OK, I understand. The approach works even better if you multiply by 10:

  int16_t celsius2fahrenheit10(int16_t c)
  {
    int16_t f = 0;
    f += c << 4;
    f -= c;
    f -= c >> 1;
    f -= c >> 3;
    f += c >> 5;
    f += 320 * 8;
    f >>= 3;
    return f;
  }

This is really accurate:

  C=0    (int 0)    F=32   (int: 320,  exact: 32)
  C=15.3 (int 153)  F=59.5 (int: 595,  exact: 59.54)
  C=37   (int 370)  F=98.6 (int: 986,  exact: 98.6)
  C=100  (int 1000) F=212  (int: 2120, exact: 212)