On Sat, 03 May 2008 18:50:34 +0200, Szabolcs Horvát wrote: > I did the following calculation: Generated a list of a million random > numbers between 0 and 1, constructed a new list by subtracting the mean > value from each number, and then calculated the mean again. > > The result should be 0, but of course it will differ from 0 slightly > because of rounding errors. > > However, I noticed that the simple Python program below gives a result > of ~ 10^-14, while an equivalent Mathematica program (also using double > precision) gives a result of ~ 10^-17, i.e. three orders of magnitude > more precise. > > Here's the program (pardon my style, I'm a newbie/occasional user): > > from random import random > > data = [random() for x in xrange(1000000)] > > mean = sum(data)/len(data) > print sum(x - mean for x in data)/len(data) > > A little research shows that Mathematica uses a "compensated summation" > algorithm. Indeed, using the algorithm described at > http://en.wikipedia.org/wiki/Kahan_summation_algorithm gives us a result > around ~ 10^-17: > > def compSum(arr): > s = 0.0 > c = 0.0 > for x in arr: > y = x-c > t = s+y > c = (t-s) - y > s = t > return s > > mean = compSum(data)/len(data) > print compSum(x - mean for x in data)/len(data) > > > I thought that it would be very nice if the built-in sum() function used > this algorithm by default. Has this been brought up before? Would this > have any disadvantages (apart from a slight performance impact, but > Python is a high-level language anyway ...)? > > Szabolcs Horvát
Built-in sum should work with everything, not just floats. I think it would be useful addition to standard math module. If you know C you could write a patch to mathmodule.c and submit it to Python devs. -- Ivan -- http://mail.python.org/mailman/listinfo/python-list
