random.jumpahead: How to jump ahead exactly N steps?

[Ben Cartwright]

Matthew Wilson wrote:
> The random.jumpahead documentation says this:
>
>     Changed in version 2.3: Instead of jumping to a specific state, n steps
>     ahead, jumpahead(n) jumps to another state likely to be separated by
>     many steps..

This change was necessary because the random module got a new default
generator in 2.3.  The new generator uses the Mersenne Twister
algorithm.  Pre 2.3, Wichmann-Hill was used.  (For more details, search
for "jumpahead" in
http://www.python.org/download/releases/2.3/NEWS.txt)

Unlike WH, there isn't a way to directly compute the Nth number in the
sequence using MT.  If you're curious as to why,
textbooks/journals/Google are your friends. :-)

> I really want a way to get to the Nth value in a random series started
> with a particular seed.  Is there any way to quickly do what jumpahead
> apparently used to do?

You can always use the old WH generator.  It's still available:
  >>> import random
  >>> wh = random.WichmannHill()
  >>> N, SEED = 100, 0
  >>> wh.seed(SEED)
  >>> for i in range(N): dummy = wh.random()
  >>> wh.random()
  0.68591619673484816
  >>> wh.seed(SEED)
  >>> wh.jumpahead(N)
  >>> wh.random()
  0.68591619673484816

> I devised this function, but I suspect it runs really slowly:

Don't just suspect.  Experiment, too. :-)

> def trudgeforward(n):
>     '''Advance the random generator's state by n calls.'''
>     for _ in xrange(n): random.random()
>
> So any speed tips would be very appreciated.

Python's random generator is implemented in C and is quite fast.  In my
tests, your trudgeforward performs acceptably with n<~100000.

"import psyco" usually worth a try when improving execution speed, but
it won't help you here.  All the real work is being done in C; the
overhead of the Python interpreter is neglible.

Hope that helps,
--Ben