Magic Methods and Operator Overloading
Introduction
The socalled magic methods have nothing to do with wizardry. You have already seen them in previous chapters of our tutorial. They are special methods with fixed names. They are the methods with this clumsy syntax, i.e. the double underscores at the beginning and the end. They are also hard to talk about. How do you pronounce or say a method name like __init__? "Underscore underscore init underscore underscore" sounds horrible and is nearly a tongue twister. "Double underscore init double underscore" is a lot better, but the ideal way is "dunder init dunder"^{1} That's why magic methods methods are sometimes called dunder methods!So what's magic about the __init__ method? The answer is, you don't have to invoke it directly. The invocation is realized behind the scenes. When you create an instance x of a class A with the statement "x = A()", Python will do the necessary calls to __new__ and __init__.
Nearly at the end of this chapter of our tutorial we will introduce the __call__ method. It is overlooked by many beginners and even advanced programmers of Python. It is a functionality which many programming languages do not have, so programmers are generally not looking for. The __call__ method enables Python programmers to write classes where the instances behave like functions. Both functions and the instances of such classes are called callables.
We have encountered the concept of operator overloading many times in the course of this tutorial. We had used the plus sign to add numerical values, to concatenate strings or to combine lists:
>>> 4 + 5 9 >>> 3.8 + 9 12.8 >>> "Peter" + " " + "Pan" 'Peter Pan' >>> [3,6,8] + [7,11,13] [3, 6, 8, 7, 11, 13] >>>It's even possible to overload the "+" operator as well as all the other operators for the purposes of your own class. To do this, you need to understand the underlying mechanism. There is a special (or a "magic") method for every operator sign. The magic method for the "+" sign is the __add__ method. For "" it is "__sub__" and so on. We have a complete listing of all the magic methods a little bit further down.
The mechanism works like this: If we have an expression "x + y" and x is an instance of class K, then Python will check the class definition of K. If K has a method __add__ it will be called with x.__add__(y), otherwise we will get an error message.
Traceback (most recent call last): File "<stdin>", line 1, in <module> TypeError: unsupported operand type(s) for +: 'K' and 'K'
Overview of Magic Methods
Binary Operators
Operator  Method 

+  object.__add__(self, other) 
  object.__sub__(self, other) 
*  object.__mul__(self, other) 
//  object.__floordiv__(self, other) 
/  object.__truediv__(self, other) 
%  object.__mod__(self, other) 
**  object.__pow__(self, other[, modulo]) 
<<  object.__lshift__(self, other) 
>>  object.__rshift__(self, other) 
&  object.__and__(self, other) 
^  object.__xor__(self, other) 
  object.__or__(self, other) 
Extended Assignments
Operator  Method 

+=  object.__iadd__(self, other) 
=  object.__isub__(self, other) 
*=  object.__imul__(self, other) 
/=  object.__idiv__(self, other) 
//=  object.__ifloordiv__(self, other) 
%=  object.__imod__(self, other) 
**=  object.__ipow__(self, other[, modulo]) 
<<=  object.__ilshift__(self, other) 
>>=  object.__irshift__(self, other) 
&=  object.__iand__(self, other) 
^=  object.__ixor__(self, other) 
=  object.__ior__(self, other) 
Unary Operators
Operator  Method 

  object.__neg__(self) 
+  object.__pos__(self) 
abs()  object.__abs__(self) 
~  object.__invert__(self) 
complex()  object.__complex__(self) 
int()  object.__int__(self) 
long()  object.__long__(self) 
float()  object.__float__(self) 
oct()  object.__oct__(self) 
hex()  object.__hex__(self 
Comparison Operators
Operator  Method 

<  object.__lt__(self, other) 
<=  object.__le__(self, other) 
==  object.__eq__(self, other) 
!=  object.__ne__(self, other) 
>=  object.__ge__(self, other) 
>  object.__gt__(self, other) 
Example class: Length
We will demonstrate in the following Length class, how you can overload the "+" operator for your own class. To do this, we have to overload the __add__ method. Our class contains the __str__ and __repr__ methods as well. The instances of the class Length contain length or distance information. The attributes of an instance are self.value and self.unit.This class allows us to calculate expressions with mixed units like this one:
2.56 m + 3 yd + 7.8 in + 7.03 cm
The class can be used like this:
>>> from unit_conversions import Length >>> L = Length >>> print(L(2.56,"m") + L(3,"yd") + L(7.8,"in") + L(7.03,"cm")) 5.57162 >>>
The listing of the class:
