Conclusion

Based on our statistical tests, we conclude that Tausworthe and MT19937 are excellent RNGs. They have excellent statistical properties, and very high performance. They fail only 2 and 3 tests respectively, and have periods of $2^{19937}-1$ and $2^{88}$ respectively. Hence they would be well suited to the purpose of large-scale simulations. The LCGs (UNIX and PMMLCG) have reasonable statistical randomness, however they are approximately 3 to 9 times slower than Tausworthe and MT19937 RNGs. In addition, their periods are also much lesser, i.e, $2^{31}-1$ for PMMLCG, and $2^{48}$ for UNIX, making them less suitable for large-scale simulations.

Although TT800 is almost as fast as Tausworthe, the numbers generated have high autocorrelations. ICG and BBS are much slower than the rest of the generators and do not have reasonable statistical properties.