#include <cstdio>
#include <gmp.h>

static long double makefraction
    (const long double orig,
     unsigned long long& hi, unsigned long long& lo)
{
  const int maxdepth = 10;
  const int END = 0;

  long double work = orig;
  
  unsigned long long cf[maxdepth];
  
  int i;
  for(i = 0; i < maxdepth; ++i)
  {
    cf[i] = work;
    //if(cf[i] > work+1) break; // if overflown.
   	work = 1.0 / (work - cf[i]);
  }
  unsigned long long u = cf[--i];
  unsigned long long v = 1;
  while(--i >= END)
  {
    unsigned long long w = cf[i] * u + v;
    v = u;
    u = w;
  }
  hi = u;
  lo = v;
  return orig - (u / (long double)v);
}

int main()
{
    long double desired_fps       = 59.9487437186;
    long double samples_per_frame = 32000.0 / desired_fps;
    
    unsigned long long hi, lo;
    long double error = makefraction(samples_per_frame, hi,lo);
    
    std::printf("Using fraction: %llu/%llu (error=%.12llf)\n", hi,lo, error);
    
    unsigned framecounter=0;
    unsigned long long balance = hi;
    for(;;)
    {
        unsigned nsamples = 2*(balance/lo);
        balance %= lo;
        balance += hi;
        
        std::printf("Frame %u: %u samples\n", framecounter, nsamples);
        
        ++framecounter;
    }
}