# Large integer handling in Python (optimization)

The definition of optimization is to make the best out of something. It is the process of finding the most efficient way of doing or performing specific tasks to achieve the required results. There are various elements of optimization, and they can be implemented either in day-to-day chores, like taking the smallest route to reach point A to B to save fuel, or they can be used to solve complex mathematical problems.

Large integers, which can be termed arbitrary precision integers or big integers, are numbers that are extremely precise and larger than normal integers. They are more complex than normal integers or floats in programming and cannot be represented by regular int or float types.

Dynamic memory allocation is a process through which these integers can be implemented and used in programming. Dynamic allocation allows flexibility rather than fixing the size of the integers.

Large integers can be managed using the built-in `int` type, the `Decimal` module for precision, and with caution, the NumPy library. These methods enable handling of enormous numbers for applications in cryptography, astrophysics, finance, genetics, computer graphics, and big data analytics.

## Some applications of large integers

Large integers are used in many fields. Some of them are:

• Cryptography: Large text is used to encrypt messages such as in the RSA algorithm.
• Astrophysics: For calculating astronomical distances, light year distances these numbers are used.
• Finances: For tracking financial transactions, preventing rounding off errors.
• Genetic data analysis: To analyze large chromosomes and store genetic data.
• Computer Graphics: To generate computer graphics and coordinate transformations.
• Big data analytics: One of the most common applications of large numbers lies in big data analytics where it is used to process data that isn’t constrained into traditional data types.

## Handling large integers in Python

There are three main ways in which Python can store large integers. The int method which by default allows Python to store large integers, the decimal library, and the numpy module. We will take a look at these three methods one by one.

### Method 1: Using Python’s int Type for Large Numbers

In Python, the built-in int literal type can store large integers by default. It can be implemented as normal numbers in Python.

```x = 88888888888888888888888888888888888888888888888888  # Huge integer
y = 77777777777777777777777777777777777777777777777777  # Another huge integer
z = x * y  # No overflow, result stored as a larger integer
print(z)  # Output
```

The output will be a large integer without any rounding off or elimination.

```6913580246913580246913580246913580246913580246913441975308641975308641975308641975308641975308641976
```

### Method 2: Precision with Python’s Decimal Module

The decimal module in python is also used for precise calculations. It provides correctly rounded decimal floating point arithmetic.

The module is designed around three central concepts, the decimal number, the context for arithmetic and signals. You can read more about the decimal library here.

```from decimal import Decimal

input1 = Decimal('1.76554637462189012345')
input2 = Decimal('0.2121112887919008762345')
output = input1 * input2
print(output)
```

You would get the following output:

```0.3744923169429173481751780860
```

Suggested: Formatting Floating Points Before Decimal Separator in Python

### Method 3: Large Numbers with NumPy (with caution)

The numerical Python or NumPy library is one of the most important and useful Python libraries that is used for scientific calculation and to process complex numerical problems. It supports multi-dimensional arrays and matrices with a huge library of functions to operate on these arrays. We can store these numbers as elements of an array and perform various functions on them.

This library can also be used for dealing with large numbers in Python and to perform operations on them. Let’s take a look at its implementation:

```import numpy as np

#import required modules

arr1 = np.array([246913578024691357802469135780])
arr2 = np.array([246913578024691357802469135780])
output = arr1 * arr2 # Multiplication with large integers
print(output)

```

The output would be:

```[60966315012955347001981406250144795150007620799500076208400]
```