Explination of Mersenne Twister algorithm

Question

I am looking to implement the Mersenne Twister random number generator in a project. However, since this is for an embedded application, I will be later optimizing the code for my architecture. However, I can find little documentation on how the code works, and I'm almost certain it's not pixie dust and magic. Is there any good documentation out there that I am perhaps overlooking? Flowcharts would be nice. If not, I would appreciate if someone could give me a step-by-step explanation of the algorithm. Thanks!

Answer 1

An actual explanation would require first taking a few years to get a math degree, but I can give you my version of the main state advance code from ojrandlib, which is simpler than most of what you'll find on the net. My structure g holds the generator state: g->state is the MT state vector itself, g->buf is an output buffer of the returned random bits:

int i, j, k, n = g->statesize;
uint32_t y, m, *s = g->state, *bp = g->buf + g->bufsize;

for (i = 0; i < n; ++i) {
    j = i + 1;      if (j >= n) j -= n;
    k = i + 397;    if (k >= n) k -= n;

    m = (s[j] & 1) ? 0x9908b0df : 0;
    s[i] = m ^ s[k] ^ (((s[i] & 0x80000000) | (s[j] & 0x7FFFFFFF)) >> 1);
}
for (i = 0; i < n; ++i) {
    y = s[i] ^ (s[i] >> 11);
    y ^= (y << 7) & 0x9d2c5680U;
    y ^= (y << 15) & 0xefc60000U;
    *--bp = y ^ (y >> 18);
}

Answer 2

There are a number of papers on the algorithm behind the Mersenne Twister random number generator listed on the Mersenne Twister site. You can also find a condensed explanation on Wikipedia.