/* Test file for mpfr_fma.
Copyright 2001-2020 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
https://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"
/* When a * b is exact, the FMA is equivalent to the separate operations. */
static void
test_exact (void)
{
const char *val[] =
{ "@NaN@", "-@Inf@", "-2", "-1", "-0", "0", "1", "2", "@Inf@" };
int sv = numberof (val);
int i, j, k;
int rnd;
mpfr_t a, b, c, r1, r2;
mpfr_inits2 (8, a, b, c, r1, r2, (mpfr_ptr) 0);
for (i = 0; i < sv; i++)
for (j = 0; j < sv; j++)
for (k = 0; k < sv; k++)
RND_LOOP (rnd)
{
if (mpfr_set_str (a, val[i], 10, MPFR_RNDN) ||
mpfr_set_str (b, val[j], 10, MPFR_RNDN) ||
mpfr_set_str (c, val[k], 10, MPFR_RNDN) ||
mpfr_mul (r1, a, b, (mpfr_rnd_t) rnd) ||
mpfr_add (r1, r1, c, (mpfr_rnd_t) rnd))
{
if (rnd == MPFR_RNDF)
continue;
printf ("test_exact internal error for (%d,%d,%d,%d,%s)\n",
i, j, k, rnd, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
exit (1);
}
if (mpfr_fma (r2, a, b, c, (mpfr_rnd_t) rnd))
{
printf ("test_exact(%d,%d,%d,%d): mpfr_fma should be exact\n",
i, j, k, rnd);
exit (1);
}
if (MPFR_IS_NAN (r1))
{
if (MPFR_IS_NAN (r2))
continue;
printf ("test_exact(%d,%d,%d,%d): mpfr_fma should be NaN\n",
i, j, k, rnd);
exit (1);
}
if (! mpfr_equal_p (r1, r2) || MPFR_SIGN (r1) != MPFR_SIGN (r2))
{
printf ("test_exact(%d,%d,%d,%d):\nexpected ", i, j, k, rnd);
mpfr_out_str (stdout, 10, 0, r1, MPFR_RNDN);
printf ("\n got ");
mpfr_out_str (stdout, 10, 0, r2, MPFR_RNDN);
printf ("\n");
exit (1);
}
}
mpfr_clears (a, b, c, r1, r2, (mpfr_ptr) 0);
}
static void
test_overflow1 (void)
{
mpfr_t x, y, z, r;
int inex;
mpfr_inits2 (8, x, y, z, r, (mpfr_ptr) 0);
MPFR_SET_POS (x);
mpfr_setmax (x, mpfr_get_emax ()); /* x = 2^emax - ulp */
mpfr_set_ui (y, 2, MPFR_RNDN); /* y = 2 */
mpfr_neg (z, x, MPFR_RNDN); /* z = -x = -(2^emax - ulp) */
mpfr_clear_flags ();
/* The intermediate multiplication x * y overflows, but x * y + z = x
is representable. */
inex = mpfr_fma (r, x, y, z, MPFR_RNDN);
if (inex || ! mpfr_equal_p (r, x))
{
printf ("Error in test_overflow1\nexpected ");
mpfr_out_str (stdout, 2, 0, x, MPFR_RNDN);
printf (" with inex = 0\n got ");
mpfr_out_str (stdout, 2, 0, r, MPFR_RNDN);
printf (" with inex = %d\n", inex);
exit (1);
}
if (mpfr_overflow_p ())
{
printf ("Error in test_overflow1: overflow flag set\n");
exit (1);
}
mpfr_clears (x, y, z, r, (mpfr_ptr) 0);
}
static void
test_overflow2 (void)
{
mpfr_t x, y, z, r;
int i, inex, rnd, err = 0;
mpfr_inits2 (8, x, y, z, r, (mpfr_ptr) 0);
MPFR_SET_POS (x);
mpfr_setmin (x, mpfr_get_emax ()); /* x = 0.1@emax */
mpfr_set_si (y, -2, MPFR_RNDN); /* y = -2 */
/* The intermediate multiplication x * y will overflow. */
for (i = -9; i <= 9; i++)
RND_LOOP_NO_RNDF (rnd)
{
int inf, overflow;
inf = rnd == MPFR_RNDN || rnd == MPFR_RNDD || rnd == MPFR_RNDA;
overflow = inf || i <= 0;
inex = mpfr_set_si_2exp (z, i, mpfr_get_emin (), MPFR_RNDN);
MPFR_ASSERTN (inex == 0);
mpfr_clear_flags ();
/* One has: x * y = -1@emax exactly (but not representable). */
inex = mpfr_fma (r, x, y, z, (mpfr_rnd_t) rnd);
if (overflow ^ (mpfr_overflow_p () != 0))
{
printf ("Error in test_overflow2 (i = %d, %s): wrong overflow"
" flag (should be %d)\n", i,
mpfr_print_rnd_mode ((mpfr_rnd_t) rnd), overflow);
err = 1;
}
if (mpfr_nanflag_p ())
{
printf ("Error in test_overflow2 (i = %d, %s): NaN flag should"
" not be set\n", i, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
err = 1;
}
if (mpfr_nan_p (r))
{
printf ("Error in test_overflow2 (i = %d, %s): got NaN\n",
i, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
err = 1;
}
else if (MPFR_IS_POS (r))
{
printf ("Error in test_overflow2 (i = %d, %s): wrong sign "
"(+ instead of -)\n", i,
mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
err = 1;
}
else if (inf && ! mpfr_inf_p (r))
{
printf ("Error in test_overflow2 (i = %d, %s): expected -Inf,"
" got\n", i, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
mpfr_dump (r);
err = 1;
}
else if (!inf && (mpfr_inf_p (r) ||
(mpfr_nextbelow (r), ! mpfr_inf_p (r))))
{
printf ("Error in test_overflow2 (i = %d, %s): expected -MAX,"
" got\n", i, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
mpfr_dump (r);
err = 1;
}
if (inf ? inex >= 0 : inex <= 0)
{
printf ("Error in test_overflow2 (i = %d, %s): wrong inexact"
" flag (got %d)\n", i,
mpfr_print_rnd_mode ((mpfr_rnd_t) rnd), inex);
err = 1;
}
}
if (err)
exit (1);
mpfr_clears (x, y, z, r, (mpfr_ptr) 0);
}
static void
test_overflow3 (void)
{
mpfr_t x, y, z, r;
int inex;
mpfr_prec_t p = 8;
mpfr_flags_t ex_flags = MPFR_FLAGS_OVERFLOW | MPFR_FLAGS_INEXACT, flags;
int i, j, k;
unsigned int neg;
mpfr_inits2 (p, x, y, z, (mpfr_ptr) 0);
for (i = 0; i < 2; i++)
{
mpfr_init2 (r, 2 * p + i);
mpfr_set_ui_2exp (x, 1, mpfr_get_emax () - 1, MPFR_RNDN);
mpfr_set_ui (y, 2, MPFR_RNDN); /* y = 2 */
for (j = 1; j <= 2; j++)
for (k = 0; k <= 1; k++)
{
mpfr_set_si_2exp (z, -1, mpfr_get_emax () - mpfr_get_prec (r) - j,
MPFR_RNDN);
if (k)
mpfr_nextabove (z);
for (neg = 0; neg <= 3; neg++)
{
mpfr_clear_flags ();
/* (The following applies for neg = 0 or 2, all the signs
need to be reversed for neg = 1 or 3.)
