/*
        The purpose of this function is to convert an unsigned
        binary number to reflected binary Gray code.

        The operator >> is shift right. The operator ^ is exclusive or.
*/
unsigned int binaryToGray(unsigned int num)
{
        return (num >> 1) ^ num;
}

/*
        The purpose of this function is to convert a reflected binary
        Gray code number to a binary number.
*/
unsigned int grayToBinary(unsigned int num)
{
    unsigned int mask;
    for (mask = num >> 1; mask != 0; mask = mask >> 1)
    {
        num = num ^ mask;
    }
    return num;
}

unsigned int nextGray(unsigned int num)
{
    return binaryToGray((grayToBinary(num) + 1) & 0x3F);
}

unsigned int prevGray(unsigned int num)
{
    return binaryToGray((grayToBinary(num) - 1) & 0x3F);
}

unsigned next_gray(unsigned gray)
{
    if (is_gray_odd(gray))
    {
        unsigned y = gray & -gray;
        return gray ^ (y << 1);
    }
    else
    {
        // Flip rightmost bit
        return gray ^ 1;
    }
}

bool is_gray_odd(unsigned gray)
{
    // A gray code is odd when the number
    // of bits set in its representation
    // is odd
    // If you have a popcount function
    // available, use it instead of the
    // following manual one

    unsigned nb_bits = 0u;
    for (; gray ; ++nb_bits)
    {
        // clear the least significant bit set
        gray &= gray - 1;
    }
    return (bool)(nb_bits % 2);
}

bool is_gray_odd(unsigned gray)
{
    return (bool) __builtin_parity(gray);
}