tommath/demo/demo.c

#include <string.h>
#include <time.h>

/*
 * Configuration
 */
#ifndef LTM_DEMO_TEST_VS_MTEST
#define LTM_DEMO_TEST_VS_MTEST 1
#endif

#ifndef LTM_DEMO_TEST_REDUCE_2K_L
/* This test takes a moment so we disable it by default, but it can be:
 * 0 to disable testing
 * 1 to make the test with P = 2^1024 - 0x2A434 B9FDEC95 D8F9D550 FFFFFFFF FFFFFFFF
 * 2 to make the test with P = 2^2048 - 0x1 00000000 00000000 00000000 00000000 4945DDBF 8EA2A91D 5776399B B83E188F
 */
#define LTM_DEMO_TEST_REDUCE_2K_L 0
#endif

#ifdef LTM_DEMO_REAL_RAND
#define LTM_DEMO_RAND_SEED  time(NULL)
#else
#define LTM_DEMO_RAND_SEED  23
#endif

#include "tommath.h"

static void ndraw(mp_int *a, const char *name)
{
   char buf[16000];

   printf("%s: ", name);
   mp_toradix(a, buf, 10);
   printf("%s\n", buf);
   mp_toradix(a, buf, 16);
   printf("0x%s\n", buf);
}

#if LTM_DEMO_TEST_VS_MTEST
static void draw(mp_int *a)
{
   ndraw(a, "");
}
#endif

#if defined(LTM_DEMO_REAL_RAND) && !defined(_WIN32)
static FILE *fd_urandom;
#endif
#if LTM_DEMO_TEST_VS_MTEST == 0
static int myrng(unsigned char *dst, int len, void *dat)
{
   int x;
   (void)dat;
#if defined(LTM_DEMO_REAL_RAND)
   if (!fd_urandom) {
#   if !defined(_WIN32)
      fprintf(stderr, "\nno /dev/urandom\n");
#   endif
   } else {
      return fread(dst, 1uL, len, fd_urandom);
   }
#endif
   for (x = 0; x < len;) {
      unsigned int r = (unsigned int)rand();
      do {
         dst[x++] = r & 0xFFu;
         r >>= 8;
      } while ((r != 0u) && (x < len));
   }
   return len;
}
#endif

#if LTM_DEMO_TEST_VS_MTEST != 0
static void _panic(int l)
{
   fprintf(stderr, "\n%d: fgets failed\n", l);
   exit(EXIT_FAILURE);
}
#endif

#define FGETS(str, size, stream) \
   { \
      char *ret = fgets(str, size, stream); \
      if (!ret) { _panic(__LINE__); } \
   }

static mp_int a, b, c, d, e, f;

static void _cleanup(void)
{
   mp_clear_multi(&a, &b, &c, &d, &e, &f, NULL);
   printf("\n");

#ifdef LTM_DEMO_REAL_RAND
   if (fd_urandom)
      fclose(fd_urandom);
#endif
}
#if LTM_DEMO_TEST_VS_MTEST == 0
struct mp_sqrtmod_prime_st {
   unsigned long p;
   unsigned long n;
   mp_digit r;
};
static struct mp_sqrtmod_prime_st sqrtmod_prime[] = {
   { 5, 14, 3 },
   { 7, 9, 4 },
   { 113, 2, 62 }
};
struct mp_jacobi_st {
   unsigned long n;
   int c[16];
};
static struct mp_jacobi_st jacobi[] = {
   { 3, {  1, -1,  0,  1, -1,  0,  1, -1,  0,  1, -1,  0,  1, -1,  0,  1 } },
   { 5, {  0,  1, -1, -1,  1,  0,  1, -1, -1,  1,  0,  1, -1, -1,  1,  0 } },
   { 7, {  1, -1,  1, -1, -1,  0,  1,  1, -1,  1, -1, -1,  0,  1,  1, -1 } },
   { 9, { -1,  1,  0,  1,  1,  0,  1,  1,  0,  1,  1,  0,  1,  1,  0,  1 } },
};
#endif

#if LTM_DEMO_TEST_VS_MTEST != 0
static char cmd[4096];
#endif
static char buf[4096];
int main(void)
{
   unsigned rr;
   int cnt, ix;
#if LTM_DEMO_TEST_VS_MTEST
   unsigned long expt_n, add_n, sub_n, mul_n, div_n, sqr_n, mul2d_n, div2d_n,
            gcd_n, lcm_n, inv_n, div2_n, mul2_n, add_d_n, sub_d_n;
#else
   unsigned long s, t;
   unsigned long long q, r;
   mp_digit mp;
   int i, n, err, should;
#endif

   if (mp_init_multi(&a, &b, &c, &d, &e, &f, NULL)!= MP_OKAY)
      return EXIT_FAILURE;

   atexit(_cleanup);

#if defined(LTM_DEMO_REAL_RAND)
   if (!fd_urandom) {
      fd_urandom = fopen("/dev/urandom", "r");
      if (!fd_urandom) {
#   if !defined(_WIN32)
         fprintf(stderr, "\ncould not open /dev/urandom\n");
#   endif
      }
   }
#endif
   srand(LTM_DEMO_RAND_SEED);

