Beispiel #1
0
int
main (int argc, char **argv)
{
  gmp_randstate_ptr rands;
  unsigned long maxnbits, maxdbits, nbits, dbits;
  mpz_t n, d, q, r, tz, junk;
  mp_size_t maxnn, maxdn, nn, dn, clearn, i;
  mp_ptr np, dup, dnp, qp, rp, junkp;
  mp_limb_t t;
  gmp_pi1_t dinv;
  long count = COUNT;
  mp_ptr scratch;
  mp_limb_t ran;
  mp_size_t alloc, itch;
  mp_limb_t rran0, rran1, qran0, qran1;
  TMP_DECL;

  if (argc > 1)
    {
      char *end;
      count = strtol (argv[1], &end, 0);
      if (*end || count <= 0)
	{
	  fprintf (stderr, "Invalid test count: %s.\n", argv[1]);
	  return 1;
	}
    }

  maxdbits = MAX_DN;
  maxnbits = MAX_NN;

  tests_start ();
  rands = RANDS;

  mpz_init (n);
  mpz_init (d);
  mpz_init (q);
  mpz_init (r);
  mpz_init (tz);
  mpz_init (junk);

  maxnn = maxnbits / GMP_NUMB_BITS + 1;
  maxdn = maxdbits / GMP_NUMB_BITS + 1;

  TMP_MARK;

  qp = TMP_ALLOC_LIMBS (maxnn + 2) + 1;
  rp = TMP_ALLOC_LIMBS (maxnn + 2) + 1;
  dnp = TMP_ALLOC_LIMBS (maxdn);

  alloc = 1;
  scratch = __GMP_ALLOCATE_FUNC_LIMBS (alloc);

  for (test = -300; test < count; test++)
    {
      nbits = random_word (rands) % (maxnbits - GMP_NUMB_BITS) + 2 * GMP_NUMB_BITS;

      if (test < 0)
	dbits = (test + 300) % (nbits - 1) + 1;
      else
	dbits = random_word (rands) % (nbits - 1) % maxdbits + 1;

#if RAND_UNIFORM
#define RANDFUNC mpz_urandomb
#else
#define RANDFUNC mpz_rrandomb
#endif

      do
	RANDFUNC (d, rands, dbits);
      while (mpz_sgn (d) == 0);
      dn = SIZ (d);
      dup = PTR (d);
      MPN_COPY (dnp, dup, dn);
      dnp[dn - 1] |= GMP_NUMB_HIGHBIT;

      if (test % 2 == 0)
	{
	  RANDFUNC (n, rands, nbits);
	  nn = SIZ (n);
	  ASSERT_ALWAYS (nn >= dn);
	}
      else
	{
	  do
	    {
	      RANDFUNC (q, rands, random_word (rands) % (nbits - dbits + 1));
	      RANDFUNC (r, rands, random_word (rands) % mpz_sizeinbase (d, 2));
	      mpz_mul (n, q, d);
	      mpz_add (n, n, r);
	      nn = SIZ (n);
	    }
	  while (nn > maxnn || nn < dn);
	}

      ASSERT_ALWAYS (nn <= maxnn);
      ASSERT_ALWAYS (dn <= maxdn);

      mpz_urandomb (junk, rands, nbits);
      junkp = PTR (junk);

      np = PTR (n);

      mpz_urandomb (tz, rands, 32);
      t = mpz_get_ui (tz);

      if (t % 17 == 0)
	{
	  dnp[dn - 1] = GMP_NUMB_MAX;
	  dup[dn - 1] = GMP_NUMB_MAX;
	}

      switch ((int) t % 16)
	{
	case 0:
	  clearn = random_word (rands) % nn;
	  for (i = clearn; i < nn; i++)
	    np[i] = 0;
	  break;
	case 1:
	  mpn_sub_1 (np + nn - dn, dnp, dn, random_word (rands));
	  break;
	case 2:
	  mpn_add_1 (np + nn - dn, dnp, dn, random_word (rands));
	  break;
	}

