isc/tests/random_test.c

/*
 * Copyright (C) 2014-2018  Internet Systems Consortium, Inc. ("ISC")
 *
 * This Source Code Form is subject to the terms of the Mozilla Public
 * License, v. 2.0. If a copy of the MPL was not distributed with this
 * file, You can obtain one at http://mozilla.org/MPL/2.0/.
 */

#include <config.h>

#include <isc/random.h>
#include <isc/result.h>
#include <isc/mem.h>
#include <isc/print.h>
#include <isc/util.h>

#include <atf-c.h>

#include <stdlib.h>
#include <stdint.h>
#include <math.h>

typedef double (pvalue_func_t)(isc_mem_t *mctx,
                   isc_uint16_t *values, size_t length);

/* igamc(), igam(), etc. were adapted (and cleaned up) from the Cephes
 * math library:
 *
 * Cephes Math Library Release 2.8:  June, 2000
 * Copyright 1985, 1987, 2000 by Stephen L. Moshier
 *
 * The Cephes math library was released into the public domain as part
 * of netlib.
*/

static double MACHEP = 1.11022302462515654042E-16;
static double MAXLOG = 7.09782712893383996843E2;
static double big = 4.503599627370496e15;
static double biginv =  2.22044604925031308085e-16;

static double igamc(double a, double x);
static double igam(double a, double x);

static double
igamc(double a, double x) {
    double ans, ax, c, yc, r, t, y, z;
    double pk, pkm1, pkm2, qk, qkm1, qkm2;

    if ((x <= 0) || (a <= 0))
        return (1.0);

    if ((x < 1.0) || (x < a))
        return (1.0 - igam(a, x));

    ax = a * log(x) - x - lgamma(a);
    if (ax < -MAXLOG) {
        fprintf(stderr, "igamc: UNDERFLOW, ax=%f\n", ax);
        return (0.0);
    }
    ax = exp(ax);

    /* continued fraction */
    y = 1.0 - a;
    z = x + y + 1.0;
    c = 0.0;
    pkm2 = 1.0;
    qkm2 = x;
    pkm1 = x + 1.0;
    qkm1 = z * x;
    ans = pkm1 / qkm1;

    do {
        c += 1.0;
        y += 1.0;
        z += 2.0;
        yc = y * c;
        pk = pkm1 * z  -  pkm2 * yc;
        qk = qkm1 * z  -  qkm2 * yc;
        if (qk != 0) {
            r = pk / qk;
            t = fabs((ans - r) / r);
            ans = r;
        } else
            t = 1.0;

        pkm2 = pkm1;
        pkm1 = pk;
        qkm2 = qkm1;
        qkm1 = qk;

        if (fabs(pk) > big) {
            pkm2 *= biginv;
            pkm1 *= biginv;
            qkm2 *= biginv;
            qkm1 *= biginv;
        }
    } while (t > MACHEP);

    return (ans * ax);
}

static double
igam(double a, double x) {
    double ans, ax, c, r;

    if ((x <= 0) || (a <= 0))
        return (0.0);

    if ((x > 1.0) && (x > a))
        return (1.0 - igamc(a, x));

    /* Compute  x**a * exp(-x) / md_gamma(a)  */
    ax = a * log(x) - x - lgamma(a);
    if( ax < -MAXLOG ) {
        fprintf(stderr, "igam: UNDERFLOW, ax=%f\n", ax);
        return (0.0);
    }
    ax = exp(ax);

    /* power series */
    r = a;
    c = 1.0;
    ans = 1.0;

    do {
        r += 1.0;
        c *= x / r;
        ans += c;
    } while (c / ans > MACHEP);

    return (ans * ax / a);
}

static isc_int8_t scounts_table[65536];
static isc_uint8_t bitcounts_table[65536];

static isc_int8_t
scount_calculate(isc_uint16_t n) {
    int i;
    isc_int8_t sc;

    sc = 0;
    for (i = 0; i < 16; i++) {
        isc_uint16_t lsb;

        lsb = n & 1;
        if (lsb != 0)
            sc += 1;
        else
            sc -= 1;

        n >>= 1;
    }

    return (sc);
}

static isc_uint8_t
bitcount_calculate(isc_uint16_t n) {
    int i;
    isc_uint8_t bc;

    bc = 0;
    for (i = 0; i < 16; i++) {
        isc_uint16_t lsb;

        lsb = n & 1;
        if (lsb != 0)
            bc += 1;

        n >>= 1;
    }

    return (bc);
}

static void
tables_init(void) {
    isc_uint32_t i;

    for (i = 0; i < 65536; i++) {
        scounts_table[i] = scount_calculate(i);
        bitcounts_table[i] = bitcount_calculate(i);
    }
}

