Since there are only log(N) numbers that are powers of 4, and here we are limited by the 32(64) bits of basic integral type, just check them all:

```
class Solution(object):
def isPowerOfFour(self, num):
"""
:type num: int
:rtype: bool
"""
if num <0 :
return False
if num==0:
return False
if num==1:
return True
powers4 = set([1,4,16,64,256,1024,4096,16384,65536,0x40000,0x100000,0x400000,0x1000000,0x4000000,0x10000000,0x40000000])
return num in powers4
```