approximately twenty times faster than the hardware-implemented, processor-based RDRAND instruction set. Disadvantages Relatively large state buffer, of 2.5 KiB, unless the TinyMT variant (discussed below) is used. Mediocre throughput by modern standards, unless the SFMT variant (discussed below) is used. Exhibits two clear failures (linear complexity) in both Crush and BigCrush in the TestU01 suite. The test, like Mersenne Twister, is based on an -algebra. There are a number of other generators that pass all the tests (and numerous generators that fail badly). Multiple instances that differ only in seed value (but not other parameters) are not generally appropriate for Monte-Carlo simulations that require independent random number generators, though there exists a method for choosing multiple sets of parameter values. Poor diffusion: can take a long time to start generating output that passes randomness tests, if the initial state is highly non-random—particularly if the initial state has many zeros. A consequence of this is that two instances of the generator, started with initial states that are almost the same, will usually output nearly the same sequence for many iterations, before eventually diverging. The 2002 update to the MT algorithm has improved initialization, so that beginning with such a state is very unlikely. The GPU version (MTGP) is said to be even better. Contains subsequences with more 0's than 1's. This adds to the poor diffusion property to make recovery from many-zero states difficult. Is not cryptographically secure, unless the CryptMT variant (discussed below) is used. The reason is that observing a sufficient number of iterations (624 in the case of MT19937, since this is the size of the state vector from which future iterations are produced) allows one to predict all future iterations. Alternatives An alternative generator, WELL ("Well Equidistributed Long-period Linear"), offers quicker recovery, and equal randomness, and nearly equal speed. Marsaglia's xorshift generators and variants are the fastest in the class of LFSRs. 64-bit MELGs ("64-bit Maximally Equidistributed -Linear Generators with Mersenne Prime Period") are completely optimized in terms of the k-distribution properties. The ACORN family (published 1989) is another k-distributed PRNG, which shows similar computational speed to MT, and better statistical properties as it satisfies all the current (2019) TestU01 criteria; when used with appropriate choices of parameters, ACORN can have arbitrarily long period and precision. The PCG family is a more modern long-period generator, with better cache locality, and less detectable bias using modern analysis methods.