E. Antelo et al., ERROR ANALYSIS AND REDUCTION FOR ANGLE CALCULATION USING THE CORDIC ALGORITHM, I.E.E.E. transactions on computers, 46(11), 1997, pp. 1264-1271
In this paper, we consider the errors appearing in angle computations
with the CORDIC algorithm (circular and hyperbolic coordinate systems)
using fixed-point arithmetic. We include errors arising not only from
the finite number of iterations and the finite width of the data path
, but also from the finite number of bits of the input. We show that t
his last contribution is significant when both operands are small and
that the error is acceptable only if an input normalization stage is i
ncluded, making unsatisfactory other previous proposals to reduce the
error. We propose a method based on the prescaling of the input operan
ds and a modified CORDIC recurrence and show that it is a suitable alt
ernative to the input normalization with a smaller hardware cost. This
solution can also be used in pipelined architectures with redundant c
arry-save arithmetic.