Martin Kalbfuß wrote:
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.
Then this is not a true random number generator as needed for any
serious application. Then I guess this is actually an attempt to
randomize, if it would work with unknown statistical properties, since
they may depend on internal system workings. I would call such a
solution a toy random number generator at best usful for seeding a
random number generator.
Andreas
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.
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--
________________________________________________________________________
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!
________________________________________________________________________
--
________________________________________________________________________
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
+41 44 633-6090 phone
+41 44 633-1136 fax
Make it as simple as possible, but distrust it!
________________________________________________________________________
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andreas_fischlin.vcf