Numerical methods for computer science, engineering, and mathematics
Numerical methods for computer science, engineering, and mathematics
The evolution of Babbage's calculating engines
IEEE Annals of the History of Computing
Elementary functions: algorithms and implementation
Elementary functions: algorithms and implementation
Approximating Elementary Functions with Symmetric Bipartite Tables
IEEE Transactions on Computers
IEEE Transactions on Computers - Special issue on computer arithmetic
MATLAB Programming for Engineers (2nd Edition)
MATLAB Programming for Engineers (2nd Edition)
The Symmetric Table Addition Method for Accurate Function Approximation
Journal of VLSI Signal Processing Systems
Function Evaluation by Table Look-up and Addition
ARITH '95 Proceedings of the 12th Symposium on Computer Arithmetic
DSD '07 Proceedings of the 10th Euromicro Conference on Digital System Design Architectures, Methods and Tools
On the number of segments needed in a piecewise linear approximation
Journal of Computational and Applied Mathematics
PWL function approximation circuit with diodes and current input and output
ICOSSSE'11 Proceedings of the 10th WSEAS international conference on System science and simulation in engineering
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We give an efficient algorithm for partitioning the domain of a numeric function f into segments. The function f is realized as a polynomial in each segment, and a lookup table stores the coefficients of the polynomial. Such an algorithm is an essential part of the design of lookup table methods Ercepovac et al. (2000) [5], Lee et al. (2003) [7], Nagayama et al. (2007) [12], Paul et al. (2007) [6] and Sasao et al. (2004) [8] for realizing numeric functions, such as sin(@px), ln(x), and -ln(x). Our algorithm requires many fewer steps than a previous algorithm given in Frenzen et al. (2010) [10] and makes tractable the design of numeric function generators based on table lookup for high-accuracy applications. We show that an estimate of segment width based on local derivatives greatly reduces the search needed to determine the exact segment width. We apply the new algorithm to a suite of 15 numeric functions and show that the estimates are sufficiently accurate to produce a minimum or near-minimum number of computational steps.