/* rng/test.c * * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 James Theiler, Brian Gough * * This program is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation; either version 3 of the License, or (at * your option) any later version. * * This program is distributed in the hope that it will be useful, but * WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU * General Public License for more details. * * You should have received a copy of the GNU General Public License * along with this program; if not, write to the Free Software * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. */ #include #include #include #include #include #include #include void rng_test (const gsl_rng_type * T, unsigned long int seed, unsigned int n, unsigned long int result); void rng_float_test (const gsl_rng_type * T); void generic_rng_test (const gsl_rng_type * T); void rng_state_test (const gsl_rng_type * T); void rng_parallel_state_test (const gsl_rng_type * T); void rng_read_write_test (const gsl_rng_type * T); int rng_max_test (gsl_rng * r, unsigned long int *kmax, unsigned long int ran_max) ; int rng_min_test (gsl_rng * r, unsigned long int *kmin, unsigned long int ran_min, unsigned long int ran_max) ; int rng_sum_test (gsl_rng * r, double *sigma); int rng_bin_test (gsl_rng * r, double *sigma); void rng_seed_test (const gsl_rng_type * T); #define N 10000 #define N2 200000 int main (void) { const gsl_rng_type ** rngs = gsl_rng_types_setup(); /* get all rng types */ const gsl_rng_type ** r ; gsl_ieee_env_setup (); gsl_rng_env_setup (); /* specific tests of known results for 10000 iterations with seed = 1 */ rng_test (gsl_rng_rand, 1, 10000, 1910041713); rng_test (gsl_rng_randu, 1, 10000, 1623524161); rng_test (gsl_rng_cmrg, 1, 10000, 719452880); rng_test (gsl_rng_minstd, 1, 10000, 1043618065); rng_test (gsl_rng_mrg, 1, 10000, 2064828650); rng_test (gsl_rng_taus, 1, 10000, 2733957125UL); rng_test (gsl_rng_taus2, 1, 10000, 2733957125UL); rng_test (gsl_rng_taus113, 1, 1000, 1925420673UL); rng_test (gsl_rng_transputer, 1, 10000, 1244127297UL); rng_test (gsl_rng_vax, 1, 10000, 3051034865UL); /* Borosh13 test value from PARI: (1812433253^10000)%(2^32) */ rng_test (gsl_rng_borosh13, 1, 10000, 2513433025UL); /* Fishman18 test value from PARI: (62089911^10000)%(2^31-1) */ rng_test (gsl_rng_fishman18, 1, 10000, 330402013UL); /* Fishman2x test value from PARI: ((48271^10000)%(2^31-1) - (40692^10000)%(2^31-249))%(2^31-1) */ rng_test (gsl_rng_fishman2x, 1, 10000, 540133597UL); /* Knuthran2 test value from PARI: { xn1=1; xn2=1; for (n=1,10000, xn = (271828183*xn1 - 314159269*xn2)%(2^31-1); xn2=xn1; xn1=xn; print(xn); ) } */ rng_test (gsl_rng_knuthran2, 1, 10000, 1084477620UL); /* Knuthran test value taken from p188 in Knuth Vol 2. 