We have x*y = 2^emax and
z = - 2^(emax-2p-i-j) * (1-k*2^(-p)), thus
x*y+z = 2^emax - 2^(emax-2p-i-j) + k*2^(emax-3p-i-j)
should overflow. Indeed it is >= the midpoint of
2^emax - 2^(emax-2p-i) and 2^emax, the midpoint
being obtained for j = 1 and k = 0. */
inex = mpfr_fma (r, x, y, z, MPFR_RNDN);
flags = __gmpfr_flags;
if (! mpfr_inf_p (r) || flags != ex_flags ||
((neg & 1) == 0 ?
(inex <= 0 || MPFR_IS_NEG (r)) :
(inex >= 0 || MPFR_IS_POS (r))))
{
printf ("Error in test_overflow3 for "
"i=%d j=%d k=%d neg=%u\n", i, j, k, neg);
printf ("Expected %c@Inf@\n with inex %c 0 and flags:",
(neg & 1) == 0 ? '+' : '-',
(neg & 1) == 0 ? '>' : '<');
flags_out (ex_flags);
printf ("Got ");
mpfr_dump (r);
printf (" with inex = %d and flags:", inex);
flags_out (flags);
exit (1);
}
if (neg == 0 || neg == 2)
mpfr_neg (x, x, MPFR_RNDN);
if (neg == 1 || neg == 3)
mpfr_neg (y, y, MPFR_RNDN);
mpfr_neg (z, z, MPFR_RNDN);
} /* neg */
} /* k */
mpfr_clear (r);
} /* i */
mpfr_clears (x, y, z, (mpfr_ptr) 0);
}
static void
test_overflow4 (void)
{
mpfr_t x, y, z, r1, r2;
mpfr_exp_t emax, e;
mpfr_prec_t px;
mpfr_flags_t flags1, flags2;
int inex1, inex2;
int ei, i, j;
int below;
unsigned int neg;
emax = mpfr_get_emax ();
mpfr_init2 (y, MPFR_PREC_MIN);
mpfr_set_ui (y, 2, MPFR_RNDN); /* y = 2 */
mpfr_init2 (z, 8);
for (px = 17; px < 256; px *= 2)
{
mpfr_init2 (x, px);
mpfr_inits2 (px - 8, r1, r2, (mpfr_ptr) 0);
for (ei = 0; ei <= 1; ei++)
{
e = ei ? emax : 0;
mpfr_set_ui_2exp (x, 1, e - 1, MPFR_RNDN);
mpfr_nextabove (x); /* x = 2^(e - 1) + 2^(e - px) */
/* x*y = 2^e + 2^(e - px + 1), which internally overflows
when e = emax. */
for (i = -4; i <= 4; i++)
for (j = 2; j <= 3; j++)
{
mpfr_set_si_2exp (z, -j, e - px + i, MPFR_RNDN);
/* If |z| <= 2^(e - px + 1), then x*y + z >= 2^e and
RZ(x*y + z) = 2^e with an unbounded exponent range.
If |z| > 2^(e - px + 1), then RZ(x*y + z) is the
predecessor of 2^e (since |z| < ulp(r)/2); this
occurs when i > 0 and when i = 0 and j > 2 */
mpfr_set_ui_2exp (r1, 1, e - 1, MPFR_RNDN);
below = i > 0 || (i == 0 && j > 2);
if (below)
mpfr_nextbelow (r1);
mpfr_clear_flags ();
inex1 = mpfr_mul_2ui (r1, r1, 1, MPFR_RNDZ);
if (below || e < emax)
{
inex1 = i == 0 && j == 2 ? 0 : -1;
flags1 = inex1 ? MPFR_FLAGS_INEXACT : 0;
}
else
{
MPFR_ASSERTN (inex1 < 0);
flags1 = MPFR_FLAGS_INEXACT | MPFR_FLAGS_OVERFLOW;
MPFR_ASSERTN (flags1 == __gmpfr_flags);
}
for (neg = 0; neg <= 3; neg++)
{
mpfr_clear_flags ();
inex2 = mpfr_fma (r2, x, y, z, MPFR_RNDZ);
flags2 = __gmpfr_flags;
if (! (mpfr_equal_p (r1, r2) &&
SAME_SIGN (inex1, inex2) &&
flags1 == flags2))
{
printf ("Error in test_overflow4 for "
"px=%d ei=%d i=%d j=%d neg=%u\n",
(int) px, ei, i, j, neg);
printf ("Expected ");
mpfr_dump (r1);
printf ("with inex = %d and flags:", inex1);
flags_out (flags1);
printf ("Got ");
mpfr_dump (r2);
printf ("with inex = %d and flags:", inex2);
flags_out (flags2);
exit (1);
}
if (neg == 0 || neg == 2)
mpfr_neg (x, x, MPFR_RNDN);
if (neg == 1 || neg == 3)
mpfr_neg (y, y, MPFR_RNDN);
mpfr_neg (z, z, MPFR_RNDN);
mpfr_neg (r1, r1, MPFR_RNDN);
inex1 = - inex1;
}
}
}
mpfr_clears (x, r1, r2, (mpfr_ptr) 0);
}
mpfr_clears (y, z, (mpfr_ptr) 0);
}
static void
test_overflow5 (void)
{
mpfr_t x, y, z, r1, r2;
mpfr_exp_t emax;
int inex1, inex2;
int i, rnd;
unsigned int neg, negr;
emax = mpfr_get_emax ();
mpfr_init2 (x, 123);
mpfr_init2 (y, 45);
mpfr_init2 (z, 67);
mpfr_inits2 (89, r1, r2, (mpfr_ptr) 0);
mpfr_set_ui_2exp (x, 1, emax - 1, MPFR_RNDN);
for (i = 3; i <= 17; i++)
{
mpfr_set_ui (y, i, MPFR_RNDN);
mpfr_set_ui_2exp (z, 1, emax - 1, MPFR_RNDN);
for (neg = 0; neg < 8; neg++)
{
mpfr_setsign (x, x, neg & 1, MPFR_RNDN);
mpfr_setsign (y, y, neg & 2, MPFR_RNDN);
mpfr_setsign (z, z, neg & 4, MPFR_RNDN);
/* |x*y + z| = (i +/- 1) * 2^(emax - 1) >= 2^emax (overflow)
