Akbarpour, Behzad, Tahar, Sofiène and Dekdouk, Abdelkader
(2005)
*Formalization of Fixed-Point Arithmetic in HOL.*
Formal Methods in System Design, 27
(1-2).
pp. 173-200.
ISSN 0925-9856

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Official URL: http://dx.doi.org/10.1007/s10703-005-2256-8

## Abstract

This paper addresses the formalization in higher-order logic of fixed-point arithmetic. We encoded the fixed-point number system and specified the different quantization modes in fixed-point arithmetic such as the directed and even quantization modes. We also considered the formalization of exceptions detection and their handling like overflow and invalid operation. An error analysis is then performed to check the correctness of the quantized result after carrying out basic arithmetic operations, such as addition, subtraction, multiplication and division against their mathematical counterparts. Finally, we showed by an example how this formalization can be used to enable the verification of the transition from floating-point to fixed-point algorithmic level in the signal processing design flow.

Divisions: | Concordia University > Gina Cody School of Engineering and Computer Science > Electrical and Computer Engineering |
---|---|

Item Type: | Article |

Refereed: | Yes |

Authors: | Akbarpour, Behzad and Tahar, Sofiène and Dekdouk, Abdelkader |

Journal or Publication: | Formal Methods in System Design |

Date: | 2005 |

Digital Object Identifier (DOI): | 10.1007/s10703-005-2256-8 |

Keywords: | fixed-point arithmetic floating-point arithmetic theorem-proving HOL |

ID Code: | 977379 |

Deposited By: | Danielle Dennie |

Deposited On: | 14 Jun 2013 15:36 |

Last Modified: | 18 Jan 2018 17:44 |

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