      if (dn >= 2)
	invert_pi1 (dinv, dnp[dn - 1], dnp[dn - 2]);

      rran0 = random_word (rands);
      rran1 = random_word (rands);
      qran0 = random_word (rands);
      qran1 = random_word (rands);

      qp[-1] = qran0;
      qp[nn - dn + 1] = qran1;
      rp[-1] = rran0;

      ran = random_word (rands);

      if ((double) (nn - dn) * dn < 1e5)
	{
	  /* Test mpn_sbpi1_div_qr */
	  if (dn > 2)
	    {
	      MPN_COPY (rp, np, nn);
	      if (nn > dn)
		MPN_COPY (qp, junkp, nn - dn);
	      qp[nn - dn] = mpn_sbpi1_div_qr (qp, rp, nn, dnp, dn, dinv.inv32);
	      check_one (qp, rp, np, nn, dnp, dn, "mpn_sbpi1_div_qr", 0);
	    }

	  /* Test mpn_sbpi1_divappr_q */
	  if (dn > 2)
	    {
	      MPN_COPY (rp, np, nn);
	      if (nn > dn)
		MPN_COPY (qp, junkp, nn - dn);
	      qp[nn - dn] = mpn_sbpi1_divappr_q (qp, rp, nn, dnp, dn, dinv.inv32);
	      check_one (qp, NULL, np, nn, dnp, dn, "mpn_sbpi1_divappr_q", 1);
	    }

	  /* Test mpn_sbpi1_div_q */
	  if (dn > 2)
	    {
	      MPN_COPY (rp, np, nn);
	      if (nn > dn)
		MPN_COPY (qp, junkp, nn - dn);
	      qp[nn - dn] = mpn_sbpi1_div_q (qp, rp, nn, dnp, dn, dinv.inv32);
	      check_one (qp, NULL, np, nn, dnp, dn, "mpn_sbpi1_div_q", 0);
	    }

	  /* Test mpn_sb_div_qr_sec */
	  itch = 3 * nn + 4;
	  if (itch + 1 > alloc)
	    {
	      scratch = __GMP_REALLOCATE_FUNC_LIMBS (scratch, alloc, itch + 1);
	      alloc = itch + 1;
	    }
	  scratch[itch] = ran;
	  MPN_COPY (rp, np, nn);
	  if (nn >= dn)
	    MPN_COPY (qp, junkp, nn - dn + 1);
	  mpn_sb_div_qr_sec (qp, rp, nn, dup, dn, scratch);
	  ASSERT_ALWAYS (ran == scratch[itch]);
	  check_one (qp, rp, np, nn, dup, dn, "mpn_sb_div_qr_sec", 0);

	  /* Test mpn_sb_div_r_sec */
	  itch = nn + 2 * dn + 2;
	  if (itch + 1 > alloc)
	    {
	      scratch = __GMP_REALLOCATE_FUNC_LIMBS (scratch, alloc, itch + 1);
	      alloc = itch + 1;
	    }
	  scratch[itch] = ran;
	  MPN_COPY (rp, np, nn);
	  mpn_sb_div_r_sec (rp, nn, dup, dn, scratch);
	  ASSERT_ALWAYS (ran == scratch[itch]);
	  /* Note: Since check_one cannot cope with random-only functions, we
	     pass qp[] from the previous function, mpn_sb_div_qr_sec.  */
	  check_one (qp, rp, np, nn, dup, dn, "mpn_sb_div_r_sec", 0);
	}