and x*y + z has the same sign as x*y. */
negr = (neg ^ (neg >> 1)) & 1;
RND_LOOP (rnd)
{
mpfr_set_inf (r1, 1);
if (MPFR_IS_LIKE_RNDZ ((mpfr_rnd_t) rnd, negr))
{
mpfr_nextbelow (r1);
inex1 = -1;
}
else
inex1 = 1;
if (negr)
{
mpfr_neg (r1, r1, MPFR_RNDN);
inex1 = - inex1;
}
mpfr_clear_flags ();
inex2 = mpfr_fma (r2, x, y, z, (mpfr_rnd_t) rnd);
MPFR_ASSERTN (__gmpfr_flags ==
(MPFR_FLAGS_INEXACT | MPFR_FLAGS_OVERFLOW));
if (! (mpfr_equal_p (r1, r2) && SAME_SIGN (inex1, inex2)))
{
printf ("Error in test_overflow5 for i=%d neg=%u %s\n",
i, neg, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
printf ("Expected ");
mpfr_dump (r1);
printf ("with inex = %d\n", inex1);
printf ("Got ");
mpfr_dump (r2);
printf ("with inex = %d\n", inex2);
exit (1);
}
} /* rnd */
} /* neg */
} /* i */
mpfr_clears (x, y, z, r1, r2, (mpfr_ptr) 0);
}
static void
test_underflow1 (void)
{
mpfr_t x, y, z, r;
int inex, signy, signz, rnd, err = 0;
mpfr_inits2 (8, x, y, z, r, (mpfr_ptr) 0);
MPFR_SET_POS (x);
mpfr_setmin (x, mpfr_get_emin ()); /* x = 0.1@emin */
for (signy = -1; signy <= 1; signy += 2)
{
mpfr_set_si_2exp (y, signy, -1, MPFR_RNDN); /* |y| = 1/2 */
for (signz = -3; signz <= 3; signz += 2)
{
RND_LOOP (rnd)
{
mpfr_set_si (z, signz, MPFR_RNDN);
if (ABS (signz) != 1)
mpfr_setmax (z, mpfr_get_emax ());
/* |z| = 1 or 2^emax - ulp */
mpfr_clear_flags ();
inex = mpfr_fma (r, x, y, z, (mpfr_rnd_t) rnd);
#define STRTU1 "Error in test_underflow1 (signy = %d, signz = %d, %s)\n "
if (mpfr_nanflag_p ())
{
printf (STRTU1 "NaN flag is set\n", signy, signz,
mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
err = 1;
}
if (signy < 0 && MPFR_IS_LIKE_RNDD(rnd, signz))
mpfr_nextbelow (z);
if (signy > 0 && MPFR_IS_LIKE_RNDU(rnd, signz))
mpfr_nextabove (z);
if ((mpfr_overflow_p () != 0) ^ (mpfr_inf_p (z) != 0))
{
printf (STRTU1 "wrong overflow flag\n", signy, signz,
mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
err = 1;
}
if (mpfr_underflow_p ())
{
printf (STRTU1 "underflow flag is set\n", signy, signz,
mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
err = 1;
}
if (! mpfr_equal_p (r, z))
{
printf (STRTU1 "got ", signy, signz,
mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
mpfr_dump (r);
printf (" instead of ");
mpfr_dump (z);
err = 1;
}
if (inex >= 0 && (rnd == MPFR_RNDD ||
(rnd == MPFR_RNDZ && signz > 0) ||
(rnd == MPFR_RNDN && signy > 0)))
{
printf (STRTU1 "ternary value = %d instead of < 0\n",
signy, signz, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd),
inex);
err = 1;
}
if (inex <= 0 && (rnd == MPFR_RNDU ||
(rnd == MPFR_RNDZ && signz < 0) ||
(rnd == MPFR_RNDN && signy < 0)))
{
printf (STRTU1 "ternary value = %d instead of > 0\n",
signy, signz, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd),
inex);
err = 1;
}
}
}
}
if (err)
exit (1);
mpfr_clears (x, y, z, r, (mpfr_ptr) 0);
}
static void
test_underflow2 (void)
{
mpfr_t x, y, z, r1, r2;
int e, b, i, prec = 32, pz, inex;
unsigned int neg;
mpfr_init2 (x, MPFR_PREC_MIN);
mpfr_inits2 (prec, y, z, r1, r2, (mpfr_ptr) 0);
mpfr_set_si_2exp (x, 1, mpfr_get_emin () - 1, MPFR_RNDN);
/* x = 2^(emin-1) */
for (e = -1; e <= prec + 2; e++)
{
mpfr_set (z, x, MPFR_RNDN);
/* z = x = 2^(emin+e) */
for (b = 0; b <= 1; b++)
{
for (pz = prec - 4 * (b == 0); pz <= prec + 4; pz++)
{
inex = mpfr_prec_round (z, pz, MPFR_RNDZ);
MPFR_ASSERTN (inex == 0);
for (i = 15; i <= 17; i++)
{
mpfr_flags_t flags1, flags2;
int inex1, inex2;
mpfr_set_si_2exp (y, i, -4 - prec, MPFR_RNDN);
/* <--- r --->
* z = 1.000...00b with b = 0 or 1
* xy = 01111 (i = 15)
* or 10000 (i = 16)
* or 10001 (i = 17)
*
* x, y, and z will be modified to test the different sign
* combinations. In the case b = 0 (i.e. |z| is a power of
* 2) and x*y has a different sign from z, then y will be
* divided by 2, so that i = 16 corresponds to a midpoint.
