ieee_754 implementation in python

ieee_754.py

def float_to_binary_32(f):
    """
    Converts a 32-bit floating-point number to its binary representation.

    Args:
        f (float): The floating-point number to encode.

    Returns:
        str: The binary representation of the floating-point number.
    """
    # For 32-bit float, we manually handle the sign, exponent, and mantissa
    # by extracting integer and decimal parts and computing the binary representation.
    # Then, we adjust the exponent and mantissa to fit the IEEE 754 format.
    # Finally, we concatenate the sign, exponent, and mantissa to get the binary string.
    if f == 0.0:
        return '0' * 32

    sign = '1' if f < 0 else '0'
    f = abs(f)
    integer_part = int(f)
    decimal_part = f - integer_part

    integer_binary = bin(integer_part)[2:]
    decimal_binary = ''

    while decimal_part != 0:
        decimal_part *= 2
        if decimal_part >= 1:
            decimal_binary += '1'
            decimal_part -= 1
        else:
            decimal_binary += '0'

    binary_representation = integer_binary + '.' + decimal_binary

    exponent = 0
    if '.' in binary_representation:
        exponent = binary_representation.index('.') - 1
        binary_representation = binary_representation.replace('.', '')
    else:
        binary_representation = binary_representation.rstrip('0')

    exponent_binary = bin(127 + exponent)[2:].zfill(8)

    mantissa = binary_representation[1:].ljust(23, '0')

    return sign + exponent_binary + mantissa

def binary_to_float_32(binary):
    """
    Converts a binary representation to a 32-bit floating-point number.

    Args:
        binary (str): The binary representation of the floating-point number.

    Returns:
        float: The decoded floating-point number.
    """
    # For 32-bit float, we extract the sign, exponent, and mantissa from the binary string.
    # Then, we compute the floating-point number by applying the formula based on IEEE 754 format.
    sign = int(binary[0])
    exponent = int(binary[1:9], 2) - 127
    mantissa = 1 + sum(int(binary[i]) * 2**(-i+8) for i in range(9, 32))

    if exponent == -127:
        if mantissa == 0:
            return 0.0
        else:
            return (-1) ** sign * mantissa * 2**(-126)
    if exponent == 128:
        if mantissa == 0:
            return float('inf') if sign == 0 else float('-inf')
        else:
            return float('nan')

    return (-1) ** sign * mantissa * 2**exponent

def float_to_binary_64(f):
    """
    Converts a 64-bit floating-point number to its binary representation.

    Args:
        f (float): The floating-point number to encode.

    Returns:
        str: The binary representation of the floating-point number.
    """
    # For 64-bit float, the process is similar to 32-bit float but with a larger mantissa.
    # We manually handle the sign, exponent, and mantissa,
    # adjust them to fit the IEEE 754 format, and concatenate to get the binary string.
    if f == 0.0:
        return '0' * 64

    sign = '1' if f < 0 else '0'
    f = abs(f)
    integer_part = int(f)
    decimal_part = f - integer_part

    integer_binary = bin(integer_part)[2:]
    decimal_binary = ''

    while decimal_part != 0:
        decimal_part *= 2
        if decimal_part >= 1:
            decimal_binary += '1'
            decimal_part -= 1
        else:
            decimal_binary += '0'

    binary_representation = integer_binary + '.' + decimal_binary

    exponent = 0
    if '.' in binary_representation:
        exponent = binary_representation.index('.') - 1
        binary_representation = binary_representation.replace('.', '')
    else:
        binary_representation = binary_representation.rstrip('0')

    exponent_binary = bin(1023 + exponent)[2:].zfill(11)

    mantissa = binary_representation[1:].ljust(52, '0')

    return sign + exponent_binary + mantissa

def binary_to_float_64(binary):
    """
    Converts a binary representation to a 64-bit floating-point number.

    Args:
        binary (str): The binary representation of the floating-point number.

    Returns:
        float: The decoded floating-point number.
    """
    # For 64-bit float, we extract the sign, exponent, and mantissa from the binary string.
    # Then, we compute the floating-point number using the formula based on IEEE 754 format.
    sign = int(binary[0])
    exponent = int(binary[1:12], 2) - 1023
    mantissa = 1 + sum(int(binary[i]) * 2**(-i+11) for i in range(12, 64))

    if exponent == -1023:
        if mantissa == 0:
            return 0.0
        else:
            return (-1) ** sign * mantissa * 2**(-1022)
    if exponent == 1024:
        if mantissa == 0:
            return float('inf') if sign == 0 else float('-inf')
        else:
            return float('nan')

    return (-1) ** sign * mantissa * 2**exponent

def main():
    examples = [3.14, 123.456, -0.001]
    for example in examples:
        binary_encoded_32 = float_to_binary_32(example)
        decoded_32 = binary_to_float_32(binary_encoded_32)
        binary_encoded_64 = float_to_binary_64(example)
        decoded_64 = binary_to_float_64(binary_encoded_64)

        print(f"Original: {example}")
        print(f"32-bit Encoded: {binary_encoded_32}, Decoded: {decoded_32}")
        print(f"64-bit Encoded: {binary_encoded_64}, Decoded: {decoded_64}")
        print()

if __name__ == "__main__":
    main()