static void
check (const char *xis, const char *xfs, const char *xs,
mpfr_prec_t xip, mpfr_prec_t xfp, mpfr_prec_t xp,
int expected_return, mpfr_rnd_t rnd_mode)
{
int inexact;
mpfr_t xi, xf, x;
mpfr_init2 (xi, xip);
mpfr_init2 (xf, xfp);
mpfr_init2 (x, xp);
mpfr_set_str1 (x, xs);
inexact = mpfr_modf (xi, xf, x, rnd_mode);
if (mpfr_cmp_str1 (xi, xis))
{
printf ("mpfr_modf failed for x=%s, rnd=%s\n",
xs, mpfr_print_rnd_mode(rnd_mode));
printf ("got integer value: ");
mpfr_out_str (stdout, 10, 0, xi, MPFR_RNDN);
printf ("\nexpected %s\n", xis);
exit (1);
}
if (mpfr_cmp_str1 (xf, xfs))
{
printf ("mpfr_modf failed for x=%s, rnd=%s\n",
xs, mpfr_print_rnd_mode(rnd_mode));
printf ("got fractional value: ");
mpfr_out_str (stdout, 10, 0, xf, MPFR_RNDN);
printf ("\nexpected %s\n", xfs);
exit (1);
}
if (inexact != expected_return)
{
printf ("mpfr_modf failed for x=%s, rnd=%s\n",
xs, mpfr_print_rnd_mode(rnd_mode));
printf ("got return value: %d, expected %d\n", inexact, expected_return);
exit (1);
}
mpfr_clears (xi, xf, x, (mpfr_ptr) 0);
}
static void
check_regression (void)
{
mpfr_t x, y;
mpfr_prec_t p;
int i;
p = strlen (xs) - 2 - 3;
mpfr_inits2 (p, x, y, (mpfr_ptr) 0);
mpfr_set_str (x, xs, 2, MPFR_RNDN);
i = mpfr_sin (y, x, MPFR_RNDN);
if (i >= 0
|| mpfr_cmp_str (y, "0.111001110011110011110001010110011101110E-1",
2, MPFR_RNDN))
{
printf ("Regression test failed (1) i=%d\ny=", i);
mpfr_dump (y);
exit (1);
}
mpfr_clears (x, y, (mpfr_ptr) 0);
}
/* TODO: A test with more inputs (but can't be compared to mpfr_add). */
static void
check_extreme (void)
{
mpfr_t u, v, w, x, y;
mpfr_ptr t[2];
int i, inex1, inex2, r;
t[0] = u;
t[1] = v;
mpfr_inits2 (32, u, v, w, x, y, (mpfr_ptr) 0);
mpfr_setmin (u, mpfr_get_emax ());
mpfr_setmax (v, mpfr_get_emin ());
mpfr_setmin (w, mpfr_get_emax () - 40);
RND_LOOP (r)
for (i = 0; i < 2; i++)
{
mpfr_set_prec (x, 64);
inex1 = mpfr_add (x, u, w, MPFR_RNDN);
MPFR_ASSERTN (inex1 == 0);
inex1 = mpfr_prec_round (x, 32, (mpfr_rnd_t) r);
inex2 = mpfr_sum (y, t, 2, (mpfr_rnd_t) r);
if (!(mpfr_equal_p (x, y) && SAME_SIGN (inex1, inex2)))
{
printf ("Error in check_extreme (%s, i = %d)\n",
mpfr_print_rnd_mode ((mpfr_rnd_t) r), i);
printf ("Expected ");
mpfr_dump (x);
printf ("with inex = %d\n", inex1);
printf ("Got ");
mpfr_dump (y);
printf ("with inex = %d\n", inex2);
exit (1);
}
mpfr_neg (v, v, MPFR_RNDN);
mpfr_neg (w, w, MPFR_RNDN);
}
mpfr_clears (u, v, w, x, y, (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 void
check4 (const char *as, const char *bs, mpfr_rnd_t rnd_mode, const char *res)
{
mpfr_t ta, tb, tres;
mpfr_inits2 (53, ta, tb, tres, (mpfr_ptr) 0);
mpfr_set_str1 (ta, as);
mpfr_set_str1 (tb, bs);
mpfr_agm(tres, ta, tb, rnd_mode);
if (mpfr_cmp_str1 (tres, res))
{
printf ("mpfr_agm failed for a=%s, b=%s, rnd_mode=%d\n",as,bs,rnd_mode);
printf ("expected result is %s, got ",res);
mpfr_out_str(stdout, 10, 0, tres, MPFR_RNDN);
putchar('\n');
exit (1);
}
mpfr_clears (ta, tb, tres, (mpfr_ptr) 0);
}
static void
check_large (void)
{
mpfr_t x, y;
