uint<N>_t numerator = num;        // input
uint<N>_t denominator = den;      // input

uint<N>_t quotient = 0;

while (numerator >= denominator) {
  numerator -= denominator;
  ++quotient;
}

uint<N>_t quo = quotient;         // output
uint<N>_t rmn = numerator;        // output

uint<2*N + 1>_t numerator = num;  // input
uint<N>_t denominator = den;      // input

uint<N>_t quotient = 0;
uint<N>_t remainder = 0;
uint<log2(N-1)>_t k;
uint<N>_t ap = 0;
uint<N>_t an = 0;

k = leading_zeros(denominator);
denominator <<= k;
numerator <<= k;

for (int i = 0; i < N; ++i) {
  switch (top_3_bits(numerator)) {
    case 0:
    case 7:
      ap <<= 1;
      an <<= 1;
      numerator <<= 1;
      break;
    case 4:
    case 5:
    case 6:
      ap <<= 1;
      an = (an << 1) | 1;
      numerator <<= 1;
      numerator += (denominator << N);
      break;
    default:  // case 1, 2, 3
      ap = (ap << 1) | 1;
      an <<= 1;
      numerator <<= 1;
      numerator -= (denominator << N);
      break;
  }
}

quotient = ap - an;
remainder = numerator >> N;

if (msb(numerator) == 1) {
  remainder += denominator;
  --quotient;
}

uint<N>_t quo = quotient;         // output
uint<N>_t rmn = remainder >> k;   // output