Re: [Gm2] Problem with urandom

[Martin Kalbfuß]

Thank you for your answers. But /dev/urandom or dev/random aren't normal
files. They are device files on unixoid systems. When you read from
them, you get a random number. But I don't. Works fine with C. I never
used file access with Modula-2 so I think I do something wrong here.  

Am Donnerstag, den 22.10.2009, 02:29 +0200 schrieb Andreas Fischlin:
> Dear Martin,
> 
> That is correct, that you get all the time the same result, since you
> do only access the variable without actually calling any random number
> generator. AFAIK your implementation of RandInt is wrong, since
> urandom is not a call to the random number generator but merely a
> variable of type SeqFile.ChanId. It does not matter that you call it
> urandom nor that you call your procedure RandInt. This only misleads
> you; if you call the varaible someInteger and and the procedure
> TheInteger then it becomes clearer what you actually do. I find it
> also very confusing that you call procedure WholeIO.ReadInt, i.e. as
> if you would try to read from a file those random numbers. That would
> only work if you would have first generated and written the wanted
> random numbers to that file and then you would read them back from
> there. But such an approach makes bascially no sense. All practical
> random number generation is done such that you generate random numbers
> only in the memory by having a single global variable storing a
> sequence of integers. To get a decent random number generator you need
> a 32 bit integer or even better 3 integers used by 3 multiplicative
> linear congruential random number generators. Such random number
> generators follow the formula:
> 
> z(k+1) = A*z(k) MOD M
> 
> Having a single one research tells that it has to be:
> 
> M = 2**31 - 1 = 2147483647 = MAX(LONGINT)
> 
> with A = 950'706'376 (Fischman & Moore III, 1982). Implementation in
> Modula-2 is tricky unless you have 64-bit integer arithmetic
> available, then it is straightforward.
> 
> Having three multiplicative linear congruential random number
> generators is easier and considered even superior to above solution.
> The interface to a basic random number generator then looks similar to
> this:
> 
> DEFINITION MODULE Randoms;
>   PROCEDURE Seed(z0: LONGINT); (*default z0 = 1*)       
>   PROCEDURE U(): REAL;  (* returns within (0,1] uniformly distributed
> variates *)
> END Randoms.
> 
> DEFINITION MODULE Randoms;
>   
>   PROCEDURE SetSeeds(z0,z1,z2: INTEGER);
>     (*defaults:  z0 = 1, z1 = 10000, z2 = 3000 *)
> 
>   PROCEDURE U(): REAL;
>     (*returns within (0,1) uniformly distributed variates*)
> 
>     (*
>       Based on a combination of three multiplicative linear
>       congruential random number generators of the form   z(k+1) =
>       A*z(k) MOD M   with a prime modulus and a primitive root
>       multiplier (=> individual generator full length period). The
>       multipliers A are: 171, 172, and 170; the modulus' M are:
>       30269, 30307, and 30323.
>     *)
> END Randoms.
> 
> implementation of key routine:
> 
>   PROCEDURE U() : REAL;
>     VAR
>       temp : REAL;
>   BEGIN
> 
>     (* 1st generator: *)
>     x:= 171*(x MOD 177) -  2*(x DIV 177);
>     IF x < 0 THEN x:= x+m1 END;
> 
>     (* 2nd generator: *)
>     y:= 172*(y MOD 176) - 35*(y DIV 176);
>     IF y < 0 THEN y:= y+m2 END;
> 
>     (* 3rd generator: *)
>     z:= 170*(z MOD 178) - 63*(z DIV 178);
>     IF z < 0 THEN z:= z+m3 END;
> 
>     (* combine to give function value: *)
>     temp:= FLOAT(x)/m1R + FLOAT(y)/m2R + FLOAT(z)/m3R;
>     RETURN temp-FLOAT(TRUNC(temp));
> 
>   END U;
> 
> to generate decent integer random numbers in the interval [min, max]
> use an algorithm similar to this:
> 
>   PROCEDURE Jp(min,max: INTEGER): INTEGER;
>     CONST absTolerance = 1.0E-7; (* assuming U() returns a 32-bit
> single precision real *)
>   BEGIN