      /* Test mpn_dcpi1_div_qr */
      if (dn >= 6 && nn - dn >= 3)
	{
	  MPN_COPY (rp, np, nn);
	  if (nn > dn)
	    MPN_COPY (qp, junkp, nn - dn);
	  qp[nn - dn] = mpn_dcpi1_div_qr (qp, rp, nn, dnp, dn, &dinv);
	  ASSERT_ALWAYS (qp[-1] == qran0);  ASSERT_ALWAYS (qp[nn - dn + 1] == qran1);
	  ASSERT_ALWAYS (rp[-1] == rran0);
	  check_one (qp, rp, np, nn, dnp, dn, "mpn_dcpi1_div_qr", 0);
	}

      /* Test mpn_dcpi1_divappr_q */
      if (dn >= 6 && nn - dn >= 3)
	{
	  MPN_COPY (rp, np, nn);
	  if (nn > dn)
	    MPN_COPY (qp, junkp, nn - dn);
	  qp[nn - dn] = mpn_dcpi1_divappr_q (qp, rp, nn, dnp, dn, &dinv);
	  ASSERT_ALWAYS (qp[-1] == qran0);  ASSERT_ALWAYS (qp[nn - dn + 1] == qran1);
	  ASSERT_ALWAYS (rp[-1] == rran0);
	  check_one (qp, NULL, np, nn, dnp, dn, "mpn_dcpi1_divappr_q", 1);
	}

      /* Test mpn_dcpi1_div_q */
      if (dn >= 6 && nn - dn >= 3)
	{
	  MPN_COPY (rp, np, nn);
	  if (nn > dn)
	    MPN_COPY (qp, junkp, nn - dn);
	  qp[nn - dn] = mpn_dcpi1_div_q (qp, rp, nn, dnp, dn, &dinv);
	  ASSERT_ALWAYS (qp[-1] == qran0);  ASSERT_ALWAYS (qp[nn - dn + 1] == qran1);
	  ASSERT_ALWAYS (rp[-1] == rran0);
	  check_one (qp, NULL, np, nn, dnp, dn, "mpn_dcpi1_div_q", 0);
	}

     /* Test mpn_mu_div_qr */
      if (nn - dn > 2 && dn >= 2)
	{
	  itch = mpn_mu_div_qr_itch (nn, dn, 0);
	  if (itch + 1 > alloc)
	    {
	      scratch = __GMP_REALLOCATE_FUNC_LIMBS (scratch, alloc, itch + 1);
	      alloc = itch + 1;
	    }
	  scratch[itch] = ran;
	  MPN_COPY (qp, junkp, nn - dn);
	  MPN_ZERO (rp, dn);
	  rp[dn] = rran1;
	  qp[nn - dn] = mpn_mu_div_qr (qp, rp, np, nn, dnp, dn, scratch);
	  ASSERT_ALWAYS (ran == scratch[itch]);
	  ASSERT_ALWAYS (qp[-1] == qran0);  ASSERT_ALWAYS (qp[nn - dn + 1] == qran1);
	  ASSERT_ALWAYS (rp[-1] == rran0);  ASSERT_ALWAYS (rp[dn] == rran1);
	  check_one (qp, rp, np, nn, dnp, dn, "mpn_mu_div_qr", 0);
	}

      /* Test mpn_mu_divappr_q */
      if (nn - dn > 2 && dn >= 2)
	{
	  itch = mpn_mu_divappr_q_itch (nn, dn, 0);
	  if (itch + 1 > alloc)
	    {
	      scratch = __GMP_REALLOCATE_FUNC_LIMBS (scratch, alloc, itch + 1);
	      alloc = itch + 1;
	    }
	  scratch[itch] = ran;
	  MPN_COPY (qp, junkp, nn - dn);
	  qp[nn - dn] = mpn_mu_divappr_q (qp, np, nn, dnp, dn, scratch);
	  ASSERT_ALWAYS (ran == scratch[itch]);
	  ASSERT_ALWAYS (qp[-1] == qran0);  ASSERT_ALWAYS (qp[nn - dn + 1] == qran1);
	  check_one (qp, NULL, np, nn, dnp, dn, "mpn_mu_divappr_q", 4);
	}

