histogram with Freedman Diaconis estimator crashes on small numbers

np.histogram crashes with MemoryError when the input contains very small numbers.

In [13]:  print(sys.version)
2.7.6 (default, Jun 22 2015, 17:58:13) 
[GCC 4.8.2]

In [14]: print(np.__version__)
1.11.2

In [15]: x = np.array([ 2, 2, 2 - 1e-15, 2 - 1e-15, 1], dtype=np.float64)

In [16]: np.histogram(x, bins='fd')
---------------------------------------------------------------------------
MemoryError                               Traceback (most recent call last)
<ipython-input-16-4ee7362b8a29> in <module>()
----> 1 np.histogram(x, bins='fd')

/home/artem/.local/lib/python2.7/site-packages/numpy/lib/function_base.pyc in histogram(a, bins, range, normed, weights, density)
    562 
    563         # Initialize empty histogram
--> 564         n = np.zeros(bins, ntype)
    565         # Pre-compute histogram scaling factor
    566         norm = bins / (mx - mn)

MemoryError: 

I did some debugging and figured out that in numpy.lib.function_base._hist_bin_fd returns bin width 1.29852472695e-15

def _hist_bin_fd(x):  # x: array([ 2, 2, 2 - 1e-15, 2 - 1e-15, 1])
    iqr = np.subtract(*np.percentile(x, [75, 25]))  # iqr: 1.11022302463e-15
    return 2.0 * iqr * x.size ** (-1.0 / 3.0)  # returns 1.29852472695e-15

I think that in numpy/lib/function_base.py:533 it would be good to check that we get a reasonable number of bins (may be max size of the array) or at least show a warning.

[madphysicist]

Not in the general case, no. Imagine a dataset with two clumps of data separated by a huge gap for an example of why not. It may, however, be worth considering merging together empty bins. To remove what I imagine to be the most common cause for the issue you are describing.

[madphysicist]

And raise a warning about the data having too fine a structure or something.