>     RETURN min + INTEGER( TRUNC( (FLOAT(max-min
> +1)-absTolerance)*U() ) )
>   END Jp;
> 
> You might also find Press et al. (1986, 2002) useful.
> 
> It may be that ISO Modula-2 provides a useful random number generator.
> But in general be aware, unless you know exactly what algorithm any
> random number generator is using, any scientific applications require
> careful investigation. Only games may work fine with using predefined
> random number generators using an unknown generator. Randomization,
> useful typically in the context of games but not scientific
> applications, instead of seeding is an entire other issue, I don't
> have the time to touch upon.
> 
> Regards,
> Andreas
> 
> 
> Cited references:
> --------------------
> Fishman, G. & L.R. Moore III, 1982. A statistical
>                 evaluation of multiplicative congruential random
>                 number generators with modulus 2^31-1.  J.  Amer.
>                 Statist.  Assoc., 77: 129ff.
> 
> Wichmann, B.A. & Hill, I.D., 1982.  An efficient and
>                   portable pseudo-random number generator.  Algorithm
>                   AS 183. Applied Statistics, 31(2): 188-190.
> 
> Press, W.H., Teukolsky, S.A., Vetterling, W.T. & Flannery, B.P., 2002.
> Numerical recipes multi-language source code CD-ROMs with Windows,
> DOS, or Mac single screen license. v 2.10, Cambridge University Press,
> Cambridge, 2 CD ROM pp. 
> 
> Press, H.W., Flannery, B.P., Teukolsky, S.A. & Vetterling, W.T., 1986.
> Numerical recipes: the art of scientific computing. Cambridge
> University Press: New York, 818 pp.
> 
> 
>  
> 
> Martin Kalbfuß wrote: 
> > Hi,
> > 
> > I created the following module to produce random integers. But when I
> > call RandInt I always get the same value. Maybe I do something wrong
> > about The stream. Opening the file with fopen in C an read a value from
> > it produces a random number. Do you see anything wrong here? I tried it
> > with stream file, too. 
> > 
> > Thanks
> > 
> > IMPLEMENTATION MODULE Dice;
> > 
> > IMPORT SeqFile,
> >        WholeIO,
> >        IOChan,
> >        EXCEPTIONS,
> >        SYSTEM;
> > 
> > VAR urandom : SeqFile.ChanId; 
> >     res     : SeqFile.OpenResults;
> >     source  : EXCEPTIONS.ExceptionSource;
> > 
> > PROCEDURE RandInt() : INTEGER;
> > VAR result : INTEGER;
> > BEGIN
> >     WholeIO.ReadInt(urandom, result);
> >     RETURN result;
> > END RandInt;
> > 
> > BEGIN
> >     EXCEPTIONS.AllocateSource(source);
> > 
> >     SeqFile.OpenRead(urandom, '/dev/urandom', SeqFile.raw, res);
> >     IF urandom = IOChan.InvalidChan() THEN
> >                             EXCEPTIONS.RAISE(source, 0, 'Error: Could not 
> > access /dev/urandom');
> >     END;
> > FINALLY
> >     SeqFile.Close(urandom);
> > END Dice.
> > 
> > The calling module:
> > MODULE Kniffel;
> > 
> > IMPORT Dice,
> >        SWholeIO,
> >        STextIO;
> > BEGIN
> >     SWholeIO.WriteInt(Dice.RandInt(), 0);
> >     STextIO.WriteLn;        
> >     SWholeIO.WriteInt(Dice.RandInt(), 0);
> >     STextIO.WriteLn;
> >     SWholeIO.WriteInt(Dice.RandInt(), 0);
> >     STextIO.WriteLn;                
> > END Kniffel.
> > 
> > The results:
> > 
> > +134653772
> > +134653772
> > +134653772
> > 
> > Always the same number. All the time. No matter what I do.
> > 
> > 
> > 
> > 
> > _______________________________________________
> > gm2 mailing list
> > address@hidden
> > http://lists.nongnu.org/mailman/listinfo/gm2
> >   
> 
> -- 
> ________________________________________________________________________
> ETH Zurich
> Prof. Dr. Andreas Fischlin
> Systems Ecology - Institute of Integrative Biology
> CHN E 21.1
> Universitaetstrasse 16
> 8092 Zurich
> SWITZERLAND 
> 
> address@hidden
> www.sysecol.ethz.ch/staff/af
> 
> +41 44 633-6090 phone
> +41 44 633-1136 fax
> 
> Make it as simple as possible, but distrust it!
> ________________________________________________________________________
>  
> 
>