niceSOFT/mpfr | Gitverse

tests/tdiv.c
1 564 строки48 KB
Vincent Lefèvre
03 янв 2018, 13:53
03 янв 2018, 13:532fce388
/* Test file for mpfr_div (and some mpfr_div_ui, etc. tests).

Copyright 1999, 2001-2018 Free Software Foundation, Inc.
Contributed by the AriC and Caramba projects, INRIA.

This file is part of the GNU MPFR Library.

The GNU MPFR Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 3 of the License, or (at your
option) any later version.

The GNU MPFR Library is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
License for more details.

You should have received a copy of the GNU Lesser General Public License
along with the GNU MPFR Library; see the file COPYING.LESSER.  If not, see
http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */

#include "mpfr-test.h"

static void
check_equal (mpfr_srcptr a, mpfr_srcptr a2, char *s,
             mpfr_srcptr b, mpfr_srcptr c, mpfr_rnd_t r)
{
  if (SAME_VAL (a, a2))
    return;
  if (r == MPFR_RNDF) /* RNDF might return different values */
    return;
  printf ("Error in %s\n", mpfr_print_rnd_mode (r));
  printf ("b  = ");
  mpfr_dump (b);
  printf ("c  = ");
  mpfr_dump (c);
  printf ("mpfr_div    result: ");
  mpfr_dump (a);
  printf ("%s result: ", s);
  mpfr_dump (a2);
  exit (1);
}

static int
mpfr_all_div (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mpfr_rnd_t r)
{
  mpfr_t a2;
  unsigned int oldflags, newflags;
  int inex, inex2;

  oldflags = __gmpfr_flags;
  inex = mpfr_div (a, b, c, r);

  /* this test makes no sense for RNDF, since it compares the ternary value
     and the flags */
  if (a == b || a == c || r == MPFR_RNDF)
    return inex;

  newflags = __gmpfr_flags;

  mpfr_init2 (a2, MPFR_PREC (a));

  if (mpfr_integer_p (b) && ! (MPFR_IS_ZERO (b) && MPFR_IS_NEG (b)))
    {
      /* b is an integer, but not -0 (-0 is rejected as
         it becomes +0 when converted to an integer). */
      if (mpfr_fits_ulong_p (b, MPFR_RNDA))
        {
          __gmpfr_flags = oldflags;
          inex2 = mpfr_ui_div (a2, mpfr_get_ui (b, MPFR_RNDN), c, r);
          MPFR_ASSERTN (SAME_SIGN (inex2, inex));
          MPFR_ASSERTN (__gmpfr_flags == newflags);
          check_equal (a, a2, "mpfr_ui_div", b, c, r);
        }
      if (mpfr_fits_slong_p (b, MPFR_RNDA))
        {
          __gmpfr_flags = oldflags;
          inex2 = mpfr_si_div (a2, mpfr_get_si (b, MPFR_RNDN), c, r);
          MPFR_ASSERTN (SAME_SIGN (inex2, inex));
          MPFR_ASSERTN (__gmpfr_flags == newflags);
          check_equal (a, a2, "mpfr_si_div", b, c, r);
        }
    }

  if (mpfr_integer_p (c) && ! (MPFR_IS_ZERO (c) && MPFR_IS_NEG (c)))
    {
      /* c is an integer, but not -0 (-0 is rejected as
         it becomes +0 when converted to an integer). */
      if (mpfr_fits_ulong_p (c, MPFR_RNDA))
        {
          __gmpfr_flags = oldflags;
          inex2 = mpfr_div_ui (a2, b, mpfr_get_ui (c, MPFR_RNDN), r);
          MPFR_ASSERTN (SAME_SIGN (inex2, inex));
          MPFR_ASSERTN (__gmpfr_flags == newflags);
          check_equal (a, a2, "mpfr_div_ui", b, c, r);
        }
      if (mpfr_fits_slong_p (c, MPFR_RNDA))
        {
          __gmpfr_flags = oldflags;
          inex2 = mpfr_div_si (a2, b, mpfr_get_si (c, MPFR_RNDN), r);
          MPFR_ASSERTN (SAME_SIGN (inex2, inex));
          MPFR_ASSERTN (__gmpfr_flags == newflags);
          check_equal (a, a2, "mpfr_div_si", b, c, r);
        }
    }

  mpfr_clear (a2);

  return inex;
}

#ifdef CHECK_EXTERNAL
static int
test_div (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mpfr_rnd_t rnd_mode)
{
  int res;
  int ok = rnd_mode == MPFR_RNDN && mpfr_number_p (b) && mpfr_number_p (c);
  if (ok)
    {
      mpfr_print_raw (b);
      printf (" ");
      mpfr_print_raw (c);
    }
  res = mpfr_all_div (a, b, c, rnd_mode);
  if (ok)
    {
      printf (" ");
      mpfr_print_raw (a);
      printf ("\n");
    }
  return res;
}
#else
#define test_div mpfr_all_div
#endif

#define check53(n, d, rnd, res) check4(n, d, rnd, 53, res)

/* return 0 iff a and b are of the same sign */
static int
inex_cmp (int a, int b)
{
  if (a > 0)
    return (b > 0) ? 0 : 1;
  else if (a == 0)
    return (b == 0) ? 0 : 1;
  else
    return (b < 0) ? 0 : 1;
}

static void
check4 (const char *Ns, const char *Ds, mpfr_rnd_t rnd_mode, int p,
        const char *Qs)
{
  mpfr_t q, n, d;

  mpfr_inits2 (p, q, n, d, (mpfr_ptr) 0);
  mpfr_set_str1 (n, Ns);
  mpfr_set_str1 (d, Ds);
  test_div(q, n, d, rnd_mode);
  if (mpfr_cmp_str (q, Qs, ((p==53) ? 10 : 2), MPFR_RNDN) )
    {
      printf ("mpfr_div failed for n=%s, d=%s, p=%d, rnd_mode=%s\n",
              Ns, Ds, p, mpfr_print_rnd_mode (rnd_mode));
      printf ("got      ");
      mpfr_dump (q);
      mpfr_set_str (q, Qs, ((p==53) ? 10 : 2), MPFR_RNDN);
      printf ("expected ");
      mpfr_dump (q);
      exit (1);
    }
  mpfr_clears (q, n, d, (mpfr_ptr) 0);
}

static void
check24 (const char *Ns, const char *Ds, mpfr_rnd_t rnd_mode, const char *Qs)
{
  mpfr_t q, n, d;

  mpfr_inits2 (24, q, n, d, (mpfr_ptr) 0);

  mpfr_set_str1 (n, Ns);
  mpfr_set_str1 (d, Ds);
  test_div(q, n, d, rnd_mode);
  if (mpfr_cmp_str1 (q, Qs) )
    {
      printf ("mpfr_div failed for n=%s, d=%s, prec=24, rnd_mode=%s\n",
             Ns, Ds, mpfr_print_rnd_mode(rnd_mode));
      printf ("expected quotient is %s, got ", Qs);
      mpfr_out_str(stdout,10,0,q, MPFR_RNDN); putchar('\n');
      exit (1);
    }
  mpfr_clears (q, n, d, (mpfr_ptr) 0);
}

