as being congruent
to n modulo m. It means that
is the remainder
is supplied,
a string of distinct values can be generated.
we find a sequence
of numbers distributed on [0,1].
and the set of multipliers is a= (a
a
,..,a
).
By taking a value of just 2 for k and suitable multipliers a
and
a, a compound generator with acceptable result structure
can be obtained, described next.
, and the first p bits are provided; the constant
c has been set equal to zero. There is a maximum of
2
distinct possible iterations before sequence repeats
itself.Interesting is the existence of sequences with only two non-zero coefficients,
i.e. b
is of the form
denotes
the `exclusive or' operation.
is conventionally the `exclusive-or'.
It may be however just simple addition or subtraction, and recent studies favour
the latter operation, giving rise to a subtracted Fibonacci generator.And especially
interesting development is the subtract-with-borrow generator of this type.
The algorithm is
, which must
be set to 0 or 1, arbitrarily, at initialization, is reassigned in each call
as follows; if the quantity in brackets is negative, so that m must be added
to it to carry out the modulo m operation,
is
set to zero otherwise it assumes the value unity. If m, p, and q satisfy certain
conditions, the period of this generator is m
-m
.