Progressive Register Allocation for Irregular Architectures

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Progressive Register Allocation for Irregular
Architectures

• David Koes
• dkoes_at_cs.cmu.edu
• Seth Copen Goldstein
• seth_at_cs.cmu.edu
• March 23, 2005

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Irregular Architectures

• Few registers
• Register usage restrictions
• address registers, hardwired registers...
• Memory operands
• Examples
• x86, 68k, ColdFire, ARM Thumb, MIPS16, V800,
  various DSPs...

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Fewer Registers ? More Spills

• Used gcc to compile gt10,000 functions from
  Mediabench, Spec95, Spec2000, and
  micro-benchmarks
• Recorded which functions spilled

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Register Usage Restrictions

• Instructions may prefer or require a specific
  subset of registers
• x86 multiply instruction
• imul edx,eax // 2 byte instruction
• imul edx,ecx // 3 byte instruction
• x86 divide instruction
• idivl ecx // eax edxeax/ecx

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Memory Operands

• Load/store not always needed to access variables
  allocated to memory
• depends upon instruction
• still less efficient than register access
• addl 8(ebp), eax
• vs
• movl 8(ebp), edx
• addl edx, eax

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Register Allocation Challenges

• Optimize spill code
• with few registers, spilling unavoidable
• Model register usage restrictions
• Exploit memory operands
• affects spilling decisions

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Previous Work
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Our Goals

• Expressive
• Explicitly represent architectural irregularities
  and costs
• Proper model
• An optimum solution results in optimal register
  allocation
• Progressive solution algorithm
• more computation ? better solution
• decent feasible solution obtained quickly
• competitive with current allocators

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Multicommodity Network Flow (MCNF)
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Modeling Usage Constraints
int foo(int a, int b, int c) a ab
return a/c
not quite right
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Modeling Spills and Moves
int foo(int a, int b, int c) a ab
return a/c
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Modeling Stores

• Simple approach flawed
• doesnt model memory persistency

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Register Allocation as MCNF

• Variables ? Commodities
• Variable Usage ? Network Design
• Nodes ? Allocation Classes (Reg/Mem)
• Registers Limits ? Node Capacities
• Spill Costs ? Edge Costs
• Variable Definition ? Source
• Variable Last Use ? Sink

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Solving an MCNF

• Integer solution NP-complete
• Use standard IP solvers
• commercial solvers (CPLEX) are impressive
• Exploit structure of problem
• variety of MCNF specific solvers
• empirically faster than IP solvers
• Lagrangian Relaxation technique

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Lagrangian Relaxation Intuition

• Relaxes the hard constraints
• only have to solve single commodity flow
• Combines easy subproblems using a Lagrangian
  multiplier
• an additional price on each edge

Example edges have unit capacity
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Solution Procedure

• Compute prices using iterative subgradient
  optimization
• converge to optimal prices
• At each iteration, greedily construct a feasible
  solution using current prices
• allocate most expensive vars first
• can always find an allocation

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Solution Procedure

• Advantages
• have feasible solution at each step
• iterative nature ? progressive
• Lagrangian relaxation theory provides means for
  computing a lower bound
• Can compute optimality bound
• Disadvantages
• No guarantee of optimality of solution

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Evaluation

• Replace gccs local allocator
• Optimize for code size
• easy to statically evaluate
• Evaluate on MediaBench, MiBench, SpecInt95,
  SpecInt2000
• consider only blocks where local allocation is
  interesting (enough variables to spill)

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Behavior of Solver
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Proven Optimality
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Comprehensive Results
artifact of interaction with gcc
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Progressive Nature
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Contributions

• New MCNF model for register allocation
• expressive, can model irregular architectures
• can be solved using conventional ILP solvers
• Progressive solution procedure
• decent initial solution
• maintains feasible solution
• improves solution over time
• no optimality guarantees

Progressive