Efficient Implementation of Constant Coefficient Division Under Quantization Constraints

Abstract: Division is one of the basic operations of arithmetic algorithms, but the cost associated to its hardware implementation exceeds the reasonable limits for most dedicated architectures. This paper provides a systematic algorithm that (a) transforms the constant coefficient division into a constant coefficient multiplication, selectable under some given constraints, and (b) optimizes the resulting multiplier by analyzing the quantization noise inherent to the finite wordlength implementation process. Consequently, this algorithm achieves reduced-area, high-speed constant coefficient dividers that maintain the accuracy in the range of represented numbers. The theorems and presented results confirm that the proposed algorithm computes the most suitable fraction under a given set of noise constraints