The A09225 Program utilizes
the multiplicative congruential method of generating random numbers. The general
formula for producing the random number is: r n = ar n-1 (Modulo m)
which is a congruential random number generator, hereafter referred to as the
generator.
The parameters a
and m, and the seed r n-1 are specified to give desirable statistical
properties of the resultant sequence of numbers. When using a typical computer
system such as the IBM-4381, the value of a is chosen to yield the longest
cycle of numbers, before the cycle begins to repeat itself. The value of
a equals 65539 and remains constant for all operations of the generator.
The modulus m is fixed by the design of the computer, which has a radix
of 2 and a word length of 31 bits. Therefore, m = 231. The seed r n-1 is supplied
to the generator and is always an odd positive integer. The initial seeds are
random numbers supplied externally from the generator, and converted to an odd
number prior to entry into the generator.
The seed r n-1, such as a date from which is subtracted the time in seconds of the current day, provides the generator with the initial seed, which when multiplied by the constant a and then divided by the modulus m, results in a congruential remainder U n, expressed as a decimal.