a uniform optimization technique for offset assignment problems

1Rainer Leupers, University of Dortmund, Computer Science Dept. ISSS ´98

A Uniform Optimization A Uniform Optimization Technique Technique

for Offset Assignment Problemsfor Offset Assignment Problems

Rainer Leupers, Fabian David

University of Dortmund, Germany

Dept. of Computer Science 12


OverviewOverview

• Offset assignment problem

• Related work

• Genetic algorithm approach

• Exploitation of modify registers

• Results & conclusions


Offset assignment problemOffset assignment problem

Context: Code generation for DSPsGiven: DSP address generation unit (AGU) with

# address registers (ARs): k# modify registers (MRs): mauto-increment range (AIR): r

Auto-increment capabilities:AR[i] += d, d <= rAR[i] += MR[j]

Other address computations cause extra code !

Problem: Assign program variables to memory addressesand ARs, such that the use of auto-increment address computations is maximized !


Offset assignment: exampleOffset assignment: example

variables: { a, b, c, d }access sequence: (b, d, a, c, d, a, c, b, a, d, a, c, d)

AR = 1AR += 2AR -= 3AR += 2AR ++AR -= 3AR += 2AR - -AR - - AR += 3AR -= 3AR += 2AR ++

AR = 3AR - -AR - -AR - -AR += 2AR - -AR - -AR += 3AR -= 2AR ++AR - - AR - -AR += 2

c

a

d

b

0123

a

b

c

d

0123

Layout 1 Layout 2

cost: 9 cost: 5

Simple OffsetAssignment:

k = 1m = 0r = 1


Related workRelated work

#ARs #MRs AIR

[Bartley92] 1 - 1

[Liao95] k - 1

[Leupers96] k m 1

[Wess97] 1 - 2

[Sudarsanam97] k - r

this work k m r

Offset assignment for different AGU models:

Further work on address optimization for fixed layout


Genetic algorithm approach (1)Genetic algorithm approach (1)

Chromosomal representation: n variables, k address registers each individual is a permutation of { 1, ..., n + k - 1} example: n = 6, k = 2

2 5 3 1 7 6 4 0 1 2 3 4 5 offset mapping

switch to next AR

Fitness function:F(I) = # transitions (v,w) in access sequence, such that

v, w assigned to different ARs, or|off(v) - off(w) | <= r

AR[1] AR[2]


Genetic algorithm approach (2)Genetic algorithm approach (2)

Mutation: exchange two gene values

x y y x

Crossover: standard order crossover operation

Optimization procedure: form initial population for N generations do: select parent individuals generate offspring mutate offspring emit best individual


Exploitation of modify registers Exploitation of modify registers (1)(1)

[Leupers96]: Modification of Belady‘s optimal page replacement algorithm can be used for optimal exploitation of m MRs for a fixed offset assignment (only postpass optimization)

PRA(I) = # address computations that can be saved by exploiting MRs for a given offset assignment

modified fitness function: F´(I) = F(I) + PRA(I)

=> exploitation of MRs included into GA !


Exploitation of modify registers Exploitation of modify registers (2)(2)

AR = 2AR - -AR += 3AR ++AR -= 2AR - -AR += 3AR -= 3AR += 2AR - -AR += 0AR += 0AR -= 2AR ++AR - -AR += 0AR += 3

AR = 2AR - -MR = 3AR += MRAR ++AR -= 2AR - - AR ++AR - - AR += MRAR -= MRMR = 2AR += MRAR - -AR += 0AR += 0AR -= MRAR ++AR - -AR ++AR += 0AR += 3

AR = 4AR ++MR = 2AR -= MRAR -= MRAR ++AR += MRAR -= MRAR += MRMR = 3AR -= MRAR += MRAR - - AR - - AR += 0AR += 0AR += MRAR - -AR ++AR - -AR += 0AR -= MR

v4

v0

v2

v1

v3

v4

v0

v2

v1

v3

v3

v2

v1

v0

v4

0

1

2

3

4

0

1

2

3

4

0

1

2

3

4

heuristic OA heuristic OA+ PRA

geneticalgorithm


Results & conclusionsResults & conclusions

Statistical evaluation: 32 % improvement over OA heuristic with postpass MR optimization 32 % improvement over Wess‘ simulated annealing technique Runtime: typically 10 CPU seconds (Pentium II)

Main contributions: First uniform offset assignment technique, arbitrary k, m, r values Significant improvements in code quality over previous techniques, largely due to better exploitation of MRs

a uniform optimization technique for offset assignment problems

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