allocation under SSA ; Part 5
Florent Bouchez
[email protected] Indian Institute of Science Bangalore
LCPC ’09 — University of Delaware
1 / 30 F. Bouchez (IISc – India)
SSA Destruction after Register Allocation
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
How to get the hell out of SSA? Tutorial on Register Allocation under SSA ; Part 5
Florent Bouchez
[email protected] Indian Institute of Science Bangalore
LCPC ’09 — University of Delaware
2 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Outline Background: classical out-of-SSA Differences with out-of-SSA after register allocation under SSA Statement of the problem Moving parallel copies out of edges Experiments
3 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Outline Background: classical out-of-SSA Differences with out-of-SSA after register allocation under SSA Statement of the problem Moving parallel copies out of edges Experiments
4 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Cytron et al.’s out-of-SSA Cytron, Ferrante, Rosen, Wegman, Zadeck (1991) Efficiently computing static single assignment form and the control dependence graph. Na¨ıvely, a k -input φ-function at entrance to a node X can be replaced by k ordinary assignments, one at the end of each control flow predecessor of X . This is always correct.
5 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Cytron et al.’s out-of-SSA Cytron, Ferrante, Rosen, Wegman, Zadeck (1991) Efficiently computing static single assignment form and the control dependence graph.
Example a ← ...
b ← ...
c ← φ(a , b )
5 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Cytron et al.’s out-of-SSA Cytron, Ferrante, Rosen, Wegman, Zadeck (1991) Efficiently computing static single assignment form and the control dependence graph.
Example a ← ...
b ← ...
a ← ... c←a
b ← ... c←b
c ← φ(a , b )
5 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Briggs’s, Cooper’s out-of-SSA Briggs, Cooper, Harvey, Simpson (1998) Practical improvements to the construction and destruction of static single assignment form. Cytron et al.’s out-of-SSA works after some optimizations: • constant propagation • dead code elimination
6 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Briggs’s, Cooper’s out-of-SSA Briggs, Cooper, Harvey, Simpson (1998) Practical improvements to the construction and destruction of static single assignment form. Cytron et al.’s out-of-SSA works after some optimizations: • constant propagation • dead code elimination
But NOT if done after more aggressive ones: • copy folding • value numbering 6 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Lost copy problem Example a←1
c ← φ(a , b ) b ←c+1
··· ← c
7 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Lost copy problem Example a←1 c←a
a←1
c ← φ(a , b ) b ←c+1
b ←c+1 c←b
··· ← c
··· ← c
7 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Lost copy problem Example a←1 c←a
a←1
c ← φ(a , b ) b ←c+1
b ←c+1 c←b
··· ← c
··· ← c This is due to the critical edge.
7 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Swap problem Example
a ← φ(a , b ) b ← φ(b , a )
8 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Swap problem Example a←a b←b
a←b b←a
a ← φ(a , b ) b ← φ(b , a )
8 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Swap problem Example a←a b←b
a←b b←a
a ← φ(a , b ) b ← φ(b , a ) Copies induced by φ-functions must be executed in parallel. We call them ∥copies . 8 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Sreedhar et al.’s out-of-SSA Sreedhar, Ju, Gillies, Santhanam (1999) Translating out of Static Single Assignment form.
Example a ← ...
b ← ...
c ← φ(a , b )
9 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Sreedhar et al.’s out-of-SSA Sreedhar, Ju, Gillies, Santhanam (1999) Translating out of Static Single Assignment form.
Example a ← ...
b ← ...
a ← ... a0 ← a
b ← ... b0 ← b
c 0 ← φ(a 0 , b 0 ) c ← c0
c ← φ(a , b )
Adding primed variables à conventional SSA.
9 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Sreedhar et al.’s out-of-SSA Sreedhar, Ju, Gillies, Santhanam (1999) Translating out of Static Single Assignment form.
