#define _USE_MATH_DEFINES 
#define _CRT_SECURE_NO_WARNINGS
#include <stdio.h>
#include <stdlib.h>
#include <math.h>

int main(void) 
{
    int k, i, nmax = 1000000;
    int out[7] = {1, 10, 100, 1000, 10000, 100000, 1000000};
    float  sf = 0.0f;
    double sd = 0.0;
    double exact = M_PI * M_PI / 6.0;  
    double rf, rd;
    FILE *fp;

    if ((fp = fopen("basel.csv", "w")) == NULL) 
    {
        printf("cannot open file\n");
        exit(-1);
    }
    fprintf(fp, "n,float,double,rel.err.flt,rel.err.dbl\n");
    printf("%8s %24s %24s %16s %16s\n", "i", "float", "double", "rel.err.flt.", "rel.err.dbl.");

    i = 0;
    for (k = 1; k <= nmax; k++) 
    {
        sf += 1.0f / ((float)k * (float)k);
        sd += 1.0 / ((double)k * (double)k);
        if (k == out[i]) {
            rf = fabs((double)sf - exact) / exact;
            rd = fabs(sd - exact) / exact;
            printf("%8d: %.18e %.18e %.15e %.15e\n", k, (double)sf, sd, rf, rd);
            fprintf(fp, "%d,%.18e,%.18e,%.15e,%.15e\n", k, (double)sf, sd, rf, rd);
            i++;
        }
    }
    fclose(fp);
    return 0;
}