numpy.linalg.norm returns nan for an array of int16

[WarrenWeckesser]

Example:

In [1]: np.__version__
Out[1]: '1.10.0.dev0+a92c4a1'

In [2]: x = np.array([ -91, -119, -137, -132], dtype=np.int16)

In [3]: np.linalg.norm(x)
/Users/warren/local_scipy/lib/python2.7/site-packages/numpy/linalg/linalg.py:2126: RuntimeWarning: invalid value encountered in sqrt
  ret = sqrt(sqnorm)
Out[3]: nan

The example is from http://stackoverflow.com/questions/31685156/normalizing-vector-produces-nan-in-numpy, although it is not clear in that question if the array has type int16.

[WarrenWeckesser]

Possibly related issues:
#5626
#4851

[argriffing]

I think the explanation is #4126, so for example

>>> x = np.array([ -91, -119, -137, -132], dtype=np.int16)
>>> x.dot(x)
-6901
>>> (x*x).sum()
58635

[jakirkham]

So, this should also be helped by @charris's proposal ( #5626 (comment) ) to converting everything to floats or similar before computing.

[WarrenWeckesser]

Fixed by #7088.