Beispiel #1
0
void
checkprimes (unsigned long p1, unsigned long p2, unsigned long p3)
{
  mpz_t          b, f;

  if (p1 - 1 != p2 - 1 + p3 - 1)
    {
      printf ("checkprimes(%lu, %lu, %lu) wrong\n", p1, p2, p3);
      printf (" %lu - 1 != %lu - 1 + %lu - 1 \n", p1, p2, p3);
      abort ();
    }

  mpz_init (b);
  mpz_init (f);

  checkWilson (b, p1); /* b = (p1-1)! */
  checkWilson (f, p2); /* f = (p2-1)! */
  mpz_divexact (b, b, f);
  checkWilson (f, p3); /* f = (p3-1)! */
  mpz_divexact (b, b, f); /* b = (p1-1)!/((p2-1)!(p3-1)!) */
  mpz_bin_uiui (f, p1 - 1, p2 - 1);
  if (mpz_cmp (f, b) != 0)
    {
      printf ("checkprimes(%lu, %lu, %lu) wrong\n", p1, p2, p3);
      printf ("  got  "); mpz_out_str (stdout, 10, b); printf("\n");
      printf ("  want "); mpz_out_str (stdout, 10, f); printf("\n");
      abort ();
    }

  mpz_clear (b);
  mpz_clear (f);

}
Beispiel #2
0
int bern41_acceptable(mpz_t n, UV r, UV s, mpz_t t1, mpz_t t2)
{
  double scmp = ceil(sqrt( (r-1)/3.0 )) * mpz_log2(n);
  UV d = (UV) (0.5 * (r-1));
  UV i = (UV) (0.475 * (r-1));
  UV j = i;
  /* Ensure conditions are correct */
  if (d > r-2)     d = r-2;
  if (i > d)       i = d;
  if (j > (r-2-d)) j = r-2-d;

  mpz_bin_uiui(t2, 2*s, i);
  mpz_bin_uiui(t1, d, i);       mpz_mul(t2, t2, t1);
  mpz_bin_uiui(t1, 2*s-i, j);   mpz_mul(t2, t2, t1);
  mpz_bin_uiui(t1, r-2-d, j);   mpz_mul(t2, t2, t1);
  return (mpz_log2(t2) >= scmp);
}
Beispiel #3
0
int main(int argc, char **argv)
{
	unsigned long i, j;
	int tally;
	mpz_t n;

	mpz_init(n);
	tally = 0;
	for (i = 1; i <= 100; i++)
		for (j = 1; j <= i; j++) {
			mpz_bin_uiui(n, i, j);
			if (mpz_cmp_ui(n, 1000000) > 0)
				tally++;
		}
	printf("%d\n", tally);
	return EXIT_SUCCESS;
}
Beispiel #4
0
void
try_mpz_bin_uiui (mpz_srcptr want, unsigned long n, unsigned long k)
{
  mpz_t  got;

  mpz_init (got);
  mpz_bin_uiui (got, n, k);
  if (mpz_cmp (got, want) != 0)
    {
      printf ("mpz_bin_uiui wrong\n");
      printf ("  n=%lu\n", n);
      printf ("  k=%lu\n", k);
      printf ("  got="); mpz_out_str (stdout, 10, got); printf ("\n");
      printf ("  want="); mpz_out_str (stdout, 10, want); printf ("\n");
      abort();
    }
  mpz_clear (got);
}
Beispiel #5
0
int main(void)
{
	/* The number of paths from the origin to (a, b) is given by the binomial
	 * coefficient (a + b over b), which in this case is (40 over 20).
	 * This is equal to 40! / 20! * (40 - 20)!
	 */

	mpz_t x;
	mpz_init(x);

	mpz_bin_uiui(x, 40, 20);

	mpz_out_str(stdout, 10, x);

	mpz_clear(x);

	return 0;
}
Beispiel #6
0
static PyObject *
GMPy_MPZ_Function_Bincoef(PyObject *self, PyObject *args)
{
    MPZ_Object *result = NULL, *tempx;
    unsigned long n, k;

    if (PyTuple_GET_SIZE(args) != 2) {
        TYPE_ERROR("bincoef() requires two integer arguments");
        return NULL;
    }

    if (!(result = GMPy_MPZ_New(NULL))) {
        /* LCOV_EXCL_START */
        return NULL;
        /* LCOV_EXCL_STOP */
    }

    k = c_ulong_From_Integer(PyTuple_GET_ITEM(args, 1));
    if (k == (unsigned long)(-1) && PyErr_Occurred()) {
        Py_DECREF((PyObject*)result);
        return NULL;
    }

