# Python __pow__() Magic Method

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## Syntax

`object.__pow__(self, other)`

The Python `__pow__()` method implements the built-in exponentiation operation. So, when you call `pow(a, b)` or `a ** b`, Python attempts to call `x.__pow__(y)`. If the method is not implemented, Python first attempts to call `__rpow__` on the right operand and if this isn’t implemented either, it raises a `TypeError`.

We call this a “Dunder Method” for Double Underscore Method” (also called “magic method”). To get a list of all dunder methods with explanation, check out our dunder cheat sheet article on this blog.

## Background Default pow()

The double asterisk (**) symbol is used as an exponentiation operator. The left operand is the base and the right operand is the power. For example, the expression `x**n` multiplies the value `x` with itself, `n` times.

To understand this operation in detail, feel free to read over our tutorial or watch the following video:

## Example Custom __pow__()

In the following example, you create a custom class `Data` and overwrite the `__pow__()` method so that it returns a dummy string when trying to calculate the power of two numbers.

```class Data:

def __pow__(self, other):
return '... my result of expoentiation...'

a = Data()
b = Data()

print(pow(a, b))
# ... my result of exponentiation...

print(a ** b)
# ... my result of exponentiation...
```

If you hadn’t defined the `__pow__()` method, Python would’ve raised a `TypeError`.

## TypeError: unsupported operand type(s) for ** or pow()

Consider the following code snippet where you try to calculate the exponent of two custom objects without defining the dunder method `__pow__()`:

```class Data:
pass

a = Data()
b = Data()

print(pow(a, b))
# ... my result of exponentiation...

print(a ** b)
# ... my result of exponentiation...```

Running this leads to the following error message on my computer:

```Traceback (most recent call last):
File "C:\Users\xcent\Desktop\code.py", line 8, in <module>
print(pow(a, b))
TypeError: unsupported operand type(s) for ** or pow(): 'Data' and 'Data'```

The reason for this error is that the `__pow__()` method has never been defined—and it is not defined for a custom object by default. So, to resolve the `TypeError: unsupported operand type(s) for ** or pow()`, you need to provide the `__pow__(self, other)` method in your class definition as shown previously:

```class Data:

def __pow__(self, other):
return '... my result of expoentiation...'```

Of course, you’d use another return value in practice as explained in the “Background pow()” section.

## Python __pow__ Modulo

The third argument of the `__pow__` method is the `mod` argument. If present, it calculates the base (first argument) to the power of the exponent (second argument) modulo the third argument. Semantically, `__pow(x, y, mod)__` calculates `(x ** y) % mod` but it is much faster because of modular exponentiation that avoids calculating `x ** y` as an intermediate result.

The following experiment shows that `pow(x, y, mod)` can be more than twice as fast than `(x**y) % mod`:

```import time

x, y, mod = 999, 888, 44

start = time.time()
print((x ** y) % mod)
stop = time.time()
print('Elapsed time for (x ** y) % mod:', stop - start)

start = time.time()
print(pow(x, y, mod))
stop = time.time()
print('Elapsed time for pow(x, y, mod):', stop - start)
```

Output:

```25
Elapsed time for (x ** y) % mod: 0.026185274124145508
25
Elapsed time for pow(x, y, mod): 0.009267568588256836```

To overwrite the `__pow__()` method with the third modulo argument, simply add the third argument like so:

```class Data:
def __pow__(self, other, modulo):
return (self, other, modulo)

x, y, m = Data(), Data(), Data()
print(pow(x, y, m))
# (<__main__.Data object at 0x0000015EC6C86FA0>, <__main__.Data object at 0x0000015EC89FD4F0>, <__main__.Data object at 0x0000015EC8A570A0>)
```

You can see that the built-in `pow()` method internally calls `Data.__pow__()` on the three provided arguments. The result is a tuple of object references of type `Data`.

## Python __pow__ vs __rpow__

Say, you want to calculate the exponent of two custom objects `x` and `y`:

`print(x ** y)`

Python first tries to call the left object’s `__pow__()` method `x.__pow__(y)`. But this may fail for two reasons:

1. The method `x.__pow__()` is not implemented in the first place, or
2. The method `x.__pow__()` is implemented but returns a `NotImplemented` value indicating that the data types are incompatible.

If this fails, Python tries to fix it by calling the `y.__rpow__()` for reverse power on the right operand `y`.

If this method is implemented, Python knows that it doesn’t run into a potential problem of a non-commutative operation. If it would just execute `y.__pow__(x)` instead of `x.__pow__(y)`, the result would be wrong because the exponentiation operation may be non-commutative when custom defined. That’s why `y.__rpow__(x)` is needed.

So, the difference between `x.__pow__(y)` and `x.__rpow__(y)` is that the former calculates `x ** y` whereas the latter calculates `y ** x` — both calling the respective exponentiation method defined on object `x`.

You can see this in effect here where we attempt to call the exponentiation operation on the left operand `x`—but as it’s not implemented, Python simply calls the reverse exponentiation operation on the right operand `y`.

```class Data_1:
pass

class Data_2:
def __rpow__(self, other):
return 'called exponentiation'

x = Data_1()
y = Data_2()

print(x ** y)
# called exponentiation
```

References:

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