/*
 * The following code for computing Marsaglia's rank is based on the
 * implementation in cdbinrnk.c from the diehard tests by George
 * Marsaglia.
 *
 * This function destroys (modifies) the data passed in bits.
 */
static isc_uint32_t
matrix_binaryrank(isc_uint32_t *bits, size_t rows, size_t cols) {
    size_t i, j, k;
    unsigned int rt = 0;
    isc_uint32_t rank = 0;
    isc_uint32_t tmp;

    for (k = 0; k < rows; k++) {
        i = k;

        while (rt >= cols || ((bits[i] >> rt) & 1) == 0) {
            i++;

            if (i < rows)
                continue;
            else {
                rt++;
                if (rt < cols) {
                    i = k;
                    continue;
                }
            }

            return (rank);
        }

        rank++;
        if (i != k) {
            tmp = bits[i];
            bits[i] = bits[k];
            bits[k] = tmp;
        }

        for (j = i + 1; j < rows; j++) {
            if (((bits[j] >> rt) & 1) == 0)
                continue;
            else
                bits[j] ^= bits[k];
        }

        rt++;
    }

    return (rank);
}

static void
random_test(pvalue_func_t *func) {
    isc_mem_t *mctx = NULL;
    isc_result_t result;
    isc_rng_t *rng;
    isc_uint32_t m;
    isc_uint32_t j;
    isc_uint32_t histogram[11];
    isc_uint32_t passed;
    double proportion;
    double p_hat;
    double lower_confidence;
    double chi_square;
    double p_value_t;

    tables_init();

    result = isc_mem_create(0, 0, &mctx);
    ATF_REQUIRE_EQ(result, ISC_R_SUCCESS);

    rng = NULL;
    result = isc_rng_create(mctx, NULL, &rng);
    ATF_REQUIRE_EQ(result, ISC_R_SUCCESS);

    m = 1000;
    passed = 0;

    for (j = 0; j < 11; j++)
        histogram[j] = 0;

    for (j = 0; j < m; j++) {
        isc_uint32_t i;
        isc_uint16_t values[128000];
        double p_value;

        for (i = 0; i < 128000; i++)
            values[i] = isc_rng_random(rng);

        p_value = (*func)(mctx, values, 128000);
        if (p_value >= 0.01)
            passed++;

        ATF_REQUIRE(p_value >= 0.0);
        ATF_REQUIRE(p_value <= 1.0);

        i = (int) floor(p_value * 10);
        histogram[i]++;
    }

    isc_rng_detach(&rng);

    /* Fold histogram[10] (p_value = 1.0) into histogram[9] for
     * interval [0.9, 1.0]
     */
    histogram[9] += histogram[10];
    histogram[10] = 0;

    /*
     * Check proportion of sequences passing a test (see section
     * 4.2.1 in NIST SP 800-22).
     */
    proportion = (double) passed / (double) m;
    p_hat = 1 - 0.01; /* alpha is 0.01 in the NIST tests */
    lower_confidence = p_hat - (3.0 * sqrt((p_hat * (1 - p_hat)) / m));

    /* Debug message, not displayed when running via atf-run */
    printf("passed=%u/1000\n", passed);
    printf("lower_confidence=%f, proportion=%f\n",
           lower_confidence, proportion);

    ATF_REQUIRE(proportion >= lower_confidence);

    /*
     * Check uniform distribution of p-values (see section 4.2.2 in
     * NIST SP 800-22).
     */

    /* Pre-requisite that at least 55 sequences are processed. */
    ATF_REQUIRE(m >= 55);

    chi_square = 0.0;
    for (j = 0; j < 10; j++) {
        double numer;
        double denom;

        /* Debug message, not displayed when running via atf-run */
        printf("hist%u=%u ", j, histogram[j]);

        numer = (histogram[j] - (m / 10.0)) *
            (histogram[j] - (m / 10.0));
        denom = m / 10.0;
        chi_square += numer / denom;
    }

    printf("\n");

    p_value_t = igamc(9 / 2.0, chi_square / 2.0);

    ATF_REQUIRE(p_value_t >= 0.0001);
}

/*
 * This is a frequency (monobits) test taken from the NIST SP 800-22
 * RNG test suite.
 */
static double
monobit(isc_mem_t *mctx, isc_uint16_t *values, size_t length) {
    size_t i;
    isc_int32_t scount;
    isc_uint32_t numbits;
    double s_obs;
    double p_value;

    UNUSED(mctx);

    numbits = length * 16;
    scount = 0;

    for (i = 0; i < length; i++)
        scount += scounts_table[values[i]];

