Exploratory Ideas in Using RTL Symbolic Simulation for Test Instruction Generation

1
Exploratory Ideas in Using RTL Symbolic
Simulation for Test Instruction Generation

• Supratik Chakraborty, Sasidhar Sunkari, Kailas
  Maneparambil, Vivek Vedula

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Overall Problem Statement

• Given
• RTL description of large design
• Properties (possibly spanning multiple cycles) on
  specific signals
• We wish to
• Symbolically simulate the design
• Derive symbolic relations between inputs and
  signals of interest under given conditions
• Solve symbolic constraints to identify
  instruction sequences for checking given
  properties

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Why work at RTL-level?

• Circuits of the scale of microprocessors
• Bit-level representation Tens of millions of
  signals
• Inefficient reasoning even with state-of-the-art
  techniques
• Abstraction is key to scaling
• With increasing abstraction level
• Size of abstract model reduces easier to reason
• Additional behaviours allowed by model increases
• RTL description
• Design-structure preserving abstraction
• Datapath operations on words instead of bits
• Can keep spurious behaviours under control to
  significant extent by appropriate word-level
  reasoning

4
RTL vs Bit-level Expressions

RTL description
Symbols
Symbolic Expressions

• Must represent and manipulate symbolic expr
  efficiently
• DAG representation of symbolic expressions
• Word-level Size grows as word-level RTL
  description of circuit
• Requires use of (complex)
  word-level functions
• Complex reasoning on
  large expressions
• Bit-level Size grows as bit-level description
  of circuit
• Requires use of basic
  bit-level functions only
• Simpler reasoning on extremely
  large expressions

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High-level Breakup of Approach

• First phase
• Symbolic simulation for getting RTL-level
  relations between inputs and signals of interest
• Manage the complexity of representing and
  manipulating large symbolic expressions
• Second phase
• Develop ability to solve RTL-level expressions to
  yield test instruction sequences
• Leverage existing work on word-level SAT solving
  and also develop new techniques
• Fault-grade generated test instructions
• Extensive experimentation needed to fine-tune
  strategies for generating solving expressions

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Some Initial Observations

• Problem of scale
• Symbolic expressions can get complicated,
  unwieldy
• Affects performance of simulation and solving
• End goal of test instr generation offers more
  freedom than formal verification in managing
  problem of scale
• Can use approximation strategies for generating
  symbolic expressions and also for solving them
• Con Generated test may not hit desired condition
• Fault grading of tests essential
• Hope Significant percentage of tests can be made
  useful with right choice of approximation
  strategies

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Some Initial Observations

• End goal Test instruction generation
• Not interested in yes/no questions (formal
  verification) that limit scope of approximations
• Interested in instruction sequences useful for
  testing corner-case scenarios
• Acceptable even if instruction sequence obtained
  by solving an approximate constraint
• Offers more possibility of using approx to our
  benefit
• Important distinction
• Symbolic simulation for test generation allows
  more freedom for approximation than for formal
  verification
• Can we exploit this effectively?

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Some Initial Observations

• Approximations in symbolic simulation
• When RTL symbolic expressions are created, use
  suitable approximations if they get complicated
• Good approximations expected to exploit
  functional information embedded in RTL/domain
  knowledge
• Main focus of todays talk
• Approximations for making RTL symbolic simulation
  more tractable

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Approximation in CAD

• Approximation methods widely used in CAD
• Gives practically useful solutions to problems
  whose exact solutions are computationally hard
• Boolean function minimization in synthesis
• Static timing analysis with false paths,
  reconvergent fanouts
• Reachability analysis in formal verification
• Power estimation from HDL description
• Scheduling and allocation in high-level synthesis
• Automatic test pattern generation ..

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Success of Approximation (partial list)

• Automated logic synthesis tools
• Approximate Boolean function minimization
• Exact Quine-McCluskey minimization exponentially
  hard
• Spin model checker
• Bit-state hashing an approximation technique
• Widely used in FV community
• Approximate state space reachability
• Work of Cabodi, Cho, Govindaraju, Gupta, Ganai
• Made possible the approximate exploration of
  state spaces of large sequential circuits
• Abstractions (approximations) in program
  verification
• SLAM project at Microsoft Research
• Rich theory Cousot Cousot

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Approximation in Symbolic Simulation

• Not a brand new idea
• C.-J.H. Seger and R.E. Bryants seminal work
  (multiple papers) on symbolic simulation and
  symbolic trajectory evaluation using ternary
  valued logic (approximating bit-level values)
• Symbolic Simulation with Approximate Values, C.
  Wilson, David L. Dill, R.E. Bryant, FMCAD 2000
• Demonstrated to work well on medium-sized
  industrial circuits at bit-level
• Hope We can make it work for RTL-expressions
  with the objective of test instruction generation.