class Length: __metric = {"mm" : 0.001, "cm" : 0.01, "m" : 1, "km" : 1000, "in" : 0.0254, "ft" : 0.3048, "yd" : 0.9144, "mi" : 1609.344 } def __init__(self, value, unit = "m" ): self.value = value self.unit = unit def Converse2Metres(self): return self.value * Length.__metric[self.unit] def __add__(self, other): l = self.Converse2Metres() + other.Converse2Metres() return Length(l / Length.__metric[self.unit], self.unit ) def __str__(self): return str(self.Converse2Metres()) def __repr__(self): return "Length(" + str(self.value) + ", '" + self.unit + "')" if __name__ == "__main__": x = Length(4) print(x) y = eval(repr(x)) z = Length(4.5, "yd") + Length(1) print(repr(z)) print(z)
If we start this program, we get the following output:
4 Length(5.593613298337708, 'yd') 5.1148
We use the method__iadd__ to implement the extended assignment:
def __iadd__(self, other): l = self.Converse2Metres() + other.Converse2Metres() self.value = l / Length.__metric[self.unit] return self
Now we are capable to write the following assignments:
x += Length(1) x += Length(4, "yd")
We have added 1 metre in the example above by writing "x += Length(1))". Most certainly, you will agree with us that it would be more convenient to simply write "x += 1" instead. We also want to treat expressions like "Length(5,"yd") + 4.8" similarly. So, if somebody uses a type int or float, our class takes it automatically for "metre" and converts it into a Length object. It's easy to adapt our __add__ and "__iadd__" method for this task. All we have to do is to check the type of the parameter "other":
def __add__(self, other): if type(other) == int or type(other) == float: l = self.Converse2Metres() + other else: l = self.Converse2Metres() + other.Converse2Metres() return Length(l / Length.__metric[self.unit], self.unit ) def __iadd__(self, other): if type(other) == int or type(other) == float: l = self.Converse2Metres() + other else: l = self.Converse2Metres() + other.Converse2Metres() self.value = l / Length.__metric[self.unit] return self
It's a safe bet that if somebody works for a while with adding integers and floats from the right sight that he or she wants to the same from the left side! So let's try it out:
>>> from unit_conversions import Length >>> x = Length(3, "yd") + 5 >>> x = 5 + Length(3, "yd") Traceback (most recent call last): File "<stdin>", line 1, in <module> TypeError: unsupported operand type(s) for +: 'int' and 'Length' >>>
Of course, the left side has to be of type "Length", because otherwise Python tries to apply the __add__ method from int, which can't cope with Length objects as second arguments!
Python provides a solution for this problem as well. It's the __radd__ method. It works like this: Python tries to evaluate the expression "5 + Length(3, 'yd')". First it calls int.__add__(5,Length(3, 'yd')), which will raise an exception. After this it will try to invoke Length.__radd__(Length(3, "yd"), 5). It's easy to recognize that the implementation of __radd__ is analogue to __add__:
def __radd__(self, other): if type(other) == int or type(other) == float: l = self.Converse2Metres() + otherLength.__radd__(Length(3, "yd"), 5) else: l = self.Converse2Metres() + other.Converse2Metres() return Length(l / Length.__metric[self.unit], self.unit )
It's advisable to make use of the __add__ method in the __radd__ method:
def __radd__(self, other): return Length.__add__(self,other)
The following diagram illustrates the relationship between __add__ and __radd__:
The __call__ method
The __call__ method can be used to turn the instances of the class into callables. Functions are callable objects. A callable object is an object which can be used and behaves like a function but might not be a function. By using the __call__ method it is possible to define classes in a way that the instances will be callable objects. The __call__ method is called, if the instance is called "like a function", i.e. using brackets. The following class definition is the simplest possible way to define a class with a __call__ method.class FoodSupply: def __call__(self): return "spam" foo = FoodSupply() bar = FoodSupply() print(foo(), bar())The output is:
spam spamThe previous class example is extremely simple, but useless in practical terms. Whenever we create an instance of the class, we get a callable. These callables are always defining the same constant function. A function without any input and a constant output "spam". We define now a class which is slightly more useful. We define a class with the name TriangleArea. This class has only one method, which is the __call__method. The __call__ method calculates the area of an arbitrary triangle, if the lengthes of the three sides are given.
