[Greg Ewing] > But isn't the problem with the Twister that for *some > initial states* the period could be much *shorter* than > the theoretical maximum? > > Or is the probability of getting such an initial state > too small to worry about?
The Twister's state is held in a vector of 624 32-bit words. 31 of the bits aren't actually used, and the number of meaningful state bits is actually 624 * 32 - 31 = 19937. There are exactly 2 orbits in the state space under the state transformation operation (STO): 1. A trivial orbit of length 1, consisting of the state in which all meaningful bits are 0. That's a fixed point for the STO. There are no other fixed points. 2. All not-entirely-0 states are in the other orbit, of length 2**19937 - 1. All not-0 states are reachable from all other not-0 states, and you get back to the non-zero state you start from for the first time after exactly 2**19937 - 1 iterations of the STO. So as long as you don't start with the all-0 state, you're in the second orbit, and see the advertised period (2**19937 - 1). >From Python code, it's impossible to get the all-0 state. All Python-visible initialization methods guarantee there's at least one bit set in the meaningful bits of the state vector, so the probability of not seeing a period of 2**19937 - 1 from Python is exactly 0. Hmm. Well, there _is_ a way to screw yourself here, but you have to work at it: you can force the all-0 state by hand-crafting the right input to random.setstate(). _______________________________________________ Python-Dev mailing list Python-Dev@python.org http://mail.python.org/mailman/listinfo/python-dev Unsubscribe: http://mail.python.org/mailman/options/python-dev/archive%40mail-archive.com
