dist/tests/tset_ld.c

/* Test file for mpfr_set_ld and mpfr_get_ld.

Copyright 2002-2018 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 <float.h>
#ifdef WITH_FPU_CONTROL
#include <fpu_control.h>
#endif

#include "mpfr-test.h"

static void
check_gcc33_bug (void)
{
  volatile long double x;

  x = (long double) 9007199254740992.0 + 1.0;
  if (x != 0.0)
    return;  /* OK */
  printf
    ("Detected optimization bug of gcc 3.3 on Alpha concerning long double\n"
     "comparisons; set_ld tests might fail (set_ld won't work correctly).\n"
     "See https://gcc.gnu.org/ml/gcc-bugs/2003-10/msg00853.html for more\n"
     "information.\n");
}

static int
Isnan_ld (long double d)
{
  /* Do not convert d to double as this can give an overflow, which
     may confuse compilers without IEEE 754 support (such as clang
     -fsanitize=undefined), or trigger a trap if enabled.
     The DOUBLE_ISNAN macro should work fine on long double. */
  if (DOUBLE_ISNAN (d))
    return 1;
  LONGDOUBLE_NAN_ACTION (d, goto yes);
  return 0;
 yes:
  return 1;
}

/* Return the minimal number of bits to represent d exactly (0 for zero).
   If flag is non-zero, also print d. */
/* FIXME: This function doesn't work if the rounding precision is reduced. */
static mpfr_prec_t
print_binary (long double d, int flag)
{
  long double e, f, r;
  long exp = 1;
  mpfr_prec_t prec = 0;

  if (Isnan_ld (d))
    {
      if (flag)
        printf ("NaN\n");
      return 0;
    }
  if (d < (long double) 0.0
#if !defined(MPFR_ERRDIVZERO)
      || (d == (long double) 0.0 && (1.0 / (double) d < 0.0))
#endif
      )
    {
      if (flag)
        printf ("-");
      d = -d;
    }
  /* now d >= 0 */
  /* Use 2 differents tests for Inf, to avoid potential bugs
     in implementations. */
  if (Isnan_ld (d - d) || (d > 1 && d * 0.5 == d))
    {
      if (flag)
        printf ("Inf\n");
      return 0;
    }
  if (d == (long double) 0.0)
    {
      if (flag)
        printf ("0.0\n");
      return prec;
    }
  MPFR_ASSERTN (d > 0);
  e = (long double) 1.0;
  while (e > d)
    {
      e = e * (long double) 0.5;
      exp --;
    }
  if (flag == 2) printf ("1: e=%.36Le\n", e);
  MPFR_ASSERTN (d >= e);
  /* FIXME: There can be an overflow here, which may not be supported
     on all platforms. */
  while (f = e + e, d >= f)
    {
      e = f;
      exp ++;
    }
  if (flag == 2) printf ("2: e=%.36Le\n", e);
  MPFR_ASSERTN (e <= d && d < f);
  if (flag == 1)
    printf ("0.");
  if (flag == 2) printf ("3: d=%.36Le e=%.36Le prec=%ld\n", d, e,
                         (long) prec);
  /* Note: the method we use here to extract the bits of d is the following,
     to deal with the case where the rounding precision is less than the
     precision of d:
     (1) we accumulate the upper bits of d into f
     (2) when accumulating a new bit into f is not exact, we subtract
         f from d and reset f to 0
     This is guaranteed to work only when the rounding precision is at least
     half the precision of d, since otherwise d-f might not be exact.
     This method does not work with flush-to-zero on underflow. */
  f = 0.0; /* will hold accumulated powers of 2 */
  while (1)
    {
      prec++;
      r = f + e;
      /* r is close to f (in particular in the cases where f+e may
         not be exact), so that r - f should be exact. */
      if (r - f != e) /* f+e is not exact */
        {
          d -= f; /* should be exact */
          f = 0.0;
          r = e;
        }
      if (d >= r)
        {
          if (flag == 1)
            printf ("1");
          if (d == r)
            break;
          f = r;
        }
      else
        {
          if (flag == 1)
            printf ("0");
        }
      e *= (long double) 0.5;
      MPFR_ASSERTN (e != 0); /* may fail with flush-to-zero on underflow */
      if (flag == 2) printf ("4: d=%.36Le e=%.36Le prec=%ld\n", d, e,
                             (long) prec);
    }
  if (flag == 1)
    printf ("e%ld\n", exp);
  return prec;
}

