float32_rng.ipynb

smarter_float32_rng.ipynb

not sure if it makes much difference, but I think your "smarter" version is preferred these days, i.e.:

(uint32_values >> 8).astype(np.float32) * np.float32(1 / (1 << 24))

the bottom of https://prng.di.unimi.it/ has some comments on some different definitions of uniformity that could apply here

I noticed that your twitter message said you wanted $[0..1]$, so you might want a -1 in there. Operator precedence is a bit annoying so it needs more brackets than you might expect:

(uint32_values >> 8).astype(np.float32) * np.float32(1 / ((1 << 24) - 1))

e.g. test with:

uint32_values = np.uint32(-1)

Thanks @smason!

float32(np.uint32(x >> uint32(32)) >> uint32(8)) * (float32(1) / float32(uint32(1) << uint32(24))) seems to be better, it seems equivalent to casting an intermediate float64 to float32, without actually materializing the float64 !