Integer Divisions (ifloor, iceil, remainder)

template <typename T, typename U>
auto ifloor(T t, U u) {
  assert(u != 0);
  return t / u - ((t ^ u) < 0 && t % u != 0);
}

template <typename T, typename U>
auto iceil(T t, U u) {
  assert(u != 0);
  return t / u + ((t ^ u) > 0 && t % u != 0);
}

template <typename T, typename U>
auto remainder(T t, U u) {
  assert(u != 0);
  if (u < 0) {
    t = -t;
    u = -u;
  }
  t %= u;
  if (t < 0) {
    t += u;
  }
  return t;
}