/* Checks that a long double converted exactly to a MPFR number, then
   converted back to a long double gives the initial value, or in other
   words, mpfr_get_ld(mpfr_set_ld(d)) = d.
*/
static void
check_set_get (long double d)
{
  mpfr_exp_t emin, emax;
  mpfr_t x;
  mpfr_prec_t prec;
  int r;
  long double e;
  int inex;
  int red;

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

  /* Select a precision to ensure that the conversion of d to x be exact. */
  prec = print_binary (d, 0);
  if (prec < MPFR_PREC_MIN)
    prec = MPFR_PREC_MIN;
  mpfr_init2 (x, prec);

  RND_LOOP(r)
    {
      inex = mpfr_set_ld (x, d, (mpfr_rnd_t) r);
      if (inex != 0)
        {
          printf ("Error: mpfr_set_ld should be exact (rnd = %s)\n",
                  mpfr_print_rnd_mode ((mpfr_rnd_t) r));
          /* We use 36 digits here, as the maximum LDBL_MANT_DIG value
             seen in the current implementations is 113 (binary128),
             and ceil(1+113*log(2)/log(10)) = 36. But the current glibc
             implementation of printf with double-double arithmetic
             (e.g. on PowerPC) is not accurate. */
          printf ("  d ~= %.36Le (output may be wrong!)\n", d);
          printf ("  inex = %d\n", inex);
          if (emin >= LONG_MIN)
            printf ("  emin = %ld\n", (long) emin);
          if (emax <= LONG_MAX)
            printf ("  emax = %ld\n", (long) emax);
          ld_trace ("  d", d);
          printf ("  d = ");
          print_binary (d, 1);
          printf ("  x = ");
          mpfr_dump (x);
          printf ("  MPFR_LDBL_MANT_DIG=%u\n", MPFR_LDBL_MANT_DIG);
          printf ("  prec=%lu\n", prec);
          print_binary (d, 2);
          exit (1);
        }
      for (red = 0; red < 2; red++)
        {
          if (red)
            {
              mpfr_exp_t ex;

              if (MPFR_IS_SINGULAR (x))
                break;
              ex = MPFR_GET_EXP (x);
              set_emin (ex);
              set_emax (ex);
            }
          e = mpfr_get_ld (x, (mpfr_rnd_t) r);
          set_emin (emin);
          set_emax (emax);
          if (inex == 0 && ((Isnan_ld(d) && ! Isnan_ld(e)) ||
                            (Isnan_ld(e) && ! Isnan_ld(d)) ||
                            (e != d && !(Isnan_ld(e) && Isnan_ld(d)))))
            {
              printf ("Error: mpfr_get_ld o mpfr_set_ld <> Id%s\n",
                      red ? ", reduced exponent range" : "");
              printf ("  rnd = %s\n", mpfr_print_rnd_mode ((mpfr_rnd_t) r));
              printf ("  d ~= %.36Le (output may be wrong!)\n", d);
              printf ("  e ~= %.36Le (output may be wrong!)\n", e);
              ld_trace ("  d", d);
              printf ("  x = "); mpfr_out_str (NULL, 16, 0, x, MPFR_RNDN);
              printf ("\n");
              ld_trace ("  e", e);
              printf ("  d = ");
              print_binary (d, 1);
              printf ("  x = ");
              mpfr_dump (x);
              printf ("  e = ");
              print_binary (e, 1);
              printf ("  MPFR_LDBL_MANT_DIG=%u\n", MPFR_LDBL_MANT_DIG);
#ifdef MPFR_NANISNAN
              if (Isnan_ld(d) || Isnan_ld(e))
                printf ("The reason is that NAN == NAN. Please look at the "
                        "configure output\nand Section \"In case of problem\""
                        " of the INSTALL file.\n");
#endif
              exit (1);
            }
        }
    }

  mpfr_clear (x);
}

static void
test_small (void)
{
  mpfr_t x, y, z;
  long double d;

  mpfr_init2 (x, MPFR_LDBL_MANT_DIG);
  mpfr_init2 (y, MPFR_LDBL_MANT_DIG);
  mpfr_init2 (z, MPFR_LDBL_MANT_DIG);

