Base64 Fixed Point Calculator in Python

base64_fixedpoint.py

#!/usr/bin/env python3

import sys

def get6bits(bytes, offset):
    "Get 6-bit value from offset in bits in a string"
    byte_offset = offset // 8
    bit_offset = offset % 8
    if bit_offset <= 2:
        # The 6 bits of input are all in the same byte:
        val = ord(bytes[byte_offset]) >> (2 - bit_offset)
    else:
        # Take the last bits of the first input byte and combine with some bits of the next byte:
        val = ((ord(bytes[byte_offset])     << (bit_offset - 2)) |
               (ord(bytes[byte_offset + 1]) >> (10 - bit_offset)))
    # Mask out 6 bits
    return val % 64

def b64fp():
    "Yield the base64 fixed point (infinite) string one character at a time."
    # Base 64 alphabet:
    alphabet="ABCDEFGHIJKLMNOPQRSTUVWXYZ" + \
             "abcdefghijklmnopqrstuvwxyz" + \
             "0123456789+/"
    # Choose an arbitrary 3-char seed
    input = '...'
    prev = None
    # Repeatedly base64 encode it (taking 3 chars) until it doesn't change.
    # Note: for the normal base64 alphabet there is exactly one fixed point.
    # If you change the alphabet there may be no fixed point (loops indefinitely)
    # or multiple fixed points (changes depending on the seed value).
    while input != prev:
        prev = input
        input = ''.join(alphabet[get6bits(input, i*6)] for i in range(3))
    # Yield first 3 chars (18 bits of input):
    yield from input
    # After 18 bits, we are 2 bits into the 3rd (last) input char:
    input = input[-1]
    bit = 2
    while True:
        val = get6bits(input, bit)
        # We have used up 6 bits of the input
        bit += 6
        if bit >= 8:
            # We've finished with the first byte of input, so throw it away and reset bit counter:
            input = input[1:]
            bit -= 8
        # Look up the character for the next 6 bits and append it to the input
        input += alphabet[val]
        # And yield that next character
        yield input[-1]

def main(num=None):
    if num: num = int(num)
    for n, c in enumerate(b64fp()):
        print(c, end='', flush=True)
        if num and n >= num - 1:
            print()
            break

if __name__ == '__main__':
    main(*sys.argv[1:])

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