Optimistic%20Register%20Coalescing

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Optimistic Register Coalescing

• Sobeeh Almukhaizim
• UC San Diego
• Computer Science Engineering
• Based on the work of
• J. Park and S. Moon
• School of Electrical Engineering
• Seoul National University

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Outline

• Motivation and problem definition.
• Register Allocation
• Copy Coalescing
• Optimistic Coalescing
• Aggressive coalescing.
• Live range splitting.
• Experimental Results and Analyses
• Summary

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Motivation and problem definition.

• Register allocation and copy coalescing.
• Goal Minimize number of registers for a program
  ( faster execution ).
• Live range variables that interfere with each
  other ? interference graph with minimum color k
  ( number of registers ).
• NP-complete ? search for heuristics.

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Register Allocation

• Interference Graph
• A node represents a live range
• An edge represents concurrent liveness
• Coloring Theorem
• In a graph G, a node x with degree lower than k
  will have a color no matter how G-x is colored

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Register Allocators

• Yorktown Allocator (Chaitin et. al)
• Spills a node whenever every node is significant
• Optimistic Coloring Register Allocator (Briggs
  et. al)
• Delays spill decision later
• Differentiates potential-spill and actual-spill

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Copy Coalescing

• Coalescing in Graph Coloring
• Merging two non-interfering nodes
• Makes two nodes have the same color
• Effective for copy elimination
• Copy Coalescing
• Merging two non-interfering copy-related nodes
• Makes copies meaningless
• Includes both negative and positive impact on
  colorability

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Coalescing Impact on Colorability

• Negative Impact
• Produce higher-degree coalesced nodes
• Positive Impact
• Reduce the degrees of neighbors by one

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1
1
2
a
b
ad
b
a
b
ab
k2
1
c
d
c
c
d
d
c
Positive Impact
Negative Impact
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Previous Coalescing Heuristics

• Aggressive Coalescing(Chaitin et. al)
• Coalesce any non-interfering copy operands
• Conservative Coalescing(Briggs et. al)
• Coalesce if the coalesced node will not be
  potentially-spilled
• Iterated Coalescing(George and Appel)
• Repeat simplification and conservative coalescing

Aggressive
Conservative
Iterated
Copy Removal
best
worst
mid
Positive Impact
mid
small
big
Negative Impact
big
none
none
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Optimistic Coalescing

• Aggressive Coalescing
• Live Range Splitting

Motivation of Optimistic Coalescing
Aggressive Coalescing
Copy Removal
Positive Impact
Optimistic View
Live Range Splitting
Negative Impact
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Aggressive Coalescing

• Advantages of Aggressive Coalescing
• Removes many copies
• Fully exploits the positive impact
• Optimistically, aggressively coalesced node is
  not necessarily spilled

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Live Range Splitting

• Compensate for Negative Impact
• What to Split
• Coalesced live ranges
• When to Split
• At the color phase before spilling them actually
• How to Split
• Reproduce the primitive live ranges by undoing
  coalescing

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Example of Live Range Splitting
a
k3
e
b
e
stack
abcd
f
d
f
g
c
g
Graph simplification
Aggressive coalescing
ab3
e1
e1
d
f2
f2
c1
g3
g3
Allocation result
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Register Allocator Implementation

• Base-case allocator
• Yorktown allocator with aggressive coalescing
• Briggs allocators with four different heuristics
• with conservative coalescing (conservative)
• with iterated coalescing (iterated)
• with aggressive coalescing (aggressive)
• with optimistic coalescing (optimistic)

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Experimental Results
Ratio of removed copies
Ratio of introduced spill ops
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Analysis of Aggressive Coalescing and Spilling

• Due to aggressiveness, aggressive coalescing
  coalesces 66.0 more nodes
• Due to optimistic view, aggressive coalescing
  spills only 5.6 of aggressively coalesced nodes
• Due to live range splitting, optimistic
  coalescing reduces spills by 2.4

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Analysis of Live Range Splitting

• Due to live range splitting, 52 of otherwise
  spilled nodes are colored

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Analysis of Positive impact

• Due to positive impact, coalescing removes
  interference edges
• Optimistic coalescing exploits 3.8 times more
  positive impact than iterated coalescing

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Summary

• Optimistic Coalescing
• Aggressive coalescing
• Aggressive copy elimination
• Positive impact
• Optimistic view
• Live range splitting
• Reduce negative impact