random.uniform documentation suggests `high` is excluded

There’s a possibility of confusion from the np.random.uniform documentation, which says:

Samples are uniformly distributed over the half-open interval [low, high) (includes low, but excludes high).

Arguably, that’s true, in the sense that we’re using an expression that (mathematically) draws from [low, high), but rounding and numerical errors mean that in practice, high can be generated:

>>> low = 1.0
>>> high = 1.0 + 2**-40
>>> low, high, low < high
(1.0, 1.0000000000009095, True)
>>> np.random.uniform(low, high, size=10**6).max() == high
True

The current documentation leads to people (well, at least one SO user) writing things like np.random.uniform(low, np.nextafter(high, np.inf)) when they want a closed interval, which probably isn’t a good idea:

>>> np.random.uniform(low, np.nextafter(high, np.inf), size=10**6).max() > high
True

[rkern]

Okay, let’s just document the current behavior. 😃

[mdickinson]

Surely round-towards-minus-infinity (FE_DOWNWARD) solves this?

Ah yes, true; I was (wrongly) thinking in terms of round-towards-zero. Sorry. So for low < high, with round-towards-negative-infinity, yes, all three rounds go the right way (regardless of the sign of low or high) in low + random() * (high - low).

For low > high (which is currently supported), you’d need to be a bit more careful to make sure everything rounds the right way. I think

- (random() * (low - high) - low)

should do it, again using FE_DOWNWARD.

For low == high (which is also currently supported), you’d need to make that an error if you want to forbid high from ever being produced. I’d expect that to break some corner cases in real code, so it’s probably better just to allow high to be produced in that case.