/* the following examples come from the paper "Number-theoretic Test
   Generation for Directed Rounding" from Michael Parks, Table 2 */
static void
check_float(void)
{
  check24("70368760954880.0", "8388609.0", MPFR_RNDN, "8.388609e6");
  check24("140737479966720.0", "16777213.0", MPFR_RNDN, "8.388609e6");
  check24("70368777732096.0", "8388611.0", MPFR_RNDN, "8.388609e6");
  check24("105553133043712.0", "12582911.0", MPFR_RNDN, "8.38861e6");
  /* the exponent for the following example was forgotten in
     the Arith'14 version of Parks' paper */
  check24 ("12582913.0", "12582910.0", MPFR_RNDN, "1.000000238");
  check24 ("105553124655104.0", "12582910.0", MPFR_RNDN, "8388610.0");
  check24("140737479966720.0", "8388609.0", MPFR_RNDN, "1.6777213e7");
  check24("70368777732096.0", "8388609.0", MPFR_RNDN, "8.388611e6");
  check24("105553133043712.0", "8388610.0", MPFR_RNDN, "1.2582911e7");
  check24("105553124655104.0", "8388610.0", MPFR_RNDN, "1.258291e7");

  check24("70368760954880.0", "8388609.0", MPFR_RNDZ, "8.388608e6");
  check24("140737479966720.0", "16777213.0", MPFR_RNDZ, "8.388609e6");
  check24("70368777732096.0", "8388611.0", MPFR_RNDZ, "8.388608e6");
  check24("105553133043712.0", "12582911.0", MPFR_RNDZ, "8.38861e6");
  check24("12582913.0", "12582910.0", MPFR_RNDZ, "1.000000238");
  check24 ("105553124655104.0", "12582910.0", MPFR_RNDZ, "8388610.0");
  check24("140737479966720.0", "8388609.0", MPFR_RNDZ, "1.6777213e7");
  check24("70368777732096.0", "8388609.0", MPFR_RNDZ, "8.38861e6");
  check24("105553133043712.0", "8388610.0", MPFR_RNDZ, "1.2582911e7");
  check24("105553124655104.0", "8388610.0", MPFR_RNDZ, "1.258291e7");

  check24("70368760954880.0", "8388609.0", MPFR_RNDU, "8.388609e6");
  check24("140737479966720.0", "16777213.0", MPFR_RNDU, "8.38861e6");
  check24("70368777732096.0", "8388611.0", MPFR_RNDU, "8.388609e6");
  check24("105553133043712.0", "12582911.0", MPFR_RNDU, "8.388611e6");
  check24("12582913.0", "12582910.0", MPFR_RNDU, "1.000000357");
  check24 ("105553124655104.0", "12582910.0", MPFR_RNDU, "8388611.0");
  check24("140737479966720.0", "8388609.0", MPFR_RNDU, "1.6777214e7");
  check24("70368777732096.0", "8388609.0", MPFR_RNDU, "8.388611e6");
  check24("105553133043712.0", "8388610.0", MPFR_RNDU, "1.2582912e7");
  check24("105553124655104.0", "8388610.0", MPFR_RNDU, "1.2582911e7");

  check24("70368760954880.0", "8388609.0", MPFR_RNDD, "8.388608e6");
  check24("140737479966720.0", "16777213.0", MPFR_RNDD, "8.388609e6");
  check24("70368777732096.0", "8388611.0", MPFR_RNDD, "8.388608e6");
  check24("105553133043712.0", "12582911.0", MPFR_RNDD, "8.38861e6");
  check24("12582913.0", "12582910.0", MPFR_RNDD, "1.000000238");
  check24 ("105553124655104.0", "12582910.0", MPFR_RNDD, "8388610.0");
  check24("140737479966720.0", "8388609.0", MPFR_RNDD, "1.6777213e7");
  check24("70368777732096.0", "8388609.0", MPFR_RNDD, "8.38861e6");
  check24("105553133043712.0", "8388610.0", MPFR_RNDD, "1.2582911e7");
  check24("105553124655104.0", "8388610.0", MPFR_RNDD, "1.258291e7");

  check24("70368760954880.0", "8388609.0", MPFR_RNDA, "8.388609e6");
}

static void
check_double(void)
{
  check53("0.0", "1.0", MPFR_RNDZ, "0.0");
  check53("-7.4988969224688591e63", "4.8816866450288732e306", MPFR_RNDD,
          "-1.5361282826510687291e-243");
  check53("-1.33225773037748601769e+199", "3.63449540676937123913e+79",
          MPFR_RNDZ, "-3.6655920045905428978e119");
  check53("9.89438396044940256501e-134", "5.93472984109987421717e-67",MPFR_RNDU,
          "1.6672003992376663654e-67");
  check53("9.89438396044940256501e-134", "5.93472984109987421717e-67",MPFR_RNDA,
          "1.6672003992376663654e-67");
  check53("9.89438396044940256501e-134", "-5.93472984109987421717e-67",
          MPFR_RNDU, "-1.6672003992376663654e-67");
  check53("-4.53063926135729747564e-308", "7.02293374921793516813e-84",
          MPFR_RNDD, "-6.4512060388748850857e-225");
  check53("6.25089225176473806123e-01","-2.35527154824420243364e-230",
          MPFR_RNDD, "-2.6540006635008291192e229");
  check53("6.25089225176473806123e-01","-2.35527154824420243364e-230",
          MPFR_RNDA, "-2.6540006635008291192e229");
  check53("6.52308934689126e15", "-1.62063546601505417497e273", MPFR_RNDN,
          "-4.0250194961676020848e-258");
  check53("1.04636807108079349236e-189", "3.72295730823253012954e-292",
          MPFR_RNDZ, "2.810583051186143125e102");
  /* problems found by Kevin under HP-PA */
  check53 ("2.861044553323177e-136", "-1.1120354257068143e+45", MPFR_RNDZ,
           "-2.5727998292003016e-181");
  check53 ("-4.0559157245809205e-127", "-1.1237723844524865e+77", MPFR_RNDN,
           "3.6091968273068081e-204");
  check53 ("-1.8177943561493235e-93", "-8.51233984260364e-104", MPFR_RNDU,
           "2.1354814184595821e+10");
}

static void
check_64(void)
{
  mpfr_t x,y,z;

  mpfr_inits2 (64, x, y, z, (mpfr_ptr) 0);

  mpfr_set_str_binary(x, "1.00100100110110101001010010101111000001011100100101010000000000E54");
  mpfr_set_str_binary(y, "1.00000000000000000000000000000000000000000000000000000000000000E584");
  test_div(z, x, y, MPFR_RNDU);
  if (mpfr_cmp_str (z, "0.1001001001101101010010100101011110000010111001001010100000000000E-529", 2, MPFR_RNDN))
    {
      printf ("Error for tdiv for MPFR_RNDU and p=64\nx=");
      mpfr_dump (x);
      printf ("y=");
      mpfr_dump (y);
      printf ("got      ");
      mpfr_dump (z);
      printf ("expected 0.1001001001101101010010100101011110000010111001001010100000000000E-529\n");
      exit (1);
    }

  mpfr_clears (x, y, z, (mpfr_ptr) 0);
}

static void
check_convergence (void)
{
  mpfr_t x, y; int i, j;

  mpfr_init2(x, 130);
  mpfr_set_str_binary(x, "0.1011111101011010101000001010011111101000011100011101010011111011000011001010000000111100100111110011001010110100100001001000111001E6944");
  mpfr_init2(y, 130);
  mpfr_set_ui(y, 5, MPFR_RNDN);
  test_div(x, x, y, MPFR_RNDD); /* exact division */

  mpfr_set_prec(x, 64);
  mpfr_set_prec(y, 64);
  mpfr_set_str_binary(x, "0.10010010011011010100101001010111100000101110010010101E55");
  mpfr_set_str_binary(y, "0.1E585");
  test_div(x, x, y, MPFR_RNDN);
  mpfr_set_str_binary(y, "0.10010010011011010100101001010111100000101110010010101E-529");
  if (mpfr_cmp (x, y))
    {
      printf ("Error in mpfr_div for prec=64, rnd=MPFR_RNDN\n");
      printf ("got        "); mpfr_dump (x);
      printf ("instead of "); mpfr_dump (y);
      exit(1);
    }

  for (i=32; i<=64; i+=32)
    {
      mpfr_set_prec(x, i);
      mpfr_set_prec(y, i);
      mpfr_set_ui(x, 1, MPFR_RNDN);
      RND_LOOP(j)
        {
          mpfr_set_ui (y, 1, MPFR_RNDN);
          test_div (y, x, y, (mpfr_rnd_t) j);
          if (mpfr_cmp_ui (y, 1))
            {
              printf ("mpfr_div failed for x=1.0, y=1.0, prec=%d rnd=%s\n",
                      i, mpfr_print_rnd_mode ((mpfr_rnd_t) j));
              printf ("got "); mpfr_dump (y);
              exit (1);
            }
        }
    }