mpfr_init2 (x, 25000);
mpfr_init2 (y, 26000);
(mpfr_const_log2) (x, MPFR_RNDN); /* First one ! */
(mpfr_const_log2) (y, MPFR_RNDN); /* Then the other - cache - */
mpfr_prec_round (y, 25000, MPFR_RNDN);
if (mpfr_cmp (x, y))
{
printf ("const_log2: error for large prec\n");
exit (1);
}
/* worst-case with 15 successive ones after last bit,
to exercise can_round loop */
mpfr_set_prec (x, 26249);
mpfr_const_log2 (x, MPFR_RNDZ);
mpfr_clears (x, y, (mpfr_ptr) 0);
}
static void
check4 (const char *Ns, const char *Ds, mpfr_rnd_t rnd_mode, int p,
const char *Qs)
{
mpfr_t q, n, d;
mpfr_inits2 (p, q, n, d, (mpfr_ptr) 0);
mpfr_set_str1 (n, Ns);
mpfr_set_str1 (d, Ds);
test_div(q, n, d, rnd_mode);
if (mpfr_cmp_str (q, Qs, ((p==53) ? 10 : 2), MPFR_RNDN) )
{
printf ("mpfr_div failed for n=%s, d=%s, p=%d, rnd_mode=%s\n",
Ns, Ds, p, mpfr_print_rnd_mode (rnd_mode));
printf ("got ");mpfr_print_binary(q);
mpfr_set_str (q, Qs, ((p==53) ? 10 : 2), MPFR_RNDN);
printf("\nexpected "); mpfr_print_binary(q);
putchar('\n');
exit (1);
}
mpfr_clears (q, n, d, (mpfr_ptr) 0);
}
int mpfr_sub1sp (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mpfr_rnd_t rnd_mode)
{
mpfr_t tmpa, tmpb, tmpc;
int inexb, inexc, inexact, inexact2;
mpfr_init2 (tmpa, MPFR_PREC (a));
mpfr_init2 (tmpb, MPFR_PREC (b));
mpfr_init2 (tmpc, MPFR_PREC (c));
inexb = mpfr_set (tmpb, b, MPFR_RNDN);
MPFR_ASSERTN (inexb == 0);
inexc = mpfr_set (tmpc, c, MPFR_RNDN);
MPFR_ASSERTN (inexc == 0);
inexact2 = mpfr_sub1 (tmpa, tmpb, tmpc, rnd_mode);
inexact = mpfr_sub1sp2(a, b, c, rnd_mode);
if (mpfr_cmp (tmpa, a) || inexact != inexact2)
{
fprintf (stderr, "sub1 & sub1sp return different values for %s\n"
"Prec_a = %lu, Prec_b = %lu, Prec_c = %lu\nB = ",
mpfr_print_rnd_mode (rnd_mode), (unsigned long) MPFR_PREC (a),
(unsigned long) MPFR_PREC (b), (unsigned long) MPFR_PREC (c));
mpfr_fprint_binary (stderr, tmpb);
fprintf (stderr, "\nC = ");
mpfr_fprint_binary (stderr, tmpc);
fprintf (stderr, "\nSub1 : ");
mpfr_fprint_binary (stderr, tmpa);
fprintf (stderr, "\nSub1sp: ");
mpfr_fprint_binary (stderr, a);
fprintf (stderr, "\nInexact sp = %d | Inexact = %d\n",
inexact, inexact2);
MPFR_ASSERTN (0);
}
mpfr_clears (tmpa, tmpb, tmpc, (mpfr_ptr) 0);
return inexact;
}
void MathUtils::GetSmoothnessBase(mpz_class& ret_base, mpz_class& N)
{
mpfr_t f_N, log_N, log_log_N;
mpz_t base_mpz;
mpz_init(base_mpz);
mpfr_init(f_N); mpfr_init(log_N); mpfr_init(log_log_N);
mpfr_set_z(f_N, N.get_mpz_t(), MPFR_RNDU); //f_N = N
mpfr_log(log_N, f_N, MPFR_RNDU); //log_N = log(N)
mpfr_log(log_log_N, log_N, MPFR_RNDU); //log_log_N = log(log(N))
mpfr_mul(f_N, log_N, log_log_N, MPFR_RNDU); //f_N = log(N) * log(log(N))
mpfr_sqrt(f_N, f_N, MPFR_RNDU); //f_N = sqrt(f_N)
mpfr_div_ui(f_N, f_N, 2, MPFR_RNDU); //f_N = f_N/2
mpfr_exp(f_N, f_N, MPFR_RNDU); //f_N = e^f_N
mpfr_get_z(base_mpz, f_N, MPFR_RNDU);
ret_base = mpz_class(base_mpz);
mpfr_clears(f_N, log_N, log_log_N, NULL);
}
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);
}
/* expx is the value of exp(X) rounded toward -infinity */
