(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)
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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, Institute of Electrical and Electronics Engineers (IEEE), 2014, 61 (9), pp.711-715. ⟨10.1109/TCSII.2014.2331094⟩. ⟨ensl-01001673⟩

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