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

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.
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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〉
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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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