  mpfr_clear (x);
  mpfr_clear (y);
}

#define KMAX 10000

/* given y = o(x/u), x, u, find the inexact flag by
   multiplying y by u */
static int
get_inexact (mpfr_t y, mpfr_t x, mpfr_t u)
{
  mpfr_t xx;
  int inex;
  mpfr_init2 (xx, mpfr_get_prec (y) + mpfr_get_prec (u));
  mpfr_mul (xx, y, u, MPFR_RNDN); /* exact */
  inex = mpfr_cmp (xx, x);
  mpfr_clear (xx);
  return inex;
}

static void
check_hard (void)
{
  mpfr_t u, v, q, q2;
  mpfr_prec_t precu, precv, precq;
  int rnd;
  int inex, inex2, i, j;

  mpfr_init (q);
  mpfr_init (q2);
  mpfr_init (u);
  mpfr_init (v);

  for (precq = MPFR_PREC_MIN; precq <= 64; precq ++)
    {
      mpfr_set_prec (q, precq);
      mpfr_set_prec (q2, precq + 1);
      for (j = 0; j < 2; j++)
        {
          if (j == 0)
            {
              do
                {
                  mpfr_urandomb (q2, RANDS);
                }
              while (mpfr_cmp_ui (q2, 0) == 0);
            }
          else /* use q2=1 */
            mpfr_set_ui (q2, 1, MPFR_RNDN);
      for (precv = precq; precv <= 10 * precq; precv += precq)
        {
          mpfr_set_prec (v, precv);
          do
            {
              mpfr_urandomb (v, RANDS);
            }
          while (mpfr_cmp_ui (v, 0) == 0);
          for (precu = precq; precu <= 10 * precq; precu += precq)
            {
              mpfr_set_prec (u, precu);
              mpfr_mul (u, v, q2, MPFR_RNDN);
              mpfr_nextbelow (u);
              for (i = 0; i <= 2; i++)
                {
                  RND_LOOP_NO_RNDF (rnd)
                    {
                      inex = test_div (q, u, v, (mpfr_rnd_t) rnd);
                      inex2 = get_inexact (q, u, v);
                      if (inex_cmp (inex, inex2))
                        {
                          printf ("Wrong inexact flag for rnd=%s: expected %d, got %d\n",
                                  mpfr_print_rnd_mode ((mpfr_rnd_t) rnd), inex2, inex);
                          printf ("u=  "); mpfr_dump (u);
                          printf ("v=  "); mpfr_dump (v);
                          printf ("q=  "); mpfr_dump (q);
                          mpfr_set_prec (q2, precq + precv);
                          mpfr_mul (q2, q, v, MPFR_RNDN);
                          printf ("q*v="); mpfr_dump (q2);
                          exit (1);
                        }
                    }
                  mpfr_nextabove (u);
                }
            }
        }
        }
    }

  mpfr_clear (q);
  mpfr_clear (q2);
  mpfr_clear (u);
  mpfr_clear (v);
}

static void
check_lowr (void)
{
  mpfr_t x, y, z, z2, z3, tmp;
  int k, c, c2;


  mpfr_init2 (x, 1000);
  mpfr_init2 (y, 100);
  mpfr_init2 (tmp, 850);
  mpfr_init2 (z, 10);
  mpfr_init2 (z2, 10);
  mpfr_init2 (z3, 50);

  for (k = 1; k < KMAX; k++)
    {
      do
        {
          mpfr_urandomb (z, RANDS);
        }
      while (mpfr_cmp_ui (z, 0) == 0);
      do
        {
          mpfr_urandomb (tmp, RANDS);
        }
      while (mpfr_cmp_ui (tmp, 0) == 0);
      mpfr_mul (x, z, tmp, MPFR_RNDN); /* exact */
      c = test_div (z2, x, tmp, MPFR_RNDN);

      if (c || mpfr_cmp (z2, z))
        {
          printf ("Error in mpfr_div rnd=MPFR_RNDN\n");
          printf ("got        "); mpfr_dump (z2);
          printf ("instead of "); mpfr_dump (z);
          printf ("inex flag = %d, expected 0\n", c);
          exit (1);
        }
    }

  /* x has still precision 1000, z precision 10, and tmp prec 850 */
  mpfr_set_prec (z2, 9);
  for (k = 1; k < KMAX; k++)
    {
      mpfr_urandomb (z, RANDS);
      do
        {
          mpfr_urandomb (tmp, RANDS);
        }
      while (mpfr_cmp_ui (tmp, 0) == 0);
      mpfr_mul (x, z, tmp, MPFR_RNDN); /* exact */
      c = test_div (z2, x, tmp, MPFR_RNDN);
      /* since z2 has one less bit that z, either the division is exact
         if z is representable on 9 bits, or we have an even round case */

      c2 = get_inexact (z2, x, tmp);
      if ((mpfr_cmp (z2, z) == 0 && c) || inex_cmp (c, c2))
        {
          printf ("Error in mpfr_div rnd=MPFR_RNDN\n");
          printf ("got        "); mpfr_dump (z2);
          printf ("instead of "); mpfr_dump (z);
          printf ("inex flag = %d, expected %d\n", c, c2);
          exit (1);
        }
      else if (c == 2)
        {
          mpfr_nexttoinf (z);
          if (mpfr_cmp(z2, z))
            {
              printf ("Error in mpfr_div [even rnd?] rnd=MPFR_RNDN\n");
              printf ("Dividing ");
              printf ("got        "); mpfr_dump (z2);
              printf ("instead of "); mpfr_dump (z);
              printf ("inex flag = %d\n", 1);
              exit (1);
            }
        }
      else if (c == -2)
        {
          mpfr_nexttozero (z);
          if (mpfr_cmp(z2, z))
            {
              printf ("Error in mpfr_div [even rnd?] rnd=MPFR_RNDN\n");
              printf ("Dividing ");
              printf ("got        "); mpfr_dump (z2);
              printf ("instead of "); mpfr_dump (z);
              printf ("inex flag = %d\n", 1);
              exit (1);
            }
        }
    }

  mpfr_set_prec(x, 1000);
  mpfr_set_prec(y, 100);
  mpfr_set_prec(tmp, 850);
  mpfr_set_prec(z, 10);
  mpfr_set_prec(z2, 10);

  /* almost exact divisions */
  for (k = 1; k < KMAX; k++)
    {
      do
        {
          mpfr_urandomb (z, RANDS);
        }
      while (mpfr_cmp_ui (z, 0) == 0);
      do
        {
          mpfr_urandomb (tmp, RANDS);
        }
      while (mpfr_cmp_ui (tmp, 0) == 0);
      mpfr_mul(x, z, tmp, MPFR_RNDN);
      mpfr_set(y, tmp, MPFR_RNDD);
      mpfr_nexttoinf (x);

      c = test_div(z2, x, y, MPFR_RNDD);
      test_div(z3, x, y, MPFR_RNDD);
      mpfr_set(z, z3, MPFR_RNDD);

      if (c != -1 || mpfr_cmp(z2, z))
        {
          printf ("Error in mpfr_div rnd=MPFR_RNDD\n");
          printf ("got        "); mpfr_dump (z2);
          printf ("instead of "); mpfr_dump (z);
          printf ("inex flag = %d\n", c);
          exit (1);
        }

      mpfr_set (y, tmp, MPFR_RNDU);
      test_div (z3, x, y, MPFR_RNDU);
      mpfr_set (z, z3, MPFR_RNDU);
      c = test_div (z2, x, y, MPFR_RNDU);
      if (c != 1 || mpfr_cmp (z2, z))
        {
          printf ("Error in mpfr_div rnd=MPFR_RNDU\n");
          printf ("u="); mpfr_dump (x);
          printf ("v="); mpfr_dump (y);
          printf ("got        "); mpfr_dump (z2);
          printf ("instead of "); mpfr_dump (z);
          printf ("inex flag = %d\n", c);
          exit (1);
        }
    }

  mpfr_clear (x);
  mpfr_clear (y);
  mpfr_clear (z);
  mpfr_clear (z2);
  mpfr_clear (z3);
  mpfr_clear (tmp);
}

