Table-driven implementation of the logarithm function in IEEE floating-point arithmetic
ACM Transactions on Mathematical Software (TOMS)
Evaluating Elementary Functions in a Numerical Coprocessor Based on Rational Approximations
IEEE Transactions on Computers
The PowerPC architecture: a specification for a new family of RISC processors
The PowerPC architecture: a specification for a new family of RISC processors
Computer arithmetic systems: algorithms, architecture and implementation
Computer arithmetic systems: algorithms, architecture and implementation
Computer graphics (2nd ed. in C): principles and practice
Computer graphics (2nd ed. in C): principles and practice
Elementary functions: algorithms and implementation
Elementary functions: algorithms and implementation
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
Computer Approximations
Division and Square Root: Digit-Recurrence Algorithms and Implementations
Division and Square Root: Digit-Recurrence Algorithms and Implementations
The Symmetric Table Addition Method for Accurate Function Approximation
Journal of VLSI Signal Processing Systems
Hardware Designs for Exactly Rounded Elementary Functions
IEEE Transactions on Computers
High-Speed Double-Precision Computation of Reciprocal, Division, Square Root and Inverse Square Root
IEEE Transactions on Computers
Faithful Interpolation in Reciprocal Tables
ARITH '97 Proceedings of the 13th Symposium on Computer Arithmetic (ARITH '97)
High-Performance Hardware for Function Generation
ARITH '97 Proceedings of the 13th Symposium on Computer Arithmetic (ARITH '97)
High-Speed Inverse Square Roots
ARITH '99 Proceedings of the 14th IEEE Symposium on Computer Arithmetic
Floating Point Division and Square Root Algorithms and Implementation in the AMD-K7 Microprocessor
ARITH '99 Proceedings of the 14th IEEE Symposium on Computer Arithmetic
"Partially Rounded" Small-Order Approximations for Accurate, Hardware-Oriented, Table-Based Methods
ARITH '03 Proceedings of the 16th IEEE Symposium on Computer Arithmetic (ARITH-16'03)
ICCD '98 Proceedings of the International Conference on Computer Design
Faithful Powering Computation Using Table Look-Up and a Fused Accumulation Tree
ARITH '01 Proceedings of the 15th IEEE Symposium on Computer Arithmetic
High-Performance Architectures for Elementary Function Generation
ARITH '01 Proceedings of the 15th IEEE Symposium on Computer Arithmetic
Software Manual for the Elementary Functions (Prentice-Hall series in computational mathematics)
Software Manual for the Elementary Functions (Prentice-Hall series in computational mathematics)
Partial product reduction by using look-up tables for M×N multiplier
Integration, the VLSI Journal
Design Method for Numerical Function Generators Using Recursive Segmentation and EVBDDs
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
High-performance special function unit for programmable 3-D graphics processors
IEEE Transactions on Circuits and Systems Part I: Regular Papers
Truncated binary multipliers with variable correction and minimum mean square error
IEEE Transactions on Circuits and Systems Part I: Regular Papers
A goldschmidt division method with faster than quadratic convergence
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Hierarchical segmentation for hardware function evaluation
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
An efficient hardware architecture for a neural network activation function generator
ISNN'06 Proceedings of the Third international conference on Advances in Neural Networks - Volume Part III
A dynamic non-uniform segmentation method for first-order polynomial function evaluation
Microprocessors & Microsystems
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A table-based method for high-speed function approximation in single-precision floating-point format is presented in this paper. Our focus is the approximation of reciprocal, square root, square root reciprocal, exponentials, logarithms, trigonometric functions, powering (with a fixed exponent p), or special functions. The algorithm presented here combines table look-up, an enhanced minimax quadratic approximation, and an efficient evaluation of the second-degree polynomial (using a specialized squaring unit, redundant arithmetic, and multioperand addition). The execution times and area costs of an architecture implementing our method are estimated, showing the achievement of the fast execution times of linear approximation methods and the reduced area requirements of other second-degree interpolation algorithms. Moreover, the use of an enhanced minimax approximation which, through an iterative process, takes into account the effect of rounding the polynomial coefficients to a finite size allows for a further reduction in the size of the look-up tables to be used, making our method very suitable for the implementation of an elementary function generator in state-of-the-art DSPs or graphics processing units (GPUs).