    n = c_ulong_From_Integer(PyTuple_GET_ITEM(args, 0));
    if (!(n == (unsigned long)(-1) && PyErr_Occurred())) {
        /* Use mpz_bin_uiui which should be faster. */
        mpz_bin_uiui(result->z, n, k);
        return (PyObject*)result;
    }

    if (!(tempx = GMPy_MPZ_From_Integer(PyTuple_GET_ITEM(args, 0), NULL))) {
        Py_DECREF((PyObject*)result);
        return NULL;
    }

    mpz_bin_ui(result->z, tempx->z, k);
    Py_DECREF((PyObject*)tempx);
    return (PyObject*)result;
}
Beispiel #7
0
/* returns 0 on success		*/
int
gen_consts (int numb, int nail, int limb)
{
  mpz_t x, mask, y, last;
  unsigned long a, b;
  unsigned long ofl, ofe;

  printf ("/* This file is automatically generated by gen-fac.c */\n\n");
  printf ("#if GMP_NUMB_BITS != %d\n", numb);
  printf ("Error , error this data is for %d GMP_NUMB_BITS only\n", numb);
  printf ("#endif\n");
#if 0
  printf ("#if GMP_LIMB_BITS != %d\n", limb);
  printf ("Error , error this data is for %d GMP_LIMB_BITS only\n", limb);
  printf ("#endif\n");
#endif

  printf
    ("/* This table is 0!,1!,2!,3!,...,n! where n! has <= GMP_NUMB_BITS bits */\n");
  printf
    ("#define ONE_LIMB_FACTORIAL_TABLE CNST_LIMB(0x1),CNST_LIMB(0x1");
  mpz_init_set_ui (x, 1);
  mpz_init (last);
  for (b = 2;; b++)
    {
      mpz_mul_ui (x, x, b);	/* so b!=a       */
      if (mpz_sizeinbase (x, 2) > numb)
	break;
      printf ("),CNST_LIMB(0x");
      mpz_out_str (stdout, 16, x);
    }
  printf (")\n");

  printf
    ("\n/* This table is 0!,1!,2!/2,3!/2,...,n!/2^sn where n!/2^sn is an */\n");
  printf
    ("/* odd integer for each n, and n!/2^sn has <= GMP_NUMB_BITS bits */\n");
  printf
    ("#define ONE_LIMB_ODD_FACTORIAL_TABLE CNST_LIMB(0x1),CNST_LIMB(0x1),CNST_LIMB(0x1");
  mpz_set_ui (x, 1);
  for (b = 3;; b++)
    {
      for (a = b; (a & 1) == 0; a >>= 1);
      mpz_swap (last, x);
      mpz_mul_ui (x, last, a);
      if (mpz_sizeinbase (x, 2) > numb)
	break;
      printf ("),CNST_LIMB(0x");
      mpz_out_str (stdout, 16, x);
    }
  printf (")\n");
  printf
    ("#define ODD_FACTORIAL_TABLE_MAX CNST_LIMB(0x");
  mpz_out_str (stdout, 16, last);
  printf (")\n");

  ofl = b - 1;
  printf
    ("#define ODD_FACTORIAL_TABLE_LIMIT (%lu)\n", ofl);
  mpz_init2 (mask, numb + 1);
  mpz_setbit (mask, numb);
  mpz_sub_ui (mask, mask, 1);
  printf
    ("\n/* Previous table, continued, values modulo 2^GMP_NUMB_BITS */\n");
  printf
    ("#define ONE_LIMB_ODD_FACTORIAL_EXTTABLE CNST_LIMB(0x");
  mpz_and (x, x, mask);
  mpz_out_str (stdout, 16, x);
  mpz_init (y);
  mpz_bin_uiui (y, b, b/2);
  b++;
  for (;; b++)
    {
      for (a = b; (a & 1) == 0; a >>= 1);
      if (a == b) {
	mpz_divexact_ui (y, y, a/2+1);
	mpz_mul_ui (y, y, a);
      } else
	mpz_mul_2exp (y, y, 1);
      if (mpz_sizeinbase (y, 2) > numb)
	break;
      mpz_mul_ui (x, x, a);
      mpz_and (x, x, mask);
      printf ("),CNST_LIMB(0x");
      mpz_out_str (stdout, 16, x);
    }
  printf (")\n");
  ofe = b - 1;
  printf
    ("#define ODD_FACTORIAL_EXTTABLE_LIMIT (%lu)\n", ofe);

