Python's sum not returning same result as NumPy's numpy.sum

Question

Numpy's sum function is returning the correct expected result, but the default python's sum is not (at least not for uint8 datatype, which makes it even more confusing):

In [1]: import numpy as np                                                      

In [2]: x = np.random.randint(2, size = (1000,100))                             

In [3]: x                                                                       
Out[3]: 
array([[1, 1, 0, ..., 0, 1, 1],
       [1, 1, 1, ..., 0, 0, 0],
       [1, 1, 0, ..., 1, 0, 1],
       ...,
       [1, 0, 0, ..., 1, 0, 1],
       [0, 0, 1, ..., 0, 1, 1],
       [1, 1, 0, ..., 1, 1, 1]])

In [4]: np.sum(x)                                                               
Out[4]: 50318

In [5]: sum(sum(x))                                                             
Out[5]: 50318

In [6]: x = x.astype('uint8')                                                   

In [7]: np.sum(x)                                                               
Out[7]: 50318

In [8]: sum(sum(x))                                                             
Out[8]: 16014

Answer 1

By specifying uint8 you are telling numpy to use 8 bits per element. The maximum number that can be stored in 8 bits is 255. So when you sum, you get an overflow.
Practical example:

>>> arr = np.array([[255],[1]],dtype=np.uint8)
>>> arr
array([[255],
       [1]], dtype=uint8)
>>> sum(arr)
array([0], dtype=uint8)
>> arr[0]+arr[1]
array([0], dtype=uint8)

Note that sum(arr) corresponds to arr[0] + arr[1] in this case. As stated in the docs:

Arithmetic is modular when using integer types, and no error is raised on overflow.