static void
regular (void)
{
mpfr_t x, y, r;
mpfr_inits (x, y, r, (mpfr_ptr) 0);
/* remainder = 0 */
mpfr_set_str (y, "FEDCBA987654321p-64", 16, MPFR_RNDN);
mpfr_pow_ui (x, y, 42, MPFR_RNDN);
check (r, x, y, MPFR_RNDN);
/* x < y */
mpfr_set_ui_2exp (x, 64723, -19, MPFR_RNDN);
mpfr_mul (x, x, y, MPFR_RNDN);
check (r, x, y, MPFR_RNDN);
/* sign(x) = sign (r) */
mpfr_set_ui (x, 123798, MPFR_RNDN);
mpfr_set_ui (y, 10, MPFR_RNDN);
check (r, x, y, MPFR_RNDN);
/* huge difference between precisions */
mpfr_set_prec (x, 314);
mpfr_set_prec (y, 8);
mpfr_set_prec (r, 123);
mpfr_const_pi (x, MPFR_RNDD); /* x = pi */
mpfr_set_ui_2exp (y, 1, 3, MPFR_RNDD); /* y = 1/8 */
check (r, x, y, MPFR_RNDD);
mpfr_clears (x, y, r, (mpfr_ptr) 0);
}
/* Test case bk == 0 in add1.c (b has entirely been read and
c hasn't been taken into account). */
static void
coverage_bk_eq_0 (void)
{
mpfr_t a, b, c;
int inex;
mpfr_init2 (a, GMP_NUMB_BITS);
mpfr_init2 (b, 2 * GMP_NUMB_BITS);
mpfr_init2 (c, GMP_NUMB_BITS);
mpfr_set_ui_2exp (b, 1, 2 * GMP_NUMB_BITS, MPFR_RNDN);
mpfr_sub_ui (b, b, 1, MPFR_RNDN);
/* b = 111...111 (in base 2) where the 1's fit 2 whole limbs */
mpfr_set_ui_2exp (c, 1, -1, MPFR_RNDN); /* c = 1/2 */
inex = mpfr_add (a, b, c, MPFR_RNDU);
mpfr_set_ui_2exp (c, 1, 2 * GMP_NUMB_BITS, MPFR_RNDN);
if (! mpfr_equal_p (a, c))
{
printf ("Error in coverage_bk_eq_0\n");
printf ("Expected ");
mpfr_dump (c);
printf ("Got ");
mpfr_dump (a);
exit (1);
}
MPFR_ASSERTN (inex > 0);
mpfr_clear (a);
mpfr_clear (b);
mpfr_clear (c);
}
/* bug found in nightly tests */
static void
test20071214 (void)
{
mpfr_t a, b;
int inex;
mpfr_init2 (a, 4);
mpfr_init2 (b, 4);
mpfr_set_ui_2exp (a, 3, -4, MPFR_RNDN);
inex = mpfr_sin_cos (a, b, a, MPFR_RNDD);
MPFR_ASSERTN(mpfr_cmp_ui_2exp (a, 11, -6) == 0);
MPFR_ASSERTN(mpfr_cmp_ui_2exp (b, 15, -4) == 0);
MPFR_ASSERTN(inex == 10);
mpfr_set_ui_2exp (a, 3, -4, MPFR_RNDN);
inex = mpfr_sin_cos (a, b, a, MPFR_RNDU);
MPFR_ASSERTN(mpfr_cmp_ui_2exp (a, 3, -4) == 0);
MPFR_ASSERTN(mpfr_cmp_ui (b, 1) == 0);
MPFR_ASSERTN(inex == 5);
mpfr_set_ui_2exp (a, 3, -4, MPFR_RNDN);
inex = mpfr_sin_cos (a, b, a, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui_2exp (a, 3, -4) == 0);
MPFR_ASSERTN(mpfr_cmp_ui (b, 1) == 0);
MPFR_ASSERTN(inex == 5);
mpfr_clear (a);
mpfr_clear (b);
}
/* Bug found by Jakub Jelinek
* http://bugzilla.redhat.com/643657
* https://gforge.inria.fr/tracker/index.php?func=detail&aid=11301
* The consequence can be either an assertion failure (i = 2 in the
* testcase below, in debug mode) or an incorrectly rounded value.
*/
static void
bug20101017 (void)
{
mpfr_t a, b, c;
int inex;
int i;
mpfr_init2 (a, GMP_NUMB_BITS * 2);
mpfr_init2 (b, GMP_NUMB_BITS);
mpfr_init2 (c, GMP_NUMB_BITS);
/* a = 2^(2N) + k.2^(2N-1) + 2^N and b = 1
with N = GMP_NUMB_BITS and k = 0 or 1.
c = a - b should round to the same value as a. */
for (i = 2; i <= 3; i++)
{
mpfr_set_ui_2exp (a, i, GMP_NUMB_BITS - 1, MPFR_RNDN);
mpfr_add_ui (a, a, 1, MPFR_RNDN);
mpfr_mul_2ui (a, a, GMP_NUMB_BITS, MPFR_RNDN);
mpfr_set_ui (b, 1, MPFR_RNDN);
inex = mpfr_sub (c, a, b, MPFR_RNDN);
mpfr_set (b, a, MPFR_RNDN);
if (! mpfr_equal_p (c, b))
{
printf ("Error in bug20101017 for i = %d.\n", i);
printf ("Expected ");
mpfr_out_str (stdout, 16, 0, b, MPFR_RNDN);
putchar ('\n');
printf ("Got ");
mpfr_out_str (stdout, 16, 0, c, MPFR_RNDN);
putchar ('\n');
exit (1);
}
if (inex >= 0)
{
printf ("Error in bug20101017 for i = %d: bad inex value.\n", i);
printf ("Expected negative, got %d.\n", inex);
exit (1);
}
}
mpfr_set_prec (a, 64);
mpfr_set_prec (b, 129);
mpfr_set_prec (c, 2);
mpfr_set_str_binary (b, "0.100000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000001E65");
mpfr_set_str_binary (c, "0.10E1");
inex = mpfr_sub (a, b, c, MPFR_RNDN);
if (mpfr_cmp_ui_2exp (a, 1, 64) != 0 || inex >= 0)
{
printf ("Error in mpfr_sub for b-c for b=2^64+1+2^(-64), c=1\n");
printf ("Expected result 2^64 with inex < 0\n");
printf ("Got ");
mpfr_print_binary (a);
printf (" with inex=%d\n", inex);
exit (1);
}
mpfr_clears (a, b, c, (mpfr_ptr) 0);
}
/* tests intermediate underflow; WONTFIX */
static int
test_underflow (void)
{
mpc_t z;
mpfr_exp_t emin = mpfr_get_emin ();
mpfr_set_emin (-10);
mpc_init2 (z, 21);
mpfr_set_si (mpc_realref(z), -1, GMP_RNDZ);
mpfr_set_ui_2exp (mpc_imagref(z), 1, 20, GMP_RNDZ);
mpfr_add_ui (mpc_imagref(z), mpc_imagref(z), 1, GMP_RNDZ);
mpfr_div_2exp (mpc_imagref(z), mpc_imagref(z), 20, GMP_RNDZ);
mpc_atan (z, z, MPC_RNDNN);
if (mpfr_cmp_si_2exp (mpc_realref(z), -1066635, 20) != 0 ||
mpfr_cmp_si_2exp (mpc_imagref(z), 1687619, 22))
{
printf ("Error in test_coverage\n");
printf ("expected (-1066635/2^20 1687619/2^22)\n");
printf ("got ");
mpc_out_str (stdout, 10, 20, z, MPC_RNDNN);
printf ("\n");
exit (1);
}
mpc_clear (z);
mpfr_set_emin (emin);
}
/* From a bug reported by Joseph S. Myers
https://sympa.inria.fr/sympa/arc/mpfr/2012-08/msg00005.html */
static void
bug20120814 (void)
{
mpfr_exp_t emin = -30, e;
mpfr_t x, y;
int r;