*/
for (neg = 0; neg < 8; neg++)
{
int xyneg, prev_binade;
mpfr_setsign (x, x, neg & 1, MPFR_RNDN);
mpfr_setsign (y, y, neg & 2, MPFR_RNDN);
mpfr_setsign (z, z, neg & 4, MPFR_RNDN);
xyneg = (neg ^ (neg >> 1)) & 1; /* true iff x*y < 0 */
/* If a change of binade occurs by adding x*y to z
exactly, then take into account the fact that the
midpoint has a different exponent. */
prev_binade = b == 0 && (xyneg ^ MPFR_IS_NEG (z));
if (prev_binade)
mpfr_div_2ui (y, y, 1, MPFR_RNDN);
mpfr_set (r1, z, MPFR_RNDN);
flags1 = MPFR_FLAGS_INEXACT;
if (e == -1 && i == 17 && b == 0 &&
(xyneg ^ (neg >> 2)) != 0)
{
/* Special underflow case. */
flags1 |= MPFR_FLAGS_UNDERFLOW;
inex1 = xyneg ? 1 : -1;
}
else if (i == 15 || (i == 16 && b == 0))
{
/* round toward z */
inex1 = xyneg ? 1 : -1;
}
else if (xyneg)
{
/* round away from z, with x*y < 0 */
mpfr_nextbelow (r1);
inex1 = -1;
}
else
{
/* round away from z, with x*y > 0 */
mpfr_nextabove (r1);
inex1 = 1;
}
mpfr_clear_flags ();
inex2 = mpfr_fma (r2, x, y, z, MPFR_RNDN);
flags2 = __gmpfr_flags;
if (! (mpfr_equal_p (r1, r2) &&
SAME_SIGN (inex1, inex2) &&
flags1 == flags2))
{
printf ("Error in test_underflow2 for "
"e=%d b=%d pz=%d i=%d neg=%u\n",
e, b, pz, i, neg);
printf ("Expected ");
mpfr_dump (r1);
printf ("with inex = %d and flags:", inex1);
flags_out (flags1);
printf ("Got ");
mpfr_dump (r2);
printf ("with inex = %d and flags:", inex2);
flags_out (flags2);
exit (1);
}
/* Restore y. */
if (prev_binade)
mpfr_mul_2ui (y, y, 1, MPFR_RNDN);
} /* neg */
} /* i */
} /* pz */
inex = mpfr_prec_round (z, prec, MPFR_RNDZ);
MPFR_ASSERTN (inex == 0);
MPFR_SET_POS (z);
mpfr_nextabove (z);
} /* b */
mpfr_mul_2ui (x, x, 1, MPFR_RNDN);
} /* e */
mpfr_clears (x, y, z, r1, r2, (mpfr_ptr) 0);
}
static void
test_underflow3 (int n)
{
mpfr_t x, y, z, t1, t2;
int sign, k, s, rnd, inex1, inex2;
mpfr_exp_t e;
mpfr_flags_t flags1, flags2;
mpfr_inits2 (4, x, z, t1, t2, (mpfr_ptr) 0);
mpfr_init2 (y, 6);
e = mpfr_get_emin () - 1;
for (sign = 1; sign >= -1; sign -= 2)
for (k = 1; k <= 7; k++)
for (s = -1; s <= 1; s++)
{
mpfr_set_si_2exp (x, sign, e, MPFR_RNDN);
mpfr_set_si_2exp (y, 8*k+s, -6, MPFR_RNDN);
mpfr_neg (z, x, MPFR_RNDN);
/* x = sign * 2^(emin-1)
y = (8 * k + s) * 2^(-6) = k / 8 + s * 2^(-6)
z = -x = -sign * 2^(emin-1)
FMA(x,y,z) = sign * ((k-8) * 2^(emin-4) + s * 2^(emin-7)) exactly.
Note: The purpose of the s * 2^(emin-7) term is to yield
double rounding when scaling for k = 4, s != 0, MPFR_RNDN. */
RND_LOOP_NO_RNDF (rnd)
{
mpfr_clear_flags ();
inex1 = mpfr_set_si_2exp (t1, sign * (8*k+s-64), e-6,
(mpfr_rnd_t) rnd);
flags1 = __gmpfr_flags;
mpfr_clear_flags ();
inex2 = mpfr_fma (t2, x, y, z, (mpfr_rnd_t) rnd);
flags2 = __gmpfr_flags;
if (! (mpfr_equal_p (t1, t2) &&
SAME_SIGN (inex1, inex2) &&
flags1 == flags2))
{
printf ("Error in test_underflow3, n = %d, sign = %d,"
" k = %d, s = %d, %s\n", n, sign, k, s,
mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
printf ("Expected ");
mpfr_dump (t1);
printf (" with inex ~ %d, flags =", inex1);
flags_out (flags1);
printf ("Got ");
mpfr_dump (t2);
printf (" with inex ~ %d, flags =", inex2);
flags_out (flags2);
exit (1);
}
}
}
mpfr_clears (x, y, z, t1, t2, (mpfr_ptr) 0);
}
/* Test s = x*y + z with PREC(z) > PREC(s) + 1, x*y underflows, where
z + x*y and z + sign(x*y) * 2^(emin-1) do not give the same result.
x = 2^emin
y = 2^(-8)
z = 2^emin * (2^PREC(s) + k - 2^(-1))
with k = 3 for MPFR_RNDN and k = 2 for the directed rounding modes.
