/* Test file for mpfr_fms.
Copyright 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"
/* When a * b is exact, the FMS 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_sub (r1, r1, c, (mpfr_rnd_t) rnd))
{
if (rnd == MPFR_RNDF)
break;
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_fms (r2, a, b, c, (mpfr_rnd_t) rnd))
{
printf ("test_exact(%d,%d,%d,%d): mpfr_fms 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_fms 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_set (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_fms (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_fms (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_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_fms (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;
}
mpfr_neg (z, z, MPFR_RNDN);
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, r;
int b, i, inex, same, err = 0;
mpfr_inits2 (32, x, y, z, r, (mpfr_ptr) 0);
mpfr_set_si_2exp (z, -1, mpfr_get_emin (), MPFR_RNDN); /* z = -2^emin */
mpfr_set_si_2exp (x, 1, mpfr_get_emin (), MPFR_RNDN); /* x = 2^emin */
for (b = 0; b <= 1; b++)
{
for (i = 15; i <= 17; i++)
{
mpfr_set_si_2exp (y, i, -4 - MPFR_PREC (z), MPFR_RNDN);
/* z = -1.000...00b
* xy = 01111
* or 10000
* or 10001
*/
mpfr_clear_flags ();
inex = mpfr_fms (r, x, y, z, MPFR_RNDN);
#define STRTU2 "Error in test_underflow2 (b = %d, i = %d)\n "
if (__gmpfr_flags != MPFR_FLAGS_INEXACT)
{
printf (STRTU2 "flags = %u instead of %u\n", b, i,
(unsigned int) __gmpfr_flags,
(unsigned int) MPFR_FLAGS_INEXACT);
err = 1;
}
same = i == 15 || (i == 16 && b == 0);
if (same ? (inex >= 0) : (inex <= 0))
{
printf (STRTU2 "incorrect ternary value (%d instead of %c 0)\n",
b, i, inex, same ? '<' : '>');
err = 1;
}
mpfr_neg (y, z, MPFR_RNDN);
if (!same)
mpfr_nextabove (y);
if (! mpfr_equal_p (r, y))
{
printf (STRTU2 "expected ", b, i);
mpfr_dump (y);
printf (" got ");
mpfr_dump (r);
err = 1;
}
}
mpfr_nextbelow (z);
}
if (err)
exit (1);
mpfr_clears (x, y, z, r, (mpfr_ptr) 0);
}
int
main (int argc, char *argv[])
{
mpfr_t x, y, z, s;
MPFR_SAVE_EXPO_DECL (expo);
tests_start_mpfr ();
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_fms (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_fms (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_fms (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_fms (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_fms (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_fms (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_fms (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_fms (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_fms (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_fms (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_fms (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_fms (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_fms (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_fms (s, x, y, z, MPFR_RNDN);
if (!mpfr_inf_p (s) || mpfr_sgn (s) < 0)
{
printf ("evaluation of function at 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_fms (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_fms (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_fms (s, x, y, z, MPFR_RNDN);
mpfr_neg (z, 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_fms (s, x, y, z, MPFR_RNDN);
mpfr_neg (z, 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_sub (t, slong, z, rnd);
inexact = mpfr_fms (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 ();
MPFR_SAVE_EXPO_MARK (expo);
test_overflow1 ();
test_overflow2 ();
test_underflow1 ();
test_underflow2 ();
MPFR_SAVE_EXPO_FREE (expo);
tests_end_mpfr ();
return 0;
}