On Nov 25, 7:00 pm, Dick Moores <[EMAIL PROTECTED]> wrote: > 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>
(1) Replace line 8 (from mpmath import factorial as f) with Fredrik's code. (2) Test it to see that it gave the same answers as before ... [time passes] Wow! [w/o psyco] Pi to 1000 decimal places takes 13 seconds with original code and 0.2 seconds with Fredrik's suggestion. 2000: 99 seconds -> 0.5 seconds. -- http://mail.python.org/mailman/listinfo/python-list
