Evaluating Elementary Functions in a Numerical Coprocessor Based on Rational Approximations
IEEE Transactions on Computers
Optimal absolute error starting values for Newton-Raphson calculation of square root
Computing - Special issue on archives for informatics and numerical computation
IEEE Transactions on Computers
Elementary functions: algorithms and implementation
Elementary functions: algorithms and implementation
The Symmetric Table Addition Method for Accurate Function Approximation
Journal of VLSI Signal Processing Systems
Measuring the Accuracy of ROM Reciprocal Tables
IEEE Transactions on Computers
Hardware Designs for Exactly Rounded Elementary Functions
IEEE Transactions on Computers
Function Evaluation by Table Look-up and Addition
ARITH '95 Proceedings of the 12th Symposium on Computer Arithmetic
Faithful Bipartite ROM Reciprocal Tables
ARITH '95 Proceedings of the 12th Symposium on Computer Arithmetic
Cascaded Implementation of an Iterative Inverse--Square--Root Algorithm, with Overflow Lookahead
ARITH '95 Proceedings of the 12th Symposium on Computer Arithmetic
High-speed double precision computation of nonlinear functions
ARITH '95 Proceedings of the 12th Symposium on Computer Arithmetic
The K5 transcendental functions
ARITH '95 Proceedings of the 12th Symposium on Computer Arithmetic
Redundant Binary Booth Recoding
ARITH '95 Proceedings of the 12th Symposium on Computer Arithmetic
Symmetric Bipartite Tables for Accurate Function Approximation
ARITH '97 Proceedings of the 13th Symposium on Computer Arithmetic (ARITH '97)
Generating a Power of an Operand by a Table Look-up and a Multiplication
ARITH '97 Proceedings of the 13th Symposium on Computer Arithmetic (ARITH '97)
Further Reducing the Redundancy of a Notation Over a Minimally Redundant Digit Set
Journal of VLSI Signal Processing Systems
Implementation of the Exponential Function in a Floating-Point Unit
Journal of VLSI Signal Processing Systems
Parameterized Function Evaluation for FPGAs
FPL '01 Proceedings of the 11th International Conference on Field-Programmable Logic and Applications
Radix-4 Reciprocal Square-Root and Its Combination with Division and Square Root
IEEE Transactions on Computers
Parameterized High Throughput Function Evaluation for FPGAs
Journal of VLSI Signal Processing Systems
An Exponentiation Unit for an OpenGL Lighting Engine
IEEE Transactions on Computers
Algorithm and Architecture for Logarithm, Exponential, and Powering Computation
IEEE Transactions on Computers
High-Speed Function Approximation Using a Minimax Quadratic Interpolator
IEEE Transactions on Computers
IEEE Transactions on Computers
ASP-DAC '06 Proceedings of the 2006 Asia and South Pacific Design Automation Conference
Numerical Function Generators Using LUT Cascades
IEEE Transactions on Computers
Complex Square Root with Operand Prescaling
Journal of VLSI Signal Processing Systems
A Digit-by-Digit Algorithm for mth Root Extraction
IEEE Transactions on Computers
High-performance hardware operators for polynomial evaluation
International Journal of High Performance Systems Architecture
A fast segmentation algorithm for piecewise polynomial numeric function generators
Journal of Computational and Applied Mathematics
Multi-Gb/s LDPC code design and implementation
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
A dynamic non-uniform segmentation method for first-order polynomial function evaluation
Microprocessors & Microsystems
ICA3PP'12 Proceedings of the 12th international conference on Algorithms and Architectures for Parallel Processing - Volume Part I
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This paper presents a high-speed method for function approximation that employs symmetric bipartite tables. This method performs two parallel table lookups to obtain a carry-save (borrow-save) function approximation, which is either converted to a two's complement number or is Booth encoded. Compared to previous methods for bipartite table approximations, this method uses less memory by taking advantage of symmetry and leading zeros in one of the two tables. It also has a closed-form solution for the table entries, provides tight bounds on the maximum absolute error, and can be applied to a wide range of functions. A variation of this method provides accurate initial approximations that are useful in multiplicative divide and square root algorithms.