Very-high radix CORDIC vectoring with scalings and selection by rounding

Abstract

A very-high radix algorithm and implementation for circular CORDIC in vectoring mode is presented. As for division, to simplify the selection function, the operands are pre-scaled. However in the CORDIC algorithm the coordinate x varies during the execution so several scalings might be needed; we show that two scalings are sufficient. Moreover, the compensation of the variable scale factor is done by computing the logarithm of the scale factor and performing the compensation by an exponential. Estimations of the delay for 32 bit precision show a speed up of about two with respect to the radix-4 case with redundant addition. This speed up is obtained at the cost of an increase in the hardware complexity, which is moderate for the pipelined implementation.