New redundant CORDIC algorithms with fast variable scale factor compensations

In this work, new redundant CORDIC algorithms based on a fast variable scale factor compensation algorithm are proposed. By decomposing the complicated variable scale factor Π(1+δ_i ²2^-2i)^-0.5 as Exp(-Σln(1+δ_i²2^-2i)/2), then in turn as Π(1+s_i2^-i), where s_i∈{-1,0,1}, we can easily determine the direction factor δ_i∈{-1,0,1}, and at the same time do variable scale factor compensation by simply performing shift-and-add operations. The value of s_i can be easily obtained by estimating only a few most-significant digits (MSD) value of an intermediate variable. The new redundant CORDICs achieve high speed rotation iterations, as well as high-speed and low-complexity scale factor compensations, which are hard to attain simultaneously by the existing redundant CORDICs with variable scale factors