#ifdef MP_8BIT
   printf("Digit size 8 Bit \n");
#endif
#ifdef MP_16BIT
   printf("Digit size 16 Bit \n");
#endif
#ifdef MP_32BIT
   printf("Digit size 32 Bit \n");
#endif
#ifdef MP_64BIT
   printf("Digit size 64 Bit \n");
#endif
   printf("Size of mp_digit: %u\n", (unsigned int)sizeof(mp_digit));
   printf("Size of mp_word: %u\n", (unsigned int)sizeof(mp_word));
   printf("DIGIT_BIT: %d\n", DIGIT_BIT);
   printf("MP_PREC: %d\n", MP_PREC);

#if LTM_DEMO_TEST_VS_MTEST == 0
   /* trivial stuff */
   /* a: 0->5 */
   mp_set_int(&a, 5);
   /* a: 5-> b: -5 */
   mp_neg(&a, &b);
   if (mp_cmp(&a, &b) != MP_GT) {
      return EXIT_FAILURE;
   }
   if (mp_cmp(&b, &a) != MP_LT) {
      return EXIT_FAILURE;
   }
   /* a: 5-> a: -5 */
   mp_neg(&a, &a);
   if (mp_cmp(&b, &a) != MP_EQ) {
      return EXIT_FAILURE;
   }
   /* a: -5-> b: 5 */
   mp_abs(&a, &b);
   if (mp_isneg(&b) != MP_NO) {
      return EXIT_FAILURE;
   }
   /* a: -5-> b: -4 */
   mp_add_d(&a, 1uL, &b);
   if (mp_isneg(&b) != MP_YES) {
      return EXIT_FAILURE;
   }
   if (mp_get_int(&b) != 4) {
      return EXIT_FAILURE;
   }
   /* a: -5-> b: 1 */
   mp_add_d(&a, 6uL, &b);
   if (mp_get_int(&b) != 1) {
      return EXIT_FAILURE;
   }
   /* a: -5-> a: 1 */
   mp_add_d(&a, 6uL, &a);
   if (mp_get_int(&a) != 1) {
      return EXIT_FAILURE;
   }
   mp_zero(&a);
   /* a: 0-> a: 6 */
   mp_add_d(&a, 6uL, &a);
   if (mp_get_int(&a) != 6) {
      return EXIT_FAILURE;
   }

   mp_set_int(&a, 42);
   mp_set_int(&b, 1);
   mp_neg(&b, &b);
   mp_set_int(&c, 1);
   mp_exptmod(&a, &b, &c, &d);

   mp_set_int(&c, 7);
   mp_exptmod(&a, &b, &c, &d);


   mp_set_int(&a, 0);
   mp_set_int(&b, 1);
   if ((err = mp_jacobi(&a, &b, &i)) != MP_OKAY) {
      printf("Failed executing mp_jacobi(0 | 1) %s.\n", mp_error_to_string(err));
      return EXIT_FAILURE;
   }
   if (i != 1) {
      printf("Failed trivial mp_jacobi(0 | 1) %d != 1\n", i);
      return EXIT_FAILURE;
   }
   for (cnt = 0; cnt < (int)(sizeof(jacobi)/sizeof(jacobi[0])); ++cnt) {
      mp_set_int(&b, jacobi[cnt].n);
      /* only test positive values of a */
      for (n = -5; n <= 10; ++n) {
         mp_set_int(&a, abs(n));
         should = MP_OKAY;
         if (n < 0) {
            mp_neg(&a, &a);
            /* Until #44 is fixed the negative a's must fail */
            should = MP_VAL;
         }
         if ((err = mp_jacobi(&a, &b, &i)) != should) {
            printf("Failed executing mp_jacobi(%d | %lu) %s.\n", n, jacobi[cnt].n, mp_error_to_string(err));
            return EXIT_FAILURE;
         }
         if (err == MP_OKAY && i != jacobi[cnt].c[n + 5]) {
            printf("Failed trivial mp_jacobi(%d | %lu) %d != %d\n", n, jacobi[cnt].n, i, jacobi[cnt].c[n + 5]);
            return EXIT_FAILURE;
         }
      }
   }

   /* test mp_complement */
   printf("\n\nTesting: mp_complement");
   for (i = 0; i < 1000; ++i) {
      int l = (rand() * rand() + 1) * (rand() % 1 ? -1 : 1);
      mp_set_int(&a, labs(l));
      if (l < 0)
         mp_neg(&a, &a);
      mp_complement(&a, &b);

      l = ~l;
      mp_set_int(&c, labs(l));
      if (l < 0)
         mp_neg(&c, &c);

      if (mp_cmp(&b, &c) != MP_EQ) {
         printf("\nmp_complement() bad result!");
         return EXIT_FAILURE;
      }
   }

   /* test mp_tc_div_2d */
   printf("\n\nTesting: mp_tc_div_2d");
   for (i = 0; i < 1000; ++i) {
      int l, em;

      l = (rand() * rand() + 1) * (rand() % 1 ? -1 : 1);
      mp_set_int(&a, labs(l));
      if (l < 0)
         mp_neg(&a, &a);

      em = rand() % 32;

      mp_set_int(&d, labs(l >> em));
      if ((l >> em) < 0)
         mp_neg(&d, &d);

      mp_tc_div_2d(&a, em, &b);
      if (mp_cmp(&b, &d) != MP_EQ) {
         printf("\nmp_tc_div_2d() bad result!");
         return EXIT_FAILURE;
      }
   }