#define MAX_PREC 128

static void
check_inexact (void)
{
  mpfr_t x, y, z, u;
  mpfr_prec_t px, py, pu;
  int inexact, cmp;
  mpfr_rnd_t rnd;

  mpfr_init (x);
  mpfr_init (y);
  mpfr_init (z);
  mpfr_init (u);

  mpfr_set_prec (x, 28);
  mpfr_set_prec (y, 28);
  mpfr_set_prec (z, 1023);
  mpfr_set_str_binary (x, "0.1000001001101101111100010011E0");
  mpfr_set_str (z, "48284762641021308813686974720835219181653367326353400027913400579340343320519877153813133510034402932651132854764198688352364361009429039801248971901380781746767119334993621199563870113045276395603170432175354501451429471578325545278975153148347684600400321033502982713296919861760382863826626093689036010394", 10, MPFR_RNDN);
  mpfr_div (x, x, z, MPFR_RNDN);
  mpfr_set_str_binary (y, "0.1111001011001101001001111100E-1023");
  if (mpfr_cmp (x, y))
    {
      printf ("Error in mpfr_div for prec=28, RNDN\n");
      printf ("Expected "); mpfr_dump (y);
      printf ("Got      "); mpfr_dump (x);
      exit (1);
    }

  mpfr_set_prec (x, 53);
  mpfr_set_str_binary (x, "0.11101100110010100011011000000100001111011111110010101E0");
  mpfr_set_prec (u, 127);
  mpfr_set_str_binary (u, "0.1000001100110110110101110110101101111000110000001111111110000000011111001010110100110010111111111101000001011011101011101101000E-2");
  mpfr_set_prec (y, 95);
  inexact = test_div (y, x, u, MPFR_RNDN);
  if (inexact != (cmp = get_inexact (y, x, u)))
    {
      printf ("Wrong inexact flag (0): expected %d, got %d\n", cmp, inexact);
      printf ("x="); mpfr_out_str (stdout, 10, 99, x, MPFR_RNDN); printf ("\n");
      printf ("u="); mpfr_out_str (stdout, 10, 99, u, MPFR_RNDN); printf ("\n");
      printf ("y="); mpfr_out_str (stdout, 10, 99, y, MPFR_RNDN); printf ("\n");
      exit (1);
    }

  mpfr_set_prec (x, 33);
  mpfr_set_str_binary (x, "0.101111100011011101010011101100001E0");
  mpfr_set_prec (u, 2);
  mpfr_set_str_binary (u, "0.1E0");
  mpfr_set_prec (y, 28);
  inexact = test_div (y, x, u, MPFR_RNDN);
  if (inexact >= 0)
    {
      printf ("Wrong inexact flag (1): expected -1, got %d\n",
              inexact);
      exit (1);
    }

  mpfr_set_prec (x, 129);
  mpfr_set_str_binary (x, "0.111110101111001100000101011100101100110011011101010001000110110101100101000010000001110110100001101010001010100010001111001101010E-2");
  mpfr_set_prec (u, 15);
  mpfr_set_str_binary (u, "0.101101000001100E-1");
  mpfr_set_prec (y, 92);
  inexact = test_div (y, x, u, MPFR_RNDN);
  if (inexact <= 0)
    {
      printf ("Wrong inexact flag for rnd=MPFR_RNDN(1): expected 1, got %d\n",
              inexact);
      mpfr_dump (x);
      mpfr_dump (u);
      mpfr_dump (y);
      exit (1);
    }

  for (px=2; px<MAX_PREC; px++)
    {
      mpfr_set_prec (x, px);
      mpfr_urandomb (x, RANDS);
      for (pu=2; pu<=MAX_PREC; pu++)
        {
          mpfr_set_prec (u, pu);
          do { mpfr_urandomb (u, RANDS); } while (mpfr_cmp_ui (u, 0) == 0);
            {
              py = MPFR_PREC_MIN + (randlimb () % (MAX_PREC - MPFR_PREC_MIN));
              mpfr_set_prec (y, py);
              mpfr_set_prec (z, py + pu);
                {
                  /* inexact is undefined for RNDF */
                  rnd = RND_RAND_NO_RNDF ();
                  inexact = test_div (y, x, u, rnd);
                  if (mpfr_mul (z, y, u, rnd))
                    {
                      printf ("z <- y * u should be exact\n");
                      exit (1);
                    }
                  cmp = mpfr_cmp (z, x);
                  if (((inexact == 0) && (cmp != 0)) ||
                      ((inexact > 0) && (cmp <= 0)) ||
                      ((inexact < 0) && (cmp >= 0)))
                    {
                      printf ("Wrong inexact flag for rnd=%s\n",
                              mpfr_print_rnd_mode(rnd));
                      printf ("expected %d, got %d\n", cmp, inexact);
                      printf ("x="); mpfr_dump (x);
                      printf ("u="); mpfr_dump (u);
                      printf ("y="); mpfr_dump (y);
                      printf ("y*u="); mpfr_dump (z);
                      exit (1);
                    }
                }
            }
        }
    }

  mpfr_clear (x);
  mpfr_clear (y);
  mpfr_clear (z);
  mpfr_clear (u);
}

static void
check_special (void)
{
  mpfr_t  a, d, q;
  mpfr_exp_t emax, emin;
  int i;

  mpfr_init2 (a, 100L);
  mpfr_init2 (d, 100L);
  mpfr_init2 (q, 100L);

  /* 1/nan == nan */
  mpfr_set_ui (a, 1L, MPFR_RNDN);
  MPFR_SET_NAN (d);
  mpfr_clear_flags ();
  MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */
  MPFR_ASSERTN (__gmpfr_flags == MPFR_FLAGS_NAN);

  /* nan/1 == nan */
  MPFR_SET_NAN (a);
  mpfr_set_ui (d, 1L, MPFR_RNDN);
  mpfr_clear_flags ();
  MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */
  MPFR_ASSERTN (__gmpfr_flags == MPFR_FLAGS_NAN);

  /* +inf/1 == +inf */
  MPFR_SET_INF (a);
  MPFR_SET_POS (a);
  mpfr_set_ui (d, 1L, MPFR_RNDN);
  mpfr_clear_flags ();
  MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */
  MPFR_ASSERTN (mpfr_inf_p (q));
  MPFR_ASSERTN (mpfr_sgn (q) > 0);
  MPFR_ASSERTN (__gmpfr_flags == 0);

  /* +inf/-1 == -inf */
  MPFR_SET_INF (a);
  MPFR_SET_POS (a);
  mpfr_set_si (d, -1, MPFR_RNDN);
  mpfr_clear_flags ();
  MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */
  MPFR_ASSERTN (mpfr_inf_p (q));
  MPFR_ASSERTN (mpfr_sgn (q) < 0);
  MPFR_ASSERTN (__gmpfr_flags == 0);

  /* -inf/1 == -inf */
  MPFR_SET_INF (a);
  MPFR_SET_NEG (a);
  mpfr_set_ui (d, 1L, MPFR_RNDN);
  mpfr_clear_flags ();
  MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */
  MPFR_ASSERTN (mpfr_inf_p (q));
  MPFR_ASSERTN (mpfr_sgn (q) < 0);
  MPFR_ASSERTN (__gmpfr_flags == 0);

  /* -inf/-1 == +inf */
  MPFR_SET_INF (a);
  MPFR_SET_NEG (a);
  mpfr_set_si (d, -1, MPFR_RNDN);
  mpfr_clear_flags ();
  MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */
  MPFR_ASSERTN (mpfr_inf_p (q));
  MPFR_ASSERTN (mpfr_sgn (q) > 0);
  MPFR_ASSERTN (__gmpfr_flags == 0);

