1. 1 Rainer Leupers, University of Dortmund, Computer Science Dept. ISSS ´98 A Uniform Optimization Technique for Offset Assignment Problems Rainer Leupers, Fabian David University of Dortmund, Germany Dept. of Computer Science 12

2. 2 Rainer Leupers, University of Dortmund, Computer Science Dept. ISSS ´98 Overview Offset assignment problem Related work Genetic algorithm approach Exploitation of modify registers Results & conclusions

3. 3 Rainer Leupers, University of Dortmund, Computer Science Dept. ISSS ´98 Offset assignment problem Context: Code generation for DSPs Given: DSP address generation unit (AGU) with # address registers (ARs): k # modify registers (MRs): m auto-increment range (AIR): r Auto-increment capabilities: AR[i] += d, d <= r AR[i] += MR[j] Other address computations cause extra code ! Problem: Assign program variables to memory addresses and ARs, such that the use of auto-increment address computations is maximized !

4. 4 Rainer Leupers, University of Dortmund, Computer Science Dept. ISSS ´98 Offset assignment: example variables: { a, b, c, d } access sequence: (b, d, a, c, d, a, c, b, a, d, a, c, d) AR = 1 AR += 2 AR -= 3 AR += 2 AR ++ AR -= 3 AR += 2 AR - - AR += 3 AR -= 3 AR += 2 AR ++ AR = 3 AR - - AR += 2 AR - - AR += 3 AR -= 2 AR ++ AR - - AR += 2 c a d b 01230123 a b c d 01230123 Layout 1Layout 2 cost: 9cost: 5 Simple Offset Assignment: k = 1 m = 0 r = 1

5. 5 Rainer Leupers, University of Dortmund, Computer Science Dept. ISSS ´98 Related work #ARs#MRsAIR [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

6. 6 Rainer Leupers, University of Dortmund, Computer Science Dept. ISSS ´98 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]

7. 7 Rainer Leupers, University of Dortmund, Computer Science Dept. ISSS ´98 Genetic algorithm approach (2) Mutation: exchange two gene values x yy 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

8. 8 Rainer Leupers, University of Dortmund, Computer Science Dept. ISSS ´98 Exploitation of modify registers (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 !

9. 9 Rainer Leupers, University of Dortmund, Computer Science Dept. ISSS ´98 Exploitation of modify registers (2) AR = 2 AR - - AR += 3 AR ++ AR -= 2 AR - - AR += 3 AR -= 3 AR += 2 AR - - AR += 0 AR -= 2 AR ++ AR - - AR += 0 AR += 3 AR = 2 AR - - MR = 3 AR += MR AR ++ AR -= 2 AR - - AR ++ AR - - AR += MR AR -= MR MR = 2 AR += MR AR - - AR += 0 AR -= MR AR ++ AR - - AR ++ AR += 0 AR += 3 AR = 4 AR ++ MR = 2 AR -= MR AR ++ AR += MR AR -= MR AR += MR MR = 3 AR -= MR AR += MR AR - - AR += 0 AR += MR AR - - AR ++ AR - - AR += 0 AR -= MR v4 v0 v2 v1 v3 v4 v0 v2 v1 v3 v2 v1 v0 v4 0123401234 0123401234 0123401234 heuristic OA + PRA genetic algorithm

10. 10 Rainer Leupers, University of Dortmund, Computer Science Dept. ISSS ´98 Results & 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