  printf
    ("\n/* This table is 1!!,3!!,...,(2n+1)!! where (2n+1)!! has <= GMP_NUMB_BITS bits */\n");
  printf
    ("#define ONE_LIMB_ODD_DOUBLEFACTORIAL_TABLE CNST_LIMB(0x1");
  mpz_set_ui (x, 1);
  for (b = 3;; b+=2)
    {
      mpz_swap (last, x);
      mpz_mul_ui (x, last, b);
      if (mpz_sizeinbase (x, 2) > numb)
	break;
      printf ("),CNST_LIMB(0x");
      mpz_out_str (stdout, 16, x);
    }
  printf (")\n");
  printf
    ("#define ODD_DOUBLEFACTORIAL_TABLE_MAX CNST_LIMB(0x");
  mpz_out_str (stdout, 16, last);
  printf (")\n");

  printf
    ("#define ODD_DOUBLEFACTORIAL_TABLE_LIMIT (%lu)\n", b - 2);

  printf
    ("\n/* This table x_1, x_2,... contains values s.t. x_n^n has <= GMP_NUMB_BITS bits */\n");
  printf
    ("#define NTH_ROOT_NUMB_MASK_TABLE (GMP_NUMB_MASK");
  for (b = 2;b <= 8; b++)
    {
      mpz_root (x, mask, b);
      printf ("),CNST_LIMB(0x");
      mpz_out_str (stdout, 16, x);
    }
  printf (")\n");

  mpz_add_ui (mask, mask, 1);
  printf
    ("\n/* This table contains inverses of odd factorials, modulo 2^GMP_NUMB_BITS */\n");
  printf
    ("\n/* It begins with (2!/2)^-1=1 */\n");
  printf
    ("#define ONE_LIMB_ODD_FACTORIAL_INVERSES_TABLE CNST_LIMB(0x1");
  mpz_set_ui (x, 1);
  for (b = 3;b <= ofe - 2; b++)
    {
      for (a = b; (a & 1) == 0; a >>= 1);
      mpz_mul_ui (x, x, a);
      mpz_invert (y, x, mask);
      printf ("),CNST_LIMB(0x");
      mpz_out_str (stdout, 16, y);
    }
  printf (")\n");

  ofe = (ofe / 16 + 1) * 16;

  printf
    ("\n/* This table contains 2n-popc(2n) for small n */\n");
  printf
    ("\n/* It begins with 2-1=1 (n=1) */\n");
  printf
    ("#define TABLE_2N_MINUS_POPC_2N 1");
  for (b = 4; b <= ofe; b += 2)
    {
      mpz_set_ui (x, b);
      printf (",%lu",b - mpz_popcount (x));
    }
  printf ("\n");
  printf
    ("#define TABLE_LIMIT_2N_MINUS_POPC_2N %lu\n", ofe + 1);


  ofl = (ofl + 1) / 2;
  printf
    ("#define ODD_CENTRAL_BINOMIAL_OFFSET (%lu)\n", ofl);
  printf
    ("\n/* This table contains binomial(2k,k)/2^t */\n");
  printf
    ("\n/* It begins with ODD_CENTRAL_BINOMIAL_TABLE_MIN */\n");
  printf
    ("#define ONE_LIMB_ODD_CENTRAL_BINOMIAL_TABLE ");
  for (b = ofl;; b++)
    {
      mpz_bin_uiui (x, 2 * b, b);
      mpz_remove_twos (x);
      if (mpz_sizeinbase (x, 2) > numb)
	break;
      if (b != ofl)
	printf ("),");
      printf("CNST_LIMB(0x");
      mpz_out_str (stdout, 16, x);
    }
  printf (")\n");

  ofe = b - 1;
  printf
    ("#define ODD_CENTRAL_BINOMIAL_TABLE_LIMIT (%lu)\n", ofe);

  printf
    ("\n/* This table contains the inverses of elements in the previous table. */\n");
  printf
    ("#define ONE_LIMB_ODD_CENTRAL_BINOMIAL_INVERSE_TABLE CNST_LIMB(0x");
  for (b = ofl; b <= ofe; b++)
    {
      mpz_bin_uiui (x, 2 * b, b);
      mpz_remove_twos (x);
      mpz_invert (x, x, mask);
      mpz_out_str (stdout, 16, x);
      if (b != ofe)
	printf ("),CNST_LIMB(0x");
    }
  printf (")\n");

