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, (void *) 0);
mpfr_set_si_2exp (z, 1, mpfr_get_emin (), GMP_RNDN); /* z = 2^emin */
mpfr_set_si_2exp (x, 1, mpfr_get_emin (), GMP_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), GMP_RNDN);
/* z = 1.000...00b
* xy = 01111
* or 10000
* or 10001
*/
mpfr_clear_flags ();
inex = mpfr_fma (r, x, y, z, GMP_RNDN);
#define ERRTU2 "Error in test_underflow2 (b = %d, i = %d)\n "
if (__gmpfr_flags != MPFR_FLAGS_INEXACT)
{
printf (ERRTU2 "flags = %u instead of %u\n", b, i,
__gmpfr_flags, (unsigned int) MPFR_FLAGS_INEXACT);
err = 1;
}
same = i == 15 || (i == 16 && b == 0);
if (same ? (inex >= 0) : (inex <= 0))
{
printf (ERRTU2 "incorrect ternary value (%d instead of %c 0)\n",
b, i, inex, same ? '<' : '>');
err = 1;
}
mpfr_set (y, z, GMP_RNDN);
if (!same)
mpfr_nextabove (y);
if (! mpfr_equal_p (r, y))
{
printf (ERRTU2 "expected ", b, i);
mpfr_dump (y);
printf (" got ");
mpfr_dump (r);
err = 1;
}
}
mpfr_nextabove (z);
}
if (err)
exit (1);
mpfr_clears (x, y, z, r, (void *) 0);
}
static void
pow_si_long_min (void)
{
mpfr_t x, y, z;
int inex;
mpfr_inits2 (sizeof(long) * CHAR_BIT + 32, x, y, z, (void *) 0);
mpfr_set_si_2exp (x, 3, -1, GMP_RNDN); /* 1.5 */
inex = mpfr_set_si (y, LONG_MIN, GMP_RNDN);
MPFR_ASSERTN (inex == 0);
mpfr_nextbelow (y);
mpfr_pow (y, x, y, GMP_RNDD);
inex = mpfr_set_si (z, LONG_MIN, GMP_RNDN);
MPFR_ASSERTN (inex == 0);
mpfr_nextabove (z);
mpfr_pow (z, x, z, GMP_RNDU);
mpfr_pow_si (x, x, LONG_MIN, GMP_RNDN); /* 1.5^LONG_MIN */
if (mpfr_cmp (x, y) < 0 || mpfr_cmp (x, z) > 0)
{
printf ("Error in pow_si_long_min\n");
exit (1);
}
mpfr_clears (x, y, z, (void *) 0);
}
int
fmpr_get_mpfr(mpfr_t x, const fmpr_t y, mpfr_rnd_t rnd)
{
int r;
if (fmpr_is_special(y))
{
if (fmpr_is_zero(y)) mpfr_set_zero(x, 0);
else if (fmpr_is_pos_inf(y)) mpfr_set_inf(x, 1);
else if (fmpr_is_neg_inf(y)) mpfr_set_inf(x, -1);
else mpfr_set_nan(x);
r = 0;
}
else if (COEFF_IS_MPZ(*fmpr_expref(y)))
{
flint_printf("exception: exponent too large to convert to mpfr");
abort();
}
else
{
if (!COEFF_IS_MPZ(*fmpr_manref(y)))
#if defined(__MINGW64__)
r = mpfr_set_sj_2exp(x, *fmpr_manref(y), *fmpr_expref(y), rnd);
#else
r = mpfr_set_si_2exp(x, *fmpr_manref(y), *fmpr_expref(y), rnd);
#endif
else
r = mpfr_set_z_2exp(x, COEFF_TO_PTR(*fmpr_manref(y)), *fmpr_expref(y), rnd);
if (!mpfr_regular_p(x))
{
flint_printf("exception: exponent too large to convert to mpfr");
abort();
}
}
static void
test_small (void)
{
mpfr_t x, y, z1, z2;
int inex1, inex2;
unsigned int flags;
/* Test hypot(x,x) with x = 2^(emin-1). Result is x * sqrt(2). */
mpfr_inits2 (8, x, y, z1, z2, (mpfr_ptr) 0);
mpfr_set_si_2exp (x, 1, mpfr_get_emin () - 1, MPFR_RNDN);
mpfr_set_si_2exp (y, 1, mpfr_get_emin () - 1, MPFR_RNDN);
mpfr_set_ui (z1, 2, MPFR_RNDN);
inex1 = mpfr_sqrt (z1, z1, MPFR_RNDN);
inex2 = mpfr_mul (z1, z1, x, MPFR_RNDN);
MPFR_ASSERTN (inex2 == 0);
mpfr_clear_flags ();
inex2 = mpfr_hypot (z2, x, y, MPFR_RNDN);
flags = __gmpfr_flags;
if (mpfr_cmp (z1, z2) != 0)
{
printf ("Error in test_small%s\nExpected ",
ext ? ", extended exponent range" : "");
mpfr_out_str (stdout, 2, 0, z1, MPFR_RNDN);
printf ("\nGot ");
mpfr_out_str (stdout, 2, 0, z2, MPFR_RNDN);
printf ("\n");
exit (1);
}
if (! SAME_SIGN (inex1, inex2))
{
printf ("Bad ternary value in test_small%s\nExpected %d, got %d\n",
ext ? ", extended exponent range" : "", inex1, inex2);
exit (1);
}
if (flags != MPFR_FLAGS_INEXACT)
{
printf ("Bad flags in test_small%s\nExpected %u, got %u\n",
ext ? ", extended exponent range" : "",
(unsigned int) MPFR_FLAGS_INEXACT, flags);
exit (1);
}
mpfr_clears (x, y, z1, z2, (mpfr_ptr) 0);
}
static void
test_get_uj_smallneg (void)
{
mpfr_t x;
int i;
mpfr_init2 (x, 64);
for (i = 1; i <= 4; i++)
{
int r;
mpfr_set_si_2exp (x, -i, -2, MPFR_RNDN);
RND_LOOP (r)
{
intmax_t s;
uintmax_t u;
mpfr_clear_erangeflag ();
s = mpfr_get_sj (x, (mpfr_rnd_t) r);
if (mpfr_erangeflag_p ())
{
printf ("ERROR for get_sj + ERANGE + small negative op"
" for rnd = %s and x = -%d/4\n",
mpfr_print_rnd_mode ((mpfr_rnd_t) r), i);
exit (1);
}
u = mpfr_get_uj (x, (mpfr_rnd_t) r);
if (u != 0)
{
printf ("ERROR for get_uj + ERANGE + small negative op"
" for rnd = %s and x = -%d/4\n",
mpfr_print_rnd_mode ((mpfr_rnd_t) r), i);
printf ("Expected 0, got %ju\n", u);
exit (1);
}
if ((s == 0) ^ !mpfr_erangeflag_p ())
{
char *not = s == 0 ? "" : " not";
printf ("ERROR for get_uj + ERANGE + small negative op"
" for rnd = %s and x = -%d/4\n",
mpfr_print_rnd_mode ((mpfr_rnd_t) r), i);
printf ("The rounding integer (%jd) is%s representable in "
"unsigned long,\nbut the erange flag is%s set.\n",
s, not, not);
exit (1);
}
}
}
mpfr_clear (x);
}
static void
check_sj (intmax_t s, mpfr_ptr x)
{
mpfr_t y;
int i;
mpfr_init2 (y, MPFR_PREC (x));
for (i = -1; i <= 1; i++)
{
int rnd;
mpfr_set_si_2exp (y, i, -2, MPFR_RNDN);
mpfr_add (y, y, x, MPFR_RNDN);
for (rnd = 0; rnd < MPFR_RND_MAX; rnd++)
{
intmax_t r;
if (rnd == MPFR_RNDZ && i < 0 && s >= 0)
continue;
if (rnd == MPFR_RNDZ && i > 0 && s <= 0)
continue;
if (rnd == MPFR_RNDD && i < 0)
continue;
if (rnd == MPFR_RNDU && i > 0)
continue;
if (rnd == MPFR_RNDA && ((MPFR_IS_POS(y) && i > 0) ||
(MPFR_IS_NEG(y) && i < 0)))
continue;
/* rint (y) == x == s */
r = mpfr_get_sj (y, (mpfr_rnd_t) rnd);
if (r != s)
{
printf ("Error in check_sj for y = ");
mpfr_out_str (stdout, 2, 0, y, MPFR_RNDN);
printf (" in %s\n", mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
printf ("Got %jd instead of %jd.\n", r, s);
exit (1);
}
}
}
mpfr_clear (y);
}
static void
test_erfc (void)
{
mpfr_t x, y, z;
int inex;
mpfr_exp_t emin;
mpfr_inits2 (40, x, y, z, (mpfr_ptr) 0);
mpfr_set_si_2exp (x, -1, -10, MPFR_RNDN);
mpfr_set_str_binary (z, "0.1000000000100100000110111010110111100000E1");
mpfr_erfc (y, x, MPFR_RNDN);
if (mpfr_cmp (y, z) != 0)
{
printf ("mpfr_erfc failed for x = ");
mpfr_dump (x);
printf ("got ");
mpfr_dump (y);
printf ("instead of ");
mpfr_dump (z);
exit (1);
}
/* slowness detected by Kevin Rauch on 26 Oct 2007 */
mpfr_set_prec (x, 128);
mpfr_set_si (x, -256, MPFR_RNDN);
inex = mpfr_erfc (x, x, MPFR_RNDN);
MPFR_ASSERTN(inex > 0 && mpfr_cmp_ui (x, 2) == 0);
/* bug found by Pascal Molin on March 10, 2011 */
emin = mpfr_get_emin ();
if (! mpfr_set_emin (-1073808789))
{
/* Typically, a 64-bit machine. */
mpfr_set_si (x, 27282, MPFR_RNDN);
mpfr_erfc (y, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui (y, 0) != 0);
mpfr_set_emin (emin);
}
mpfr_clears (x, y, z, (mpfr_ptr) 0);
}
/* Bug found while adding tests for mpfr_cot */
static void
test_20070628 (void)
{
mpfr_exp_t old_emax;
mpfr_t x, y;
int inex, err = 0;
old_emax = mpfr_get_emax ();
if (mpfr_set_emax (256))
{
printf ("Can't change exponent range\n");
exit (1);
}
mpfr_inits2 (53, x, y, (mpfr_ptr) 0);
mpfr_set_si (x, -1, MPFR_RNDN);
mpfr_set_si_2exp (y, 1, -256, MPFR_RNDN);
mpfr_clear_flags ();
inex = mpfr_div (x, x, y, MPFR_RNDD);
if (MPFR_SIGN (x) >= 0 || ! mpfr_inf_p (x))
{
printf ("Error in test_20070628: expected -Inf, got\n");
mpfr_dump (x);
err++;
}
if (inex >= 0)
{
printf ("Error in test_20070628: expected inex < 0, got %d\n", inex);
err++;
}
if (! mpfr_overflow_p ())
{
printf ("Error in test_20070628: overflow flag is not set\n");
err++;
}
mpfr_clears (x, y, (mpfr_ptr) 0);
mpfr_set_emax (old_emax);
}
static int
decimal (void)
{
mpfr_prec_t p = 128;
mpfr_t x;
mpfr_t z;
mpfr_init (z);
mpfr_init2 (x, p);
/* specifier 'P' for precision */
check_vsprintf ("128", "%Pu", p);
check_vsprintf ("00128", "%.5Pu", p);
/* special numbers */
mpfr_set_inf (x, 1);
check_sprintf (pinf_str, "%Re", x);
check_sprintf (pinf_str, "%RUe", x);
check_sprintf (pinf_uc_str, "%RE", x);
check_sprintf (pinf_uc_str, "%RDE", x);
check_sprintf (pinf_str, "%Rf", x);
check_sprintf (pinf_str, "%RYf", x);
check_sprintf (pinf_uc_str, "%RF", x);
check_sprintf (pinf_uc_str, "%RZF", x);
check_sprintf (pinf_str, "%Rg", x);
check_sprintf (pinf_str, "%RNg", x);
check_sprintf (pinf_uc_str, "%RG", x);
check_sprintf (pinf_uc_str, "%RUG", x);
check_sprintf (" inf", "%010Re", x);
check_sprintf (" inf", "%010RDe", x);
mpfr_set_inf (x, -1);
check_sprintf (minf_str, "%Re", x);
check_sprintf (minf_str, "%RYe", x);
check_sprintf (minf_uc_str, "%RE", x);
check_sprintf (minf_uc_str, "%RZE", x);
check_sprintf (minf_str, "%Rf", x);
check_sprintf (minf_str, "%RNf", x);
check_sprintf (minf_uc_str, "%RF", x);
check_sprintf (minf_uc_str, "%RUF", x);
check_sprintf (minf_str, "%Rg", x);
check_sprintf (minf_str, "%RDg", x);
check_sprintf (minf_uc_str, "%RG", x);
check_sprintf (minf_uc_str, "%RYG", x);
check_sprintf (" -inf", "%010Re", x);
check_sprintf (" -inf", "%010RZe", x);
mpfr_set_nan (x);
check_sprintf (nan_str, "%Re", x);
check_sprintf (nan_str, "%RNe", x);
check_sprintf (nan_uc_str, "%RE", x);
check_sprintf (nan_uc_str, "%RUE", x);
check_sprintf (nan_str, "%Rf", x);
check_sprintf (nan_str, "%RDf", x);
check_sprintf (nan_uc_str, "%RF", x);
check_sprintf (nan_uc_str, "%RYF", x);
check_sprintf (nan_str, "%Rg", x);
check_sprintf (nan_str, "%RZg", x);
check_sprintf (nan_uc_str, "%RG", x);
check_sprintf (nan_uc_str, "%RNG", x);
check_sprintf (" nan", "%010Re", x);
/* positive numbers */
mpfr_set_str (x, "18993474.61279296875", 10, MPFR_RNDN);
mpfr_set_ui (z, 0, MPFR_RNDD);
/* simplest case right justified */
check_sprintf (" 1.899347461279296875e+07", "%30Re", x);
check_sprintf (" 2e+07", "%30.0Re", x);
check_sprintf (" 18993474.612793", "%30Rf", x);
check_sprintf (" 18993474.6127930", "%30.7Rf", x);
check_sprintf (" 1.89935e+07", "%30Rg", x);
check_sprintf (" 2e+07", "%30.0Rg", x);
check_sprintf (" 18993474.61279296875", "%30.19Rg", x);
check_sprintf (" 0e+00", "%30.0Re", z);
check_sprintf (" 0", "%30.0Rf", z);
check_sprintf (" 0.0000", "%30.4Rf", z);
check_sprintf (" 0", "%30.0Rg", z);
check_sprintf (" 0", "%30.4Rg", z);
/* sign or space, pad with leading zeros */
check_sprintf (" 000001.899347461279296875E+07", "% 030RE", x);
check_sprintf (" 0000000000000000001.89935E+07", "% 030RG", x);
check_sprintf (" 0000000000000000000000002E+07", "% 030.0RE", x);
check_sprintf (" 0000000000000000000000000E+00", "% 030.0RE", z);
check_sprintf (" 00000000000000000000000000000", "% 030.0RF", z);
/* sign + or -, left justified */
check_sprintf ("+1.899347461279296875e+07 ", "%+-30Re", x);
check_sprintf ("+2e+07 ", "%+-30.0Re", x);
check_sprintf ("+0e+00 ", "%+-30.0Re", z);
check_sprintf ("+0 ", "%+-30.0Rf", z);
/* decimal point, left justified, precision and rounding parameter */
check_vsprintf ("1.9E+07 ", "%#-10.*R*E", 1, MPFR_RNDN, x);
check_vsprintf ("2.E+07 ", "%#*.*R*E", -10, 0, MPFR_RNDN, x);
check_vsprintf ("2.E+07 ", "%#-10.*R*G", 0, MPFR_RNDN, x);
check_vsprintf ("0.E+00 ", "%#-10.*R*E", 0, MPFR_RNDN, z);
check_vsprintf ("0. ", "%#-10.*R*F", 0, MPFR_RNDN, z);
check_vsprintf ("0. ", "%#-10.*R*G", 0, MPFR_RNDN, z);
/* sign or space */
