Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP
Posting-Version: version B 2.10.2 9/18/84; site decwrl.UUCP
Path: utzoo!watmath!clyde!cbosgd!ukma!psuvm.bitnet!psuvax1!burdvax!sdcrdcf!ucla-cs!ucbvax!decwrl!dec-rhea!dec-sprite!osman
From: osman@sprite.DEC (Eric, DIGITAL, Burlington Ma.  617 273-7484)
Newsgroups: net.puzzle
Subject: random number wanted between neg inf and pos inf
Message-ID: <33@decwrl.UUCP>
Date: Mon, 16-Dec-85 16:13:28 EST
Article-I.D.: decwrl.33
Posted: Mon Dec 16 16:13:28 1985
Date-Received: Fri, 20-Dec-85 06:03:40 EST
Sender: daemon@decwrl.UUCP
Organization: Digital Equipment Corporation
Lines: 43

>> >    Now he tells us that it's got to be uniformly distributed?  If such
>> >a function exists, the probability of it generating a number between any
>> >two arbitrarily large, but finite limits is exactly 0!  Why would
>> >anyone want a random number generator like that?
>> Not zero, since the random number generator will in fact come up with a
>> number.  The chances are infinitesimal.  The difference is admittedly
>> very subtle.
>
>I haven't been able to market this, so here, ABSOLUTELY FREE, is my
>generator!  It's GUARANTEED to generate ALL positive integers with
>equal frequency, if you only run it long enough.
>
>
>               int rand() {
>                       return 6;
>               }
>--
>Col. G. L. Sicherman
>UU: ...{rocksvax|decvax}!sunybcs!colonel
>CS: colonel@buffalo-cs
>BI: csdsicher@sunyabva

I disagree that this one's output is evenly distributed.  There will be
a rather high spike at x=6.

I'm the original poser of the problem.  I'm surprised at the high
smart-ass/serious ratio on the responses.

The best I've thought of so far for a random number between neg inf and
pos inf is:

        f() = tan (rnd()*pi - pi/2)

In words, take a random number between 0 and 1, scale it to an angle
between -pi/2 and pi/2.  Then take the tangent.  Since tangent of such
angles ranges from -oo to oo, this produces a random number in desired
range.

However, I don't think this is evenly distributed.  (If not, what is
it's distribution ??)  Can we scale this function to make it evenly
distributed ?

/Eric