char s[64], *p;
mpfr_init2 (x, 2);
mpfr_set_ui_2exp (x, 3, emin - 2, MPFR_RNDN);
mpfr_get_str (s + 1, &e, 10, 19, x, MPFR_RNDD);
s[0] = s[1];
s[1] = '.';
for (p = s; *p != 0; p++) ;
*p = 'e';
sprintf (p + 1, "%d", (int) e - 1);
mpfr_init2 (y, 4);
r = mpfr_strtofr (y, s, NULL, 0, MPFR_RNDN);
if (r <= 0 || ! mpfr_equal_p (x, y))
{
printf ("Error in bug20120814\n");
printf ("mpfr_strtofr failed on string \"%s\"\n", s);
printf ("Expected inex > 0 and y = 0.1100E%d\n", (int) emin);
printf ("Got inex = %-6d and y = ", r);
mpfr_dump (y);
exit (1);
}
mpfr_clear (x);
mpfr_clear (y);
}
static void
reuse_bug (void)
{
/* bug found by the automatic builds on
http://hydra.nixos.org/build/1469029/log/raw */
mpc_t x, y, z;
mp_prec_t prec = 2;
for (prec = 2; prec <= 20; prec ++)
{
mpc_init2 (x, prec);
mpc_init2 (y, prec);
mpc_init2 (z, prec);
mpfr_set_ui (mpc_realref (x), 0ul, MPFR_RNDN);
mpfr_set_ui_2exp (mpc_imagref (x), 3ul, -2, MPFR_RNDN);
mpc_set_ui (y, 8ul, MPC_RNDNN);
mpc_pow (z, x, y, MPC_RNDNN);
mpc_pow (y, x, y, MPC_RNDNN);
if (mpfr_signbit (mpc_imagref (y)) != mpfr_signbit (mpc_imagref (z)))
{
printf ("Error: regression, reuse_bug reproduced\n");
exit (1);
}
mpc_clear (x);
mpc_clear (y);
mpc_clear (z);
}
}
static void
atan2_pow_of_2 (void)
{
mpfr_t x, y, r, g;
int i;
int d[] = { 0, -1, 1 };
int ntests = sizeof (d) / sizeof (int);
mpfr_init2 (x, 53);
mpfr_init2 (y, 53);
mpfr_init2 (r, 53);
mpfr_init2 (g, 53);
/* atan(42) */
mpfr_set_str_binary (g, "1100011000000011110011111001100110101000011010010011E-51");
for (i = 0; i < ntests; ++i)
{
mpfr_set_ui (y, 42, MPFR_RNDN);
mpfr_mul_2si (y, y, d[i], MPFR_RNDN);
mpfr_set_ui_2exp (x, 1, d[i], MPFR_RNDN);
mpfr_atan2 (r, y, x, MPFR_RNDN);
if (mpfr_equal_p (r, g) == 0)
{
printf ("Error in mpfr_atan2 (5)\n");
printf ("Expected "); mpfr_print_binary (g); printf ("\n");
printf ("Got "); mpfr_print_binary (r); printf ("\n");
exit (1);
}
}
mpfr_clear (x);
mpfr_clear (y);
mpfr_clear (r);
mpfr_clear (g);
}
/* bug reported by Eric Veach */
static void
bug20090519 (void)
{
mpfr_t x, y, r;
int inexact;
mpfr_inits2 (100, x, y, r, (mpfr_ptr) 0);
mpfr_set_prec (x, 3);
mpfr_set_prec (y, 3);
mpfr_set_prec (r, 3);
mpfr_set_si (x, 8, MPFR_RNDN);
mpfr_set_si (y, 7, MPFR_RNDN);
check (r, x, y, MPFR_RNDN);
mpfr_set_prec (x, 10);
mpfr_set_prec (y, 10);
mpfr_set_prec (r, 10);
mpfr_set_ui_2exp (x, 3, 26, MPFR_RNDN);
mpfr_set_si (y, (1 << 9) - 1, MPFR_RNDN);
check (r, x, y, MPFR_RNDN);
mpfr_set_prec (x, 100);
mpfr_set_prec (y, 100);
mpfr_set_prec (r, 100);
mpfr_set_str (x, "3.5", 10, MPFR_RNDN);
mpfr_set_str (y, "1.1", 10, MPFR_RNDN);
check (r, x, y, MPFR_RNDN);
/* double check, with a pre-computed value */
{
mpfr_t er;
mpfr_init2 (er, 100);
mpfr_set_str (er, "CCCCCCCCCCCCCCCCCCCCCCCC8p-102", 16, MPFR_RNDN);
inexact = mpfr_fmod (r, x, y, MPFR_RNDN);
if (!mpfr_equal_p (r, er) || inexact != 0)
test_failed (er, r, 0, inexact, x, y, MPFR_RNDN);
mpfr_clear (er);
}
mpfr_set_si (x, 20, MPFR_RNDN);
mpfr_set_ui_2exp (y, 1, 1, MPFR_RNDN); /* exact */
mpfr_sin (y, y, MPFR_RNDN);
check (r, x, y, MPFR_RNDN);
mpfr_clears(r, x, y, (mpfr_ptr) 0);
}
int main (int argc, char *argv[])
{
int dmax, n, p;
mpfr_t VARS;
if (argc != 3 && argc != 4)
{
fprintf (stderr, "Usage: divworst <dmax> <n> [ <p> ]\n");
exit (EXIT_FAILURE);
}
dmax = atoi (argv[1]);
n = atoi (argv[2]);
p = argc == 3 ? n : atoi (argv[3]);
if (p < n)
{
fprintf (stderr, "divworst: p must be greater or equal to n\n");
exit (EXIT_FAILURE);
}
mpfr_inits2 (n, PRECN, (mpfr_ptr) 0);
mpfr_init2 (t, p);
for (mpfr_set_ui_2exp (x, 1, -1, MPFR_RNDN);
mpfr_get_exp (x) <= dmax;
mpfr_nextabove (x))
for (mpfr_set_ui_2exp (y, 1, -1, MPFR_RNDN);
mpfr_get_exp (y) == 0;
mpfr_nextabove (y))
{
unsigned long rz, rn;
if (mpfr_sub (z, x, y, MPFR_RNDZ) != 0)
continue; /* x - y is not representable in precision n */
rz = eval (x, y, z, t, MPFR_RNDZ);
rn = eval (x, y, z, t, MPFR_RNDN);
if (rz == rn)
continue;
mpfr_printf ("x = %.*Rb ; y = %.*Rb ; Z: %lu ; N: %lu\n",
n - 1, x, n - 1, y, rz, rn);
}
mpfr_clears (VARS, (mpfr_ptr) 0);
return 0;
}
/* bug found by Kevin P. Rauch on 22 Oct 2007 */
static void
check3 (void)
{
mpfr_t x, y, z;
int tern;
mpfr_exp_t emin;
emin = mpfr_get_emin ();
mpfr_init2 (x, 32);
mpfr_init2 (y, 32);
mpfr_init2 (z, 32);
mpfr_set_ui (x, 0xBFFFFFFFU, MPFR_RNDN); /* 3221225471/2^32 */
mpfr_set_ui (y, 0x80000001U, MPFR_RNDN); /* 2147483649/2^32 */
mpfr_set_exp (x, 0);
mpfr_set_exp (y, 0);
mpfr_set_emin (-1);
/* the exact product is 6917529028714823679/2^64, which is rounded to
3/8 = 0.375, which is smaller, thus tern < 0 */
tern = mpfr_mul (z, x, y, MPFR_RNDN);
MPFR_ASSERTN (tern < 0 && mpfr_cmp_ui_2exp (z, 3, -3) == 0);
tern = mpfr_subnormalize (z, tern, MPFR_RNDN);
/* since emin = -1, and EXP(z)=-1, z should be rounded to precision
EXP(z)-emin+1 = 1, i.e., z should be a multiple of the smallest possible
positive representable value with emin=-1, which is 1/4. The two
possible values are 1/4 and 2/4, which are at equal distance of z.