Example a ← ...
b ← ...
a ← ... X ←a
b ← ... X ←b
c ← φ(a , b ) c←X Adding primed variables à conventional SSA. Then, all variables of the same φ-congruence class can be replaced by a common name. 9 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Outline Background: classical out-of-SSA Differences with out-of-SSA after register allocation under SSA Statement of the problem Moving parallel copies out of edges Experiments
10 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Flow of SSA vs. classical register allocation Prog. optim. Interm. repr. (IR)
SSA conversion
SSA form IR
SSA destruction
post SSA IR
Register allocation
Assembly
11 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Flow of SSA vs. classical register allocation Prog. optim. Interm. repr. (IR)
SSA conversion
SSA form IR
SSA destruction
post SSA IR
Register allocation
Assembly
Prog. optim. Interm. repr. (IR)
SSA conversion
SSA form IR
Assembly
11 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Flow of SSA vs. classical register allocation Prog. optim. Interm. repr. (IR)
SSA conversion
SSA form IR
SSA destruction
post SSA IR
Register allocation
Assembly
Prog. optim. Interm. repr. (IR)
SSA conversion
SSA form IR
Register allocation
Assembly
11 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Flow of SSA vs. classical register allocation Prog. optim. Interm. repr. (IR)
SSA conversion
SSA form IR
SSA destruction
post SSA IR
Register allocation
Assembly
SSA destruction
Assembly
Prog. optim. Interm. repr. (IR)
SSA conversion
SSA form IR
Register allocation
11 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Flow of SSA vs. classical register allocation Prog. optim. Interm. repr. (IR)
SSA conversion
SSA form IR
SSA destruction
post SSA IR
Register allocation
Assembly
Register allocation
Colored SSA form
SSA destruction
Assembly
Prog. optim. Interm. repr. (IR)
SSA conversion
SSA form IR
Only registers remains when translating out-of-SSA! à not possible to add new variables. F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
11 / 30
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Deal with the differences Without temporary variables: • Imitate Sreedhar using available registers as new variables.
But what if there are not enough registers? spill? à bad idea.
12 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Deal with the differences Without temporary variables: • Imitate Sreedhar using available registers as new variables.
But what if there are not enough registers? spill? à bad idea. • Problems are back: • ”swap problem” since copies order is important • critical edge poses the problem of where to put copies
12 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Deal with the differences Without temporary variables: • Imitate Sreedhar using available registers as new variables.
But what if there are not enough registers? spill? à bad idea. • Problems are back: • ”swap problem” since copies order is important • critical edge poses the problem of where to put copies
Back to semantics of φ-function: depends on the flow à split all incoming edges to place ∥copies, but performance problem!
12 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Splitting edges can be bad
Folk assumption that splitting edges is a bad thing to do: • adds a jump instruction • prevents mapping on hardware accelerator • code cannot be scheduled
13 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Splitting edges can be bad
Folk assumption that splitting edges is a bad thing to do: • adds a jump instruction • prevents mapping on hardware accelerator • code cannot be scheduled
We would like to have a way to not split (at least some) edges. Is it possible and how to do it?
13 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Outline Background: classical out-of-SSA Differences with out-of-SSA after register allocation under SSA Statement of the problem Moving parallel copies out of edges Experiments
14 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Problem statement
Goal: reduce the overhead due to the added copies and edge splitting during SSA destruction. We suppose there still remains ∥copies on edges after coalescing.
Problems • “parallel” problem: ∥copies must be sequentialized
à how to find a correct ordering? • if a ∥copy is placed on an edge, it must be split
à possible to move ∥copies out of edges?
15 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Modeling of ∥copies Simplifying fact: register allocation is done. ∥copies involves registers, not variables. à register transfer graphs (RTG), a graphical representation: R1 R1
R3
R2
R1
R2
R2
16 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Modeling of ∥copies Simplifying fact: register allocation is done. ∥copies involves registers, not variables. à register transfer graphs (RTG), a graphical representation: R1 R1
R3
R2
R1
R2
R2
Properties of an RTG: • Maximum in-degree equals 1 • 3 types of RTG (tree, cycle, F. Bouchez (IISc – India)
How to get the hell out of SSA?