  printf
    ("\n/* This table contains the values t in the formula binomial(2k,k)/2^t */\n");
  printf
    ("#define CENTRAL_BINOMIAL_2FAC_TABLE ");
  for (b = ofl; b <= ofe; b++)
    {
      mpz_bin_uiui (x, 2 * b, b);
      printf ("%d", mpz_remove_twos (x));
      if (b != ofe)
	printf (",");
    }
  printf ("\n");

  return 0;
}
Beispiel #8
0
int is_aks_prime(mpz_t n)
{
  mpz_t *px, *py;
  int retval;
  UV i, s, r, a;
  UV starta = 1;
  int _verbose = get_verbose_level();

  if (mpz_cmp_ui(n, 4) < 0)
    return (mpz_cmp_ui(n, 1) <= 0) ? 0 : 1;

  /* Just for performance: check small divisors: 2*3*5*7*11*13*17*19*23 */
  if (mpz_gcd_ui(0, n, 223092870UL) != 1 && mpz_cmp_ui(n, 23) > 0)
    return 0;

  if (mpz_perfect_power_p(n))
    return 0;

#if AKS_VARIANT == AKS_VARIANT_V6    /* From the V6 AKS paper */
  {
    mpz_t sqrtn, t;
    double log2n;
    UV limit, startr;
    PRIME_ITERATOR(iter);

    mpz_init(sqrtn);
    mpz_sqrt(sqrtn, n);

    log2n = mpz_log2(n);
    limit = (UV) floor( log2n * log2n );

    if (_verbose>1) gmp_printf("# AKS checking order_r(%Zd) to %"UVuf"\n", n, (unsigned long) limit);

    /* Using a native r limits us to ~2000 digits in the worst case (r ~ log^5n)
     * but would typically work for 100,000+ digits (r ~ log^3n).  This code is
     * far too slow to matter either way.  Composite r is ok here, but it will
     * always end up prime, so save time and just check primes. */
    retval = 0;
    /* Start order search at a good spot.  Idea from Nemana and Venkaiah. */
    startr = (mpz_sizeinbase(n,2)-1) * (mpz_sizeinbase(n,2)-1);
    startr = (startr < 1002) ? 2 : startr - 100;
    for (r = 2; /* */; r = prime_iterator_next(&iter)) {
      if (mpz_divisible_ui_p(n, r) ) /* r divides n.  composite. */
        { retval = 0; break; }
      if (mpz_cmp_ui(sqrtn, r) <= 0) /* no r <= sqrtn divides n.  prime. */
        { retval = 1; break; }
      if (r < startr) continue;
      if (mpz_order_ui(r, n, limit) > limit)
        { retval = 2; break; }
    }
    prime_iterator_destroy(&iter);
    mpz_clear(sqrtn);
    if (retval != 2) return retval;

    /* Since r is prime, phi(r) = r-1. */
    s = (UV) floor( sqrt(r-1) * log2n );
  }
#elif AKS_VARIANT == AKS_VARIANT_BORNEMANN /* Bernstein + Voloch */
  {
    UV slim;
    double c2, x;
    /* small t = few iters of big poly.  big t = many iters of small poly */
    double const t = (mpz_sizeinbase(n, 2) <= 64) ? 32 : 40;
    double const t1 = (1.0/((t+1)*log(t+1)-t*log(t)));
    double const dlogn = mpz_logn(n);
    mpz_t tmp;
    PRIME_ITERATOR(iter);

    mpz_init(tmp);
    prime_iterator_setprime(&iter, (UV) (t1*t1 * dlogn*dlogn) );
    r = prime_iterator_next(&iter);
    while (!is_primitive_root_uiprime(n,r))
      r = prime_iterator_next(&iter);
    prime_iterator_destroy(&iter);

