A Global Progressive Register Allocator

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A Global Progressive Register Allocator

• David Ryan Koes
• Seth Copen Goldstein
• Carnegie Mellon University
• dkoes,seth_at_cs.cmu.edu

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Register Allocation Problem
unbounded number of program variables
limited number of processor registers slow
memory
spill code optimization
v 1 w v 3 x w v u v t u
x print(x) print(w) print(t) print(u)
register preferences
rematerialization
register allocator
live range splitting
memory operands
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A More Principled Register Allocator

• fully utilize machine description
• explicit and expressive model of costs of
  allocation for given architecture
• optimal solutions

reg alloc
machine description
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Multi-commodity Network Flow An Expressive Model

• Given network (directed graph) with
• cost and capacity on each edge
• sources sinks for multiple commodities
• Find lowest cost flow of commodities
• NP-complete for integer flows

b
a
Example edges have unit capacity
0
1
b
a
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Register Allocation as a MCNF
Variables ? Commodities Variable Definition ?
Source Variable Last Use ? Sink Nodes ?
Allocation Classes (Reg/Mem/Const) Registers
Limits ? Node Capacities Spill Costs ? Edge
Costs Allocation ? Flow
r1
mem
1
3
Also need anti-variables to model persistent
memory
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Example
load cost
Source Code int example(int a, int b) int d
1 int c a - b return cd
insn pref cost
Pre-alloc Assembly MOVE 1 -gt d SUB a,b -gt c ADD
c,d -gt c MOVE c -gt r0
mem access cost
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Control Flow

• MCNF can only represent straight-line code
• need to link together networks from basic blocks

New nodes to handle block entry/exit constraints
a eax
a mem
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A More Principled Register Allocator

• fully utilize machine description
• explicit and expressive model of costs of
  allocation for given architecture Global MCNF
• optimal solutions
• NP-hard, so use progressive solution technique

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Solution Procedure

• Compute Lagrangian prices using iterative
  subgradient optimization
• guaranteed converge to optimal prices
• for linear relaxation of the problem
• Prices used by allocator to find solution
• solution improves as prices converge
• two allocators
• iterative heuristic allocator
• simultaneous heuristic allocator

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Solution Procedure

• Advantages
• iterative nature ? progressive
• Lagrangian relaxation theory provides means for
  computing a good lower bound
• Can compute optimality bound
• Disadvantages
• No guarantee of finding optimal solution
• Optimality bound poor if integrality gap large

99 of the time integrality gap 0
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Iterative Heuristic Allocator
Edges to/from memory cost 3
Allocation order a, b, c, d
Cost
Total 2
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Simultaneous Heuristic Allocator
Edges to/from memory cost 3
Current cost
-1
-3
-2
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Evaluation

• Implemented in gcc 3.4.3 targeting x86
• Optimize for code size
• perfect static evaluation
• important metric in its own right
• MediaBench, MiBench, Spec95, Spec2000
• over 10,000 functions

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Progressiveness
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Progressiveness
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Code Size
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Optimality
Proven maximum distance from optimal
Proven optimality
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Compile Time Slowdown -(
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A More Principled Register Allocator

• fully utilize machine description
• explicit and expressive model of costs of
  allocation for given architecture Global MCNF
• optimal solutions
• approach optimality using progressive solution
  technique Lagrangian directed allocators

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Questions?
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(No Transcript)
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Accuracy of the Model
Global MCNF model correctly predicts costs of
register allocation within 2 for 71 of
functions compiled
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Code Size
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Compile Time Asymptotic Complexity
one iteration O(nv)
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Code Performance
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Compile Time Slowdown -(
10x slower