3rd Ed */ rng_test (gsl_rng_knuthran, 310952, 1009 * 2009 + 1, 461390032); /* Knuthran improved test value from Knuth's source */ rng_test (gsl_rng_knuthran2002, 310952, 1, 708622036); rng_test (gsl_rng_knuthran2002, 310952, 2, 1005450560); rng_test (gsl_rng_knuthran2002, 310952, 100 * 2009 + 1, 995235265); rng_test (gsl_rng_knuthran2002, 310952, 1009 * 2009 + 1, 704987132); /* Lecuyer21 test value from PARI: (40692^10000)%(2^31-249) */ rng_test (gsl_rng_lecuyer21, 1, 10000, 2006618587UL); /* Waterman14 test value from PARI: (1566083941^10000)%(2^32) */ rng_test (gsl_rng_waterman14, 1, 10000, 3776680385UL); /* specific tests of known results for 10000 iterations with seed = 6 */ /* Coveyou test value from PARI: x=6; for(n=1,10000,x=(x*(x+1))%(2^32);print(x);) */ rng_test (gsl_rng_coveyou, 6, 10000, 1416754246UL); /* Fishman20 test value from PARI: (6*48271^10000)%(2^31-1) */ rng_test (gsl_rng_fishman20, 6, 10000, 248127575UL); /* FIXME: the ranlux tests below were made by running the fortran code and getting the expected value from that. An analytic calculation would be preferable. */ rng_test (gsl_rng_ranlux, 314159265, 10000, 12077992); rng_test (gsl_rng_ranlux389, 314159265, 10000, 165942); rng_test (gsl_rng_ranlxs0, 1, 10000, 11904320); /* 0.709552764892578125 * ldexp(1.0,24) */ rng_test (gsl_rng_ranlxs1, 1, 10000, 8734328); /* 0.520606517791748047 * ldexp(1.0,24) */ rng_test (gsl_rng_ranlxs2, 1, 10000, 6843140); /* 0.407882928848266602 * ldexp(1.0,24) */ rng_test (gsl_rng_ranlxd1, 1, 10000, 1998227290UL); /* 0.465248546261094020 * ldexp(1.0,32) */ rng_test (gsl_rng_ranlxd2, 1, 10000, 3949287736UL); /* 0.919515205581550532 * ldexp(1.0,32) */ /* FIXME: the tests below were made by running the original code in the ../random directory and getting the expected value from that. An analytic calculation would be preferable. */ rng_test (gsl_rng_slatec, 1, 10000, 45776); rng_test (gsl_rng_uni, 1, 10000, 9214); rng_test (gsl_rng_uni32, 1, 10000, 1155229825); rng_test (gsl_rng_zuf, 1, 10000, 3970); /* The tests below were made by running the original code and getting the expected value from that. An analytic calculation would be preferable. */ rng_test (gsl_rng_r250, 1, 10000, 1100653588); rng_test (gsl_rng_mt19937, 4357, 1000, 1186927261); rng_test (gsl_rng_mt19937_1999, 4357, 1000, 1030650439); rng_test (gsl_rng_mt19937_1998, 4357, 1000, 1309179303); rng_test (gsl_rng_tt800, 0, 10000, 2856609219UL); rng_test (gsl_rng_ran0, 0, 10000, 1115320064); rng_test (gsl_rng_ran1, 0, 10000, 1491066076); rng_test (gsl_rng_ran2, 0, 10000, 1701364455); rng_test (gsl_rng_ran3, 0, 10000, 186340785); rng_test (gsl_rng_ranmar, 1, 10000, 14428370); rng_test (gsl_rng_rand48, 0, 10000, 0xDE095043UL); rng_test (gsl_rng_rand48, 1, 10000, 0xEDA54977UL); rng_test (gsl_rng_random_glibc2, 0, 10000, 1908609430); rng_test (gsl_rng_random8_glibc2, 0, 10000, 1910041713); rng_test (gsl_rng_random32_glibc2, 0, 10000, 1587395585); rng_test (gsl_rng_random64_glibc2, 0, 10000, 52848624); rng_test (gsl_rng_random128_glibc2, 0, 10000, 1908609430); rng_test (gsl_rng_random256_glibc2, 0, 10000, 179943260); rng_test (gsl_rng_random_bsd, 0, 10000, 1457025928); rng_test (gsl_rng_random8_bsd, 0, 10000, 1910041713); rng_test (gsl_rng_random32_bsd, 0, 10000, 1663114331); rng_test (gsl_rng_random64_bsd, 0, 10000, 864469165); rng_test (gsl_rng_random128_bsd, 0, 10000, 1457025928); rng_test (gsl_rng_random256_bsd, 0, 10000, 1216357476); rng_test (gsl_rng_random_libc5, 0, 10000, 