random number including 1 - i.e. [0,1]

Mark Dickinson dickinsm at gmail.com
Wed Jun 10 17:47:53 EDT 2009

```Robert Kern <robert.kern at gmail.com> wrote:
> On 2009-06-10 15:54, Mark Dickinson wrote:
>> [...] I'm not sure I'm capable of coming up with extra wording
>> for the docs that won't just cause more confusion, so I'll leave that
>> to someone else.
>
> I did make a concrete suggestion.

Yes, you did.  Thank you.  Submitted as http://bugs.python.org/issue6261

>
>> I seem to recall that when this originally came up in the tracker
>> (issue 4979) the fun part of the analysis was proving that
>> random.uniform(a, b) can never produce values *outside* the interval
>> [a, b].  :-)
>
> I was a bit worried about that part myself for a little bit. :-)
>

I think the key was to show that multiplication by (1-2**-53) (the
largest possible output of random.random()) always makes any float
smaller in magnitude[*], so assuming that a <= b the value of the Python
expression random.random()*(b-a) can't be larger than the exact real
value of (b-a), which in turn means that a + random.random()*(b-a)
can't exceed b.

[*] Well, almost.  This isn't true for subnormals.  But if the result
of the subtraction b-a is subnormal then that subtraction was also
necessarily exact, so everything works in this case, too.

And of course I'm wrong.  I shouldn't have said *never*, above:

>>> from random import uniform
>>> uniform(-1e308, 1e308)
inf

:-(

Somehow this doesn't seem worth either fixing or documenting, though.

--
Mark Dickinson

```