On Roundoff Errors in Block-Floating-Point Arithmetic

Abstract

A special case of floating point data representation is block floating point format where a block of operands are forced to have a joint exponent term. This paper deals with the finite wordlength properties of this data format. The theoretical errors associated with the error model for block floating point quantization process is investigated with the help of error distribution functions. A fast and easy approximation formula for calculating signal-to-noise ratio in quantization to block floating point format is derived. This representation is found to be efficient compared to the fixed point and floating point format.

Indexing terms:

• Block floating point
• Roundoff error
• Block exponent distribution function
• Signal factor

Additional information

Notes on contributors

Abhijit Mitra

Abhijit Mitra was born in Serampore in 1975. He received the BE(Honors) degree from Regional Engineering College, Durgapur in 1997, the METelE degree from Jadavpur University in 1999 and the PhD degree from indian Institute of Technology, Kharagpur in 2004, all in Electronics and Communication Engineering. Since 2004, he has been with Indian Institute of Technology, Guwahati, as an Assistant Professor. His research interests include adaptive and statistical signal processing, and signal processing applications in wireless communications.

Dr Mitra is a member of IEEE and presently serves as a reviewer of IEEE Transactions on Signal Processing and IEEE Signal Processing Letters. He is the recipient of several national scholarships and research fellowships.