Section: New Results

Elementary Functions

(M,p,k)-friendly points: a table-based method for trigonometric function evaluation

N. Brisebarre, M. Ercegovac (U. California at Los Angeles) and J.-M. Muller [25] present a new way of approximating the sine and cosine functions by a few table look-ups and additions. It consists in first reducing the input range to a very small interval by using rotations with “$(M,p,k)$ friendly angles”, proposed in this work, and then by using a bipartite table method in a small interval. An implementation of the method for 24-bit case is described and compared with CORDIC. Roughly, the proposed scheme offers a speedup of 2 compared with an unfolded double-rotation radix-2 CORDIC.

On Ziv's rounding test

With Ch. Lauter (LIP6), F. de Dinechin, J.-M. Muller and S. Torres proved and generalized a code sequence due to Ziv, which is used to round correctly a real value approximated (with a known error bound) as the unevaluated sum of two floating-point numbers [52] .