#include <stdio.h>
#include <math.h>
#include <assert.h>
static const double Sqr2Pi    = 2.50662827463100050240;      /* sqrt(2*pi) */

/* I do *not* recommend using the following pseudo random number generator for
 * important applications. Use one from a proper scientific library. */
#include <stdlib.h>
#define u01rand() ((double)rand()/RAND_MAX)


double crude_randn() {
    int i;
    double sum = 0;
    for (i=0; i<12; i++) {
        sum += u01rand();
    }
    return (sum - 6.0);
}

int main() {
#define NUM_BINS 50
    const int num_trials = 1e6;
    const double min_x = -6.0;
    const double max_x = +6.0;
    int counts[NUM_BINS];
    double bin_width = (max_x - min_x) / NUM_BINS;

    FILE* fid;
    int i;
    int bin;
    double bin_mid;
    double rn;
    double clt_est;
    
    for (i=0; i<NUM_BINS; i++)
        counts[i] = 0;

    /* Draw samples and record histogram counts */
    for (i=0; i<num_trials; i++) {
        rn = crude_randn();
        bin = floor((rn - min_x) / bin_width);
        assert(bin >= 0);
        assert(bin < NUM_BINS);
        counts[bin] += 1;
    }

    /* Output to space-separated text file with columns:
     * bin-center count expected-count */
    fid = fopen("hist.txt", "w"); 
    assert(fid);
    for (i=0; i<NUM_BINS; i++) {
        bin_mid = min_x + (i+0.5)*bin_width;
        clt_est = num_trials * bin_width * exp(-0.5*bin_mid*bin_mid) / Sqr2Pi;
        fprintf(fid, "%g %d %g\n", bin_mid, counts[i], clt_est);
    }
    fclose(fid);

    return 0;
}