   /* test mp_tc_xor */
   printf("\n\nTesting: mp_tc_xor");
   for (i = 0; i < 1000; ++i) {
      int l, em;

      l = (rand() * rand() + 1) * (rand() % 1 ? -1 : 1);
      mp_set_int(&a, labs(l));
      if (l < 0)
         mp_neg(&a, &a);

      em = (rand() * rand() + 1) * (rand() % 1 ? -1 : 1);
      mp_set_int(&b, labs(em));
      if (em < 0)
         mp_neg(&b, &b);

      mp_set_int(&d, labs(l ^ em));
      if ((l ^ em) < 0)
         mp_neg(&d, &d);

      mp_tc_xor(&a, &b, &c);
      if (mp_cmp(&c, &d) != MP_EQ) {
         printf("\nmp_tc_xor() bad result!");
         return EXIT_FAILURE;
      }
   }

   /* test mp_tc_or */
   printf("\n\nTesting: mp_tc_or");
   for (i = 0; i < 1000; ++i) {
      int l, em;

      l = (rand() * rand() + 1) * (rand() % 1 ? -1 : 1);
      mp_set_int(&a, labs(l));
      if (l < 0)
         mp_neg(&a, &a);

      em = (rand() * rand() + 1) * (rand() % 1 ? -1 : 1);
      mp_set_int(&b, labs(em));
      if (em < 0)
         mp_neg(&b, &b);

      mp_set_int(&d, labs(l | em));
      if ((l | em) < 0)
         mp_neg(&d, &d);

      mp_tc_or(&a, &b, &c);
      if (mp_cmp(&c, &d) != MP_EQ) {
         printf("\nmp_tc_or() bad result!");
         return EXIT_FAILURE;
      }
   }

   /* test mp_tc_and */
   printf("\n\nTesting: mp_tc_and");
   for (i = 0; i < 1000; ++i) {
      int l, em;

      l = (rand() * rand() + 1) * (rand() % 1 ? -1 : 1);
      mp_set_int(&a, labs(l));
      if (l < 0)
         mp_neg(&a, &a);

      em = (rand() * rand() + 1) * (rand() % 1 ? -1 : 1);
      mp_set_int(&b, labs(em));
      if (em < 0)
         mp_neg(&b, &b);

      mp_set_int(&d, labs(l & em));
      if ((l & em) < 0)
         mp_neg(&d, &d);

      mp_tc_and(&a, &b, &c);
      if (mp_cmp(&c, &d) != MP_EQ) {
         printf("\nmp_tc_and() bad result!");
         return EXIT_FAILURE;
      }
   }

   /* mp_invmod corner-case of https://github.com/libtom/libtommath/issues/118 */
   printf("\n\nTesting: mp_invmod");
   {
      const char *a_ = "47182BB8DF0FFE9F61B1F269BACC066B48BA145D35137D426328DC3F88A5EA44";
      const char *b_ = "FFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFF";
      const char *should_ = "0521A82E10376F8E4FDEF9A32A427AC2A0FFF686E00290D39E3E4B5522409596";

      if (mp_read_radix(&a, a_, 16) != MP_OKAY) {
         printf("\nmp_read_radix(a) failed!");
         return EXIT_FAILURE;
      }
      if (mp_read_radix(&b, b_, 16) != MP_OKAY) {
         printf("\nmp_read_radix(b) failed!");
         return EXIT_FAILURE;
      }
      if (mp_read_radix(&c, should_, 16) != MP_OKAY) {
         printf("\nmp_read_radix(should) failed!");
         return EXIT_FAILURE;
      }

      if (mp_invmod(&a, &b, &d) != MP_OKAY) {
         printf("\nmp_invmod() failed!");
         return EXIT_FAILURE;
      }

      if (mp_cmp(&c, &d) != MP_EQ) {
         printf("\nmp_invmod() bad result!");
         return EXIT_FAILURE;
      }
   }

   /* test mp_get_double/mp_set_double */
#if defined(__STDC_IEC_559__) || defined(__GCC_IEC_559)
   printf("\n\nTesting: mp_get_double");
   if (mp_set_double(&a, +1.0/0.0) != MP_VAL) {
      printf("\nmp_set_double should return MP_VAL for +inf");
      return EXIT_FAILURE;
   }
   if (mp_set_double(&a, -1.0/0.0) != MP_VAL) {
      printf("\nmp_set_double should return MP_VAL for -inf");
      return EXIT_FAILURE;
   }
   if (mp_set_double(&a, +0.0/0.0) != MP_VAL) {
      printf("\nmp_set_double should return MP_VAL for NaN");
      return EXIT_FAILURE;
   }
   if (mp_set_double(&a, -0.0/0.0) != MP_VAL) {
      printf("\nmp_set_double should return MP_VAL for NaN");
      return EXIT_FAILURE;
   }

   for (i = 0; i < 1000; ++i) {
      int tmp = rand();
      double dbl = (double)tmp * rand() + 1;
      if (mp_set_double(&a, dbl) != MP_OKAY) {
         printf("\nmp_set_double() failed");
         return EXIT_FAILURE;
      }
      if (dbl != mp_get_double(&a)) {
         printf("\nmp_get_double() bad result!");
         return EXIT_FAILURE;
      }
      if (mp_set_double(&a, -dbl) != MP_OKAY) {
         printf("\nmp_set_double() failed");
         return EXIT_FAILURE;
      }
      if (-dbl != mp_get_double(&a)) {
         printf("\nmp_get_double() bad result!");
         return EXIT_FAILURE;
      }
   }
#endif