    /* Preconditions (section 2.1.7 in NIST SP 800-22) */
    ATF_REQUIRE(numbits >= 100);

    /* Debug message, not displayed when running via atf-run */
    printf("numbits=%u, scount=%d\n", numbits, scount);

    s_obs = abs(scount) / sqrt(numbits);
    p_value = erfc(s_obs / sqrt(2.0));

    return (p_value);
}

/*
 * This is the runs test taken from the NIST SP 800-22 RNG test suite.
 */
static double
runs(isc_mem_t *mctx, isc_uint16_t *values, size_t length) {
    size_t i;
    isc_uint32_t bcount;
    isc_uint32_t numbits;
    double pi;
    double tau;
    isc_uint32_t j;
    isc_uint32_t b;
    isc_uint8_t bit_this;
    isc_uint8_t bit_prev;
    isc_uint32_t v_obs;
    double numer;
    double denom;
    double p_value;

    UNUSED(mctx);

    numbits = length * 16;
    bcount = 0;

    for (i = 0; i < 128000; i++)
        bcount += bitcounts_table[values[i]];

    /* Debug message, not displayed when running via atf-run */
    printf("numbits=%u, bcount=%u\n", numbits, bcount);

    pi = (double) bcount / (double) numbits;
    tau = 2.0 / sqrt(numbits);

    /* Preconditions (section 2.3.7 in NIST SP 800-22) */
    ATF_REQUIRE(numbits >= 100);

    /*
     * Pre-condition implied from the monobit test. This can fail
     * for some sequences, and the p-value is taken as 0 in these
     * cases.
     */
    if (fabs(pi - 0.5) >= tau)
        return (0.0);

    /* Compute v_obs */
    j = 0;
    b = 14;
    bit_prev = (values[j] & (1U << 15)) == 0 ? 0 : 1;

    v_obs = 0;

    for (i = 1; i < numbits; i++) {
        bit_this = (values[j] & (1U << b)) == 0 ? 0 : 1;
        if (b == 0) {
            b = 15;
            j++;
        } else {
            b--;
        }

        v_obs += bit_this ^ bit_prev;

        bit_prev = bit_this;
    }

    v_obs += 1;

    numer = fabs(v_obs - (2.0 * numbits * pi * (1.0 - pi)));
    denom = 2.0 * sqrt(2.0 * numbits) * pi * (1.0 - pi);

    p_value = erfc(numer / denom);

    return (p_value);
}

/*
 * This is the block frequency test taken from the NIST SP 800-22 RNG
 * test suite.
 */
static double
blockfrequency(isc_mem_t *mctx, isc_uint16_t *values, size_t length) {
    isc_uint32_t i;
    isc_uint32_t numbits;
    isc_uint32_t mbits;
    isc_uint32_t mwords;
    isc_uint32_t numblocks;
    double *pi;
    isc_uint32_t cur_word;
    double chi_square;
    double p_value;

    numbits = length * 16;
    mbits = 32000;
    mwords = mbits / 16;
    numblocks = numbits / mbits;

    /* Debug message, not displayed when running via atf-run */
    printf("numblocks=%u\n", numblocks);

    /* Preconditions (section 2.2.7 in NIST SP 800-22) */
    ATF_REQUIRE(numbits >= 100);
    ATF_REQUIRE(mbits >= 20);
    ATF_REQUIRE((double) mbits > (0.01 * numbits));
    ATF_REQUIRE(numblocks < 100);
    ATF_REQUIRE(numbits >= (mbits * numblocks));

    pi = isc_mem_get(mctx, numblocks * sizeof(double));
    ATF_REQUIRE(pi != NULL);

    cur_word = 0;
    for (i = 0; i < numblocks; i++) {
        isc_uint32_t j;
        pi[i] = 0.0;
        for (j = 0; j < mwords; j++) {
            isc_uint32_t idx;

            idx = i * mwords + j;
            pi[i] += bitcounts_table[values[idx]];
            cur_word++;
        }
        pi[i] /= mbits;
    }

    /* Compute chi_square */
    chi_square = 0.0;
    for (i = 0; i < numblocks; i++)
        chi_square += (pi[i] - 0.5) * (pi[i] - 0.5);

    chi_square *= 4 * mbits;

    isc_mem_put(mctx, pi, numblocks * sizeof(double));