check_sprintf (" 1.899e+07", "% .3RNe", x);
check_sprintf (" 2e+07", "% .0RNe", x);
/* sign + or -, decimal point, pad with leading zeros */
check_sprintf ("+0001.8E+07", "%0+#11.1RZE", x);
check_sprintf ("+00001.E+07", "%0+#11.0RZE", x);
check_sprintf ("+0000.0E+00", "%0+#11.1RZE", z);
check_sprintf ("+00000000.0", "%0+#11.1RZF", z);
/* pad with leading zero */
check_sprintf ("0000001.899347461279296875e+07", "%030RDe", x);
check_sprintf ("00000000000000000000000001e+07", "%030.0RDe", x);
/* sign or space, decimal point, left justified */
check_sprintf (" 1.8E+07 ", "%- #11.1RDE", x);
check_sprintf (" 1.E+07 ", "%- #11.0RDE", x);
/* negative numbers */
mpfr_mul_si (x, x, -1, MPFR_RNDD);
mpfr_mul_si (z, z, -1, MPFR_RNDD);
/* sign + or - */
check_sprintf (" -1.8e+07", "%+10.1RUe", x);
check_sprintf (" -1e+07", "%+10.0RUe", x);
check_sprintf (" -0e+00", "%+10.0RUe", z);
check_sprintf (" -0", "%+10.0RUf", z);
/* neighborhood of 1 */
mpfr_set_str (x, "0.99993896484375", 10, MPFR_RNDN);
check_sprintf ("9.9993896484375E-01 ", "%-20RE", x);
check_sprintf ("9.9993896484375E-01 ", "%-20.RE", x);
check_sprintf ("1E+00 ", "%-20.0RE", x);
check_sprintf ("1.0E+00 ", "%-20.1RE", x);
check_sprintf ("1.00E+00 ", "%-20.2RE", x);
check_sprintf ("9.999E-01 ", "%-20.3RE", x);
check_sprintf ("9.9994E-01 ", "%-20.4RE", x);
check_sprintf ("0.999939 ", "%-20RF", x);
check_sprintf ("0.999939 ", "%-20.RF", x);
check_sprintf ("1 ", "%-20.0RF", x);
check_sprintf ("1.0 ", "%-20.1RF", x);
check_sprintf ("1.00 ", "%-20.2RF", x);
check_sprintf ("1.000 ", "%-20.3RF", x);
check_sprintf ("0.9999 ", "%-20.4RF", x);
check_sprintf ("0.999939 ", "%-#20RF", x);
check_sprintf ("0.999939 ", "%-#20.RF", x);
check_sprintf ("1. ", "%-#20.0RF", x);
check_sprintf ("1.0 ", "%-#20.1RF", x);
check_sprintf ("1.00 ", "%-#20.2RF", x);
check_sprintf ("1.000 ", "%-#20.3RF", x);
check_sprintf ("0.9999 ", "%-#20.4RF", x);
check_sprintf ("1 ", "%-20.0RG", x);
check_sprintf ("1 ", "%-20.1RG", x);
check_sprintf ("1 ", "%-20.2RG", x);
check_sprintf ("1 ", "%-20.3RG", x);
check_sprintf ("0.9999 ", "%-20.4RG", x);
check_sprintf ("0.999939 ", "%-#20RG", x);
check_sprintf ("0.999939 ", "%-#20.RG", x);
check_sprintf ("1. ", "%-#20.0RG", x);
check_sprintf ("1. ", "%-#20.1RG", x);
check_sprintf ("1.0 ", "%-#20.2RG", x);
check_sprintf ("1.00 ", "%-#20.3RG", x);
check_sprintf ("0.9999 ", "%-#20.4RG", x);
/* multiple of 10 */
mpfr_set_str (x, "1e17", 10, MPFR_RNDN);
check_sprintf ("1e+17", "%Re", x);
check_sprintf ("1.000e+17", "%.3Re", x);
check_sprintf ("100000000000000000", "%.0Rf", x);
check_sprintf ("100000000000000000.0", "%.1Rf", x);
check_sprintf ("100000000000000000.000000", "%'Rf", x);
check_sprintf ("100000000000000000.0", "%'.1Rf", x);
mpfr_ui_div (x, 1, x, MPFR_RNDN); /* x=1e-17 */
check_sprintf ("1e-17", "%Re", x);
check_sprintf ("0.000000", "%Rf", x);
check_sprintf ("1e-17", "%Rg", x);
check_sprintf ("0.0", "%.1RDf", x);
check_sprintf ("0.0", "%.1RZf", x);
check_sprintf ("0.1", "%.1RUf", x);
check_sprintf ("0.1", "%.1RYf", x);
check_sprintf ("0", "%.0RDf", x);
check_sprintf ("0", "%.0RZf", x);
check_sprintf ("1", "%.0RUf", x);
check_sprintf ("1", "%.0RYf", x);
/* multiple of 10 with 'g' style */
mpfr_set_str (x, "10", 10, MPFR_RNDN);
check_sprintf ("10", "%Rg", x);
check_sprintf ("1e+01", "%.0Rg", x);
check_sprintf ("1e+01", "%.1Rg", x);
check_sprintf ("10", "%.2Rg", x);
mpfr_ui_div (x, 1, x, MPFR_RNDN);
check_sprintf ("0.1", "%Rg", x);
check_sprintf ("0.1", "%.0Rg", x);
check_sprintf ("0.1", "%.1Rg", x);
mpfr_set_str (x, "1000", 10, MPFR_RNDN);
check_sprintf ("1000", "%Rg", x);
check_sprintf ("1e+03", "%.0Rg", x);
check_sprintf ("1e+03", "%.3Rg", x);
check_sprintf ("1000", "%.4Rg", x);
mpfr_ui_div (x, 1, x, MPFR_RNDN);
check_sprintf ("0.001", "%Rg", x);
check_sprintf ("0.001", "%.0Rg", x);
check_sprintf ("0.001", "%.1Rg", x);
mpfr_set_str (x, "100000", 10, MPFR_RNDN);
check_sprintf ("100000", "%Rg", x);
check_sprintf ("1e+05", "%.0Rg", x);
check_sprintf ("1e+05", "%.5Rg", x);
check_sprintf ("100000", "%.6Rg", x);
mpfr_ui_div (x, 1, x, MPFR_RNDN);
check_sprintf ("1e-05", "%Rg", x);
check_sprintf ("1e-05", "%.0Rg", x);
check_sprintf ("1e-05", "%.1Rg", x);
/* check rounding mode */
mpfr_set_str (x, "0.0076", 10, MPFR_RNDN);
check_sprintf ("0.007", "%.3RDF", x);
check_sprintf ("0.007", "%.3RZF", x);
check_sprintf ("0.008", "%.3RF", x);
check_sprintf ("0.008", "%.3RUF", x);
check_sprintf ("0.008", "%.3RYF", x);
check_vsprintf ("0.008", "%.3R*F", MPFR_RNDA, x);
/* check limit between %f-style and %g-style */
mpfr_set_str (x, "0.0000999", 10, MPFR_RNDN);
check_sprintf ("0.0001", "%.0Rg", x);
check_sprintf ("9e-05", "%.0RDg", x);
check_sprintf ("0.0001", "%.1Rg", x);
check_sprintf ("0.0001", "%.2Rg", x);
check_sprintf ("9.99e-05", "%.3Rg", x);
/* trailing zeros */
mpfr_set_si_2exp (x, -1, -15, MPFR_RNDN); /* x=-2^-15 */
check_sprintf ("-3.0517578125e-05", "%.30Rg", x);
check_sprintf ("-3.051757812500000000000000000000e-05", "%.30Re", x);
check_sprintf ("-3.05175781250000000000000000000e-05", "%#.30Rg", x);
check_sprintf ("-0.000030517578125000000000000000", "%.30Rf", x);
/* bug 20081023 */
check_sprintf ("-3.0517578125e-05", "%.30Rg", x);
mpfr_set_str (x, "1.9999", 10, MPFR_RNDN);
check_sprintf ("1.999900 ", "%-#10.7RG", x);
check_sprintf ("1.9999 ", "%-10.7RG", x);
mpfr_set_ui (x, 1, MPFR_RNDN);
check_sprintf ("1.00000000000000000000000000000", "%#.30Rg", x);
check_sprintf ("1", "%.30Rg", x);
mpfr_set_ui (x, 0, MPFR_RNDN);
check_sprintf ("0.000000000000000000000000000000", "%#.30Rg", x);
check_sprintf ("0", "%.30Rg", x);
/* following tests with precision 53 bits */
mpfr_set_prec (x, 53);
/* Exponent zero has a plus sign */
mpfr_set_str (x, "-9.95645044213728791504536275169812142849e-01", 10,
MPFR_RNDN);
check_sprintf ("-1.0e+00", "%- #0.1Re", x);
/* Decimal point and no figure after it with '#' flag and 'G' style */
mpfr_set_str (x, "-9.90597761233942053494e-01", 10, MPFR_RNDN);
check_sprintf ("-1.", "%- #0.1RG", x);
/* precision zero */
mpfr_set_d (x, 9.5, MPFR_RNDN);
check_sprintf ("9", "%.0RDf", x);
check_sprintf ("10", "%.0RUf", x);
mpfr_set_d (x, 19.5, MPFR_RNDN);
check_sprintf ("19", "%.0RDf", x);
check_sprintf ("20", "%.0RUf", x);
mpfr_set_d (x, 99.5, MPFR_RNDN);
check_sprintf ("99", "%.0RDf", x);
check_sprintf ("100", "%.0RUf", x);
mpfr_set_d (x, -9.5, MPFR_RNDN);
check_sprintf ("-10", "%.0RDf", x);
check_sprintf ("-10", "%.0RYf", x);
check_sprintf ("-10", "%.0Rf", x);
check_sprintf ("-1e+01", "%.0Re", x);
check_sprintf ("-1e+01", "%.0Rg", x);
mpfr_set_ui_2exp (x, 1, -1, MPFR_RNDN);
check_sprintf ("0", "%.0Rf", x);
check_sprintf ("5e-01", "%.0Re", x);
check_sprintf ("0.5", "%.0Rg", x);
mpfr_set_ui_2exp (x, 3, -1, MPFR_RNDN);
check_sprintf ("2", "%.0Rf", x);
mpfr_set_ui_2exp (x, 5, -1, MPFR_RNDN);
check_sprintf ("2", "%.0Rf", x);
mpfr_set_ui (x, 0x1f, MPFR_RNDN);
check_sprintf ("0x1p+5", "%.0Ra", x);
mpfr_set_ui (x, 3, MPFR_RNDN);
check_sprintf ("1p+2", "%.0Rb", x);
/* round to next ten power with %f but not with %g */
mpfr_set_str (x, "-6.64464380544039223686e-02", 10, MPFR_RNDN);
check_sprintf ("-0.1", "%.1Rf", x);
check_sprintf ("-0.0", "%.1RZf", x);
check_sprintf ("-0.07", "%.1Rg", x);
check_sprintf ("-0.06", "%.1RZg", x);
/* round to next ten power and do not remove trailing zeros */
mpfr_set_str (x, "9.98429393291486722006e-02", 10, MPFR_RNDN);
check_sprintf ("0.1", "%#.1Rg", x);
check_sprintf ("0.10", "%#.2Rg", x);
check_sprintf ("0.099", "%#.2RZg", x);
/* Halfway cases */
mpfr_set_str (x, "1.5", 10, MPFR_RNDN);
check_sprintf ("2e+00", "%.0Re", x);
mpfr_set_str (x, "2.5", 10, MPFR_RNDN);
check_sprintf ("2e+00", "%.0Re", x);
mpfr_set_str (x, "9.5", 10, MPFR_RNDN);
check_sprintf ("1e+01", "%.0Re", x);
mpfr_set_str (x, "1.25", 10, MPFR_RNDN);
check_sprintf ("1.2e+00", "%.1Re", x);
mpfr_set_str (x, "1.75", 10, MPFR_RNDN);
check_sprintf ("1.8e+00", "%.1Re", x);
mpfr_set_str (x, "-0.5", 10, MPFR_RNDN);
check_sprintf ("-0", "%.0Rf", x);
mpfr_set_str (x, "1.25", 10, MPFR_RNDN);
check_sprintf ("1.2", "%.1Rf", x);
mpfr_set_str (x, "1.75", 10, MPFR_RNDN);
check_sprintf ("1.8", "%.1Rf", x);
mpfr_set_str (x, "1.5", 10, MPFR_RNDN);
check_sprintf ("2", "%.1Rg", x);
mpfr_set_str (x, "2.5", 10, MPFR_RNDN);
check_sprintf ("2", "%.1Rg", x);
mpfr_set_str (x, "9.25", 10, MPFR_RNDN);
check_sprintf ("9.2", "%.2Rg", x);
mpfr_set_str (x, "9.75", 10, MPFR_RNDN);
check_sprintf ("9.8", "%.2Rg", x);
/* assertion failure in r6320 */
mpfr_set_str (x, "-9.996", 10, MPFR_RNDN);
check_sprintf ("-10.0", "%.1Rf", x);
/* regression in MPFR 3.1.0 (bug introduced in r7761, fixed in r7931) */
check_sprintf ("-10", "%.2Rg", x);
mpfr_clears (x, z, (mpfr_ptr) 0);
return 0;
}
static void
special (void)
{
mpfr_t x, y;
int inex;
mpfr_init (x);
mpfr_init (y);
mpfr_set_nan (x);
mpfr_lngamma (y, x, MPFR_RNDN);
if (!mpfr_nan_p (y))
{
printf ("Error for lngamma(NaN)\n");
exit (1);
}
mpfr_set_inf (x, -1);
mpfr_lngamma (y, x, MPFR_RNDN);
if (!mpfr_nan_p (y))
{
printf ("Error for lngamma(-Inf)\n");
exit (1);
}
mpfr_set_inf (x, 1);
mpfr_lngamma (y, x, MPFR_RNDN);
if (!mpfr_inf_p (y) || mpfr_sgn (y) < 0)
{
printf ("Error for lngamma(+Inf)\n");
exit (1);
}
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_lngamma (y, x, MPFR_RNDN);
if (!mpfr_inf_p (y) || mpfr_sgn (y) < 0)
{
printf ("Error for lngamma(+0)\n");
exit (1);
}
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_neg (x, x, MPFR_RNDN);
mpfr_lngamma (y, x, MPFR_RNDN);
if (!mpfr_nan_p (y))
{
printf ("Error for lngamma(-0)\n");
exit (1);
}
mpfr_set_ui (x, 1, MPFR_RNDN);
mpfr_lngamma (y, x, MPFR_RNDN);
if (MPFR_IS_NAN (y) || mpfr_cmp_ui (y, 0) || MPFR_IS_NEG (y))
{
printf ("Error for lngamma(1)\n");
exit (1);
}
mpfr_set_si (x, -1, MPFR_RNDN);
mpfr_lngamma (y, x, MPFR_RNDN);
if (!mpfr_nan_p (y))
{
printf ("Error for lngamma(-1)\n");
exit (1);
}
mpfr_set_ui (x, 2, MPFR_RNDN);
mpfr_lngamma (y, x, MPFR_RNDN);
if (MPFR_IS_NAN (y) || mpfr_cmp_ui (y, 0) || MPFR_IS_NEG (y))
{
printf ("Error for lngamma(2)\n");
exit (1);
}
mpfr_set_prec (x, 53);
mpfr_set_prec (y, 53);
#define CHECK_X1 "1.0762904832837976166"
#define CHECK_Y1 "-0.039418362817587634939"
mpfr_set_str (x, CHECK_X1, 10, MPFR_RNDN);
mpfr_lngamma (y, x, MPFR_RNDN);
mpfr_set_str (x, CHECK_Y1, 10, MPFR_RNDN);
if (MPFR_IS_NAN (y) || mpfr_cmp (y, x))
{
printf ("mpfr_lngamma("CHECK_X1") is wrong:\n"
"expected ");
mpfr_print_binary (x); putchar ('\n');
printf ("got ");
mpfr_print_binary (y); putchar ('\n');
exit (1);
}
#define CHECK_X2 "9.23709516716202383435e-01"
#define CHECK_Y2 "0.049010669407893718563"
mpfr_set_str (x, CHECK_X2, 10, MPFR_RNDN);
mpfr_lngamma (y, x, MPFR_RNDN);
mpfr_set_str (x, CHECK_Y2, 10, MPFR_RNDN);
if (MPFR_IS_NAN (y) || mpfr_cmp (y, x))
{
printf ("mpfr_lngamma("CHECK_X2") is wrong:\n"
"expected ");
mpfr_print_binary (x); putchar ('\n');
printf ("got ");