static void
check_worst_case (const char *Xs, const char *expxs)
{
mpfr_t x, y;
mpfr_inits2 (53, x, y, (mpfr_ptr) 0);
mpfr_set_str1(x, Xs);
test_exp(y, x, MPFR_RNDD);
if (mpfr_cmp_str1 (y, expxs))
{
printf ("exp(x) rounded toward -infinity is wrong\n");
exit(1);
}
mpfr_set_str1(x, Xs);
test_exp(x, x, MPFR_RNDU);
mpfr_nexttoinf (y);
if (mpfr_cmp(x,y))
{
printf ("exp(x) rounded toward +infinity is wrong\n");
exit(1);
}
mpfr_clears (x, y, (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 bool
do_mpfr_sincos (real_value *result_sin, real_value *result_cos,
const real_value *arg, const real_format *format)
{
/* To proceed, MPFR must exactly represent the target floating point
format, which only happens when the target base equals two. */
if (format->b != 2 || !real_isfinite (arg))
return false;
int prec = format->p;
mp_rnd_t rnd = format->round_towards_zero ? GMP_RNDZ : GMP_RNDN;
mpfr_t m, ms, mc;
mpfr_inits2 (prec, m, ms, mc, NULL);
mpfr_from_real (m, arg, GMP_RNDN);
mpfr_clear_flags ();
bool inexact = mpfr_sin_cos (ms, mc, m, rnd);
bool ok = (do_mpfr_ckconv (result_sin, ms, inexact, format)
&& do_mpfr_ckconv (result_cos, mc, inexact, format));
mpfr_clears (m, ms, mc, NULL);
return ok;
}
/* Worst case incorrectly rounded in r5573, found with the bad_cases test */
static void
bad_case1 (void)
{
mpfr_t x, y, z;
mpfr_init2 (x, 72);
mpfr_inits2 (6, y, z, (mpfr_ptr) 0);
mpfr_set_str (x, "1.08310518720928b30e@-120", 16, MPFR_RNDN);
mpfr_set_str (z, "f.8@59", 16, MPFR_RNDN);
/* z = rec_sqrt(x) rounded on 6 bits toward 0, the exact value
being ~= f.bffffffffffffffffa11@59. */
mpfr_rec_sqrt (y, x, MPFR_RNDZ);
if (mpfr_cmp0 (y, z) != 0)
{
printf ("Error in bad_case1\nexpected ");
mpfr_out_str (stdout, 16, 0, z, MPFR_RNDN);
printf ("\ngot ");
mpfr_out_str (stdout, 16, 0, y, MPFR_RNDN);
printf ("\n");
exit (1);
}
mpfr_clears (x, y, z, (mpfr_ptr) 0);
}
/* expx is the value of exp(X) rounded towards -infinity */
static void
check_worst_case (const char *Xs, const char *expxs)
{
mpfr_t x, y;
mpfr_inits2(53, x, y, NULL);
mpfr_set_str1(x, Xs);
mpfr_exp(y, x, GMP_RNDD);
if (mpfr_cmp_str1 (y, expxs))
{
printf ("exp(x) rounded towards -infinity is wrong\n");
exit(1);
}
mpfr_set_str1(x, Xs);
mpfr_exp(x, x, GMP_RNDU);
mpfr_add_one_ulp(y, GMP_RNDN);
if (mpfr_cmp(x,y))
{
printf ("exp(x) rounded towards +infinity is wrong\n");
exit(1);
}
mpfr_clears(x,y,NULL);
}
/* checks that xs+ys gives the expected result zs */
static void
check (const char *xs, const char *ys, mpfr_rnd_t rnd_mode,
unsigned int px, unsigned int py, unsigned int pz, const char *zs)
{
mpfr_t xx,yy,zz;
mpfr_init2 (xx, px);
mpfr_init2 (yy, py);
mpfr_init2 (zz, pz);
mpfr_set_str1 (xx, xs);
mpfr_set_str1 (yy, ys);
test_add (zz, xx, yy, rnd_mode);
if (mpfr_cmp_str1 (zz, zs) )
{
printf ("expected sum is %s, got ", zs);
mpfr_out_str(stdout, 10, 0, zz, MPFR_RNDN);
printf ("mpfr_add failed for x=%s y=%s with rnd_mode=%s\n",
xs, ys, mpfr_print_rnd_mode (rnd_mode));
exit (1);
}