) LCPC ’09
16 / 30
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Modeling of ∥copies Simplifying fact: register allocation is done. ∥copies involves registers, not variables. à register transfer graphs (RTG), a graphical representation:
R8 R9
R1
R7
R2 R10
R5
R6
R3 R4 Properties of an RTG: • Maximum in-degree equals 1 • 3 types of RTG (tree, cycle, windmill(general case)) F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
16 / 30
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Modeling of ∥copies Simplifying fact: register allocation is done. ∥copies involves registers, not variables. à register transfer graphs (RTG), a graphical representation: duplications R8 R9
R1
R7
R2 R10
R5
R6
R3 R4 Properties of an RTG: • Maximum in-degree equals 1 • 3 types of RTG (tree, cycle, windmill(general case)) F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
16 / 30
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Outline Background: classical out-of-SSA Differences with out-of-SSA after register allocation under SSA Statement of the problem Moving parallel copies out of edges Experiments
17 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Is it possible to move ∥copies out of edges? On a simple edge (i.e., non-critical): code can be placed on predecessor or successor basic block.
Example Bs
∥copy Bd
18 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Is it possible to move ∥copies out of edges? On a simple edge (i.e., non-critical): code can be placed on predecessor or successor basic block.
Example Bs
Bs
∥copy
∥copy
move up Bd
Bd
18 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Is it possible to move ∥copies out of edges? On a simple edge (i.e., non-critical): code can be placed on predecessor or successor basic block.
Example Bs
Bs
∥copy
move down
Bd
Bd
∥copy
18 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Is it possible to move ∥copies out of edges? On a simple edge (i.e., non-critical): code can be placed on predecessor or successor basic block.
Example Bs
Bs
∥copy
move down
Bd
Bd
∥copy
But what if Bs has more than one successor? Bd has more than one predecessor? 18 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
∥copies are hard to move out of critical edges Example B
A
D
C
19 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
∥copies are hard to move out of critical edges Example B
A
D
C x ← φ(y , z )
19 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
∥copies are hard to move out of critical edges Example B
A
D
C R1 ← φ(R2 , R3 )
19 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
∥copies are hard to move out of critical edges Example B
D R1 ← R3
R1 R3 R2
A
C
19 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
∥copies are hard to move out of critical edges Example D R1 ← R3
B
A
C R1 ← R2
Moving down erases R1 if path comes from D. 19 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
∥copies are hard to move out of critical edges Example B
R1 ← . . . R1 ← R2
A · · · ← R1
C
D R1 ← R3
Moving up might erase a live variable in R1 . 19 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Reversing the effect of parallel copies Idea: a ∥copy can be moved if its effects are cancelled on the other edges.
20 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Reversing the effect of parallel copies Idea: a ∥copy can be moved if its effects are cancelled on the other edges.
Example (Cancelling R1 ← R2 ) R1 ← . . . B R3 ← R1 R1 ← R2
A R1 ← R3
C
D R1 ← R3
R1 ← φ(R2 , R3 ) 20 / 30
F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Reversing the effect of parallel copies Idea: a ∥copy can be moved if its effects are cancelled on the other edges.
Example (Cancelling R1 ← R2 ) B R1 ← . . .
A
C
D
R1 ← R3 R2 ← R1
R1 ← R2 R1 ← φ(R2 , R3 ) 20 / 30
F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Reversing the effect of parallel copies Idea: a ∥copy can be moved if its effects are cancelled on the other edges.
Example (Duplication problem) B
D R1
A
C
R1 ← R2 R2 ← R3
R2
R1 ← φ(R1 , R2 ) R2 ← φ(R1 , R3 ) 20 / 30
F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Reversing the effect of parallel copies Idea: a ∥copy can be moved if its effects are cancelled on the other edges. • Effects must be reversed if moving up. • Effects must be pre-reversed if moving down.
