Using a stream cipher in the background, one can simulate uniform random samples of infinite precision floating point numbers within a bound, e.g., between 0 and 1. Behind the scenes, only a random key for the stream cipher is being sampled. The sampled infinite precision floating point number can have as many digits or bits as needed generated on demand.
Comparing such a number against another, or against a rational number, is easy. Arithmetic is harder, including radix conversion.
Can one do non-uniform random samples, e.g., normal distribution?
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