Optimization and Quantization Effects for Sine and Cosine Computation Using a Sum of Bit-Products
Oscar Gustafsson, Kenny Johansson, Lars Wanhammar · 2006
Recently, a novel technique to compute sine and co- sine has been proposed. By rewriting the expressions using trigo- nometric equations a weighted sum of bit-products is used to compute the values. This can then be mapped onto a bit-product generator followed by an adder tree. This provides an efficient ar- chitecture that can be pipelined to an arbitrary degree. It was shown in previous work that it is possible to remove a large portion of the bit-products and still obtain accurate results. The objective of this work is to study the effects of this removal and also the finite wordlength representation of the weights. Furthermore, optimiza- tion problems are formulated that can be used to minimize the maximum absolute error, the average absolute error, and the mean square error for the output values, respectively, as well as implementation complexity under error constraints.