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6.2 Multiple Streams

It is often advantageous to be able to generate variates from multiple, independent, streams. For example when running a simulation in parallel on several processors. There are four ways of generating multiple streams using the routines available in the ACML:

The four methods are detailed in the following sections. Of the four, (a) should be avoided in most cases, (b) is only really of any practical use when using the Wichmann-Hill generator, and is then still limited to 273 streams. Both block-splitting and leap-frogging work using the sequence from a single generator, both guarantee that the different sequences will not overlap and both can be scaled to an arbitrary number of streams. Leap-frogging requires no a-priori knowledge about the number of variates being generated, whereas block-splitting requires the user to know (approximately) the maximum number of variates required from each stream. Block-splitting requires no a-priori information on the number of streams required. In contrast leap-frogging requires the user to know the maximum number of streams required, prior to generating the first value.

It is known that, dependent on the number of streams required, leap-frogging can lead to sequences with poor statistical properties, especially when applied to linear congruential generators (see Leap Frogging for a brief explanation). In addition, for more complicated generators like a L'Ecuyer's multiple recursive generator leap-frogging can increase the time required to generate each variate compared to block-splitting. The additional time required by block-splitting occurs at the initialization stage, and not at the variate generation stage. Therefore in most instances block-splitting would be the preferred method for generating multiple sequences.