Optimized random number generation in an interval

We present a universal optimization for generating a uniformly distributed integer in an interval, based on the underlying uniform distribution. This optimization provides up to 25% run-time improvement, and what is sometimes more important, up to 25% reduction in usage of (pseudo-)random bits. The optimization entails no run-time penalty for all but the most primitive pseudo-random number generators, and can be easily employed by existing software and hardware. For hardware implementations we present additional improvements.