  /* 1/+inf == +0 */
  mpfr_set_ui (a, 1L, MPFR_RNDN);
  MPFR_SET_INF (d);
  MPFR_SET_POS (d);
  mpfr_clear_flags ();
  MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */
  MPFR_ASSERTN (MPFR_IS_ZERO (q));
  MPFR_ASSERTN (MPFR_IS_POS (q));
  MPFR_ASSERTN (__gmpfr_flags == 0);

  /* 1/-inf == -0 */
  mpfr_set_ui (a, 1L, MPFR_RNDN);
  MPFR_SET_INF (d);
  MPFR_SET_NEG (d);
  mpfr_clear_flags ();
  MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */
  MPFR_ASSERTN (MPFR_IS_ZERO (q));
  MPFR_ASSERTN (MPFR_IS_NEG (q));
  MPFR_ASSERTN (__gmpfr_flags == 0);

  /* -1/+inf == -0 */
  mpfr_set_si (a, -1, MPFR_RNDN);
  MPFR_SET_INF (d);
  MPFR_SET_POS (d);
  mpfr_clear_flags ();
  MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */
  MPFR_ASSERTN (MPFR_IS_ZERO (q));
  MPFR_ASSERTN (MPFR_IS_NEG (q));
  MPFR_ASSERTN (__gmpfr_flags == 0);

  /* -1/-inf == +0 */
  mpfr_set_si (a, -1, MPFR_RNDN);
  MPFR_SET_INF (d);
  MPFR_SET_NEG (d);
  mpfr_clear_flags ();
  MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */
  MPFR_ASSERTN (MPFR_IS_ZERO (q));
  MPFR_ASSERTN (MPFR_IS_POS (q));
  MPFR_ASSERTN (__gmpfr_flags == 0);

  /* 0/0 == nan */
  mpfr_set_ui (a, 0L, MPFR_RNDN);
  mpfr_set_ui (d, 0L, MPFR_RNDN);
  mpfr_clear_flags ();
  MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */
  MPFR_ASSERTN (__gmpfr_flags == MPFR_FLAGS_NAN);

  /* +inf/+inf == nan */
  MPFR_SET_INF (a);
  MPFR_SET_POS (a);
  MPFR_SET_INF (d);
  MPFR_SET_POS (d);
  mpfr_clear_flags ();
  MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */
  MPFR_ASSERTN (__gmpfr_flags == MPFR_FLAGS_NAN);

  /* 1/+0 = +inf */
  mpfr_set_ui (a, 1, MPFR_RNDZ);
  mpfr_set_ui (d, 0, MPFR_RNDZ);
  mpfr_clear_flags ();
  MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */
  MPFR_ASSERTN (mpfr_inf_p (q) && mpfr_sgn (q) > 0);
  MPFR_ASSERTN (__gmpfr_flags == MPFR_FLAGS_DIVBY0);

  /* 1/-0 = -inf */
  mpfr_set_ui (a, 1, MPFR_RNDZ);
  mpfr_set_ui (d, 0, MPFR_RNDZ);
  mpfr_neg (d, d, MPFR_RNDZ);
  mpfr_clear_flags ();
  MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */
  MPFR_ASSERTN (mpfr_inf_p (q) && mpfr_sgn (q) < 0);
  MPFR_ASSERTN (__gmpfr_flags == MPFR_FLAGS_DIVBY0);

  /* -1/+0 = -inf */
  mpfr_set_si (a, -1, MPFR_RNDZ);
  mpfr_set_ui (d, 0, MPFR_RNDZ);
  mpfr_clear_flags ();
  MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */
  MPFR_ASSERTN (mpfr_inf_p (q) && mpfr_sgn (q) < 0);
  MPFR_ASSERTN (__gmpfr_flags == MPFR_FLAGS_DIVBY0);

  /* -1/-0 = +inf */
  mpfr_set_si (a, -1, MPFR_RNDZ);
  mpfr_set_ui (d, 0, MPFR_RNDZ);
  mpfr_neg (d, d, MPFR_RNDZ);
  mpfr_clear_flags ();
  MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */
  MPFR_ASSERTN (mpfr_inf_p (q) && mpfr_sgn (q) > 0);
  MPFR_ASSERTN (__gmpfr_flags == MPFR_FLAGS_DIVBY0);

  /* +inf/+0 = +inf */
  MPFR_SET_INF (a);
  MPFR_SET_POS (a);
  mpfr_set_ui (d, 0, MPFR_RNDZ);
  mpfr_clear_flags ();
  MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */
  MPFR_ASSERTN (mpfr_inf_p (q) && mpfr_sgn (q) > 0);
  MPFR_ASSERTN (__gmpfr_flags == 0);

  /* +inf/-0 = -inf */
  MPFR_SET_INF (a);
  MPFR_SET_POS (a);
  mpfr_set_ui (d, 0, MPFR_RNDZ);
  mpfr_neg (d, d, MPFR_RNDZ);
  mpfr_clear_flags ();
  MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */
  MPFR_ASSERTN (mpfr_inf_p (q) && mpfr_sgn (q) < 0);
  MPFR_ASSERTN (__gmpfr_flags == 0);

  /* -inf/+0 = -inf */
  MPFR_SET_INF (a);
  MPFR_SET_NEG (a);
  mpfr_set_ui (d, 0, MPFR_RNDZ);
  mpfr_clear_flags ();
  MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */
  MPFR_ASSERTN (mpfr_inf_p (q) && mpfr_sgn (q) < 0);
  MPFR_ASSERTN (__gmpfr_flags == 0);

  /* -inf/-0 = +inf */
  MPFR_SET_INF (a);
  MPFR_SET_NEG (a);
  mpfr_set_ui (d, 0, MPFR_RNDZ);
  mpfr_neg (d, d, MPFR_RNDZ);
  mpfr_clear_flags ();
  MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */
  MPFR_ASSERTN (mpfr_inf_p (q) && mpfr_sgn (q) > 0);
  MPFR_ASSERTN (__gmpfr_flags == 0);

  /* check overflow */
  emax = mpfr_get_emax ();
  set_emax (1);
  mpfr_set_ui (a, 1, MPFR_RNDZ);
  mpfr_set_ui (d, 1, MPFR_RNDZ);
  mpfr_div_2exp (d, d, 1, MPFR_RNDZ);
  mpfr_clear_flags ();
  test_div (q, a, d, MPFR_RNDU); /* 1 / 0.5 = 2 -> overflow */
  MPFR_ASSERTN (mpfr_inf_p (q) && mpfr_sgn (q) > 0);
  MPFR_ASSERTN (__gmpfr_flags == (MPFR_FLAGS_OVERFLOW | MPFR_FLAGS_INEXACT));
  set_emax (emax);

  /* check underflow */
  emin = mpfr_get_emin ();
  set_emin (-1);
  mpfr_set_ui (a, 1, MPFR_RNDZ);
  mpfr_div_2exp (a, a, 2, MPFR_RNDZ);
  mpfr_set_prec (d, mpfr_get_prec (q) + 8);
  for (i = -1; i <= 1; i++)
    {
      int sign;