Also test the opposite versions with neg != 0.
*/
static void
test_underflow4 (void)
{
mpfr_t x, y, z, s1, s2;
mpfr_prec_t ps = 32;
int inex, rnd;
mpfr_inits2 (MPFR_PREC_MIN, x, y, (mpfr_ptr) 0);
mpfr_inits2 (ps, s1, s2, (mpfr_ptr) 0);
mpfr_init2 (z, ps + 2);
inex = mpfr_set_si_2exp (x, 1, mpfr_get_emin (), MPFR_RNDN);
MPFR_ASSERTN (inex == 0);
inex = mpfr_set_si_2exp (y, 1, -8, MPFR_RNDN);
MPFR_ASSERTN (inex == 0);
RND_LOOP_NO_RNDF (rnd)
{
mpfr_flags_t flags1, flags2;
int inex1, inex2;
unsigned int neg;
inex = mpfr_set_si_2exp (z, 1 << 1, ps, MPFR_RNDN);
MPFR_ASSERTN (inex == 0);
inex = mpfr_sub_ui (z, z, 1, MPFR_RNDN);
MPFR_ASSERTN (inex == 0);
inex = mpfr_div_2ui (z, z, 1, MPFR_RNDN);
MPFR_ASSERTN (inex == 0);
inex = mpfr_add_ui (z, z, rnd == MPFR_RNDN ? 3 : 2, MPFR_RNDN);
MPFR_ASSERTN (inex == 0);
inex = mpfr_mul (z, z, x, MPFR_RNDN);
MPFR_ASSERTN (inex == 0);
for (neg = 0; neg <= 3; neg++)
{
inex1 = mpfr_set (s1, z, (mpfr_rnd_t) rnd);
flags1 = MPFR_FLAGS_INEXACT;
mpfr_clear_flags ();
inex2 = mpfr_fma (s2, x, y, z, (mpfr_rnd_t) rnd);
flags2 = __gmpfr_flags;
if (! (mpfr_equal_p (s1, s2) &&
SAME_SIGN (inex1, inex2) &&
flags1 == flags2))
{
printf ("Error in test_underflow4 for neg=%u %s\n",
neg, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
printf ("Expected ");
mpfr_dump (s1);
printf (" with inex ~ %d, flags =", inex1);
flags_out (flags1);
printf ("Got ");
mpfr_dump (s2);
printf (" with inex ~ %d, flags =", inex2);
flags_out (flags2);
exit (1);
}
if (neg == 0 || neg == 2)
mpfr_neg (x, x, MPFR_RNDN);
if (neg == 1 || neg == 3)
mpfr_neg (y, y, MPFR_RNDN);
mpfr_neg (z, z, MPFR_RNDN);
}
}
mpfr_clears (x, y, z, s1, s2, (mpfr_ptr) 0);
}
/* Test s = x*y + z on:
x = +/- 2^emin
y = +/- 2^(-3)
z = +/- 2^(emin + PREC(s)) and MPFR numbers close to this value.
with PREC(z) from PREC(s) - 2 to PREC(s) + 8.
*/
static void
test_underflow5 (void)
{
mpfr_t w, x, y, z, s1, s2, t;
mpfr_exp_t emin;
mpfr_prec_t ps = 32;
int inex, i, j, rnd;
unsigned int neg;
mpfr_inits2 (MPFR_PREC_MIN, w, x, y, (mpfr_ptr) 0);
mpfr_inits2 (ps, s1, s2, (mpfr_ptr) 0);
mpfr_init2 (t, ps + 9);
emin = mpfr_get_emin ();
inex = mpfr_set_si_2exp (w, 1, emin, MPFR_RNDN); /* w = 2^emin */
MPFR_ASSERTN (inex == 0);
inex = mpfr_set_si (x, 1, MPFR_RNDN);
MPFR_ASSERTN (inex == 0);
inex = mpfr_set_si_2exp (y, 1, -3, MPFR_RNDN);
MPFR_ASSERTN (inex == 0);
for (i = -2; i <= 8; i++)
{
mpfr_init2 (z, ps + i);
inex = mpfr_set_si_2exp (z, 1, ps, MPFR_RNDN);
MPFR_ASSERTN (inex == 0);
for (j = 1; j <= 32; j++)
mpfr_nextbelow (z);
for (j = -32; j <= 32; j++)
{
for (neg = 0; neg < 8; neg++)
{
mpfr_setsign (x, x, neg & 1, MPFR_RNDN);
mpfr_setsign (y, y, neg & 2, MPFR_RNDN);
mpfr_setsign (z, z, neg & 4, MPFR_RNDN);
inex = mpfr_fma (t, x, y, z, MPFR_RNDN);
MPFR_ASSERTN (inex == 0);
inex = mpfr_mul (x, x, w, MPFR_RNDN);
MPFR_ASSERTN (inex == 0);
inex = mpfr_mul (z, z, w, MPFR_RNDN);
MPFR_ASSERTN (inex == 0);
RND_LOOP_NO_RNDF (rnd)
{
mpfr_flags_t flags1, flags2;
int inex1, inex2;
mpfr_clear_flags ();
inex1 = mpfr_mul (s1, w, t, (mpfr_rnd_t) rnd);
flags1 = __gmpfr_flags;
mpfr_clear_flags ();
inex2 = mpfr_fma (s2, x, y, z, (mpfr_rnd_t) rnd);
flags2 = __gmpfr_flags;
if (! (mpfr_equal_p (s1, s2) &&
SAME_SIGN (inex1, inex2) &&
flags1 == flags2))
{
printf ("Error in test_underflow5 on "
"i=%d j=%d neg=%u %s\n", i, j, neg,
mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
printf ("Expected ");
mpfr_dump (s1);
printf (" with inex ~ %d, flags =", inex1);
flags_out (flags1);
printf ("Got ");
mpfr_dump (s2);
printf (" with inex ~ %d, flags =", inex2);
flags_out (flags2);
exit (1);
}
} /* rnd */
inex = mpfr_div (x, x, w, MPFR_RNDN);
MPFR_ASSERTN (inex == 0);
inex = mpfr_div (z, z, w, MPFR_RNDN);
MPFR_ASSERTN (inex == 0);
} /* neg */
