Change of Masks in MixColumns

[sayma10]

static void MixColumns(state_t *state)
{
uint8_t i;
uint8_t Tmp, Tm, t;
for (i = 0; i < 4; ++i)
{
t = (*state)[i][0];
Tmp = (*state)[i][0] ^ (*state)[i][1] ^ (*state)[i][2] ^ (*state)[i][3];
Tm = (*state)[i][0] ^ (*state)[i][1];
Tm = xtime(Tm);
(*state)[i][0] ^= Tm ^ Tmp;
Tm = (*state)[i][1] ^ (*state)[i][2];
Tm = xtime(Tm);
(*state)[i][1] ^= Tm ^ Tmp;
Tm = (*state)[i][2] ^ (*state)[i][3];
Tm = xtime(Tm);
(*state)[i][2] ^= Tm ^ Tmp;
Tm = (*state)[i][3] ^ t;
Tm = xtime(Tm);
(*state)[i][3] ^= Tm ^ Tmp;
}
}
Hello i wanted to ask how mix columns mask take place . I understand we need to precalculate last four mask with this function
static void calcMixColmask(uint8_t mask[10])
{
mask[6] = mul_02[mask[0]] ^ mul_03[mask[1]] ^ mask[2] ^ mask[3];
mask[7] = mask[0] ^ mul_02[mask[1]] ^ mul_03[mask[2]] ^ mask[3];
mask[8] = mask[0] ^ mask[1] ^ mul_02[mask[2]] ^ mul_03[mask[3]];
mask[9] = mul_03[mask[0]] ^ mask[1] ^ mask[2] ^ mul_02[mask[3]];
}

so in above MixColumns function with xtime ...how state masks are changed from M1 to M1', M2 to M2' etc..

[sayma10]

Also, i just noticed xtime function
static uint8_t xtime(uint8_t x)
{
return ((x << 1) ^ (((x >> 7) & 1) * 0x1b));
}
shouldnot * be & operator ?