      /* Test 2^(-2) / (+/- (2 + eps)), with eps < 0, eps = 0, eps > 0.
         -> underflow.
         With div.c r5513, this test fails for eps > 0 in MPFR_RNDN. */
      mpfr_set_ui (d, 2, MPFR_RNDZ);
      if (i < 0)
        mpfr_nextbelow (d);
      if (i > 0)
        mpfr_nextabove (d);
      for (sign = 0; sign <= 1; sign++)
        {
          mpfr_clear_flags ();
          test_div (q, a, d, MPFR_RNDZ); /* result = 0 */
          MPFR_ASSERTN (__gmpfr_flags ==
                        (MPFR_FLAGS_UNDERFLOW | MPFR_FLAGS_INEXACT));
          MPFR_ASSERTN (sign ? MPFR_IS_NEG (q) : MPFR_IS_POS (q));
          MPFR_ASSERTN (MPFR_IS_ZERO (q));
          mpfr_clear_flags ();
          test_div (q, a, d, MPFR_RNDN); /* result = 0 iff eps >= 0 */
          MPFR_ASSERTN (__gmpfr_flags ==
                        (MPFR_FLAGS_UNDERFLOW | MPFR_FLAGS_INEXACT));
          MPFR_ASSERTN (sign ? MPFR_IS_NEG (q) : MPFR_IS_POS (q));
          if (i < 0)
            mpfr_nexttozero (q);
          MPFR_ASSERTN (MPFR_IS_ZERO (q));
          mpfr_neg (d, d, MPFR_RNDN);
        }
    }
  set_emin (emin);

  mpfr_clear (a);
  mpfr_clear (d);
  mpfr_clear (q);
}

static void
consistency (void)
{
  mpfr_t x, y, z1, z2;
  int i;

  mpfr_inits (x, y, z1, z2, (mpfr_ptr) 0);

  for (i = 0; i < 10000; i++)
    {
      mpfr_rnd_t rnd;
      mpfr_prec_t px, py, pz, p;
      int inex1, inex2;

      /* inex is undefined for RNDF */
      rnd = RND_RAND_NO_RNDF ();
      px = (randlimb () % 256) + 2;
      py = (randlimb () % 128) + 2;
      pz = (randlimb () % 256) + 2;
      mpfr_set_prec (x, px);
      mpfr_set_prec (y, py);
      mpfr_set_prec (z1, pz);
      mpfr_set_prec (z2, pz);
      mpfr_urandomb (x, RANDS);
      do
        mpfr_urandomb (y, RANDS);
      while (mpfr_zero_p (y));
      inex1 = mpfr_div (z1, x, y, rnd);
      MPFR_ASSERTN (!MPFR_IS_NAN (z1));
      p = MAX (MAX (px, py), pz);
      if (mpfr_prec_round (x, p, MPFR_RNDN) != 0 ||
          mpfr_prec_round (y, p, MPFR_RNDN) != 0)
        {
          printf ("mpfr_prec_round error for i = %d\n", i);
          exit (1);
        }
      inex2 = mpfr_div (z2, x, y, rnd);
      MPFR_ASSERTN (!MPFR_IS_NAN (z2));
      if (inex1 != inex2 || mpfr_cmp (z1, z2) != 0)
        {
          printf ("Consistency error for i = %d, rnd = %s\n", i,
                  mpfr_print_rnd_mode (rnd));
          printf ("inex1=%d inex2=%d\n", inex1, inex2);
          printf ("z1="); mpfr_dump (z1);
          printf ("z2="); mpfr_dump (z2);
          exit (1);
        }
    }

  mpfr_clears (x, y, z1, z2, (mpfr_ptr) 0);
}

/* Reported by Carl Witty on 2007-06-03 */
static void
test_20070603 (void)
{
  mpfr_t n, d, q, c;

  mpfr_init2 (n, 128);
  mpfr_init2 (d, 128);
  mpfr_init2 (q, 31);
  mpfr_init2 (c, 31);

  mpfr_set_str (n, "10384593717069655257060992206846485", 10, MPFR_RNDN);
  mpfr_set_str (d, "10384593717069655257060992206847132", 10, MPFR_RNDN);
  mpfr_div (q, n, d, MPFR_RNDU);

  mpfr_set_ui (c, 1, MPFR_RNDN);
  if (mpfr_cmp (q, c) != 0)
    {
      printf ("Error in test_20070603\nGot        ");
      mpfr_dump (q);
      printf ("instead of ");
      mpfr_dump (c);
      exit (1);
    }

  /* same for 64-bit machines */
  mpfr_set_prec (n, 256);
  mpfr_set_prec (d, 256);
  mpfr_set_prec (q, 63);
  mpfr_set_str (n, "822752278660603021077484591278675252491367930877209729029898240", 10, MPFR_RNDN);
  mpfr_set_str (d, "822752278660603021077484591278675252491367930877212507873738752", 10, MPFR_RNDN);
  mpfr_div (q, n, d, MPFR_RNDU);
  if (mpfr_cmp (q, c) != 0)
    {
      printf ("Error in test_20070603\nGot        ");
      mpfr_dump (q);
      printf ("instead of ");
      mpfr_dump (c);
      exit (1);
    }

  mpfr_clear (n);
  mpfr_clear (d);
  mpfr_clear (q);
  mpfr_clear (c);
}

/* Bug found while adding tests for mpfr_cot */
static void
test_20070628 (void)
{
  mpfr_exp_t old_emax;
  mpfr_t x, y;
  int inex, err = 0;

  old_emax = mpfr_get_emax ();

  if (mpfr_set_emax (256))
    {
      printf ("Can't change exponent range\n");
      exit (1);
    }

  mpfr_inits2 (53, x, y, (mpfr_ptr) 0);
  mpfr_set_si (x, -1, MPFR_RNDN);
  mpfr_set_si_2exp (y, 1, -256, MPFR_RNDN);
  mpfr_clear_flags ();
  inex = mpfr_div (x, x, y, MPFR_RNDD);
  if (MPFR_IS_POS (x) || ! mpfr_inf_p (x))
    {
      printf ("Error in test_20070628: expected -Inf, got\n");
      mpfr_dump (x);
      err++;
    }
  if (inex >= 0)
    {
      printf ("Error in test_20070628: expected inex < 0, got %d\n", inex);
      err++;
    }
  if (! mpfr_overflow_p ())
    {
      printf ("Error in test_20070628: overflow flag is not set\n");
      err++;
    }
  mpfr_clears (x, y, (mpfr_ptr) 0);
  mpfr_set_emax (old_emax);
}

/* Bug in mpfr_divhigh_n_basecase when all limbs of q (except the most
   significant one) are B-1 where B=2^GMP_NUMB_BITS. Since we truncate
   the divisor at each step, it might happen at some point that
   (np[n-1],np[n-2]) > (d1,d0), and not only the equality.
   Reported by Ricky Farr
   <https://sympa.inria.fr/sympa/arc/mpfr/2015-10/msg00023.html>
   To get a failure, a MPFR_DIVHIGH_TAB entry below the MPFR_DIV_THRESHOLD
   limit must have a value 0. With most mparam.h files, this cannot occur. To
   make the bug appear, one can configure MPFR with -DMPFR_TUNE_COVERAGE. */
static void
test_20151023 (void)
{
  mpfr_prec_t p;
  mpfr_t n, d, q, q0;
  int inex, i;

  for (p = GMP_NUMB_BITS; p <= 2000; p++)
    {
      mpfr_init2 (n, 2*p);
      mpfr_init2 (d, p);
      mpfr_init2 (q, p);
      mpfr_init2 (q0, GMP_NUMB_BITS);

      /* generate a random divisor of p bits */
      mpfr_urandomb (d, RANDS);
      /* generate a random quotient of GMP_NUMB_BITS bits */
      mpfr_urandomb (q0, RANDS);
      /* zero-pad the quotient to p bits */
      inex = mpfr_prec_round (q0, p, MPFR_RNDN);
      MPFR_ASSERTN(inex == 0);

      for (i = 0; i < 3; i++)
        {
          /* i=0: try with the original quotient xxx000...000
             i=1: try with the original quotient minus one ulp
             i=2: try with the original quotient plus one ulp */
          if (i == 1)
            mpfr_nextbelow (q0);
          else if (i == 2)
            {
              mpfr_nextabove (q0);
              mpfr_nextabove (q0);
            }

          inex = mpfr_mul (n, d, q0, MPFR_RNDN);
          MPFR_ASSERTN(inex == 0);
          mpfr_nextabove (n);
          mpfr_div (q, n, d, MPFR_RNDN);
          MPFR_ASSERTN(mpfr_cmp (q, q0) == 0);

          inex = mpfr_mul (n, d, q0, MPFR_RNDN);
          MPFR_ASSERTN(inex == 0);
          mpfr_nextbelow (n);
          mpfr_div (q, n, d, MPFR_RNDN);
          MPFR_ASSERTN(mpfr_cmp (q, q0) == 0);
        }

      mpfr_clear (n);
      mpfr_clear (d);
      mpfr_clear (q);
      mpfr_clear (q0);
    }
}

/* test a random division of p+extra bits divided by p+extra bits,
   with quotient of p bits only, where the p+extra bit approximation
   of the quotient is very near a rounding frontier. */
static void
test_bad_aux (mpfr_prec_t p, mpfr_prec_t extra)
{
  mpfr_t u, v, w, q0, q;

  mpfr_init2 (u, p + extra);
  mpfr_init2 (v, p + extra);
  mpfr_init2 (w, p + extra);
  mpfr_init2 (q0, p);
  mpfr_init2 (q, p);
  do mpfr_urandomb (q0, RANDS); while (mpfr_zero_p (q0));
  do mpfr_urandomb (v, RANDS); while (mpfr_zero_p (v));

  mpfr_set (w, q0, MPFR_RNDN); /* exact */
  mpfr_nextabove (w); /* now w > q0 */
  mpfr_mul (u, v, w, MPFR_RNDU); /* thus u > v*q0 */
  mpfr_div (q, u, v, MPFR_RNDU); /* should have q > q0 */
  MPFR_ASSERTN (mpfr_cmp (q, q0) > 0);
  mpfr_div (q, u, v, MPFR_RNDZ); /* should have q = q0 */
  MPFR_ASSERTN (mpfr_cmp (q, q0) == 0);

  mpfr_set (w, q0, MPFR_RNDN); /* exact */
  mpfr_nextbelow (w); /* now w < q0 */
  mpfr_mul (u, v, w, MPFR_RNDZ); /* thus u < v*q0 */
  mpfr_div (q, u, v, MPFR_RNDZ); /* should have q < q0 */
  MPFR_ASSERTN (mpfr_cmp (q, q0) < 0);
  mpfr_div (q, u, v, MPFR_RNDU); /* should have q = q0 */
  MPFR_ASSERTN (mpfr_cmp (q, q0) == 0);

  mpfr_clear (u);
  mpfr_clear (v);
  mpfr_clear (w);
  mpfr_clear (q0);
  mpfr_clear (q);
}

static void
test_bad (void)
{
  mpfr_prec_t p, extra;

  for (p = MPFR_PREC_MIN; p <= 1024; p += 17)
    for (extra = 2; extra <= 64; extra++)
      test_bad_aux (p, extra);
}

#define TEST_FUNCTION test_div
#define TWO_ARGS
#define RAND_FUNCTION(x) mpfr_random2(x, MPFR_LIMB_SIZE (x), randlimb () % 100, RANDS)
#include "tgeneric.c"

static void
test_extreme (void)
{
  mpfr_t x, y, z;
  mpfr_exp_t emin, emax;
  mpfr_prec_t p[4] = { 8, 32, 64, 256 };
  int xi, yi, zi, j, r;
  unsigned int flags, ex_flags;

  emin = mpfr_get_emin ();
  emax = mpfr_get_emax ();

  mpfr_set_emin (MPFR_EMIN_MIN);
  mpfr_set_emax (MPFR_EMAX_MAX);

  for (xi = 0; xi < 4; xi++)
    {
      mpfr_init2 (x, p[xi]);
      mpfr_setmax (x, MPFR_EMAX_MAX);
      MPFR_ASSERTN (mpfr_check (x));
      for (yi = 0; yi < 4; yi++)
        {
          mpfr_init2 (y, p[yi]);
          mpfr_setmin (y, MPFR_EMIN_MIN);
          for (j = 0; j < 2; j++)
            {
              MPFR_ASSERTN (mpfr_check (y));
              for (zi = 0; zi < 4; zi++)
                {
                  mpfr_init2 (z, p[zi]);
                  RND_LOOP (r)
                    {
                      mpfr_clear_flags ();
                      mpfr_div (z, x, y, (mpfr_rnd_t) r);
                      flags = __gmpfr_flags;
                      MPFR_ASSERTN (mpfr_check (z));
                      ex_flags = MPFR_FLAGS_OVERFLOW | MPFR_FLAGS_INEXACT;
                      if (flags != ex_flags)
                        {
                          printf ("Bad flags in test_extreme on z = a/b"
                                  " with %s and\n",
                                  mpfr_print_rnd_mode ((mpfr_rnd_t) r));
                          printf ("a = ");
                          mpfr_dump (x);
                          printf ("b = ");
                          mpfr_dump (y);
                          printf ("Expected flags:");
                          flags_out (ex_flags);
                          printf ("Got flags:     ");
                          flags_out (flags);
                          printf ("z = ");
                          mpfr_dump (z);
                          exit (1);
                        }
                      mpfr_clear_flags ();
                      mpfr_div (z, y, x, (mpfr_rnd_t) r);
                      flags = __gmpfr_flags;
                      MPFR_ASSERTN (mpfr_check (z));
                      ex_flags = MPFR_FLAGS_UNDERFLOW | MPFR_FLAGS_INEXACT;
                      if (flags != ex_flags)
                        {
                          printf ("Bad flags in test_extreme on z = a/b"
                                  " with %s and\n",
                                  mpfr_print_rnd_mode ((mpfr_rnd_t) r));
                          printf ("a = ");
                          mpfr_dump (y);
                          printf ("b = ");
                          mpfr_dump (x);
                          printf ("Expected flags:");
                          flags_out (ex_flags);
                          printf ("Got flags:     ");
                          flags_out (flags);
                          printf ("z = ");
                          mpfr_dump (z);
                          exit (1);
                        }
                    }
                  mpfr_clear (z);
                }  /* zi */
              mpfr_nextabove (y);
            }  /* j */
          mpfr_clear (y);
        }  /* yi */
      mpfr_clear (x);
    }  /* xi */

  set_emin (emin);
  set_emax (emax);
}

static void
testall_rndf (mpfr_prec_t pmax)
{
  mpfr_t a, b, c, d;
  mpfr_prec_t pa, pb, pc;

  for (pa = MPFR_PREC_MIN; pa <= pmax; pa++)
    {
      mpfr_init2 (a, pa);
      mpfr_init2 (d, pa);
      for (pb = MPFR_PREC_MIN; pb <= pmax; pb++)
        {
          mpfr_init2 (b, pb);
          mpfr_set_ui (b, 1, MPFR_RNDN);
          while (mpfr_cmp_ui (b, 2) < 0)
            {
              for (pc = MPFR_PREC_MIN; pc <= pmax; pc++)
                {
                  mpfr_init2 (c, pc);
                  mpfr_set_ui (c, 1, MPFR_RNDN);
                  while (mpfr_cmp_ui (c, 2) < 0)
                    {
                      mpfr_div (a, b, c, MPFR_RNDF);
                      mpfr_div (d, b, c, MPFR_RNDD);
                      if (!mpfr_equal_p (a, d))
                        {
                          mpfr_div (d, b, c, MPFR_RNDU);
                          if (!mpfr_equal_p (a, d))
                            {
                              printf ("Error: mpfr_div(a,b,c,RNDF) does not "
                                      "match RNDD/RNDU\n");
                              printf ("b="); mpfr_dump (b);
                              printf ("c="); mpfr_dump (c);
                              printf ("a="); mpfr_dump (a);
                              exit (1);
                            }
                        }
                      mpfr_nextabove (c);
                    }
                  mpfr_clear (c);
                }
              mpfr_nextabove (b);
            }
          mpfr_clear (b);
        }
      mpfr_clear (a);
      mpfr_clear (d);
    }
}

static void
test_mpfr_divsp2 (void)
{
  mpfr_t u, v, q;