   /* test mp_get_int */
   printf("\n\nTesting: mp_get_int");
   for (i = 0; i < 1000; ++i) {
      t = (unsigned long)(rand() * rand() + 1) & 0xFFFFFFFFuL;
      mp_set_int(&a, t);
      if (t != mp_get_int(&a)) {
         printf("\nmp_get_int() bad result!");
         return EXIT_FAILURE;
      }
   }
   mp_set_int(&a, 0);
   if (mp_get_int(&a) != 0) {
      printf("\nmp_get_int() bad result!");
      return EXIT_FAILURE;
   }
   mp_set_int(&a, 0xFFFFFFFFuL);
   if (mp_get_int(&a) != 0xFFFFFFFFuL) {
      printf("\nmp_get_int() bad result!");
      return EXIT_FAILURE;
   }

   printf("\n\nTesting: mp_get_long\n");
   for (i = 0; i < (int)(sizeof(unsigned long)*CHAR_BIT) - 1; ++i) {
      t = (1ULL << (i+1)) - 1;
      if (!t)
         t = -1;
      printf(" t = 0x%lx i = %d\r", t, i);
      do {
         if (mp_set_long(&a, t) != MP_OKAY) {
            printf("\nmp_set_long() error!");
            return EXIT_FAILURE;
         }
         s = mp_get_long(&a);
         if (s != t) {
            printf("\nmp_get_long() bad result! 0x%lx != 0x%lx", s, t);
            return EXIT_FAILURE;
         }
         t <<= 1;
      } while (t);
   }

   printf("\n\nTesting: mp_get_long_long\n");
   for (i = 0; i < (int)(sizeof(unsigned long long)*CHAR_BIT) - 1; ++i) {
      r = (1ULL << (i+1)) - 1;
      if (!r)
         r = -1;
      printf(" r = 0x%llx i = %d\r", r, i);
      do {
         if (mp_set_long_long(&a, r) != MP_OKAY) {
            printf("\nmp_set_long_long() error!");
            return EXIT_FAILURE;
         }
         q = mp_get_long_long(&a);
         if (q != r) {
            printf("\nmp_get_long_long() bad result! 0x%llx != 0x%llx", q, r);
            return EXIT_FAILURE;
         }
         r <<= 1;
      } while (r);
   }

   /* test mp_sqrt */
   printf("\n\nTesting: mp_sqrt\n");
   for (i = 0; i < 1000; ++i) {
      printf("%6d\r", i);
      fflush(stdout);
      n = (rand() & 15) + 1;
      mp_rand(&a, n);
      if (mp_sqrt(&a, &b) != MP_OKAY) {
         printf("\nmp_sqrt() error!");
         return EXIT_FAILURE;
      }
      mp_n_root_ex(&a, 2, &c, 0);
      mp_n_root_ex(&a, 2, &d, 1);
      if (mp_cmp_mag(&c, &d) != MP_EQ) {
         printf("\nmp_n_root_ex() bad result!");
         return EXIT_FAILURE;
      }
      if (mp_cmp_mag(&b, &c) != MP_EQ) {
         printf("mp_sqrt() bad result!\n");
         return EXIT_FAILURE;
      }
   }

   printf("\n\nTesting: mp_is_square\n");
   for (i = 0; i < 1000; ++i) {
      printf("%6d\r", i);
      fflush(stdout);

      /* test mp_is_square false negatives */
      n = (rand() & 7) + 1;
      mp_rand(&a, n);
      mp_sqr(&a, &a);
      if (mp_is_square(&a, &n) != MP_OKAY) {
         printf("\nfn:mp_is_square() error!");
         return EXIT_FAILURE;
      }
      if (n == 0) {
         printf("\nfn:mp_is_square() bad result!");
         return EXIT_FAILURE;
      }

      /* test for false positives */
      mp_add_d(&a, 1uL, &a);
      if (mp_is_square(&a, &n) != MP_OKAY) {
         printf("\nfp:mp_is_square() error!");
         return EXIT_FAILURE;
      }
      if (n == 1) {
         printf("\nfp:mp_is_square() bad result!");
         return EXIT_FAILURE;
      }

   }
   printf("\n\n");

   /* r^2 = n (mod p) */
   for (i = 0; i < (int)(sizeof(sqrtmod_prime)/sizeof(sqrtmod_prime[0])); ++i) {
      mp_set_int(&a, sqrtmod_prime[i].p);
      mp_set_int(&b, sqrtmod_prime[i].n);
      if (mp_sqrtmod_prime(&b, &a, &c) != MP_OKAY) {
         printf("Failed executing %d. mp_sqrtmod_prime\n", (i+1));
         return EXIT_FAILURE;
      }
      if (mp_cmp_d(&c, sqrtmod_prime[i].r) != MP_EQ) {
         printf("Failed %d. trivial mp_sqrtmod_prime\n", (i+1));
         ndraw(&c, "r");
         return EXIT_FAILURE;
      }
   }

   /* test for size */
   for (ix = 10; ix < 128; ix++) {
      printf("Testing (not safe-prime): %9d bits    \r", ix);
      fflush(stdout);
      err = mp_prime_random_ex(&a, 8, ix,
                               (rand() & 1) ? 0 : LTM_PRIME_2MSB_ON, myrng,
                               NULL);
      if (err != MP_OKAY) {
         printf("failed with err code %d\n", err);
         return EXIT_FAILURE;
      }
      if (mp_count_bits(&a) != ix) {
         printf("Prime is %d not %d bits!!!\n", mp_count_bits(&a), ix);
         return EXIT_FAILURE;
      }
   }
   printf("\n");

