School of Computer Science A Global Progressive Register Allocator David Ryan Koes Seth Copen Goldstein Carnegie Mellon University {dkoes,seth}@cs.cmu.edu

School of Computer Science

A Global Progressive Register Allocator

A Global Progressive Register Allocator

David Ryan KoesSeth Copen GoldsteinCarnegie Mellon UniversityCarnegie Mellon University

{dkoes,seth}@cs.cmu.edu

2School of Computer Science

Register Allocation ProblemRegister Allocation Problem

…

v = 1

w = v + 3

x = w + v

u = v

t = u + x

print(x);

print(w);

print(t);

print(u);

…

registerregisterallocatorallocatorregisterregisterallocatorallocator

unbounded number of unbounded number of program variablesprogram variables

limited number of limited number of processor registers + processor registers + slow memoryslow memory

eaxebxecxedxesiedi

ebpesp

spill code optimizationspill code optimizationspill code optimizationspill code optimization

memory operandsmemory operandsmemory operandsmemory operands

register preferencesregister preferencesregister preferencesregister preferencesrematerializationrematerializationrematerializationrematerialization

live range splittinglive range splittinglive range splittinglive range splitting


A More Principled Register AllocatorA More Principled Register Allocator– fully utilize machine description

• explicit and expressive model of costs of allocation for given architecture

– optimal solutions

reg allocreg

alloc

machine description


Multi-commodity Network Flow: An Expressive ModelMulti-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

Example:edges have unit capacity

a b

a b

01


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

Register Allocation as a MCNFRegister Allocation as a MCNF

a

a

r0 r1 mem 1

r1 mem 1

r0 r1 mem 1

3

Also need Also need anti-variablesanti-variables to to model persistent memorymodel persistent memoryAlso need Also need anti-variablesanti-variables to to model persistent memorymodel persistent memory


ExampleExampleSource Codeint example(int a, int b){ int d = 1; int c = a - b; return c+d;}

Pre-alloc AssemblyMOVE 1 -> dSUB a,b -> cADD c,d -> cMOVE c -> r0

load cost

insn pref cost

mem access cost


Control FlowControl FlowMCNF can only represent straight-line code

– need to link together networks from basic blocks

a: %eaxa: %eax

a: %eaxa: %eaxa: %eaxa: %eax

a: mema: mem

a: mema: mema: mema: mem

a: mema: mem

New nodes to handle block entry/exit constraints

Normal

ini outi

Merge

ini out,i

Split

in outi,i



• explicit and expressive model of costs of allocation for given architecture: Global MCNF

– optimal solutions• NP-hard, so use progressive

solution technique

Compile Time

Allo

catio

n Q

ualit

y

Lagrangian relaxation directed allocatorsLagrangian relaxation directed allocators

Technique:Technique:

reg alloc

reg alloc

machine description


Solution ProcedureSolution ProcedureCompute 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


Solution ProcedureSolution ProcedureAdvantages

+ 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 99% of the time integrality gap = 0integrality gap = 099% of the time 99% of the time integrality gap = 0integrality gap = 0


Iterative Heuristic AllocatorIterative Heuristic AllocatorAllocation order:

a, b, c, d

Cost:

a

0

b

4

c

0

d

-2

Total: 22

Edges to/from memory cost 3


Simultaneous Heuristic AllocatorSimultaneous Heuristic Allocator

XX XX

Current cost:-1-1-3-3-2-2

Edges to/from memory cost 3


EvaluationEvaluationImplemented in gcc 3.4.3 targeting x86

Optimize for code sizecode size– perfect static evaluation– important metric in its own right

MediaBench, MiBench, Spec95, Spec2000– over 10,000 functions


ProgressivenessProgressiveness

CPLEX

default allocator: 1121graph allocator: 1422


ProgressivenessProgressiveness

graph allocator

default allocator

CPLEX


Code SizeCode Size

Progressive!


OptimalityOptimality

Proven optimality

Proven maximum distance from optimal


10x slower

Compile Time Slowdown :-(Compile Time Slowdown :-(



• explicit and expressive model of costs of allocation for given architecture: Global MCNF

– optimal solutions• approach optimality using

progressive solution technique: Lagrangian directed allocators

reg allocreg

alloc

machine description


Questions?Questions?

?



0%

10%

20%

30%

40%

50%

60%

<10%

10–5%

5–2%

2–1%

1–0% 0%

0–1%

1–2%

2–3%

3–4%

4–5%

5–10%

10–100%

>100%

Percent predicted size larger than actual size

Perc

en

t of

fun

ctio

ns

Accuracy of the ModelAccuracy of the ModelGlobal MCNF model correctly predicts costs of register allocation within 2% for 71% of functions compiled


Code SizeCode Size


Compile Time Asymptotic ComplexityCompile Time Asymptotic Complexity

one iteration: O(nv)


Code PerformanceCode Performance


Compile Time Slowdown :-(Compile Time Slowdown :-(

10x slower

Documents

School of Computer Science A Global Progressive Register Allocator David Ryan Koes Seth Copen Goldstein Carnegie Mellon University {dkoes,seth}@cs.cmu.edu