MPFR_SET_POS (z); /* restore the value before the loop on neg */
mpfr_nextabove (z);
} /* j */
mpfr_clear (z);
} /* i */
mpfr_clears (w, x, y, s1, s2, t, (mpfr_ptr) 0);
}
static void
bug20101018 (void)
{
mpfr_t x, y, z, t, u;
int i;
mpfr_init2 (x, 64);
mpfr_init2 (y, 64);
mpfr_init2 (z, 64);
mpfr_init2 (t, 64);
mpfr_init2 (u, 64);
mpfr_set_str (x, "0xf.fffffffffffffffp-14766", 16, MPFR_RNDN);
mpfr_set_str (y, "-0xf.fffffffffffffffp+317", 16, MPFR_RNDN);
mpfr_set_str (z, "0x8.3ffffffffffe3ffp-14443", 16, MPFR_RNDN);
mpfr_set_str (t, "0x8.7ffffffffffc7ffp-14444", 16, MPFR_RNDN);
i = mpfr_fma (u, x, y, z, MPFR_RNDN);
if (! mpfr_equal_p (u, t))
{
printf ("Wrong result in bug20101018 (a)\n");
printf ("Expected ");
mpfr_out_str (stdout, 16, 0, t, MPFR_RNDN);
printf ("\nGot ");
mpfr_out_str (stdout, 16, 0, u, MPFR_RNDN);
printf ("\n");
exit (1);
}
if (i <= 0)
{
printf ("Wrong ternary value in bug20101018 (a)\n");
printf ("Expected > 0\n");
printf ("Got %d\n", i);
exit (1);
}
mpfr_set_str (x, "-0xf.fffffffffffffffp-11420", 16, MPFR_RNDN);
mpfr_set_str (y, "0xf.fffffffffffffffp+9863", 16, MPFR_RNDN);
mpfr_set_str (z, "0x8.fffff80ffffffffp-1551", 16, MPFR_RNDN);
mpfr_set_str (t, "0x9.fffff01ffffffffp-1552", 16, MPFR_RNDN);
i = mpfr_fma (u, x, y, z, MPFR_RNDN);
if (! mpfr_equal_p (u, t))
{
printf ("Wrong result in bug20101018 (b)\n");
printf ("Expected ");
mpfr_out_str (stdout, 16, 0, t, MPFR_RNDN);
printf ("\nGot ");
mpfr_out_str (stdout, 16, 0, u, MPFR_RNDN);
printf ("\n");
exit (1);
}
if (i <= 0)
{
printf ("Wrong ternary value in bug20101018 (b)\n");
printf ("Expected > 0\n");
printf ("Got %d\n", i);
exit (1);
}
mpfr_set_str (x, "0xf.fffffffffffffffp-2125", 16, MPFR_RNDN);
mpfr_set_str (y, "-0xf.fffffffffffffffp-6000", 16, MPFR_RNDN);
mpfr_set_str (z, "0x8p-8119", 16, MPFR_RNDN);
mpfr_set_str (t, "0x8.000000000000001p-8120", 16, MPFR_RNDN);
i = mpfr_fma (u, x, y, z, MPFR_RNDN);
if (! mpfr_equal_p (u, t))
{
printf ("Wrong result in bug20101018 (c)\n");
printf ("Expected ");
mpfr_out_str (stdout, 16, 0, t, MPFR_RNDN);
printf ("\nGot ");
mpfr_out_str (stdout, 16, 0, u, MPFR_RNDN);
printf ("\n");
exit (1);
}
if (i <= 0)
{
printf ("Wrong ternary value in bug20101018 (c)\n");
printf ("Expected > 0\n");
printf ("Got %d\n", i);
exit (1);
}
mpfr_clear (x);
mpfr_clear (y);
mpfr_clear (z);
mpfr_clear (t);
mpfr_clear (u);
}
/* bug found with GMP_CHECK_RANDOMIZE=1514407719 */
static void
bug20171219 (void)
{
mpfr_t x, y, z, t, u;
int i;
mpfr_init2 (x, 60);
mpfr_init2 (y, 60);
mpfr_init2 (z, 60);
mpfr_init2 (t, 68);
mpfr_init2 (u, 68);
mpfr_set_ui (x, 1, MPFR_RNDN);
mpfr_set_ui (y, 1, MPFR_RNDN);
mpfr_set_ui (z, 1, MPFR_RNDN);
mpfr_set_ui (t, 2, MPFR_RNDN);
i = mpfr_fma (u, x, y, z, MPFR_RNDA);
if (! mpfr_equal_p (u, t))
{
printf ("Wrong result in bug20171219 (a)\n");
printf ("Expected ");
mpfr_out_str (stdout, 16, 0, t, MPFR_RNDN);
printf ("\nGot ");
mpfr_out_str (stdout, 16, 0, u, MPFR_RNDN);
printf ("\n");
exit (1);
}
if (i != 0)
{
printf ("Wrong ternary value in bug20171219\n");
printf ("Expected 0\n");
printf ("Got %d\n", i);
exit (1);
}
mpfr_clear (x);
mpfr_clear (y);
mpfr_clear (z);
mpfr_clear (t);
mpfr_clear (u);
}
/* coverage test for mpfr_set_1_2, case prec < GMP_NUMB_BITS,
inex > 0, rb <> 0, sb = 0 */
static void
coverage (void)
{
mpfr_t x, y, z, s;
int inex;
mpfr_exp_t emax;
mpfr_inits2 (GMP_NUMB_BITS - 1, x, y, z, s, (mpfr_ptr) 0);
/* set x to 2^(GMP_NUMB_BITS/2) + 1, y to 2^(GMP_NUMB_BITS/2) - 1 */
MPFR_ASSERTN((GMP_NUMB_BITS % 2) == 0);
mpfr_set_ui_2exp (x, 1, GMP_NUMB_BITS / 2, MPFR_RNDN);
mpfr_sub_ui (y, x, 1, MPFR_RNDN);
mpfr_add_ui (x, x, 1, MPFR_RNDN);
/* we have x*y = 2^GMP_NUMB_BITS - 1, thus has exponent GMP_NUMB_BITS */
/* set z to 2^(1-GMP_NUMB_BITS), with exponent 2-GMP_NUMB_BITS */
mpfr_set_ui_2exp (z, 1, 1 - GMP_NUMB_BITS, MPFR_RNDN);
