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Validating High-Level Synthesis

Validating High-Level Synthesis. Sudipta Kundu , Sorin Lerner, Rajesh Gupta Department of Computer Science and Engineering, University of California, San Diego. …. x = a * b; c = a < b; if (c) then a = b – x; else a = b + x; a = a + x; b = b * x; …. C/C++, SystemC

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Validating High-Level Synthesis

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  1. Validating High-Level Synthesis Sudipta Kundu, Sorin Lerner, Rajesh Gupta Department of Computer Science and Engineering, University of California, San Diego

  2. …. x = a * b; c = a < b; if (c) then a = b – x; else a = b + x; a = a + x; b = b * x; …. • C/C++, SystemC < 100 – 10K lines > Functionally Equivalent Data path Functionally Equivalent S0 Controller S1 !f f S3 S2 • Verilog, VHDL < 1K – 100K lines > S4 High-Level Synthesis Algorithmic Design  Functionally Equivalent High-Level Synthesis (HLS) Scheduled Design Register Transfer Level Design (RTL)

  3. Equivalence Checker • Once and for all • HLS tool always produce correct results • For each translation • Does not guarantee • => HLS tool is bug free Checker The Problem Transformed Program (Implementation) • Translation Validation (TV) • Optimizing Compiler [Pnueli et al. 98] [Necula 00] [Zuck et al. 05] Input Program (Specification) Transformations Is the Specification “functionally equivalent” to the Implementation? Does guarantee => any errors in translation will be caught when tool runs

  4. Contributions • Developed TV techniques for a new setting: HLS • Algorithm uses a bisimulation relation approach. • Implemented TV for a realistic HLS tool: SPARK • Widely used: 4,000 downloads, over 100 active users. • Large Software: around 125, 000 LoC. • Ran it on 12 benchmarks • Modular: works on one procedure at a time. • Practical: took on average 6 secs to run per procedure. • Easy to Implement: only a fraction of development cost of SPARK. • Useful: found 2 previously unknown bugs.

  5. Outline • Motivation and Problem definition • Our Approach using an Example • Definition of Equivalence • Translation Validation Algorithm • Generate Constraints • Solve Constraints • Experiments and Results • SPARK: Parallelizing HLS Framework • Conclusion

  6. + + < a0 a0 a2 i3: (k < 10) i6: ¬ (k < 10) a3 a5 i7: return sum a6 a4 i1: sum = 0 a1 i1: sum = 0 i2: k = p Resource Allocation: a1 i2: k = p a2 i3: (k < 10) i6: ¬ (k < 10) i4: k = k + 1 a3 a5 i7: return sum i4: k = k + 1 i5: sum = sum + k a6 a4 i5: sum = sum + k An Example of HLS Specification: Original Program: intSumTo10 (int p) int sum = 0, k = p; while (k < 10) sum += ++k; return sum; intSumTo10 (int p) int sum = 0, k = p; while (k < 10) sum += ++k; return sum; 10 sum = ∑k p+1

  7. + + < a0 a0 a0 a2 i3: (k < 10) i6: ¬ (k < 10) i1: sum = 0 a1 a3 a5 i2: k = p i7: return sum a6 a4 i1: sum = 0 a1 i1: sum = 0 i2: k = p Resource Allocation: a1 i2: k = p a2 i3: (k < 10) i6: ¬ (k < 10) a3 a5 i7: return sum i4: k = k + 1 a6 a4 i5: sum = sum + k An Example of HLS Specification: Loop Pipelining: intSumTo10 (int p) int sum = 0, k = p; while (k < 10) sum += ++k; return sum; t = k + 1 i4: k = k + 1 i4: k = t i5: sum = sum + k t = k + 1

  8. + + < a0 a0 a2 i3: (k < 10) i6: ¬ (k < 10) i1: sum = 0 a1 a3 a5 i2: k = p i7: return sum a6 a4 i1: sum = 0 Resource Allocation: a1 i2: k = p a2 i3: (k < 10) i6: ¬ (k < 10) a3 a5 i7: return sum i4: k = k + 1 a6 a4 i5: sum = sum + k An Example of HLS Specification: Copy Propagation: intSumTo10 (int p) int sum = 0, k = p; while (k < 10) sum += ++k; return sum; t = p + 1 t = k + 1 i4: k = t i5: sum = sum + t i5: sum = sum + k t = k + 1 t = t + 1

