For a binary array sum(array) and numpy.count_nonzero(array) give different answers for big arrays, when array is uint8. Why?

Question

I have 3D arrays filled with ones and zeros (created through pyellipsoid). The array is uint8. I wanted to know the number of 1s. I used sum(sum(sum(array))) to do this and it worked fine for small arrays (up to approx.5000 entries).

I compared sum(sum(sum(array))) to numpy.count_nonzero(array) for a known number of nonzero entries. For bigger arrays the answers from "sum" are always wrong and lower than they should be.

If I use float64 arrays it works fine with big arrays. If I change the data type to uint8 it does not work.

Why is that? I am sure there is a very simple reason, but I can't find an answer.

Small array example:

test = numpy.zeros((2,2,2))
test[0,0,0] = 1  
test[1,0,0] = 1
In: test
Out: 
array([[[1., 0.],
        [0., 0.]],
In: sum(sum(sum(test)))
Out: 2.0

Big example (8000 entries, only one zero, 7999 ones):

test_big=np.ones((20,20,20))
test_big[0,0,0] = 0
test_big
Out[77]: 
array([[[0., 1., 1., ..., 1., 1., 1.],
        [1., 1., 1., ..., 1., 1., 1.],
        [1., 1., 1., ..., 1., 1., 1.],
        ...,
        [1., 1., 1., ..., 1., 1., 1.],
        [1., 1., 1., ..., 1., 1., 1.],
        [1., 1., 1., ..., 1., 1., 1.]],

       [[1., 1., 1., ..., 1., 1., 1.],
        [1., 1., 1., ..., 1., 1., 1.],
        [1., 1., 1., ..., 1., 1., 1.],
        ...,
        [1., 1., 1., ..., 1., 1., 1.],
        [1., 1., 1., ..., 1., 1., 1.],
        [1., 1., 1., ..., 1., 1., 1.]],

       [[1., 1., 1., ..., 1., 1., 1.],
        [1., 1., 1., ..., 1., 1., 1.],
        [1., 1., 1., ..., 1., 1., 1.],
        ...,
        [1., 1., 1., ..., 1., 1., 1.],
        [1., 1., 1., ..., 1., 1., 1.],
        [1., 1., 1., ..., 1., 1., 1.]],

       ...,

       [[1., 1., 1., ..., 1., 1., 1.],
        [1., 1., 1., ..., 1., 1., 1.],
        [1., 1., 1., ..., 1., 1., 1.],
        ...,
        [1., 1., 1., ..., 1., 1., 1.],
        [1., 1., 1., ..., 1., 1., 1.],
        [1., 1., 1., ..., 1., 1., 1.]],

       [[1., 1., 1., ..., 1., 1., 1.],
        [1., 1., 1., ..., 1., 1., 1.],
        [1., 1., 1., ..., 1., 1., 1.],
        ...,
        [1., 1., 1., ..., 1., 1., 1.],
        [1., 1., 1., ..., 1., 1., 1.],
        [1., 1., 1., ..., 1., 1., 1.]],

       [[1., 1., 1., ..., 1., 1., 1.],
        [1., 1., 1., ..., 1., 1., 1.],
        [1., 1., 1., ..., 1., 1., 1.],
        ...,
        [1., 1., 1., ..., 1., 1., 1.],
        [1., 1., 1., ..., 1., 1., 1.],
        [1., 1., 1., ..., 1., 1., 1.]]])
In: sum(sum(sum(test_big)))
Out: 7999.0

So far so good. Here, the data type of the sum output is float64. But if I now change the data type of the array to the type that is used with pyellipsoid (uint8)...

In: test_big = test_big.astype('uint8')
In: sum(sum(sum(test_big)))
Out: 2879

So obviously 2879 is not 7999. Here, the data type of the sum output is int32 (-2147483648 to 2147483647) so this should be big enough for 7999, right? I guess it has something to do with the data type, but how? Why?

(I am using Spyder in Anaconda on Windows).