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Modeling SystemC Fixed-Point Arithmetic in HOL

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Formal Methods and Software Engineering (ICFEM 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2885))

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Abstract

SystemC is a new C-based system level design language whose ultimate objective is to enable System-on-a-Chip (SoC) design and verification. Fixed-point design based on the SystemC data types is rapidly becoming the standard for optimizing DSP systems. In this paper, we propose to create a formalization of SystemC fixed-point arithmetic in the HOL theorem proving environment. The SystemC fixed-point number representation which contains a new generalized format and different rounding and overflow modes is described, and then it is formalized in higher-order logic. This formalization is then compared with the formalization of IEEE standard based floating-point arithmetic in HOL. A set of theorems are proved to bound the error in fixed-point rounding and to verify the fixed-point arithmetic operations against their abstract mathematical counterparts. Finally, we show by an example how this formalization can be used in verification of the translation from floating-point and fixed-point algorithmic, down to register transfer and netlist gate levels in the design flow of SoC systems.

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Author information

Authors and Affiliations

  1. Dept. of Electrical & Computer Engineering, Concordia University, 1455 de Maisonneuve W., Montreal, Quebec, H3H 1M8, Canada

    Behzad Akbarpour & Sofiène Tahar

Authors
  1. Behzad Akbarpour
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  2. Sofiène Tahar
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Editor information

Editors and Affiliations

  1. School of Computing, National University of Singapore, Singapore

    Jin Song Dong

  2. University of York,  

    Jim Woodcock

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Akbarpour, B., Tahar, S. (2003). Modeling SystemC Fixed-Point Arithmetic in HOL. In: Dong, J.S., Woodcock, J. (eds) Formal Methods and Software Engineering. ICFEM 2003. Lecture Notes in Computer Science, vol 2885. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39893-6_13

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  • DOI: https://doi.org/10.1007/978-3-540-39893-6_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20461-9

  • Online ISBN: 978-3-540-39893-6

  • eBook Packages: Springer Book Archive

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