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From: CDCKAB%EMUVM1.BITNET@cunyvm.cuny.edu ( Karl Brendel)
Newsgroups: comp.lang.pascal
Subject: Re: Random numbers
Message-ID: <26218@adm.brl.mil>
Date: 8 Mar 91 15:23:00 GMT
Sender: news@adm.brl.mil
Lines: 90

In article <1991Mar8.031013.14902@casbah.acns.nwu.edu>,
  ajburke@casbah.acns.nwu.edu (Austin Burke) wrote:


>In article 1624 John Mitchell writes:
>
>>   How does TP 5.5 generate random numbers?
>
>        The numbers generated are not really random. Each number is
>derived from the preceding "random" number by a complex math
>equation, and then forced (by another formula) to fit into the given
>range.

>
>>   We are using this statement:  r := random;  which returns a
>>real number in the range [0,1).  Does TP use some kind of formula
>>to generate these values?  Or is there an internal list of random
>>numbers that is accessed?  Does "randomize" seed a formula or
>>find a spot in the list to start from?
>
>        There is no internal list. The formula used is,
>approximately, the following:
>
>     seed = (multiplier * seed) + (incrementor mod modulus)
>
>        where "seed" is the previous number generated, "multiplier"
>is some very large constant number, as is "increment," and "modulus"
>is 65536. The result of this formula is then forced to fit into the
>range given by the user.
>        The "randomize" command gives TP its first "seed." This
>first seed is derived (I think) from the current time, measured in
>hundreths of a second (or even more exact - I'm not sure).

Specifics of the random number generator have been discussed at
length in the list by Duncan Murdoch
<dmurdoch@watstat.waterloo.edu>. If he doesn't respond directly to
this question, email to him or a check of the archives would be
appropriate. See particularly articles
<1991Jan14.213834.26624@maytag.waterloo.edu> and
<1991Jan15.163811.15107@maytag.waterloo.edu>. (Yes, Duncan, I keep a
_lot_ of your stuff. :) )

>        Through this process, seemingly random numbers are
>generated. It is conceivable, but not likely, that the exact same
>sequence of "random" numbers may be generated if the initial seed is
>the same. This is why the current time is used - it makes this
>possiblity all the more unlikely.

See the documentation for Randomize. A seed value can be _assigned_.
Reuse of a seed value _will_ result in 'the exact same sequence of
"random" numbers" being generated.

>
>>   My students are writing a program to approximate pi using the
>>Monte Carlo method.  Our problem is that we are experiencing a
>>relatively wide range of answers for pi (+/- 0.2) which is not
>>improved by running the program with more iterations.

I wonder if the source of the problem is really in the random number
generator itself. Would you like to throw out some code for us to
look at? :)

>
>        Sorry, I'm not familiar with the Monte Carlo method.
>
>>P.S.  Does TP generate random integers using the same method?
>>P.P.S.  Would anyone be able to send me a formula for generating
>>good random numbers that might be substituted for the TP function
>>call?

This routine is based on "Abramowitz & Stegun (1965)", implemented
in code received from a statistician whose name I have misplaced.
You should be able to modify it for real numbers as well.

var
    seed : longint;

   function randomInteger(least, most : integer):integer;

   begin
   seed :=  (seed * 23) mod (100000001);
   randomInteger := least + round((most - least)*seed/100000000);
   end; {of randomInteger}

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| Karl Brendel                           Centers for Disease Control |
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