"Sergey E. Koposov" <m...@sai.msu.ru> writes:
> So among 10^5 random numbers there are already 3 collisions. Which doesn't 
> seem right for the function which generate randoms of double precision

The underlying random() function only generates 31-bit integers, so
collisions aren't as improbable as they might seem.  See
http://en.wikipedia.org/wiki/Birthday_paradox

> It is also interesting that in the table tmpx1 (if I actually output the 
> values using select id from tmpx1) I do not see equal numbers at all but I 
> see 
> for example two values which are close to each other:
>     0.511193082667887
>     0.511194097343832

> First it seems strange that they have been merged into one group by 
> "groupby". 

They aren't; or at least you've not provided any evidence that they were.

                        regards, tom lane

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