   for (ix = 16; ix < 128; ix++) {
      printf("Testing (    safe-prime): %9d bits    \r", ix);
      fflush(stdout);
      err = mp_prime_random_ex(
               &a, 8, ix, ((rand() & 1) ? 0 : LTM_PRIME_2MSB_ON) | LTM_PRIME_SAFE,
               myrng, NULL);
      if (err != MP_OKAY) {
         printf("failed with err code %d\n", err);
         return EXIT_FAILURE;
      }
      if (mp_count_bits(&a) != ix) {
         printf("Prime is %d not %d bits!!!\n", mp_count_bits(&a), ix);
         return EXIT_FAILURE;
      }
      /* let's see if it's really a safe prime */
      mp_sub_d(&a, 1uL, &a);
      mp_div_2(&a, &a);
      mp_prime_is_prime(&a, 8, &cnt);
      if (cnt != MP_YES) {
         printf("sub is not prime!\n");
         return EXIT_FAILURE;
      }
   }

   printf("\n\n");

   /* test montgomery */
   printf("Testing: montgomery...\n");
   for (i = 1; i <= 10; i++) {
      if (i == 10)
         i = 1000;
      printf(" digit size: %2d\r", i);
      fflush(stdout);
      for (n = 0; n < 1000; n++) {
         mp_rand(&a, i);
         a.dp[0] |= 1;

         /* let's see if R is right */
         mp_montgomery_calc_normalization(&b, &a);
         mp_montgomery_setup(&a, &mp);

         /* now test a random reduction */
         for (ix = 0; ix < 100; ix++) {
            mp_rand(&c, 1 + abs(rand()) % (2*i));
            mp_copy(&c, &d);
            mp_copy(&c, &e);

            mp_mod(&d, &a, &d);
            mp_montgomery_reduce(&c, &a, mp);
            mp_mulmod(&c, &b, &a, &c);

            if (mp_cmp(&c, &d) != MP_EQ) {
/* *INDENT-OFF* */
printf("d = e mod a, c = e MOD a\n");
mp_todecimal(&a, buf); printf("a = %s\n", buf);
mp_todecimal(&e, buf); printf("e = %s\n", buf);
mp_todecimal(&d, buf); printf("d = %s\n", buf);
mp_todecimal(&c, buf); printf("c = %s\n", buf);
printf("compare no compare!\n"); return EXIT_FAILURE;
/* *INDENT-ON* */
            }
            /* only one big montgomery reduction */
            if (i > 10) {
               n = 1000;
               ix = 100;
            }
         }
      }
   }

   printf("\n\n");

   mp_read_radix(&a, "123456", 10);
   mp_toradix_n(&a, buf, 10, 3);
   printf("a == %s\n", buf);
   mp_toradix_n(&a, buf, 10, 4);
   printf("a == %s\n", buf);
   mp_toradix_n(&a, buf, 10, 30);
   printf("a == %s\n", buf);


#if 0
   for (;;) {
      fgets(buf, sizeof(buf), stdin);
      mp_read_radix(&a, buf, 10);
      mp_prime_next_prime(&a, 5, 1);
      mp_toradix(&a, buf, 10);
      printf("%s, %lu\n", buf, a.dp[0] & 3);
   }
#endif

   /* test mp_cnt_lsb */
   printf("\n\nTesting: mp_cnt_lsb");
   mp_set(&a, 1uL);
   for (ix = 0; ix < 1024; ix++) {
      if (mp_cnt_lsb(&a) != ix) {
         printf("Failed at %d, %d\n", ix, mp_cnt_lsb(&a));
         return EXIT_FAILURE;
      }
      mp_mul_2(&a, &a);
   }

   /* test mp_reduce_2k */
   printf("\n\nTesting: mp_reduce_2k\n");
   for (cnt = 3; cnt <= 128; ++cnt) {
      mp_digit tmp;

      mp_2expt(&a, cnt);
      mp_sub_d(&a, 2uL, &a);  /* a = 2**cnt - 2 */

      printf("\r %4d bits", cnt);
      printf("(%d)", mp_reduce_is_2k(&a));
      mp_reduce_2k_setup(&a, &tmp);
      printf("(%lu)", (unsigned long) tmp);
      for (ix = 0; ix < 1000; ix++) {
         if (!(ix & 127)) {
            printf(".");
            fflush(stdout);
         }
         mp_rand(&b, (cnt / DIGIT_BIT + 1) * 2);
         mp_copy(&c, &b);
         mp_mod(&c, &a, &c);
         mp_reduce_2k(&b, &a, 2uL);
         if (mp_cmp(&c, &b)) {
            printf("FAILED\n");
            return EXIT_FAILURE;
         }
      }
   }

   /* test mp_div_3  */
   printf("\n\nTesting: mp_div_3...\n");
   mp_set(&d, 3uL);
   for (cnt = 0; cnt < 10000;) {
      mp_digit r2;

      if (!(++cnt & 127)) {
         printf("%9d\r", cnt);
         fflush(stdout);
      }
      mp_rand(&a, abs(rand()) % 128 + 1);
      mp_div(&a, &d, &b, &e);
      mp_div_3(&a, &c, &r2);

      if (mp_cmp(&b, &c) || mp_cmp_d(&e, r2)) {
         printf("\nmp_div_3 => Failure\n");
      }
   }
   printf("\nPassed div_3 testing");

