On Finite Wordlength Properties of Block-Floating-Point Arithmetic

A special case of floating point data representation is block are generally very bit efficient schemes. More recent work of floating point format where a block of operands are forced to have a joint Mitra [8][9] has proved the effectiveness of this representaexponent term. This paper deals with the finite wordlength properties of tion in the complicated area of adaptive filtering. However, this data format. The theoretical errors associated with the error model for to the best of our knowledge, no extensive work on the finiteblock floating point quantization process is investigated with the help of error precision properties of this data format has so far been reported distribution functions. A fast and easy approximation formula for calculating in the literature. signal-to-noise ratio in quantization to block floating point format is derived. In this paper, the finite wordlength properties of BFP is studThis representation is found to be a useful compromise between fixed point ied from a deterministic viewpoint. In particular, theoretical and floating point format due to its acceptable numerical error properties over analysis of a significant quantization error model associated a wide dynamic range. with the BFP format is carried out by deriving the distribution Keywords— Block floating point, Roundoff error, Block exponent disof block exponents. The signal to quantization noise ratio of tribution fuction, Signal factor. the BFP format is found to be dependent on this block exponent distribution, which requires precise information about