Very High Radix Square Root with Prescaling and Rounding and a Combined Division/Square Root Unit
IEEE Transactions on Computers
Approximating Elementary Functions with Symmetric Bipartite Tables
IEEE Transactions on Computers
IEEE Transactions on Computers - Special issue on computer arithmetic
Arithmetic on the European Logarithmic Microprocessor
IEEE Transactions on Computers - Special issue on computer arithmetic
Error Analysis of the Kmetz/Maenner Algorithm
Journal of VLSI Signal Processing Systems
The Symmetric Table Addition Method for Accurate Function Approximation
Journal of VLSI Signal Processing Systems
High-Speed Double-Precision Computation of Reciprocal, Division, Square Root and Inverse Square Root
IEEE Transactions on Computers
Accurate Function Approximations by Symmetric Table Lookup and Addition
ASAP '97 Proceedings of the IEEE International Conference on Application-Specific Systems, Architectures and Processors
VLSI Implementation of a Low-Power Antilogarithmic Converter
IEEE Transactions on Computers
High-Radix Logarithm with Selection by Rounding: Algorithm and Implementation
Journal of VLSI Signal Processing Systems
Numerical Function Generators Using LUT Cascades
IEEE Transactions on Computers
A goldschmidt division method with faster than quadratic convergence
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Mathematical model of stored logic based computation
Mathematical and Computer Modelling: An International Journal
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This paper presents a methodology for designing bipartite tables for accurate function approximation. Bipartite tables use two parallel table lookups to obtain a carry-save (borrow-save) function approximation. A carry propagate adder can then convert this approximation to a two's complement number or the approximation can be directly Booth encoded. Our method for designing bipartite tables, called the Symmetric Bipartite Table Method, utilizes symmetry in the table entries to reduce the overall memory requirements. It has several advantages over previous bipartite table methods in that it (1) provides a closed form solution for the table entries, (2) has tight bounds on the maximum absolute error, (3) requires smaller table lookups to achieve a given accuracy, and (4) can be applied to a wide range of functions. Compared to conventional table lookups, the symmetric bipartite tables presented in this paper are 15.0 to 41.7 times smaller when the operand size is 16 bits and 99.1 to 273.9 times smaller when the operand size is 24 bits.