Josiah Carlson <[EMAIL PROTECTED]> wrote: > > Alex Martelli <[EMAIL PROTECTED]> wrote: > > > > ...claims: > > > > Note that for even rather small len(x), the total number of > > permutations of x is larger than the period of most random number > > generators; this implies that "most" permutations of a long > > sequence can never be generated. > [snip] > > I suspect that the note is just a fossil from a time when the default > > random number generator was Whichman-Hill, with a much shorter > > period. Should this note just be removed, or instead somehow > > reworded to point out that this is not in fact a problem for the > > module's current default random number generator? Opinions welcome! > > I'm recovering from a migraine, but here are my thoughts on the topic... > > The number of permutations of n items is n!, which is > (n/2)^(n/2). > Solve: 2**19997 < (n/2)^(n/2) > log_2(2**19997) < log_2((n/2)^(n/2)) > 19997 < (n/2)*log(n/2) > > Certainly with n >= 4096, the above holds (2048 * 11 = 22528) > > - Josiah
I would also point out that even if MT had a larger period, there would still be no guarantee that all permutations of a given sequence would be able to be generated from the PRNG given some aribtrary internal state. - Josiah _______________________________________________ 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