inex = mpfr_fms (s, x, y, z, MPFR_RNDN);
/* s should be 2^GMP_NUMB_BITS-2 */
MPFR_ASSERTN(inex < 0);
inex = mpfr_add_ui (s, s, 2, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui_2exp (s, 1, GMP_NUMB_BITS) == 0);
/* same example, but with overflow */
emax = mpfr_get_emax ();
mpfr_set_emax (GMP_NUMB_BITS + 1);
mpfr_set_ui_2exp (z, 1, mpfr_get_emax () - 1, MPFR_RNDZ);
mpfr_clear_flags ();
inex = mpfr_fma (s, x, y, z, MPFR_RNDN);
/* x*y = 2^GMP_NUMB_BITS - 1, z = 2^GMP_NUMB_BITS, thus
x*y+z = 2^(GMP_NUMB_BITS+1) - 1 should round to 2^(GMP_NUMB_BITS+1),
thus give an overflow */
MPFR_ASSERTN(inex > 0);
MPFR_ASSERTN(mpfr_inf_p (s) && mpfr_sgn (s) > 0);
MPFR_ASSERTN(mpfr_overflow_p ());
mpfr_set_emax (emax);
mpfr_clear (x);
mpfr_clear (y);
mpfr_clear (z);
mpfr_clear (s);
}
int
main (int argc, char *argv[])
{
mpfr_t x, y, z, s;
mpfr_exp_t emin, emax;
int i;
tests_start_mpfr ();
coverage ();
emin = mpfr_get_emin ();
emax = mpfr_get_emax ();
bug20171219 ();
bug20101018 ();
mpfr_init (x);
mpfr_init (s);
mpfr_init (y);
mpfr_init (z);
/* check special cases */
mpfr_set_prec (x, 2);
mpfr_set_prec (y, 2);
mpfr_set_prec (z, 2);
mpfr_set_prec (s, 2);
mpfr_set_str (x, "-0.75", 10, MPFR_RNDN);
mpfr_set_str (y, "0.5", 10, MPFR_RNDN);
mpfr_set_str (z, "0.375", 10, MPFR_RNDN);
mpfr_fma (s, x, y, z, MPFR_RNDU); /* result is 0 */
if (mpfr_cmp_ui (s, 0))
{
printf ("Error: -0.75 * 0.5 + 0.375 should be equal to 0 for prec=2\n");
printf ("got instead ");
mpfr_dump (s);
exit (1);
}
mpfr_set_prec (x, 27);
mpfr_set_prec (y, 27);
mpfr_set_prec (z, 27);
mpfr_set_prec (s, 27);
mpfr_set_str_binary (x, "1.11111111111111111111111111e-1");
mpfr_set (y, x, MPFR_RNDN);
mpfr_set_str_binary (z, "-1.00011110100011001011001001e-1");
if (mpfr_fma (s, x, y, z, MPFR_RNDN) >= 0)
{
printf ("Wrong inexact flag for x=y=1-2^(-27)\n");
exit (1);
}
mpfr_set_nan (x);
mpfr_urandomb (y, RANDS);
mpfr_urandomb (z, RANDS);
mpfr_fma (s, x, y, z, MPFR_RNDN);
if (!mpfr_nan_p (s))
{
printf ("evaluation of function in x=NAN does not return NAN\n");
exit (1);
}
mpfr_set_nan (y);
mpfr_urandomb (x, RANDS);
mpfr_urandomb (z, RANDS);
mpfr_fma (s, x, y, z, MPFR_RNDN);
if (!mpfr_nan_p(s))
{
printf ("evaluation of function in y=NAN does not return NAN\n");
exit (1);
}
mpfr_set_nan (z);
mpfr_urandomb (y, RANDS);
mpfr_urandomb (x, RANDS);
mpfr_fma (s, x, y, z, MPFR_RNDN);
if (!mpfr_nan_p (s))
{
printf ("evaluation of function in z=NAN does not return NAN\n");
exit (1);
}
mpfr_set_inf (x, 1);
mpfr_set_inf (y, 1);
mpfr_set_inf (z, 1);
mpfr_fma (s, x, y, z, MPFR_RNDN);
if (!mpfr_inf_p (s) || mpfr_sgn (s) < 0)
{
printf ("Error for (+inf) * (+inf) + (+inf)\n");
exit (1);
}
mpfr_set_inf (x, -1);
mpfr_set_inf (y, -1);
mpfr_set_inf (z, 1);
mpfr_fma (s, x, y, z, MPFR_RNDN);
if (!mpfr_inf_p (s) || mpfr_sgn (s) < 0)
{
printf ("Error for (-inf) * (-inf) + (+inf)\n");
exit (1);
}
mpfr_set_inf (x, 1);
mpfr_set_inf (y, -1);
mpfr_set_inf (z, -1);
mpfr_fma (s, x, y, z, MPFR_RNDN);
if (!mpfr_inf_p (s) || mpfr_sgn (s) > 0)
{
printf ("Error for (+inf) * (-inf) + (-inf)\n");
exit (1);
}
mpfr_set_inf (x, -1);
mpfr_set_inf (y, 1);
mpfr_set_inf (z, -1);
mpfr_fma (s, x, y, z, MPFR_RNDN);
if (!mpfr_inf_p (s) || mpfr_sgn (s) > 0)
{
printf ("Error for (-inf) * (+inf) + (-inf)\n");
exit (1);
}
mpfr_set_inf (x, 1);
mpfr_set_ui (y, 0, MPFR_RNDN);
mpfr_urandomb (z, RANDS);
mpfr_fma (s, x, y, z, MPFR_RNDN);
if (!mpfr_nan_p (s))
{
printf ("evaluation of function in x=INF y=0 does not return NAN\n");
exit (1);
}
mpfr_set_inf (y, 1);
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_urandomb (z, RANDS);
mpfr_fma (s, x, y, z, MPFR_RNDN);
if (!mpfr_nan_p (s))
{
printf ("evaluation of function in x=0 y=INF does not return NAN\n");
exit (1);
}
mpfr_set_inf (x, 1);
