An Algorithm for Redundant Binary Bit-Pipelined Rational Arithmetic


AbsfmctWe introduce a redundant binary representation of the rationals and an associated algorithm for computing the sum, difference, product, quotient, and other useful functions of two rational operands, employing our representation. Our algorithm extends Gosper’s partial quotient arithmetic algorithm and allows the design of an on-line arithmetic unit with computations granularized at the signed bit level. Each input or output port can independently be set to receivehroduce operandshesult in either binary radix or our binary rational representation. We investigate by simulation the interconnection of several such units for the parallel computation of more complicated expressions in a tree-pipelined manner, with particular regards to measuring individual and compounded on-line delays.

DOI: 10.1109/12.57048

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@article{Kornerup1990AnAF, title={An Algorithm for Redundant Binary Bit-Pipelined Rational Arithmetic}, author={Peter Kornerup and David W. Matula}, journal={IEEE Trans. Computers}, year={1990}, volume={39}, pages={1106-1115} }