// Report some extrema.
#include <stdio.h>
#include <stdlib.h>
#define C const
typedef double R;
typedef unsigned long int ul;
typedef union{R r; ul i;} U;
static R rf(){return 0x1.p-31*random() + 0x1.p-62*random();}
static R l2R(ul x){return ((U)x).r;}
static ul R2l(R x){return ((U)x).i;}
static ul j(short h, ul a){return (ul)h<<52 | (a & ((1L<<52)-1));}
static int max = 0, min = 1<<12, mer = 0, ser = 0;
static ul Ndmin = -1;
R fdiv(C R n, C R d){C ul a = R2l(n), b = R2l(d);
  C ul nf = j(1, a), df = j(1, b);
  C char ad = nf < df;
  C short N = (1<<20)/((df>>42)+1); // table lookup! M=8, z=2
  max = max<N?N:max; min = min<N?min:N;
  C ul Nd = N*df; Ndmin = Ndmin<Nd?Ndmin:Nd;
  ul r = (N*nf)<<ad, q = 0; short rb = 53;
  while(rb>=0) {C short nq = r>>54; r = (r<<8) - Nd*nq; q = (q<<8)+nq; rb -= 8;}
  {int uer = r/Nd; ser += uer; mer = mer<uer?uer:mer;}
  while(r >= Nd){r -= Nd; ++q;}
  return l2R(j(1023 + (a>>52) - (b>>52) - ad, ((q>>-rb)+1)>>1));}
void t(R a, R b) {if (a/b != fdiv(a, b)) exit(printf("%20.17f %20.17f\n", a, b));}
int main(){for(int r=0; r<100000000; ++r) t(rf(), rf());
  printf("max = %d, min = %d, mer = %d, ser = %d, Ndmin = %016lX 😊\n",
    max, min, mer, ser, Ndmin); return 0;}
// max = 1023, min = 512, mer = 2, ser = 20663718, Ndmin = 3FD92003E8983150