Area and performance tradeoffs in floating-point divide and square-root implementations
ACM Computing Surveys (CSUR)
Powering by a Table Look-Up and a Multiplication with Operand Modification
IEEE Transactions on Computers
Approximating Elementary Functions with Symmetric Bipartite Tables
IEEE Transactions on Computers
IEEE Transactions on Computers - Special issue on computer arithmetic
Improving Goldschmidt Division, Square Root, and Square Root Reciprocal
IEEE Transactions on Computers - Special issue on computer arithmetic
Further Reducing the Redundancy of a Notation Over a Minimally Redundant Digit Set
Journal of VLSI Signal Processing Systems
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
Multipartite Tables in JBits for the Evaluation of Functions on FPGAs
IPDPS '02 Proceedings of the 16th International Parallel and Distributed Processing Symposium
Technology Trends and Adaptive Computing
FPL '01 Proceedings of the 11th International Conference on Field-Programmable Logic and Applications
Accurate Function Approximations by Symmetric Table Lookup and Addition
ASAP '97 Proceedings of the IEEE International Conference on Application-Specific Systems, Architectures and Processors
Radix-4 Reciprocal Square-Root and Its Combination with Division and Square Root
IEEE Transactions on Computers
An Exponentiation Unit for an OpenGL Lighting Engine
IEEE Transactions on Computers
A Gaussian Noise Generator for Hardware-Based Simulations
IEEE Transactions on Computers
IEEE Transactions on Computers
A parametric error analysis of Goldschmidt's division algorithm
Journal of Computer and System Sciences
Optimizing Hardware Function Evaluation
IEEE Transactions on Computers
Direct Digital Frequency Synthesis Based on a Two-Level Table-Lookup Scheme
Journal of VLSI Signal Processing Systems
Complex Square Root with Operand Prescaling
Journal of VLSI Signal Processing Systems
Journal of Signal Processing Systems
Low precision table based complex reciprocal approximation
Asilomar'09 Proceedings of the 43rd Asilomar conference on Signals, systems and computers
A goldschmidt division method with faster than quadratic convergence
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
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We describe bipartite reciprocal tables that employ separate table lookup of the positive and negative portions of a borrow-save reciprocal value. The fusion of the parts includes a rounding so the output reciprocals are guaranteed correct to a unit in the last place, and typically provide a round-to-nearest reciprocal for over 90% of input arguments. The output rounding can be accomplished in conjunction with multiplier recoding yielding practically no cost in logic complexity or time in employing bipartite tables. We demonstrate these tables to be 2 to 4 times smaller than conventional 4-9 bit reciprocal tables. For 10-16 bit reciprocal table lookup the compression grows from a factor of 4 to over 16, making possible the use of larger seed reciprocals than previously considered cost effective.