Numpy error: invalid value encountered in power

Question

I have the following code:

import numpy

def numpysum(n):
   a = numpy.arange(n) ** 2
   b = numpy.arange(n) ** 3
   c = a + b
   return c


size = 3000
c = numpysum(size)

When running, I get the error:

D:\Work\programming\python\test_1\src\test1_numpy.py:6: RuntimeWarning: invalid value encountered in power b = numpy.arange(n) ** 3

Note that the following numpyless function works fine:

def pythonsum(n):
   a = list(range(n))
   b = list(range(n))
   c = []
   for i in range(len(a)):
      a[i] = i ** 2
      b[i] = i ** 3
      c.append(a[i] + b[i])
   return c

I guess it happens because I try to raise a large number to power three. What can I do, beside working with floating point numbers?

I am working with Python 3.2.

Answer 1

numpy is actually looking out for you on this one. Unlke in standard Python, its integer operations don't work on arbitrary-precision objects. I'd guess you were running a 32-bit python, because the same operations don't overflow for me:

>>> sys.maxsize
9223372036854775807
>>> size = 3000
>>> c = numpysum(size)
>>>

but they will eventually. Even easier to see if you control the size of the type manually:

>>> numpy.arange(10, dtype=numpy.int8)**10
__main__:1: RuntimeWarning: invalid value encountered in power
array([  0,   1,   0, -87,   0,  -7,   0, -15,   0,   0], dtype=int8)
>>> numpy.arange(10, dtype=numpy.int16)**10
array([     0,      1,   1024,  -6487,      0,    761, -23552,  15089,
            0,      0], dtype=int16)
>>> numpy.arange(10, dtype=numpy.int32)**10
array([          0,           1,        1024,       59049,     1048576,
           9765625,    60466176,   282475249,  1073741824, -2147483648], dtype=int32)
>>> numpy.arange(10, dtype=numpy.int64)**10
array([         0,          1,       1024,      59049,    1048576,
          9765625,   60466176,  282475249, 1073741824, 3486784401])

where things improve as the number of bits increases. If you really want numpy array operations on Python arbitrary-size integers, you can set dtype to object:

>>> numpy.arange(10, dtype=object)**20
array([0, 1, 1048576, 3486784401, 1099511627776, 95367431640625,
       3656158440062976, 79792266297612001, 1152921504606846976,
       12157665459056928801], dtype=object)