Approximate Reachability With Combined Symbolic And Ternary Simulation - PowerPoint PPT Presentation

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Approximate Reachability With Combined Symbolic And Ternary Simulation

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Title: Approximate Reachability With Combined Symbolic And Ternary Simulation


1
Approximate Reachability With Combined Symbolic
And Ternary Simulation
  • Mike Case, Jason Baumgartner, Hari Mony, Bob
    Kanzelman IBM System and Technology Group
  • FMCAD 2011

Now with Calypto Design Systems
2
Outline
  • Approximate Reachability
  • Our Contributions
  • Symbolic Simulation
  • X-Saturation
  • Experimental Results

3
Ternary Simulation
  • Ternary Simulationsimulate an AIG over 3-valued
    logic

Input 1 AND Input 2 0 1 X
0 0 0 0
1 0 1 X
X 0 X X
4
Convergence Criterion
  • Sequence of 3-valued states
  • Converge when the current state ? past states


Cycle 0000000
Cycle 21X0000
Cycle 300XX00
Cycle 410XXX0
Cycle 500XX00
5
Applications
  1. Oscillators ? phase abstraction
  2. Transients ? temporal decomposition
  3. Constant and equivalent signals ? simplification

Oscillator
Constant
000000
1X0000
00XX00
10XXX0
Transient
6
Outline
  • Approximate Reachability
  • Our Contributions
  • Symbolic Simulation
  • X-Saturation
  • Experimental Results

7
Problem 1 X-Initialized Latches
X
X
X
X
Fanout Cone
NS
X
Init
X
X
8
Symbolic Simulation
  • Lack of resolution X ? X
  • Symbols dont have this problem XA XA
  • New vocabulary 0, 1, X, XA, XB,
  • Handle initial values symbolically
  • Symbols introduced judiciously
  • Runtime vs. precision tradeoff

9
Problem 2 Convergence
  • Convergence can require many iterations
  • Counters other deep designs are problematic

?
Cycle 0000000
Cycle 21X0000
Cycle 300XX00
Cycle 410XXX0
Cycle 5001X00
?
10
X-Saturation
  • More abstraction ? Faster convergence
  • X-Saturate force a signal to have value X in all
    future iterations
  • When approximate reachability is slow
  • Identify a set of not-important signals
  • X-Saturate these signals

11
Outline
  • Approximate Reachability
  • Our Contributions
  • Symbolic Simulation
  • X-Saturation
  • Experimental Results

12
Simulating 0, 1, X, XA, XB,
0 0 1 X X
XA XA XA XA ?XA 0 XA (XA XB ) XA
XB XA XB hash_lookup(XA, XB) XA XB
new_symbol()
precidence
  • ?0 1 ?X X ?XA tracked explicitly

13
Limiting Symbolic Analysis
  • Problems
  • Symbols hurt convergence
  • Processing millions of symbols is slow
  • Solution only create new symbols in cycle 0

00XAXB
00XAXC
00XAXD
14
Limiting Symbolic Analysis
Cycle 0
Cycle 1
Cycle 2
TR
NS
TR
NS
TR
NS
Inputs
Regs
Inputs
Regs
Inputs
Regs
Init values symbols
symbols
X
X
XA XA XA XA ?XA 0 XA (XA XB ) XA
XB XA XB hash_lookup() XA XB new_symbol()
XA XA XA XA ?XA 0 XA (XA XB ) XA
XB XA XB hash_lookup() XA XB X
15
Enhanced Applications
  • Oscillators
  • Some registers oscillate over symbolic values
  • 0, XA, 0, XA, 0, XA, 0, XA,
  • Transients
  • Previously, transients defined as signals that
    settle to 0 or 1
  • Transients can now settle to 0,1, XA, XB,
  • Constant and equivalent signals
  • Signals can be stuck at a symbolic value XA
  • XA XA ? more equivalent signals

16
Outline
  • Approximate Reachability
  • Our Contributions
  • Symbolic Simulation
  • X-Saturation
  • Experimental Results

17
X-Saturation
  • Problem simulation may not converge
  • X-Saturate force a signal to have value X in all
    future iterations
  • Solution X-saturate a set of registers after
    resource limits are exhausted
  • Dont X-saturate oscillators, constant registers
  • Would limit the applications
  • Oscillators have high fanout ? X values on
    oscillators bleed to a large part of the design

18
X-Saturation Example
Cycle 0000000
Cycle 21X0000
Cycle 300XX00
Cycle 410XXX0
Cycle 5001X00
Cycle limit reachedEnable X-Saturation
Cycle 61XXXX0
19
Outline
  • Approximate Reachability
  • Our Contributions
  • Symbolic Simulation
  • X-Saturation
  • Experimental Results

20
Experiment Setup
  • Implemented in SixthSense
  • Suite of 1122 industrial SEC problems
  • Largest was 5.3M ANDs, 330k registers
  • Pairs of correlated registers are initialized
    with the same nondetermistic random value
  • HWMCC10 SEC
  • Subset of the most challenging HWMCC problems
  • Modified to have characteristics found in
    industrial SEC problems
  • http//case-home.com/publications/hwmcc10_sec.tgz

21
Symbolic Simulation Results
  • Small runtime overhead
  • Can reduce design size where the previous
    approach fails

22
X-Saturation Results
  • 1122 IBM designs
  • 13 designs converge in between 512 and 1M
    iterations
  • 8 take gt 1M iterations
  • For 13 that converge, we decrease runtime by 67
    (average) preserve 94 of the gate reductions
    (average)
  • Cumulatively, decrease runtime by 97 increase
    gate reductions by 77

23
Conclusion
  • Approximate reachability with ternary simulation
    is useful / problematic
  • Use partial symbolic simulation
  • Little runtime overhead
  • Dramatically enhances the precision
  • Use X-saturation
  • Helps convergence for deep designs
  • Small impact to the overall precision
  • Used every day within IBM
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