# [Numpy-discussion] Integer overflow in test_einsum (1.7.1)

Toder, Evgeny evgeny.toder at jpmorgan.com
Tue May 14 13:26:13 EDT 2013

```Hello,

One of the test cases in test_einsum causes integer overflow for i2 type. The test goes like this:

>>> import numpy as np
>>> dtype = 'i2'
>>> n = 15
>>> a = np.arange(4*n, dtype=dtype).reshape(4,n)
>>> b = np.arange(n*6, dtype=dtype).reshape(n,6)
>>> c = np.arange(24, dtype=dtype).reshape(4,6)

It then calculates AxB using einsum. The problem is that the values in the last row of the result do not fit into i2:

>>> np.einsum("ij,jk", a, b, dtype='f8', casting='unsafe')
array([[  6090.,   6195.,   6300.,   6405.,   6510.,   6615.],
[ 15540.,  15870.,  16200.,  16530.,  16860.,  17190.],
[ 24990.,  25545.,  26100.,  26655.,  27210.,  27765.],
[ 34440.,  35220.,  36000.,  36780.,  37560.,  38340.]])

In my build this produces different results depending on whether out or .astype is used:

>>> np.einsum("ij,jk", a, b, dtype='f8', casting='unsafe').astype(dtype)
array([[  6090,   6195,   6300,   6405,   6510,   6615],
[ 15540,  15870,  16200,  16530,  16860,  17190],
[ 24990,  25545,  26100,  26655,  27210,  27765],
[-31096, -30316, -29536, -28756, -27976, -27196]], dtype=int16)

>>> np.einsum("ij,jk", a, b, out=c, dtype='f8', casting='unsafe')
array([[  6090,   6195,   6300,   6405,   6510,   6615],
[ 15540,  15870,  16200,  16530,  16860,  17190],
[ 24990,  25545,  26100,  26655,  27210,  27765],
[-32768, -32768, -32768, -32768, -32768, -32768]], dtype=int16)

The test wants these (actually the same using numpy.dot) to be equal, so this difference causes it to fail. Both ways to handle overflow seem reasonable to me.

Does numpy in general assign a defined behavior to integer overflow (e.g. two's complement)?
Is this use of integer overflow in the test intentional and is expected to work, or is my build broken?

Best regards,
Eugene

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