Python Language Exponentiation Magic methods and exponentiation: builtin, math and cmath


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__,
    def __pow__(self, other, modulo=None):
        if modulo is None:
            print('Using __pow__')
            return self.__class__(self.value ** other)
            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