Faster uniform() in [0.0 - 1.0(

[Don]

bearophile wrote:
> Don:
> 
>> Since the probability of actually generating a 
>> zero is 1e-4000, it shouldn't affect the speed at all <g>.
> 
> If bits in double have the same probability then I think there is a much higher probability to hit a zero, about 1 in 2^^63, and I'm not counting NaNs (but it's low enough to not change the substance of what you have said).

Yes, but randomly generated bits doesn't give a uniform distribution.
With a uniform distribution, there should be as much chance of getting 
[1-real.epsilon .. 1]
as
[0.. real.epsilon]

But there are only two representable numbers in the first range, and 
approx 2^^70 in the second.

Further, there are 2^^63 numbers in the range [0..real.min] which are 
all equally likely.

So, if you want a straightforward uniform distribution, you're better 
off using [1..2) or [0.5..1) than [0..1), because every possible result 
is equally likely.