      /* Test mpn_mu_div_q */
      if (nn - dn > 2 && dn >= 2)
	{
	  itch = mpn_mu_div_q_itch (nn, dn, 0);
	  if (itch + 1> alloc)
	    {
	      scratch = __GMP_REALLOCATE_FUNC_LIMBS (scratch, alloc, itch + 1);
	      alloc = itch + 1;
	    }
	  scratch[itch] = ran;
	  MPN_COPY (qp, junkp, nn - dn);
	  qp[nn - dn] = mpn_mu_div_q (qp, np, nn, dnp, dn, scratch);
	  ASSERT_ALWAYS (ran == scratch[itch]);
	  ASSERT_ALWAYS (qp[-1] == qran0);  ASSERT_ALWAYS (qp[nn - dn + 1] == qran1);
	  check_one (qp, NULL, np, nn, dnp, dn, "mpn_mu_div_q", 0);
	}

      if (1)
	{
	  itch = nn + 1;
	  if (itch + 1> alloc)
	    {
	      scratch = __GMP_REALLOCATE_FUNC_LIMBS (scratch, alloc, itch + 1);
	      alloc = itch + 1;
	    }
	  scratch[itch] = ran;
	  mpn_div_q (qp, np, nn, dup, dn, scratch);
	  ASSERT_ALWAYS (ran == scratch[itch]);
	  ASSERT_ALWAYS (qp[-1] == qran0);  ASSERT_ALWAYS (qp[nn - dn + 1] == qran1);
	  check_one (qp, NULL, np, nn, dup, dn, "mpn_div_q", 0);
	}

      if (dn >= 2 && nn >= 2)
	{
	  mp_limb_t qh;

	  /* mpn_divrem_2 */
	  MPN_COPY (rp, np, nn);
	  qp[nn - 2] = qp[nn-1] = qran1;

	  qh = mpn_divrem_2 (qp, 0, rp, nn, dnp + dn - 2);
	  ASSERT_ALWAYS (qp[nn - 2] == qran1);
	  ASSERT_ALWAYS (qp[-1] == qran0);  ASSERT_ALWAYS (qp[nn - 1] == qran1);
	  qp[nn - 2] = qh;
	  check_one (qp, rp, np, nn, dnp + dn - 2, 2, "mpn_divrem_2", 0);

	  /* Missing: divrem_2 with fraction limbs. */

	  /* mpn_div_qr_2 */
	  qp[nn - 2] = qran1;

	  qh = mpn_div_qr_2 (qp, rp, np, nn, dup + dn - 2);
	  ASSERT_ALWAYS (qp[nn - 2] == qran1);
	  ASSERT_ALWAYS (qp[-1] == qran0);  ASSERT_ALWAYS (qp[nn - 1] == qran1);
	  qp[nn - 2] = qh;
	  check_one (qp, rp, np, nn, dup + dn - 2, 2, "mpn_div_qr_2", 0);
	}
    }

  __GMP_FREE_FUNC_LIMBS (scratch, alloc);

  TMP_FREE;

  mpz_clear (n);
  mpz_clear (d);
  mpz_clear (q);
  mpz_clear (r);
  mpz_clear (tz);
  mpz_clear (junk);

  tests_end ();
  return 0;
}
Beispiel #2
0
void
mpn_div_q (mp_ptr qp,
	   mp_srcptr np, mp_size_t nn,
	   mp_srcptr dp, mp_size_t dn, mp_ptr scratch)
{
  mp_ptr new_dp, new_np, tp, rp;
  mp_limb_t cy, dh, qh;
  mp_size_t new_nn, qn;
  gmp_pi1_t dinv;
  int cnt;
  TMP_DECL;
  TMP_MARK;

