Can't compute block entropy when k > 31

[kjaquier]

This seems like an overflow problem where the base b is multiplied k times without any check in block_entropy.c.

I got the issue using PyInform's block entropy function, but the issue clearly seems to be due to Inform.

Code:

from pyinform.blockentropy import block_entropy

x = (np.random.random([100]) > .5).astype(np.uint8)
for k in range(1, 50):
    print(k, block_entropy(x, k))

Output:

1 0.9953784388202257
2 1.9878129812393763
...
31 6.129283016944973

---------------------------------------------------------------------------
OSError                                   Traceback (most recent call last)
<ipython-input-311-af5262631fbd> in <module>
      3 x = (np.random.random([100]) > .5).astype(np.uint8)
      4 for k in range(1, 50):
----> 5     print(k, block_entropy(x, k))

~\AppData\Roaming\Python\Python36\site-packages\pyinform\blockentropy.py in block_entropy(series, k, local)
    109         _local_block_entropy(data, c_ulong(n), c_ulong(m), c_int(b), c_ulong(k), out, byref(e))
    110     else:
--> 111         ai = _block_entropy(data, c_ulong(n), c_ulong(m), c_int(b), c_ulong(k), byref(e))
    112 
    113     error_guard(e)

OSError: exception: access violation writing 0x00000217586956EC

A better solution would be to use the biggest int type available, or at least raise an appropriate error message.

Obviously memory and computational complexity are always going to be limiting factors here. Any suggestion for working around this? Curve-fitting has been suggested here, but in my case I don't think that block entropy converges fast enough to a "fittable" curve (referring to the fact that it is supposed to converge to a straight line with a slope corresponding to the entropy rate, as k goes to infinity).