At 01:32 PM 11/20/2007, Fredrik Johansson wrote: >On Nov 20, 2007 10:00 PM, Dick Moores <[EMAIL PROTECTED]> 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 -- http://mail.python.org/mailman/listinfo/python-list
