Expanding a number in Python

by Alex
Expanding a number in Python

In this tutorial, we’re going to break down the process of exponentiation in Python. In mathematics, exponentiation is an operation that multiplies a number by itself several times. Python provides built-in operators and functions for performing exponentiation.

The ** operator for exponentiation

Many developers think of the caret symbol(^) as the operator for powers, because that is what it stands for in mathematics. In most programming languages, however, this symbol acts as a bitwise xor. In Python, the powers up operator is denoted by two asterisk characters ** between the base and the number of the power. The functionality of this operator complements that of the multiplication operator *: the only difference is that the second operator specifies how many times the first operand will be multiplied by itself.

print(5**6)

To multiply the number 5 by itself 6 times, we use ** between the base 5 and the operand of degree 6. Conclusion:

15625

Let’s check the operator with other values. Initialize an integer, a negative integer, zero, and two float numbers, one greater than zero and one less than zero. We assign random values to the degrees.


num1 = 2
num2 = -5
num3 = 0
num4 = 1.025
num5 = 0.5
print(num1, '^12 =', num1**12)
print(num2, '^4 =', num2**4)
print(num3, '^9999 =', num3**9999)
print(num4, '^-3 =', num4**-3)
print(num5, '^8 =', num5**8)

Output:

2 ^12 = 4096
-5 ^4 = 625
0 ^9999 = 0
1.025 ^-3 = 0.928599410919749
0.5 ^8 = 0.00390625

pow() or math.power() for powers

You can also power up in Python using pow() or the math module, which has its own implementation of the same module. In both functions, we need to pass two arguments: the base and the power itself. Let’s try calling both functions and see the result.


import math
print(pow(-8, 7))
print(math.pow(-8, 7))
print(pow(2, 1.5))
print(math.pow(2, 1.5))
print(pow(4, 3))
print(math.pow(4,3))
print(pow(2.0, 5))
print(math.pow(2.0, 5))

Conclusion:

-2097152
-2097152.0
2.8284271247461903
2.8284271247461903
64
64.0
32.0
32.0

The only difference is that math.pow() always returns a floating-point number, even if you pass integers. But pow() will return a floating-point number if at least one of the arguments was the same.

numpy.np() for exponentiation

The numpy module has its own power() function for multiplication. It takes the same arguments as pow(), where the first is the base and the second is the value of the degree. Let’s display the same results.


print(np.power(-8, 7))
print(np.power(2, 1.5))
print(np.power(4, 3))
print(np.power(2.0, 5))
-2097152
2.8284271247461903
64
32.0

How do I get the square of a number in Python? To square a number, you need to specify 2 as a power. There is no built-in function for getting the square in Python. For example, the square of a number is 6 – 6**2 -> 36.

Comparing the running times of different solutions

Now let’s compare how long it takes for each of the three functions and the ** operator to execute. To do this, we use the timeit module. The base is 2 and the value of the power is 9999999.


import numpy as np
import math
import time
start = time.process_time()
val = 2**9999999
print('** for', time.process_time() - start, 'ms')
start = time.process_time()
val = pow(2, 9999999)
print('pow() per', time.process_time() - start, 'ms')
start = time.process_time()
val = np.power(2, 9999999)
print('np.power() per', time.process_time() - start, 'ms')
start = time.process_time()
val = math.pow(2, 9999999)
print('math.pow() per', time.process_time() - start, 'ms')
** for 0.078125 ms
pow() for 0.0625 ms
np.power() in 0.0 ms
Traceback (most recent call last):
File "C:\Programs\Python\Python38\test.py", line 18, in
val = math.pow(2, 9999999)
OverflowError: math range error

The first thing to note is that math.pow() returned an OverflowError. This means that the function does not support large degree values. The differences between the others are quite simple, but you can see that np.power() is the fastest.

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