mpfr_print_binary (y); putchar ('\n');
exit (1);
}
mpfr_set_prec (x, 8);
mpfr_set_prec (y, 175);
mpfr_set_ui (x, 33, MPFR_RNDN);
mpfr_lngamma (y, x, MPFR_RNDU);
mpfr_set_prec (x, 175);
mpfr_set_str_binary (x, "0.1010001100011101101011001101110010100001000001000001110011000001101100001111001001000101011011100100010101011110100111110101010100010011010010000101010111001100011000101111E7");
if (MPFR_IS_NAN (y) || mpfr_cmp (x, y))
{
printf ("Error in mpfr_lngamma (1)\n");
exit (1);
}
mpfr_set_prec (x, 21);
mpfr_set_prec (y, 8);
mpfr_set_ui (y, 120, MPFR_RNDN);
mpfr_lngamma (x, y, MPFR_RNDZ);
mpfr_set_prec (y, 21);
mpfr_set_str_binary (y, "0.111000101000001100101E9");
if (MPFR_IS_NAN (x) || mpfr_cmp (x, y))
{
printf ("Error in mpfr_lngamma (120)\n");
printf ("Expected "); mpfr_print_binary (y); puts ("");
printf ("Got "); mpfr_print_binary (x); puts ("");
exit (1);
}
mpfr_set_prec (x, 3);
mpfr_set_prec (y, 206);
mpfr_set_str_binary (x, "0.110e10");
inex = mpfr_lngamma (y, x, MPFR_RNDN);
mpfr_set_prec (x, 206);
mpfr_set_str_binary (x, "0.10000111011000000011100010101001100110001110000111100011000100100110110010001011011110101001111011110110000001010100111011010000000011100110110101100111000111010011110010000100010111101010001101000110101001E13");
if (MPFR_IS_NAN (y) || mpfr_cmp (x, y))
{
printf ("Error in mpfr_lngamma (768)\n");
exit (1);
}
if (inex >= 0)
{
printf ("Wrong flag for mpfr_lngamma (768)\n");
exit (1);
}
mpfr_set_prec (x, 4);
mpfr_set_prec (y, 4);
mpfr_set_str_binary (x, "0.1100E-66");
mpfr_lngamma (y, x, MPFR_RNDN);
mpfr_set_str_binary (x, "0.1100E6");
if (MPFR_IS_NAN (y) || mpfr_cmp (x, y))
{
printf ("Error for lngamma(0.1100E-66)\n");
exit (1);
}
mpfr_set_prec (x, 256);
mpfr_set_prec (y, 32);
mpfr_set_si_2exp (x, -1, 200, MPFR_RNDN);
mpfr_add_ui (x, x, 1, MPFR_RNDN);
mpfr_div_2ui (x, x, 1, MPFR_RNDN);
mpfr_lngamma (y, x, MPFR_RNDN);
mpfr_set_prec (x, 32);
mpfr_set_str_binary (x, "-0.10001000111011111011000010100010E207");
if (MPFR_IS_NAN (y) || mpfr_cmp (x, y))
{
printf ("Error for lngamma(-2^199+0.5)\n");
printf ("Got ");
mpfr_dump (y);
printf ("instead of ");
mpfr_dump (x);
exit (1);
}
mpfr_set_prec (x, 256);
mpfr_set_prec (y, 32);
mpfr_set_si_2exp (x, -1, 200, MPFR_RNDN);
mpfr_sub_ui (x, x, 1, MPFR_RNDN);
mpfr_div_2ui (x, x, 1, MPFR_RNDN);
mpfr_lngamma (y, x, MPFR_RNDN);
if (!mpfr_nan_p (y))
{
printf ("Error for lngamma(-2^199-0.5)\n");
exit (1);
}
mpfr_clear (x);
mpfr_clear (y);
}
int
main (void)
{
mpfr_t x, y;
int i, r;
tests_start_mpfr ();
mpfr_init2 (x, 256);
mpfr_init2 (y, 8);
RND_LOOP (r)
{
/* Check NAN */
mpfr_set_nan (x);
if (mpfr_fits_ulong_p (x, (mpfr_rnd_t) r))
ERROR1 (1);
if (mpfr_fits_slong_p (x, (mpfr_rnd_t) r))
ERROR1 (2);
if (mpfr_fits_uint_p (x, (mpfr_rnd_t) r))
ERROR1 (3);
if (mpfr_fits_sint_p (x, (mpfr_rnd_t) r))
ERROR1 (4);
if (mpfr_fits_ushort_p (x, (mpfr_rnd_t) r))
ERROR1 (5);
if (mpfr_fits_sshort_p (x, (mpfr_rnd_t) r))
ERROR1 (6);
/* Check INF */
mpfr_set_inf (x, 1);
if (mpfr_fits_ulong_p (x, (mpfr_rnd_t) r))
ERROR1 (7);
if (mpfr_fits_slong_p (x, (mpfr_rnd_t) r))
ERROR1 (8);
if (mpfr_fits_uint_p (x, (mpfr_rnd_t) r))
ERROR1 (9);
if (mpfr_fits_sint_p (x, (mpfr_rnd_t) r))
ERROR1 (10);
if (mpfr_fits_ushort_p (x, (mpfr_rnd_t) r))
ERROR1 (11);
if (mpfr_fits_sshort_p (x, (mpfr_rnd_t) r))
ERROR1 (12);
/* Check Zero */
MPFR_SET_ZERO (x);
if (!mpfr_fits_ulong_p (x, (mpfr_rnd_t) r))
ERROR1 (13);
if (!mpfr_fits_slong_p (x, (mpfr_rnd_t) r))
ERROR1 (14);
if (!mpfr_fits_uint_p (x, (mpfr_rnd_t) r))
ERROR1 (15);
if (!mpfr_fits_sint_p (x, (mpfr_rnd_t) r))
ERROR1 (16);
if (!mpfr_fits_ushort_p (x, (mpfr_rnd_t) r))
ERROR1 (17);
if (!mpfr_fits_sshort_p (x, (mpfr_rnd_t) r))
ERROR1 (18);
/* Check small positive op */
mpfr_set_str1 (x, "1@-1");
if (!mpfr_fits_ulong_p (x, (mpfr_rnd_t) r))
ERROR1 (19);
if (!mpfr_fits_slong_p (x, (mpfr_rnd_t) r))
ERROR1 (20);
if (!mpfr_fits_uint_p (x, (mpfr_rnd_t) r))
ERROR1 (21);
if (!mpfr_fits_sint_p (x, (mpfr_rnd_t) r))
ERROR1 (22);
if (!mpfr_fits_ushort_p (x, (mpfr_rnd_t) r))
ERROR1 (23);
if (!mpfr_fits_sshort_p (x, (mpfr_rnd_t) r))
ERROR1 (24);
/* Check 17 */
mpfr_set_ui (x, 17, MPFR_RNDN);
if (!mpfr_fits_ulong_p (x, (mpfr_rnd_t) r))
ERROR1 (25);
if (!mpfr_fits_slong_p (x, (mpfr_rnd_t) r))
ERROR1 (26);
if (!mpfr_fits_uint_p (x, (mpfr_rnd_t) r))
ERROR1 (27);
if (!mpfr_fits_sint_p (x, (mpfr_rnd_t) r))
ERROR1 (28);
if (!mpfr_fits_ushort_p (x, (mpfr_rnd_t) r))
ERROR1 (29);
if (!mpfr_fits_sshort_p (x, (mpfr_rnd_t) r))
ERROR1 (30);
/* Check all other values */
mpfr_set_ui (x, ULONG_MAX, MPFR_RNDN);
mpfr_mul_2exp (x, x, 1, MPFR_RNDN);
if (mpfr_fits_ulong_p (x, (mpfr_rnd_t) r))
ERROR1 (31);
if (mpfr_fits_slong_p (x, (mpfr_rnd_t) r))
ERROR1 (32);
mpfr_mul_2exp (x, x, 40, MPFR_RNDN);
if (mpfr_fits_ulong_p (x, (mpfr_rnd_t) r))
ERROR1 (33);
if (mpfr_fits_uint_p (x, (mpfr_rnd_t) r))
ERROR1 (34);
if (mpfr_fits_sint_p (x, (mpfr_rnd_t) r))
ERROR1 (35);
if (mpfr_fits_ushort_p (x, (mpfr_rnd_t) r))
ERROR1 (36);
if (mpfr_fits_sshort_p (x, (mpfr_rnd_t) r))
ERROR1 (37);
mpfr_set_ui (x, ULONG_MAX, MPFR_RNDN);
if (!mpfr_fits_ulong_p (x, (mpfr_rnd_t) r))
ERROR1 (38);
mpfr_set_ui (x, LONG_MAX, MPFR_RNDN);
if (!mpfr_fits_slong_p (x, (mpfr_rnd_t) r))
ERROR1 (39);
mpfr_set_ui (x, UINT_MAX, MPFR_RNDN);
if (!mpfr_fits_uint_p (x, (mpfr_rnd_t) r))
ERROR1 (40);
mpfr_set_ui (x, INT_MAX, MPFR_RNDN);
if (!mpfr_fits_sint_p (x, (mpfr_rnd_t) r))
ERROR1 (41);
mpfr_set_ui (x, USHRT_MAX, MPFR_RNDN);
if (!mpfr_fits_ushort_p (x, (mpfr_rnd_t) r))
ERROR1 (42);
mpfr_set_ui (x, SHRT_MAX, MPFR_RNDN);
if (!mpfr_fits_sshort_p (x, (mpfr_rnd_t) r))
ERROR1 (43);
mpfr_set_si (x, 1, MPFR_RNDN);
if (!mpfr_fits_sint_p (x, (mpfr_rnd_t) r))
ERROR1 (44);
if (!mpfr_fits_sshort_p (x, (mpfr_rnd_t) r))
ERROR1 (45);
/* Check negative op */
for (i = 1; i <= 4; i++)
{
int inv;
mpfr_set_si_2exp (x, -i, -2, MPFR_RNDN);
mpfr_rint (y, x, (mpfr_rnd_t) r);
inv = MPFR_NOTZERO (y);
if (!mpfr_fits_ulong_p (x, (mpfr_rnd_t) r) ^ inv)
ERROR1 (46);
if (!mpfr_fits_slong_p (x, (mpfr_rnd_t) r))
ERROR1 (47);
if (!mpfr_fits_uint_p (x, (mpfr_rnd_t) r) ^ inv)
ERROR1 (48);
if (!mpfr_fits_sint_p (x, (mpfr_rnd_t) r))
ERROR1 (49);
if (!mpfr_fits_ushort_p (x, (mpfr_rnd_t) r) ^ inv)
ERROR1 (50);
if (!mpfr_fits_sshort_p (x, (mpfr_rnd_t) r))
ERROR1 (51);
}
}
mpfr_clear (x);
mpfr_clear (y);
check_intmax ();
tests_end_mpfr ();
return 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, (void *) 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, GMP_RNDN); /* |y| = 1/2 */
for (signz = -3; signz <= 3; signz += 2)
{
RND_LOOP (rnd)
{
mpfr_set_si (z, signz, GMP_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, rnd);
#define ERRTU1 "Error in test_underflow1 (signy = %d, signz = %d, %s)\n "
if (mpfr_nanflag_p ())
{
printf (ERRTU1 "NaN flag is set\n", signy, signz,
mpfr_print_rnd_mode (rnd));
err = 1;
}
if (signy < 0 && (rnd == GMP_RNDD ||
(rnd == GMP_RNDZ && signz > 0)))
mpfr_nextbelow (z);
if (signy > 0 && (rnd == GMP_RNDU ||
(rnd == GMP_RNDZ && signz < 0)))
mpfr_nextabove (z);
if ((mpfr_overflow_p () != 0) ^ (mpfr_inf_p (z) != 0))
{
printf (ERRTU1 "wrong overflow flag\n", signy, signz,
mpfr_print_rnd_mode (rnd));
err = 1;
}
if (mpfr_underflow_p ())
{
printf (ERRTU1 "underflow flag is set\n", signy, signz,
mpfr_print_rnd_mode (rnd));
err = 1;
}
if (! mpfr_equal_p (r, z))
{
printf (ERRTU1 "got ", signy, signz,
mpfr_print_rnd_mode (rnd));
mpfr_print_binary (r);
printf (" instead of ");
mpfr_print_binary (z);
printf ("\n");
err = 1;
}
if (inex >= 0 && (rnd == GMP_RNDD ||
(rnd == GMP_RNDZ && signz > 0) ||
(rnd == GMP_RNDN && signy > 0)))
{
printf (ERRTU1 "ternary value = %d instead of < 0\n",
signy, signz, mpfr_print_rnd_mode (rnd), inex);
err = 1;
}
if (inex <= 0 && (rnd == GMP_RNDU ||
(rnd == GMP_RNDZ && signz < 0) ||
(rnd == GMP_RNDN && signy < 0)))
{
printf (ERRTU1 "ternary value = %d instead of > 0\n",
signy, signz, mpfr_print_rnd_mode (rnd), inex);
err = 1;
}
}
}
}
if (err)
exit (1);
mpfr_clears (x, y, z, r, (void *) 0);
}
static void
special (void)
{
mpfr_t x, y;
int inex;
int sign;
mpfr_init (x);
mpfr_init (y);
mpfr_set_nan (x);
mpfr_lgamma (y, &sign, x, GMP_RNDN);
if (!mpfr_nan_p (y))
{
printf ("Error for lgamma(NaN)\n");
exit (1);
}
mpfr_set_inf (x, -1);
mpfr_lgamma (y, &sign, x, GMP_RNDN);
if (!mpfr_inf_p (y) || mpfr_sgn (y) < 0)
{
printf ("Error for lgamma(-Inf)\n");
exit (1);
}
mpfr_set_inf (x, 1);
sign = -17;
mpfr_lgamma (y, &sign, x, GMP_RNDN);
if (!mpfr_inf_p (y) || mpfr_sgn (y) < 0 || sign != 1)
{
printf ("Error for lgamma(+Inf)\n");
exit (1);
}
mpfr_set_ui (x, 0, GMP_RNDN);
sign = -17;
mpfr_lgamma (y, &sign, x, GMP_RNDN);
if (!mpfr_inf_p (y) || mpfr_sgn (y) < 0 || sign != 1)
{
printf ("Error for lgamma(+0)\n");
exit (1);
}
mpfr_set_ui (x, 0, GMP_RNDN);
mpfr_neg (x, x, GMP_RNDN);
sign = -17;
mpfr_lgamma (y, &sign, x, GMP_RNDN);
if (!mpfr_inf_p (y) || mpfr_sgn (y) < 0 || sign != -1)
{
printf ("Error for lgamma(-0)\n");
exit (1);
}
mpfr_set_ui (x, 1, GMP_RNDN);
sign = -17;
mpfr_lgamma (y, &sign, x, GMP_RNDN);
if (MPFR_IS_NAN (y) || mpfr_cmp_ui (y, 0) || MPFR_IS_NEG (y) || sign != 1)
{
printf ("Error for lgamma(1)\n");
exit (1);
}
mpfr_set_si (x, -1, GMP_RNDN);
mpfr_lgamma (y, &sign, x, GMP_RNDN);
if (!mpfr_inf_p (y) || mpfr_sgn (y) < 0)
{
printf ("Error for lgamma(-1)\n");
exit (1);
}
mpfr_set_ui (x, 2, GMP_RNDN);
sign = -17;
mpfr_lgamma (y, &sign, x, GMP_RNDN);
if (MPFR_IS_NAN (y) || mpfr_cmp_ui (y, 0) || MPFR_IS_NEG (y) || sign != 1)
{
printf ("Error for lgamma(2)\n");
exit (1);
}
mpfr_set_prec (x, 53);
mpfr_set_prec (y, 53);
#define CHECK_X1 "1.0762904832837976166"
#define CHECK_Y1 "-0.039418362817587634939"
mpfr_set_str (x, CHECK_X1, 10, GMP_RNDN);
sign = -17;
mpfr_lgamma (y, &sign, x, GMP_RNDN);
mpfr_set_str (x, CHECK_Y1, 10, GMP_RNDN);
if (mpfr_equal_p (y, x) == 0 || sign != 1)
{
printf ("mpfr_lgamma("CHECK_X1") is wrong:\n"
"expected ");
mpfr_print_binary (x); putchar ('\n');
printf ("got ");
mpfr_print_binary (y); putchar ('\n');
exit (1);
}
#define CHECK_X2 "9.23709516716202383435e-01"
#define CHECK_Y2 "0.049010669407893718563"
mpfr_set_str (x, CHECK_X2, 10, GMP_RNDN);
sign = -17;
mpfr_lgamma (y, &sign, x, GMP_RNDN);
mpfr_set_str (x, CHECK_Y2, 10, GMP_RNDN);
if (mpfr_equal_p (y, x) == 0 || sign != 1)
{
printf ("mpfr_lgamma("CHECK_X2") is wrong:\n"
"expected ");
mpfr_print_binary (x); putchar ('\n');
printf ("got ");
mpfr_print_binary (y); putchar ('\n');
exit (1);
}
mpfr_set_prec (x, 8);
mpfr_set_prec (y, 175);
mpfr_set_ui (x, 33, GMP_RNDN);
sign = -17;
mpfr_lgamma (y, &sign, x, GMP_RNDU);
mpfr_set_prec (x, 175);
mpfr_set_str_binary (x, "0.1010001100011101101011001101110010100001000001000001110011000001101100001111001001000101011011100100010101011110100111110101010100010011010010000101010111001100011000101111E7");
if (mpfr_equal_p (x, y) == 0 || sign != 1)
{
printf ("Error in mpfr_lgamma (1)\n");
