from decimal import Decimal, getcontext

def convert_quad_hex_to_float(hex_str):
    # Set high enough precision
    getcontext().prec = 100

    # Remove 0x prefix if present
    hex_str = hex_str.lower().lstrip('0x')

    if len(hex_str) != 32:
        raise ValueError("Hex string must be exactly 32 characters (128 bits).")

    # Convert to integer, then to binary string
    int_val = int(hex_str, 16)
    bin_str = f"{int_val:0128b}"

    # Extract parts
    sign_bit = int(bin_str[0], 2)
    exponent_bits = bin_str[1:16]
    fraction_bits = bin_str[16:]

    # Interpret fields
    sign = (-1) ** sign_bit
    exponent = int(exponent_bits, 2)
    bias = 16383  # Bias for quadruple precision

    # Special cases
    if exponent == 0 and int(fraction_bits, 2) == 0:
        return Decimal(sign * 0)
    elif exponent == 0x7FFF:
        if int(fraction_bits, 2) == 0:
            return Decimal('Infinity') if sign > 0 else Decimal('-Infinity')
        else:
            return Decimal('NaN')

    # Compute fraction
    fraction = Decimal(0)
    for i, bit in enumerate(fraction_bits):
        if bit == '1':
            fraction += Decimal(1) / (Decimal(2) ** (i + 1))

    # Add implicit 1 if normalized
    if exponent != 0:
        fraction = Decimal(1) + fraction
        exponent_val = exponent - bias
    else:
        # Subnormal
        exponent_val = 1 - bias

    # Compute final value
    value = Decimal(sign) * fraction * (Decimal(2) ** exponent_val)
    return value
print(convert_quad_hex_to_float("0x4000921fb54442d18469898cc51701b8"))