mpfr_urandomb (y, RANDS); /* always positive */
mpfr_set_inf (z, -1);
mpfr_fma (s, x, y, z, MPFR_RNDN);
if (!mpfr_nan_p (s))
{
printf ("evaluation of function in x=INF y>0 z=-INF does not return NAN\n");
exit (1);
}
mpfr_set_inf (y, 1);
mpfr_urandomb (x, RANDS);
mpfr_set_inf (z, -1);
mpfr_fma (s, x, y, z, MPFR_RNDN);
if (!mpfr_nan_p (s))
{
printf ("evaluation of function in x>0 y=INF z=-INF does not return NAN\n");
exit (1);
}
mpfr_set_inf (x, 1);
do mpfr_urandomb (y, RANDS); while (MPFR_IS_ZERO(y));
mpfr_urandomb (z, RANDS);
mpfr_fma (s, x, y, z, MPFR_RNDN);
if (!mpfr_inf_p (s) || mpfr_sgn (s) < 0)
{
printf ("evaluation of function in x=INF does not return INF\n");
exit (1);
}
mpfr_set_inf (y, 1);
do mpfr_urandomb (x, RANDS); while (MPFR_IS_ZERO(x));
mpfr_urandomb (z, RANDS);
mpfr_fma (s, x, y, z, MPFR_RNDN);
if (!mpfr_inf_p (s) || mpfr_sgn (s) < 0)
{
printf ("evaluation of function at y=INF does not return INF\n");
exit (1);
}
mpfr_set_inf (z, 1);
mpfr_urandomb (x, RANDS);
mpfr_urandomb (y, RANDS);
mpfr_fma (s, x, y, z, MPFR_RNDN);
if (!mpfr_inf_p (s) || mpfr_sgn (s) < 0)
{
printf ("evaluation of function in z=INF does not return INF\n");
exit (1);
}
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_urandomb (y, RANDS);
mpfr_urandomb (z, RANDS);
mpfr_fma (s, x, y, z, MPFR_RNDN);
if (! mpfr_equal_p (s, z))
{
printf ("evaluation of function in x=0 does not return z\n");
exit (1);
}
mpfr_set_ui (y, 0, MPFR_RNDN);
mpfr_urandomb (x, RANDS);
mpfr_urandomb (z, RANDS);
mpfr_fma (s, x, y, z, MPFR_RNDN);
if (! mpfr_equal_p (s, z))
{
printf ("evaluation of function in y=0 does not return z\n");
exit (1);
}
{
mpfr_prec_t prec;
mpfr_t t, slong;
mpfr_rnd_t rnd;
int inexact, compare;
unsigned int n;
mpfr_prec_t p0 = 2, p1 = 200;
unsigned int N = 200;
mpfr_init (t);
mpfr_init (slong);
/* generic test */
for (prec = p0; prec <= p1; prec++)
{
mpfr_set_prec (x, prec);
mpfr_set_prec (y, prec);
mpfr_set_prec (z, prec);
mpfr_set_prec (s, prec);
mpfr_set_prec (t, prec);
for (n = 0; n < N; n++)
{
mpfr_urandomb (x, RANDS);
mpfr_urandomb (y, RANDS);
mpfr_urandomb (z, RANDS);
if (randlimb () % 2)
mpfr_neg (x, x, MPFR_RNDN);
if (randlimb () % 2)
mpfr_neg (y, y, MPFR_RNDN);
if (randlimb () % 2)
mpfr_neg (z, z, MPFR_RNDN);
rnd = RND_RAND_NO_RNDF ();
mpfr_set_prec (slong, 2 * prec);
if (mpfr_mul (slong, x, y, rnd))
{
printf ("x*y should be exact\n");
exit (1);
}
compare = mpfr_add (t, slong, z, rnd);
inexact = mpfr_fma (s, x, y, z, rnd);
if (! mpfr_equal_p (s, t))
{
printf ("results differ for\n");
printf (" x=");
mpfr_dump (x);
printf (" y=");
mpfr_dump (y);
printf (" z=");
mpfr_dump (z);
printf (" with prec=%u rnd_mode=%s\n", (unsigned int) prec,
mpfr_print_rnd_mode (rnd));
printf ("got ");
mpfr_dump (s);
printf ("expected ");
mpfr_dump (t);
printf ("approx ");
mpfr_dump (slong);
exit (1);
}
if (! SAME_SIGN (inexact, compare))
{
printf ("Wrong inexact flag for rnd=%s: expected %d, got %d\n",
mpfr_print_rnd_mode (rnd), compare, inexact);
printf (" x="); mpfr_dump (x);
printf (" y="); mpfr_dump (y);
printf (" z="); mpfr_dump (z);
printf (" s="); mpfr_dump (s);
exit (1);
}
}
}
mpfr_clear (t);
mpfr_clear (slong);
}
mpfr_clear (x);
mpfr_clear (y);
mpfr_clear (z);
mpfr_clear (s);
test_exact ();
for (i = 0; i <= 2; i++)
{
if (i == 0)
{
/* corresponds to the generic code + mpfr_check_range */
set_emin (-1024);
set_emax (1024);
}
else if (i == 1)
{
set_emin (MPFR_EMIN_MIN);
set_emax (MPFR_EMAX_MAX);
}
else
{
MPFR_ASSERTN (i == 2);
if (emin == MPFR_EMIN_MIN && emax == MPFR_EMAX_MAX)
break;
set_emin (emin);
set_emax (emax);
}
test_overflow1 ();
test_overflow2 ();
test_overflow3 ();
test_overflow4 ();
test_overflow5 ();
test_underflow1 ();
test_underflow2 ();
test_underflow3 (i);
test_underflow4 ();
test_underflow5 ();
}
tests_end_mpfr ();
return 0;
}