   /* test the DR reduction */
   printf("\n\nTesting: mp_dr_reduce...\n");
   for (cnt = 2; cnt < 32; cnt++) {
      printf("\r%d digit modulus", cnt);
      mp_grow(&a, cnt);
      mp_zero(&a);
      for (ix = 1; ix < cnt; ix++) {
         a.dp[ix] = MP_MASK;
      }
      a.used = cnt;
      a.dp[0] = 3;

      mp_rand(&b, cnt - 1);
      mp_copy(&b, &c);

      rr = 0;
      do {
         if (!(rr & 127)) {
            printf(".");
            fflush(stdout);
         }
         mp_sqr(&b, &b);
         mp_add_d(&b, 1uL, &b);
         mp_copy(&b, &c);

         mp_mod(&b, &a, &b);
         mp_dr_setup(&a, &mp),
                     mp_dr_reduce(&c, &a, mp);

         if (mp_cmp(&b, &c) != MP_EQ) {
            printf("Failed on trial %u\n", rr);
            return EXIT_FAILURE;
         }
      } while (++rr < 500);
      printf(" passed");
      fflush(stdout);
   }

#   if LTM_DEMO_TEST_REDUCE_2K_L
   /* test the mp_reduce_2k_l code */
#      if LTM_DEMO_TEST_REDUCE_2K_L == 1
   /* first load P with 2^1024 - 0x2A434 B9FDEC95 D8F9D550 FFFFFFFF FFFFFFFF */
   mp_2expt(&a, 1024);
   mp_read_radix(&b, "2A434B9FDEC95D8F9D550FFFFFFFFFFFFFFFF", 16);
   mp_sub(&a, &b, &a);
#      elif LTM_DEMO_TEST_REDUCE_2K_L == 2
   /*  p = 2^2048 - 0x1 00000000 00000000 00000000 00000000 4945DDBF 8EA2A91D 5776399B B83E188F  */
   mp_2expt(&a, 2048);
   mp_read_radix(&b,
                 "1000000000000000000000000000000004945DDBF8EA2A91D5776399BB83E188F",
                 16);
   mp_sub(&a, &b, &a);
#      else
#         error oops
#      endif

   mp_todecimal(&a, buf);
   printf("\n\np==%s\n", buf);
   /* now mp_reduce_is_2k_l() should return */
   if (mp_reduce_is_2k_l(&a) != 1) {
      printf("mp_reduce_is_2k_l() return 0, should be 1\n");
      return EXIT_FAILURE;
   }
   mp_reduce_2k_setup_l(&a, &d);
   /* now do a million square+1 to see if it varies */
   mp_rand(&b, 64);
   mp_mod(&b, &a, &b);
   mp_copy(&b, &c);
   printf("Testing: mp_reduce_2k_l...");
   fflush(stdout);
   for (cnt = 0; cnt < (int)(1UL << 20); cnt++) {
      mp_sqr(&b, &b);
      mp_add_d(&b, 1uL, &b);
      mp_reduce_2k_l(&b, &a, &d);
      mp_sqr(&c, &c);
      mp_add_d(&c, 1uL, &c);
      mp_mod(&c, &a, &c);
      if (mp_cmp(&b, &c) != MP_EQ) {
         printf("mp_reduce_2k_l() failed at step %d\n", cnt);
         mp_tohex(&b, buf);
         printf("b == %s\n", buf);
         mp_tohex(&c, buf);
         printf("c == %s\n", buf);
         return EXIT_FAILURE;
      }
   }
   printf("...Passed\n");
#   endif /* LTM_DEMO_TEST_REDUCE_2K_L */

#else
   div2_n = mul2_n = inv_n = expt_n = lcm_n = gcd_n = add_n =
                                         sub_n = mul_n = div_n = sqr_n = mul2d_n = div2d_n = cnt = add_d_n = sub_d_n = 0;

   /* force KARA and TOOM to enable despite cutoffs */
   KARATSUBA_SQR_CUTOFF = KARATSUBA_MUL_CUTOFF = 8;
   TOOM_SQR_CUTOFF = TOOM_MUL_CUTOFF = 16;

   for (;;) {
      /* randomly clear and re-init one variable, this has the affect of triming the alloc space */
      switch (abs(rand()) % 7) {
      case 0:
         mp_clear(&a);
         mp_init(&a);
         break;
      case 1:
         mp_clear(&b);
         mp_init(&b);
         break;
      case 2:
         mp_clear(&c);
         mp_init(&c);
         break;
      case 3:
         mp_clear(&d);
         mp_init(&d);
         break;
      case 4:
         mp_clear(&e);
         mp_init(&e);
         break;
      case 5:
         mp_clear(&f);
         mp_init(&f);
         break;
      case 6:
         break;        /* don't clear any */
      }


      printf("%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu ",
             add_n, sub_n, mul_n, div_n, sqr_n, mul2d_n, div2d_n, gcd_n, lcm_n,
             expt_n, inv_n, div2_n, mul2_n, add_d_n, sub_d_n);
      FGETS(cmd, 4095, stdin);
      cmd[strlen(cmd) - 1u] = '\0';
      printf("%-6s ]\r", cmd);
      fflush(stdout);
      if (strcmp(cmd, "mul2d") == 0) {
         ++mul2d_n;
         FGETS(buf, 4095, stdin);
         mp_read_radix(&a, buf, 64);
         FGETS(buf, 4095, stdin);
         sscanf(buf, "%u", &rr);
         FGETS(buf, 4095, stdin);
         mp_read_radix(&b, buf, 64);