  /* x = 11906603631607553907/2^(16381+64) */
  mpfr_set_str (x, "0.1010010100111100110000001110101101000111010110000001111101110011E-16381", 2, MPFR_RNDN);
  d = mpfr_get_ld (x, MPFR_RNDN);  /* infinite loop? */
  mpfr_set_ld (y, d, MPFR_RNDN);
  mpfr_sub (z, x, y, MPFR_RNDN);
  mpfr_abs (z, z, MPFR_RNDN);
  mpfr_clear_erangeflag ();
  /* If long double = double, d should be equal to 0;
     in this case, everything is OK. */
  if (d != 0 && (mpfr_cmp_str (z, "1E-16434", 2, MPFR_RNDN) > 0 ||
                 mpfr_erangeflag_p ()))
    {
      printf ("Error with x = ");
      mpfr_out_str (NULL, 10, 21, x, MPFR_RNDN);
      printf (" = ");
      mpfr_out_str (NULL, 16, 0, x, MPFR_RNDN);
      printf ("\n        -> d = %.33Le", d);
      printf ("\n        -> y = ");
      mpfr_out_str (NULL, 10, 21, y, MPFR_RNDN);
      printf (" = ");
      mpfr_out_str (NULL, 16, 0, y, MPFR_RNDN);
      printf ("\n        -> |x-y| = ");
      mpfr_out_str (NULL, 16, 0, z, MPFR_RNDN);
      printf ("\n");
      exit (1);
    }

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

static void
test_fixed_bugs (void)
{
  mpfr_t x;
  long double l, m;

  /* bug found by Steve Kargl (2009-03-14) */
  mpfr_init2 (x, MPFR_LDBL_MANT_DIG);
  mpfr_set_ui_2exp (x, 1, -16447, MPFR_RNDN);
  mpfr_get_ld (x, MPFR_RNDN);  /* an assertion failed in init2.c:50 */

  /* bug reported by Jakub Jelinek (2010-10-17)
     https://gforge.inria.fr/tracker/?func=detail&aid=11300 */
  mpfr_set_prec (x, MPFR_LDBL_MANT_DIG);
  /* l = 0x1.23456789abcdef0123456789abcdp-914L; */
  l = 8.215640181713713164092636634579e-276;
  mpfr_set_ld (x, l, MPFR_RNDN);
  m = mpfr_get_ld (x, MPFR_RNDN);
  if (m != l)
    {
      printf ("Error in get_ld o set_ld for l=%Le\n", l);
      printf ("Got m=%Le instead of l\n", m);
      exit (1);
    }

  /* another similar test which failed with extended double precision and the
     generic code for mpfr_set_ld */
  /* l = 0x1.23456789abcdef0123456789abcdp-968L; */
  l = 4.560596445887084662336528403703e-292;
  mpfr_set_ld (x, l, MPFR_RNDN);
  m = mpfr_get_ld (x, MPFR_RNDN);
  if (m != l)
    {
      printf ("Error in get_ld o set_ld for l=%Le\n", l);
      printf ("Got m=%Le instead of l\n", m);
      exit (1);
    }

  mpfr_clear (x);
}

static void
check_subnormal (void)
{
  long double d, e;
  mpfr_t x;

  d = 17.0;
  mpfr_init2 (x, MPFR_LDBL_MANT_DIG);
  while (d != 0.0)
    {
      mpfr_set_ld (x, d, MPFR_RNDN);
      e = mpfr_get_ld (x, MPFR_RNDN);
      if (e != d)
        {
          printf ("Error for mpfr_get_ld o mpfr_set_ld\n");
          printf ("d=%Le\n", d);
          printf ("x="); mpfr_dump (x);
          printf ("e=%Le\n", e);
          exit (1);
        }
      d *= 0.5;
    }
  mpfr_clear (x);
}

static void
check_overflow (void)
{
  long double d, e;
  mpfr_t x;
  int i;

  mpfr_init2 (x, MPFR_LDBL_MANT_DIG);
  for (i = 0; i < 2; i++)
    {
      d = i == 0 ? LDBL_MAX : -LDBL_MAX;
      mpfr_set_ld (x, d, MPFR_RNDN);
      mpfr_mul_2ui (x, x, 1, MPFR_RNDN);
      e = mpfr_get_ld (x, MPFR_RNDN);
      if (! DOUBLE_ISINF (e) || (i == 0 ? (e < 0) : (e > 0)))
        {
          printf ("Error in check_overflow.\n");
          printf ("d=%Le\n", d);
          printf ("x="); mpfr_dump (x);
          printf ("e=%Le\n", e);
          exit (1);
        }
    }
  mpfr_clear (x);
}