exit (1);
}
mpfr_set_prec (x, 21);
mpfr_set_prec (y, 8);
mpfr_set_ui (y, 120, GMP_RNDN);
sign = -17;
mpfr_lgamma (x, &sign, y, GMP_RNDZ);
mpfr_set_prec (y, 21);
mpfr_set_str_binary (y, "0.111000101000001100101E9");
if (mpfr_equal_p (x, y) == 0 || sign != 1)
{
printf ("Error in mpfr_lgamma (120)\n");
printf ("Expected "); mpfr_print_binary (y); puts ("");
printf ("Got "); mpfr_print_binary (x); puts ("");
exit (1);
}
mpfr_set_prec (x, 3);
mpfr_set_prec (y, 206);
mpfr_set_str_binary (x, "0.110e10");
sign = -17;
inex = mpfr_lgamma (y, &sign, x, GMP_RNDN);
mpfr_set_prec (x, 206);
mpfr_set_str_binary (x, "0.10000111011000000011100010101001100110001110000111100011000100100110110010001011011110101001111011110110000001010100111011010000000011100110110101100111000111010011110010000100010111101010001101000110101001E13");
if (mpfr_equal_p (x, y) == 0 || sign != 1)
{
printf ("Error in mpfr_lgamma (768)\n");
exit (1);
}
if (inex >= 0)
{
printf ("Wrong flag for mpfr_lgamma (768)\n");
exit (1);
}
mpfr_set_prec (x, 4);
mpfr_set_prec (y, 4);
mpfr_set_str_binary (x, "0.1100E-66");
sign = -17;
mpfr_lgamma (y, &sign, x, GMP_RNDN);
mpfr_set_str_binary (x, "0.1100E6");
if (mpfr_equal_p (x, y) == 0 || sign != 1)
{
printf ("Error for lgamma(0.1100E-66)\n");
printf ("Expected ");
mpfr_dump (x);
printf ("Got ");
mpfr_dump (y);
exit (1);
}
mpfr_set_prec (x, 256);
mpfr_set_prec (y, 32);
mpfr_set_si_2exp (x, -1, 200, GMP_RNDN);
mpfr_add_ui (x, x, 1, GMP_RNDN);
mpfr_div_2ui (x, x, 1, GMP_RNDN);
sign = -17;
mpfr_lgamma (y, &sign, x, GMP_RNDN);
mpfr_set_prec (x, 32);
mpfr_set_str_binary (x, "-0.10001000111011111011000010100010E207");
if (mpfr_equal_p (x, y) == 0 || sign != 1)
{
printf ("Error for lgamma(-2^199+0.5)\n");
printf ("Got ");
mpfr_dump (y);
printf ("instead of ");
mpfr_dump (x);
exit (1);
}
mpfr_set_prec (x, 256);
mpfr_set_prec (y, 32);
mpfr_set_si_2exp (x, -1, 200, GMP_RNDN);
mpfr_sub_ui (x, x, 1, GMP_RNDN);
mpfr_div_2ui (x, x, 1, GMP_RNDN);
sign = -17;
mpfr_lgamma (y, &sign, x, GMP_RNDN);
mpfr_set_prec (x, 32);
mpfr_set_str_binary (x, "-0.10001000111011111011000010100010E207");
if (mpfr_equal_p (x, y) == 0 || sign != -1)
{
printf ("Error for lgamma(-2^199-0.5)\n");
printf ("Got ");
mpfr_dump (y);
printf ("with sign %d instead of ", sign);
mpfr_dump (x);
printf ("with sign -1.\n");
exit (1);
}
mpfr_set_prec (x, 10);
mpfr_set_prec (y, 10);
mpfr_set_str_binary (x, "-0.1101111000E-3");
inex = mpfr_lgamma (y, &sign, x, GMP_RNDN);
mpfr_set_str_binary (x, "10.01001011");
if (mpfr_equal_p (x, y) == 0 || sign != -1 || inex >= 0)
{
printf ("Error for lgamma(-0.1101111000E-3)\n");
printf ("Got ");
mpfr_dump (y);
printf ("instead of ");
mpfr_dump (x);
printf ("with sign %d instead of -1 (inex=%d).\n", sign, inex);
exit (1);
}
mpfr_set_prec (x, 18);
mpfr_set_prec (y, 28);
mpfr_set_str_binary (x, "-1.10001101010001101e-196");
inex = mpfr_lgamma (y, &sign, x, GMP_RNDN);
mpfr_set_prec (x, 28);
mpfr_set_str_binary (x, "0.100001110110101011011010011E8");
MPFR_ASSERTN (mpfr_equal_p (x, y) && inex < 0);
/* values reported by Kaveh Ghazi on 14 Jul 2007, where mpfr_lgamma()
takes forever */
#define VAL1 "-0.11100001001010110111001010001001001011110100110000110E-55"
#define OUT1 "100110.01000000010111001110110101110101001001100110111"
#define VAL2 "-0.11100001001010110111001010001001001011110011111111100E-55"
#define OUT2 "100110.0100000001011100111011010111010100100110011111"
#define VAL3 "-0.11100001001010110111001010001001001001110101101010100E-55"
#define OUT3 "100110.01000000010111001110110101110101001011110111011"
#define VAL4 "-0.10001111110110110100100100000000001111110001001001011E-57"
#define OUT4 "101000.0001010111110011101101000101111111010001100011"
#define VAL5 "-0.10001111110110110100100100000000001111011111100001000E-57"
#define OUT5 "101000.00010101111100111011010001011111110100111000001"
#define VAL6 "-0.10001111110110110100100100000000001111011101100011001E-57"
#define OUT6 "101000.0001010111110011101101000101111111010011101111"
mpfr_set_prec (x, 53);
mpfr_set_prec (y, 53);
mpfr_set_str_binary (x, VAL1);
mpfr_lgamma (y, &sign, x, GMP_RNDN);
mpfr_set_str_binary (x, OUT1);
MPFR_ASSERTN(sign == -1 && mpfr_equal_p(x, y));
mpfr_set_str_binary (x, VAL2);
mpfr_lgamma (y, &sign, x, GMP_RNDN);
mpfr_set_str_binary (x, OUT2);
MPFR_ASSERTN(sign == -1 && mpfr_equal_p (x, y));
mpfr_set_str_binary (x, VAL3);
mpfr_lgamma (y, &sign, x, GMP_RNDN);
mpfr_set_str_binary (x, OUT3);
MPFR_ASSERTN(sign == -1 && mpfr_equal_p (x, y));
mpfr_set_str_binary (x, VAL4);
mpfr_lgamma (y, &sign, x, GMP_RNDN);
mpfr_set_str_binary (x, OUT4);
MPFR_ASSERTN(sign == -1 && mpfr_equal_p (x, y));
mpfr_set_str_binary (x, VAL5);
mpfr_lgamma (y, &sign, x, GMP_RNDN);
mpfr_set_str_binary (x, OUT5);
MPFR_ASSERTN(sign == -1 && mpfr_equal_p (x, y));
mpfr_set_str_binary (x, VAL6);
mpfr_lgamma (y, &sign, x, GMP_RNDN);
mpfr_set_str_binary (x, OUT6);
MPFR_ASSERTN(sign == -1 && mpfr_equal_p (x, y));
/* further test from Kaveh Ghazi */
mpfr_set_str_binary (x, "-0.10011010101001010010001110010111010111011101010111001E-53");
mpfr_lgamma (y, &sign, x, GMP_RNDN);
mpfr_set_str_binary (x, "100101.00111101101010000000101010111010001111001101111");
MPFR_ASSERTN(sign == -1 && mpfr_equal_p (x, y));
mpfr_clear (x);
mpfr_clear (y);
}
tree
ubsan_instrument_float_cast (location_t loc, tree type, tree expr)
{
tree expr_type = TREE_TYPE (expr);
tree t, tt, fn, min, max;
enum machine_mode mode = TYPE_MODE (expr_type);
int prec = TYPE_PRECISION (type);
bool uns_p = TYPE_UNSIGNED (type);
/* Float to integer conversion first truncates toward zero, so
even signed char c = 127.875f; is not problematic.
Therefore, we should complain only if EXPR is unordered or smaller
or equal than TYPE_MIN_VALUE - 1.0 or greater or equal than
TYPE_MAX_VALUE + 1.0. */
if (REAL_MODE_FORMAT (mode)->b == 2)
{
/* For maximum, TYPE_MAX_VALUE might not be representable
in EXPR_TYPE, e.g. if TYPE is 64-bit long long and
EXPR_TYPE is IEEE single float, but TYPE_MAX_VALUE + 1.0 is
either representable or infinity. */
REAL_VALUE_TYPE maxval = dconst1;
SET_REAL_EXP (&maxval, REAL_EXP (&maxval) + prec - !uns_p);
real_convert (&maxval, mode, &maxval);
max = build_real (expr_type, maxval);
/* For unsigned, assume -1.0 is always representable. */
if (uns_p)
min = build_minus_one_cst (expr_type);
else
{
/* TYPE_MIN_VALUE is generally representable (or -inf),
but TYPE_MIN_VALUE - 1.0 might not be. */
REAL_VALUE_TYPE minval = dconstm1, minval2;
SET_REAL_EXP (&minval, REAL_EXP (&minval) + prec - 1);
real_convert (&minval, mode, &minval);
real_arithmetic (&minval2, MINUS_EXPR, &minval, &dconst1);
real_convert (&minval2, mode, &minval2);
if (real_compare (EQ_EXPR, &minval, &minval2)
&& !real_isinf (&minval))
{
/* If TYPE_MIN_VALUE - 1.0 is not representable and
rounds to TYPE_MIN_VALUE, we need to subtract
more. As REAL_MODE_FORMAT (mode)->p is the number
of base digits, we want to subtract a number that
will be 1 << (REAL_MODE_FORMAT (mode)->p - 1)
times smaller than minval. */
minval2 = dconst1;
gcc_assert (prec > REAL_MODE_FORMAT (mode)->p);
SET_REAL_EXP (&minval2,
REAL_EXP (&minval2) + prec - 1
- REAL_MODE_FORMAT (mode)->p + 1);
real_arithmetic (&minval2, MINUS_EXPR, &minval, &minval2);
real_convert (&minval2, mode, &minval2);
}
min = build_real (expr_type, minval2);
}
}
else if (REAL_MODE_FORMAT (mode)->b == 10)
{
/* For _Decimal128 up to 34 decimal digits, - sign,
dot, e, exponent. */
char buf[64];
mpfr_t m;
int p = REAL_MODE_FORMAT (mode)->p;
REAL_VALUE_TYPE maxval, minval;
/* Use mpfr_snprintf rounding to compute the smallest
representable decimal number greater or equal than
1 << (prec - !uns_p). */
mpfr_init2 (m, prec + 2);
mpfr_set_ui_2exp (m, 1, prec - !uns_p, GMP_RNDN);
mpfr_snprintf (buf, sizeof buf, "%.*RUe", p - 1, m);
decimal_real_from_string (&maxval, buf);
max = build_real (expr_type, maxval);
/* For unsigned, assume -1.0 is always representable. */
if (uns_p)
min = build_minus_one_cst (expr_type);
else
{
/* Use mpfr_snprintf rounding to compute the largest
representable decimal number less or equal than
(-1 << (prec - 1)) - 1. */
mpfr_set_si_2exp (m, -1, prec - 1, GMP_RNDN);
mpfr_sub_ui (m, m, 1, GMP_RNDN);
mpfr_snprintf (buf, sizeof buf, "%.*RDe", p - 1, m);
decimal_real_from_string (&minval, buf);
min = build_real (expr_type, minval);
}
mpfr_clear (m);
}
else
return NULL_TREE;
if (flag_sanitize_undefined_trap_on_error)
fn = build_call_expr_loc (loc, builtin_decl_explicit (BUILT_IN_TRAP), 0);
else
{
/* Create the __ubsan_handle_float_cast_overflow fn call. */
tree data = ubsan_create_data ("__ubsan_float_cast_overflow_data", NULL,
NULL, ubsan_type_descriptor (expr_type),
ubsan_type_descriptor (type), NULL_TREE);
enum built_in_function bcode
= flag_sanitize_recover
? BUILT_IN_UBSAN_HANDLE_FLOAT_CAST_OVERFLOW
: BUILT_IN_UBSAN_HANDLE_FLOAT_CAST_OVERFLOW_ABORT;
fn = builtin_decl_explicit (bcode);
fn = build_call_expr_loc (loc, fn, 2,
build_fold_addr_expr_loc (loc, data),
ubsan_encode_value (expr, false));
}
t = fold_build2 (UNLE_EXPR, boolean_type_node, expr, min);
tt = fold_build2 (UNGE_EXPR, boolean_type_node, expr, max);
return fold_build3 (COND_EXPR, void_type_node,
fold_build2 (TRUTH_OR_EXPR, boolean_type_node, t, tt),
fn, integer_zero_node);
}
static void
underflows (void)
{
mpfr_t x, y, z;
int err = 0;
int inexact;
int i;
mp_exp_t emin;
mpfr_init2 (x, 64);
mpfr_init2 (y, 64);
mpfr_set_ui (x, 1, GMP_RNDN);
mpfr_set_exp (x, mpfr_get_emin());
for (i = 3; i < 10; i++)
{
mpfr_set_ui (y, i, GMP_RNDN);
mpfr_div_2ui (y, y, 1, GMP_RNDN);
test_pow (y, x, y, GMP_RNDN);
if (!MPFR_IS_FP(y) || mpfr_cmp_ui (y, 0))
{
printf ("Error in mpfr_pow for ");
mpfr_out_str (stdout, 2, 0, x, GMP_RNDN);
printf (" ^ (%d/2)\nGot ", i);
mpfr_out_str (stdout, 2, 0, y, GMP_RNDN);
printf (" instead of 0.\n");
exit (1);
}
}
mpfr_init2 (z, 55);
mpfr_set_str (x, "0.110011010011101001110001110100010000110111101E0",
2, GMP_RNDN);
mpfr_set_str (y, "0.101110010011111001011010100011011100111110011E40",
2, GMP_RNDN);
mpfr_clear_flags ();
inexact = mpfr_pow (z, x, y, GMP_RNDU);
if (!mpfr_underflow_p ())
{
printf ("Underflow flag is not set for special underflow test.\n");
err = 1;
}
if (inexact <= 0)
{
printf ("Ternary value is wrong for special underflow test.\n");
err = 1;
}
mpfr_set_ui (x, 0, GMP_RNDN);
mpfr_nextabove (x);
if (mpfr_cmp (x, z) != 0)
{
printf ("Wrong value for special underflow test.\nGot ");
mpfr_out_str (stdout, 2, 0, z, GMP_RNDN);
printf ("\ninstead of ");
mpfr_out_str (stdout, 2, 2, x, GMP_RNDN);
printf ("\n");
err = 1;
}
if (err)
exit (1);
/* MPFR currently (2006-08-19) segfaults on the following code (and
possibly makes other programs crash due to the lack of memory),
because y is converted into an mpz_t, and the required precision
is too high. */
mpfr_set_prec (x, 2);
mpfr_set_prec (y, 2);
mpfr_set_prec (z, 12);
mpfr_set_ui_2exp (x, 3, -2, GMP_RNDN);
mpfr_set_ui_2exp (y, 1, mpfr_get_emax () - 1, GMP_RNDN);
mpfr_clear_flags ();
mpfr_pow (z, x, y, GMP_RNDN);
if (!mpfr_underflow_p () || MPFR_NOTZERO (z))
{
printf ("Underflow test with large y fails.\n");
exit (1);
}
emin = mpfr_get_emin ();
mpfr_set_emin (-256);
mpfr_set_prec (x, 2);
mpfr_set_prec (y, 2);
mpfr_set_prec (z, 12);
mpfr_set_ui_2exp (x, 3, -2, GMP_RNDN);
mpfr_set_ui_2exp (y, 1, 38, GMP_RNDN);
mpfr_clear_flags ();
inexact = mpfr_pow (z, x, y, GMP_RNDN);
if (!mpfr_underflow_p () || MPFR_NOTZERO (z) || inexact >= 0)
{
printf ("Bad underflow detection for 0.75^(2^38). Obtained:\n"
"Underflow flag... %-3s (should be 'yes')\n"
"Zero result...... %-3s (should be 'yes')\n"
"Inexact value.... %-3d (should be negative)\n",
mpfr_underflow_p () ? "yes" : "no",
MPFR_IS_ZERO (z) ? "yes" : "no", inexact);
exit (1);
}
mpfr_set_emin (emin);
emin = mpfr_get_emin ();
mpfr_set_emin (-256);
mpfr_set_prec (x, 2);
mpfr_set_prec (y, 40);
mpfr_set_prec (z, 12);
mpfr_set_ui_2exp (x, 3, -1, GMP_RNDN);
mpfr_set_si_2exp (y, -1, 38, GMP_RNDN);
for (i = 0; i < 4; i++)
{
if (i == 2)
mpfr_neg (x, x, GMP_RNDN);
mpfr_clear_flags ();
inexact = mpfr_pow (z, x, y, GMP_RNDN);
if (!mpfr_underflow_p () || MPFR_NOTZERO (z) ||
(i == 3 ? (inexact <= 0) : (inexact >= 0)))
{
printf ("Bad underflow detection for (");
mpfr_out_str (stdout, 10, 0, x, GMP_RNDN);
printf (")^(-2^38-%d). Obtained:\n"
"Overflow flag.... %-3s (should be 'no')\n"
"Underflow flag... %-3s (should be 'yes')\n"
"Zero result...... %-3s (should be 'yes')\n"
"Inexact value.... %-3d (should be %s)\n", i,
mpfr_overflow_p () ? "yes" : "no",
mpfr_underflow_p () ? "yes" : "no",
MPFR_IS_ZERO (z) ? "yes" : "no", inexact,
i == 3 ? "positive" : "negative");
exit (1);
}
inexact = mpfr_sub_ui (y, y, 1, GMP_RNDN);
MPFR_ASSERTN (inexact == 0);
}
mpfr_set_emin (emin);
mpfr_clears (x, y, z, (void *) 0);
}
int
mpfr_zeta (mpfr_t z, mpfr_srcptr s, mp_rnd_t rnd_mode)
{
mpfr_t z_pre, s1, y, p;
double sd, eps, m1, c;
long add;
mp_prec_t precz, prec1, precs, precs1;
int inex;
MPFR_GROUP_DECL (group);
MPFR_ZIV_DECL (loop);
MPFR_SAVE_EXPO_DECL (expo);
MPFR_LOG_FUNC (("s[%#R]=%R rnd=%d", s, s, rnd_mode),
("z[%#R]=%R inexact=%d", z, z, inex));
/* Zero, Nan or Inf ? */
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (s)))
{
if (MPFR_IS_NAN (s))
{
MPFR_SET_NAN (z);
MPFR_RET_NAN;
}
else if (MPFR_IS_INF (s))
{
if (MPFR_IS_POS (s))
return mpfr_set_ui (z, 1, GMP_RNDN); /* Zeta(+Inf) = 1 */
MPFR_SET_NAN (z); /* Zeta(-Inf) = NaN */
MPFR_RET_NAN;
}
else /* s iz zero */
{
MPFR_ASSERTD (MPFR_IS_ZERO (s));
mpfr_set_ui (z, 1, rnd_mode);
mpfr_div_2ui (z, z, 1, rnd_mode);
MPFR_CHANGE_SIGN (z);
MPFR_RET (0);
}
}
/* s is neither Nan, nor Inf, nor Zero */
/* check tiny s: we have zeta(s) = -1/2 - 1/2 log(2 Pi) s + ... around s=0,
and for |s| <= 0.074, we have |zeta(s) + 1/2| <= |s|.
Thus if |s| <= 1/4*ulp(1/2), we can deduce the correct rounding
(the 1/4 covers the case where |zeta(s)| < 1/2 and rounding to nearest).
A sufficient condition is that EXP(s) + 1 < -PREC(z). */
if (MPFR_EXP(s) + 1 < - (mp_exp_t) MPFR_PREC(z))
{
int signs = MPFR_SIGN(s);
mpfr_set_si_2exp (z, -1, -1, rnd_mode); /* -1/2 */
if ((rnd_mode == GMP_RNDU || rnd_mode == GMP_RNDZ) && signs < 0)
{
mpfr_nextabove (z); /* z = -1/2 + epsilon */
inex = 1;
}
else if (rnd_mode == GMP_RNDD && signs > 0)
{
mpfr_nextbelow (z); /* z = -1/2 - epsilon */
inex = -1;
}
else
{
if (rnd_mode == GMP_RNDU) /* s > 0: z = -1/2 */
inex = 1;
else if (rnd_mode == GMP_RNDD)
inex = -1; /* s < 0: z = -1/2 */
else /* (GMP_RNDZ and s > 0) or GMP_RNDN: z = -1/2 */
inex = (signs > 0) ? 1 : -1;
}
return mpfr_check_range (z, inex, rnd_mode);
}
/* Check for case s= -2n */
if (MPFR_IS_NEG (s))
{
mpfr_t tmp;
tmp[0] = *s;
MPFR_EXP (tmp) = MPFR_EXP (s) - 1;
if (mpfr_integer_p (tmp))
{
MPFR_SET_ZERO (z);
MPFR_SET_POS (z);
MPFR_RET (0);
}
}
MPFR_SAVE_EXPO_MARK (expo);
/* Compute Zeta */
if (MPFR_IS_POS (s) && MPFR_GET_EXP (s) >= 0) /* Case s >= 1/2 */
inex = mpfr_zeta_pos (z, s, rnd_mode);
else /* use reflection formula
zeta(s) = 2^s*Pi^(s-1)*sin(Pi*s/2)*gamma(1-s)*zeta(1-s) */
{
precz = MPFR_PREC (z);
precs = MPFR_PREC (s);
/* Precision precs1 needed to represent 1 - s, and s + 2,
without any truncation */
precs1 = precs + 2 + MAX (0, - MPFR_GET_EXP (s));
sd = mpfr_get_d (s, GMP_RNDN) - 1.0;
if (sd < 0.0)
sd = -sd; /* now sd = abs(s-1.0) */
/* Precision prec1 is the precision on elementary computations;
it ensures a final precision prec1 - add for zeta(s) */
/* eps = pow (2.0, - (double) precz - 14.0); */
eps = __gmpfr_ceil_exp2 (- (double) precz - 14.0);
m1 = 1.0 + MAX(1.0 / eps, 2.0 * sd) * (1.0 + eps);
c = (1.0 + eps) * (1.0 + eps * MAX(8.0, m1));
/* add = 1 + floor(log(c*c*c*(13 + m1))/log(2)); */
add = __gmpfr_ceil_log2 (c * c * c * (13.0 + m1));
prec1 = precz + add;
prec1 = MAX (prec1, precs1) + 10;
MPFR_GROUP_INIT_4 (group, prec1, z_pre, s1, y, p);
MPFR_ZIV_INIT (loop, prec1);
for (;;)
{
mpfr_sub (s1, __gmpfr_one, s, GMP_RNDN);/* s1 = 1-s */
mpfr_zeta_pos (z_pre, s1, GMP_RNDN); /* zeta(1-s) */
mpfr_gamma (y, s1, GMP_RNDN); /* gamma(1-s) */
if (MPFR_IS_INF (y)) /* Zeta(s) < 0 for -4k-2 < s < -4k,
Zeta(s) > 0 for -4k < s < -4k+2 */
{
MPFR_SET_INF (z_pre);
mpfr_div_2ui (s1, s, 2, GMP_RNDN); /* s/4, exact */
mpfr_frac (s1, s1, GMP_RNDN); /* exact, -1 < s1 < 0 */
if (mpfr_cmp_si_2exp (s1, -1, -1) > 0)
MPFR_SET_NEG (z_pre);
else
MPFR_SET_POS (z_pre);
break;
}
mpfr_mul (z_pre, z_pre, y, GMP_RNDN); /* gamma(1-s)*zeta(1-s) */
mpfr_const_pi (p, GMP_RNDD);
mpfr_mul (y, s, p, GMP_RNDN);
mpfr_div_2ui (y, y, 1, GMP_RNDN); /* s*Pi/2 */
mpfr_sin (y, y, GMP_RNDN); /* sin(Pi*s/2) */
mpfr_mul (z_pre, z_pre, y, GMP_RNDN);
mpfr_mul_2ui (y, p, 1, GMP_RNDN); /* 2*Pi */
mpfr_neg (s1, s1, GMP_RNDN); /* s-1 */
mpfr_pow (y, y, s1, GMP_RNDN); /* (2*Pi)^(s-1) */
mpfr_mul (z_pre, z_pre, y, GMP_RNDN);
mpfr_mul_2ui (z_pre, z_pre, 1, GMP_RNDN);
if (MPFR_LIKELY (MPFR_CAN_ROUND (z_pre, prec1 - add, precz,
rnd_mode)))
break;
MPFR_ZIV_NEXT (loop, prec1);
MPFR_GROUP_REPREC_4 (group, prec1, z_pre, s1, y, p);
}
MPFR_ZIV_FREE (loop);
inex = mpfr_set (z, z_pre, rnd_mode);
MPFR_GROUP_CLEAR (group);
}
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range (z, inex, rnd_mode);
}
static void
check_pow_si (void)
{
mpfr_t x;
mpfr_init (x);
mpfr_set_nan (x);
mpfr_pow_si (x, x, -1, GMP_RNDN);
MPFR_ASSERTN(mpfr_nan_p (x));
mpfr_set_inf (x, 1);
mpfr_pow_si (x, x, -1, GMP_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui (x, 0) == 0 && MPFR_IS_POS(x));
mpfr_set_inf (x, -1);
mpfr_pow_si (x, x, -1, GMP_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui (x, 0) == 0 && MPFR_IS_NEG(x));
mpfr_set_inf (x, -1);
mpfr_pow_si (x, x, -2, GMP_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui (x, 0) == 0 && MPFR_IS_POS(x));
mpfr_set_ui (x, 0, GMP_RNDN);
mpfr_pow_si (x, x, -1, GMP_RNDN);
MPFR_ASSERTN(mpfr_inf_p (x) && mpfr_sgn (x) > 0);
mpfr_set_ui (x, 0, GMP_RNDN);
mpfr_neg (x, x, GMP_RNDN);
mpfr_pow_si (x, x, -1, GMP_RNDN);
MPFR_ASSERTN(mpfr_inf_p (x) && mpfr_sgn (x) < 0);
mpfr_set_ui (x, 0, GMP_RNDN);
mpfr_neg (x, x, GMP_RNDN);
mpfr_pow_si (x, x, -2, GMP_RNDN);
MPFR_ASSERTN(mpfr_inf_p (x) && mpfr_sgn (x) > 0);
mpfr_set_si (x, 2, GMP_RNDN);
mpfr_pow_si (x, x, LONG_MAX, GMP_RNDN); /* 2^LONG_MAX */
if (LONG_MAX > mpfr_get_emax () - 1) /* LONG_MAX + 1 > emax */
{
MPFR_ASSERTN (mpfr_inf_p (x));
}
else
{
MPFR_ASSERTN (mpfr_cmp_si_2exp (x, 1, LONG_MAX));
}
mpfr_set_si (x, 2, GMP_RNDN);
mpfr_pow_si (x, x, LONG_MIN, GMP_RNDN); /* 2^LONG_MIN */
if (LONG_MIN + 1 < mpfr_get_emin ())
{
MPFR_ASSERTN (mpfr_zero_p (x));
}
else
{
MPFR_ASSERTN (mpfr_cmp_si_2exp (x, 1, LONG_MIN));
}
mpfr_set_si (x, 2, GMP_RNDN);
mpfr_pow_si (x, x, LONG_MIN + 1, GMP_RNDN); /* 2^(LONG_MIN+1) */
if (mpfr_nan_p (x))
{
printf ("Error in pow_si(2, LONG_MIN+1): got NaN\n");
exit (1);
}
if (LONG_MIN + 2 < mpfr_get_emin ())
{
MPFR_ASSERTN (mpfr_zero_p (x));
}
else
{
MPFR_ASSERTN (mpfr_cmp_si_2exp (x, 1, LONG_MIN + 1));
}
mpfr_set_si_2exp (x, 1, -1, GMP_RNDN); /* 0.5 */
mpfr_pow_si (x, x, LONG_MIN, GMP_RNDN); /* 2^(-LONG_MIN) */
if (LONG_MIN < 1 - mpfr_get_emax ()) /* 1 - LONG_MIN > emax */
{
MPFR_ASSERTN (mpfr_inf_p (x));
}
else
{
MPFR_ASSERTN (mpfr_cmp_si_2exp (x, 2, - (LONG_MIN + 1)));
}
mpfr_clear (x);
}
int
mpfr_frexp (mpfr_exp_t *exp, mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd)
{
int inex;
mpfr_flags_t saved_flags = __gmpfr_flags;
MPFR_BLOCK_DECL (flags);
MPFR_LOG_FUNC
(("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (x), mpfr_log_prec, x, rnd),
("y[%Pu]=%.*Rg exp=%" MPFR_EXP_FSPEC "d inex=%d", mpfr_get_prec (y),
mpfr_log_prec, y, (mpfr_eexp_t) *exp, inex));
if (MPFR_UNLIKELY(MPFR_IS_SINGULAR(x)))
{
if (MPFR_IS_NAN(x))
{
MPFR_SET_NAN(y);
MPFR_RET_NAN; /* exp is unspecified */
}
else if (MPFR_IS_INF(x))
{
MPFR_SET_INF(y);
MPFR_SET_SAME_SIGN(y,x);
MPFR_RET(0); /* exp is unspecified */
}
else
{
MPFR_SET_ZERO(y);
MPFR_SET_SAME_SIGN(y,x);
*exp = 0;
MPFR_RET(0);
}
}
MPFR_BLOCK (flags, inex = mpfr_set (y, x, rnd));
__gmpfr_flags = saved_flags;
/* Possible overflow due to the rounding, no possible underflow. */
if (MPFR_UNLIKELY (MPFR_OVERFLOW (flags)))
{
int inex2;
/* An overflow here means that the exponent of y would be larger than
the one of x, thus x would be rounded to the next power of 2, and
the returned y should be 1/2 in absolute value, rounded (i.e. with
possible underflow or overflow). This also implies that x and y are
different objects, so that the exponent of x has not been lost. */
MPFR_LOG_MSG (("Internal overflow\n", 0));
MPFR_ASSERTD (x != y);
*exp = MPFR_GET_EXP (x) + 1;
inex2 = mpfr_set_si_2exp (y, MPFR_INT_SIGN (x), -1, rnd);
MPFR_LOG_MSG (("inex=%d inex2=%d\n", inex, inex2));
if (inex2 != 0)
inex = inex2;
MPFR_RET (inex);
}
*exp = MPFR_GET_EXP (y);
/* Do not use MPFR_SET_EXP because the range has not been checked yet. */
MPFR_EXP (y) = 0;
return mpfr_check_range (y, inex, rnd);
}
int
mpfr_pow_si (mpfr_ptr y, mpfr_srcptr x, long int n, mpfr_rnd_t rnd)
{
MPFR_LOG_FUNC
(("x[%Pu]=%.*Rg n=%ld rnd=%d",
mpfr_get_prec (x), mpfr_log_prec, x, n, rnd),
("y[%Pu]=%.*Rg", mpfr_get_prec (y), mpfr_log_prec, y));
if (n >= 0)
return mpfr_pow_ui (y, x, n, rnd);
else
{
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
{
if (MPFR_IS_NAN (x))
{
MPFR_SET_NAN (y);
MPFR_RET_NAN;
}
else
{
int positive = MPFR_IS_POS (x) || ((unsigned long) n & 1) == 0;
if (MPFR_IS_INF (x))
MPFR_SET_ZERO (y);
else /* x is zero */
{
MPFR_ASSERTD (MPFR_IS_ZERO (x));
MPFR_SET_INF (y);
mpfr_set_divby0 ();
}
if (positive)
MPFR_SET_POS (y);
else
MPFR_SET_NEG (y);
MPFR_RET (0);
}
}
/* detect exact powers: x^(-n) is exact iff x is a power of 2 */
if (mpfr_cmp_si_2exp (x, MPFR_SIGN(x), MPFR_EXP(x) - 1) == 0)
{
mpfr_exp_t expx = MPFR_EXP (x) - 1, expy;
MPFR_ASSERTD (n < 0);
/* Warning: n * expx may overflow!
*
* Some systems (apparently alpha-freebsd) abort with
* LONG_MIN / 1, and LONG_MIN / -1 is undefined.
* http://www.freebsd.org/cgi/query-pr.cgi?pr=72024
*
* Proof of the overflow checking. The expressions below are
* assumed to be on the rational numbers, but the word "overflow"
* still has its own meaning in the C context. / still denotes
* the integer (truncated) division, and // denotes the exact
* division.
* - First, (__gmpfr_emin - 1) / n and (__gmpfr_emax - 1) / n
* cannot overflow due to the constraints on the exponents of
* MPFR numbers.
* - If n = -1, then n * expx = - expx, which is representable
* because of the constraints on the exponents of MPFR numbers.
* - If expx = 0, then n * expx = 0, which is representable.
* - If n < -1 and expx > 0:
* + If expx > (__gmpfr_emin - 1) / n, then
* expx >= (__gmpfr_emin - 1) / n + 1
* > (__gmpfr_emin - 1) // n,
* and
* n * expx < __gmpfr_emin - 1,
* i.e.
* n * expx <= __gmpfr_emin - 2.
* This corresponds to an underflow, with a null result in
* the rounding-to-nearest mode.
* + If expx <= (__gmpfr_emin - 1) / n, then n * expx cannot
* overflow since 0 < expx <= (__gmpfr_emin - 1) / n and
* 0 > n * expx >= n * ((__gmpfr_emin - 1) / n)
* >= __gmpfr_emin - 1.
* - If n < -1 and expx < 0:
* + If expx < (__gmpfr_emax - 1) / n, then
* expx <= (__gmpfr_emax - 1) / n - 1
* < (__gmpfr_emax - 1) // n,
* and
* n * expx > __gmpfr_emax - 1,
* i.e.
* n * expx >= __gmpfr_emax.
* This corresponds to an overflow (2^(n * expx) has an
* exponent > __gmpfr_emax).
* + If expx >= (__gmpfr_emax - 1) / n, then n * expx cannot
* overflow since 0 > expx >= (__gmpfr_emax - 1) / n and
* 0 < n * expx <= n * ((__gmpfr_emax - 1) / n)
* <= __gmpfr_emax - 1.
* Note: one could use expx bounds based on MPFR_EXP_MIN and
* MPFR_EXP_MAX instead of __gmpfr_emin and __gmpfr_emax. The
* current bounds do not lead to noticeably slower code and
* allow us to avoid a bug in Sun's compiler for Solaris/x86
* (when optimizations are enabled); known affected versions:
* cc: Sun C 5.8 2005/10/13
* cc: Sun C 5.8 Patch 121016-02 2006/03/31
* cc: Sun C 5.8 Patch 121016-04 2006/10/18
*/
expy =
n != -1 && expx > 0 && expx > (__gmpfr_emin - 1) / n ?
MPFR_EMIN_MIN - 2 /* Underflow */ :
n != -1 && expx < 0 && expx < (__gmpfr_emax - 1) / n ?
MPFR_EMAX_MAX /* Overflow */ : n * expx;
return mpfr_set_si_2exp (y, n % 2 ? MPFR_INT_SIGN (x) : 1,
expy, rnd);
}
/* General case */
{
/* Declaration of the intermediary variable */
mpfr_t t;
/* Declaration of the size variable */
mpfr_prec_t Ny; /* target precision */
mpfr_prec_t Nt; /* working precision */
mpfr_rnd_t rnd1;
int size_n;
int inexact;
unsigned long abs_n;
MPFR_SAVE_EXPO_DECL (expo);
MPFR_ZIV_DECL (loop);
abs_n = - (unsigned long) n;
count_leading_zeros (size_n, (mp_limb_t) abs_n);
size_n = GMP_NUMB_BITS - size_n;
/* initial working precision */
Ny = MPFR_PREC (y);
Nt = Ny + size_n + 3 + MPFR_INT_CEIL_LOG2 (Ny);
MPFR_SAVE_EXPO_MARK (expo);
/* initialise of intermediary variable */
mpfr_init2 (t, Nt);
/* We will compute rnd(rnd1(1/x) ^ |n|), where rnd1 is the rounding
toward sign(x), to avoid spurious overflow or underflow, as in
mpfr_pow_z. */
rnd1 = MPFR_EXP (x) < 1 ? MPFR_RNDZ :
(MPFR_SIGN (x) > 0 ? MPFR_RNDU : MPFR_RNDD);
MPFR_ZIV_INIT (loop, Nt);
for (;;)
{
MPFR_BLOCK_DECL (flags);
/* compute (1/x)^|n| */
MPFR_BLOCK (flags, mpfr_ui_div (t, 1, x, rnd1));
MPFR_ASSERTD (! MPFR_UNDERFLOW (flags));
/* t = (1/x)*(1+theta) where |theta| <= 2^(-Nt) */
if (MPFR_UNLIKELY (MPFR_OVERFLOW (flags)))
goto overflow;
MPFR_BLOCK (flags, mpfr_pow_ui (t, t, abs_n, rnd));
/* t = (1/x)^|n|*(1+theta')^(|n|+1) where |theta'| <= 2^(-Nt).
If (|n|+1)*2^(-Nt) <= 1/2, which is satisfied as soon as
Nt >= bits(n)+2, then we can use Lemma \ref{lemma_graillat}
from algorithms.tex, which yields x^n*(1+theta) with
|theta| <= 2(|n|+1)*2^(-Nt), thus the error is bounded by
2(|n|+1) ulps <= 2^(bits(n)+2) ulps. */
if (MPFR_UNLIKELY (MPFR_OVERFLOW (flags)))
{
overflow:
MPFR_ZIV_FREE (loop);
mpfr_clear (t);
MPFR_SAVE_EXPO_FREE (expo);
MPFR_LOG_MSG (("overflow\n", 0));
return mpfr_overflow (y, rnd, abs_n & 1 ?
MPFR_SIGN (x) : MPFR_SIGN_POS);
}
if (MPFR_UNLIKELY (MPFR_UNDERFLOW (flags)))
{
MPFR_ZIV_FREE (loop);
mpfr_clear (t);
MPFR_LOG_MSG (("underflow\n", 0));
if (rnd == MPFR_RNDN)
{
mpfr_t y2, nn;
/* We cannot decide now whether the result should be
rounded toward zero or away from zero. So, like
in mpfr_pow_pos_z, let's use the general case of
mpfr_pow in precision 2. */
MPFR_ASSERTD (mpfr_cmp_si_2exp (x, MPFR_SIGN (x),
MPFR_EXP (x) - 1) != 0);
mpfr_init2 (y2, 2);
mpfr_init2 (nn, sizeof (long) * CHAR_BIT);
inexact = mpfr_set_si (nn, n, MPFR_RNDN);
MPFR_ASSERTN (inexact == 0);
inexact = mpfr_pow_general (y2, x, nn, rnd, 1,
(mpfr_save_expo_t *) NULL);
mpfr_clear (nn);
mpfr_set (y, y2, MPFR_RNDN);
mpfr_clear (y2);
MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, MPFR_FLAGS_UNDERFLOW);
goto end;
}
else
{
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_underflow (y, rnd, abs_n & 1 ?
MPFR_SIGN (x) : MPFR_SIGN_POS);
}
}
/* error estimate -- see pow function in algorithms.ps */
if (MPFR_LIKELY (MPFR_CAN_ROUND (t, Nt - size_n - 2, Ny, rnd)))
break;
/* actualisation of the precision */
MPFR_ZIV_NEXT (loop, Nt);
mpfr_set_prec (t, Nt);
}
MPFR_ZIV_FREE (loop);
inexact = mpfr_set (y, t, rnd);
mpfr_clear (t);
end:
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range (y, inexact, rnd);
}
}
}
static void
normal (void)
{
int inexact;
mpfr_t x, y;
mpfr_init (x);
mpfr_init (y);
/* x1 = 2^-3 */
mpfr_set_str (x, "1p-3", 2, MPFR_RNDD);
mpfr_li2 (x, x, MPFR_RNDN);
if (mpfr_cmp_str (x, "0x1087a7a9e42141p-55", 16, MPFR_RNDN) != 0)
{
printf ("Error for li2(x1)\n");
exit (1);
}
/* check MPFR_FAST_COMPUTE_IF_SMALL_INPUT */
mpfr_set_prec (x, 2);
mpfr_set_prec (y, 20);
mpfr_set_ui_2exp (x, 1, -21, MPFR_RNDN);
mpfr_li2 (y, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp (y, x) == 0);
mpfr_set_si_2exp (x, -1, -21, MPFR_RNDN);
mpfr_li2 (y, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp (y, x) == 0);
/* worst case */
/* x2 = 0x7F18EA6537E00E983196CDDC6EFAC57Fp-129
Li2(x2) = 2^-2 + 2^-6 + 2^-120 */
mpfr_set_prec (x, 128);
mpfr_set_str (x, "7F18EA6537E00E983196CDDC6EFAC57Fp-129", 16, MPFR_RNDN);
/* round to nearest mode and 4 bits of precision,
it should be rounded to 2^-2 + 2^-5 and */
mpfr_set_prec (y, 4);
inexact = mpfr_li2 (y, x, MPFR_RNDN);
if (inexact != 1 || mpfr_cmp_str (y, "0.1001p-1", 2, MPFR_RNDN) != 0)
{
printf ("Error for li2(x2, RNDN)\n");
exit (1);
}
/* round toward zero mode and 5 bits of precision,
it should be rounded to 2^-2 + 2^-6 */
mpfr_set_prec (y, 5);
inexact = mpfr_li2 (y, x, MPFR_RNDZ);
if (inexact != -1 || mpfr_cmp_str (y, "0.10001p-1", 2, MPFR_RNDN) != 0)
{
printf ("Error for li2(x2, RNDZ)\n");
exit (1);
}
/* round away from zero mode and 5 bits of precision,
it should be rounded to 2^-2 + 2^-5 */
inexact = mpfr_li2 (y, x, MPFR_RNDU);
if (inexact != 1 || mpfr_cmp_str (y, "0.10010p-1", 2, MPFR_RNDN) != 0)
{
printf ("Error for li2(x2, RNDU)\n");
exit (1);
}
mpfr_clear (x);
mpfr_clear (y);
}
static void
test_2exp (void)
{
mpfr_t x;
int res;
mpfr_init2 (x, 32);
mpfr_set_ui_2exp (x, 1, 0, MPFR_RNDN);
if (mpfr_cmp_ui(x, 1))
ERROR("(1U,0)");
mpfr_set_ui_2exp (x, 1024, -10, MPFR_RNDN);
if (mpfr_cmp_ui(x, 1))
ERROR("(1024U,-10)");
mpfr_set_ui_2exp (x, 1024, 10, MPFR_RNDN);
if (mpfr_cmp_ui(x, 1024*1024))
ERROR("(1024U,+10)");
mpfr_set_si_2exp (x, -1024L * 1024L, -10, MPFR_RNDN);
if (mpfr_cmp_si(x, -1024))
ERROR("(1M,-10)");
mpfr_set_ui_2exp (x, 0x92345678, 16, MPFR_RNDN);
if (mpfr_cmp_str (x, "92345678@4", 16, MPFR_RNDN))
ERROR("(x92345678U,+16)");
mpfr_set_si_2exp (x, -0x1ABCDEF0, -256, MPFR_RNDN);
if (mpfr_cmp_str (x, "-1ABCDEF0@-64", 16, MPFR_RNDN))
ERROR("(-x1ABCDEF0,-256)");
mpfr_set_prec (x, 2);
res = mpfr_set_si_2exp (x, 7, 10, MPFR_RNDU);
if (mpfr_cmp_ui (x, 1<<13) || res <= 0)
ERROR ("Prec 2 + si_2exp");
res = mpfr_set_ui_2exp (x, 7, 10, MPFR_RNDU);
if (mpfr_cmp_ui (x, 1<<13) || res <= 0)
ERROR ("Prec 2 + ui_2exp");
mpfr_clear_flags ();
mpfr_set_ui_2exp (x, 17, MPFR_EMAX_MAX, MPFR_RNDN);
if (!mpfr_inf_p (x) || MPFR_IS_NEG (x))
ERROR ("mpfr_set_ui_2exp and overflow (bad result)");
if (!mpfr_overflow_p ())
ERROR ("mpfr_set_ui_2exp and overflow (overflow flag not set)");
mpfr_clear_flags ();
mpfr_set_si_2exp (x, 17, MPFR_EMAX_MAX, MPFR_RNDN);
if (!mpfr_inf_p (x) || MPFR_IS_NEG (x))
ERROR ("mpfr_set_si_2exp (pos) and overflow (bad result)");
if (!mpfr_overflow_p ())
ERROR ("mpfr_set_si_2exp (pos) and overflow (overflow flag not set)");
mpfr_clear_flags ();
mpfr_set_si_2exp (x, -17, MPFR_EMAX_MAX, MPFR_RNDN);
if (!mpfr_inf_p (x) || MPFR_IS_POS (x))
ERROR ("mpfr_set_si_2exp (neg) and overflow (bad result)");
if (!mpfr_overflow_p ())
ERROR ("mpfr_set_si_2exp (neg) and overflow (overflow flag not set)");
mpfr_clear (x);
}
static void
overflowed_sec0 (void)
{
mpfr_t x, y;
int emax, i, inex, rnd, err = 0;
mpfr_exp_t old_emax;
old_emax = mpfr_get_emax ();
mpfr_init2 (x, 8);
mpfr_init2 (y, 8);
for (emax = -1; emax <= 0; emax++)
{
mpfr_set_ui_2exp (y, 1, emax, MPFR_RNDN);
mpfr_nextbelow (y);
set_emax (emax); /* 1 is not representable. */
for (i = -1; i <= 1; i++)
RND_LOOP (rnd)
{
mpfr_set_si_2exp (x, i, -512 * ABS (i), MPFR_RNDN);
mpfr_clear_flags ();
inex = mpfr_sec (x, x, (mpfr_rnd_t) rnd);
if (! mpfr_overflow_p ())
{
printf ("Error in overflowed_sec0 (i = %d, rnd = %s):\n"
" The overflow flag is not set.\n",
i, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
err = 1;
}
if (rnd == MPFR_RNDZ || rnd == MPFR_RNDD)
{
if (inex >= 0)
{
printf ("Error in overflowed_sec0 (i = %d, rnd = %s):\n"
" The inexact value must be negative.\n",
i, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
err = 1;
}
if (! mpfr_equal_p (x, y))
{
printf ("Error in overflowed_sec0 (i = %d, rnd = %s):\n"
" Got ", i, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
mpfr_print_binary (x);
printf (" instead of 0.11111111E%d.\n", emax);
err = 1;
}
}
else
{
if (inex <= 0)
{
printf ("Error in overflowed_sec0 (i = %d, rnd = %s):\n"
" The inexact value must be positive.\n",
i, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
err = 1;
}
if (! (mpfr_inf_p (x) && MPFR_SIGN (x) > 0))
{
printf ("Error in overflowed_sec0 (i = %d, rnd = %s):\n"
" Got ", i, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
mpfr_print_binary (x);
printf (" instead of +Inf.\n");
err = 1;
}
}
}
set_emax (old_emax);
}
if (err)
exit (1);
mpfr_clear (x);
mpfr_clear (y);
}
int
main (void)
{
mpfr_prec_t prec;
mpfr_t x, y;
intmax_t s;
uintmax_t u;
tests_start_mpfr ();
for (u = MPFR_UINTMAX_MAX, prec = 0; u != 0; u /= 2, prec++)
{ }
mpfr_init2 (x, prec + 4);
mpfr_init2 (y, prec + 4);
mpfr_set_ui (x, 0, MPFR_RNDN);
check_sj (0, x);
check_uj (0, x);
mpfr_set_ui (x, 1, MPFR_RNDN);
check_sj (1, x);
check_uj (1, x);
mpfr_neg (x, x, MPFR_RNDN);
check_sj (-1, x);
mpfr_set_si_2exp (x, 1, prec, MPFR_RNDN);
mpfr_sub_ui (x, x, 1, MPFR_RNDN); /* UINTMAX_MAX */
mpfr_div_ui (y, x, 2, MPFR_RNDZ);
mpfr_trunc (y, y); /* INTMAX_MAX */
for (s = MPFR_INTMAX_MAX; s != 0; s /= 17)
{
check_sj (s, y);
mpfr_div_ui (y, y, 17, MPFR_RNDZ);
mpfr_trunc (y, y);
}
mpfr_div_ui (y, x, 2, MPFR_RNDZ);
mpfr_trunc (y, y); /* INTMAX_MAX */
mpfr_neg (y, y, MPFR_RNDN);
if (MPFR_INTMAX_MIN + MPFR_INTMAX_MAX != 0)
mpfr_sub_ui (y, y, 1, MPFR_RNDN); /* INTMAX_MIN */
for (s = MPFR_INTMAX_MIN; s != 0; s /= 17)
{
check_sj (s, y);
mpfr_div_ui (y, y, 17, MPFR_RNDZ);
mpfr_trunc (y, y);
}
for (u = MPFR_UINTMAX_MAX; u != 0; u /= 17)
{
check_uj (u, x);
mpfr_div_ui (x, x, 17, MPFR_RNDZ);
mpfr_trunc (x, x);
}
mpfr_clear (x);
mpfr_clear (y);
check_erange ();
tests_end_mpfr ();
return 0;
}
static void
large_arg (void)
{
mpfr_t x, y;
unsigned int flags;
mpfr_init2 (x, 88);
mpfr_init2 (y, 98);
mpfr_set_si_2exp (x, -1, 173, MPFR_RNDN);
mpfr_clear_flags ();
mpfr_erfc (y, x, MPFR_RNDN);
flags = __gmpfr_flags;
if (mpfr_cmp_ui (y, 2) != 0)
{
printf ("mpfr_erfc failed for large x (1)\n");
exit (1);
}
if (flags != MPFR_FLAGS_INEXACT)
{
printf ("mpfr_erfc sets incorrect flags for large x (1)\n");
printf ("Expected %u, got %u\n",
(unsigned int) MPFR_FLAGS_INEXACT, flags);
exit (1);
}
mpfr_set_si_2exp (x, -1, mpfr_get_emax () - 3, MPFR_RNDN);
mpfr_clear_flags ();
mpfr_erfc (y, x, MPFR_RNDN);
flags = __gmpfr_flags;
if (mpfr_cmp_ui (y, 2) != 0)
{
printf ("mpfr_erfc failed for large x (1b)\n");
exit (1);
}
if (flags != MPFR_FLAGS_INEXACT)
{
printf ("mpfr_erfc sets incorrect flags for large x (1b)\n");
printf ("Expected %u, got %u\n",
(unsigned int) MPFR_FLAGS_INEXACT, flags);
exit (1);
}
mpfr_set_prec (x, 33);
mpfr_set_prec (y, 43);
mpfr_set_str_binary (x, "1.11000101010111011000111100101001e6");
mpfr_erfc (y, x, MPFR_RNDD);
mpfr_set_prec (x, 43);
mpfr_set_str_binary (x, "100010011100101100001101100101011101101E-18579");
if (mpfr_cmp (x, y) != 0)
{
printf ("mpfr_erfc failed for large x (2)\n");
exit (1);
}
mpfr_set_prec (y, 43);
mpfr_set_si_2exp (x, 1, 11, MPFR_RNDN);
mpfr_erfc (y, x, MPFR_RNDN);
mpfr_set_str_binary (x, "0.1100000100100010101111001111010010001000110E-6051113");
if (mpfr_cmp (x, y) != 0)
{
printf ("mpfr_erfc failed for large x (3)\n");
exit (1);
}
mpfr_set_prec (x, 75);
mpfr_set_prec (y, 85);
mpfr_set_str_binary (x, "0.111110111111010011101011001100001010011110101010011111010010111101010001011E15");
mpfr_erfc (y, x, MPFR_RNDN);
if (mpfr_cmp_ui (y, 0) || mpfr_sgn (y) < 0)
{
printf ("mpfr_erfc failed for large x (3b)\n");
exit (1);
}
mpfr_set_prec (x, 2);
mpfr_set_prec (y, 21);
mpfr_set_str_binary (x, "-1.0e3");
mpfr_clear_flags ();
mpfr_erfc (y, x, MPFR_RNDZ);
flags = __gmpfr_flags;
mpfr_set_prec (x, 21);
mpfr_set_str_binary (x, "1.11111111111111111111");
if (mpfr_cmp (x, y) != 0)
{
printf ("mpfr_erfc failed for large x (4)\n");
exit (1);
}
if (flags != MPFR_FLAGS_INEXACT)
{
printf ("mpfr_erfc sets incorrect flags for large x (4)\n");
printf ("Expected %u, got %u\n",
(unsigned int) MPFR_FLAGS_INEXACT, flags);
exit (1);
}
mpfr_set_prec (x, 2);
mpfr_set_prec (y, 31);
mpfr_set_str_binary (x, "-1.0e3");
mpfr_clear_flags ();
mpfr_erfc (y, x, MPFR_RNDZ);
flags = __gmpfr_flags;
mpfr_set_prec (x, 31);
mpfr_set_str_binary (x, "1.111111111111111111111111111111");
if (mpfr_cmp (x, y) != 0)
{
printf ("mpfr_erfc failed for x=-8, prec=31 (5)\n");
printf ("expected "); mpfr_dump (x);
printf ("got "); mpfr_dump (y);
exit (1);
}
if (flags != MPFR_FLAGS_INEXACT)
{
printf ("mpfr_erfc sets incorrect flags for large x (5)\n");
printf ("Expected %u, got %u\n",
(unsigned int) MPFR_FLAGS_INEXACT, flags);
exit (1);
}
/* Reported by Christopher Creutzig on 2007-07-10. */
mpfr_set_prec (x, 53);
mpfr_set_prec (y, 53);
mpfr_set_si_2exp (x, 54563, -1, MPFR_RNDN);
mpfr_erfc (y, x, MPFR_RNDZ);
mpfr_set_ui (x, 0, MPFR_RNDN);
if (! mpfr_equal_p (y, x))
{
printf ("mpfr_erfc failed for x=27281.5, prec=53 (6)\n");
printf ("expected "); mpfr_dump (x);
printf ("got "); mpfr_dump (y);
exit (1);
}
/* same test with rounding away from zero */
mpfr_set_si_2exp (x, 54563, -1, MPFR_RNDN);
mpfr_erfc (y, x, MPFR_RNDU);
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_nextabove (x);
if (! mpfr_equal_p (y, x))
{
printf ("mpfr_erfc failed for x=27281.5, prec=53 (7)\n");
printf ("expected "); mpfr_dump (x);
printf ("got "); mpfr_dump (y);
exit (1);
}
mpfr_clear (x);
mpfr_clear (y);
}
static void
test_overflow2 (void)
{
mpfr_t x, y, z, r;
int i, inex, rnd, err = 0;
mpfr_inits2 (8, x, y, z, r, (void *) 0);
MPFR_SET_POS (x);
mpfr_setmin (x, mpfr_get_emax ()); /* x = 0.1@emax */
mpfr_set_si (y, -2, GMP_RNDN); /* y = -2 */
/* The intermediate multiplication x * y will overflow. */
for (i = -9; i <= 9; i++)
RND_LOOP (rnd)
{
int inf, overflow;
inf = rnd == GMP_RNDN || rnd == GMP_RNDD;
overflow = inf || i <= 0;
inex = mpfr_set_si_2exp (z, i, mpfr_get_emin (), GMP_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, 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 (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 (rnd));
err = 1;
}
if (mpfr_nan_p (r))
{
printf ("Error in test_overflow2 (i = %d, %s): got NaN\n",
i, mpfr_print_rnd_mode (rnd));
err = 1;
}
else if (MPFR_SIGN (r) >= 0)
{
printf ("Error in test_overflow2 (i = %d, %s): wrong sign "
"(+ instead of -)\n", i, mpfr_print_rnd_mode (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 (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 (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 (rnd), inex);
err = 1;
}
}
if (err)
exit (1);
mpfr_clears (x, y, z, r, (void *) 0);
}
int
mpfr_pow_si (mpfr_ptr y, mpfr_srcptr x, long int n, mp_rnd_t rnd)
{
if (n >= 0)
return mpfr_pow_ui (y, x, n, rnd);
else
{
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
{
if (MPFR_IS_NAN (x))
{
MPFR_SET_NAN (y);
MPFR_RET_NAN;
}
else if (MPFR_IS_INF (x))
{
MPFR_SET_ZERO (y);
if (MPFR_IS_POS (x) || ((unsigned) n & 1) == 0)
MPFR_SET_POS (y);
else
MPFR_SET_NEG (y);
MPFR_RET (0);
}
else /* x is zero */
{
MPFR_ASSERTD (MPFR_IS_ZERO (x));
MPFR_SET_INF(y);
if (MPFR_IS_POS (x) || ((unsigned) n & 1) == 0)
MPFR_SET_POS (y);
else
MPFR_SET_NEG (y);
MPFR_RET(0);
}
}
MPFR_CLEAR_FLAGS (y);
/* detect exact powers: x^(-n) is exact iff x is a power of 2 */
if (mpfr_cmp_si_2exp (x, MPFR_SIGN(x), MPFR_EXP(x) - 1) == 0)
{
mp_exp_t expx = MPFR_EXP (x) - 1, expy;
MPFR_ASSERTD (n < 0);
/* Warning: n * expx may overflow!
* Some systems (apparently alpha-freebsd) abort with
* LONG_MIN / 1, and LONG_MIN / -1 is undefined.
* Proof of the overflow checking. The expressions below are
* assumed to be on the rational numbers, but the word "overflow"
* still has its own meaning in the C context. / still denotes
* the integer (truncated) division, and // denotes the exact
* division.
* - First, (__gmpfr_emin - 1) / n and (__gmpfr_emax - 1) / n
* cannot overflow due to the constraints on the exponents of
* MPFR numbers.
* - If n = -1, then n * expx = - expx, which is representable
* because of the constraints on the exponents of MPFR numbers.
* - If expx = 0, then n * expx = 0, which is representable.
* - If n < -1 and expx > 0:
* + If expx > (__gmpfr_emin - 1) / n, then
* expx >= (__gmpfr_emin - 1) / n + 1
* > (__gmpfr_emin - 1) // n,
* and
* n * expx < __gmpfr_emin - 1,
* i.e.
* n * expx <= __gmpfr_emin - 2.
* This corresponds to an underflow, with a null result in
* the rounding-to-nearest mode.
* + If expx <= (__gmpfr_emin - 1) / n, then n * expx cannot
* overflow since 0 < expx <= (__gmpfr_emin - 1) / n and
* 0 > n * expx >= n * ((__gmpfr_emin - 1) / n)
* >= __gmpfr_emin - 1.
* - If n < -1 and expx < 0:
* + If expx < (__gmpfr_emax - 1) / n, then
* expx <= (__gmpfr_emax - 1) / n - 1
* < (__gmpfr_emax - 1) // n,
* and
* n * expx > __gmpfr_emax - 1,
* i.e.
* n * expx >= __gmpfr_emax.
* This corresponds to an overflow (2^(n * expx) has an
* exponent > __gmpfr_emax).
* + If expx >= (__gmpfr_emax - 1) / n, then n * expx cannot
* overflow since 0 > expx >= (__gmpfr_emax - 1) / n and
* 0 < n * expx <= n * ((__gmpfr_emax - 1) / n)
* <= __gmpfr_emax - 1.
* Note: one could use expx bounds based on MPFR_EXP_MIN and
* MPFR_EXP_MAX instead of __gmpfr_emin and __gmpfr_emax. The
* current bounds do not lead to noticeably slower code and
* allow us to avoid a bug in Sun's compiler for Solaris/x86
* (when optimizations are enabled).
*/
expy =
n != -1 && expx > 0 && expx > (__gmpfr_emin - 1) / n ?
MPFR_EMIN_MIN - 2 /* Underflow */ :
n != -1 && expx < 0 && expx < (__gmpfr_emax - 1) / n ?
MPFR_EMAX_MAX /* Overflow */ : n * expx;
return mpfr_set_si_2exp (y, n % 2 ? MPFR_INT_SIGN (x) : 1,
expy, rnd);
}
/* General case */
{
/* Declaration of the intermediary variable */
mpfr_t t;
/* Declaration of the size variable */
mp_prec_t Ny = MPFR_PREC (y); /* target precision */
mp_prec_t Nt; /* working precision */
mp_exp_t err; /* error */
int inexact;
unsigned long abs_n;
MPFR_SAVE_EXPO_DECL (expo);
MPFR_ZIV_DECL (loop);
abs_n = - (unsigned long) n;
/* compute the precision of intermediary variable */
/* the optimal number of bits : see algorithms.tex */
Nt = Ny + 3 + MPFR_INT_CEIL_LOG2 (Ny);
MPFR_SAVE_EXPO_MARK (expo);
/* initialise of intermediary variable */
mpfr_init2 (t, Nt);
MPFR_ZIV_INIT (loop, Nt);
for (;;)
{
/* compute 1/(x^n), with n > 0 */
mpfr_pow_ui (t, x, abs_n, GMP_RNDN);
mpfr_ui_div (t, 1, t, GMP_RNDN);
/* FIXME: old code improved, but I think this is still incorrect. */
if (MPFR_UNLIKELY (MPFR_IS_ZERO (t)))
{
MPFR_ZIV_FREE (loop);
mpfr_clear (t);
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_underflow (y, rnd == GMP_RNDN ? GMP_RNDZ : rnd,
abs_n & 1 ? MPFR_SIGN (x) :
MPFR_SIGN_POS);
}
if (MPFR_UNLIKELY (MPFR_IS_INF (t)))
{
MPFR_ZIV_FREE (loop);
mpfr_clear (t);
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_overflow (y, rnd, abs_n & 1 ? MPFR_SIGN (x) :
MPFR_SIGN_POS);
}
/* error estimate -- see pow function in algorithms.ps */
err = Nt - 3;
if (MPFR_LIKELY (MPFR_CAN_ROUND (t, err, Ny, rnd)))
break;
/* actualisation of the precision */
Nt += BITS_PER_MP_LIMB;
mpfr_set_prec (t, Nt);
}
MPFR_ZIV_FREE (loop);
inexact = mpfr_set (y, t, rnd);
mpfr_clear (t);
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range (y, inexact, rnd);
}
}
}
static int
tiny_aux (int stop, mpfr_exp_t e)
{
mpfr_t x, y, z;
int r, s, spm, inex, err = 0;
int expected_dir[2][5] = { { 1, -1, 1, -1, 1 }, { 1, 1, 1, -1, -1 } };
mpfr_exp_t saved_emax;
saved_emax = mpfr_get_emax ();
mpfr_init2 (x, 32);
mpfr_inits2 (8, y, z, (mpfr_ptr) 0);
mpfr_set_ui_2exp (x, 1, e, MPFR_RNDN);
spm = 1;
for (s = 0; s < 2; s++)
{
RND_LOOP(r)
{
mpfr_rnd_t rr = (mpfr_rnd_t) r;
mpfr_exp_t exponent, emax;
/* Exponent of the rounded value in unbounded exponent range. */
exponent = expected_dir[s][r] < 0 && s == 0 ? - e : 1 - e;
for (emax = exponent - 1; emax <= exponent; emax++)
{
unsigned int flags, expected_flags = MPFR_FLAGS_INEXACT;
int overflow, expected_inex = expected_dir[s][r];
if (emax > MPFR_EMAX_MAX)
break;
mpfr_set_emax (emax);
mpfr_clear_flags ();
inex = mpfr_gamma (y, x, rr);
flags = __gmpfr_flags;
mpfr_clear_flags ();
mpfr_set_si_2exp (z, spm, - e, MPFR_RNDU);
overflow = mpfr_overflow_p ();
/* z is 1/x - euler rounded toward +inf */
if (overflow && rr == MPFR_RNDN && s == 1)
expected_inex = -1;
if (expected_inex < 0)
mpfr_nextbelow (z); /* 1/x - euler rounded toward -inf */
if (exponent > emax)
expected_flags |= MPFR_FLAGS_OVERFLOW;
if (!(mpfr_equal_p (y, z) && flags == expected_flags
&& SAME_SIGN (inex, expected_inex)))
{
printf ("Error in tiny for s = %d, r = %s, emax = %"
MPFR_EXP_FSPEC "d%s\n on ",
s, mpfr_print_rnd_mode (rr), emax,
exponent > emax ? " (overflow)" : "");
mpfr_dump (x);
printf (" expected inex = %2d, ", expected_inex);
mpfr_dump (z);
printf (" got inex = %2d, ", SIGN (inex));
mpfr_dump (y);
printf (" expected flags = %u, got %u\n",
expected_flags, flags);
if (stop)
exit (1);
err = 1;
}
}
}
mpfr_neg (x, x, MPFR_RNDN);
spm = - spm;
}
mpfr_clears (x, y, z, (mpfr_ptr) 0);
mpfr_set_emax (saved_emax);
return err;
}
static void
check_intmax (void)
{
#ifdef _MPFR_H_HAVE_INTMAX_T
mpfr_t x, y;
int i, r;
mpfr_init2 (x, sizeof (uintmax_t) * CHAR_BIT);
mpfr_init2 (y, 8);
RND_LOOP (r)
{
/* Check NAN */
mpfr_set_nan (x);
if (mpfr_fits_uintmax_p (x, (mpfr_rnd_t) r))
ERROR1 (52);
if (mpfr_fits_intmax_p (x, (mpfr_rnd_t) r))
ERROR1 (53);
/* Check INF */
mpfr_set_inf (x, 1);
if (mpfr_fits_uintmax_p (x, (mpfr_rnd_t) r))
ERROR1 (54);
if (mpfr_fits_intmax_p (x, (mpfr_rnd_t) r))
ERROR1 (55);
/* Check Zero */
MPFR_SET_ZERO (x);
if (!mpfr_fits_uintmax_p (x, (mpfr_rnd_t) r))
ERROR1 (56);
if (!mpfr_fits_intmax_p (x, (mpfr_rnd_t) r))
ERROR1 (57);
/* Check positive small op */
mpfr_set_str1 (x, "1@-1");
if (!mpfr_fits_uintmax_p (x, (mpfr_rnd_t) r))
ERROR1 (58);
if (!mpfr_fits_intmax_p (x, (mpfr_rnd_t) r))
ERROR1 (59);
/* Check 17 */
mpfr_set_ui (x, 17, MPFR_RNDN);
if (!mpfr_fits_uintmax_p (x, (mpfr_rnd_t) r))
ERROR1 (60);
if (!mpfr_fits_intmax_p (x, (mpfr_rnd_t) r))
ERROR1 (61);
/* Check hugest */
mpfr_set_ui_2exp (x, 42, sizeof (uintmax_t) * 32, MPFR_RNDN);
if (mpfr_fits_uintmax_p (x, (mpfr_rnd_t) r))
ERROR1 (62);
if (mpfr_fits_intmax_p (x, (mpfr_rnd_t) r))
ERROR1 (63);
/* Check all other values */
mpfr_set_uj (x, MPFR_UINTMAX_MAX, MPFR_RNDN);
mpfr_add_ui (x, x, 1, MPFR_RNDN);
if (mpfr_fits_uintmax_p (x, (mpfr_rnd_t) r))
ERROR1 (64);
mpfr_set_uj (x, MPFR_UINTMAX_MAX, MPFR_RNDN);
if (!mpfr_fits_uintmax_p (x, (mpfr_rnd_t) r))
ERROR1 (65);
mpfr_set_sj (x, MPFR_INTMAX_MAX, MPFR_RNDN);
mpfr_add_ui (x, x, 1, MPFR_RNDN);
if (mpfr_fits_intmax_p (x, (mpfr_rnd_t) r))
ERROR1 (66);
mpfr_set_sj (x, MPFR_INTMAX_MAX, MPFR_RNDN);
if (!mpfr_fits_intmax_p (x, (mpfr_rnd_t) r))
ERROR1 (67);
mpfr_set_sj (x, MPFR_INTMAX_MIN, MPFR_RNDN);
if (!mpfr_fits_intmax_p (x, (mpfr_rnd_t) r))
ERROR1 (68);
mpfr_sub_ui (x, x, 1, MPFR_RNDN);
if (mpfr_fits_intmax_p (x, (mpfr_rnd_t) r))
ERROR1 (69);
/* Check negative op */
for (i = 1; i <= 4; i++)
{
int inv;
mpfr_set_si_2exp (x, -i, -2, MPFR_RNDN);
mpfr_rint (y, x, (mpfr_rnd_t) r);
inv = MPFR_NOTZERO (y);
if (!mpfr_fits_uintmax_p (x, (mpfr_rnd_t) r) ^ inv)
ERROR1 (70);
if (!mpfr_fits_intmax_p (x, (mpfr_rnd_t) r))
ERROR1 (71);
}
}
mpfr_clear (x);
mpfr_clear (y);
#endif
}
int
main (void)
{
mpfr_t x, y;
float f, g, infp;
int i;
infp = (float) DBL_POS_INF;
if (infp * 0.5 != infp)
{
fprintf (stderr, "Error, FLT_MAX + FLT_MAX does not yield INFP\n");
fprintf (stderr, "(this is probably a compiler bug, please report)\n");
exit (1);
}
tests_start_mpfr ();
mpfr_init2 (x, 24);
mpfr_init2 (y, 24);
#if !defined(MPFR_ERRDIVZERO)
mpfr_set_nan (x);
f = mpfr_get_flt (x, MPFR_RNDN);
if (f == f)
{
printf ("Error for mpfr_get_flt(NaN)\n");
exit (1);
}
mpfr_set_flt (x, f, MPFR_RNDN);
if (mpfr_nan_p (x) == 0)
{
printf ("Error for mpfr_set_flt(NaN)\n");
exit (1);
}
mpfr_set_inf (x, 1);
f = mpfr_get_flt (x, MPFR_RNDN);
mpfr_set_flt (x, f, MPFR_RNDN);
if (mpfr_inf_p (x) == 0 || mpfr_sgn (x) < 0)
{
printf ("Error for mpfr_set_flt(mpfr_get_flt(+Inf)):\n");
printf ("f=%f, expected -Inf\n", f);
printf ("got "); mpfr_dump (x);
exit (1);
}
mpfr_set_inf (x, -1);
f = mpfr_get_flt (x, MPFR_RNDN);
mpfr_set_flt (x, f, MPFR_RNDN);
if (mpfr_inf_p (x) == 0 || mpfr_sgn (x) > 0)
{
printf ("Error for mpfr_set_flt(mpfr_get_flt(-Inf)):\n");
printf ("f=%f, expected -Inf\n", f);
printf ("got "); mpfr_dump (x);
exit (1);
}
#endif
mpfr_set_ui (x, 0, MPFR_RNDN);
f = mpfr_get_flt (x, MPFR_RNDN);
mpfr_set_flt (x, f, MPFR_RNDN);
if (mpfr_zero_p (x) == 0 || MPFR_SIGN (x) < 0)
{
printf ("Error for mpfr_set_flt(mpfr_get_flt(+0))\n");
exit (1);
}
#ifdef HAVE_SIGNEDZ
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_neg (x, x, MPFR_RNDN);
f = mpfr_get_flt (x, MPFR_RNDN);
mpfr_set_flt (x, f, MPFR_RNDN);
if (mpfr_zero_p (x) == 0 || MPFR_SIGN (x) > 0)
{
printf ("Error for mpfr_set_flt(mpfr_get_flt(-0))\n");
exit (1);
}
#endif /* HAVE_SIGNEDZ */
mpfr_set_ui (x, 17, MPFR_RNDN);
f = mpfr_get_flt (x, MPFR_RNDN);
mpfr_set_flt (x, f, MPFR_RNDN);
if (mpfr_cmp_ui (x, 17) != 0)
{
printf ("Error for mpfr_set_flt(mpfr_get_flt(17))\n");
printf ("expected 17\n");
printf ("got ");
mpfr_dump (x);
exit (1);
}
mpfr_set_si (x, -42, MPFR_RNDN);
f = mpfr_get_flt (x, MPFR_RNDN);
mpfr_set_flt (x, f, MPFR_RNDN);
if (mpfr_cmp_si (x, -42) != 0)
{
printf ("Error for mpfr_set_flt(mpfr_get_flt(-42))\n");
printf ("expected -42\n");
printf ("got ");
mpfr_dump (x);
exit (1);
}
mpfr_set_si_2exp (x, 1, -126, MPFR_RNDN);
for (i = -126; i < 128; i++)
{
f = mpfr_get_flt (x, MPFR_RNDN);
mpfr_set_flt (y, f, MPFR_RNDN);
if (mpfr_cmp (x, y) != 0)
{
printf ("Error for mpfr_set_flt(mpfr_get_flt(x))\n");
printf ("expected "); mpfr_dump (x);
printf ("got "); mpfr_dump (y);
exit (1);
}
mpfr_mul_2exp (x, x, 1, MPFR_RNDN);
}
mpfr_set_prec (x, 53);
mpfr_set_si_2exp (x, 1, -126, MPFR_RNDN);
for (i = -126; i < 128; i++)
{
mpfr_nextbelow (x);
f = mpfr_get_flt (x, MPFR_RNDN);
mpfr_nextabove (x);
mpfr_set_flt (y, f, MPFR_RNDN);
if (mpfr_cmp (x, y) != 0)
{
printf ("Error for mpfr_set_flt(mpfr_get_flt(x))\n");
printf ("expected "); mpfr_dump (x);
printf ("got "); mpfr_dump (y);
exit (1);
}
mpfr_mul_2exp (x, x, 1, MPFR_RNDN);
}
mpfr_set_prec (x, 53);
mpfr_set_si_2exp (x, 1, -126, MPFR_RNDN);
for (i = -126; i < 128; i++)
{
mpfr_nextabove (x);
f = mpfr_get_flt (x, MPFR_RNDN);
mpfr_nextbelow (x);
mpfr_set_flt (y, f, MPFR_RNDN);
if (mpfr_cmp (x, y) != 0)
{
printf ("Error for mpfr_set_flt(mpfr_get_flt(x))\n");
printf ("expected "); mpfr_dump (x);
printf ("got "); mpfr_dump (y);
exit (1);
}
mpfr_mul_2exp (x, x, 1, MPFR_RNDN);
}
mpfr_set_si_2exp (x, 1, -150, MPFR_RNDN);
g = 0.0;
f = mpfr_get_flt (x, MPFR_RNDN);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^(-150),RNDN)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDZ);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^(-150),RNDZ)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDD);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^(-150),RNDD)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
g = FLT_MIN * FLT_EPSILON;
f = mpfr_get_flt (x, MPFR_RNDU);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^(-150),RNDU)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDA);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^(-150),RNDA)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
mpfr_set_si_2exp (x, 1, -151, MPFR_RNDN);
g = 0.0;
f = mpfr_get_flt (x, MPFR_RNDN);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^(-151),RNDN)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDZ);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^(-151),RNDZ)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDD);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^(-151),RNDD)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
g = FLT_MIN * FLT_EPSILON;
f = mpfr_get_flt (x, MPFR_RNDU);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^(-151),RNDU)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDA);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^(-151),RNDA)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
mpfr_set_si_2exp (x, 1, -149, MPFR_RNDN);
g = FLT_MIN * FLT_EPSILON;
f = mpfr_get_flt (x, MPFR_RNDN);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^(-149),RNDN)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDZ);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^(-149),RNDZ)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDD);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^(-149),RNDD)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDU);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^(-149),RNDU)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDA);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^(-149),RNDA)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
mpfr_set_si_2exp (x, 1, 128, MPFR_RNDN);
g = FLT_MAX;
f = mpfr_get_flt (x, MPFR_RNDZ);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^128,RNDZ)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDD);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^128,RNDD)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
#if !defined(MPFR_ERRDIVZERO)
f = mpfr_get_flt (x, MPFR_RNDN); /* 2^128 rounds to itself with extended
exponent range, we should get +Inf */
g = infp;
if (f != g)
{
printf ("Error for mpfr_get_flt(2^128,RNDN)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDU);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^128,RNDU)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDA);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^128,RNDA)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
#endif
/* corner case: take x with 25 bits just below 2^128 */
mpfr_set_prec (x, 25);
mpfr_set_si_2exp (x, 1, 128, MPFR_RNDN);
mpfr_nextbelow (x);
g = FLT_MAX;
f = mpfr_get_flt (x, MPFR_RNDZ);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^128*(1-2^(-25)),RNDZ)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDD);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^128*(1-2^(-25)),RNDD)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDN); /* first round to 2^128 (even rule),
thus we should get +Inf */
g = infp;
if (f != g)
{
printf ("Error for mpfr_get_flt(2^128*(1-2^(-25)),RNDN)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDU);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^128*(1-2^(-25)),RNDU)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDA);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^128*(1-2^(-25)),RNDA)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
mpfr_clear (x);
mpfr_clear (y);
tests_end_mpfr ();
return 0;
}
int
mpfr_set_si (mpfr_ptr x, long i, mpfr_rnd_t rnd_mode)
{
return mpfr_set_si_2exp (x, i, 0, rnd_mode);
}