    slim = (UV) (2*t*(r-1));
    c2 = dlogn * floor(sqrt(r));
    { /* Binary search for first s in [1,slim] where x >= 0 */
      UV bi = 1;
      UV bj = slim;
      while (bi < bj) {
        s = bi + (bj-bi)/2;
        mpz_bin_uiui(tmp, r+s-1, s);
        x = mpz_logn(tmp) / c2 - 1.0;
        if (x < 0)  bi = s+1;
        else        bj = s;
      }
      s = bi-1;
    }
    s = (s+3) >> 1;
    /* Bornemann checks factors up to (s-1)^2, we check to max(r,s) */
    /* slim = (s-1)*(s-1); */
    slim = (r > s) ? r : s;
    if (_verbose > 1) printf("# aks trial to %"UVuf"\n", slim);
    if (_GMP_trial_factor(n, 2, slim) > 1)
      { mpz_clear(tmp); return 0; }
    mpz_sqrt(tmp, n);
    if (mpz_cmp_ui(tmp, slim) <= 0)
      { mpz_clear(tmp); return 1; }
    mpz_clear(tmp);
  }
#elif AKS_VARIANT == AKS_VARIANT_BERN21
  { /* Bernstein 2003, theorem 2.1 (simplified) */
    UV q;
    double slim, scmp, x;
    mpz_t t, t2;
    PRIME_ITERATOR(iter);
    mpz_init(t);  mpz_init(t2);
    r = s = 0;
    while (1) {
      /* todo: Check r|n and r >= sqrt(n) here instead of waiting */
      if (mpz_cmp_ui(n, r) <= 0) break;
      r = prime_iterator_next(&iter);
      q = largest_factor(r-1);
      mpz_set_ui(t, r);
      mpz_powm_ui(t, n, (r-1)/q, t);
      if (mpz_cmp_ui(t, 1) <= 0) continue;
      scmp = 2 * floor(sqrt(r)) * mpz_log2(n);

      slim = 20 * (r-1);

      /* Check viability */
      mpz_bin_uiui(t, q+slim-1, slim); if (mpz_log2(t) < scmp) continue;

      for (s = 2; s < slim; s++) {
        mpz_bin_uiui(t, q+s-1, s);
        if (mpz_log2(t) > scmp) break;
      }
      if (s < slim) break;
    }
    mpz_clear(t);  mpz_clear(t2);
    prime_iterator_destroy(&iter);
    if (_GMP_trial_factor(n, 2, s) > 1)
      return 0;
  }
#elif AKS_VARIANT == AKS_VARIANT_BERN22
  { /* Bernstein 2003, theorem 2.2 (simplified) */
    UV q;
    double slim, scmp, x;
    mpz_t t, t2;
    PRIME_ITERATOR(iter);
    mpz_init(t);  mpz_init(t2);
    r = s = 0;
    while (1) {
      /* todo: Check r|n and r >= sqrt(n) here instead of waiting */
      if (mpz_cmp_ui(n, r) <= 0) break;
      r = prime_iterator_next(&iter);
      if (!is_primitive_root_uiprime(n,r)) continue;
      q = r-1;   /* Since r is prime, phi(r) = r-1 */
      scmp = 2 * floor(sqrt(r-1)) * mpz_log2(n);

      slim = 20 * (r-1);

      /* Check viability */
      mpz_bin_uiui(t, q+slim-1, slim); if (mpz_log2(t) < scmp) continue;

      for (s = 2; s < slim; s++) {
        mpz_bin_uiui(t, q+s-1, s);
        if (mpz_log2(t) > scmp) break;
      }
      if (s < slim) break;
    }
    mpz_clear(t);  mpz_clear(t2);
    prime_iterator_destroy(&iter);
    if (_GMP_trial_factor(n, 2, s) > 1)
      return 0;
  }
#elif AKS_VARIANT == AKS_VARIANT_BERN23
  { /* Bernstein 2003, theorem 2.3 (simplified) */
    UV q, d, limit;
    double slim, scmp, sbin, x, log2n;
    mpz_t t, t2;
    PRIME_ITERATOR(iter);
    mpz_init(t);  mpz_init(t2);
    log2n = mpz_log2(n);
    limit = (UV) floor( log2n * log2n );
    r = 2;
    s = 0;
    while (1) {
      /* todo: Check r|n and r >= sqrt(n) here instead of waiting */
      if (mpz_cmp_ui(n, r) <= 0) break;
      r++;
      UV gcd = mpz_gcd_ui(NULL, n, r);
      if (gcd != 1) { mpz_clear(t); mpz_clear(t2); return 0; }
      UV v = mpz_order_ui(r, n, limit);
      if (v >= limit) continue;

      mpz_set_ui(t2, r);
      totient(t, t2);
      q = mpz_get_ui(t);
      UV phiv = q/v;
      /* printf("phi(%lu)/v = %lu/%lu = %lu\n", r, q, v, phiv); */

      /* This is extremely inefficient. */

      /* Choose an s value we'd be happy with */
      slim = 20 * (r-1);