    /* Debug message, not displayed when running via atf-run */
    printf("chi_square=%f\n", chi_square);

    p_value = igamc(numblocks * 0.5, chi_square * 0.5);

    return (p_value);
}

/*
 * This is the binary matrix rank test taken from the NIST SP 800-22 RNG
 * test suite.
 */
static double
binarymatrixrank(isc_mem_t *mctx, isc_uint16_t *values, size_t length) {
    isc_uint32_t i;
    size_t matrix_m;
    size_t matrix_q;
    isc_uint32_t num_matrices;
    size_t numbits;
    isc_uint32_t fm_0;
    isc_uint32_t fm_1;
    isc_uint32_t fm_rest;
    double term1;
    double term2;
    double term3;
    double chi_square;
    double p_value;

    UNUSED(mctx);

    matrix_m = 32;
    matrix_q = 32;
    num_matrices = length / ((matrix_m * matrix_q) / 16);
    numbits = num_matrices * matrix_m * matrix_q;

    /* Preconditions (section 2.5.7 in NIST SP 800-22) */
    ATF_REQUIRE(matrix_m == 32);
    ATF_REQUIRE(matrix_q == 32);
    ATF_REQUIRE(numbits >= (38 * matrix_m * matrix_q));

    fm_0 = 0;
    fm_1 = 0;
    fm_rest = 0;
    for (i = 0; i < num_matrices; i++) {
        /*
         * Each isc_uint32_t supplies 32 bits, so a 32x32 bit matrix
         * takes up isc_uint32_t array of size 32.
         */
        isc_uint32_t bits[32];
        int j;
        isc_uint32_t rank;

        for (j = 0; j < 32; j++) {
            size_t idx;
            isc_uint32_t r1;
            isc_uint32_t r2;

            idx = i * ((matrix_m * matrix_q) / 16);
            idx += j * 2;

            r1 = values[idx];
            r2 = values[idx + 1];
            bits[j] = (r1 << 16) | r2;
        }

        rank = matrix_binaryrank(bits, matrix_m, matrix_q);

        if (rank == matrix_m)
            fm_0++;
        else if (rank == (matrix_m - 1))
            fm_1++;
        else
            fm_rest++;
    }

    /* Compute chi_square */
    term1 = ((fm_0 - (0.2888 * num_matrices)) *
         (fm_0 - (0.2888 * num_matrices))) / (0.2888 * num_matrices);
    term2 = ((fm_1 - (0.5776 * num_matrices)) *
         (fm_1 - (0.5776 * num_matrices))) / (0.5776 * num_matrices);
    term3 = ((fm_rest - (0.1336 * num_matrices)) *
         (fm_rest - (0.1336 * num_matrices))) / (0.1336 * num_matrices);

    chi_square = term1 + term2 + term3;

    /* Debug message, not displayed when running via atf-run */
    printf("fm_0=%u, fm_1=%u, fm_rest=%u, chi_square=%f\n",
           fm_0, fm_1, fm_rest, chi_square);

    p_value = exp(-chi_square * 0.5);

    return (p_value);
}

ATF_TC(isc_rng_monobit);
ATF_TC_HEAD(isc_rng_monobit, tc) {
    atf_tc_set_md_var(tc, "descr", "Monobit test for the RNG");
}

ATF_TC_BODY(isc_rng_monobit, tc) {
    UNUSED(tc);

    random_test(monobit);
}

ATF_TC(isc_rng_runs);
ATF_TC_HEAD(isc_rng_runs, tc) {
    atf_tc_set_md_var(tc, "descr", "Runs test for the RNG");
}

ATF_TC_BODY(isc_rng_runs, tc) {
    UNUSED(tc);

    random_test(runs);
}

ATF_TC(isc_rng_blockfrequency);
ATF_TC_HEAD(isc_rng_blockfrequency, tc) {
    atf_tc_set_md_var(tc, "descr", "Block frequency test for the RNG");
}

ATF_TC_BODY(isc_rng_blockfrequency, tc) {
    UNUSED(tc);

    random_test(blockfrequency);
}

ATF_TC(isc_rng_binarymatrixrank);
ATF_TC_HEAD(isc_rng_binarymatrixrank, tc) {
    atf_tc_set_md_var(tc, "descr", "Binary matrix rank test for the RNG");
}

/*
 * This is the binary matrix rank test taken from the NIST SP 800-22 RNG
 * test suite.
 */
ATF_TC_BODY(isc_rng_binarymatrixrank, tc) {
    UNUSED(tc);

    random_test(binarymatrixrank);
}

/*
 * Main
 */
ATF_TP_ADD_TCS(tp) {
    ATF_TP_ADD_TC(tp, isc_rng_monobit);
    ATF_TP_ADD_TC(tp, isc_rng_runs);
    ATF_TP_ADD_TC(tp, isc_rng_blockfrequency);
    ATF_TP_ADD_TC(tp, isc_rng_binarymatrixrank);

    return (atf_no_error());
}