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Based on an algorithm introduced by Wichmann and Hill [43],
L'Ecuyer [32] has shown how to additively combine two different
32-bit LCGs to produce a generator that passes all known statistical tests
and has a long period of around 
,
thus overcoming the major drawbacks of standard 32-bit LCGs.
This has been implemented in a program known as RANECU
[32, 5].
Combining two LCGs in this way is effectively a more efficient way of
implementing an LCG with a much larger modulus [44].
Recently L'Ecuyer et al. [41] have implemented
combined 48-bit and 64-bit LCGs and MRGs, with even larger periods
and better randomness properties.
A combined 32-bit LCG is substantially slower than a standard 32-bit LCG,
although it is more appropriate to compare it to a 64-bit LCG (which has
the same period), in which case the performance is similar, at least on
a 32-bit machine where multiple-precision arithmetic is required for the
64-bit LCG.
Other proposed combined generators include algorithms combining an LFG with an LCG [2], or an LFG with a simple Weyl (or arithmetic sequence) generator, which is the basis for the RANMAR generator [5, 45] commonly used in computational physics applications. The addition of the Weyl generator greatly improves the randomness properties over the single additive LFG, but RANMAR still fails some Monte Carlo tests [15], since the lag used (p=97) is much too small. If you are using this generator, you should greatly increase the lags, to at least (1279,1063).
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