Because the Mt19937 (“Mersenne Twister”) engine accepts only a single 32 bit integer as the
seed, the number of possible random sequences is limited to just 232
(i.e. 4,294,967,296), despite Mt19937’s huge period of 219937-1.
When relying on either implicit or explicit random seeding, duplications will appear
much earlier. Duplicated seeds are expected with 50% probability after less than
80,000 randomly generated seeds according to the birthday problem. A 10% probability
of a duplicated seed happens after randomly generating roughly 30,000 seeds.
This makes Mt19937 unsuitable for applications where duplicated sequences must not happen with
more than a negligible probability. If reproducible seeding is required, both the
Random\Engine\Xoshiro256StarStar and Random\Engine\PcgOneseq128XslRr64
engines support much larger seeds that are unlikely to collide randomly. If reproducibility
is not required, the Random\Engine\Secure engine provides cryptographically
secure randomness.
Parameters
seed
Fills the state with values generated with a linear congruential generator
that was seeded with seed interpreted as an unsigned
32 bit integer.
If seed is omitted or null, a random unsigned
32 bit integer will be used.
mode
Use one of the following constants to specify the implementation of the algorithm to use.