         mp_mul_2d(&a, rr, &a);
         a.sign = b.sign;
         if (mp_cmp(&a, &b) != MP_EQ) {
            printf("mul2d failed, rr == %u\n", rr);
            draw(&a);
            draw(&b);
            return EXIT_FAILURE;
         }
      } else if (strcmp(cmd, "div2d") == 0) {
         ++div2d_n;
         FGETS(buf, 4095, stdin);
         mp_read_radix(&a, buf, 64);
         FGETS(buf, 4095, stdin);
         sscanf(buf, "%u", &rr);
         FGETS(buf, 4095, stdin);
         mp_read_radix(&b, buf, 64);

         mp_div_2d(&a, rr, &a, &e);
         a.sign = b.sign;
         if ((a.used == b.used) && (a.used == 0)) {
            a.sign = b.sign = MP_ZPOS;
         }
         if (mp_cmp(&a, &b) != MP_EQ) {
            printf("div2d failed, rr == %u\n", rr);
            draw(&a);
            draw(&b);
            return EXIT_FAILURE;
         }
      } else if (strcmp(cmd, "add") == 0) {
         ++add_n;
         FGETS(buf, 4095, stdin);
         mp_read_radix(&a, buf, 64);
         FGETS(buf, 4095, stdin);
         mp_read_radix(&b, buf, 64);
         FGETS(buf, 4095, stdin);
         mp_read_radix(&c, buf, 64);
         mp_copy(&a, &d);
         mp_add(&d, &b, &d);
         if (mp_cmp(&c, &d) != MP_EQ) {
            printf("add %lu failure!\n", add_n);
            draw(&a);
            draw(&b);
            draw(&c);
            draw(&d);
            return EXIT_FAILURE;
         }

         /* test the sign/unsigned storage functions */

         rr = mp_signed_bin_size(&c);
         mp_to_signed_bin(&c, (unsigned char *) cmd);
         memset(cmd + rr, rand() & 0xFFu, sizeof(cmd) - rr);
         mp_read_signed_bin(&d, (unsigned char *) cmd, rr);
         if (mp_cmp(&c, &d) != MP_EQ) {
            printf("mp_signed_bin failure!\n");
            draw(&c);
            draw(&d);
            return EXIT_FAILURE;
         }


         rr = mp_unsigned_bin_size(&c);
         mp_to_unsigned_bin(&c, (unsigned char *) cmd);
         memset(cmd + rr, rand() & 0xFFu, sizeof(cmd) - rr);
         mp_read_unsigned_bin(&d, (unsigned char *) cmd, rr);
         if (mp_cmp_mag(&c, &d) != MP_EQ) {
            printf("mp_unsigned_bin failure!\n");
            draw(&c);
            draw(&d);
            return EXIT_FAILURE;
         }

      } else if (strcmp(cmd, "sub") == 0) {
         ++sub_n;
         FGETS(buf, 4095, stdin);
         mp_read_radix(&a, buf, 64);
         FGETS(buf, 4095, stdin);
         mp_read_radix(&b, buf, 64);
         FGETS(buf, 4095, stdin);
         mp_read_radix(&c, buf, 64);
         mp_copy(&a, &d);
         mp_sub(&d, &b, &d);
         if (mp_cmp(&c, &d) != MP_EQ) {
            printf("sub %lu failure!\n", sub_n);
            draw(&a);
            draw(&b);
            draw(&c);
            draw(&d);
            return EXIT_FAILURE;
         }
      } else if (strcmp(cmd, "mul") == 0) {
         ++mul_n;
         FGETS(buf, 4095, stdin);
         mp_read_radix(&a, buf, 64);
         FGETS(buf, 4095, stdin);
         mp_read_radix(&b, buf, 64);
         FGETS(buf, 4095, stdin);
         mp_read_radix(&c, buf, 64);
         mp_copy(&a, &d);
         mp_mul(&d, &b, &d);
         if (mp_cmp(&c, &d) != MP_EQ) {
            printf("mul %lu failure!\n", mul_n);
            draw(&a);
            draw(&b);
            draw(&c);
            draw(&d);
            return EXIT_FAILURE;
         }
      } else if (strcmp(cmd, "div") == 0) {
         ++div_n;
         FGETS(buf, 4095, stdin);
         mp_read_radix(&a, buf, 64);
         FGETS(buf, 4095, stdin);
         mp_read_radix(&b, buf, 64);
         FGETS(buf, 4095, stdin);
         mp_read_radix(&c, buf, 64);
         FGETS(buf, 4095, stdin);
         mp_read_radix(&d, buf, 64);

         mp_div(&a, &b, &e, &f);
         if ((mp_cmp(&c, &e) != MP_EQ) || (mp_cmp(&d, &f) != MP_EQ)) {
            printf("div %lu %d, %d, failure!\n", div_n, mp_cmp(&c, &e),
                   mp_cmp(&d, &f));
            draw(&a);
            draw(&b);
            draw(&c);
            draw(&d);
            draw(&e);
            draw(&f);
            return EXIT_FAILURE;
         }

