Low latency word serial CORDIC

In this paper we present a modiication of the CORDIC algorithm which reduces the number of iterations almost to half by merging two successive iterations of the basic algorithm. The two coeecients per iteration are obtained with only a small increase in the cycle time by estimating one of the coeecients. A correcting iteration method is used to correct the possible errors produced by the estimate. Moreover, the modiied iteration permits the reduction of the number of cycles required for the compensation of the scaling factor. The resulting architecture is word serial, working both in rotation and vectoring operation modes, presenting a low latency in comparison with the classical CORDIC approach. The CORDIC algorithm (COordinate Rotation DIgital Computer) was introduced to compute trigonometric functions and generalized to compute linear and hyperbolic functions 10]]11]. Moreover , it is eeective in performing rotations. It is an iterative algorithm suitable for VLSI implementation because it employs only adders and shifters and it has a wide application eld. Special attention has been paid by diierent researchers to the improvement of the algorithm in the last few years, as referenced in 3]. By means of the CORDIC algorithm, a vector (x; y) is rotated an angle (rotation mode) or it is taken to the coordinate axis (vectoring mode). The algorithm is based on rotations over preexed known elementary angles. The basic iteration or microrotation is: x(j + 1) = x(j) ? j 2 ?j y(j) y(j + 1) = y(j) + j 2 ?j x(j) (1) z(j + 1) = z(j) ? j tan ?1 (2 ?j) where (x(0); y(0)) are the initial coordinates of the vector and the z coordinate accumulates the angle. The coeecient j 2 f?1; +1g speciies the direction of each microrotation. n + 1 iterations are needed to produce n bit of precision. The nal coordinates are scaled by the factor K = n Y j=0 q 1 + 2 j 2 ?2j (2) which is a constant since j j j= 1. We propose a modiication of the algorithm by merging two successive iterations into one. Two coeecients are required per iteration, the second one being dependent on the result of the rst classic iteration. This dependency would increase the cycle time, eliminating the advantage of the merge. To avoid this increase, we estimate the second coeecient and this estimate is performed in parallel with the variable shift. The …