      /* Quick check to see if it could work with s=slim, d=1 */
      mpz_bin_uiui(t, q+slim-1, slim);
      sbin = mpz_log2(t);
      if (sbin < 2*floor(sqrt(q))*log2n)
        continue;

      for (s = 2; s < slim; s++) {
        mpz_bin_uiui(t, q+s-1, s);
        sbin = mpz_log2(t);
        if (sbin < 2*floor(sqrt(q))*log2n) continue;   /* d=1 */
        /* Check each number dividing phi(r)/v */
        for (d = 2; d < phiv; d++) {
          if ((phiv % d) != 0) continue;
          scmp = 2 * d * floor(sqrt(q/d)) * log2n;
          if (sbin < scmp) break;
        }
        /* if we did not exit early, this s worked for each d.  This s wins. */
        if (d >= phiv) break;
      }
      if (s < slim) break;
    }
    mpz_clear(t);  mpz_clear(t2);
    prime_iterator_destroy(&iter);
    if (_GMP_trial_factor(n, 2, s) > 1)
      return 0;
  }
#elif AKS_VARIANT == AKS_VARIANT_BERN41
  {
    double const log2n = mpz_log2(n);
    /* Tuning: Initial 'r' selection */
    double const r0 = 0.008 * log2n * log2n;
    /* Tuning: Try a larger 'r' if 's' looks very large */
    UV const rmult = 8;
    UV slim;
    mpz_t tmp, tmp2;
    PRIME_ITERATOR(iter);

    mpz_init(tmp);  mpz_init(tmp2);
    /* r has to be at least 3. */
    prime_iterator_setprime(&iter, (r0 < 2) ? 2 : (UV) r0);
    r = prime_iterator_next(&iter);

    /* r must be a primitive root.  For performance, skip if s looks too big. */
    while ( !is_primitive_root_uiprime(n, r) ||
            !bern41_acceptable(n, r, rmult*(r-1), tmp, tmp2) )
      r = prime_iterator_next(&iter);
    prime_iterator_destroy(&iter);

    { /* Binary search for first s in [1,lim] where conditions met */
      UV bi = 1;
      UV bj = rmult * (r-1);
      while (bi < bj) {
        s = bi + (bj-bi)/2;
        if (!bern41_acceptable(n,r,s,tmp,tmp2))  bi = s+1;
        else                                     bj = s;
      }
      s = bj;
      /* Our S goes from 2 to s+1. */
      starta = 2;
      s = s+1;
    }
    /* printf("chose r=%lu s=%lu d = %lu i = %lu j = %lu\n", r, s, d, i, j); */

    /* Check divisibility to s(s-1) to cover both gcd conditions */
    slim = s * (s-1);
    if (_verbose > 1) printf("# aks trial to %"UVuf"\n", slim);
    if (_GMP_trial_factor(n, 2, slim) > 1)
      { mpz_clear(tmp); mpz_clear(tmp2); return 0; }
    /* If we checked divisibility to sqrt(n), then it is prime. */
    mpz_sqrt(tmp, n);
    if (mpz_cmp_ui(tmp, slim) <= 0)
      { mpz_clear(tmp); mpz_clear(tmp2); return 1; }

    /* Check b^(n-1) = 1 mod n for b in [2..s] */
    if (_verbose > 1) printf("# aks checking fermat to %"UVuf"\n", s);
    mpz_sub_ui(tmp2, n, 1);
    for (i = 2; i <= s; i++) {
      mpz_set_ui(tmp, i);
      mpz_powm(tmp, tmp, tmp2, n);
      if (mpz_cmp_ui(tmp, 1) != 0)
        { mpz_clear(tmp); mpz_clear(tmp2); return 0; }
    }

    mpz_clear(tmp);  mpz_clear(tmp2);
  }

#endif

  if (_verbose) gmp_printf("# AKS %Zd.  r = %"UVuf" s = %"UVuf"\n", n, (unsigned long) r, (unsigned long) s);

  /* Create the three polynomials we will use */
  New(0, px, r, mpz_t);
  New(0, py, r, mpz_t);
  if ( !px || !py )
    croak("allocation failure\n");
  for (i = 0; i < r; i++) {
    mpz_init(px[i]);
    mpz_init(py[i]);
  }

  retval = 1;
  for (a = starta; a <= s; a++) {
    retval = test_anr(a, n, r, px, py);
    if (!retval) break;
    if (_verbose>1) { printf("."); fflush(stdout); }
  }
  if (_verbose>1) { printf("\n"); fflush(stdout); };

  /* Free the polynomials */
  for (i = 0; i < r; i++) {
    mpz_clear(px[i]);
    mpz_clear(py[i]);
  }
  Safefree(px);
  Safefree(py);

  return retval;
}