/* issue reported by Sisyphus on powerpc */
static void
test_20140212 (void)
{
  mpfr_t fr1, fr2;
  long double ld, h, l, ld2;
  int i, c1, c2;

  mpfr_init2 (fr1, 106);
  mpfr_init2 (fr2, 2098);

  for (h = 1.0L, i = 0; i < 1023; i++)
    h *= 2.0L;
  for (l = 1.0L, i = 0; i < 1074; i++)
    l *= 0.5L;
  ld = h + l; /* rounding of 2^1023 + 2^(-1074) */

  mpfr_set_ld (fr1, ld, MPFR_RNDN);
  mpfr_set_ld (fr2, ld, MPFR_RNDN);

  c1 = mpfr_cmp_ld (fr1, ld);
  c2 = mpfr_cmp_ld (fr2, ld);

  /* If long double is binary64, then ld = fr1 = fr2 = 2^1023.
     If long double is double-double, then ld = 2^1023 + 2^(-1074),
     fr1 = 2^1023 and fr2 = 2^1023 + 2^(-1074) */
  MPFR_ASSERTN(ld == h ? (c1 == 0) : (c1 < 0));

  MPFR_ASSERTN(c2 == 0);

  ld2 = mpfr_get_ld (fr2, MPFR_RNDN);
  MPFR_ASSERTN(ld2 == ld);

  mpfr_clear (fr1);
  mpfr_clear (fr2);
}

/* bug reported by Walter Mascarenhas
   https://sympa.inria.fr/sympa/arc/mpfr/2016-09/msg00005.html */
static void
bug_20160907 (void)
{
#if HAVE_LDOUBLE_IEEE_EXT_LITTLE
  long double dn, ld;
  mpfr_t mp;
  long e;
  mpfr_long_double_t x;

  /* the following is the encoding of the smallest subnormal number
     for HAVE_LDOUBLE_IEEE_EXT_LITTLE */
  x.s.manl = 1;
  x.s.manh = 0;
  x.s.expl = 0;
  x.s.exph = 0;
  x.s.sign= 0;
  dn = x.ld;
  e = -16445;
  /* dn=2^e is now the smallest subnormal. */

  mpfr_init2 (mp, 64);
  mpfr_set_ui_2exp (mp, 1, e - 1, MPFR_RNDN);
  ld = mpfr_get_ld (mp, MPFR_RNDU);
  /* since mp = 2^(e-1) and ld is rounded upwards, we should have
     ld = 2^e */
  if (ld != dn)
    {
      printf ("Error, ld = %Le <> dn = %Le\n", ld, dn);
      printf ("mp=");
      mpfr_out_str (stdout, 10, 0, mp, MPFR_RNDN);
      printf ("\n");
      printf ("mp="); mpfr_dump (mp);
      exit (1);
    }

  /* check a few more numbers */
  for (e = -16446; e <= -16381; e++)
    {
      mpfr_set_ui_2exp (mp, 1, e, MPFR_RNDN);
      ld = mpfr_get_ld (mp, MPFR_RNDU);
      mpfr_set_ld (mp, ld, MPFR_RNDU);
      /* mp is 2^e rounded up, thus should be >= 2^e */
      MPFR_ASSERTN(mpfr_cmp_ui_2exp (mp, 1, e) >= 0);

      mpfr_set_ui_2exp (mp, 1, e, MPFR_RNDN);
      ld = mpfr_get_ld (mp, MPFR_RNDD);
      mpfr_set_ld (mp, ld, MPFR_RNDD);
      /* mp is 2^e rounded down, thus should be <= 2^e */
      if (mpfr_cmp_ui_2exp (mp, 3, e) > 0)
        {
          printf ("Error, expected value <= 2^%ld\n", e);
          printf ("got "); mpfr_dump (mp);
          exit (1);
        }
    }

  mpfr_clear (mp);
#endif
}

int
main (int argc, char *argv[])
{
  volatile long double d, e, maxp2;
  mpfr_t x;
  int i;
  mpfr_exp_t emax;

  tests_start_mpfr ();
  mpfr_test_init ();

  check_gcc33_bug ();
  test_fixed_bugs ();

  mpfr_init2 (x, MPFR_LDBL_MANT_DIG + 64);

