tommath/demo/demo.c

#include <time.h>

#ifdef IOWNANATHLON
#include <unistd.h>
#define SLEEP sleep(4)
#else
#define SLEEP
#endif

#include "tommath.h"

void ndraw(mp_int *a, char *name)
{
   char buf[4096];
   printf("%s: ", name);
   mp_toradix(a, buf, 64);
   printf("%s\n", buf);
}

static void draw(mp_int *a)
{
   ndraw(a, "");
}


unsigned long lfsr = 0xAAAAAAAAUL;

int lbit(void)
{
   if (lfsr & 0x80000000UL) {
      lfsr = ((lfsr << 1) ^ 0x8000001BUL) & 0xFFFFFFFFUL;
      return 1;
   } else {
      lfsr <<= 1;
      return 0;
   }
}

int myrng(unsigned char *dst, int len, void *dat)
{
   int x;
   for (x = 0; x < len; x++) dst[x] = rand() & 0xFF;
   return len;
}



   char cmd[4096], buf[4096];
int main(void)
{
   mp_int a, b, c, d, e, f;
   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, t;
   unsigned rr;
   int i, n, err, cnt, ix, old_kara_m, old_kara_s;


   mp_init(&a);
   mp_init(&b);
   mp_init(&c);
   mp_init(&d);
   mp_init(&e);
   mp_init(&f);

   srand(time(NULL));

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

  // test mp_sqrt
  printf("Testing: 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("mp_sqrt() error!\n");
      return 1;
    }
    mp_n_root(&a,2,&a);
    if (mp_cmp_mag(&b,&a) != MP_EQ)
    { printf("mp_sqrt() bad result!\n");
      return 1;
    }
  }

  printf("\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("fn:mp_is_square() error!\n");
      return 1;
    }
    if (n==0) { 
      printf("fn:mp_is_square() bad result!\n");
      return 1;
    }

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

  }
  printf("\n\n");

   /* test for size */
   for (ix = 10; ix < 256; ix++) {
       printf("Testing (not safe-prime): %9d bits    \r", ix); fflush(stdout);
       err = mp_prime_random_ex(&a, 8, ix, (rand()&1)?LTM_PRIME_2MSB_OFF: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;
       }
   }

   for (ix = 16; ix < 256; ix++) {
       printf("Testing (   safe-prime): %9d bits    \r", ix); fflush(stdout);
       err = mp_prime_random_ex(&a, 8, ix, ((rand()&1)?LTM_PRIME_2MSB_OFF: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, 1, &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");

   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("testing mp_cnt_lsb...\n");
   mp_set(&a, 1);
   for (ix = 0; ix < 1024; ix++) {
       if (mp_cnt_lsb(&a) != ix) {
          printf("Failed at %d, %d\n", ix, mp_cnt_lsb(&a));
          return 0;
       }
       mp_mul_2(&a, &a);
   }

/* test mp_reduce_2k */
   printf("Testing mp_reduce_2k...\n");
   for (cnt = 3; cnt <= 128; ++cnt) {
       mp_digit tmp;
       mp_2expt(&a, cnt);
       mp_sub_d(&a, 2, &a);  /* a = 2**cnt - 2 */


       printf("\nTesting %4d bits", cnt);
       printf("(%d)", mp_reduce_is_2k(&a));
       mp_reduce_2k_setup(&a, &tmp);
       printf("(%d)", 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, 1);
           if (mp_cmp(&c, &b)) {
              printf("FAILED\n");
              exit(0);
           }
        }
    }

/* test mp_div_3  */
   printf("Testing mp_div_3...\n");
   mp_set(&d, 3);
   for (cnt = 0; cnt < 10000; ) {
      mp_digit r1, r2;

      if (!(++cnt & 127)) printf("%9d\r", cnt);
      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("\n\nmp_div_3 => Failure\n");
      }
   }
   printf("\n\nPassed div_3 testing\n");

/* test the DR reduction */
   printf("testing mp_dr_reduce...\n");
   for (cnt = 2; cnt < 32; cnt++) {
       printf("%d digit modulus\n", 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("%9lu\r", rr); fflush(stdout); }
         mp_sqr(&b, &b); mp_add_d(&b, 1, &b);
         mp_copy(&b, &c);

         mp_mod(&b, &a, &b);
         mp_dr_reduce(&c, &a, (((mp_digit)1)<<DIGIT_BIT)-a.dp[0]);

         if (mp_cmp(&b, &c) != MP_EQ) {
            printf("Failed on trial %lu\n", rr); exit(-1);

         }
      } while (++rr < 500);
      printf("Passed DR test for %d digits\n", cnt);
   }

#endif

   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 = 110;
   TOOM_SQR_CUTOFF      = TOOM_MUL_CUTOFF      = 150;

   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)-1] = 0;
       printf("%s  ]\r",cmd); fflush(stdout);
       if (!strcmp(cmd, "mul2d")) { ++mul2d_n;
          fgets(buf, 4095, stdin); mp_read_radix(&a, buf, 64);
          fgets(buf, 4095, stdin); sscanf(buf, "%d", &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 == %d\n",rr);
             draw(&a);
             draw(&b);
             return 0;
          }
       } else if (!strcmp(cmd, "div2d")) { ++div2d_n;
          fgets(buf, 4095, stdin); mp_read_radix(&a, buf, 64);
          fgets(buf, 4095, stdin); sscanf(buf, "%d", &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 == %d\n",rr);
             draw(&a);
             draw(&b);
             return 0;
          }
       } else if (!strcmp(cmd, "add")) { ++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 0;
          }

          /* test the sign/unsigned storage functions */

          rr = mp_signed_bin_size(&c);
          mp_to_signed_bin(&c, (unsigned char *)cmd);
          memset(cmd+rr, rand()&255, 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 0;
          }


          rr = mp_unsigned_bin_size(&c);
          mp_to_unsigned_bin(&c, (unsigned char *)cmd);
          memset(cmd+rr, rand()&255, 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 0;
          }

       } else if (!strcmp(cmd, "sub")) { ++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 0;
          }
       } else if (!strcmp(cmd, "mul")) { ++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 0;
          }
       } else if (!strcmp(cmd, "div")) { ++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 failure!\n", div_n);
draw(&a);draw(&b);draw(&c);draw(&d); draw(&e); draw(&f);
             return 0;
          }

       } else if (!strcmp(cmd, "sqr")) { ++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 0;
          }
       } else if (!strcmp(cmd, "gcd")) { ++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 0;
          }
       } else if (!strcmp(cmd, "lcm")) { ++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 0;
             }
       } else if (!strcmp(cmd, "expt")) {  ++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 0;
             }
       } else if (!strcmp(cmd, "invmod")) {  ++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, 1) != MP_EQ) {
                printf("inv [wrong value from MPI?!] failure\n");
                draw(&a);draw(&b);draw(&c);draw(&d);
                mp_gcd(&a, &b, &e);
                draw(&e);
                return 0;
             }

       } else if (!strcmp(cmd, "div2")) { ++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 0;
             }
       } else if (!strcmp(cmd, "mul2")) { ++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 0;
             }
       } else if (!strcmp(cmd, "add_d")) { ++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 0;
              }
       } else if (!strcmp(cmd, "sub_d")) { ++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 0;
              }
       }
   }
   return 0;
}