It is well known that adding up numbers can result in numerical errors (for example, if the first number is really large, whereas there are many other small numbers).
This can be solved adding up the numbers in a non straight-forward way. See for example: https://en.wikipedia.org/wiki/Kahan_summation_algorithm
Is numpy.sum implemented in such a way that numerical errors are avoided?
Searching on numpy kahan turned up a closed bug/issue
https://github.com/numpy/numpy/issues/2448 Numerical-stable sum (similar to math.fsum)
I haven't read it in detail. Note the reference to math.fsum
fsum(iterable)
Return an accurate floating point sum of values in the iterable.
Assumes IEEE-754 floating point arithmetic.
(from the Python math docs)
Return an accurate floating point sum of values in the iterable. Avoids loss of precision by tracking multiple intermediate partial sums
And a SO question, with some discussion, but no real answer:
Is there any documentation of numpy numerical stability?
A simple comparison:
In [320]: x=np.ones(100000)/100000
In [321]: sum(x)-1
Out[321]: -1.9162449405030202e-12
In [322]: np.sum(x)-1
Out[322]: 1.3322676295501878e-15
In [323]: math.fsum(x)-1
Out[323]: 0.0
respective times are 72 ms, 304 µs, 23.8 ms
np.sum is clearly fastest; but fsum is better than sum, probably because of its sepecialized C implementation.
