An on-line arithmetic unit for bit-pipelined rational arithmetic
Journal of Parallel and Distributed Computing - Parallelism in Computer Arithmetic
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
IEEE Transactions on Computers
A p × p bit fraction model of binary floating point division and extremal rounding cases
Theoretical Computer Science - Real numbers and computers
A Survey of Exact Arithmetic Implementations
CCA '00 Selected Papers from the 4th International Workshop on Computability and Complexity in Analysis
Exact arithmetic on the Stern-Brocot tree
Journal of Discrete Algorithms
Finite state transducers for modular möbius number systems
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
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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.