  9. + + < a0 a0 a0 i1: sum = 0 a1 i1: sum = 0 i2: k = p i41: t = p + 1 i2: k = p i1: sum = 0 t = p + 1 Resource Allocation: a1 a2 i3: (k < 10) i6: ¬ (k < 10) i2: k = p a3 a5 a2 i3: (k < 10) i6: ¬ (k < 10) i7: return sum i4: k = t a3 a5 a6 a4 i7: return sum i4: k = k + 1 i5: sum = sum + t a6 a4 Read After Write dependency i5: sum = sum + k t = t + 1 i4: k = t i5: sum = sum + t i42: t = t + 1 An Example of HLS Specification: Scheduling: intSumTo10 (int p) int sum = 0, k = p; while (k < 10) sum += ++k; return sum;

  10. a0 b0 j1: sum = 0 j2: k = p j41: t = p + 1 Re-labeled i1: sum = 0 a1 b1 j3: (k < 10) j6: ¬ (k < 10) i2: k = p b2 b3 a2 i3: (k < 10) i6: ¬ (k < 10) j7: return sum a3 a5 b4 i7: return sum i4: k = k + 1 a6 a4 i5: sum = sum + k j4: k = t j5: sum = sum + t j42: t = t + 1 An Example of HLS Specification: Implementation: intSumTo10 (int p) int sum = 0, k = p; while (k < 10) sum += ++k; return sum; ≡

  11. Definition of Equivalence • Specification ≡ Implementation => They have the same set of execution sequences of visible instructions. • Visible instructions are: • Function call and return statements. • Two function calls are equivalent if the state of globals and the arguments are the same. • Two returns are equivalent if the state of the globals and the returned values are the same.

  12. Specification Implementation s’1 s1 i i s2 s’2 Technique for Proving Equivalence • Bisimulation Relation: relates a given program state in the implementation with the corresponding state in the specification and vice versa. • It satisfies the following properties: • The start states are related. Visible Instruction • Theorem: If there exists a bisimulationrelation between the specification and the implementation, then they are equivalent.

  13. Our Approach • Split program state space in two parts: • control flow state, which is finite. => explored by traversing the CFGs. • dataflow state, which may be infinite. => explored using Automated Theorem Prover (ATP). • Bisimulation relation: set of entries of the form (p1, p2, Ф). • p1 – program point in Specification. • p2 – program point in Implementation. • Ф – formula that relates the data.

  14. a0 Specification ps = pi Implementation b0 i1: sum = 0 j1: sum = 0 j2: k = p j41: t = p + 1 a1 ks = kiΛ sums = sumi Λ (ks + 1) = ti i2: k = p a2 b1 i3: (k < 10) j3: (k < 10) i6: ¬ (k < 10) j6: ¬ (k < 10) a3 b2 sums = sumi a5 i4: k = k + 1 b3 j7: return sum i7: return sum j4: k = t j5: sum = sum + t j42: t = t + 1 a4 a6 b4 i5: sum = sum + k Bisimulation Relation • Bisimulation relation: set of entries of the form (p1, p2, Ф). • p1 – program point in Specification. • p2 – program point in Implementation. • Ф – formula that relates the data.

  15. Translation Validation Algorithm • Two step approach. • Generate Constraints: traverses the CFGs simultaneously and generates the constraints required for the visible instructions to be matched. • Solve Constraints: solves the constraints using a fixpoint algorithm. • For loops: iterate to a fixed point. • May not terminate in general. • But in practice can find the bisimulation relation.

