Implementing Base64 Encoding in Python

Base64 encoding is a widely used method for representing binary data in an ASCII string format. This is particularly useful when transmitting data over channels that only support text, such as email or HTTP. Your task is to implement a base64 encoding function in Python, allowing you to convert arbitrary byte strings into their base64 representation.

Problem Description

You are required to implement a function base64_encode(data) that takes a byte string data as input and returns its base64 encoded string representation. The encoding process involves:

1. Padding: If the input byte string's length is not a multiple of 3, padding with null bytes ('\x00') is necessary to make it a multiple of 3.
2. Grouping: The byte string is divided into groups of 3 bytes.
3. Conversion: Each group of 3 bytes is converted into 4 base64 characters using the base64 alphabet. The formula is:
   • (data[0] << 16) + (data[1] << 8) + data[2] is divided by 64. The quotient is the first base64 character.
   • The remainder of the division by 64 is multiplied by 64. (remainder << 16) + (data[1] << 8) + data[2] is divided by 64. The quotient is the second base64 character.
   • And so on for the third and fourth base64 characters.
4. Padding (Base64): If the input length was not a multiple of 3, the output string needs to be padded with the '=' character. One '=' character is added for each missing byte in the final group.

The base64 alphabet is: ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/

Examples

Example 1:

Input: b'abc'
Output: 'YWJj'
Explanation: 'abc' is 3 bytes.  (97*256*256 + 98*256 + 99) / 64 = 4986, which is 'Y'. (4986 % 64) * 64 + 98*256 + 99 = 10147, which is 'W'. (10147 % 64) * 64 + 99 = 147, which is 'J'.  Therefore, 'YWJj'.

Example 2:

Input: b'abcd'
Output: 'YWJjZA=='
Explanation: 'abcd' is 4 bytes.  It's divided into 'abc' and 'd'. 'abc' is encoded as 'YWJj'. 'd' is padded with two null bytes to become 'd00'.  (100*256*256 + 100*256 + 0) / 64 = 15875, which is 'Z'.  Two padding characters ('==') are added to the end.

Example 3:

Input: b'abcdef'
Output: 'YWFhYmFjaGVm'
Explanation: 'abcdef' is 6 bytes. It's divided into 'abc' and 'def'. 'abc' is encoded as 'YWJj'. 'def' is encoded as 'YWFhYmFjaGVm'.

Constraints

• The input data will be a byte string.
• The length of the input data can be any non-negative integer.
• The base64 alphabet is fixed as ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/.
• The function should handle edge cases where the input is an empty byte string.
• The function should be reasonably efficient for typical input sizes (up to a few kilobytes).

Notes

• Remember to handle padding correctly, both for the initial input and for the final base64 string.
• Consider using bitwise operations (<<, >>, &, |) for efficient manipulation of bytes.
• The base64 alphabet can be stored as a string for easy character lookup.
• Think about how to handle the division and remainder operations to determine the base64 characters.
• The modulo operator (%) is crucial for determining the base64 characters.