428084942); rng_test (gsl_rng_random8_libc5, 0, 10000, 1910041713); rng_test (gsl_rng_random32_libc5, 0, 10000, 1967452027); rng_test (gsl_rng_random64_libc5, 0, 10000, 2106639801); rng_test (gsl_rng_random128_libc5, 0, 10000, 428084942); rng_test (gsl_rng_random256_libc5, 0, 10000, 116367984); rng_test (gsl_rng_ranf, 0, 10000, 2152890433UL); rng_test (gsl_rng_ranf, 2, 10000, 339327233); /* Test constant relationship between int and double functions */ for (r = rngs ; *r != 0; r++) rng_float_test (*r); /* Test save/restore functions */ for (r = rngs ; *r != 0; r++) rng_state_test (*r); for (r = rngs ; *r != 0; r++) rng_parallel_state_test (*r); for (r = rngs ; *r != 0; r++) rng_read_write_test (*r); /* generic statistical tests (these are just to make sure that we don't get any crazy results back from the generator, i.e. they aren't a test of the algorithm, just the implementation) */ for (r = rngs ; *r != 0; r++) generic_rng_test (*r); #ifdef TEST_SEEDS rng_seed_test (gsl_rng_mt19937); rng_seed_test (gsl_rng_ranlxs0); rng_seed_test (gsl_rng_ranlxs1); rng_seed_test (gsl_rng_ranlxs2); rng_seed_test (gsl_rng_ranlxd1); rng_seed_test (gsl_rng_ranlxd2); rng_seed_test (gsl_rng_ranlux); rng_seed_test (gsl_rng_ranlux389); rng_seed_test (gsl_rng_cmrg); rng_seed_test (gsl_rng_mrg); rng_seed_test (gsl_rng_taus); rng_seed_test (gsl_rng_taus2); rng_seed_test (gsl_rng_gfsr4); #endif exit (gsl_test_summary ()); } void rng_test (const gsl_rng_type * T, unsigned long int seed, unsigned int n, unsigned long int result) { gsl_rng *r = gsl_rng_alloc (T); unsigned int i; unsigned long int k = 0; int status; if (seed != 0) { gsl_rng_set (r, seed); } for (i = 0; i < n; i++) { k = gsl_rng_get (r); } status = (k != result); gsl_test (status, "%s, %u steps (%u observed vs %u expected)", gsl_rng_name (r), n, k, result); gsl_rng_free (r); } void rng_float_test (const gsl_rng_type * T) { gsl_rng *ri = gsl_rng_alloc (T); gsl_rng *rf = gsl_rng_alloc (T); double u, c ; unsigned int i; unsigned long int k = 0; int status = 0 ; do { k = gsl_rng_get (ri); u = gsl_rng_get (rf); } while (k == 0) ; c = k / u ; for (i = 0; i < N2; i++) { k = gsl_rng_get (ri); u = gsl_rng_get (rf); if (c*k != u) { status = 1 ; break ; } } gsl_test (status, "%s, ratio of int to double (%g observed vs %g expected)", gsl_rng_name (ri), c, k/u); gsl_rng_free (ri); gsl_rng_free (rf); } void rng_state_test (const gsl_rng_type * T) { unsigned long int test_a[N], test_b[N]; int i; gsl_rng *r = gsl_rng_alloc (T); gsl_rng *r_save = gsl_rng_alloc (T); for (i = 0; i < N; ++i) { gsl_rng_get (r); /* throw away N iterations */ } gsl_rng_memcpy (r_save, r); /* save the intermediate state */ for (i = 0; i < N; ++i) { test_a[i] = gsl_rng_get (r); } gsl_rng_memcpy (r, r_save); /* restore the intermediate state */ gsl_rng_free (r_save); for (i = 0; i < N; ++i) { test_b[i] = gsl_rng_get (r); } { int status = 0; for (i = 0; i < N; ++i) { status |= (test_b[i] != test_a[i]); } gsl_test (status, "%s, random number state consistency", gsl_rng_name (r)); } gsl_rng_free (r); } void rng_parallel_state_test (const gsl_rng_type * T) { unsigned long int