Trouble getting loop to break

[Dick Moores]

At 01:32 PM 11/20/2007, Fredrik Johansson wrote:
>On Nov 20, 2007 10:00 PM, Dick Moores <rdm at rcblue.com> wrote:
> > And also with the amazing Chudnovsky algorithm for pi. See
> > <http://python.pastebin.com/f4410f3dc>
>
>Nice! I'd like to suggest two improvements for speed.
>
>First, the Chudnovsky algorithm uses lots of factorials, and it's
>rather inefficient to call mpmath's factorial function from scratch
>each time. You could instead write a custom factorial function that
>only uses multiplications and caches results, something like this:
>
>cached_factorials = [mpf(1)]
>
>def f(n):
>     n = int(n)
>     if n < len(cached_factorials):
>         return cached_factorials[n]
>     p = cached_factorials[-1]
>     for i in range(len(cached_factorials), n+1):
>         p *= i
>         cached_factorials.append(p)
>     return p
>
>(In some future version of mpmath, the factorial function might be
>optimized so that you won't have to do this.)
>
>Second, to avoid unnecessary work, factor out the fractional power of
>640320 that occurs in each term. That is, change the "denom =" line to
>
>     denom = (f(3*k) * ((f(k))**3) * (640320**(3*k)))
>
>and then multiply it back in at the end:
>
>     print 1/(12*sum/640320**(mpf(3)/2))
>
>With these changes, the time to compute 1,000 digits drops to only 
>0.05 seconds!
>
>Further improvements are possible.
>
>Fredrik

Fredrik,

I'm afraid I'm just too dumb to see how to use your first suggestion 
of cached_factorials. Where do I put it and def()? Could you show me, 
even on-line, what to do? <http://py77.python.pastebin.com/f48e4151c> 
You (or anyone) can submit an amendment to my code using the textbox.

I did make the denom change, and see that it does improve the speed a bit.

Thanks,

Dick