  16. a0 Ψ(a0, b0) b0 i1: sum = 0 j1: sum = 0 j2: k = p j41: t = p + 1 a1 Ψ(a2, b1) i2: k = p a2 b1 i3: (k < 10) j3: (k < 10) i6: ¬ (k < 10) j6: ¬ (k < 10) Ψ(a5, b3) a3 b2 a5 i4: k = k + 1 b3 j7: return sum i7: return sum j4: k = t j5: sum = sum + t j42: t = t + 1 a4 a6 b4 i5: sum = sum + k Ψ(a2, b1) Ψ(a0, b0) a2 b1 Ψ(a2, b1) a0 b0 i3 a2 b1 j3 i4 j4 j5 j42 i6 j6 i5 a5 b3 j1 j2 j41 i1 Ψ(a5, b3) a2 b1 a2 b1 Ψ(a2, b1) i2 Ψ(a2, b1) Generate Constraints Specification Implementation Constraints: Constraint Variable • Branch Correlation • Strongest Post Condition • Structure of the code Ψ(a2, b1) ⇒ks = ki Ψ(a5, b3) ⇒ sums = sumi

  17. a0 Ψ(a0, b0) Specification Implementation Ψ(a2, b1) b0 i1: sum = 0 j1: sum = 0 j2: k = p j41: t = p + 1 ATP[ Ψ(a2, b1)⇒ WP( Ψ(a2, b1)) ] a1 Ψ(a2, b1) i2: k = p a2 Ψ(a2, b1): ks = ki b1 i3: (k < 10) j3: (k < 10) i6: ¬ (k < 10) j6: ¬ (k < 10) a2 b1 Ψ(a5, b3) a3 b2 j3: (ki < 10) j4: ki = ti j5: sumi = sumi + ti j42: ti = ti + 1 a5 i4: k = k + 1 b3 i3: (ks < 10) i4: ks = ks + 1 i5: sums = sums + ks j7: return sum i7: return sum j4: k = t j5: sum = sum + t j42: t = t + 1 a4 a6 b4 i5: sum = sum + k Ψ(a2, b1) Ψ(a0, b0) a2 b1 a2 b1 Ψ(a2, b1) a0 b0 Ψ(a2, b1): ks = ki i3 a2 b1 j3 i4 j4 j5 j42 i6 j6 i5 a5 b3 j1 j2 j41 i1 Ψ(a5, b3) a2 b1 a2 b1 Ψ(a2, b1) i2 Ψ(a2, b1) Solve Constraints Ψ(a0, b0): ps = pi : ks = ki ∧ WP(Ψ(a2, b1) ) : ks = ki∧ (ks + 1) = ti Ψ(a2, b1) : ks = ki Λ (ks + 1) = ti Ψ(a2, b1) : ks = kiΛ (ks + 1) = ti Λ sums = sumi Ψ(a2, b1): ks = ki Ψ(a2, b1): True WP( Ψ(a2, b1)) : (ki + 1) ⇒ (ks + 1) ⇒ (ks + 1) = ti Ψ(a5, b3) : True Ψ(a5, b3) : sums = sumi Constraints: Ψ(a2, b1) ⇒ks = ki  X Ψ(a5, b3) ⇒ sums = sumi X   X X  X 

  18. Validation Engine SPARK: Parallelizing HLS Framework SPARK C Program Intermediate Representation (IR) No Pointer No Recursion No goto Binding Scheduled IR High Level Synthesis RTL

  19. Results

  20. Read After Write dependency Did not copy array index Bugs Found in SPARK • Array Copy Propagation • Code motion

  21. Related Work • Translation Validation • Sequential Programs [Pnueli et al. 98] [Necula 00] [Zuck et al. 05] • CSP Programs [Kundu et al. 07] • HLS Verification • Scheduling Step • Correctness preserving transformation [Eveking 99] • Symbolic Simulation [Ashar 99] • Formal assertions [Narasimhan 01] • Relational approaches for Equivalence of FSMDs [Kim 04, Karfa 06]

  22. Conclusion and Future Directions • Presented an automated algorithm for translation validation of the HLS process. • Implemented it for a HLS tool called SPARK. • Modular: works on one procedure at a time. • Practical: took on average 6 secs to run per procedure. • Easy to Implement: only a fraction of development cost of SPARK. • Useful: found 2 previously unknown bugs. • In future, • Remaining phases of SPARK: parsing, binding and code generation.

  23. Thank You

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