But since tern < 0, we should choose the largest value, i.e., 2/4. */
MPFR_ASSERTN (tern > 0 && mpfr_cmp_ui_2exp (z, 1, -1) == 0);
/* here is another test for the alternate case, where z was rounded up
first, thus we have to round down */
mpfr_set_str_binary (x, "0.11111111111010110101011011011011");
mpfr_set_str_binary (y, "0.01100000000001111100000000001110");
tern = mpfr_mul (z, x, y, MPFR_RNDN);
MPFR_ASSERTN (tern > 0 && mpfr_cmp_ui_2exp (z, 3, -3) == 0);
tern = mpfr_subnormalize (z, tern, MPFR_RNDN);
MPFR_ASSERTN (tern < 0 && mpfr_cmp_ui_2exp (z, 1, -2) == 0);
/* finally the case where z was exact, which we simulate here */
mpfr_set_ui_2exp (z, 3, -3, MPFR_RNDN);
tern = mpfr_subnormalize (z, 0, MPFR_RNDN);
MPFR_ASSERTN (tern > 0 && mpfr_cmp_ui_2exp (z, 1, -1) == 0);
mpfr_clear (x);
mpfr_clear (y);
mpfr_clear (z);
MPFR_ASSERTN (mpfr_get_emin () == -1);
set_emin (emin);
}
static int
mpfr_pow275 (mpfr_t y, mpfr_t x, mp_rnd_t r)
{
mpfr_t z;
int inex;
mpfr_init2 (z, 4);
mpfr_set_ui_2exp (z, 11, -2, GMP_RNDN);
inex = mpfr_pow (y, x, z, GMP_RNDN);
mpfr_clear (z);
return inex;
}
/* return add = 1 + floor(log(c^3*(13+m1))/log(2))
where c = (1+eps)*(1+eps*max(8,m1)),
m1 = 1 + max(1/eps,2*sd)*(1+eps),
eps = 2^(-precz-14)
sd = abs(s-1)
*/
static long
compute_add (mpfr_srcptr s, mpfr_prec_t precz)
{
mpfr_t t, u, m1;
long add;
mpfr_inits2 (64, t, u, m1, (mpfr_ptr) 0);
if (mpfr_cmp_ui (s, 1) >= 0)
mpfr_sub_ui (t, s, 1, MPFR_RNDU);
else
mpfr_ui_sub (t, 1, s, MPFR_RNDU);
/* now t = sd = abs(s-1), rounded up */
mpfr_set_ui_2exp (u, 1, - precz - 14, MPFR_RNDU);
/* u = eps */
/* since 1/eps = 2^(precz+14), if EXP(sd) >= precz+14, then
sd >= 1/2*2^(precz+14) thus 2*sd >= 2^(precz+14) >= 1/eps */
if (mpfr_get_exp (t) >= precz + 14)
mpfr_mul_2exp (t, t, 1, MPFR_RNDU);
else
mpfr_set_ui_2exp (t, 1, precz + 14, MPFR_RNDU);
/* now t = max(1/eps,2*sd) */
mpfr_add_ui (u, u, 1, MPFR_RNDU); /* u = 1+eps, rounded up */
mpfr_mul (t, t, u, MPFR_RNDU); /* t = max(1/eps,2*sd)*(1+eps) */
mpfr_add_ui (m1, t, 1, MPFR_RNDU);
if (mpfr_get_exp (m1) <= 3)
mpfr_set_ui (t, 8, MPFR_RNDU);
else
mpfr_set (t, m1, MPFR_RNDU);
/* now t = max(8,m1) */
mpfr_div_2exp (t, t, precz + 14, MPFR_RNDU); /* eps*max(8,m1) */
mpfr_add_ui (t, t, 1, MPFR_RNDU); /* 1+eps*max(8,m1) */
mpfr_mul (t, t, u, MPFR_RNDU); /* t = c */
mpfr_add_ui (u, m1, 13, MPFR_RNDU); /* 13+m1 */
mpfr_mul (u, u, t, MPFR_RNDU); /* c*(13+m1) */
mpfr_sqr (t, t, MPFR_RNDU); /* c^2 */
mpfr_mul (u, u, t, MPFR_RNDU); /* c^3*(13+m1) */
add = mpfr_get_exp (u);
mpfr_clears (t, u, m1, (mpfr_ptr) 0);
return add;
}
/* Since r10377, the following test causes a "too much memory" error
when MPFR is built with Debian's tcc 0.9.27~git20151227.933c223-1
on x86_64. The problem came from __gmpfr_ceil_log2, now fixed in
r10443 (according to the integer promotion rules, this appeared to
be a bug in tcc, not in MPFR; however relying on such an obscure
rule was not a good idea). */
static void
tcc_bug20160606 (void)
{
mpfr_t x, y;
int sign;
mpfr_init2 (x, 53);
mpfr_init2 (y, 53);
mpfr_set_ui_2exp (x, 1, -1, MPFR_RNDN);
mpfr_lgamma (y, &sign, x, MPFR_RNDN);
mpfr_clear (x);
mpfr_clear (y);
}
static void
bug_20090316 (FILE *fout)
{
mpfr_t x;
mpfr_init2 (x, 53);
/* bug 20090316: fixed in r6112 */
mpfr_set_ui_2exp (x, 0x60fa2916, -30, GMP_RNDN);
check (fout, "%-#.4095RDg\n", x);
mpfr_clear (x);
}
/* With pow.c r5497, the following test fails on a 64-bit Linux machine
* due to a double-rounding problem when rescaling the result:
* Error with underflow_up2 and extended exponent range
* x = 7.fffffffffffffff0@-1,
* y = 4611686018427387904, MPFR_RNDN
* Expected 1.0000000000000000@-1152921504606846976, inex = 1, flags = 9
* Got 0, inex = -1, flags = 9
* With pow_ui.c r5423, the following test fails on a 64-bit Linux machine
* as underflows and overflows are not handled correctly (the approximation
* error is ignored):
* Error with mpfr_pow_ui, flags cleared
* x = 7.fffffffffffffff0@-1,
* y = 4611686018427387904, MPFR_RNDN
* Expected 1.0000000000000000@-1152921504606846976, inex = 1, flags = 9
* Got 0, inex = -1, flags = 9
*/
static void
underflow_up2 (void)
{
mpfr_t x, y, z, z0, eps;
mpfr_exp_t n;
int inex;
int rnd;
n = 1 - mpfr_get_emin ();
MPFR_ASSERTN (n > 1);
if (n > ULONG_MAX)
return;
mpfr_init2 (eps, 2);
mpfr_set_ui_2exp (eps, 1, -1, MPFR_RNDN); /* 1/2 */
mpfr_div_ui (eps, eps, n, MPFR_RNDZ); /* 1/(2n) rounded toward zero */
mpfr_init2 (x, sizeof (unsigned long) * CHAR_BIT + 1);
inex = mpfr_ui_sub (x, 1, eps, MPFR_RNDN);
MPFR_ASSERTN (inex == 0); /* since n < 2^(size_of_long_in_bits) */
inex = mpfr_div_2ui (x, x, 1, MPFR_RNDN); /* 1/2 - eps/2 exactly */
MPFR_ASSERTN (inex == 0);
mpfr_init2 (y, sizeof (unsigned long) * CHAR_BIT);
inex = mpfr_set_ui (y, n, MPFR_RNDN);
MPFR_ASSERTN (inex == 0);
/* 0 < eps < 1 / (2n), thus (1 - eps)^n > 1/2,
and 1/2 (1/2)^n < (1/2 - eps/2)^n < (1/2)^n. */
mpfr_inits2 (64, z, z0, (mpfr_ptr) 0);
RND_LOOP (rnd)
{
unsigned int ufinex = MPFR_FLAGS_UNDERFLOW | MPFR_FLAGS_INEXACT;
int expected_inex;
char sy[256];
mpfr_set_ui (z0, 0, MPFR_RNDN);
expected_inex = rnd == MPFR_RNDN || rnd == MPFR_RNDU || rnd == MPFR_RNDA ?
(mpfr_nextabove (z0), 1) : -1;
sprintf (sy, "%lu", (unsigned long) n);
mpfr_clear_flags ();
inex = mpfr_pow (z, x, y, (mpfr_rnd_t) rnd);
cmpres (0, x, sy, (mpfr_rnd_t) rnd, z0, expected_inex, z, inex, ufinex,
"underflow_up2", "mpfr_pow");
test_others (NULL, sy, (mpfr_rnd_t) rnd, x, y, z, inex, ufinex,
"underflow_up2");
}
mpfr_clears (x, y, z, z0, eps, (mpfr_ptr) 0);
}
bool almostEqual(const M2::ARingRRR& R, int nbits, const M2::ARingRRR::ElementType& a, const M2::ARingRRR::ElementType& b)
{
mpfr_t epsilon;
mpfr_init2(epsilon, R.get_precision());
mpfr_set_ui_2exp(epsilon, 1, -nbits, GMP_RNDN);
M2::ARingRRR::ElementType c;
R.init(c);
R.subtract(c,a,b);
bool ret = mpfr_cmpabs(&c,epsilon) < 0;
R.clear(c);
mpfr_clear(epsilon);
return ret;
}
/* With MPFR 2.3.0, this yields an assertion failure in mpfr_acosh. */
static void
bug20070831 (void)
{
mpfr_t x, y, z;
int inex;
mpfr_init2 (x, 256);
mpfr_init2 (y, 32);
mpfr_init2 (z, 32);
mpfr_set_ui (x, 1, GMP_RNDN);
mpfr_nextabove (x);
inex = mpfr_acosh (y, x, GMP_RNDZ);
mpfr_set_ui_2exp (z, 1, -127, GMP_RNDN);