class TriangleArea: def __call__(self, a, b, c): p = (a + b + c) / 2 result = (p * (p  a) * (p  b) * (p  c)) ** 0.5 return result area = TriangleArea() print(area(3, 4, 5))This program return 6.0. This class is neither very exciting, because even though we can create an arbitrary number of instances each instance is just executing an unaltered __call__ function of the TrianlgeClass. We cannot pass parameters to the instanciation and the __call__ of each instance returns the value of the area of the triangle. So each instance behaves like the area function.
Our next example is a lot more exiting. The class FuzzyTriangleArea defines a __call__ method which implements a fuzzy behaviour in the calculations of the area. The result should be correct with a likelihood of p, e.g. 0.8. If the result is not correct the result will be in a range of ± v %. e.g. 0.1.
import random class FuzzyTriangleArea: def __init__(self, p=0.8, v=0.1): self.p, self.v = p, v def __call__(self, a, b, c): p = (a + b + c) / 2 result = (p * (p  a) * (p  b) * (p  c)) ** 0.5 if random.random() <= self.p: return result else: return random.uniform(resultself.v, result+self.v) area1 = FuzzyTriangleArea() area2 = FuzzyTriangleArea(0.5, 0.2) for i in range(12): print(f"{area1(3, 4, 5):4.3f}, {area2(3, 4, 5):4.2f}")The previous code returns the following output. Be aware that this output differs with every call! We can see the in most cases we get the right value for the area but sometimes not:
6.000, 5.94 6.000, 6.00 6.000, 6.00 6.033, 6.08 6.000, 5.86 6.000, 6.08 6.000, 6.00 6.000, 6.00 6.000, 6.07 6.000, 6.00 6.083, 6.00 6.000, 6.00We can create many different instances of the previous class. Each of these behaves like an area function, which returns a value for the area, which may or may not be correct, depending on the instantiation parameters p and v. We can see those instances as experts (expert functions) which return in most cases the correct answer, if we use p values close to 1. If the value v is close to zero, the error will be small, if at all. The next task consists in merging such experts, let's call them $exp_1$, $exp_2$, ..., $exp_n$ to get an improved result. We can perform a vote on the results, i.e. we will return the value which is most often occuring, the correct value. Alternatively, we can calculate the arithmetic mean. We will implement both possibilities in our class FuzzyTriangleArea:
from random import uniform, random from collections import Counter class FuzzyTriangleArea: def __init__(self, p=0.8, v=0.1): self.p, self.v = p, v def __call__(self, a, b, c): p = (a + b + c) / 2 result = (p * (p  a) * (p  b) * (p  c)) ** 0.5 if random.random() <= self.p: return result else: return random.uniform(resultself.v, result+self.v) class MergeExperts: def __init__(self, mode, *experts): self.mode, self.experts = mode, experts def __call__(self, a, b, c): results= [exp(a, b, c) for exp in self.experts] if self.mode == "vote": c = Counter(results) return c.most_common(1)[0][0] elif self.mode == "mean": return sum(results) / len(results) rvalues = [(uniform(0.7, 0.9), uniform(0.05, 0.2)) for _ in range(20)] experts = [FuzzyTriangleArea(p, v) for p, v in rvalues] merger1 = MergeExperts("vote", *experts) print(merger1(3, 4, 5)) merger2 = MergeExperts("mean", *experts) print(merger2(3, 4, 5))The following example defines a class with which we can create abitrary polynomial functions:
class Polynomial: def __init__(self, *coefficients): self.coefficients = coefficients[::1] def __call__(self, x): res = 0 for index, coeff in enumerate(self.coefficients): res += coeff * x** index return res # a constant function p1 = Polynomial(42) # a straight Line p2 = Polynomial(0.75, 2) # a third degree Polynomial p3 = Polynomial(1, 0.5, 0.75, 2) for i in range(1, 10): print(i, p1(i), p2(i), p3(i))These are the results of the previous function:
1 42 2.75 3.25 2 42 3.5 9.5 3 42 4.25 26.75 4 42 5.0 61.0 5 42 5.75 118.25 6 42 6.5 204.5 7 42 7.25 325.75 8 42 8.0 488.0 9 42 8.75 697.25
You will find further interesting examples of the __call__ function in our tutorial in the chapters Decorators and Memoization with Decorators. You may also consult our chapter on Polynomials
Standard Classes as Base Classes
It's possible to use standard classes  like int, float, dict or lists  as base classes as well.We extend the list class by adding a push method:
class Plist(list): def __init__(self, l): list.__init__(self, l) def push(self, item): self.append(item) if __name__ == "__main__": x = Plist([3,4]) x.push(47) print(x)
This means that all the previously introduced binary and extended assignment operators exist in the "reversed" version as well:
__radd__ __rsub__ __rmul__ ... and so on
Exercises

Write a class with the name Ccy, similar to the previously defined Length class.