  ASSERT (nn >= dn);
  ASSERT (dn > 0);
  ASSERT (dp[dn - 1] != 0);
  ASSERT (! MPN_OVERLAP_P (qp, nn - dn + 1, np, nn));
  ASSERT (! MPN_OVERLAP_P (qp, nn - dn + 1, dp, dn));
  ASSERT (MPN_SAME_OR_SEPARATE_P (np, scratch, nn));

  ASSERT_ALWAYS (FUDGE >= 2);

  if (dn == 1)
    {
      mpn_divrem_1 (qp, 0L, np, nn, dp[dn - 1]);
      return;
    }

  qn = nn - dn + 1;		/* Quotient size, high limb might be zero */

  if (qn + FUDGE >= dn)
    {
      /* |________________________|
                          |_______|  */
      new_np = scratch;

      dh = dp[dn - 1];
      if (LIKELY ((dh & GMP_NUMB_HIGHBIT) == 0))
	{
	  count_leading_zeros (cnt, dh);

	  cy = mpn_lshift (new_np, np, nn, cnt);
	  new_np[nn] = cy;
	  new_nn = nn + (cy != 0);

	  new_dp = TMP_ALLOC_LIMBS (dn);
	  mpn_lshift (new_dp, dp, dn, cnt);

	  if (dn == 2)
	    {
	      qh = mpn_divrem_2 (qp, 0L, new_np, new_nn, new_dp);
	    }
	  else if (BELOW_THRESHOLD (dn, DC_DIV_Q_THRESHOLD) ||
		   BELOW_THRESHOLD (new_nn - dn, DC_DIV_Q_THRESHOLD))
	    {
	      invert_pi1 (dinv, new_dp[dn - 1], new_dp[dn - 2]);
	      qh = mpn_sbpi1_div_q (qp, new_np, new_nn, new_dp, dn, dinv.inv32);
	    }
	  else if (BELOW_THRESHOLD (dn, MUPI_DIV_Q_THRESHOLD) ||   /* fast condition */
		   BELOW_THRESHOLD (nn, 2 * MU_DIV_Q_THRESHOLD) || /* fast condition */
		   (double) (2 * (MU_DIV_Q_THRESHOLD - MUPI_DIV_Q_THRESHOLD)) * dn /* slow... */
		   + (double) MUPI_DIV_Q_THRESHOLD * nn > (double) dn * nn)   /* ...condition */
	    {
	      invert_pi1 (dinv, new_dp[dn - 1], new_dp[dn - 2]);
	      qh = mpn_dcpi1_div_q (qp, new_np, new_nn, new_dp, dn, &dinv);
	    }
	  else
	    {
	      mp_size_t itch = mpn_mu_div_q_itch (new_nn, dn, 0);
	      mp_ptr scratch = TMP_ALLOC_LIMBS (itch);
	      qh = mpn_mu_div_q (qp, new_np, new_nn, new_dp, dn, scratch);
	    }
	  if (cy == 0)
	    qp[qn - 1] = qh;
	  else if (UNLIKELY (qh != 0))
	    {
	      /* This happens only when the quotient is close to B^n and
		 mpn_*_divappr_q returned B^n.  */
	      mp_size_t i, n;
	      n = new_nn - dn;
	      for (i = 0; i < n; i++)
		qp[i] = GMP_NUMB_MAX;
	      qh = 0;		/* currently ignored */
	    }
	}
      else  /* divisor is already normalised */
	{
	  if (new_np != np)
	    MPN_COPY (new_np, np, nn);

