6.2.3 Skip Ahead
Independent sequences of variates can be generated from a single base
generator through the use of block-splitting, or skipping-ahead. This
method consists of splitting the sequence into k
non-overlapping blocks, each of length n, where n is
larger than the maximum number of variates required from any of the
sequences. For example:
Block 1:x(1),x(2),...,x(n), Block 2:x(n + 1), x(n + 2), ..., x(2 * n), Block 3:x(2 * n + 1), x(2 * n + 2), ..., x(3 * n), etc.
Each of the k blocks provide an independent sequence.
The block splitting algorithm therefore requires the sequence to be
advanced a large number of places. Due to their form this can be done
efficiently for linear congruential generators and multiple
congruential generators. The ACML provides block-splitting for the NAG
Basic generator, the Wichmann-Hill generators and L'Ecuyer's Combined
Recursive generator.