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Symbolic Simulation and Approximation in our
Context

• Symbolic simulation of modules in microprocessors
• Use symbols for words, instructions, control
  signals
• Expressions formed by applying high-level
  operators (possibly non-arithmetic/logic) on
  these symbols
• Uninterpreted functions to be used as far as
  possible
• Interpretation may be forced when approximating
  or when solving
• Interpretation to be avoided for blocks whose
  outputs dont affect desired property on signals
• Approximation to be introduced as size of
  expression blows up
• Accuracy of symbolic relations traded off with
  complexity (space time) of manipulating and
  solving

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Simplifying Expressions

• Word-level symbolic expressions appear attractive
• But, size of expr (? size of RTL) can become
  large
• Can we simplify a bit?
• Canonicalizing expressions
• Equivalent expressions represented by unique DAG
• Often reduces DAG size makes simulation/solving
  easier
• Example (A0..15 word_plus ZERO0..15)
  equiv to A0..15
• Non-trivial to implement
• Requires word-level reasoning with complex
  functions
• Semi-canonicalization may be more practical
• Partial identification of equivalent expressions
• Conditional canonicalization
• Identifying expression equivalence under given
  conditions

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Approximate Symbolic Expressions

• Eventual use of symbolic expressions
• Getting solutions to sets of symbolic constraints
• Using solutions to obtain desired test instr
  sequences
• Approximate expressions
• Lead to approximate solutions
• Over-approximation Relaxing constraints
• All true solutions contained in approximate
  solution
• May contain spurious solutions
• Under-approximation Restricting constraints
• All approximate solutions are true solutions
• May miss some true solutions

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How to Approximate?

• Simple symbolic expression DAG

System of symbolic constraints (expressions in
prefix notation)
(E (word_plus (bitcatenate E1 E2)
time_adv(
word_mult(E3, E4)
) ) ) AND (E1 ..) AND
(E2 ..) AND (E3 ..) AND (E4 ..)

• Conjunction of sub-constraints
• Can we replace sub-constraints
• with more/less relaxed ones?

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Approximation Relations

• Original expression
• Approximate expression

(E (word_plus (bitcatenate E1 E2)
time_adv(
word_mult(E3, E4)
) ) ) AND (E1 ..) AND
(E2 ..) AND (E3 ..) AND (E4 ..)
Approximated to
E
word_plus
bitcatenate
time_adv
R1, R2 approximate relations between
subexpressions Can now eliminate subexpr
affecting only E3 or E4
word_mult
E2
E1
E3
E4
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Solving with Approximate Constraints

Example system of constraints to be solved
Actual solution
Overapprox relation
Approximated to
Underapprox relation
Possible solution space yielding test
instruction sequence
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A Naive Approximation Strategy

• Build symbolic expressions bottom up from RTL
• Semi-canonicalize once size exceeds threshold T1
• Once size exceeds threshold T2 (T2 gt T1)
• Identify subexpressions for which it is
  beneficial to introduce approximate relations
• Include approximate relations in set of
  constraints
• Exclude constraints that affect only those
  subexpressions which have been approximated.
• Continue until size reduces below T2
• Store original constraints for approximated
  subexpressions
• To be used in case approximate system of
  constraints does not yield desired results

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Finding Approximation Relations

• Several possible strategies
• A carefully designed set of syntactic rules
• E (A word_plus B),
• F (A word_plus (B word_mult C)
• A, B, C positive words
• Overapprox relation F word_greater_than_eq E
• Underapprox relation (F E) OR (F EB)
• Infer implications through a simple incomplete
  word-level decision procedure
• Constr1 ? Constr2 Constr1 is underapprox of
  Constr2
• Constr2 is
  overapprox of Constr1

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Finding Approximation Relations

• Further strategies
• Extrapolate from bit-level approximations
• Consider all words as 1-bit long
• Use bit-level techniques (e.g. BDDs / SAT
  solving) to find bit-level over- and
  under-approximations
• Extrapolate to word-level over- and
  under-approximations
• Caveat Not all bit-level approximations can be
  extrapolated in this way

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Finding Approximation Relations

