Next: , Previous: Using Different Generators, Up: Multiple Streams


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.