Problems • ∥copies involving overwriting of existing value must be carefully moved. à ∥copy motion is highly dependent on the liveness. • ∥copies with duplications cannot be pre-reversed.
20 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Extracting duplications from ∥copies Duplications can only be moved up. We want to extract them to ∥copies to get rid of them. This can be done using free registers.
Example R1
R1 R3
=
R1 R3
R2
R2
F. Bouchez (IISc – India)
How to get the hell out of SSA?
◦
R3 R2
21 / 30 LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Extracting duplications from ∥copies Duplications can only be moved up. We want to extract them to ∥copies to get rid of them. This can be done using free registers.
Example B
D
R1 ← R2 R2 ← R3
R1 R3 A
R2 R1 ← φ(R1 , R2 ) C R2 ← φ(R1 , R3 ) 21 / 30
F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Extracting duplications from ∥copies Duplications can only be moved up. We want to extract them to ∥copies to get rid of them. This can be done using free registers.
Example R1 R3
B R2
D
R1 ← R2 R2 ← R3
R1 R3
A
R2 R1 ← φ(R1 , R2 ) C R2 ← φ(R1 , R3 ) 21 / 30
F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Extracting duplications from ∥copies Duplications can only be moved up. We want to extract them to ∥copies to get rid of them. This can be done using free registers. • Extracted duplications are moved up. • If preceding basic block has not enough free registers, one
needs to split or spill.
21 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Extracting duplications from ∥copies Duplications can only be moved up. We want to extract them to ∥copies to get rid of them. This can be done using free registers. • Extracted duplications are moved up. • If preceding basic block has not enough free registers, one
needs to split or spill. • There remains a reversible ∥copy: max out-degree = 1.
Example R1
R1 R3
reverse
R2
R3 R2 21 / 30
F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Permutations to easily deal with liveness Liveness is important when moving ∥copies. Registers holding live variables must not be overwritten. We convert reversible ∥copies to permutations: à just close the open cycles in the RTG.
22 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Permutations to easily deal with liveness Liveness is important when moving ∥copies. Registers holding live variables must not be overwritten. We convert reversible ∥copies to permutations: à just close the open cycles in the RTG.
Example R1
R4 R3
R2
R6 R5
22 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Permutations to easily deal with liveness Liveness is important when moving ∥copies. Registers holding live variables must not be overwritten. We convert reversible ∥copies to permutations: à just close the open cycles in the RTG.
Example R1
R4 R3
R2
R6 R5
22 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
π-motion out of critical edges Example
B
A
D
C
23 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
π-motion out of critical edges Example
B
D
R1 R3 R2
A
C
23 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
π-motion out of critical edges Example
B
D
R1 R3 R2
A
C
23 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
π-motion out of critical edges Example R1 R3
B
D
R2 R1 R3
A
C
R2
23 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
π-motion out of critical edges Example R1 B
R3
D R2 R1
A
R3
C R2
This critical edge is weak: its adjacent edges are not critical. 23 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
π-motion follows weak critical edges
Example
Weakness is a property propagated along connected edges.
24 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
π-motion follows weak critical edges
wn do
do wn
Example
dow n
Weakness is a property propagated along connected edges.
24 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
π-motion follows weak critical edges
Example
wn do
do wn
up
up
up
dow n
Weakness is a property propagated along connected edges.
24 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
π-motion follows weak critical edges
Example up
wn do
wn do
do wn
up
up
dow n
Weakness is a property propagated along connected edges.
24 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Intrinsic difficulty strong critical edges Connected critical edges forming a cycle are strong.
Example
25 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Intrinsic difficulty strong critical edges Connected critical edges forming a cycle are strong.