mpfr_nextbelow (z);
if (!mpfr_equal_p (y, z))
{
printf ("Error in bug20070831 (1):\nexpected ");
mpfr_dump (z);
printf ("got ");
mpfr_dump (y);
exit (1);
}
MPFR_ASSERTN (inex < 0);
mpfr_nextabove (x);
mpfr_set_prec (y, 29);
inex = mpfr_acosh (y, x, GMP_RNDN);
mpfr_set_str_binary (z, "1.011010100000100111100110011E-127");
if (!mpfr_equal_p (y, z))
{
printf ("Error in bug20070831 (2):\nexpected ");
mpfr_dump (z);
printf ("got ");
mpfr_dump (y);
exit (1);
}
MPFR_ASSERTN (inex < 0);
mpfr_clears (x, y, z, (mpfr_ptr) 0);
}
static void
huge (void)
{
mpfr_t x, y, z;
int inex;
/* TODO: extend the exponent range and use mpfr_get_emax (). */
mpfr_inits2 (32, x, y, z, (mpfr_ptr) 0);
mpfr_set_ui_2exp (x, 1, 1073741822, GMP_RNDN);
inex = mpfr_acosh (y, x, GMP_RNDN);
mpfr_set_str_binary (z, "0.10110001011100100001011111110101E30");
if (!mpfr_equal_p (y, z))
{
printf ("Error in huge:\nexpected ");
mpfr_dump (z);
printf ("got ");
mpfr_dump (y);
exit (1);
}
MPFR_ASSERTN (inex < 0);
mpfr_clears (x, y, z, (mpfr_ptr) 0);
}
static void
x_near_one (void)
{
mpfr_t x, y, z;
int inex;
mpfr_init2 (x, 32);
mpfr_init2 (y, 4);
mpfr_init2 (z, 33);
mpfr_set_ui (x, 1, GMP_RNDN);
mpfr_nextbelow (x);
mpfr_set_ui_2exp (y, 11, -2, GMP_RNDN);
inex = mpfr_pow (z, x, y, GMP_RNDN);
if (mpfr_cmp_str (z, "0.111111111111111111111111111111011E0", 2, GMP_RNDN)
|| inex <= 0)
{
printf ("Failure in x_near_one, got inex = %d and\nz = ", inex);
mpfr_dump (z);
}
mpfr_clears (x, y, z, (void *) 0);
}
int
mpfr_set_ui (mpfr_ptr x, unsigned long i, mpfr_rnd_t rnd_mode)
{
return mpfr_set_ui_2exp (x, i, 0, rnd_mode);
}
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 (int argc, char *argv[])
{
mpfr_t x, y, r;
long q[1];
if (argc == 3) /* usage: tremquo x y (rnd=MPFR_RNDN implicit) */
{
mpfr_init2 (x, GMP_NUMB_BITS);
mpfr_init2 (y, GMP_NUMB_BITS);
mpfr_init2 (r, GMP_NUMB_BITS);
mpfr_set_str (x, argv[1], 10, MPFR_RNDN);
mpfr_set_str (y, argv[2], 10, MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
printf ("r=");
mpfr_out_str (stdout, 10, 0, r, MPFR_RNDN);
printf (" q=%ld\n", q[0]);
mpfr_clear (x);
mpfr_clear (y);
mpfr_clear (r);
return 0;
}
tests_start_mpfr ();
bug20090227 ();
mpfr_init (x);
mpfr_init (y);
mpfr_init (r);
/* special values */
mpfr_set_nan (x);
mpfr_set_ui (y, 1, MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN(mpfr_nan_p (r));
mpfr_set_ui (x, 1, MPFR_RNDN);
mpfr_set_nan (y);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN(mpfr_nan_p (r));
mpfr_set_inf (x, 1); /* +Inf */
mpfr_set_ui (y, 1, MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_nan_p (r));
mpfr_set_inf (x, 1); /* +Inf */
mpfr_set_ui (y, 0, MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_nan_p (r));
mpfr_set_inf (x, 1); /* +Inf */
mpfr_set_inf (y, 1);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_nan_p (r));
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_set_inf (y, 1);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_ui (r, 0) == 0 && MPFR_IS_POS (r));
MPFR_ASSERTN (q[0] == (long) 0);
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_neg (x, x, MPFR_RNDN); /* -0 */
mpfr_set_inf (y, 1);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_ui (r, 0) == 0 && MPFR_IS_NEG (r));
MPFR_ASSERTN (q[0] == (long) 0);
mpfr_set_ui (x, 17, MPFR_RNDN);
mpfr_set_inf (y, 1);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp (r, x) == 0);
MPFR_ASSERTN (q[0] == (long) 0);
mpfr_set_ui (x, 17, MPFR_RNDN);
mpfr_set_ui (y, 0, MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_nan_p (r));
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_set_ui (y, 17, MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_ui (r, 0) == 0 && MPFR_IS_POS (r));
MPFR_ASSERTN (q[0] == (long) 0);
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_neg (x, x, MPFR_RNDN);
mpfr_set_ui (y, 17, MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_ui (r, 0) == 0 && MPFR_IS_NEG (r));
MPFR_ASSERTN (q[0] == (long) 0);
mpfr_set_prec (x, 53);
mpfr_set_prec (y, 53);
/* check four possible sign combinations */
mpfr_set_ui (x, 42, MPFR_RNDN);
mpfr_set_ui (y, 17, MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_ui (r, 8) == 0);
MPFR_ASSERTN (q[0] == (long) 2);
mpfr_set_si (x, -42, MPFR_RNDN);
mpfr_set_ui (y, 17, MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_si (r, -8) == 0);
MPFR_ASSERTN (q[0] == (long) -2);
mpfr_set_si (x, -42, MPFR_RNDN);
mpfr_set_si (y, -17, MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_si (r, -8) == 0);
MPFR_ASSERTN (q[0] == (long) 2);
mpfr_set_ui (x, 42, MPFR_RNDN);
mpfr_set_si (y, -17, MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_ui (r, 8) == 0);
MPFR_ASSERTN (q[0] == (long) -2);
mpfr_set_prec (x, 100);
mpfr_set_prec (y, 50);
mpfr_set_ui (x, 42, MPFR_RNDN);
mpfr_nextabove (x); /* 42 + 2^(-94) */
mpfr_set_ui (y, 21, MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_ui_2exp (r, 1, -94) == 0);
MPFR_ASSERTN (q[0] == (long) 2);
mpfr_set_prec (x, 50);
mpfr_set_prec (y, 100);
mpfr_set_ui (x, 42, MPFR_RNDN);
mpfr_nextabove (x); /* 42 + 2^(-44) */
mpfr_set_ui (y, 21, MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_ui_2exp (r, 1, -44) == 0);
MPFR_ASSERTN (q[0] == (long) 2);
mpfr_set_prec (x, 100);
mpfr_set_prec (y, 50);
mpfr_set_ui (x, 42, MPFR_RNDN);
mpfr_set_ui (y, 21, MPFR_RNDN);
mpfr_nextabove (y); /* 21 + 2^(-45) */
mpfr_remquo (r, q, x, y, MPFR_RNDN);
/* r should be 42 - 2*(21 + 2^(-45)) = -2^(-44) */
MPFR_ASSERTN (mpfr_cmp_si_2exp (r, -1, -44) == 0);
MPFR_ASSERTN (q[0] == (long) 2);
mpfr_set_prec (x, 50);
mpfr_set_prec (y, 100);
mpfr_set_ui (x, 42, MPFR_RNDN);
mpfr_set_ui (y, 21, MPFR_RNDN);
mpfr_nextabove (y); /* 21 + 2^(-95) */
mpfr_remquo (r, q, x, y, MPFR_RNDN);
/* r should be 42 - 2*(21 + 2^(-95)) = -2^(-94) */
MPFR_ASSERTN (mpfr_cmp_si_2exp (r, -1, -94) == 0);
MPFR_ASSERTN (q[0] == (long) 2);
/* exercise large quotient */
mpfr_set_ui_2exp (x, 1, 65, MPFR_RNDN);
mpfr_set_ui (y, 1, MPFR_RNDN);
/* quotient is 2^65 */
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_si (r, 0) == 0);
MPFR_ASSERTN (q[0] % 1073741824L == 0L);
/* another large quotient */
mpfr_set_prec (x, 65);
mpfr_set_prec (y, 65);
mpfr_const_pi (x, MPFR_RNDN);
mpfr_mul_2exp (x, x, 63, MPFR_RNDN);
mpfr_const_log2 (y, MPFR_RNDN);
