dist/tests/tdiv.c

/* Test file for mpfr_div (and some mpfr_div_ui, etc. tests).

Copyright 1999, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013 Free Software Foundation, Inc.
Contributed by the AriC and Caramel 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 <stdio.h>
#include <stdlib.h>

#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 ((MPFR_IS_NAN (a) && MPFR_IS_NAN (a2)) ||
      mpfr_equal_p (a, a2))
    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);

  if (a == b || a == c)
    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_print_binary(q);
      mpfr_set_str (q, Qs, ((p==53) ? 10 : 2), MPFR_RNDN);
      printf("\nexpected "); mpfr_print_binary(q);
      putchar('\n');
      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_print_binary(x);
      printf("\ny=");
      mpfr_print_binary(y);
      printf("\ngot      ");
      mpfr_print_binary(z);
      printf("\nexpected 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_print_binary(x); puts ("");
      printf ("instead of "); mpfr_print_binary(y); puts ("");
      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_print_binary(y); puts ("");
              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(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_print_binary(z2); puts ("");
          printf ("instead of "); mpfr_print_binary(z); puts ("");
          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_print_binary(z2); puts ("");
          printf ("instead of "); mpfr_print_binary(z); puts ("");
          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_print_binary(z2); puts ("");
              printf ("instead of "); mpfr_print_binary(z); puts ("");
              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_print_binary(z2); puts ("");
              printf ("instead of "); mpfr_print_binary(z); puts ("");
              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_print_binary(z2); puts ("");
          printf ("instead of "); mpfr_print_binary(z); puts ("");
          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_print_binary (z2); puts ("");
          printf ("instead of "); mpfr_print_binary (z); puts ("");
          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);
  if ((inexact = test_div (y, x, u, MPFR_RNDN) >= 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);
  if ((inexact = test_div (y, x, u, MPFR_RNDN)) <= 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);
                {
                  rnd = RND_RAND ();
                  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_print_binary (x); puts ("");
                      printf ("u="); mpfr_print_binary (u); puts ("");
                      printf ("y="); mpfr_print_binary (y); puts ("");
                      printf ("y*u="); mpfr_print_binary (z); puts ("");
                      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_number_p (q));
  MPFR_ASSERTN (mpfr_sgn (q) == 0);
  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_number_p (q));
  MPFR_ASSERTN (mpfr_sgn (q) == 0);
  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_number_p (q));
  MPFR_ASSERTN (mpfr_sgn (q) == 0);
  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_number_p (q));
  MPFR_ASSERTN (mpfr_sgn (q) == 0);
  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;

      rnd = RND_RAND ();
      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\n", i);
          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_SIGN (x) >= 0 || ! 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);
}

#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"

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

  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_generic (2, 800, 50);

  tests_end_mpfr ();
  return 0;
}