      } else if (strcmp(cmd, "sqr") == 0) {
         ++sqr_n;
         FGETS(buf, 4095, stdin);
         mp_read_radix(&a, buf, 64);
         FGETS(buf, 4095, stdin);
         mp_read_radix(&b, buf, 64);
         mp_copy(&a, &c);
         mp_sqr(&c, &c);
         if (mp_cmp(&b, &c) != MP_EQ) {
            printf("sqr %lu failure!\n", sqr_n);
            draw(&a);
            draw(&b);
            draw(&c);
            return EXIT_FAILURE;
         }
      } else if (strcmp(cmd, "gcd") == 0) {
         ++gcd_n;
         FGETS(buf, 4095, stdin);
         mp_read_radix(&a, buf, 64);
         FGETS(buf, 4095, stdin);
         mp_read_radix(&b, buf, 64);
         FGETS(buf, 4095, stdin);
         mp_read_radix(&c, buf, 64);
         mp_copy(&a, &d);
         mp_gcd(&d, &b, &d);
         d.sign = c.sign;
         if (mp_cmp(&c, &d) != MP_EQ) {
            printf("gcd %lu failure!\n", gcd_n);
            draw(&a);
            draw(&b);
            draw(&c);
            draw(&d);
            return EXIT_FAILURE;
         }
      } else if (strcmp(cmd, "lcm") == 0) {
         ++lcm_n;
         FGETS(buf, 4095, stdin);
         mp_read_radix(&a, buf, 64);
         FGETS(buf, 4095, stdin);
         mp_read_radix(&b, buf, 64);
         FGETS(buf, 4095, stdin);
         mp_read_radix(&c, buf, 64);
         mp_copy(&a, &d);
         mp_lcm(&d, &b, &d);
         d.sign = c.sign;
         if (mp_cmp(&c, &d) != MP_EQ) {
            printf("lcm %lu failure!\n", lcm_n);
            draw(&a);
            draw(&b);
            draw(&c);
            draw(&d);
            return EXIT_FAILURE;
         }
      } else if (strcmp(cmd, "expt") == 0) {
         ++expt_n;
         FGETS(buf, 4095, stdin);
         mp_read_radix(&a, buf, 64);
         FGETS(buf, 4095, stdin);
         mp_read_radix(&b, buf, 64);
         FGETS(buf, 4095, stdin);
         mp_read_radix(&c, buf, 64);
         FGETS(buf, 4095, stdin);
         mp_read_radix(&d, buf, 64);
         mp_copy(&a, &e);
         mp_exptmod(&e, &b, &c, &e);
         if (mp_cmp(&d, &e) != MP_EQ) {
            printf("expt %lu failure!\n", expt_n);
            draw(&a);
            draw(&b);
            draw(&c);
            draw(&d);
            draw(&e);
            return EXIT_FAILURE;
         }
      } else if (strcmp(cmd, "invmod") == 0) {
         ++inv_n;
         FGETS(buf, 4095, stdin);
         mp_read_radix(&a, buf, 64);
         FGETS(buf, 4095, stdin);
         mp_read_radix(&b, buf, 64);
         FGETS(buf, 4095, stdin);
         mp_read_radix(&c, buf, 64);
         mp_invmod(&a, &b, &d);
         mp_mulmod(&d, &a, &b, &e);
         if (mp_cmp_d(&e, 1uL) != MP_EQ) {
            printf("inv [wrong value from MPI?!] failure\n");
            draw(&a);
            draw(&b);
            draw(&c);
            draw(&d);
            draw(&e);
            mp_gcd(&a, &b, &e);
            draw(&e);
            return EXIT_FAILURE;
         }

      } else if (strcmp(cmd, "div2") == 0) {
         ++div2_n;
         FGETS(buf, 4095, stdin);
         mp_read_radix(&a, buf, 64);
         FGETS(buf, 4095, stdin);
         mp_read_radix(&b, buf, 64);
         mp_div_2(&a, &c);
         if (mp_cmp(&c, &b) != MP_EQ) {
            printf("div_2 %lu failure\n", div2_n);
            draw(&a);
            draw(&b);
            draw(&c);
            return EXIT_FAILURE;
         }
      } else if (strcmp(cmd, "mul2") == 0) {
         ++mul2_n;
         FGETS(buf, 4095, stdin);
         mp_read_radix(&a, buf, 64);
         FGETS(buf, 4095, stdin);
         mp_read_radix(&b, buf, 64);
         mp_mul_2(&a, &c);
         if (mp_cmp(&c, &b) != MP_EQ) {
            printf("mul_2 %lu failure\n", mul2_n);
            draw(&a);
            draw(&b);
            draw(&c);
            return EXIT_FAILURE;
         }
      } else if (strcmp(cmd, "add_d") == 0) {
         ++add_d_n;
         FGETS(buf, 4095, stdin);
         mp_read_radix(&a, buf, 64);
         FGETS(buf, 4095, stdin);
         sscanf(buf, "%d", &ix);
         FGETS(buf, 4095, stdin);
         mp_read_radix(&b, buf, 64);
         mp_add_d(&a, ix, &c);
         if (mp_cmp(&b, &c) != MP_EQ) {
            printf("add_d %lu failure\n", add_d_n);
            draw(&a);
            draw(&b);
            draw(&c);
            printf("d == %d\n", ix);
            return EXIT_FAILURE;
         }
      } else if (strcmp(cmd, "sub_d") == 0) {
         ++sub_d_n;
         FGETS(buf, 4095, stdin);
         mp_read_radix(&a, buf, 64);
         FGETS(buf, 4095, stdin);
         sscanf(buf, "%d", &ix);
         FGETS(buf, 4095, stdin);
         mp_read_radix(&b, buf, 64);
         mp_sub_d(&a, ix, &c);
         if (mp_cmp(&b, &c) != MP_EQ) {
            printf("sub_d %lu failure\n", sub_d_n);
            draw(&a);
            draw(&b);
            draw(&c);
            printf("d == %d\n", ix);
            return EXIT_FAILURE;
         }
      } else if (strcmp(cmd, "exit") == 0) {
         printf("\nokay, exiting now\n");
         break;
      }
   }
#endif
   return 0;
}

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */