/* Test n random bad cases. A precision py in [pymin,pymax] and
* a number y of precision py are chosen randomly. One computes
* x = inv(y) in precision px = py + psup (rounded to nearest).
* Then (in general), y is a bad case for fct in precision py (in
* the directed rounding modes, but also in the rounding-to-nearest
* mode for some lower precision: see data_check).
* fct, inv, name: data related to the function.
* pos, emin, emax: arguments for tests_default_random.
*/
void
bad_cases (int (*fct)(FLIST), int (*inv)(FLIST), const char *name,
int pos, mpfr_exp_t emin, mpfr_exp_t emax,
mpfr_prec_t pymin, mpfr_prec_t pymax, mpfr_prec_t psup,
int n)
{
mpfr_t x, y, z;
char *dbgenv;
int i, dbg;
mpfr_exp_t old_emin, old_emax;
old_emin = mpfr_get_emin ();
old_emax = mpfr_get_emax ();
dbgenv = getenv ("MPFR_DEBUG_BADCASES");
dbg = dbgenv != 0 ? atoi (dbgenv) : 0; /* debug level */
mpfr_inits (x, y, z, (mpfr_ptr) 0);
for (i = 0; i < n; i++)
{
mpfr_prec_t px, py, pz;
int inex;
if (dbg)
printf ("bad_cases: i = %d\n", i);
py = pymin + (randlimb () % (pymax - pymin + 1));
mpfr_set_prec (y, py);
tests_default_random (y, pos, emin, emax);
if (dbg)
{
printf ("bad_cases: yprec =%4ld, y = ", (long) py);
mpfr_out_str (stdout, 16, 0, y, MPFR_RNDN);
printf ("\n");
}
px = py + psup;
mpfr_set_prec (x, px);
mpfr_clear_flags ();
inv (x, y, MPFR_RNDN);
if (mpfr_nanflag_p () || mpfr_overflow_p () || mpfr_underflow_p ())
{
if (dbg)
printf ("bad_cases: no normal inverse\n");
goto next_i;
}
if (dbg > 1)
{
printf ("bad_cases: x = ");
mpfr_out_str (stdout, 16, 0, x, MPFR_RNDN);
printf ("\n");
}
pz = px;
do
{
pz += 32;
mpfr_set_prec (z, pz);
if (fct (z, x, MPFR_RNDN) == 0)
{
if (dbg)
printf ("bad_cases: exact case\n");
goto next_i;
}
if (dbg)
{
if (dbg > 1)
{
printf ("bad_cases: %s(x) ~= ", name);
mpfr_out_str (stdout, 16, 0, z, MPFR_RNDN);
}
else
{
printf ("bad_cases: [MPFR_RNDZ] ~= ");
mpfr_out_str (stdout, 16, 40, z, MPFR_RNDZ);
}
printf ("\n");
}
inex = mpfr_prec_round (z, py, MPFR_RNDN);
if (mpfr_nanflag_p () || mpfr_overflow_p () || mpfr_underflow_p ()
|| ! mpfr_equal_p (z, y))
{
if (dbg)
printf ("bad_cases: inverse doesn't match\n");
goto next_i;
}
}
while (inex == 0);
/* We really have a bad case. */
do
py--;
while (py >= MPFR_PREC_MIN && mpfr_prec_round (z, py, MPFR_RNDZ) == 0);
py++;
/* py is now the smallest output precision such that we have
a bad case in the directed rounding modes. */
if (mpfr_prec_round (y, py, MPFR_RNDZ) != 0)
{
printf ("Internal error for i = %d\n", i);
exit (1);
}
if ((inex > 0 && MPFR_IS_POS (z)) ||
(inex < 0 && MPFR_IS_NEG (z)))
{
mpfr_nexttozero (y);
if (mpfr_zero_p (y))
goto next_i;
}
if (dbg)
{
printf ("bad_cases: yprec =%4ld, y = ", (long) py);
mpfr_out_str (stdout, 16, 0, y, MPFR_RNDN);
printf ("\n");
}
/* Note: y is now the expected result rounded toward zero. */
test5rm (fct, x, y, z, MPFR_RNDZ, 0, name);
next_i:
/* In case the exponent range has been changed by
tests_default_random()... */
mpfr_set_emin (old_emin);
mpfr_set_emax (old_emax);
}
mpfr_clears (x, y, z, (mpfr_ptr) 0);
}
static void
check_random (FILE *fout, int nb_tests)
{
int i;
mpfr_t x;
mp_rnd_t rnd;
char flag[] =
{
'-',
'+',
' ',
'#',
'0', /* no ambiguity: first zeros are flag zero*/
'\''
};
char specifier[] =
{
'a',
'b',
'e',
'f',
'g'
};
mp_exp_t old_emin, old_emax;
old_emin = mpfr_get_emin ();
old_emax = mpfr_get_emax ();
mpfr_init (x);
for (i = 0; i < nb_tests; ++i)
{
int ret;
int j, jmax;
int spec, prec;
#define FMT_SIZE 13
char fmt[FMT_SIZE]; /* at most something like "%-+ #0'.*R*f" */
char *ptr = fmt;
tests_default_random (x, 256, MPFR_EMIN_MIN, MPFR_EMAX_MAX);
rnd = RND_RAND ();
spec = (int) (randlimb () % 5);
jmax = (spec == 3 || spec == 4) ? 6 : 5; /* ' flag only with %f or %g */
/* advantage small precision */
prec = (int) (randlimb () % ((randlimb () % 2) ? 10 : prec_max_printf));
if (spec == 3
&& (mpfr_get_exp (x) > prec_max_printf
|| mpfr_get_exp (x) < -prec_max_printf))
/* change style 'f' to style 'e' when number x is large */
--spec;
*ptr++ = '%';
for (j = 0; j < jmax; j++)
{
if (randlimb () % 3 == 0)
*ptr++ = flag[j];
}
*ptr++ = '.';
*ptr++ = '*';
*ptr++ = 'R';
*ptr++ = '*';
*ptr++ = specifier[spec];
*ptr = '\0';
MPFR_ASSERTD (ptr - fmt < FMT_SIZE);
mpfr_fprintf (fout, "mpfr_fprintf(fout, \"%s\", %d, %s, %Re)\n",
fmt, prec, mpfr_print_rnd_mode (rnd), x);
ret = mpfr_fprintf (fout, fmt, prec, rnd, x);
if (ret == -1)
{
if (spec == 3
&& (MPFR_GET_EXP (x) > INT_MAX || MPFR_GET_EXP (x) < -INT_MAX))
/* normal failure: x is too large to be output with full precision */
{
mpfr_fprintf (fout, "too large !");
}
else
{
mpfr_printf ("Error in mpfr_fprintf(fout, \"%s\", %d, %s, %Re)\n",
fmt, prec, mpfr_print_rnd_mode (rnd), x);
exit (1);
}
}
mpfr_fprintf (fout, "\n");
}
mpfr_set_emin (old_emin);
mpfr_set_emax (old_emax);
mpfr_clear (x);
}
static void
consistency (void)
{
mpfr_t x, s1, s2, c1, c2;
mpfr_exp_t emin, emax;
mpfr_rnd_t rnd;
unsigned int flags_sin, flags_cos, flags, flags_before, flags_ref;
int inex_sin, is, inex_cos, ic, inex, inex_ref;
int i;
emin = mpfr_get_emin ();
emax = mpfr_get_emax ();
for (i = 0; i <= 10000; i++)
{
mpfr_init2 (x, MPFR_PREC_MIN + (randlimb () % 8));
mpfr_inits2 (MPFR_PREC_MIN + (randlimb () % 8), s1, s2, c1, c2,
(mpfr_ptr) 0);
if (i < 8 * MPFR_RND_MAX)
{
int j = i / MPFR_RND_MAX;
if (j & 1)
mpfr_set_emin (MPFR_EMIN_MIN);
mpfr_set_si (x, (j & 2) ? 1 : -1, MPFR_RNDN);
mpfr_set_exp (x, mpfr_get_emin ());
rnd = (mpfr_rnd_t) (i % MPFR_RND_MAX);
flags_before = 0;
if (j & 4)
mpfr_set_emax (-17);
}
else
{
tests_default_random (x, 256, -5, 50, 0);
rnd = RND_RAND ();
flags_before = (randlimb () & 1) ?
(unsigned int) (MPFR_FLAGS_ALL ^ MPFR_FLAGS_ERANGE) :
(unsigned int) 0;
}
__gmpfr_flags = flags_before;
inex_sin = mpfr_sin (s1, x, rnd);
is = inex_sin < 0 ? 2 : inex_sin > 0 ? 1 : 0;
flags_sin = __gmpfr_flags;
__gmpfr_flags = flags_before;
inex_cos = mpfr_cos (c1, x, rnd);
ic = inex_cos < 0 ? 2 : inex_cos > 0 ? 1 : 0;
flags_cos = __gmpfr_flags;
__gmpfr_flags = flags_before;
inex = mpfr_sin_cos (s2, c2, x, rnd);
flags = __gmpfr_flags;
inex_ref = is + 4 * ic;
flags_ref = flags_sin | flags_cos;
if (!(mpfr_equal_p (s1, s2) && mpfr_equal_p (c1, c2)) ||
inex != inex_ref || flags != flags_ref)
{
printf ("mpfr_sin_cos and mpfr_sin/mpfr_cos disagree on %s,"
" i = %d\nx = ", mpfr_print_rnd_mode (rnd), i);
mpfr_dump (x);
printf ("s1 = ");
mpfr_dump (s1);
printf ("s2 = ");
mpfr_dump (s2);
printf ("c1 = ");
mpfr_dump (c1);
printf ("c2 = ");
mpfr_dump (c2);
printf ("inex_sin = %d (s = %d), inex_cos = %d (c = %d), "
"inex = %d (expected %d)\n",
inex_sin, is, inex_cos, ic, inex, inex_ref);
printf ("flags_sin = 0x%x, flags_cos = 0x%x, "
"flags = 0x%x (expected 0x%x)\n",
flags_sin, flags_cos, flags, flags_ref);
exit (1);
}
mpfr_clears (x, s1, s2, c1, c2, (mpfr_ptr) 0);
mpfr_set_emin (emin);
mpfr_set_emax (emax);
}
}
static void
test_generic (mpfr_prec_t p0, mpfr_prec_t p1, unsigned int nmax)
{
mpfr_prec_t prec, xprec, yprec;
mpfr_t x, y, z, t, w;
#if defined(TWO_ARGS_ALL)
mpfr_t u;
#endif
#if defined(DOUBLE_ARG1) || defined(DOUBLE_ARG2)
double d;
#endif
#if defined(ULONG_ARG1) || defined(ULONG_ARG2)
unsigned long i;
#endif
mpfr_rnd_t rnd;
int inexact, compare, compare2;
unsigned int n;
unsigned long ctrt = 0, ctrn = 0;
int test_of = 1, test_uf = 1;
mpfr_exp_t old_emin, old_emax;
old_emin = mpfr_get_emin ();
old_emax = mpfr_get_emax ();
mpfr_inits2 (MPFR_PREC_MIN, x, y, z, t, w, (mpfr_ptr) 0);
#if defined(TWO_ARGS_ALL)
mpfr_init2 (u, MPFR_PREC_MIN);
#endif
/* generic test */
for (prec = p0; prec <= p1; prec++)
{
mpfr_set_prec (z, prec);
mpfr_set_prec (t, prec);
yprec = prec + 10;
mpfr_set_prec (y, yprec);
mpfr_set_prec (w, yprec);
/* Note: in precision p1, we test 4 special cases. */
for (n = 0; n < (prec == p1 ? nmax + 4 : nmax); n++)
{
int infinite_input = 0;
unsigned int flags;
mpfr_exp_t oemin, oemax;
xprec = prec;
if (randlimb () & 1)
{
xprec *= (double) randlimb () / MP_LIMB_T_MAX;
if (xprec < MPFR_PREC_MIN)
xprec = MPFR_PREC_MIN;
}
mpfr_set_prec (x, xprec);
#if defined(TWO_ARGS)
mpfr_set_prec (u, xprec);
#elif defined(DOUBLE_ARG1) || defined(DOUBLE_ARG2)
mpfr_set_prec (u, IEEE_DBL_MANT_DIG);
#elif defined(ULONG_ARG1) || defined(ULONG_ARG2)
mpfr_set_prec (u, sizeof (unsigned long) * CHAR_BIT);
#endif
if (n > 3 || prec < p1)
{
#if defined(RAND_FUNCTION)
RAND_FUNCTION (x);
#if defined(TWO_ARGS) || defined(DOUBLE_ARG1) || defined(DOUBLE_ARG2)
RAND_FUNCTION (u);
#endif
#else /* ! defined(RAND_FUNCTION) */
tests_default_random (x, TEST_RANDOM_POS,
TEST_RANDOM_EMIN, TEST_RANDOM_EMAX,
TEST_RANDOM_ALWAYS_SCALE);
#if defined(TWO_ARGS) || defined(DOUBLE_ARG1) || defined(DOUBLE_ARG2)
tests_default_random (u, TEST_RANDOM_POS2,
TEST_RANDOM_EMIN, TEST_RANDOM_EMAX,
TEST_RANDOM_ALWAYS_SCALE);
#endif
#endif /* ! defined(RAND_FUNCTION) */
}
else
{
/* Special cases tested in precision p1 if n <= 3. They are
useful really in the extended exponent range. */
#if (defined(DOUBLE_ARG1) || defined(DOUBLE_ARG2)) && defined(MPFR_ERRDIVZERO)
goto next_n;
#endif
set_emin (MPFR_EMIN_MIN);
set_emax (MPFR_EMAX_MAX);
if (n <= 1)
{
mpfr_set_si (x, n == 0 ? 1 : -1, MPFR_RNDN);
mpfr_set_exp (x, mpfr_get_emin ());
#if defined(TWO_ARGS) || defined(DOUBLE_ARG1) || defined(DOUBLE_ARG2)
mpfr_set_si (u, randlimb () % 2 == 0 ? 1 : -1, MPFR_RNDN);
mpfr_set_exp (u, mpfr_get_emin ());
#endif
}
else /* 2 <= n <= 3 */
{
if (getenv ("MPFR_CHECK_MAX") == NULL)
goto next_n;
mpfr_set_si (x, n == 0 ? 1 : -1, MPFR_RNDN);
mpfr_setmax (x, REDUCE_EMAX);
#if defined(TWO_ARGS) || defined(DOUBLE_ARG1) || defined(DOUBLE_ARG2)
mpfr_set_si (u, randlimb () % 2 == 0 ? 1 : -1, MPFR_RNDN);
mpfr_setmax (u, mpfr_get_emax ());
#endif
}
}
#if defined(ULONG_ARG1) || defined(ULONG_ARG2)
i = randlimb ();
inexact = mpfr_set_ui (u, i, MPFR_RNDN);
MPFR_ASSERTN (inexact == 0);
#endif
/* Exponent range for the test. */
oemin = mpfr_get_emin ();
oemax = mpfr_get_emax ();
rnd = RND_RAND ();
mpfr_clear_flags ();
#ifdef DEBUG_TGENERIC
TGENERIC_INFO (TEST_FUNCTION, MPFR_PREC (y));
#endif
#if defined(TWO_ARGS)
compare = TEST_FUNCTION (y, x, u, rnd);
#elif defined(DOUBLE_ARG1)
d = mpfr_get_d (u, rnd);
compare = TEST_FUNCTION (y, d, x, rnd);
/* d can be infinite due to overflow in mpfr_get_d */
infinite_input |= DOUBLE_ISINF (d);
#elif defined(DOUBLE_ARG2)
d = mpfr_get_d (u, rnd);
compare = TEST_FUNCTION (y, x, d, rnd);
/* d can be infinite due to overflow in mpfr_get_d */
infinite_input |= DOUBLE_ISINF (d);
#elif defined(ULONG_ARG1)
compare = TEST_FUNCTION (y, i, x, rnd);
#elif defined(ULONG_ARG2)
compare = TEST_FUNCTION (y, x, i, rnd);
#else
compare = TEST_FUNCTION (y, x, rnd);
#endif
flags = __gmpfr_flags;
if (mpfr_get_emin () != oemin ||
mpfr_get_emax () != oemax)
{
printf ("tgeneric: the exponent range has been modified"
" by the tested function!\n");
exit (1);
}
TGENERIC_CHECK ("bad inexact flag",
(compare != 0) ^ (mpfr_inexflag_p () == 0));
ctrt++;
/* Tests in a reduced exponent range. */
{
unsigned int oldflags = flags;
mpfr_exp_t e, emin, emax;
/* Determine the smallest exponent range containing the
exponents of the mpfr_t inputs (x, and u if TWO_ARGS)
and output (y). */
emin = MPFR_EMAX_MAX;
emax = MPFR_EMIN_MIN;
if (MPFR_IS_PURE_FP (x))
{
e = MPFR_GET_EXP (x);
if (e < emin)
emin = e;
if (e > emax)
emax = e;
}
#if defined(TWO_ARGS)
if (MPFR_IS_PURE_FP (u))
{
e = MPFR_GET_EXP (u);
if (e < emin)
emin = e;
if (e > emax)
emax = e;
}
#endif
if (MPFR_IS_PURE_FP (y))
{
e = MPFR_GET_EXP (y);
if (test_of && e - 1 >= emax)
{
unsigned int ex_flags;
mpfr_set_emax (e - 1);
mpfr_clear_flags ();
#if defined(TWO_ARGS)
inexact = TEST_FUNCTION (w, x, u, rnd);
#elif defined(DOUBLE_ARG1)
inexact = TEST_FUNCTION (w, d, x, rnd);
#elif defined(DOUBLE_ARG2)
inexact = TEST_FUNCTION (w, x, d, rnd);
#elif defined(ULONG_ARG1)
inexact = TEST_FUNCTION (w, i, x, rnd);
#elif defined(ULONG_ARG2)
inexact = TEST_FUNCTION (w, x, i, rnd);
#else
inexact = TEST_FUNCTION (w, x, rnd);
#endif
flags = __gmpfr_flags;
mpfr_set_emax (oemax);
ex_flags = MPFR_FLAGS_OVERFLOW | MPFR_FLAGS_INEXACT;
if (flags != ex_flags)
{
printf ("tgeneric: error for " MAKE_STR(TEST_FUNCTION)
", reduced exponent range [%"
MPFR_EXP_FSPEC "d,%" MPFR_EXP_FSPEC
"d] (overflow test) on:\n",
(mpfr_eexp_t) oemin, (mpfr_eexp_t) e - 1);
printf ("x = ");
mpfr_dump (x);
#if defined(TWO_ARGS_ALL)
printf ("u = ");
mpfr_dump (u);
#endif
printf ("yprec = %u, rnd_mode = %s\n",
(unsigned int) yprec,
mpfr_print_rnd_mode (rnd));
printf ("Expected flags =");
flags_out (ex_flags);
printf (" got flags =");
flags_out (flags);
printf ("inex = %d, w = ", inexact);
mpfr_dump (w);
exit (1);
}
test_of = 0; /* Overflow is tested only once. */
}
if (test_uf && e + 1 <= emin)
{
unsigned int ex_flags;
mpfr_set_emin (e + 1);
mpfr_clear_flags ();
#if defined(TWO_ARGS)
inexact = TEST_FUNCTION (w, x, u, rnd);
#elif defined(DOUBLE_ARG1)
inexact = TEST_FUNCTION (w, d, x, rnd);
#elif defined(DOUBLE_ARG2)
inexact = TEST_FUNCTION (w, x, d, rnd);
#elif defined(ULONG_ARG1)
inexact = TEST_FUNCTION (w, i, x, rnd);
#elif defined(ULONG_ARG2)
inexact = TEST_FUNCTION (w, x, i, rnd);
#else
inexact = TEST_FUNCTION (w, x, rnd);
#endif
flags = __gmpfr_flags;
mpfr_set_emin (oemin);
ex_flags = MPFR_FLAGS_UNDERFLOW | MPFR_FLAGS_INEXACT;
if (flags != ex_flags)
{
printf ("tgeneric: error for " MAKE_STR(TEST_FUNCTION)
", reduced exponent range [%"
MPFR_EXP_FSPEC "d,%" MPFR_EXP_FSPEC
"d] (underflow test) on:\n",
(mpfr_eexp_t) e + 1, (mpfr_eexp_t) oemax);
printf ("x = ");
mpfr_dump (x);
#if defined(TWO_ARGS_ALL)
printf ("u = ");
mpfr_dump (u);
#endif
printf ("yprec = %u, rnd_mode = %s\n",
(unsigned int) yprec,
mpfr_print_rnd_mode (rnd));
printf ("Expected flags =");
flags_out (ex_flags);
printf (" got flags =");
flags_out (flags);
printf ("inex = %d, w = ", inexact);
mpfr_dump (w);
exit (1);
}
test_uf = 0; /* Underflow is tested only once. */
}
if (e < emin)
emin = e;
if (e > emax)
emax = e;
}
if (emin > emax)
emin = emax; /* case where all values are singular */
/* Consistency test in a reduced exponent range. Doing it
for the first 10 samples and for prec == p1 (which has
some special cases) should be sufficient. */
if (ctrt <= 10 || prec == p1)
{
mpfr_set_emin (emin);
mpfr_set_emax (emax);
#ifdef DEBUG_TGENERIC
/* Useful information in case of assertion failure. */
printf ("tgeneric: reduced exponent range [%"
MPFR_EXP_FSPEC "d,%" MPFR_EXP_FSPEC "d]\n",
(mpfr_eexp_t) emin, (mpfr_eexp_t) emax);
#endif
mpfr_clear_flags ();
#if defined(TWO_ARGS)
inexact = TEST_FUNCTION (w, x, u, rnd);
#elif defined(DOUBLE_ARG1)
inexact = TEST_FUNCTION (w, d, x, rnd);
#elif defined(DOUBLE_ARG2)
inexact = TEST_FUNCTION (w, x, d, rnd);
#elif defined(ULONG_ARG1)
inexact = TEST_FUNCTION (w, i, x, rnd);
#elif defined(ULONG_ARG2)
inexact = TEST_FUNCTION (w, x, i, rnd);
#else
inexact = TEST_FUNCTION (w, x, rnd);
#endif
flags = __gmpfr_flags;
mpfr_set_emin (oemin);
mpfr_set_emax (oemax);
if (! (SAME_VAL (w, y) &&
SAME_SIGN (inexact, compare) &&
flags == oldflags))
{
printf ("tgeneric: error for " MAKE_STR(TEST_FUNCTION)
", reduced exponent range [%"
MPFR_EXP_FSPEC "d,%" MPFR_EXP_FSPEC "d] on:\n",
(mpfr_eexp_t) emin, (mpfr_eexp_t) emax);
printf ("x = ");
mpfr_dump (x);
#if defined(TWO_ARGS_ALL)
printf ("u = ");
mpfr_dump (u);
#endif
printf ("yprec = %u, rnd_mode = %s\n",
(unsigned int) yprec, mpfr_print_rnd_mode (rnd));
printf ("Expected:\n y = ");
mpfr_dump (y);
printf (" inex = %d, flags =", compare);
flags_out (oldflags);
printf ("Got:\n w = ");
mpfr_dump (w);
printf (" inex = %d, flags =", inexact);
flags_out (flags);
exit (1);
}
}
__gmpfr_flags = oldflags; /* restore the flags */
}
if (MPFR_IS_SINGULAR (y))
{
if (MPFR_IS_NAN (y) || mpfr_nanflag_p ())
TGENERIC_CHECK ("bad NaN flag",
MPFR_IS_NAN (y) && mpfr_nanflag_p ());
else if (MPFR_IS_INF (y))
{
TGENERIC_CHECK ("bad overflow flag",
(compare != 0) ^ (mpfr_overflow_p () == 0));
TGENERIC_CHECK ("bad divide-by-zero flag",
(compare == 0 && !infinite_input) ^
(mpfr_divby0_p () == 0));
}
else if (MPFR_IS_ZERO (y))
TGENERIC_CHECK ("bad underflow flag",
(compare != 0) ^ (mpfr_underflow_p () == 0));
}
else if (mpfr_divby0_p ())
{
TGENERIC_CHECK ("both overflow and divide-by-zero",
! mpfr_overflow_p ());
TGENERIC_CHECK ("both underflow and divide-by-zero",
! mpfr_underflow_p ());
TGENERIC_CHECK ("bad compare value (divide-by-zero)",
compare == 0);
}
else if (mpfr_overflow_p ())
{
TGENERIC_CHECK ("both underflow and overflow",
! mpfr_underflow_p ());
TGENERIC_CHECK ("bad compare value (overflow)", compare != 0);
mpfr_nexttoinf (y);
TGENERIC_CHECK ("should have been max MPFR number (overflow)",
MPFR_IS_INF (y));
}
else if (mpfr_underflow_p ())
{
TGENERIC_CHECK ("bad compare value (underflow)", compare != 0);
mpfr_nexttozero (y);
TGENERIC_CHECK ("should have been min MPFR number (underflow)",
MPFR_IS_ZERO (y));
}
else if (mpfr_can_round (y, yprec, rnd, rnd, prec))
{
ctrn++;
mpfr_set (t, y, rnd);
/* Risk of failures are known when some flags are already set
before the function call. Do not set the erange flag, as
it will remain set after the function call and no checks
are performed in such a case (see the mpfr_erangeflag_p
test below). */
if (randlimb () & 1)
__gmpfr_flags = MPFR_FLAGS_ALL ^ MPFR_FLAGS_ERANGE;
#ifdef DEBUG_TGENERIC
TGENERIC_INFO (TEST_FUNCTION, MPFR_PREC (z));
#endif
/* Let's increase the precision of the inputs in a random way.
In most cases, this doesn't make any difference, but for
the mpfr_fmod bug fixed in r6230, this triggers the bug. */
mpfr_prec_round (x, mpfr_get_prec (x) + (randlimb () & 15),
MPFR_RNDN);
#if defined(TWO_ARGS)
mpfr_prec_round (u, mpfr_get_prec (u) + (randlimb () & 15),
MPFR_RNDN);
inexact = TEST_FUNCTION (z, x, u, rnd);
#elif defined(DOUBLE_ARG1)
inexact = TEST_FUNCTION (z, d, x, rnd);
#elif defined(DOUBLE_ARG2)
inexact = TEST_FUNCTION (z, x, d, rnd);
#elif defined(ULONG_ARG1)
inexact = TEST_FUNCTION (z, i, x, rnd);
#elif defined(ULONG_ARG2)
inexact = TEST_FUNCTION (z, x, i, rnd);
#else
inexact = TEST_FUNCTION (z, x, rnd);
#endif
if (mpfr_erangeflag_p ())
goto next_n;
if (! mpfr_equal_p (t, z))
{
printf ("tgeneric: results differ for "
MAKE_STR(TEST_FUNCTION) " on\n x = ");
mpfr_dump (x);
#if defined(TWO_ARGS_ALL)
printf (" u = ");
mpfr_dump (u);
#endif
printf (" prec = %u, rnd_mode = %s\n",
(unsigned int) prec, mpfr_print_rnd_mode (rnd));
printf ("Got ");
mpfr_dump (z);
printf ("Expected ");
mpfr_dump (t);
printf ("Approx ");
mpfr_dump (y);
exit (1);
}
compare2 = mpfr_cmp (t, y);
/* if rounding to nearest, cannot know the sign of t - f(x)
because of composed rounding: y = o(f(x)) and t = o(y) */
if (compare * compare2 >= 0)
compare = compare + compare2;
else
compare = inexact; /* cannot determine sign(t-f(x)) */
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);
#if defined(TWO_ARGS_ALL)
printf ("u = ");
mpfr_dump (u);
#endif
printf ("y = ");
mpfr_dump (y);
printf ("t = ");
mpfr_dump (t);
exit (1);
}
}
else if (getenv ("MPFR_SUSPICIOUS_OVERFLOW") != NULL)
{
/* For developers only! */
MPFR_ASSERTN (MPFR_IS_PURE_FP (y));
mpfr_nexttoinf (y);
if (MPFR_IS_INF (y) && MPFR_IS_LIKE_RNDZ (rnd, MPFR_IS_NEG (y))
&& !mpfr_overflow_p () && TGENERIC_SO_TEST)
{
printf ("Possible bug! |y| is the maximum finite number "
"and has been obtained when\nrounding toward zero"
" (%s). Thus there is a very probable overflow,\n"
"but the overflow flag is not set!\n",
mpfr_print_rnd_mode (rnd));
printf ("x = ");
mpfr_dump (x);
#if defined(TWO_ARGS_ALL)
printf ("u = ");
mpfr_dump (u);
#endif
exit (1);
}
}
next_n:
/* In case the exponent range has been changed by
tests_default_random() or for special values... */
mpfr_set_emin (old_emin);
mpfr_set_emax (old_emax);
}
}
#ifndef TGENERIC_NOWARNING
if (3 * ctrn < 2 * ctrt)
printf ("Warning! Too few normal cases in generic tests (%lu / %lu)\n",
ctrn, ctrt);
#endif
mpfr_clears (x, y, z, t, w, (mpfr_ptr) 0);
#if defined(TWO_ARGS_ALL)
mpfr_clear (u);
#endif
}
static void
test_generic (mp_prec_t p0, mp_prec_t p1, unsigned int N)
{
mp_prec_t prec, xprec, yprec;
mpfr_t x, y, z, t;
#ifdef TWO_ARGS
mpfr_t u;
#elif defined(DOUBLE_ARG1) || defined(DOUBLE_ARG2)
mpfr_t u;
double d;
#endif
mp_rnd_t rnd;
int inexact, compare, compare2;
unsigned int n;
unsigned long ctrt = 0, ctrn = 0;
mp_exp_t old_emin, old_emax;
old_emin = mpfr_get_emin ();
old_emax = mpfr_get_emax ();
mpfr_init (x);
mpfr_init (y);
mpfr_init (z);
mpfr_init (t);
#if defined(TWO_ARGS) || defined(DOUBLE_ARG1) || defined(DOUBLE_ARG2)
mpfr_init (u);
#endif
/* generic test */
for (prec = p0; prec <= p1; prec++)
{
mpfr_set_prec (z, prec);
mpfr_set_prec (t, prec);
yprec = prec + 10;
mpfr_set_prec (y, yprec);
/* Note: in precision p1, we test 4 special cases. */
for (n = 0; n < (prec == p1 ? N + 4 : N); n++)
{
xprec = prec;
if (randlimb () & 1)
{
xprec *= (double) randlimb () / MP_LIMB_T_MAX;
if (xprec < MPFR_PREC_MIN)
xprec = MPFR_PREC_MIN;
}
mpfr_set_prec (x, xprec);
#ifdef TWO_ARGS
mpfr_set_prec (u, xprec);
#elif defined(DOUBLE_ARG1) || defined(DOUBLE_ARG2)
mpfr_set_prec (u, IEEE_DBL_MANT_DIG);
#endif
if (n > 3 || prec < p1)
{
#if defined(RAND_FUNCTION)
RAND_FUNCTION (x);
#if defined(TWO_ARGS) || defined(DOUBLE_ARG1) || defined(DOUBLE_ARG2)
RAND_FUNCTION (u);
#endif
#else
tests_default_random (x, TEST_RANDOM_POS,
TEST_RANDOM_EMIN, TEST_RANDOM_EMAX);
#if defined(TWO_ARGS) || defined(DOUBLE_ARG1) || defined(DOUBLE_ARG2)
tests_default_random (u, TEST_RANDOM_POS2,
TEST_RANDOM_EMIN, TEST_RANDOM_EMAX);
#endif
#endif
}
else
{
/* Special cases tested in precision p1 if n <= 3. They are
useful really in the extended exponent range. */
set_emin (MPFR_EMIN_MIN);
set_emax (MPFR_EMAX_MAX);
if (n <= 1)
{
mpfr_set_si (x, n == 0 ? 1 : -1, GMP_RNDN);
mpfr_set_exp (x, mpfr_get_emin ());
#if defined(TWO_ARGS) || defined(DOUBLE_ARG1) || defined(DOUBLE_ARG2)
mpfr_set_si (u, randlimb () % 2 == 0 ? 1 : -1, GMP_RNDN);
mpfr_set_exp (u, mpfr_get_emin ());
#endif
}
else /* 2 <= n <= 3 */
{
if (getenv ("MPFR_CHECK_MAX") == NULL)
goto next_n;
mpfr_set_si (x, n == 0 ? 1 : -1, GMP_RNDN);
mpfr_setmax (x, REDUCE_EMAX);
#if defined(TWO_ARGS) || defined(DOUBLE_ARG1) || defined(DOUBLE_ARG2)
mpfr_set_si (u, randlimb () % 2 == 0 ? 1 : -1, GMP_RNDN);
mpfr_setmax (u, mpfr_get_emax ());
#endif
}
}
rnd = RND_RAND ();
mpfr_clear_flags ();
#ifdef DEBUG_TGENERIC
TGENERIC_INFO (TEST_FUNCTION, MPFR_PREC (y));
#endif
#if defined(TWO_ARGS)
compare = TEST_FUNCTION (y, x, u, rnd);
#elif defined(DOUBLE_ARG1)
d = mpfr_get_d (u, rnd);
compare = TEST_FUNCTION (y, d, x, rnd);
#elif defined(DOUBLE_ARG2)
d = mpfr_get_d (u, rnd);
compare = TEST_FUNCTION (y, x, d, rnd);
#else
compare = TEST_FUNCTION (y, x, rnd);
#endif
TGENERIC_CHECK ("Bad inexact flag",
(compare != 0) ^ (mpfr_inexflag_p () == 0));
ctrt++;
if (MPFR_IS_SINGULAR (y))
{
if (MPFR_IS_NAN (y) || mpfr_nanflag_p ())
TGENERIC_CHECK ("Bad NaN flag",
MPFR_IS_NAN (y) && mpfr_nanflag_p ());
else if (MPFR_IS_INF (y))
TGENERIC_CHECK ("Bad overflow flag",
(compare != 0) ^ (mpfr_overflow_p () == 0));
else if (MPFR_IS_ZERO (y))
TGENERIC_CHECK ("Bad underflow flag",
(compare != 0) ^ (mpfr_underflow_p () == 0));
}
else if (mpfr_overflow_p ())
{
TGENERIC_CHECK ("Bad compare value (overflow)", compare != 0);
mpfr_nexttoinf (y);
TGENERIC_CHECK ("Should have been max MPFR number",
MPFR_IS_INF (y));
}
else if (mpfr_underflow_p ())
{
TGENERIC_CHECK ("Bad compare value (underflow)", compare != 0);
mpfr_nexttozero (y);
TGENERIC_CHECK ("Should have been min MPFR number",
MPFR_IS_ZERO (y));
}
else if (mpfr_can_round (y, yprec, rnd, rnd, prec))
{
ctrn++;
mpfr_set (t, y, rnd);
/* Risk of failures are known when some flags are already set
before the function call. Do not set the erange flag, as
it will remain set after the function call and no checks
are performed in such a case (see the mpfr_erangeflag_p
test below). */
if (randlimb () & 1)
__gmpfr_flags = MPFR_FLAGS_ALL ^ MPFR_FLAGS_ERANGE;
#ifdef DEBUG_TGENERIC
TGENERIC_INFO (TEST_FUNCTION, MPFR_PREC (z));
#endif
/* Let's increase the precision of the inputs in a random way.
In most cases, this doesn't make any difference, but this
triggers the mpfr_fmod bug fixed in r6235. */
mpfr_prec_round (x, mpfr_get_prec (x) + (randlimb () & 15),
GMP_RNDN);
#if defined(TWO_ARGS)
mpfr_prec_round (u, mpfr_get_prec (u) + (randlimb () & 15),
GMP_RNDN);
inexact = TEST_FUNCTION (z, x, u, rnd);
#elif defined(DOUBLE_ARG1)
inexact = TEST_FUNCTION (z, d, x, rnd);
#elif defined(DOUBLE_ARG2)
inexact = TEST_FUNCTION (z, x, d, rnd);
#else
inexact = TEST_FUNCTION (z, x, rnd);
#endif
if (mpfr_erangeflag_p ())
goto next_n;
if (mpfr_nan_p (z) || mpfr_cmp (t, z) != 0)
{
printf ("results differ for x=");
mpfr_out_str (stdout, 2, xprec, x, GMP_RNDN);
#ifdef TWO_ARGS
printf ("\nu=");
mpfr_out_str (stdout, 2, xprec, u, GMP_RNDN);
#elif defined(DOUBLE_ARG1) || defined(DOUBLE_ARG2)
printf ("\nu=");
mpfr_out_str (stdout, 2, IEEE_DBL_MANT_DIG, u, GMP_RNDN);
#endif
printf (" prec=%u rnd_mode=%s\n", (unsigned) prec,
mpfr_print_rnd_mode (rnd));
printf ("got ");
mpfr_out_str (stdout, 2, prec, z, GMP_RNDN);
puts ("");
printf ("expected ");
mpfr_out_str (stdout, 2, prec, t, GMP_RNDN);
puts ("");
printf ("approx ");
mpfr_print_binary (y);
puts ("");
exit (1);
}
compare2 = mpfr_cmp (t, y);
/* if rounding to nearest, cannot know the sign of t - f(x)
because of composed rounding: y = o(f(x)) and t = o(y) */
if (compare * compare2 >= 0)
compare = compare + compare2;
else
compare = inexact; /* cannot determine sign(t-f(x)) */
if (((inexact == 0) && (compare != 0)) ||
((inexact > 0) && (compare <= 0)) ||
((inexact < 0) && (compare >= 0)))
{
printf ("Wrong inexact flag for rnd=%s: expected %d, got %d"
"\n", mpfr_print_rnd_mode (rnd), compare, inexact);
printf ("x="); mpfr_print_binary (x); puts ("");
#if defined(TWO_ARGS) || defined(DOUBLE_ARG1) || defined(DOUBLE_ARG2)
printf ("u="); mpfr_print_binary (u); puts ("");
#endif
printf ("y="); mpfr_print_binary (y); puts ("");
printf ("t="); mpfr_print_binary (t); puts ("");
exit (1);
}
}
else if (getenv ("MPFR_SUSPICIOUS_OVERFLOW") != NULL)
{
/* For developers only! */
MPFR_ASSERTN (MPFR_IS_PURE_FP (y));
mpfr_nexttoinf (y);
if (MPFR_IS_INF (y) && MPFR_IS_LIKE_RNDZ (rnd, MPFR_IS_NEG (y))
&& !mpfr_overflow_p ())
{
printf ("Possible bug! |y| is the maximum finite number "
"and has been obtained when\nrounding toward zero"
" (%s). Thus there is a very probable overflow,\n"
"but the overflow flag is not set!\n",
mpfr_print_rnd_mode (rnd));
printf ("x="); mpfr_print_binary (x); puts ("");
#if defined(TWO_ARGS) || defined(DOUBLE_ARG1) || defined(DOUBLE_ARG2)
printf ("u="); mpfr_print_binary (u); puts ("");
#endif
exit (1);
}
}
next_n:
/* In case the exponent range has been changed by
tests_default_random() or for special values... */
mpfr_set_emin (old_emin);
mpfr_set_emax (old_emax);
}
}
#ifndef TGENERIC_NOWARNING
if (3 * ctrn < 2 * ctrt)
printf ("Warning! Too few normal cases in generic tests (%lu / %lu)\n",
ctrn, ctrt);
#endif
mpfr_clear (x);
mpfr_clear (y);
mpfr_clear (z);
mpfr_clear (t);
#if defined(TWO_ARGS) || defined(DOUBLE_ARG1) || defined(DOUBLE_ARG2)
mpfr_clear (u);
#endif
}
/* Generic random tests with cancellations.
*
* In summary, we do 4000 tests of the following form:
* 1. We set the first MPFR_NCANCEL members of an array to random values,
* with a random exponent taken in 4 ranges, depending on the value of
* i % 4 (see code below).
* 2. For each of the next MPFR_NCANCEL iterations:
* A. we randomly permute some terms of the array (to make sure that a
* particular order doesn't have an influence on the result);
* B. we compute the sum in a random rounding mode;
* C. if this sum is zero, we end the current test (there is no longer
* anything interesting to test);
* D. we check that this sum is below some bound (chosen as infinite
* for the first iteration of (2), i.e. this test will be useful
* only for the next iterations, after cancellations);
* E. we put the opposite of this sum in the array, the goal being to
* introduce a chain of cancellations;
* F. we compute the bound for the next iteration, derived from (E).
* 3. We do another iteration like (2), but with reusing a random element
* of the array. This last test allows one to check the support of
* reused arguments. Before this support (r10467), it triggers an
* assertion failure with (almost?) all seeds, and if assertions are
* not checked, tsum fails in most cases but not all.
*/
static void
cancel (void)
{
mpfr_t x[2 * MPFR_NCANCEL], bound;
mpfr_ptr px[2 * MPFR_NCANCEL];
int i, j, k, n;
mpfr_init2 (bound, 2);
/* With 4000 tests, tsum will fail in most cases without support of
reused arguments (before r10467). */
for (i = 0; i < 4000; i++)
{
mpfr_set_inf (bound, 1);
for (n = 0; n <= numberof (x); n++)
{
mpfr_prec_t p;
mpfr_rnd_t rnd;
if (n < numberof (x))
{
px[n] = x[n];
p = MPFR_PREC_MIN + (randlimb () % 256);
mpfr_init2 (x[n], p);
k = n;
}
else
{
/* Reuse of a random member of the array. */
k = randlimb () % n;
}
if (n < MPFR_NCANCEL)
{
mpfr_exp_t e;
MPFR_ASSERTN (n < numberof (x));
e = (i & 1) ? 0 : mpfr_get_emin ();
tests_default_random (x[n], 256, e,
((i & 2) ? e + 2000 : mpfr_get_emax ()),
0);
}
else
{
/* random permutation with n random transpositions */
for (j = 0; j < n; j++)
{
int k1, k2;
k1 = randlimb () % (n-1);
k2 = randlimb () % (n-1);
mpfr_swap (x[k1], x[k2]);
}
rnd = RND_RAND ();
#if DEBUG
printf ("mpfr_sum cancellation test\n");
for (j = 0; j < n; j++)
{
printf (" x%d[%3ld] = ", j, mpfr_get_prec(x[j]));
mpfr_out_str (stdout, 16, 0, x[j], MPFR_RNDN);
printf ("\n");
}
printf (" rnd = %s, output prec = %ld\n",
mpfr_print_rnd_mode (rnd), mpfr_get_prec (x[n]));
#endif
mpfr_sum (x[k], px, n, rnd);
if (mpfr_zero_p (x[k]))
{
if (k == n)
n++;
break;
}
if (mpfr_cmpabs (x[k], bound) > 0)
{
printf ("Error in cancel on i = %d, n = %d\n", i, n);
printf ("Expected bound: ");
mpfr_dump (bound);
printf ("x[%d]: ", k);
mpfr_dump (x[k]);
exit (1);
}
if (k != n)
break;
/* For the bound, use MPFR_RNDU due to possible underflow.
It would be nice to add some specific underflow checks,
though there are already ones in check_underflow(). */
mpfr_set_ui_2exp (bound, 1,
mpfr_get_exp (x[n]) - p - (rnd == MPFR_RNDN),
MPFR_RNDU);
/* The next sum will be <= bound in absolute value
(the equality can be obtained in all rounding modes
since the sum will be rounded). */
mpfr_neg (x[n], x[n], MPFR_RNDN);
}
}
while (--n >= 0)
mpfr_clear (x[n]);
}
mpfr_clear (bound);
}
