  A method for generating random $U(1)$ variables with Boltzmann distribution
is presented. It is based on the rejection method with transformation of
variables. High efficiency is achieved for all range of temparatures or
coupling parameters, which makes the present method especially suitable for
parallel and pipeline vector processing machines. Results of computer runs are
presented to illustrate the efficiency. An idea to find such algorithms is also
presented, which may be applicable to other distributions of interest in Monte
Carlo simulations.
