#include <cstdio>

static long double makefraction
    (long double a, int maxdepth,
     unsigned long long& hi, unsigned long long& lo)
{
  const long long END = 0;
  
  const long double orig = a;
  long long cf[maxdepth];
  long long i,u,v, last;

  for(i = 0; i < maxdepth; i++)
  {
    cf[i] = a;
    if(cf[i]-1 > cf[i])break;
   	a = 1.0/(a - cf[i]);
  }
  
  for(last=i-1; i < maxdepth; i++)
    cf[i] = 0;
  
  
  u = cf[last];
  v = 1;
  for(i = last-1; i >= END; i--)
  {
    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 = 59.950000;
    long double samples_per_frame = 64000.0 / desired_fps;
    
    unsigned long long hi, lo;
    long double error = makefraction(samples_per_frame, 10, hi,lo);
    
    /* This is an application of bresenham's line-drawing algorithm. */
    signed long long d = hi - lo*2;
    unsigned long long dinc1 = lo*2;
    unsigned long long dinc2 = (lo-hi)*2;
    
    std::printf("Using fraction: %llu/%llu (error=%.12llf)\n", hi,lo, error);
    
    unsigned framecounter=0;
    for(;;)
    {
        unsigned nsamples = 1;
        while(d > 0)
        {
            ++nsamples;
            d -= dinc1;
        }
        d -= dinc2;
        
        std::printf("Frame %u: %u samples\n", framecounter, nsamples);
        
        ++framecounter;
    }
}