Equivalence verification of polynomial datapaths with fixed-size bit-vectors using finite ring algebra
This paper addresses the problem of equivalence verification of RTL descriptions. The focus is on datapath-oriented designs that implement polynomial computations over fixed-size bit-vectors. When the size (m) of the entire datapath is kept constant, fixed-size bit-vector arithmetic manifests itself...
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| Veröffentlicht in: | ICCAD-2005 : International Conference on Computer Aided Design, November 6-10, 2005, DoubleTree Hotel, San Jose, CA S. 291 - 296 |
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| Sprache: | Englisch |
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Washington, DC, USA
IEEE Computer Society
31.05.2005
IEEE ACM |
| Schriftenreihe: | ACM Conferences |
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| ISBN: | 078039254X, 9780780392540 |
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| Abstract | This paper addresses the problem of equivalence verification of RTL descriptions. The focus is on datapath-oriented designs that implement polynomial computations over fixed-size bit-vectors. When the size (m) of the entire datapath is kept constant, fixed-size bit-vector arithmetic manifests itself as polynomial algebra over finite integer rings of residue classes Z/sub 2//sup m/. The verification problem then reduces to that of checking equivalence of multi-variate polynomials over Z/sub 2//sup m/. This paper exploits the concepts of polynomial reducibility over Z/sub 2//sup m/ and derives an algorithmic procedure to transform a given polynomial into a unique canonical form modulo 2/sup m/. Equivalence testing is then carried out by coefficient matching. Experiments demonstrate the effectiveness of our approach over contemporary techniques. |
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| AbstractList | This paper addresses the problem of equivalence verification of RTL descriptions. The focus is on datapath-oriented designs that implement polynomial computations over fixed-size bit-vectors. When the size (m) of the entire datapath is kept constant, fixed-size bit-vector arithmetic manifests itself as polynomial algebra over finite integer rings of residue classes Z/sub 2//sup m/. The verification problem then reduces to that of checking equivalence of multi-variate polynomials over Z/sub 2//sup m/. This paper exploits the concepts of polynomial reducibility over Z/sub 2//sup m/ and derives an algorithmic procedure to transform a given polynomial into a unique canonical form modulo 2/sup m/. Equivalence testing is then carried out by coefficient matching. Experiments demonstrate the effectiveness of our approach over contemporary techniques. This paper addresses the problem of equivalence verification of RTL descriptions. The focus is on datapath-oriented designs that implement polynomial computations over fixed-size bit-vectors. When the size (m) of the entire datapath is kept constant, fixed-size bit-vector arithmetic manifests itself as polynomial algebra over finite integer rings of residue classes Z(2)/ m/. The verification problem then reduces to that of checking equivalence of multi-variate polynomials over Z(2)/ m/. This paper exploits the concepts of polynomial reducibility over Z(2)/ m/ and derives an algorithmic procedure to transform a given polynomial into a unique canonical form modulo 2/ m/. Equivalence testing is then carried out by coefficient matching. Experiments demonstrate the effectiveness of our approach over contemporary techniques. |
| Author | Shekhar, N. Kalla, P. Gopalakrishnan, S. Enescu, F. |
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| SubjectTerms | Applied sciences Electric, optical and optoelectronic circuits Electronics Exact sciences and technology Mathematics of computing Mathematics of computing -- Mathematical analysis Mathematics of computing -- Mathematical analysis -- Numerical analysis Mathematics of computing -- Mathematical analysis -- Numerical analysis -- Computations on polynomials Theoretical study. Circuits analysis and design |
| Title | Equivalence verification of polynomial datapaths with fixed-size bit-vectors using finite ring algebra |
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