  /* test to exercise r2 = v1 in mpfr_divsp2 */
  mpfr_init2 (u, 128);
  mpfr_init2 (v, 128);
  mpfr_init2 (q, 83);

  mpfr_set_str (u, "286677858044426991425771529092412636160", 10, MPFR_RNDN);
  mpfr_set_str (v, "241810647971575979588130185988987264768", 10, MPFR_RNDN);
  mpfr_div (q, u, v, MPFR_RNDN);
  mpfr_set_str (u, "5732952910203749289426944", 10, MPFR_RNDN);
  mpfr_div_2exp (u, u, 82, MPFR_RNDN);
  MPFR_ASSERTN(mpfr_equal_p (q, u));

  mpfr_clear (u);
  mpfr_clear (v);
  mpfr_clear (q);
}

/* Assertion failure in r10769 with --enable-assert --enable-gmp-internals
   (same failure in tatan on a similar example). */
static void
test_20160831 (void)
{
  mpfr_t u, v, q;

  mpfr_inits2 (124, u, v, q, (mpfr_ptr) 0);

  mpfr_set_ui (u, 1, MPFR_RNDN);
  mpfr_set_str (v, "0x40000000000000005", 16, MPFR_RNDN);
  mpfr_div (q, u, v, MPFR_RNDN);
  mpfr_set_str (u, "0xfffffffffffffffecp-134", 16, MPFR_RNDN);
  MPFR_ASSERTN (mpfr_equal_p (q, u));

  mpfr_set_prec (u, 128);
  mpfr_set_prec (v, 128);
  mpfr_set_str (u, "186127091671619245460026015088243485690", 10, MPFR_RNDN);
  mpfr_set_str (v, "205987256581218236405412302590110119580", 10, MPFR_RNDN);
  mpfr_div (q, u, v, MPFR_RNDN);
  mpfr_set_str (u, "19217137613667309953639458782352244736", 10, MPFR_RNDN);
  mpfr_div_2exp (u, u, 124, MPFR_RNDN);
  MPFR_ASSERTN (mpfr_equal_p (q, u));

  mpfr_clears (u, v, q, (mpfr_ptr) 0);
}

/* With r11138, on a 64-bit machine:
   div.c:128: MPFR assertion failed: qx >= __gmpfr_emin
*/
static void
test_20170104 (void)
{
  mpfr_t u, v, q;
  mpfr_exp_t emin;

  emin = mpfr_get_emin ();
  set_emin (-42);

  mpfr_init2 (u, 12);
  mpfr_init2 (v, 12);
  mpfr_init2 (q, 11);
  mpfr_set_str_binary (u, "0.111111111110E-29");
  mpfr_set_str_binary (v, "0.111111111111E14");
  mpfr_div (q, u, v, MPFR_RNDN);
  mpfr_clears (u, v, q, (mpfr_ptr) 0);

  set_emin (emin);
}

/* With r11140, on a 64-bit machine with GMP_CHECK_RANDOMIZE=1484406128:
   Consistency error for i = 2577
*/
static void
test_20170105 (void)
{
  mpfr_t x, y, z, t;

  mpfr_init2 (x, 138);
  mpfr_init2 (y, 6);
  mpfr_init2 (z, 128);
  mpfr_init2 (t, 128);
  mpfr_set_str_binary (x, "0.100110111001001000101111010010011101111110111111110001110100000001110111010100111010100011101010110000010100000011100100110101101011000000E-6");
  mpfr_set_str_binary (y, "0.100100E-2");
  /* up to exponents, x/y is exactly 367625553447399614694201910705139062483,
     which has 129 bits, thus we are in the round-to-nearest-even case, and since
     the penultimate bit of x/y is 1, we should round upwards */
  mpfr_set_str_binary (t, "0.10001010010010010000110110010110111111111100011011101010000000000110101000010001011110011011010000111010000000001100101101101010E-3");
  mpfr_div (z, x, y, MPFR_RNDN);
  MPFR_ASSERTN(mpfr_equal_p (z, t));
  mpfr_clears (x, y, z, t, (mpfr_ptr) 0);
}

/* The real cause of the mpfr_ttanh failure from the non-regression test
   added in tests/ttanh.c@11993 was actually due to a bug in mpfr_div, as
   this can be seen by comparing the logs of the 3.1 branch and the trunk
   r11992 with MPFR_LOG_ALL=1 MPFR_LOG_PREC=50 on this particular test
   (this was noticed because adding this test to the 3.1 branch did not
   yield a failure like in the trunk, though the mpfr_ttanh code did not
   change until r11993). This was the bug actually fixed in r12002.
*/
static void
test_20171219 (void)
{
  mpfr_t x, y, z, t;

  mpfr_inits2 (126, x, y, z, t, (mpfr_ptr) 0);
  mpfr_set_str_binary (x, "0.111000000000000111100000000000011110000000000001111000000000000111100000000000011110000000000001111000000000000111100000000000E1");
  /* x = 36347266450315671364380109803814927 / 2^114 */
  mpfr_add_ui (y, x, 2, MPFR_RNDN);
  /* y = 77885641318594292392624080437575695 / 2^114 */
  mpfr_div (z, x, y, MPFR_RNDN);
  mpfr_set_ui_2exp (t, 3823, -13, MPFR_RNDN);
  MPFR_ASSERTN (mpfr_equal_p (z, t));
  mpfr_clears (x, y, z, t, (mpfr_ptr) 0);
}

#if !defined(MPFR_GENERIC_ABI) && GMP_NUMB_BITS == 64
/* exercise mpfr_div2_approx */
static void
test_mpfr_div2_approx (unsigned long n)
{
  mpfr_t x, y, z;

  mpfr_init2 (x, 113);
  mpfr_init2 (y, 113);
  mpfr_init2 (z, 113);
  while (n--)
    {
      mpfr_urandomb (x, RANDS);
      mpfr_urandomb (y, RANDS);
      mpfr_div (z, x, y, MPFR_RNDN);
    }
  mpfr_clear (x);
  mpfr_clear (y);
  mpfr_clear (z);
}
#endif

/* bug found in ttan with GMP_CHECK_RANDOMIZE=1514257254 */
static void
bug20171218 (void)
{
  mpfr_t s, c;
  mpfr_init2 (s, 124);
  mpfr_init2 (c, 124);
  mpfr_set_str_binary (s, "-0.1110000111100001111000011110000111100001111000011110000111100001111000011110000111100001111000011110000111100001111000011110E0");
  mpfr_set_str_binary (c, "0.1111000011110000111100001111000011110000111100001111000011110000111100001111000011110000111100001111000011110000111100001111E-1");
  mpfr_div (c, s, c, MPFR_RNDN);
  mpfr_set_str_binary (s, "-1.111000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000");
  MPFR_ASSERTN(mpfr_equal_p (c, s));
  mpfr_clear (s);
  mpfr_clear (c);
}

int
main (int argc, char *argv[])
{
  tests_start_mpfr ();

  bug20171218 ();
  testall_rndf (9);
  test_20170105 ();
  check_inexact ();
  check_hard ();
  check_special ();
  check_lowr ();
  check_float (); /* checks single precision */
  check_double ();
  check_convergence ();
  check_64 ();

  check4("4.0","4.503599627370496e15", MPFR_RNDZ, 62,
   "0.10000000000000000000000000000000000000000000000000000000000000E-49");
  check4("1.0","2.10263340267725788209e+187", MPFR_RNDU, 65,
   "0.11010011111001101011111001100111110100000001101001111100111000000E-622");
  check4("2.44394909079968374564e-150", "2.10263340267725788209e+187",MPFR_RNDU,
         65,
  "0.11010011111001101011111001100111110100000001101001111100111000000E-1119");

  consistency ();
  test_20070603 ();
  test_20070628 ();
  test_20151023 ();
  test_20160831 ();
  test_20170104 ();
  test_20171219 ();
  test_generic (MPFR_PREC_MIN, 800, 50);
  test_bad ();
  test_extreme ();
  test_mpfr_divsp2 ();
#if !defined(MPFR_GENERIC_ABI) && GMP_NUMB_BITS == 64
  test_mpfr_div2_approx (1000000);
#endif

  tests_end_mpfr ();
  return 0;
}