Efficient Function Evaluations with Lookup Tables for Structured Matrix Operations

A hardware efficient approach is introduced for elementary function evaluations in certain structured matrix computations. It is a comprehensive approach that utilizes lookup tables for compactness, employs interpolations with adders and multipliers for their adaptivity to non-tabulated values and, more distinctively, exploits the function properties and the matrix structures to claim better control over numerical dynamic ranges. We demonstrate the effectiveness of the approach with simulation and synthesis results on evaluating, in particular, the cosine function, the exponential function and the zero-order Bessel function of the first kind.

[1]  Arnold Neumaier,et al.  Introduction to Numerical Analysis , 2001 .

[2]  Behrooz Parhami,et al.  Computer arithmetic - algorithms and hardware designs , 1999 .

[3]  M. Kandemir,et al.  Algorithm-Architecture Codesign for Structured Matrix Operations on Reconfigurable Systems , .

[4]  Jie Cheng,et al.  High-performance architectures for elementary function generation , 2001, Proceedings 15th IEEE Symposium on Computer Arithmetic. ARITH-15 2001.

[5]  Ping Tak Peter Tang,et al.  Table-lookup algorithms for elementary functions and their error analysis , 1991, [1991] Proceedings 10th IEEE Symposium on Computer Arithmetic.

[6]  J. W. Hauser,et al.  Approximating functions for embedded and ASIC applications , 2001, Proceedings of the 44th IEEE 2001 Midwest Symposium on Circuits and Systems. MWSCAS 2001 (Cat. No.01CH37257).