Very few languages (or programmers!) are able to check that a function doesn’t have side effects. In particular, checking that a function doesn’t diverge generally requires a proof assistant, like in F* and Lean.
Your definition of functional programming is as valid as any, but it’s so strict that even Haskell would be mid-tier in the functional ranking.
I didn’t really understand the details of what you’re making, but if you want to generate a random variable with entropy x, the straightforward approach would be to use Σ = { n | 1≤n≤⌈2^x⌉ } as the alphabet and start with a uniform distribution (which overshoots the entropy target) and slightly skew the distribution to reduce entropy to hit the target x. Then you can map Σ to your desired set (f64 or Vec<f64> in your case?) using an injection, since that preserves entropy.
This is missing the biggest difference: ISO 8601 costs 190-450€, whereas RFC 3339 is free.