Import of tommath 0.35

1 files changed, 598 insertions, 377 deletions

diff --git a/libtommath/demo/demo.c b/libtommath/demo/demo.c
index 62615cd..0a6115a 100644
--- a/libtommath/demo/demo.c
+++ b/libtommath/demo/demo.c
@@ -9,15 +9,16 @@
 
 #include "tommath.h"
 
-void ndraw(mp_int *a, char *name)
+void ndraw(mp_int * a, char *name)
 {
    char buf[16000];
+
    printf("%s: ", name);
    mp_toradix(a, buf, 10);
    printf("%s\n", buf);
 }
 
-static void draw(mp_int *a)
+static void draw(mp_int * a)
 {
    ndraw(a, "");
 }
@@ -39,20 +40,23 @@ int lbit(void)
 int myrng(unsigned char *dst, int len, void *dat)
 {
    int x;
-   for (x = 0; x < len; x++) dst[x] = rand() & 0xFF;
+
+   for (x = 0; x < len; x++)
+      dst[x] = rand() & 0xFF;
    return len;
 }
 
 
 
-   char cmd[4096], buf[4096];
+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 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_digit mp;
 
 
    mp_init(&a);
@@ -65,108 +69,152 @@ int main(void)
    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)) { 
+   // test montgomery 
+   printf("Testing montgomery...\n");
+   for (i = 1; i < 10; i++) {
+      printf("Testing digit size: %d\n", i);
+      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) { 
+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"); exit(EXIT_FAILURE); }
+         }
+      }
+   }
+   printf("done\n");
+
+   // 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,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");
+   }
+   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;
+      }
+   }
 
-    /* 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("\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;
+      }
 
-  }
-  printf("\n\n");
+      /* 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 = 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) ? 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;
-       }
+   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) ? 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");
@@ -194,51 +242,56 @@ int main(void)
    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);
+      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);
-           }
-        }
-    }
+      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, 2);
+	 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; ) {
+   for (cnt = 0; cnt < 10000;) {
       mp_digit r1, r2;
 
-      if (!(++cnt & 127)) printf("%9d\r", cnt);
+      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\nmp_div_3 => Failure\n");
       }
    }
    printf("\n\nPassed div_3 testing\n");
@@ -246,270 +299,438 @@ int main(void)
 /* 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);
+      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);
-
-         }
+	 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
 
+/* test the mp_reduce_2k_l code */
+#if 0
+#if 0
+/* 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 1
+/*  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);
+#endif
+
+   mp_todecimal(&a, buf);
+   printf("p==%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 < (1UL << 20); cnt++) {
+      mp_sqr(&b, &b);
+      mp_add_d(&b, 1, &b);
+      mp_reduce_2k_l(&b, &a, &d);
+      mp_sqr(&c, &c);
+      mp_add_d(&c, 1, &c);
+      mp_mod(&c, &a, &c);
+      if (mp_cmp(&b, &c) != MP_EQ) {
+	 printf("mp_reduce_2k_l() failed at step %lu\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
+
    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;
+      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;
+   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 %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 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;
-              }
-       }
+      /* 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 %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 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;
 }
-