mpfr_set_prec (r, 10);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
/* q should be 41803643793084085130, r should be 605/2048 */
MPFR_ASSERTN (mpfr_cmp_ui_2exp (r, 605, -11) == 0);
MPFR_ASSERTN ((q[0] > 0) && ((q[0] % 1073741824L) == 733836170L));
/* check cases where quotient is 1.5 +/- eps */
mpfr_set_prec (x, 65);
mpfr_set_prec (y, 65);
mpfr_set_prec (r, 63);
mpfr_set_ui (x, 3, MPFR_RNDN);
mpfr_set_ui (y, 2, MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
/* x/y = 1.5, quotient should be 2 (even rule), remainder should be -1 */
MPFR_ASSERTN (mpfr_cmp_si (r, -1) == 0);
MPFR_ASSERTN (q[0] == 2L);
mpfr_set_ui (x, 3, MPFR_RNDN);
mpfr_nextabove (x); /* 3 + 2^(-63) */
mpfr_set_ui (y, 2, MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
/* x/y = 1.5 + 2^(-64), quo should be 2, r should be -1 + 2^(-63) */
MPFR_ASSERTN (mpfr_add_ui (r, r, 1, MPFR_RNDN) == 0);
MPFR_ASSERTN (mpfr_cmp_ui_2exp (r, 1, -63) == 0);
MPFR_ASSERTN (q[0] == 2L);
mpfr_set_ui (x, 3, MPFR_RNDN);
mpfr_set_ui (y, 2, MPFR_RNDN);
mpfr_nextabove (y); /* 2 + 2^(-63) */
mpfr_remquo (r, q, x, y, MPFR_RNDN);
/* x/y = 1.5 - eps, quo should be 1, r should be 1 - 2^(-63) */
MPFR_ASSERTN (mpfr_sub_ui (r, r, 1, MPFR_RNDN) == 0);
MPFR_ASSERTN (mpfr_cmp_si_2exp (r, -1, -63) == 0);
MPFR_ASSERTN (q[0] == 1L);
/* bug founds by Kaveh Ghazi, 3 May 2007 */
mpfr_set_ui (x, 2, MPFR_RNDN);
mpfr_set_ui (y, 3, MPFR_RNDN);
mpfr_remainder (r, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_si (r, -1) == 0);
mpfr_set_si (x, -1, MPFR_RNDN);
mpfr_set_ui (y, 1, MPFR_RNDN);
mpfr_remainder (r, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_si (r, 0) == 0 && MPFR_SIGN (r) < 0);
/* check argument reuse */
mpfr_set_si (x, -1, MPFR_RNDN);
mpfr_set_ui (y, 1, MPFR_RNDN);
mpfr_remainder (x, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_si (x, 0) == 0 && MPFR_SIGN (x) < 0);
mpfr_set_ui_2exp (x, 1, mpfr_get_emax () - 1, MPFR_RNDN);
mpfr_set_ui_2exp (y, 1, mpfr_get_emin (), MPFR_RNDN);
mpfr_remquo (r, q, x, y, MPFR_RNDN);
MPFR_ASSERTN (mpfr_zero_p (r) && MPFR_SIGN (r) > 0);
MPFR_ASSERTN (q[0] == 0);
mpfr_clear (x);
mpfr_clear (y);
mpfr_clear (r);
tests_end_mpfr ();
return 0;
}
/* Don't need to save/restore exponent range: the cache does it */
int
mpfr_const_pi_internal (mpfr_ptr x, mpfr_rnd_t rnd_mode)
{
mpfr_t a, A, B, D, S;
mpfr_prec_t px, p, cancel, k, kmax;
MPFR_ZIV_DECL (loop);
int inex;
MPFR_LOG_FUNC
(("rnd_mode=%d", rnd_mode),
("x[%Pu]=%.*Rg inexact=%d", mpfr_get_prec(x), mpfr_log_prec, x, inex));
px = MPFR_PREC (x);
/* we need 9*2^kmax - 4 >= px+2*kmax+8 */
for (kmax = 2; ((px + 2 * kmax + 12) / 9) >> kmax; kmax ++);
p = px + 3 * kmax + 14; /* guarantees no recomputation for px <= 10000 */
mpfr_init2 (a, p);
mpfr_init2 (A, p);
mpfr_init2 (B, p);
mpfr_init2 (D, p);
mpfr_init2 (S, p);
MPFR_ZIV_INIT (loop, p);
for (;;) {
mpfr_set_ui (a, 1, MPFR_RNDN); /* a = 1 */
mpfr_set_ui (A, 1, MPFR_RNDN); /* A = a^2 = 1 */
mpfr_set_ui_2exp (B, 1, -1, MPFR_RNDN); /* B = b^2 = 1/2 */
mpfr_set_ui_2exp (D, 1, -2, MPFR_RNDN); /* D = 1/4 */
#define b B
#define ap a
#define Ap A
#define Bp B
for (k = 0; ; k++)
{
/* invariant: 1/2 <= B <= A <= a < 1 */
mpfr_add (S, A, B, MPFR_RNDN); /* 1 <= S <= 2 */
mpfr_div_2ui (S, S, 2, MPFR_RNDN); /* exact, 1/4 <= S <= 1/2 */
mpfr_sqrt (b, B, MPFR_RNDN); /* 1/2 <= b <= 1 */
mpfr_add (ap, a, b, MPFR_RNDN); /* 1 <= ap <= 2 */
mpfr_div_2ui (ap, ap, 1, MPFR_RNDN); /* exact, 1/2 <= ap <= 1 */
mpfr_mul (Ap, ap, ap, MPFR_RNDN); /* 1/4 <= Ap <= 1 */
mpfr_sub (Bp, Ap, S, MPFR_RNDN); /* -1/4 <= Bp <= 3/4 */
mpfr_mul_2ui (Bp, Bp, 1, MPFR_RNDN); /* -1/2 <= Bp <= 3/2 */
mpfr_sub (S, Ap, Bp, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_ui (S, 1) < 0);
cancel = mpfr_cmp_ui (S, 0) ? (mpfr_uexp_t) -mpfr_get_exp(S) : p;
/* MPFR_ASSERTN (cancel >= px || cancel >= 9 * (1 << k) - 4); */
mpfr_mul_2ui (S, S, k, MPFR_RNDN);
mpfr_sub (D, D, S, MPFR_RNDN);
/* stop when |A_k - B_k| <= 2^(k-p) i.e. cancel >= p-k */
if (cancel + k >= p)
break;
}
#undef b
#undef ap
#undef Ap
#undef Bp
mpfr_div (A, B, D, MPFR_RNDN);
/* MPFR_ASSERTN(p >= 2 * k + 8); */
if (MPFR_LIKELY (MPFR_CAN_ROUND (A, p - 2 * k - 8, px, rnd_mode)))
break;
p += kmax;
MPFR_ZIV_NEXT (loop, p);
mpfr_set_prec (a, p);
mpfr_set_prec (A, p);
mpfr_set_prec (B, p);
mpfr_set_prec (D, p);
mpfr_set_prec (S, p);
}
MPFR_ZIV_FREE (loop);
inex = mpfr_set (x, A, rnd_mode);
mpfr_clear (a);
mpfr_clear (A);
mpfr_clear (B);
mpfr_clear (D);
mpfr_clear (S);
return inex;
}
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);
}
int
main (int argc, char *argv[])
{
mpfr_t x;
long k, z, d, N;
unsigned long zl, dl;
int inex;
int r;
mpfr_exp_t emin, emax;
int flag;
tests_start_mpfr ();
mpfr_init2 (x, 100);
N = (argc==1) ? 100000 : atol (argv[1]);
for (k = 1; k <= N; k++)
{
z = (long) (randlimb () & LONG_MAX) + LONG_MIN / 2;
inex = mpfr_set_si (x, z, MPFR_RNDZ);
d = mpfr_get_si (x, MPFR_RNDZ);
if (d != z)
{
printf ("Error in mpfr_set_si: expected %ld got %ld\n", z, d);
exit (1);
}
if (inex)
{
printf ("Error in mpfr_set_si: inex value incorrect for %ld: %d\n",
z, inex);
exit (1);
}
}
for (k = 1; k <= N; k++)
{
zl = randlimb ();
inex = mpfr_set_ui (x, zl, MPFR_RNDZ);
dl = mpfr_get_ui (x, MPFR_RNDZ);
if (dl != zl)
{
printf ("Error in mpfr_set_ui: expected %lu got %lu\n", zl, dl);
exit (1);
}
if (inex)
{
printf ("Error in mpfr_set_ui: inex value incorrect for %lu: %d\n",
zl, inex);
exit (1);
}
}
mpfr_set_prec (x, 2);
if (mpfr_set_si (x, 5, MPFR_RNDZ) >= 0)
{
printf ("Wrong inexact flag for x=5, rnd=MPFR_RNDZ\n");
exit (1);
}
mpfr_set_prec (x, 2);
if (mpfr_set_si (x, -5, MPFR_RNDZ) <= 0)
{
printf ("Wrong inexact flag for x=-5, rnd=MPFR_RNDZ\n");
exit (1);
}
mpfr_set_prec (x, 3);
inex = mpfr_set_si (x, 77617, MPFR_RNDD); /* should be 65536 */
if (MPFR_MANT(x)[0] != ((mp_limb_t)1 << (mp_bits_per_limb-1))
|| inex >= 0)
{
printf ("Error in mpfr_set_si(x:3, 77617, MPFR_RNDD)\n");
mpfr_print_binary (x);
puts ("");
exit (1);
}
inex = mpfr_set_ui (x, 77617, MPFR_RNDD); /* should be 65536 */
if (MPFR_MANT(x)[0] != ((mp_limb_t)1 << (mp_bits_per_limb-1))
|| inex >= 0)
{
printf ("Error in mpfr_set_ui(x:3, 77617, MPFR_RNDD)\n");
mpfr_print_binary (x);
puts ("");
exit (1);
}
