(M, p, k)-Friendly Points: A Table-based Method to Evaluate Trigonometric Function

Dong Wang; Jean-Michel Muller; Nicolas Brisebarre; Milos Ercegovac

(M, p, k)-Friendly Points: A Table-based Method to Evaluate Trigonometric Function

Dong Wang ¹ Jean-Michel Muller ^{2, 3} Nicolas Brisebarre ^{2, 3} Milos Ercegovac ⁴

1 Institute of Information Science, Beijing Jiaotong University, Beijing, China

Institute of Information Science [Bejing]

2 ARIC - Arithmetic and Computing

Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme

3 LIP - Laboratoire de l'Informatique du Parallélisme

4 Digital Arithmetic and Reconfigurable Architecture Laboratory

Abstract : Linear (order-1) function evaluation schemes, such as bipartite and multipartite tables, are usually effective for low- precision approximations. For high-output precision, the lookup table size is often too large for practical use. This brief investigates the so-called (M,p,k) scheme that reduces the range of an input argument to a very small interval so that trigonometric functions can be approximated with very small lookup tables and a few additions/subtractions. An optimized hardware architecture is presented and implemented in both a field-programmable gate array device and standard-cell-based technology. Experimental results show that the proposed scheme achieves more than a 50% reduction in total chip area compared with the best linear approach for a 24-bit evaluation.

Keywords : Bipartite table trigonometric function evaluation field-programable gate array (FPGA)

Document type :

Journal articles

Domain :

Computer Science [cs] / Other [cs.OH]

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