Now that I've actually looked at the "utl::random" code in the OP, I see that its UniformRealDistribution is a wrapper around std::generate_canonical, so the juicy bits about turning a random into into a random float are not exposed here at all. But the utl::random code does include an pointer* to an informative C++ working group note.

* https://www.open-std.org/jtc1/sc22/wg21/docs/papers/2023/p09...