Generate Scilab script to check distribution of rand() % range.

randmod_dist.cpp

#include <cstdlib>
#include <cstdio>
#include <ctime>
#include <vector>

#define square(x) ((x) * (x))

typedef unsigned int uint;
static const int trialMultipler = 15;

static int rng_out[RAND_MAX * trialMultipler];
static int rng_out_index = 0;

void generate_rng_list() {
    const int rng_count = RAND_MAX * trialMultipler;

    srand(time(NULL));
    for (int i = 0; i < rng_count; ++i) {
        rng_out[i] = rand();
    }
}

void seed_rng() {
    rng_out_index = 0;
}

int rng_next() {
    return rng_out[rng_out_index++];
}

struct TestResult {
    int modulus;
    float chi2;
    int degreeOfFreedom;
};

TestResult test_range(int range) {
    std::vector<int> counts(range, 0);

    seed_rng();
    const int trials = range * trialMultipler;
    for (int i = 0; i < trials; ++i) {
        int n = rng_next() % range;
        counts[n]++;
    }

    float expectedCount = trialMultipler;
    float chi2 = 0.0f;
    for (int i = 0; i < range; ++i) {
        float chiContributor = square(counts[i] - expectedCount) / expectedCount;
        chi2 += chiContributor;
    }

    TestResult rv;
    rv.modulus = range;
    rv.chi2 = chi2;
    rv.degreeOfFreedom = range - 1;
    return rv;
}

void write_output(const std::vector<TestResult>& results) {
    FILE * fp = fopen("out.sci", "w");
    if (!fp) {
        fprintf(stderr, "Failed to open output file.\n");
        exit(1);
    }

    fprintf(fp, "chi2 = [\n");
    for (uint i = 0; i < results.size(); ++i) {
        if (results[i].degreeOfFreedom > 0) {
            fprintf(fp, "%.4f, \n", results[i].chi2);
        }
        else {
            fprintf(stderr, "ERROR: df for mod %d is %d\n", results[i].modulus, results[i].degreeOfFreedom);
        }
    }
    fprintf(fp, "];\n");

    fprintf(fp, "df = [\n");
    for (uint i = 0; i < results.size(); ++i) {
        if (results[i].degreeOfFreedom > 0) {
            fprintf(fp, "%d, \n", results[i].degreeOfFreedom);
        }
    }
    fprintf(fp, "];\n");

    fprintf(fp, "p = distfun_chi2cdf(chi2, df, %%F);\n");
    fprintf(fp, "plot(df, p);\n");
}

int main() {
    generate_rng_list();
    printf("%d\n", RAND_MAX);
    std::vector<TestResult> results;
    results.reserve(RAND_MAX);
    for (int i = 2; i <= RAND_MAX; ++i) {
        results.push_back(test_range(i));
    }

    write_output(results);
}