mpfr_set_prec (x, 2);
inex = mpfr_set_si (x, 33096, MPFR_RNDU);
if (mpfr_get_si (x, MPFR_RNDZ) != 49152 || inex <= 0)
{
printf ("Error in mpfr_set_si, exp. 49152, got %ld, inex %d\n",
mpfr_get_si (x, MPFR_RNDZ), inex);
exit (1);
}
inex = mpfr_set_ui (x, 33096, MPFR_RNDU);
if (mpfr_get_si (x, MPFR_RNDZ) != 49152)
{
printf ("Error in mpfr_set_ui, exp. 49152, got %ld, inex %d\n",
mpfr_get_si (x, MPFR_RNDZ), inex);
exit (1);
}
/* Also test the mpfr_set_ui function (instead of macro). */
inex = (mpfr_set_ui) (x, 33096, MPFR_RNDU);
if (mpfr_get_si (x, MPFR_RNDZ) != 49152)
{
printf ("Error in mpfr_set_ui function, exp. 49152, got %ld, inex %d\n",
mpfr_get_si (x, MPFR_RNDZ), inex);
exit (1);
}
for (r = 0 ; r < MPFR_RND_MAX ; r++)
{
mpfr_set_si (x, -1, (mpfr_rnd_t) r);
mpfr_set_ui (x, 0, (mpfr_rnd_t) r);
if (MPFR_IS_NEG (x) || mpfr_get_ui (x, (mpfr_rnd_t) r) != 0)
{
printf ("mpfr_set_ui (x, 0) gives -0 for %s\n",
mpfr_print_rnd_mode ((mpfr_rnd_t) r));
exit (1);
}
mpfr_set_si (x, -1, (mpfr_rnd_t) r);
mpfr_set_si (x, 0, (mpfr_rnd_t) r);
if (MPFR_IS_NEG (x) || mpfr_get_si (x, (mpfr_rnd_t) r) != 0)
{
printf ("mpfr_set_si (x, 0) gives -0 for %s\n",
mpfr_print_rnd_mode ((mpfr_rnd_t) r));
exit (1);
}
}
/* check potential bug in case mp_limb_t is unsigned */
emax = mpfr_get_emax ();
set_emax (0);
mpfr_set_si (x, -1, MPFR_RNDN);
if (mpfr_sgn (x) >= 0)
{
printf ("mpfr_set_si (x, -1) fails\n");
exit (1);
}
set_emax (emax);
emax = mpfr_get_emax ();
set_emax (5);
mpfr_set_prec (x, 2);
mpfr_set_si (x, -31, MPFR_RNDN);
if (mpfr_sgn (x) >= 0)
{
printf ("mpfr_set_si (x, -31) fails\n");
exit (1);
}
set_emax (emax);
/* test for get_ui */
mpfr_set_ui (x, 0, MPFR_RNDN);
MPFR_ASSERTN(mpfr_get_ui (x, MPFR_RNDN) == 0);
mpfr_set_ui (x, ULONG_MAX, MPFR_RNDU);
mpfr_nextabove (x);
mpfr_get_ui (x, MPFR_RNDU);
/* another test for get_ui */
mpfr_set_prec (x, 10);
mpfr_set_str_binary (x, "10.101");
dl = mpfr_get_ui (x, MPFR_RNDN);
MPFR_ASSERTN (dl == 3);
mpfr_set_str_binary (x, "-1.0");
mpfr_get_ui (x, MPFR_RNDN);
mpfr_set_str_binary (x, "0.1");
dl = mpfr_get_ui (x, MPFR_RNDN);
MPFR_ASSERTN (dl == 0);
dl = mpfr_get_ui (x, MPFR_RNDZ);
MPFR_ASSERTN (dl == 0);
dl = mpfr_get_ui (x, MPFR_RNDD);
MPFR_ASSERTN (dl == 0);
dl = mpfr_get_ui (x, MPFR_RNDU);
MPFR_ASSERTN (dl == 1);
/* coverage tests */
mpfr_set_prec (x, 2);
mpfr_set_si (x, -7, MPFR_RNDD);
MPFR_ASSERTN(mpfr_cmp_si (x, -8) == 0);
mpfr_set_prec (x, 2);
mpfr_set_ui (x, 7, MPFR_RNDU);
MPFR_ASSERTN(mpfr_cmp_ui (x, 8) == 0);
emax = mpfr_get_emax ();
set_emax (3);
mpfr_set_ui (x, 7, MPFR_RNDU);
MPFR_ASSERTN(mpfr_inf_p (x) && mpfr_sgn (x) > 0);
set_emax (1);
MPFR_ASSERTN( mpfr_set_ui (x, 7, MPFR_RNDU) );
MPFR_ASSERTN(mpfr_inf_p (x) && mpfr_sgn (x) > 0);
set_emax (emax);
mpfr_set_ui_2exp (x, 17, -50, MPFR_RNDN);
MPFR_ASSERTN (mpfr_get_ui (x, MPFR_RNDD) == 0);
MPFR_ASSERTN (mpfr_get_si (x, MPFR_RNDD) == 0);
/* Test for ERANGE flag + correct behaviour if overflow */
mpfr_set_prec (x, 256);
mpfr_set_ui (x, ULONG_MAX, MPFR_RNDN);
mpfr_clear_erangeflag ();
dl = mpfr_get_ui (x, MPFR_RNDN);
if (dl != ULONG_MAX || mpfr_erangeflag_p ())
{
printf ("ERROR for get_ui + ERANGE + ULONG_MAX (1)\n");
exit (1);
}
mpfr_add_ui (x, x, 1, MPFR_RNDN);
dl = mpfr_get_ui (x, MPFR_RNDN);
if (dl != ULONG_MAX || !mpfr_erangeflag_p ())
{
printf ("ERROR for get_ui + ERANGE + ULONG_MAX (2)\n");
exit (1);
}
mpfr_set_si (x, -1, MPFR_RNDN);
mpfr_clear_erangeflag ();
dl = mpfr_get_ui (x, MPFR_RNDN);
if (dl != 0 || !mpfr_erangeflag_p ())
{
printf ("ERROR for get_ui + ERANGE + -1 \n");
exit (1);
}
mpfr_set_si (x, LONG_MAX, MPFR_RNDN);
mpfr_clear_erangeflag ();
d = mpfr_get_si (x, MPFR_RNDN);
if (d != LONG_MAX || mpfr_erangeflag_p ())
{
printf ("ERROR for get_si + ERANGE + LONG_MAX (1): %ld\n", d);
exit (1);
}
mpfr_add_ui (x, x, 1, MPFR_RNDN);
d = mpfr_get_si (x, MPFR_RNDN);
if (d != LONG_MAX || !mpfr_erangeflag_p ())
{
printf ("ERROR for get_si + ERANGE + LONG_MAX (2)\n");
exit (1);
}
mpfr_set_si (x, LONG_MIN, MPFR_RNDN);
mpfr_clear_erangeflag ();
d = mpfr_get_si (x, MPFR_RNDN);
if (d != LONG_MIN || mpfr_erangeflag_p ())
{
printf ("ERROR for get_si + ERANGE + LONG_MIN (1)\n");
exit (1);
}
mpfr_sub_ui (x, x, 1, MPFR_RNDN);
d = mpfr_get_si (x, MPFR_RNDN);
if (d != LONG_MIN || !mpfr_erangeflag_p ())
{
printf ("ERROR for get_si + ERANGE + LONG_MIN (2)\n");
exit (1);
}
mpfr_set_nan (x);
mpfr_clear_erangeflag ();
d = mpfr_get_ui (x, MPFR_RNDN);
if (d != 0 || !mpfr_erangeflag_p ())
{
printf ("ERROR for get_ui + NaN\n");
exit (1);
}
mpfr_clear_erangeflag ();
d = mpfr_get_si (x, MPFR_RNDN);
if (d != 0 || !mpfr_erangeflag_p ())
{
printf ("ERROR for get_si + NaN\n");
exit (1);
}
emin = mpfr_get_emin ();
mpfr_set_prec (x, 2);
mpfr_set_emin (4);
mpfr_clear_flags ();
mpfr_set_ui (x, 7, MPFR_RNDU);
flag = mpfr_underflow_p ();
mpfr_set_emin (emin);
if (mpfr_cmp_ui (x, 8) != 0)
{
printf ("Error for mpfr_set_ui (x, 7, MPFR_RNDU), prec = 2, emin = 4\n");
exit (1);
}
if (flag)
{
printf ("mpfr_set_ui (x, 7, MPFR_RNDU) should not underflow "
"with prec = 2, emin = 4\n");
exit (1);
}
mpfr_set_emin (4);
mpfr_clear_flags ();
mpfr_set_si (x, -7, MPFR_RNDD);
flag = mpfr_underflow_p ();
mpfr_set_emin (emin);
if (mpfr_cmp_si (x, -8) != 0)
{
printf ("Error for mpfr_set_si (x, -7, MPFR_RNDD), prec = 2, emin = 4\n");
exit (1);
}
if (flag)
{
printf ("mpfr_set_si (x, -7, MPFR_RNDD) should not underflow "
"with prec = 2, emin = 4\n");
exit (1);
}
mpfr_clear (x);
test_2exp ();
test_macros ();
test_macros_keyword ();
tests_end_mpfr ();
return 0;
}
static int
hexadecimal (void)
{
mpfr_t x, z;
mpfr_inits2 (64, x, z, (mpfr_ptr) 0);
/* special */
mpfr_set_inf (x, 1);
check_sprintf (pinf_str, "%Ra", x);
check_sprintf (pinf_str, "%RUa", x);
check_sprintf (pinf_str, "%RDa", x);
check_sprintf (pinf_uc_str, "%RA", x);
check_sprintf (pinf_uc_str, "%RYA", x);
check_sprintf (pinf_uc_str, "%RZA", x);
check_sprintf (pinf_uc_str, "%RNA", x);
mpfr_set_inf (x, -1);
check_sprintf (minf_str, "%Ra", x);
check_sprintf (minf_str, "%RYa", x);
check_sprintf (minf_str, "%RZa", x);
check_sprintf (minf_str, "%RNa", x);
check_sprintf (minf_uc_str, "%RA", x);
check_sprintf (minf_uc_str, "%RUA", x);
check_sprintf (minf_uc_str, "%RDA", x);
mpfr_set_nan (x);
check_sprintf (nan_str, "%Ra", x);