• Further strategies
• Simplify symbolic expressions using values from
  lattice of possible values (e.g. 0, 1, X, X as
  words)
• Using all Xs for some symbolic inputs, if we
  find that a constraint C1 simplifies to C2
• C2 over-approximates C1
• Using specific constants (0, 1, etc) for some
  symbolic inputs, if we find that C1 simplifies to
  C2
• C2 under-approximates C1

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Finding Approximation Relations

• Further strategies
• Suppose final symbolic constraint to be solved
• (constr1 ? constr2) AND constr3
• constr2 can be approximated considering
• (? constr3 ? ? constr1) as dont care
• Approximate constraints using knowledge of other
  constraints

Actual solutions
Solution space
Overapprox of const2
Underapprox of constr2
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Finding Approximation Relations

• A crucial step for simplifying expressions and
  still obtaining desired solutions
• Quality of approximation relations affects
  accuracy of results
• Quality depends on
• Choosing right subexpressions to relate through
  approximation relations
• Formulating right approximation relations
• Efficiency of constructing relations also
  important
• Soliciting suggestions from others!

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Hierarchy of Approximations

• Approximating relation between E1, E2 leads to
  lower accuracy than
• Approximating relation between E3, E4, E5, E6, OR
  
• Approximating relation between E2, E6, E5
• Gives rise to a hierarchy of approximation
  relations
• Approximation relations can also be made more
  accurate by using computationally more expensive
  inferences
• Also gives rise to a hierarchy

Symbolic expr DAG
E
E2
E1
E3
E6
E4
E5
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Hierarchy of Approximations

• Approximations between subexpressions higher up
  in DAG representation are more approximate
• Hierarchy of approximate expressions
• Quality of approximation reduces as we go higher
  in hierarchy
• Expressions become simpler as we go higher in
  hierarchy
• Separate hierarchies for over- and
  under-approximation relations
• Can use only one of over- or under-approximation
  hierarchies when simplifying expressions
• Mixing may take us out of solution space

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Proposal for Research

• Extensive experimentation needed
• Right approximation strategies to be identified
  based on structure and operators used in
  expressions
• Need to find right balance on the continuum of
  accuracy-complexity tradeoff
• Should be done primarily through experimentation
• Theoretical underpinnings to ensure that chosen
  strategies do not mix over- under-approximations
  
• Research to figure out
• Right approx strategies when building expressions
• Ability to solve expressions with these
  approximations
• of generated tests that hit conditions of
  interest

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Proposed Plan of Action

• Short-term
• Use Forte to estimate complexity/seq depth of
  symbolic expressions (at bit-level) of a part of
  x86 model developed at IIT Madras
• Feel for the complexity of expressions at
  bit-level
• Useful for quantifying benefits of word-level
  symbolic simulation
• Verilog to Exlif conversion to be done at Intel
• Environment model (providing sequence of symbolic
  instructions) for STE being done at IIT Bombay
• Should be over in a few weeks time

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Proposed Plan of Action

• First phase
• Use x86 model from IIT Madras and also picoJava
  model from Sun as benchmarks for developing
  word-level symbolic simulator
• Expect a first prototype symbolic simulator in
  6-8 months time from now
• Symbols for words -- no bit-level splitting in
  expressions (unlike Forte)
• Use high-level operators, possibly uninterpreted
• Simultaneously look for patterns of operator
  combinations that allow for replacement by sound
  approximations
• Syntactic approach to begin with

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Proposed Plan of Action

• First phase
• Incorporate simplification of expressions by
  approximation relations in simulator
• Ensure output expressions are in format that are
  easily parseable by existing word-level SAT
  solvers and also by solver to be developed in
  second phase
• Possible student visit to Intel, Bangalore to
  ensure that simulator works well for Intel
  designs
• M.Tech. Student (Sasidhar Sunkari) already
  working on this

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Proposed Plan of Action

• Second phase
• Develop capability to solve symbolic expressions
  generated by symbolic simulator
• Expect to start work on this before completion of
  first phase by student from next batch of M.Tech.
  students
• Propose to use the SMT (Satisfiability Modulo
  Theories) and ICS (Integrated Canonizer and
  Solver)-type approaches to solve this
• Incorporate special theories for high-level
  operators on words
• Integrate these theories with existing theories
  of bit-vectors, Booleans, uninterpreted
  functions, etc.
• Looking for more suggestions

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Conclusion

• Preliminary ideas for controlling size of
  symbolic expressions while still ensuring that we
  can use them to get test instruction sequence
• Need research on finding good and efficiently
  computable approximation relations
• More research on developing theories for solving
  word-level expressions
• Soliciting inputs and feedback on overall
  potential of idea
• More details to be worked out