[python] Python RuntimeWarning: overflow encountered in long scalars

Here's an example which issues the same warning:

import numpy as np
np.seterr(all='warn')
A = np.array([10])
a=A[-1]
a**a

yields

RuntimeWarning: overflow encountered in long_scalars

In the example above it happens because a is of dtype int32, and the maximim value storable in an int32 is 2**31-1. Since 10**10 > 2**32-1, the exponentiation results in a number that is bigger than that which can be stored in an int32.

Note that you can not rely on np.seterr(all='warn') to catch all overflow errors in numpy. For example, on 32-bit NumPy

>>> np.multiply.reduce(np.arange(21)+1)
-1195114496

while on 64-bit NumPy:

>>> np.multiply.reduce(np.arange(21)+1)
-4249290049419214848

Both fail without any warning, although it is also due to an overflow error. The correct answer is that 21! equals

In [47]: import math

In [48]: math.factorial(21)
Out[50]: 51090942171709440000L

According to numpy developer, Robert Kern,

Unlike true floating point errors (where the hardware FPU sets a flag whenever it does an atomic operation that overflows), we need to implement the integer overflow detection ourselves. We do it on the scalars, but not arrays because it would be too slow to implement for every atomic operation on arrays.

So the burden is on you to choose appropriate dtypes so that no operation overflows.