check_sprintf (nan_uc_str, "%RA", x);
/* regular numbers */
mpfr_set_str (x, "FEDCBA9.87654321", 16, MPFR_RNDN);
mpfr_set_ui (z, 0, MPFR_RNDZ);
/* simplest case right justified */
check_sprintf (" 0xf.edcba987654321p+24", "%25Ra", x);
check_sprintf (" 0xf.edcba987654321p+24", "%25RUa", x);
check_sprintf (" 0xf.edcba987654321p+24", "%25RDa", x);
check_sprintf (" 0xf.edcba987654321p+24", "%25RYa", x);
check_sprintf (" 0xf.edcba987654321p+24", "%25RZa", x);
check_sprintf (" 0xf.edcba987654321p+24", "%25RNa", x);
check_sprintf (" 0x1p+28", "%25.0Ra", x);
check_sprintf (" 0x0p+0", "%25.0Ra", z);
/* sign or space, pad with leading zeros */
check_sprintf (" 0X00F.EDCBA987654321P+24", "% 025RA", x);
check_sprintf (" 0X000000000000000001P+28", "% 025.0RA", x);
check_sprintf (" 0X0000000000000000000P+0", "% 025.0RA", z);
/* sign + or -, left justified */
check_sprintf ("+0xf.edcba987654321p+24 ", "%+-25Ra", x);
check_sprintf ("+0x1p+28 ", "%+-25.0Ra", x);
check_sprintf ("+0x0p+0 ", "%+-25.0Ra", z);
/* decimal point, left justified, precision and rounding parameter */
check_vsprintf ("0XF.FP+24 ", "%#-10.*R*A", 1, MPFR_RNDN, x);
check_vsprintf ("0X1.P+28 ", "%#-10.*R*A", 0, MPFR_RNDN, x);
check_vsprintf ("0X0.P+0 ", "%#-10.*R*A", 0, MPFR_RNDN, z);
/* sign or space */
check_sprintf (" 0xf.eddp+24", "% .3RNa", x);
check_sprintf (" 0x1p+28", "% .0RNa", x);
/* sign + or -, decimal point, pad with leading zeros */
check_sprintf ("+0X0F.EP+24", "%0+#11.1RZA", x);
check_sprintf ("+0X00F.P+24", "%0+#11.0RZA", x);
check_sprintf ("+0X000.0P+0", "%0+#11.1RZA", z);
/* pad with leading zero */
check_sprintf ("0x0000f.edcba987654321p+24", "%026RDa", x);
check_sprintf ("0x0000000000000000000fp+24", "%026.0RDa", x);
/* sign or space, decimal point, left justified */
check_sprintf (" 0XF.EP+24 " , "%- #11.1RDA", x);
check_sprintf (" 0XF.P+24 " , "%- #11.0RDA", x);
mpfr_mul_si (x, x, -1, MPFR_RNDD);
mpfr_mul_si (z, z, -1, MPFR_RNDD);
/* sign + or - */
check_sprintf ("-0xf.ep+24", "%+10.1RUa", x);
check_sprintf (" -0xfp+24", "%+10.0RUa", x);
check_sprintf (" -0x0p+0", "%+10.0RUa", z);
/* rounding bit is zero */
mpfr_set_str (x, "0xF.7", 16, MPFR_RNDN);
check_sprintf ("0XFP+0", "%.0RNA", x);
/* tie case in round to nearest mode */
mpfr_set_str (x, "0x0.8800000000000000p+3", 16, MPFR_RNDN);
check_sprintf ("0x9.p-1", "%#.0RNa", x);
mpfr_set_str (x, "-0x0.9800000000000000p+3", 16, MPFR_RNDN);
check_sprintf ("-0xap-1", "%.0RNa", x);
/* trailing zeros in fractional part */
check_sprintf ("-0X4.C0000000000000000000P+0", "%.20RNA", x);
/* rounding bit is one and the first non zero bit is far away */
mpfr_set_prec (x, 1024);
mpfr_set_ui_2exp (x, 29, -1, MPFR_RNDN);
mpfr_nextabove (x);
check_sprintf ("0XFP+0", "%.0RNA", x);
/* with more than one limb */
mpfr_set_prec (x, 300);
mpfr_set_str (x, "0xf.ffffffffffffffffffffffffffffffffffffffffffffffffffff"
"fffffffffffffffff", 16, MPFR_RNDN);
check_sprintf ("0x1p+4 [300]", "%.0RNa [300]", x);
check_sprintf ("0xfp+0 [300]", "%.0RZa [300]", x);
check_sprintf ("0x1p+4 [300]", "%.0RYa [300]", x);
check_sprintf ("0xfp+0 [300]", "%.0RDa [300]", x);
check_sprintf ("0x1p+4 [300]", "%.0RUa [300]", x);
check_sprintf ("0x1.0000000000000000000000000000000000000000p+4",
"%.40RNa", x);
check_sprintf ("0xf.ffffffffffffffffffffffffffffffffffffffffp+0",
"%.40RZa", x);
check_sprintf ("0x1.0000000000000000000000000000000000000000p+4",
"%.40RYa", x);
check_sprintf ("0xf.ffffffffffffffffffffffffffffffffffffffffp+0",
"%.40RDa", x);
check_sprintf ("0x1.0000000000000000000000000000000000000000p+4",
"%.40RUa", x);
mpfr_set_str (x, "0xf.7fffffffffffffffffffffffffffffffffffffffffffffffffff"
"ffffffffffffffffff", 16, MPFR_RNDN);
check_sprintf ("0XFP+0", "%.0RNA", x);
check_sprintf ("0XFP+0", "%.0RZA", x);
check_sprintf ("0X1P+4", "%.0RYA", x);
check_sprintf ("0XFP+0", "%.0RDA", x);
check_sprintf ("0X1P+4", "%.0RUA", x);
check_sprintf ("0XF.8P+0", "%.1RNA", x);
check_sprintf ("0XF.7P+0", "%.1RZA", x);
check_sprintf ("0XF.8P+0", "%.1RYA", x);
check_sprintf ("0XF.7P+0", "%.1RDA", x);
check_sprintf ("0XF.8P+0", "%.1RUA", x);
/* do not round up to the next power of the base */
mpfr_set_str (x, "0xf.fffffffffffffffffffffffffffffffffffffeffffffffffffff"
"ffffffffffffffffff", 16, MPFR_RNDN);
check_sprintf ("0xf.ffffffffffffffffffffffffffffffffffffff00p+0",
"%.40RNa", x);
check_sprintf ("0xf.fffffffffffffffffffffffffffffffffffffeffp+0",
"%.40RZa", x);
check_sprintf ("0xf.ffffffffffffffffffffffffffffffffffffff00p+0",
"%.40RYa", x);
check_sprintf ("0xf.fffffffffffffffffffffffffffffffffffffeffp+0",
"%.40RDa", x);
check_sprintf ("0xf.ffffffffffffffffffffffffffffffffffffff00p+0",
"%.40RUa", x);
mpfr_clears (x, z, (mpfr_ptr) 0);
return 0;
}
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;
}
/* hard test of rounding */
static void
check_rounding (void)
{
mpfr_t a, b, c, res;
mpfr_prec_t p;
long k, l;
int i;
#define MAXKL (2 * GMP_NUMB_BITS)
for (p = MPFR_PREC_MIN; p <= GMP_NUMB_BITS; p++)
{
mpfr_init2 (a, p);
mpfr_init2 (res, p);
mpfr_init2 (b, p + 1 + MAXKL);
mpfr_init2 (c, MPFR_PREC_MIN);
/* b = 2^p + 1 + 2^(-k), c = 2^(-l) */
for (k = 0; k <= MAXKL; k++)
for (l = 0; l <= MAXKL; l++)
{
mpfr_set_ui_2exp (b, 1, p, MPFR_RNDN);
mpfr_add_ui (b, b, 1, MPFR_RNDN);
mpfr_mul_2ui (b, b, k, MPFR_RNDN);
mpfr_add_ui (b, b, 1, MPFR_RNDN);
mpfr_div_2ui (b, b, k, MPFR_RNDN);
mpfr_set_ui_2exp (c, 1, -l, MPFR_RNDN);
i = mpfr_sub (a, b, c, MPFR_RNDN);
/* b - c = 2^p + 1 + 2^(-k) - 2^(-l), should be rounded to
2^p for l <= k, and 2^p+2 for l < k */
if (l <= k)
{
if (mpfr_cmp_ui_2exp (a, 1, p) != 0)
{
printf ("Wrong result in check_rounding\n");
printf ("p=%lu k=%ld l=%ld\n", p, k, l);
printf ("b="); mpfr_print_binary (b); puts ("");
printf ("c="); mpfr_print_binary (c); puts ("");
printf ("Expected 2^%lu\n", p);
printf ("Got "); mpfr_print_binary (a); puts ("");
exit (1);
}
if (i >= 0)
{
printf ("Wrong ternary value in check_rounding\n");
printf ("p=%lu k=%ld l=%ld\n", p, k, l);
printf ("b="); mpfr_print_binary (b); puts ("");
printf ("c="); mpfr_print_binary (c); puts ("");
printf ("a="); mpfr_print_binary (a); puts ("");
printf ("Expected < 0, got %d\n", i);
exit (1);
}
}
else /* l < k */
{
