madelung.c

#include <stdio.h>
#include <math.h>

/*
 * Compile and run:
 *
 * gcc -lm -march=native -O3 -o madelung madelung.c -lm && ./madelung
 */

#define STEPS 100000
int main(void) {
  int i,j;

  long double result=0.0d;

  for(i=1;i<STEPS;i++) {
    for(j=1;j<STEPS;j++) {
      long double temp = ((long double)1.0d)/sqrt(pow((long double)i,2.0d) + pow((long double)j,2.0d));

      if((i+j)%2 == 0) {
        result += temp;
      } else {
        result -= temp;
      }
    }
    printf("%d/%d done\n", i, STEPS);
  }

  printf("%0.100f\n", (double)result);

  return 0;
}