Original ticket http://projects.scipy.org/numpy/ticket/1855 on 2011-06-02 by trac user ling, assigned to unknown.

For some applications, having a numerical-stable sum is critical. What I mean can be well illustrated in the examples below:

math.fsum([1, 1e-10] * 1000), numpy.sum([1, 1e-10] * 1000)
(1000.0000001, 1000.0000001000171)
math.fsum([1, 1e100, 1, -1e100] * 10000), numpy.sum([1, 1e100, 1, -1e100] * 10000)
(20000.0, 0.0)

Here math.fsum is a numerical stable sum introduced in Python 2.6, which uses the Shewchuk algorithm (seems to be described in http://code.activestate.com/recipes/393090/).

Other complaints about the plain vanilla numpy.sum could be found in a recent thread: http://article.gmane.org/gmane.comp.python.numeric.general/42756.

I hope numpy.sum can also implement something similar (e.g., Shewchuk algorithm or Kahan summation algorithm or partial sum). We could add an optional argument "stable=True/False" to numpy.sum and let the user decides whether they want a more accuracy (but potentially slower) version.