mpfr_set_ui_2exp (res, 1, p, MPFR_RNDN);
mpfr_add_ui (res, res, 2, MPFR_RNDN);
if (mpfr_cmp (a, res) != 0)
{
printf ("Wrong result in check_rounding\n");
printf ("b="); mpfr_print_binary (b); puts ("");
printf ("c="); mpfr_print_binary (c); puts ("");
printf ("Expected "); mpfr_print_binary (res); puts ("");
printf ("Got "); mpfr_print_binary (a); puts ("");
exit (1);
}
if (i <= 0)
{
printf ("Wrong ternary value in check_rounding\n");
printf ("b="); mpfr_print_binary (b); puts ("");
printf ("c="); mpfr_print_binary (c); puts ("");
printf ("Expected > 0, got %d\n", i);
exit (1);
}
}
}
mpfr_clear (a);
mpfr_clear (res);
mpfr_clear (b);
mpfr_clear (c);
}
}
static void
special (void)
{
mpfr_t x, y;
int i;
mpfr_init (x);
mpfr_init (y);
/* root(NaN) = NaN */
mpfr_set_nan (x);
mpfr_root (y, x, 17, GMP_RNDN);
if (!mpfr_nan_p (y))
{
printf ("Error: root(NaN,17) <> NaN\n");
exit (1);
}
/* root(+Inf) = +Inf */
mpfr_set_inf (x, 1);
mpfr_root (y, x, 42, GMP_RNDN);
if (!mpfr_inf_p (y) || mpfr_sgn (y) < 0)
{
printf ("Error: root(+Inf,42) <> +Inf\n");
exit (1);
}
/* root(-Inf, 17) = -Inf */
mpfr_set_inf (x, -1);
mpfr_root (y, x, 17, GMP_RNDN);
if (!mpfr_inf_p (y) || mpfr_sgn (y) > 0)
{
printf ("Error: root(-Inf,17) <> -Inf\n");
exit (1);
}
/* root(-Inf, 42) = NaN */
mpfr_set_inf (x, -1);
mpfr_root (y, x, 42, GMP_RNDN);
if (!mpfr_nan_p (y))
{
printf ("Error: root(-Inf,42) <> -Inf\n");
exit (1);
}
/* root(+/-0) = +/-0 */
mpfr_set_ui (x, 0, GMP_RNDN);
mpfr_root (y, x, 17, GMP_RNDN);
if (mpfr_cmp_ui (y, 0) || mpfr_sgn (y) < 0)
{
printf ("Error: root(+0,17) <> +0\n");
exit (1);
}
mpfr_neg (x, x, GMP_RNDN);
mpfr_root (y, x, 42, GMP_RNDN);
if (mpfr_cmp_ui (y, 0) || mpfr_sgn (y) > 0)
{
printf ("Error: root(-0,42) <> -0\n");
exit (1);
}
mpfr_set_prec (x, 53);
mpfr_set_str (x, "8.39005285514734966412e-01", 10, GMP_RNDN);
mpfr_root (x, x, 3, GMP_RNDN);
if (mpfr_cmp_str1 (x, "9.43166207799662426048e-01"))
{
printf ("Error in root3 (1)\n");
printf ("expected 9.43166207799662426048e-01\n");
printf ("got ");
mpfr_dump (x);
exit (1);
}
mpfr_set_prec (x, 32);
mpfr_set_prec (y, 32);
mpfr_set_str_binary (x, "0.10000100001100101001001001011001");
mpfr_root (x, x, 3, GMP_RNDN);
mpfr_set_str_binary (y, "0.11001101011000100111000111111001");
if (mpfr_cmp (x, y))
{
printf ("Error in root3 (2)\n");
exit (1);
}
mpfr_set_prec (x, 32);
mpfr_set_prec (y, 32);
mpfr_set_str_binary (x, "-0.1100001110110000010101011001011");
mpfr_root (x, x, 3, GMP_RNDD);
mpfr_set_str_binary (y, "-0.11101010000100100101000101011001");
if (mpfr_cmp (x, y))
{
printf ("Error in root3 (3)\n");
exit (1);
}
mpfr_set_prec (x, 82);
mpfr_set_prec (y, 27);
mpfr_set_str_binary (x, "0.1010001111011101011011000111001011001101100011110110010011011011011010011001100101e-7");
mpfr_root (y, x, 3, GMP_RNDD);
mpfr_set_str_binary (x, "0.101011110001110001000100011E-2");
if (mpfr_cmp (x, y))
{
printf ("Error in root3 (4)\n");
exit (1);
}
mpfr_set_prec (x, 204);
mpfr_set_prec (y, 38);
mpfr_set_str_binary (x, "0.101000000001101000000001100111111011111001110110100001111000100110100111001101100111110001110001011011010110010011100101111001111100001010010100111011101100000011011000101100010000000011000101001010001001E-5");
mpfr_root (y, x, 3, GMP_RNDD);
mpfr_set_str_binary (x, "0.10001001111010011011101000010110110010E-1");
if (mpfr_cmp (x, y))
{
printf ("Error in root3 (5)\n");
exit (1);
}
/* Worst case found on 2006-11-25 */
mpfr_set_prec (x, 53);
mpfr_set_prec (y, 53);
mpfr_set_str_binary (x, "1.0100001101101101001100110001001000000101001101100011E28");
mpfr_root (y, x, 35, GMP_RNDN);
mpfr_set_str_binary (x, "1.1100000010110101100011101011000010100001101100100011E0");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_root (y, x, 35, GMP_RNDN) for\n"
"x = 1.0100001101101101001100110001001000000101001101100011E28\n"
"Expected ");
mpfr_dump (x);
printf ("Got ");
mpfr_dump (y);
exit (1);
}
/* Worst cases found on 2006-11-26 */
mpfr_set_str_binary (x, "1.1111010011101110001111010110000101110000110110101100E17");
mpfr_root (y, x, 36, GMP_RNDD);
mpfr_set_str_binary (x, "1.0110100111010001101001010111001110010100111111000010E0");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_root (y, x, 36, GMP_RNDD) for\n"
"x = 1.1111010011101110001111010110000101110000110110101100E17\n"
"Expected ");
mpfr_dump (x);
printf ("Got ");
mpfr_dump (y);
exit (1);
}
mpfr_set_str_binary (x, "1.1100011101101101100010110001000001110001111110010000E23");
mpfr_root (y, x, 36, GMP_RNDU);
mpfr_set_str_binary (x, "1.1001010100001110000110111111100011011101110011000100E0");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_root (y, x, 36, GMP_RNDU) for\n"
"x = 1.1100011101101101100010110001000001110001111110010000E23\n"
"Expected ");
mpfr_dump (x);
printf ("Got ");
mpfr_dump (y);
exit (1);
}
/* Check for k = 1 */
mpfr_set_ui (x, 17, GMP_RNDN);
i = mpfr_root (y, x, 1, GMP_RNDN);
if (mpfr_cmp_ui (x, 17) || i != 0)
{
printf ("Error in root (17^(1/1))\n");
exit (1);
}
#if 0
/* Check for k == 0:
For 0 <= x < 1 => +0.
For x = 1 => 1.
For x > 1, => +Inf.
For x < 0 => NaN. */
i = mpfr_root (y, x, 0, GMP_RNDN);
if (!MPFR_IS_INF (y) || !MPFR_IS_POS (y) || i != 0)
{
printf ("Error in root 17^(1/0)\n");
exit (1);
}
mpfr_set_ui (x, 1, GMP_RNDN);
i = mpfr_root (y, x, 0, GMP_RNDN);
if (mpfr_cmp_ui (y, 1) || i != 0)
{
printf ("Error in root 1^(1/0)\n");
exit (1);
}
mpfr_set_ui (x, 0, GMP_RNDN);
i = mpfr_root (y, x, 0, GMP_RNDN);
if (!MPFR_IS_ZERO (y) || !MPFR_IS_POS (y) || i != 0)
{
printf ("Error in root 0+^(1/0)\n");
exit (1);
}
MPFR_CHANGE_SIGN (x);
i = mpfr_root (y, x, 0, GMP_RNDN);
if (!MPFR_IS_ZERO (y) || !MPFR_IS_POS (y) || i != 0)
{
printf ("Error in root 0-^(1/0)\n");
exit (1);
}
mpfr_set_ui_2exp (x, 17, -5, GMP_RNDD);
i = mpfr_root (y, x, 0, GMP_RNDN);
if (!MPFR_IS_ZERO (y) || !MPFR_IS_POS (y) || i != 0)
{
printf ("Error in root (17/2^5)^(1/0)\n");
exit (1);
}
#endif
mpfr_set_ui (x, 0, GMP_RNDN);
i = mpfr_root (y, x, 0, GMP_RNDN);
if (!MPFR_IS_NAN (y) || i != 0)
{
printf ("Error in root 0+^(1/0)\n");
exit (1);
}
/* Check for k==2 */
mpfr_set_si (x, -17, GMP_RNDD);
i = mpfr_root (y, x, 2, GMP_RNDN);
if (!MPFR_IS_NAN (y) || i != 0)
{
printf ("Error in root (-17)^(1/2)\n");
exit (1);
}
mpfr_clear (x);
mpfr_clear (y);
}
