Polynomial datapath optimization using constraint solving and formal modelling

Haedicke,; Alizadeh,; Fey, Görschwin; Fujita, Katsuhide; Drechsler, Rolf

doi:10.1109/iccad.2010.5654279

Cited by 3 publications

(3 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Although Horner form is a popular representation of polynomial functions, symbolic computer algebra based manipulation and factorization with Common Sub-expression Elimination (CSE) are much better techniques to optimize polynomial functions in terms of the area and delay [1,2,3]. The CSE technique in [1] is a straightforward way of optimizing polynomial datapath designs.…”

Section: Introductionmentioning

confidence: 99%

“…The basic idea is the fact that if we are to use the original polynomials along with different related vanishing polynomials, we may get more opportunities to extract better common sub-expressions. For example, let us consider P = 6x 3 +x 2 y+x 2 z-11x 2 +6x+yz over Z 2 3 . It can be factored out as P = (x 2 +z)×(x 2 +y) if P + Y 4 (x) is taken into account where Y 4 (x)=x×(x-1)×(x-2)×(x-3) is a vanishing polynomial over Z 2 3 , i.e., Y 4 (x) mod 2 3 = 0.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Polynomial datapath synthesis and optimization based on vanishing polynomial over Z<inf>2</inf><sup>m</sup> and algebraic techniques

Ghandali

Alizadeh

Navabi

et al. 2012

Tenth ACM/IEEE International Conference on Formal Methods and Models for Codesign (MEMCODE2012)

Self Cite

View full text Add to dashboard Cite

The growing market for Digital Signal Processing (DSP), Computer graphics and embedded systems applications that can be modeled as polynomial computations in their datapath designs, requires improvements in high-level synthesis and optimization techniques for such systems. This paper concentrates on how to find common sub-expressions between s given polynomial functions over … in order to optimize the area and delay as much as possible. Our main contributions in this paper is proposing an optimization method based on adding/deleting vanishing polynomials over Z 2 m , i.e., those polynomials that are equivalent to zero over Z 2 m , to/from given polynomial functions in the hope of achieving further common sub-expressions. After applying our optimization techniques, experimental comparisons with the state-of-the-art techniques show an average improvement in the area by 36.80% with an average delay decrease of 2.41%. Regarding the comparison with our previous works, the area and delay are improved by 21.4% and 8.7% respectively.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Polynomial datapath synthesis and optimization based on vanishing polynomial over Z<inf>2</inf><sup>m</sup> and algebraic techniques

Ghandali

Alizadeh

Navabi

et al. 2012

Tenth ACM/IEEE International Conference on Formal Methods and Models for Codesign (MEMCODE2012)

Self Cite

View full text Add to dashboard Cite

show abstract

“…Decision procedures have become attractive to solve computationally hard problems and are effectively applied in many applications including model checking [10,25], circuit synthesis [3,21], and automatic test pattern generation [17].…”

Section: Introductionmentioning

confidence: 99%

metaSMT: focus on your application and not on solver integration

Riener

Haedicke

Frehse

et al. 2016

Int J Softw Tools Technol Transfer

Self Cite

View full text Add to dashboard Cite

Many applications from artificial intelligence and formal methods use decision procedures as their core solving engines. In this context, automated reasoning based on Satisfiability (SAT) or Satisfiability Modulo Theories (SMT) is very effective. For a given application, however, selecting the best reasoning engine is a daunting task requiring first-hand experience and insight into engine-specific implementation details. Developers have to decide which concrete engine to use and how to integrate the engine into an application. Although file formats, e.g., DIMACS CNF or SMT-LIB, standardize the input of SAT and SMT solvers, not all engines provide input interfaces compliant with these standards. When following the standard, advanced (and not standardized) features of the solvers remain unused and their integration is left to the users. This work presents meta-SMT, a framework that eases the integration of existing reasoning engines into applications. Inspired by SMT-LIB, metaSMT provides a domain-specific language that allows for engine-independent programming and offers a generic interface to advanced features as an extra abstraction layer. State-of-the-art solvers for satisfiability and other theories are available via metaSMT with little programming effort. Language bindings for C++ and Python are provided. We show how metaSMT can be used as a portfolio consistency checker for SMT-LIB2 instances. The benchmark set of the category quantifier-free bit-vector theory from SMT-LIB (1.6 GB) is used for these experiments.

show abstract

Formal equivalence verification and debugging techniques with auto-correction mechanism for RTL designs

Alizadeh

Behnam

2013

Microprocessors and Microsystems

View full text Add to dashboard Cite

Polynomial datapath optimization using constraint solving and formal modelling

Cited by 3 publications

References 12 publications

Polynomial datapath synthesis and optimization based on vanishing polynomial over Z<inf>2</inf><sup>m</sup> and algebraic techniques

Polynomial datapath synthesis and optimization based on vanishing polynomial over Z<inf>2</inf><sup>m</sup> and algebraic techniques

metaSMT: focus on your application and not on solver integration

Formal equivalence verification and debugging techniques with auto-correction mechanism for RTL designs

Contact Info

Product

Resources

About