This paper presents new, fast hardware for computing the exponential f
unction, sine, and cosine. The main new idea is to use low-precision a
rithmetic components to approximate high precision computations, and t
hen to correct very quickly the approximation error periodically so th
at the effect is to get high precision computation at near low-precisi
on speed. The algorithm used in the paper is a nontrivial modification
of the well-known CORDIC algorithm, and might be applicable to the co
mputation of other functions than the ones presented.