Research Interests, Projects, Collaborations

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Research Interests, Projects, Collaborations
Opportunities

• Priyank Kalla
• Electrical Computer Engineering
• University of Utah

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Typical Design Flow CAD Support
TLM Models
High-Level Analysis
Design Spec
Hardware Description
High-Level Synthesis
Testing for Defects
Circuit Models
Optimization
Fabrication
High-Level Logic Synthesis Optimization Area,
Speed, Power
Mask
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Design Verification
TLM Models
Property Verification
Design Spec
Hardware Description
High-Level Synthesis
Circuit Models
Optimization
Equivalence Verification ?
Fabrication
Core Engines for Correctness Reasoning
Constraint Solving
Mask
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My Research Projects at the U

• Boolean Reasoning Engines (concluded)
• Million variables, 10s Million Constraints
• 2 M.S. 1 PhD
• Exploring Design Automation for Photonic
  Devices
• Collaboration w/ Steve Blair his Colleagues
• 1 PhD student Learning Exploring the issues
• Synthesis Verification of Finite-Precision
  Arithmetic
• Focus on Hardware but applicable to Software
• 2 PhDs. 2 more for sure
• Recognition bread-earner 3 NSF Grants

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Datapath-Dominated Applications
Floating-point Model
Automated Fixed-point Generation
Real Number Specification
DSP Crypto Embedded ASIC
Fixed-point Model
Conversion Utility
Matlab Xilinx Altera Synplicity Synopsys Calypto G
alois
HDL Model
Optimization
Equivalence Verification ?
HDL Model
Synthesis
FPGA
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Why Verify Finite-Precision Arithmetic

• 1996 Ariane Rocket Explosion
• 64-bit floating to fixed point rounding error
• Vancouver Stock-Exchange Index
• 1982 Value initialized to 1000 1984 value 520
• Truncation error Should have been 1098
• Gulf War, Patriot Missile (28 dead, SCUD)
• German Parliament 5.0 versus 4.97 (2-bits!)
• Bug in JPEG Decode Routine (discovered in 05)
• Hacker Exploited uploaded a virus Microsoft
  website
• Network Routers, Filter instability errors

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MP3 Decoder Anti-Aliasing Function

• Taylor series expansion

Peymandoust et al, TCAD '03
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Example Anti-Aliasing Function

• F150 156x6 62724x5 17968x4 18661x3
  43593 x2 40244x 13281

• G150 156x6 5380x5 1584x4 10469x3
  27209 x2 7456x 13281

• Contemporary tools model the problem at (circuit)
  bit-level
• Too many variables/constraints infeasible
• Name of the game Abstraction model the
  details

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Fixed-Size (m) Data-path Modeling

• Control the datapath size Fixed size bit-vectors
  (m)

16-bit
16-bit

16-bit

16-bit

• Bit-vector of size m integer values in 0,, 2m-1

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Why is the Problem Difficult?

• Z2m is a non-Unique Factorization Domain
• F x2 6x in Z8 (modulo 8) can be factorized
  as
• Easy to do over Reals, Complex numbers, Integers
  (modulo p)
• Textbook algebra solutions are not available over
  Z2m
• Contacted a Mathematician Prof. Florian Enescu
• Partially unsolved Problems in classical
  mathematics

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Zero in Finite-Precision

• F150 156x6 62724x5 17968x4 18661x3
  43593 x2 40244x 13281

• G150 156x6 5380x5 1584x4 10469x3
  27209 x2 7456x 13281

• F - G 150 57344 x5 16384 x4 8192 x3
  16384 x2 32768 x

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Ideals in Finite Rings
Z2mx
Z2m

• Test for membership in the ideal of vanishing
  polynomials
• Standard Problem formulation in Computer Algebra
• But, how to mathematically generate this
  ideal?
• Hilberts Fermats results (mod p) Generalize
  to (mod pm)

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Contributions
Abstraction of Arithmetic Datapaths
Equivalence Verification Problem
Equivalence of Polyfunction
Equivalence of Polynomial systems
Generalized to cover all Bit-Vector Arithmetic
Ideal Membership Testing
Canonical Forms
Simulation Vector Generation
ADD/MULT
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Significance, Impact, Interest

• Computer-algebra research group, Univ.
  Kaiserslautern
• SINGULAR Public domain computer algebra tool
• Our approach implemented in their latest release
• Univ. Kaiserslautern Math ECE Infineon
• Extension of my work to verify production-quality
  design
• Univ. of Tokyo Fujitsu
• Use our work for Testing SoC (ATPG)
• Bay-area Start-up Calypto (NSF GOALI Partner)
• GALOIS Inc., Cryptography applications (military
  funding)
• Invited Talk Intl. Joint Conferences on
  Automated Reasoning
• Theoretical Computer Science Community

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• Thank You!