rndcon, rndmult, rndseed

Purpose

Resets the parameters of the deprecated linear congruential random number generator that is the basis for _rndu(), _rndn() and _rndng10().

Format

rndcon c;
rndmult a;
rndseed seed;

Parameters

c:(scalar) constant for the random number generator.
a:(scalar) multiplier for the random number generator.
seed:(scalar) initial seed for the random number generator.

Parameter default values and ranges:

seed    time(0)       0 < seed < 232a       1664525       0 < a < 232c       1013904223    0 < a < 232

Remarks

Even though the current versions of rndn(), rndu(), rndBeta(), etc do not use the old linear congruential RNG, you may use rndseed to set the seed for the purpose of creating repeatable pseudo-random sequences.

In years passed, a linear congruential uniform random number generator was used by rndu(), and rndn(). For backward compatibility, this generator may be accessed by the functions _rndu(), _rndn() and rndng10().

These statements allow the parameters of this generator to be changed.

The procedure used to generate the uniform random numbers is as follows. First, the current “seed” is used to generate a new seed:

\[new\_seed = (((a * seed) \% 2^{32})+ c) \% 2^{32}\]

(where % is the mod operator). Then a number between 0 and 1 is created by dividing the new seed by \(2^{32}\):

\[x = \frac{new\_seed}{2^{32}}\]

rndcon resets c.

rndmult resets a.

rndseed resets seed. This is the initial seed for the generator. The default is that GAUSS uses the clock to generate an initial seed when GAUSS is invoked.

GAUSS goes to the clock to seed the generator only when it is first started up. Therefore, if GAUSS is allowed to run for a long time, and if large numbers of random numbers are generated, there is a possibility of recycling (that is, the sequence of “random numbers” will repeat itself). However, the generator used has an extremely long cycle, so that should not usually be a problem.

The parameters set by these commands remain in effect until new commands are encountered, or until GAUSS is restarted.

See also

Functions rndu(), rndn(), rndi(), rndLCi(), rndKMi()