Functional Test Generation using Constraint Logic Programming Zhihong Zeng, Maciej Ciesielski Dept. of Electrical & Comp. Engineering University of Massachusetts, Amherst Bruno Rouzeyre LIRMM, Université de Montpellier II

3-5 Dec. 2001VLSI-SOC Outline Introduction Functional test generation for design validation Related work on satisfiability (SAT) Boolean and hybrid approaches to SAT New word-level SAT solver Unified Boolean and arithmetic domains Based on Constraint Logic Programming Experimental results, conclusions

3-5 Dec. 2001VLSI-SOC Functional Simulation A viable approach to design validation Scales well with design size Predictable run time The way engineer thinks Downsides Incomplete, low “functional” coverage Confidence: when am I done? (coverage metrics are used to help)

3-5 Dec. 2001VLSI-SOC Functional Validation - typical scenario Coverage Normalized verification test cycles 50 % 80 % 100 % Deterministic tests Pseudo-random directed tests Manual directed tests Test development time ?

3-5 Dec. 2001VLSI-SOC Deterministic Testing - Automation Functional test generation Given an RTL design and a coverage metric Goal: generate test vectors to reach predefined coverage goal Coverage metrics: code coverage, state coverage, transition coverage, etc Formulate as satisfiability (SAT) problem

3-5 Dec. 2001VLSI-SOC Our Design Validation Framework Simulation Seed Environment Symbolic Simulation (bounded time model) Symbolic Simulation (bounded time model) Convert to a SAT Problem Word-level SAT BDDs Boolean SAT BDDs Boolean SAT Next Simulation Target Done Y N

3-5 Dec. 2001VLSI-SOC Formulating a SAT Problem F s + D * A B C E 0 1 x Simulation target (value to be satisfied) state=s 3 F= b’0110 F> d’ Test vector Symbolic expression to be satisfied

3-5 Dec. 2001VLSI-SOC Design Validation of RTL Designs Behavioral or RT-level designs contain datapath and control logic Word-level arithmetic operators Boolean logic Previous approaches are not efficient Gate-level ATPG, Boolean SAT, BDDs – bit-level Word-level information is not utilized Need more abstract, word-level models

3-5 Dec. 2001VLSI-SOC Previous Work - Boolean SAT Based on Davis-Putnam procedure Tools: SATO, RelSat, GRASP, Chaff, … Conflict-based non-chronological back-jumping Conflict-based learning Variable ordering Restart Careful implementation BDD-based SAT WORD-LEVEL information is ignored!

3-5 Dec. 2001VLSI-SOC Previous Work - Hybrid SAT HSAT: [Fallah et al. DAC’98] CNF-based SAT to solve Boolean constraints Linear Programming relaxation to check consistency of arithmetic constraints ATPG + Arithmetic solver [Huang et al. DAC’00] Gate-level ATPG to justify objectives in Boolean domain Modular arithmetic solver to solve arithmetic constraints Word-level implications between two domains are attempted: weak, not robust

3-5 Dec. 2001VLSI-SOC Hybrid Approaches - Limitations Inefficient constraint propagation across domains: Boolean/arithmetic a=1 12>A A  3B+C B>C C>1 A<4C fghjfghj LKLK b  f=1, g=1 h=1, j=1 k 1  Arithmetic solver: infeasible  Conflict, backtrack 0 b

3-5 Dec. 2001VLSI-SOC Constraint Propagation – a Problem A better constraint propagation: tighter interaction between the two domains a=1 12>A A  3B+C B>C C>1 A<4C fghjfghj LKLK b 0  f=1, g=1 h=1, j=1 b Boolean to Arithmetic Arithmetic to Boolean  A=11,C=2  k=0

3-5 Dec. 2001VLSI-SOC Our approach: Word-level SAT in a unified domain Put arithmetic and Boolean constraints in same domain Constraint propagation is implicit to one engine More efficient than hybrid approach Use the state-of-the-art constraint solving techniques No need to develop your own Branch & Bound procedure Constraint solving is extensively researched by AI, CS Our previous work LPSAT: SAT based on Linear Programming A new word-level SAT Based on constraint logic programming (CLP-SAT)

3-5 Dec. 2001VLSI-SOC Why Another Unified Approach? LPSAT [DATE’01]: SAT based on ILP Non-linear constraints must be linearized Numerical convergence problem (integers) Optimization engine CPLEX ($$, not a SAT solver) Alternative: SAT based on Constraint Logic Programming (CLP-SAT)

3-5 Dec. 2001VLSI-SOC CLP-SAT: SAT using Constraint Logic Programming Use Gnu-prolog as solving engine Publicly available Constraint solving over finite domain A native Prolog compiler: fast execution time Modeling is straightforward No need to linearize complex operators (MPY) Built-in predicates for Boolean gates

3-5 Dec. 2001VLSI-SOC Design/Constraint Modeling Identify Arithmetic and Boolean domains Word-level signals: B, D, E, X, Z (Partial) bit expansion: A, C, Y Y = Y[0] + 2*Y[1] + 4*Y[2] + … Single-bit Boolean signals: s A Z X Y < s + B D * C E 1 0

3-5 Dec. 2001VLSI-SOC CLP-SAT – Modeling the Constraints Arithmetic/BooleanGnu-Prolog Predicates Z = A * BZ #= A * B Z = and (A, B) A #  B #  Z Z = or (A, B) A #  B #  Z Z = not (A)A #\ Z Z = ite(s, A, B) (s #= 1) #  (Z #= A), (s #= 0) #  (Z #= B)

3-5 Dec. 2001VLSI-SOC Handling Modular Arithmetic A 16-bit adder: Z = A + B Z <= A BZ ? D 9 Adding a free variable, D A+B = Z + D*2 8 D <= 2 9 Z <= 2 8 Z = (A+B) mod 256

3-5 Dec. 2001VLSI-SOC Handling Wide Arithmetic Operators > 56-bit s A B > 28-bit AHAH BHBH == 28-bit > 28-bit ALAL BLBL s Internal representation (computer): 32-bit words Largest domain in CLP is 28-bit Decompose using Boolean logic

3-5 Dec. 2001VLSI-SOC Experiments - Benchmarks M13 – 13-bit multipliers (sat, non) M16 – 16-bit multipliers, decomposed (sat, non) Square - compute Z 2 = X 2 + Y 2, 16-bit variables Quadratic - solve X 2 = a X + b for 16-bit X Linear-k- k-wide chain of comparators (k=40, 90), simple structure, large # inputs (over 1200) GCD-k- sequential circuit, 24-bit gcd unrolled k=20, 40 time frames Mdpe- multiplier feeding a dynamic priority encoder, taken from realistic design

3-5 Dec. 2001VLSI-SOC Benchmarks - Statistics BenchmarksCLP-SAT # lines LPSAT #constraints CNF-SAT #clauses M16x square quadratic Linear(2) gcd gcd Mpde(2)

3-5 Dec. 2001VLSI-SOC Experimental Results Run-time speed-up TestcaseCLP-SATLPSATSATOGRASPCHAFF M16*16(s) M16*16(n) Square(1) Square(0) Quadratic Linear(1) Gcd201.1sec*0.03sec*-- Gcd401.9sec*0.08sec*-- Mdpe(1) *: real CPU time

3-5 Dec. 2001VLSI-SOC Conclusions Functional test generation for design validation Symbolic simulation + word-level SAT A new word-level SAT in a unified domain Based on constraint logic programming A good alternative to LPSAT Use the state-of-the-art constraint solving techniques Preliminary results are promising: Good for mixed arithmetic and Boolean logic Limitation: not competitive for designs with large portions of random logic