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@node Random Numbers, , Complex Numbers, Mathematics
@section Random Numbers
@pindex RandomNumbers
@cindex random numbers
"Random number" generating routines, like those provided in module
@file{RandomNumbers}, are more correctly called @dfn{pseudo-random number
generators} because they have only the appearance of randomness, and
actually exhibit a specific, repeatable pattern. However, the generated
sequence of numbers should pass certain statistical tests @emph{as if} it
were a truly random sequence.
The algorithm implemented by @file{RandomNumbers} is "good" in the sense
that it passes many of these statistical tests, but it is not necessarily
useful in all cases. A different algorithm might be better suited to a
particular application simply because the inherent structure of the
generated number sequence better satisfies the application's required
properties.
Because of the deterministic quality of random number generators, the user
is required to specify an initial value, or @dfn{seed}. Sequences generated
using the same seed (and the same algorithm) will always produce the same
results. To get a different sequence, simply use a different seed. A
common way to generate different seeds is to initialize using the system's
clock time. (This is not done directly within @file{RandomNumbers} because
then it is not possible to reproduce results, which could cause difficulties
during, say, testing and debugging.)
Also note that sequences @emph{will} repeat themselves eventually. In this
case, a sequence will start to repeat after, at most, @code{modulo-1}
elements, and possibly much sooner than that.
A complete discussion of random number generating algorithms is beyond the
scope of this manual. For more information about the algorithm used in this
module, and other random number generators, consult the following
references:
@format
@cite{Random number generators: good ones are hard to find}
S.K. Park and K.W. Miller
Communications of the ACM, Vol. 31, No. 10, October 1988, pp. 1192-1201
@cite{The Art Of Computer Programming:
Volume 2, Seminumerical Algorithms, Second Edition}
Donald E. Knuth
Addison-Wesley Publishing Co., January 1981
@end format
@defvr Constant modulo
The determing parameter of the linear congruential generator being used
by @file{RandomNumbers}.
@end defvr
@deffn Procedure GetSeed @code{(VAR @var{seed}: LONGINT)}
This procedure gets the seed value currently in use by routines in module
@file{RandomNumbers}.
@end deffn
@deffn Procedure PutSeed @code{(@var{seed}: LONGINT)}
This procedure sets @var{seed} as the new seed value for routines in
@file{RandomNumbers}. Any value for @var{seed} is allowed, but all values
will be mapped into the range @code{[1..modulo-1]}.
@end deffn
@deffn Function RND @code{(@var{range}: LONGINT): LONGINT}
This function calculates a new "random" number. @var{range} has to be in
the range @code{[1..modulo-1]}, and the result is a number in the interval
@code{[0, @var{range}-1]}.
@end deffn
@deffn Function Random @code{(): REAL}
This function calculates a new "random" number. The result is a number in
the interval @code{[0, 1)}.
@end deffn
@emph{Example:}
@smallexample
VAR l: LONGINT;
r: REAL;
RandomNumbers.PutSeed(314159);
l := RandomNumbers.RND(100);
@result{} l = 19
l := RandomNumbers.RND(10000);
@result{} l = 5610
l := RandomNumbers.RND(9999999);
@result{} l = 6158792
l := RandomNumbers.RND(365);
@result{} l = 54
RandomNumbers.GetSeed(l);
@result{} l = 143441039
r := RandomNumbers.Random();
@result{} r = 0.6225381
r := RandomNumbers.Random();
@result{} r = 0.9990177
r := RandomNumbers.Random();
@result{} r = 0.4895853
r := RandomNumbers.Random();
@result{} r = 0.4605866
RandomNumbers.GetSeed(l);
@result{} l = 989102265
@end smallexample
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