test_a[N], test_b[N]; unsigned long int test_c[N], test_d[N]; double test_e[N], test_f[N]; int i; gsl_rng *r1 = gsl_rng_alloc (T); gsl_rng *r2 = gsl_rng_alloc (T); for (i = 0; i < N; ++i) { gsl_rng_get (r1); /* throw away N iterations */ } gsl_rng_memcpy (r2, r1); /* save the intermediate state */ for (i = 0; i < N; ++i) { /* check that there is no hidden state intermixed between r1 and r2 */ test_a[i] = gsl_rng_get (r1); test_b[i] = gsl_rng_get (r2); test_c[i] = gsl_rng_uniform_int (r1, 1234); test_d[i] = gsl_rng_uniform_int (r2, 1234); test_e[i] = gsl_rng_uniform (r1); test_f[i] = gsl_rng_uniform (r2); } { int status = 0; for (i = 0; i < N; ++i) { status |= (test_b[i] != test_a[i]); status |= (test_c[i] != test_d[i]); status |= (test_e[i] != test_f[i]); } gsl_test (status, "%s, parallel random number state consistency", gsl_rng_name (r1)); } gsl_rng_free (r1); gsl_rng_free (r2); } void rng_read_write_test (const gsl_rng_type * T) { unsigned long int test_a[N], test_b[N]; int i; gsl_rng *r = gsl_rng_alloc (T); for (i = 0; i < N; ++i) { gsl_rng_get (r); /* throw away N iterations */ } { /* save the state to a binary file */ FILE *f = fopen("test.dat", "wb"); gsl_rng_fwrite(f, r); fclose(f); } for (i = 0; i < N; ++i) { test_a[i] = gsl_rng_get (r); } { /* read the state from a binary file */ FILE *f = fopen("test.dat", "rb"); gsl_rng_fread(f, r); fclose(f); } for (i = 0; i < N; ++i) { test_b[i] = gsl_rng_get (r); } { int status = 0; for (i = 0; i < N; ++i) { status |= (test_b[i] != test_a[i]); } gsl_test (status, "%s, random number generator read and write", gsl_rng_name (r)); } gsl_rng_free (r); } void generic_rng_test (const gsl_rng_type * T) { gsl_rng *r = gsl_rng_alloc (T); const char *name = gsl_rng_name (r); unsigned long int kmax = 0, kmin = 1000; double sigma = 0; const unsigned long int ran_max = gsl_rng_max (r); const unsigned long int ran_min = gsl_rng_min (r); int status = rng_max_test (r, &kmax, ran_max); gsl_test (status, "%s, observed vs theoretical maximum (%lu vs %lu)", name, kmax, ran_max); status = rng_min_test (r, &kmin, ran_min, ran_max); gsl_test (status, "%s, observed vs theoretical minimum (%lu vs %lu)", name, kmin, ran_min); status = rng_sum_test (r, &sigma); gsl_test (status, "%s, sum test within acceptable sigma (observed %.2g sigma)", name, sigma); status = rng_bin_test (r, &sigma); gsl_test (status, "%s, bin test within acceptable chisq (observed %.2g sigma)", name, sigma); gsl_rng_set (r, 1); /* set seed to 1 */ status = rng_max_test (r, &kmax, ran_max); gsl_rng_set (r, 1); /* set seed to 1 */ status |= rng_min_test (r, &kmin, ran_min, ran_max); gsl_rng_set (r, 1); /* set seed to 1 */ status |= rng_sum_test (r, &sigma); gsl_test (status, "%s, max, min and sum tests for seed=1", name); gsl_rng_set (r, 12345); /* set seed to a "typical" value */ status = rng_max_test (r, &kmax, ran_max); gsl_rng_set (r, 12345); /* set seed to a "typical" value */ status |= rng_min_test (r, &kmin, ran_min, ran_max); gsl_rng_set (r, 12345); /* set seed to a "typical" value */ status |= rng_sum_test (r, &sigma); gsl_test (status, "%s, max, min and sum tests for non-default