	  if (dn == 2)
	    {
	      qh = mpn_divrem_2 (qp, 0L, new_np, nn, dp);
	    }
	  else if (BELOW_THRESHOLD (dn, DC_DIV_Q_THRESHOLD) ||
		   BELOW_THRESHOLD (nn - dn, DC_DIV_Q_THRESHOLD))
	    {
	      invert_pi1 (dinv, dh, dp[dn - 2]);
	      qh = mpn_sbpi1_div_q (qp, new_np, nn, dp, dn, dinv.inv32);
	    }
	  else if (BELOW_THRESHOLD (dn, MUPI_DIV_Q_THRESHOLD) ||   /* fast condition */
		   BELOW_THRESHOLD (nn, 2 * MU_DIV_Q_THRESHOLD) || /* fast condition */
		   (double) (2 * (MU_DIV_Q_THRESHOLD - MUPI_DIV_Q_THRESHOLD)) * dn /* slow... */
		   + (double) MUPI_DIV_Q_THRESHOLD * nn > (double) dn * nn)   /* ...condition */
	    {
	      invert_pi1 (dinv, dh, dp[dn - 2]);
	      qh = mpn_dcpi1_div_q (qp, new_np, nn, dp, dn, &dinv);
	    }
	  else
	    {
	      mp_size_t itch = mpn_mu_div_q_itch (nn, dn, 0);
	      mp_ptr scratch = TMP_ALLOC_LIMBS (itch);
	      qh = mpn_mu_div_q (qp, np, nn, dp, dn, scratch);
	    }
	  qp[nn - dn] = qh;
	}
    }
  else
    {
      /* |________________________|
                |_________________|  */
      tp = TMP_ALLOC_LIMBS (qn + 1);

      new_np = scratch;
      new_nn = 2 * qn + 1;
      if (new_np == np)
	/* We need {np,nn} to remain untouched until the final adjustment, so
	   we need to allocate separate space for new_np.  */
	new_np = TMP_ALLOC_LIMBS (new_nn + 1);


      dh = dp[dn - 1];
      if (LIKELY ((dh & GMP_NUMB_HIGHBIT) == 0))
	{
	  count_leading_zeros (cnt, dh);

	  cy = mpn_lshift (new_np, np + nn - new_nn, new_nn, cnt);
	  new_np[new_nn] = cy;

	  new_nn += (cy != 0);

	  new_dp = TMP_ALLOC_LIMBS (qn + 1);
	  mpn_lshift (new_dp, dp + dn - (qn + 1), qn + 1, cnt);
	  new_dp[0] |= dp[dn - (qn + 1) - 1] >> (GMP_NUMB_BITS - cnt);

	  if (qn + 1 == 2)
	    {
	      qh = mpn_divrem_2 (tp, 0L, new_np, new_nn, new_dp);
	    }
	  else if (BELOW_THRESHOLD (qn, DC_DIVAPPR_Q_THRESHOLD - 1))
	    {
	      invert_pi1 (dinv, new_dp[qn], new_dp[qn - 1]);
	      qh = mpn_sbpi1_divappr_q (tp, new_np, new_nn, new_dp, qn + 1, dinv.inv32);
	    }
	  else if (BELOW_THRESHOLD (qn, MU_DIVAPPR_Q_THRESHOLD - 1))
	    {
	      invert_pi1 (dinv, new_dp[qn], new_dp[qn - 1]);
	      qh = mpn_dcpi1_divappr_q (tp, new_np, new_nn, new_dp, qn + 1, &dinv);
	    }
	  else
	    {
	      mp_size_t itch = mpn_mu_divappr_q_itch (new_nn, qn + 1, 0);
	      mp_ptr scratch = TMP_ALLOC_LIMBS (itch);
	      qh = mpn_mu_divappr_q (tp, new_np, new_nn, new_dp, qn + 1, scratch);
	    }
	  if (cy == 0)
	    tp[qn] = qh;
	  else if (UNLIKELY (qh != 0))
	    {
	      /* This happens only when the quotient is close to B^n and
		 mpn_*_divappr_q returned B^n.  */
	      mp_size_t i, n;
	      n = new_nn - (qn + 1);
	      for (i = 0; i < n; i++)
		tp[i] = GMP_NUMB_MAX;
	      qh = 0;		/* currently ignored */
	    }
	}
      else  /* divisor is already normalised */
	{