Ccy should contain values in various currencies, e.g. "EUR", "GBP" or "USD". An instance should contain the amount and the currency unit.
The class, you are going to design as an excercise, might be best described with the following example session:
>>> from currencies import Ccy >>> v1 = Ccy(23.43, "EUR") >>> v2 = Ccy(19.97, "USD") >>> print(v1 + v2) 32.89 EUR >>> print(v2 + v1) 31.07 USD >>> print(v1 + 3) # an int or a float is considered to be a EUR value 27.43 EUR >>> print(3 + v1) 27.43 EUR >>>
Solutions to our Exercises
 First exercise:
""" The class "Ccy" can be used to define money values in various currencies. A Ccy instance has the string attributes 'unit' (e.g. 'CHF', 'CAD' od 'EUR' and the 'value' as a float. A currency object consists of a value and the corresponding unit. """ class Ccy: currencies = {'CHF': 1.0821202355817312, 'CAD': 1.488609845538393, 'GBP': 0.8916546282920325, 'JPY': 114.38826536281809, 'EUR': 1.0, 'USD': 1.11123458162018} def __init__(self, value, unit="EUR"): self.value = value self.unit = unit def __str__(self): return "{0:5.2f}".format(self.value) + " " + self.unit def changeTo(self, new_unit): """ An Ccy object is transformed from the unit "self.unit" to "new_unit" """ self.value = (self.value / Ccy.currencies[self.unit] * Ccy.currencies[new_unit]) self.unit = new_unit def __add__(self, other): """ Defines the '+' operator. If other is a CCy object the currency values are added and the result will be the unit of self. If other is an int or a float, other will be treated as a Euro value. """ if type(other) == int or type(other) == float: x = (other * Ccy.currencies[self.unit]) else: x = (other.value / Ccy.currencies[other.unit] * Ccy.currencies[self.unit]) return Ccy(x + self.value, self.unit) def __iadd__(self, other): """ Similar to __add__ """ if type(other) == int or type(other) == float: x = (other * Ccy.currencies[self.unit]) else: x = (other.value / Ccy.currencies[other.unit] * Ccy.currencies[self.unit]) self.value += x return self def __radd__(self, other): res = self + other if self.unit != "EUR": res.changeTo("EUR") return res # __sub__, __isub__ and __rsub__ can be defined analogue x = Ccy(10,"USD") y = Ccy(11) z = Ccy(12.34, "JPY") z = 7.8 + x + y + 255 + z print(z) lst = [Ccy(10,"USD"), Ccy(11), Ccy(12.34, "JPY"), Ccy(12.34, "CAD")] z = sum(lst) print(z)
The program returns:282.91 EUR 28.40 EUR
Another interesting aspect of this currency converter class in Python can be shown, if we add multiplication. You will easily understand that it makes no sense to allow expressions like "12.4 € * 3.4 \$" (or in praefix notation: "€ 12.4 * \$ 3.4"), but it makes perfect sense to evaluate "3 * 4.54 €". You can find the new currency converter class with the newly added methods for __mul__, __imul__ and __rmul__ in the following listing:""" The class "Ccy" can be used to define money values in various currencies. A Ccy instance has the string attributes 'unit' (e.g. 'CHF', 'CAD' od 'EUR' and the 'value' as a float. A currency object consists of a value and the corresponding unit. """ class Ccy: currencies = {'CHF': 1.0821202355817312, 'CAD': 1.488609845538393, 'GBP': 0.8916546282920325, 'JPY': 114.38826536281809, 'EUR': 1.0, 'USD': 1.11123458162018} def __init__(self, value, unit="EUR"): self.value = value self.unit = unit def __str__(self): return "{0:5.2f}".format(self.value) + " " + self.unit def __repr__(self): return 'Ccy(' + str(self.value) + ', "' + self.unit + '")' def changeTo(self, new_unit): """ An Ccy object is transformed from the unit "self.unit" to "new_unit" """ self.value = (self.value / Ccy.currencies[self.unit] * Ccy.currencies[new_unit]) self.unit = new_unit def __add__(self, other): """ Defines the '+' operator. If other is a CCy object the currency values are added and the result will be the unit of self. If other is an int or a float, other will be treated as a Euro value. """ if type(other) == int or type(other) == float: x = (other * Ccy.currencies[self.unit]) else: x = (other.value / Ccy.currencies[other.unit] * Ccy.currencies[self.unit]) return Ccy(x + self.value, self.unit) def __iadd__(self, other): """ Similar to __add__ """ if type(other) == int or type(other) == float: x = (other * Ccy.currencies[self.unit]) else: x = (other.value / Ccy.currencies[other.unit] * Ccy.currencies[self.unit]) self.value += x return self def __radd__(self, other): res = self + other if self.unit != "EUR": res.changeTo("EUR") return res # __sub__, __isub__ and __rsub__ can be defined analogue def __mul__(self, other): """ Multiplication is only defined as a scalar multiplication, i.e. a money value can be multiplied by an int or a float. It is not possible to multiply to money values """ if type(other)==int or type(other)==float: return Ccy(self.value * other, self.unit) else: raise TypeError("unsupported operand type(s) for *: 'Ccy' and " + type(other).__name__) def __rmul__(self, other): return self.__mul__(other) def __imul__(self, other): if type(other)==int or type(other)==float: self.value *= other return self else: raise TypeError("unsupported operand type(s) for *: 'Ccy' and " + type(other).__name__)
Assuming that you have saved the class under the name currency_converter, you can use it in the following way in the command shell:>>> from currency_converter import Ccy >>> x = Ccy(10.00, "EUR") >>> y = Ccy(10.00, "GBP") >>> x + y Ccy(21.215104685942173, "EUR") >>> print(x + y) 21.22 EUR >>> print(2*x + y*0.9) 30.09 EUR >>>
We can further improve our currency converter class by using a function get_currencies, which downloads the latest exchange rates from finance.yahoo.com. This function returns an exchange rates dictionary in our previously used format. The function is in a module called exchange_rates.py This is the code of the function exchange_rates.py:from urllib.request import urlopen from bs4 import BeautifulSoup def get_currency_rates(base="USD"): """ The file at location url is read in and the exchange rates are extracted """ url = "https://finance.yahoo.com/webservice/v1/symbols/allcurrencies/quote" data = urlopen(url).read() data = data.decode('utf8') soup = BeautifulSoup(data, 'html.parser') data = soup.get_text() flag = False currencies = {} for line in data.splitlines(): if flag: value = float(line) flag = False currencies[currency] = value if line.startswith("USD/"): flag = True currency = line[4:7] currencies["USD"] = 1 # we must add it, because it's not included in file if base != "USD": base_currency_rate = currencies[base] for currency in currencies: currencies[currency] /= base_currency_rate return currencies
We can import this function from our module. (You have to save it somewhare in your Python path or the directory where your program runs):from exchange_rates import get_currency_rates class Ccy: currencies = get_currencies() # continue with the code from the previous version
We save this version as currency_converter_web.>>> from currency_converter_web import Ccy >>> x = Ccy(1000, "JPY") >>> y = Ccy(10, "CHF") >>> z = Ccy(15, "CAD") >>> print(2*x + 4.11*y + z) 7722.98 JPY >>>
Footnotes
^{1} as suggested by Mark Jackson