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

Abstract—Linear (order-one) 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 study investigates the so-called (M,p, k) scheme that reduces the range of 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 FPGA device and standard cell based technology. Experimental results show that the proposed scheme achieves more than 50% reduction in total chip area compared with the best linear approach for 24-bit evaluation. Index Terms—Bipartite table, trigonometric function evalua-tion, field-programable gate array (FPGA). I