/* submitted by sgula@bellatlantic.net.remove.invalid, with fixes */

//--- Improved JSH C++ prime counter with removal of all sqrt() calls

#include <math.h>

/* for some reason this wasn't defined */

#define min(a,b) ((a) < (b) ? (a) : (b))

unsigned S2(unsigned x, unsigned yin);

unsigned JSHpi2(unsigned xin, unsigned yin)
{
  return (xin-S2(xin,yin)-1);
}

//Optionally, use a define instead of the above function to reduce function calls and stack
//overhead
//#define JSHpi2 (xin,yin) (xin-S2(xin,yin)-1)
//use at the risk of losing type safety

unsigned S2(unsigned x, unsigned yin)
{
  unsigned sum=0, i, sum1, sum2;
  const unsigned dx=1;

  for(unsigned i=2; i*i<=yin; i++)
  {

    sum2 = ( JSHpi2(i,i) - JSHpi2(i-dx,i-dx));

    if (sum2!=0){
      int tmp = (i-dx)*(i-dx),
        tmp2=x/i;
      sum1 = ( JSHpi2(x/i,min(tmp,tmp2)) -
          JSHpi2(i-dx,i-dx)) ;
      sum+=(sum1 * sum2);
    }
  } return sum;
}

unsigned long long pi(unsigned long long x)
{
	return (unsigned long long) JSHpi2(x, x);
}