#if !defined(MPFR_ERRDIVZERO)
  /* check NaN */
  mpfr_set_nan (x);
  d = mpfr_get_ld (x, MPFR_RNDN);
  check_set_get (d);
#endif

  /* check +0.0 and -0.0 */
  d = 0.0;
  check_set_get (d);
  d = DBL_NEG_ZERO;
  check_set_get (d);

  /* check that the sign of -0.0 is set */
  mpfr_set_ld (x, DBL_NEG_ZERO, MPFR_RNDN);
  if (MPFR_IS_POS (x))
    {
#if defined(HAVE_SIGNEDZ)
      printf ("Error: sign of -0.0 is not set correctly\n");
      exit (1);
#else
      /* Non IEEE doesn't support negative zero yet */
      printf ("Warning: sign of -0.0 is not set correctly\n");
#endif
    }

#if !defined(MPFR_ERRDIVZERO)
  /* check +Inf */
  mpfr_set_inf (x, 1);
  d = mpfr_get_ld (x, MPFR_RNDN);
  check_set_get (d);

  /* check -Inf */
  mpfr_set_inf (x, -1);
  d = mpfr_get_ld (x, MPFR_RNDN);
  check_set_get (d);
#endif

  /* check the largest power of two */
  maxp2 = 1.0;
  while (maxp2 < LDBL_MAX / 2.0)
    maxp2 *= 2.0;
  check_set_get (maxp2);
  check_set_get (-maxp2);

  d = LDBL_MAX;
  e = d / 2.0;
  if (e != maxp2)  /* false under NetBSD/x86 */
    {
      /* d = LDBL_MAX does not have excess precision. */
      check_set_get (d);
      check_set_get (-d);
    }

  /* check the smallest power of two */
  d = 1.0;
  while ((e = d / 2.0) != (long double) 0.0 && e != d)
    d = e;
  check_set_get (d);
  check_set_get (-d);

  /* check that 2^i, 2^i+1, 2^i-1 and 2^i-2^(i-2)-1 are correctly converted */
  d = 1.0;
  for (i = 1; i < MPFR_LDBL_MANT_DIG + 8; i++)
    {
      d = 2.0 * d; /* d = 2^i */
      check_set_get (d);
      if (d + 1.0 != d)
        check_set_get (d + 1.0);
      else
        {
          mpfr_set_ui_2exp (x, 1, i, MPFR_RNDN);
          mpfr_add_ui (x, x, 1, MPFR_RNDN);
          e = mpfr_get_ld (x, MPFR_RNDN);
          check_set_get (e);
        }
      if (d - 1.0 != d)
        check_set_get (d - 1.0);
      else
        {
          mpfr_set_ui_2exp (x, 1, i, MPFR_RNDN);
          mpfr_sub_ui (x, x, 1, MPFR_RNDN);
          e = mpfr_get_ld (x, MPFR_RNDN);
          check_set_get (e);
        }
      if (i < 3)
        continue;
      /* The following test triggers a failure in r10844 for i = 56,
         with gcc -mpc64 on x86 (64-bit ABI). */
      mpfr_set_ui_2exp (x, 3, i-2, MPFR_RNDN);
      mpfr_sub_ui (x, x, 1, MPFR_RNDN);
      e = mpfr_get_ld (x, MPFR_RNDN);
      check_set_get (e);
    }

  for (i = 0; i < 10000; i++)
    {
      mpfr_urandomb (x, RANDS);
      d = mpfr_get_ld (x, MPFR_RNDN);
      check_set_get (d);
    }

  /* check with reduced emax to exercise overflow */
  emax = mpfr_get_emax ();
  mpfr_set_prec (x, 2);
  set_emax (1);
  mpfr_set_ld (x, (long double) 2.0, MPFR_RNDN);
  MPFR_ASSERTN(mpfr_inf_p (x) && mpfr_sgn (x) > 0);
  for (d = (long double) 2.0, i = 0; i < 13; i++, d *= d);
  /* now d = 2^8192, or an infinity (e.g. with double or double-double) */
  mpfr_set_ld (x, d, MPFR_RNDN);
  MPFR_ASSERTN(mpfr_inf_p (x) && mpfr_sgn (x) > 0);
  set_emax (emax);

  mpfr_clear (x);

  test_small ();

  check_subnormal ();
#if !defined(MPFR_ERRDIVZERO)
  check_overflow ();
#endif

  test_20140212 ();
  bug_20160907 ();

  tests_end_mpfr ();

  return 0;
}