np.sum(arr) not equal to reduce(lambda a, b: a+b, arr)

[colin-zhou]

a random array of np.float64 sum not equal to reduce(lambda a, b: a+b, arr) version

Reproducing code example:

import numpy as np
import sys
x = np.random.random(200)
print("np_sum    ", np.sum(x), file=sys.stderr)
print("reduce_sum", functools.reduce(lambda a,b: b + a, x), file=sys.stderr)

Error message:

the result shows some thing like this (this should be equal)

np_sum 99.13225730835295
reduce_sum 99.13225730835288

Numpy/Python version information:

1.15.2 3.5.6 (default, Nov 16 2018, 15:50:58)
[GCC 4.8.5 20150623 (Red Hat 4.8.5-28)]

[eric-wieser]

Floating point addition is not associative, ie (a + b) + c != a + (b + c) is not always true. Numpy uses pairwise summation, so does not perform the additions in the same order. This tends to produce a more accurate answer than the left-to-right approach used by reduce.