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An Algorithm for Redundant Binary Bit-Pipelined Rational Arithmetic
August 1990 (vol. 39 no. 8)
pp. 1106-1115

The authors 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, using this representation. The algorithm extends R.W. Gosper's (1972) partial quotient arithmetic algorithm and allows the design of an online arithmetic unit with computations granularized at the signed bit level. Each input or output port can be independently set to receive/produce operands/result in either binary radix or the binary rational representation. The authors investigate by simulation the interconnection of several such units for the parallel computation of more complicated expressions in a tree-pipelined manner, with particular regard to measuring individual and compounded online delays.

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Index Terms:
tree pipeline; Gosper; redundant binary bit-pipelined rational arithmetic; redundant binary representation; sum; difference; product; quotient; rational operands; partial quotient arithmetic algorithm; online arithmetic unit; signed bit level; binary radix; binary rational representation; simulation; interconnection; parallel computation; online delays; digital arithmetic; number theory; redundancy.
P. Kornerup, D.W. Matula, "An Algorithm for Redundant Binary Bit-Pipelined Rational Arithmetic," IEEE Transactions on Computers, vol. 39, no. 8, pp. 1106-1115, Aug. 1990, doi:10.1109/12.57048
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