Example
25 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Intrinsic difficulty strong critical edges Connected critical edges forming a cycle are strong. • π-motion is not possible on strong critical edges
25 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Intrinsic difficulty strong critical edges Connected critical edges forming a cycle are strong. • π-motion is not possible on strong critical edges • removing the ∥copies on such a multiplexing region is
NP-complete
25 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Intrinsic difficulty strong critical edges Connected critical edges forming a cycle are strong. • π-motion is not possible on strong critical edges • removing the ∥copies on such a multiplexing region is
NP-complete
Example Broot
d c Ba ,b
b
d
switch Ba ,c a←0 b←1 x ←a+b
a
Ba
Bb ,d a←3 c←3 x ←a+c
Bb return a + x
Bc return b + x
c←9 d←9 x ←c+d
b←6 d←6 x ←b +d
x
b
Bc ,d
c
a
Bd return c + x
return d + x 25 / 30
F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Intrinsic difficulty strong critical edges Connected critical edges forming a cycle are strong. • π-motion is not possible on strong critical edges • removing the ∥copies on such a multiplexing region is
NP-complete
Example Broot
d c Ba ,b
b
d
switch Ba ,c a←0 b←1 x ←a+b
a
Ba
Bb ,d a←3 c←3 x ←a+c
Bb return a + x
Bc return b + x
c←9 d←9 x ←c+d
b←6 d←6 x ←b +d
x
b
Bc ,d
c
a
Bd return c + x
return d + x 25 / 30
F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Intrinsic difficulty strong critical edges Connected critical edges forming a cycle are strong. • π-motion is not possible on strong critical edges • removing the ∥copies on such a multiplexing region is
NP-complete
Example Broot
d c Ba ,b
b
d
switch Ba ,c a←0 b←1 x←a+b
a
Ba
Bb ,d a←3 c←3 x←a+c
Bb return a + x
Bc return b + x
c←9 d←9 x←c+d
b←6 d←6 x←b+d
x
b
Bc ,d
c
a
Bd return c + x
return d + x 25 / 30
F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Sequentialize permutations Permutations must eventually be converted to actual copies. Step 1. Liveness projection R8 R9
Non Live = {R5 , R7 }
R1
R7
R2 R10
R5
R6
R3 R4
26 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Sequentialize permutations Permutations must eventually be converted to actual copies. Step 2. Sequentialize chains R8 R9
R1
R7
R2 R10
R5
R6
R3 R4
26 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Sequentialize permutations Permutations must eventually be converted to actual copies. Step 2. Sequentialize chains R8 R9
R7 ← R6
R1
R7
R2 R10
R5
R6
R3 R4
26 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Sequentialize permutations Permutations must eventually be converted to actual copies. Step 2. Sequentialize chains R8 R9
R1
R7
R2 R10
R5
R7 ← R6 R5 ← R4
R6
R3 R4
26 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Sequentialize permutations Permutations must eventually be converted to actual copies. Step 2. Sequentialize chains R8 R9
R1
R7
R2 R10
R5
R7 ← R6 R5 ← R4 R4 ← R3
R6
R3 R4
26 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Sequentialize permutations Permutations must eventually be converted to actual copies. Step 2. Sequentialize chains R8 R9
R1
R7
R2 R10
R5
R6
R7 R5 R4 R3
← R6 ← R4 ← R3 ← R2
R3 R4
26 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Sequentialize permutations Permutations must eventually be converted to actual copies.
