Python Language Exponentiation Magic methods and exponentiation: builtin, math and cmath
Example
Supposing you have a class that stores purely integer values:
class Integer(object):
def __init__(self, value):
self.value = int(value) # Cast to an integer
def __repr__(self):
return '{cls}({val})'.format(cls=self.__class__.__name__,
val=self.value)
def __pow__(self, other, modulo=None):
if modulo is None:
print('Using __pow__')
return self.__class__(self.value ** other)
else:
print('Using __pow__ with modulo')
return self.__class__(pow(self.value, other, modulo))
def __float__(self):
print('Using __float__')
return float(self.value)
def __complex__(self):
print('Using __complex__')
return complex(self.value, 0)
Using the builtin pow function or ** operator always calls __pow__:
Integer(2) ** 2 # Integer(4)
# Prints: Using __pow__
Integer(2) ** 2.5 # Integer(5)
# Prints: Using __pow__
pow(Integer(2), 0.5) # Integer(1)
# Prints: Using __pow__
operator.pow(Integer(2), 3) # Integer(8)
# Prints: Using __pow__
operator.__pow__(Integer(3), 3) # Integer(27)
# Prints: Using __pow__
The second argument of the __pow__() method can only be supplied by using the builtin-pow() or by directly calling the method:
pow(Integer(2), 3, 4) # Integer(0)
# Prints: Using __pow__ with modulo
Integer(2).__pow__(3, 4) # Integer(0)
# Prints: Using __pow__ with modulo
While the math-functions always convert it to a float and use the float-computation:
import math
math.pow(Integer(2), 0.5) # 1.4142135623730951
# Prints: Using __float__
cmath-functions try to convert it to complex but can also fallback to float if there is no explicit conversion to complex:
import cmath
cmath.exp(Integer(2)) # (7.38905609893065+0j)
# Prints: Using __complex__
del Integer.__complex__ # Deleting __complex__ method - instances cannot be cast to complex
cmath.exp(Integer(2)) # (7.38905609893065+0j)
# Prints: Using __float__
Neither math nor cmath will work if also the __float__()-method is missing:
del Integer.__float__ # Deleting __complex__ method
math.sqrt(Integer(2)) # also cmath.exp(Integer(2))
TypeError: a float is required
