uint8_t gmul(uint8_t a, uint8_t b) {
    uint8_t p = 0;    /* init product value */
    uint8_t counter;  /* init loop counter */
    uint8_t carry;    /* init carry variable for checking if ax has an x^8 term */
    for (counter = 0; counter < 8; counter++) { /* for each of the 8 bits in b */
        if (b & 1) /* if the least significant bit is set */
            p ^= a; /* add a to p */
        carry = a & 0x80;  /* Set carry to the x^7 term of a */
        a <<= 1;           /* Shift a left 1, turning a into a*x */
        if (carry)         /* if ax should have had an x^8 term (x^7*x=x^8) */
                  /* Using rewrite rule, turn x^8 into x^4+x^3+x+1
                                                          =00011011=0x001B  */
            a ^= 0x001B; /* Add this on to a, so a now stores ax */
        b >>= 1;  /* right shift b, so the least significant bit is coef of x */
    }   /* end loop, and since b=b/x, a=ax; loop will now add on a*x if required */
    return p;  /* finally, return the product */
}