R8 R9
R1
R7
R2 R10
R5
R6
R7 R5 R4 R3 R2
← R6 ← R4 ← R3 ← R2 ← R1
R3 R4
26 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Sequentialize permutations Permutations must eventually be converted to actual copies. Step 3. Mark root of chain as “free” R8 R9
R1
R7
R2 R10
R5
R6
R7 R5 R4 R3 R2
← R6 ← R4 ← R3 ← R2 ← R1
R3 R4
26 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Sequentialize permutations Permutations must eventually be converted to actual copies. Step 4. Use free register for cycles R8 R9
R1
R7
R2 R10
R5
R6
R3 R4
R7 R5 R4 R3 R2 R1
← R6 ← R4 ← R3 ← R2 ← R1 ← R10
26 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Sequentialize permutations Permutations must eventually be converted to actual copies. Step 4. Use free register for cycles R8 R9
R1
R7
R2 R10
R5
R6
R3 R4
R7 ← R6 R5 ← R4 R4 ← R3 R3 ← R2 R2 ← R1 R1 ← R10 R10 ← R9
26 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Sequentialize permutations Permutations must eventually be converted to actual copies. Step 4. Use free register for cycles R8 R9
R1
R7
R2 R10
R5
R6
R3 R4
R7 ← R6 R5 ← R4 R4 ← R3 R3 ← R2 R2 ← R1 R1 ← R10 R10 ← R9 R9 ← R8
26 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Sequentialize permutations Permutations must eventually be converted to actual copies. Step 4. Use free register for cycles R8 R9
R1
R7
R2 R10
R5
R6
R3 R4
R7 ← R6 R5 ← R4 R4 ← R3 R3 ← R2 R2 ← R1 R1 ← R10 R10 ← R9 R9 ← R8 R8 ← R1 26 / 30
F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Sequentialize permutations Permutations must eventually be converted to actual copies. Step 4’. (only cycles) No free register à swap R1 R2 R5 R3 R4
26 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Sequentialize permutations Permutations must eventually be converted to actual copies. Step 4’. (only cycles) No free register à swap swap(R1 , R5 )
R1 R2 R5 R3 R4
26 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Sequentialize permutations Permutations must eventually be converted to actual copies. Step 4’. (only cycles) No free register à swap swap(R1 , R5 ) swap(R2 , R5 )
R1 R2 R5 R3 R4
26 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Sequentialize permutations Permutations must eventually be converted to actual copies. Step 4’. (only cycles) No free register à swap swap(R1 , R5 ) swap(R2 , R5 ) swap(R3 , R5 )
R1 R2 R5 R3 R4
26 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Sequentialize permutations Permutations must eventually be converted to actual copies. Step 4’. (only cycles) No free register à swap swap(R1 , R5 ) swap(R2 , R5 ) swap(R3 , R5 ) swap(R4 , R5 )
R1 R2 R5 R3
Swaps can be hardware or emulated (by using 3 XOR).
R4
If swapping is impossible, spilling is required. 26 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Outline Background: classical out-of-SSA Differences with out-of-SSA after register allocation under SSA Statement of the problem Moving parallel copies out of edges Experiments
27 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Experiments Different approaches to deal with ∥copies on edges: • split: edges are split by default • π-motion: ∥copies are moved out of edges whenever possible • done after coalescing (IRC1 ) or not
Number of split edges in SPEC2000
Average per bench Total number of edges
After coalescing split π-motion 257 45.5 2829 499
No coalescing split π-motion 1338 51.5 14725 567
For about 180 000 total edges.
1
Iterated Register Coalescing of Appel&George
F. Bouchez (IISc – India)
How to get the hell out of SSA?
28 / 30 LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
Conclusion SSA destruction after register allocation means: • new variable creation not possible • reappearance of “swap problem” and “critical edge problem”
Emergency instructions to get out-of-SSA 1. φ-functions are replaced by ∥copies on incoming edges 2. ∥copies are decomposed into duplications (moved up) and reversible ∥copies 3. ∥copies are converted to permutations for easier handling 4. permutations can be moved out of weak critical edges 5. permutations are converted back to ∥copies and sequentialized in a working order. 29 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
Background
out-of-SSA after RA
The problem
Moving ∥copies
Experiments
Conclusion
That’s all for today
30 / 30 F. Bouchez (IISc – India)
How to get the hell out of SSA?
LCPC ’09
