(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
2 ARIC - Arithmetic and Computing
3 LIP - Laboratoire de l'Informatique du Parallélisme
4 Digital Arithmetic and Reconfigurable Architecture Laboratory

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)

Domains: Computer Science [cs]; Other [cs.OH]

Dong Wang, Jean-Michel Muller, Nicolas Brisebarre, Milos Ercegovac. (M, p, k)-Friendly Points: A Table-based Method to Evaluate Trigonometric Function. IEEE Transactions on Circuits and Systems Part 2 Analog and Digital Signal Processing, 2014, 61 (9), pp.711-715. ⟨10.1109/TCSII.2014.2331094⟩. ⟨ensl-01001673⟩