seeds", name); gsl_rng_free (r); } int rng_max_test (gsl_rng * r, unsigned long int *kmax, unsigned long int ran_max) { unsigned long int actual_uncovered; double expect_uncovered; int status; unsigned long int max = 0; int i; for (i = 0; i < N2; ++i) { unsigned long int k = gsl_rng_get (r); if (k > max) max = k; } *kmax = max; actual_uncovered = ran_max - max; expect_uncovered = (double) ran_max / (double) N2; status = (max > ran_max) || (actual_uncovered > 7 * expect_uncovered) ; return status; } int rng_min_test (gsl_rng * r, unsigned long int *kmin, unsigned long int ran_min, unsigned long int ran_max) { unsigned long int actual_uncovered; double expect_uncovered; int status; unsigned long int min = 1000000000UL; int i; for (i = 0; i < N2; ++i) { unsigned long int k = gsl_rng_get (r); if (k < min) min = k; } *kmin = min; actual_uncovered = min - ran_min; expect_uncovered = (double) ran_max / (double) N2; status = (min < ran_min) || (actual_uncovered > 7 * expect_uncovered); return status; } int rng_sum_test (gsl_rng * r, double *sigma) { double sum = 0; int i, status; for (i = 0; i < N2; ++i) { double x = gsl_rng_uniform (r) - 0.5; sum += x; } sum /= N2; /* expect the average to have a variance of 1/(12 n) */ *sigma = sum * sqrt (12.0 * N2); /* more than 3 sigma is an error (increased to 3.1 to avoid false alarms) */ status = (fabs (*sigma) > 3.1 || fabs(*sigma) < 0.003); if (status) { fprintf(stderr,"sum=%g, sigma=%g\n",sum,*sigma); } return status; } #define BINS 17 #define EXTRA 10 int rng_bin_test (gsl_rng * r, double *sigma) { int count[BINS+EXTRA]; double chisq = 0; int i, status; for (i = 0; i < BINS+EXTRA; i++) count[i] = 0 ; for (i = 0; i < N2; i++) { int j = gsl_rng_uniform_int (r, BINS); count[j]++ ; } chisq = 0 ; for (i = 0; i < BINS; i++) { double x = (double)N2/(double)BINS ; double d = (count[i] - x) ; chisq += (d*d) / x; } *sigma = sqrt(chisq/BINS) ; /* more than 3 sigma is an error */ status = (fabs (*sigma) > 3 || fabs(*sigma) < 0.003); for (i = BINS; i < BINS+EXTRA; i++) { if (count[i] != 0) { status = 1 ; gsl_test (status, "%s, wrote outside range in bin test " "(%d observed vs %d expected)", gsl_rng_name(r), i, BINS - 1); } } return status; } int rng_sanity_test (gsl_rng * r) { double sum = 0, sigma; int i, status = 0; for (i = 0; i < N2; ++i) { double x = gsl_rng_uniform (r); sum += x; if (x < 0.0 || x > 1.0) { fprintf(stderr,"x=%g out of range\n", x); return 1; } } sum /= N2; /* expect the average to have a variance of 1/(12 n) */ sigma = (sum - 0.5)* sqrt (12.0 * N2); /* more than 5 sigma is an error */ status = (fabs (sigma) > 5 || fabs(sigma) < 0.0001); if (status) { fprintf(stderr,"sum=%g, sigma=%g\n",sum,sigma); } return status; } void rng_seed_test (const gsl_rng_type * T) { gsl_rng *r = gsl_rng_alloc (T); const char *name = gsl_rng_name (r); unsigned long int i; int j; int status; for (i = 0xFFFFFFFFUL ; i > 0; i >>= 1) { for (j = 1; j >= -1 ; j--) { unsigned long int seed = i + j; if (j > 0 && seed < i) continue; gsl_rng_set (r, seed); status = rng_sanity_test (r); if (status) gsl_test (status, "%s, sanity tests for seed = %#lx", name, seed); } } }