[ROOT-9733] TRandom3 does not implement perfectly a Mersenne Twister PRNG

[vepadulano]

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Description

From https://its.cern.ch/jira/browse/ROOT-9733

The {{TRandom3}} is a random number engine based on Mersenne Twister algorithm, defined in {{TRandom3.cxx}}. Since 2002 (see commit 026ec9c0f458be61825e7335ec51e115ec6cbf4c), an eventual zero return value is discarded by {{TRandom3::Rndm()}}. This does not allow the algorithm to return the same sequence of the C++11 standard implementation {{std::mt19937}} (when seeded with the same value - except for seed zero, since handled in a special way by {{TRandom3::SetSeed()}} - and multiplied by 2^-32).

A related mistake is present also in the description of the class, where it states the algorithm period to be 2^19937 - 1. If you discard the zeros, of course the period will be (very slightly) less than it.

In conclusion, {{TRandom3}} is an imperfect implementation of the Mersenne Twister 32-bit algoritm. Furthermore, the documentation does not explain this small difference.

 

Reproducer

As per the description

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