from collections.abc import Callable
from gmpy2 import mpq

MAX_BITS = 32

class REAL:
    # x = z + sum(2 ** -(i + 1) for i in A)
    # Needed arguments: z in Q and A subset N
    def __init__(self, z: int, f: Callable[[int], bool]):
        self.decide = f
        self.const = z

    @staticmethod
    def __long_division(p: int, q: int, bits: int = MAX_BITS) -> list[int]:
        bnry = []
        rem = p % q

        for i in range(bits):
            # Fill with 0 when finished
            if rem == 0:
                bnry.extend([0] * (bits - len(bnry)))
                break

            # Shift remainder left by 1 bit
            rem *= 2  # Shift <=> Doubling

            # Determine bit value
            if rem >= q:
                bnry.append(1)
                rem -= q
            else:
                bnry.append(0)
        return bnry

    @staticmethod
    def from_int(x: int):
        return REAL(z=x, f=lambda i: False)

    @staticmethod
    def from_rational(x: mpq):
        quot = x.numerator // x.denominator
        rem = x.numerator % x.denominator

        bnry = REAL.__long_division(rem, x.denominator)
        decide = lambda n: (0 <= n < len(bnry) and bnry[n] == 1)
        return REAL(z=quot, f=decide)


    def as_str(self, n: int) -> str:
        bnry_str = ''
        for i in range(n):
            bnry_str += '1' if self.decide(i) else '0'
        # Binary depiction of z not applied here
        return f"x = {self.const} + {bnry_str}"