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Pipeline Synthesis and Optimization from Branched Feedback Dataflow Programs

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Abstract

Large dataflow designs are a result of behavioral specification of modern complex digital systems and/or a result of unfolding and transforming looped and branched programs. Since deep-submicron silicon technology provides large amounts of available resources, pipelining optimization without (or with minimal) resource sharing can give significant advantages in performance. High-level synthesis of CAL-programs is particularly popular in computation intensive applications (e.g., image and video processing, cryptography, wireless communication, etc.) where feedback actors with data flows at input and output ports represent loop-like behavior. In this work, we propose techniques for transforming, analysis, speculatively pipelining and optimizing large branched feedback dataflow programs. We develop an accurate algorithm and introduce fast dynamic and mixed static / dynamic heuristics that firstly minimize the number of pipeline stages for a given pipeline-stage time-period, and secondly minimize the overall pipeline registers size by means of appropriate assignment of feedbacks and instructions to pipeline stages. We also propose a genetic algorithm for tuning the heuristics for a particular design. The experimental results show the algorithms we propose give quickly solutions that are very close to accurate solutions and overcomes the earlier developed algorithms regarding computing time and pipeline parameters.

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Acronyms

1. CAL Concurrent algorithmic language.

2. ASAP As soon as possible pipeline scheduling algorithm.

3. ALAP As late as possible pipeline scheduling algorithm.

4. P A set of operators (statements, instructions).

5. V A set of variables.

6. inputs(p) A set of input variables of operator p.

7. outputs(p) A set of output variables of operator p

8. size(v) A bit-size of variable v

9. prod(v) Operators-producers of variable v

10. cons(v) Operators-consumers of variable v.

11. T A set of conditional Boolean variables.

12. Z A set of primary Boolean variables.

13. H A set of Boolean functions that evaluate the conditional variables over the primary variables.

14. F A set of feasible Boolean functions for values of pairs of primary variables.

15. λ A Boolean function that characterizes the feasible set of vector values of primary variables.

16. μ A Boolean function that takes value 1 when two conditional variables are orthogonal.

17. Rdirect Operators direct precedence relation.

18. R Transitive closure of Rdirect.

19. succ(p) Operators-successors of operator p.

20. pred(p) Operators-predecessors of operator p.

21. G A matrix of all operator pairs longest paths lengths.

22. Fbr(s) A subset of operators in a feedback region of variable s.

23. S A set of pipeline stages.

24. stage(p) An assignment of operator p to a stage.

25. Tstage A constraint on the pipeline-stage time-period.

26. C An operator conflict relation (graph).

27. Cn An operator nonconflict relation (graph).

28. cdpred(p) A set of direct predecessors of operator p on graph C.

29. ncdpred(p) A set of direct predecessors of operator p on graph Cn

30. cdsucc (p) A set of direct successors of operator p on graph C

31. ncdsucc (p) A set of direct successors of operator p on graph Cn

32. asap A pipeline schedule that ASAP algorithm generates on conflict graph C

33. alap A pipeline schedule that ALAP algorithm generates on conflict graph C.

34. Rsize(stage) An overall pipeline registers size of the schedule described by the operators vector assignment stage

35. lifetime(v) Lifetime of variable v over pipeline stages.

36. FASAP Extension of ASAP for branched feedback programs.

37. FALAP Extension of ALAP for branched feedback programs.

38. fasap A pipeline schedule that FASAP algorithm generates on conflict graph C.

39. falap A pipeline schedule that FALAP algorithm generates on conflict graph C.

40. LCSBB Least cost search branch and bound algorithm of pipeline optimization.

41. FLCSBB Extension of LCSBB for branched feedback dataflow programs.

42. flcsbb A pipeline schedule that FLCSBB algorithm generates on conflict graph C.

43. FHADD Feedback dataflow optimization Heuristic Algorithm using dynamic heuristics for operators and stages.

44. FHASD Feedback dataflow optimization Heuristic Algorithm using static heuristics for operators and dynamic heuristics for stages.

45. early(p) A lower bound of a range of available stages for operator p.

46. late(p) A upper bound of a range of available stages for operator p

47. lifestim(v) A lower bound of lifetime of variable v over pipeline stages

48. early(v) An upper bound of the earliest stage of producers of variable v

49. late(v) A lower bound of the latest stage of consumers of variable v

50. pos(x) A function whose value equals 0 if x ≤ 0, and equals x otherwise

51. χ(p) A heuristic weight of operator p whose maximal value indicates that p is preferable for scheduling

52. ω A vector of heuristic factors

53. ρ(p) A vector of heuristic parameters of operator p.

54. GA Genetic algorithm for tuning heuristics.

55. F(ω) A fitness function of individual ω that represents quality of the corresponding pipeline solution.

56. FPS A fitness proportionate selection operation.

57. WPS A worst parent selection operation.

58. WIS A worst individual selection in the current generation.

59. HUX A half uniform crossover operation.

60. SOX A single offspring crossover operation.

61. α, β Heuristic factor weights.

62. ε A mutation factor

63. pcross Probability of choosing the crossover

64. pmut Probability of choosing the mutation

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Authors and Affiliations

  1. Computer and System Software Dpt, Belarusian National Technical University, Minsk, Belarus

    Anatoly Prihozhy

  2. EPFL SCI STI MM, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Simone Casale-Brunet & Marco Mattavelli

  3. EPFL IC IINFCOM VLSC, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Endri Bezati

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  1. Anatoly Prihozhy
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  2. Simone Casale-Brunet
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  3. Endri Bezati
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  4. Marco Mattavelli
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Correspondence to Anatoly Prihozhy.

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Prihozhy, A., Casale-Brunet, S., Bezati, E. et al. Pipeline Synthesis and Optimization from Branched Feedback Dataflow Programs. J Sign Process Syst 92, 1091–1099 (2020). https://doi.org/10.1007/s11265-020-01568-5

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