Formalization of Caden e SPW Fixed-Point Arithmeti in HOL
نویسندگان
چکیده
in HOL Behzad Akbarpour, So ene Tahar, Abdelkader Dekdouk Ele tri al and Computer Engineering Department Con ordia University, Montreal, Canada Email: fbehzad, tahar, adekdoukg e e. on ordia. a Te hni al Report Abstra t In this report we propose the formalization in higher-order logi of xed-point arithmeti based on the SPW (Signal Pro essing WorkSystem) tool. We en oded the xedpoint number system and spe i ed the di erent rounding modes in xed-point arithmeti su h as the dire ted and even rounding modes. We also onsidered the formalization of ex eptions dete tion and their handling like over ow and invalid operation. An error analysis is then performed to he k the orre tness of the rounding and to verify the basi arithmeti operations, addition, subtra tion, multipli ation and division against their mathemati al ounterparts. Finally, we showed by an example how this formalization an be used to enable the veri ation of the transition from the oating-point to xed-point algorithmi levels in the design ow of signal pro essors.
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