Examine Python's PI

pi.py

from math import pi
from fractions import Fraction
import struct


def double(bits: str) -> Fraction:
    def exponent(input_value: str):
        return int(input_value, 2) - 1023

    def fraction(b):
        return (
            sum(Fraction(int(b[i])) * Fraction(2, 2 ** (i + 2)) for i in range(52)) + 1
        )

    bits = bits.replace(" ", "")
    s = int(bits[0], 2)
    e = exponent(bits[1:12])
    m = fraction(bits[12:])

    value = (1 if s == 0 else -1) * m * 2 ** e
    return value, s, m, e


value, sign, mantissa, exponent = double(
    "".join([f"{x:08b}" for x in struct.pack(">d", pi)])
)
print(
    f"""PI, stored as a float is:
mantissa = {mantissa}
exponent = {exponent}

So it's {mantissa} * 2 ** {exponent} which is exactly {value}.

Or : {float(value)}"""
)

# From Wikipedia:
assert (
    double("0 01111111111 0000000000000000000000000000000000000000000000000000")[0] == 1
)
assert (
    double("0 01111111111 0000000000000000000000000000000000000000000000000001")[0] > 1
)
assert (
    double("0 01111111111 0000000000000000000000000000000000000000000000000001")[0]
    < 1.0001
)

mantissa = 884279719003555/562949953421312
exponent = 1

So it's 884279719003555/562949953421312 * 2 ** 1 which is exactly 884279719003555/281474976710656.

Or : 3.141592653589793