Python base64.b32hexencode not creating expected result

Question

I expect the code to return TPLIG0 as the base32 hex-extended value for 1 billion (1.000.000.000). Instead I get 7EDCK00= .

Here is my code:

import base64
num = 1000000000
needed_bytes = num.to_bytes((num.bit_length() + 7) // 8, byteorder='big')
result = base64.b32hexencode(needed_bytes).decode('utf-8')
print(result)

I have tried with b32hexencode, b32encode, as well as byteorder='little' and byteorder='big', but I cannot reproduce the expected result.

If I replace the division with the hardcoded number: num.to_bytes(5, byteorder='big') I can get the approximate result: 00TPLIG0 . But what is going on here??

I'm using python 3.10.7. on Windows and 3.11.0 on Ubuntu (both create same output).

Answer 1

num.bit_length() + 7) // 8 is 4, not 5. b32hexencode pads its result with = if not a multiple of 40 bits (5 bytes) and the bits are shifted.

>>> base64.b32hexencode (bytes([1,2,3,4]))
b'0410610='
>>> base64.b32hexencode (bytes([1,2,3,4,5]))
b'04106105'

Use (num.bit_length() + 39) // 40 * 5 to calculate needed_bytes in multiples of 5 bytes, then strip leading zeroes to use base64.b32hexencode() correctly:

import base64
num = 1_000_000_000

def convert(n):
    if n == 0:  # b32hexencode() return '=====' for zero, so special handling
        return '0'
    num_bytes = (n.bit_length() + 39) // 40 * 5
    needed_bytes = n.to_bytes(num_bytes, byteorder='big')
    result = base64.b32hexencode(needed_bytes).lstrip(b'0')
    return result.decode() # bytes -> str

def display(n):
    result = convert(n)
    verify = int(result, 32)
    print(f'{result:>9} {verify:17,}')
    
display(num)
for i in range(9):
    n = 2**(i * 5)
    display(n - 1)
    display(n)

Output testing OP value and rolling over every 5-bit binary value:

   TPLIG0     1,000,000,000
        0                 0
        1                 1
        V                31
       10                32
       VV             1,023
      100             1,024
      VVV            32,767
     1000            32,768
     VVVV         1,048,575
    10000         1,048,576
    VVVVV        33,554,431
   100000        33,554,432
   VVVVVV     1,073,741,823
  1000000     1,073,741,824
  VVVVVVV    34,359,738,367
 10000000    34,359,738,368
 VVVVVVVV 1,099,511,627,775
100000000 1,099,511,627,776