mpfr_clears (xx, yy, zz, (mpfr_ptr) 0);
}
static void
check_overflow (void)
{
mpfr_t x, y;
int inex, r;
mpfr_inits2 (8, x, y, (mpfr_ptr) 0);
mpfr_set_ui (x, 1, MPFR_RNDN);
mpfr_setmax (x, mpfr_get_emax ());
RND_LOOP(r)
{
mpfr_clear_overflow ();
inex = mpfr_hypot (y, x, x, (mpfr_rnd_t) r);
if (!mpfr_overflow_p ())
{
printf ("No overflow in check_overflow for %s%s\n",
mpfr_print_rnd_mode ((mpfr_rnd_t) r),
ext ? ", extended exponent range" : "");
exit (1);
}
MPFR_ASSERTN (MPFR_IS_POS (y));
if (r == MPFR_RNDZ || r == MPFR_RNDD)
{
MPFR_ASSERTN (inex < 0);
MPFR_ASSERTN (!mpfr_inf_p (y));
mpfr_nexttoinf (y);
}
else
{
MPFR_ASSERTN (inex > 0);
}
MPFR_ASSERTN (mpfr_inf_p (y));
}
mpfr_clears (x, y, (mpfr_ptr) 0);
}
static void dispose() {
mpfr_clears(zero, one, eps, minuseps, large, (mpfr_ptr)0);
int i, j;
for(i=0;i < m+1;i++) {
for(j=0;j < m+1;j++) {
mpfr_clear(q[i][j]);
}
free(q[i]);
}
free(q);
for(i=0;i < m+1;i++) {
for(j=0;j < n+1;j++) {
mpfr_clear(a[i][j]);
}
free(a[i]);
}
free(a);
for(j=0;j < n+1;j++) {
mpfr_clear(c[j]);
}
free(c);
for(j=0;j < m+1;j++) {
mpfr_clear(pivotcolumn[j]);
}
free(pivotcolumn);
free(col);
free(row);
free(nonzero_row);
free(inequality);
}
static void
check_random (mpfr_prec_t p)
{
mpfr_t x,y,z;
int r;
int i, inexact1, inexact2;
mpfr_inits2 (p, x, y, z, (mpfr_ptr) 0);
for(i = 0 ; i < 500 ; i++)
{
mpfr_urandomb (x, RANDS);
if (MPFR_IS_PURE_FP(x))
for (r = 0 ; r < MPFR_RND_MAX ; r++)
{
inexact1 = mpfr_mul (y, x, x, (mpfr_rnd_t) r);
inexact2 = mpfr_sqr (z, x, (mpfr_rnd_t) r);
if (mpfr_cmp (y, z))
error1 ((mpfr_rnd_t) r,p,x,y,z);
if (inexact_sign (inexact1) != inexact_sign (inexact2))
error2 ((mpfr_rnd_t) r,p,x,y,inexact1,inexact2);
}
}
mpfr_clears (x, y, z, (mpfr_ptr) 0);
}
static void
check_64(void)
{
mpfr_t x,y,z;
mpfr_inits2 (64, x, y, z, (mpfr_ptr) 0);
mpfr_set_str_binary(x, "1.00100100110110101001010010101111000001011100100101010000000000E54");
mpfr_set_str_binary(y, "1.00000000000000000000000000000000000000000000000000000000000000E584");
test_div(z, x, y, MPFR_RNDU);
if (mpfr_cmp_str (z, "0.1001001001101101010010100101011110000010111001001010100000000000E-529", 2, MPFR_RNDN))
{
printf("Error for tdiv for MPFR_RNDU and p=64\nx=");
mpfr_print_binary(x);
printf("\ny=");
mpfr_print_binary(y);
printf("\ngot ");
mpfr_print_binary(z);
printf("\nexpected 0.1001001001101101010010100101011110000010111001001010100000000000E-529\n");
exit(1);
}
mpfr_clears (x, y, z, (mpfr_ptr) 0);
}
int
mpfr_mul (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mpfr_rnd_t rnd_mode)
{
mpfr_t ta, tb, tc;
int inexact1, inexact2;
mpfr_init2 (ta, MPFR_PREC (a));
mpfr_init2 (tb, MPFR_PREC (b));
mpfr_init2 (tc, MPFR_PREC (c));
MPFR_ASSERTN (mpfr_set (tb, b, MPFR_RNDN) == 0);
MPFR_ASSERTN (mpfr_set (tc, c, MPFR_RNDN) == 0);
inexact2 = mpfr_mul3 (ta, tb, tc, rnd_mode);
inexact1 = mpfr_mul2 (a, b, c, rnd_mode);
if (mpfr_cmp (ta, a) || inexact1*inexact2 < 0
|| (inexact1*inexact2 == 0 && (inexact1|inexact2) != 0))
{
fprintf (stderr, "mpfr_mul return different values for %s\n"
"Prec_a = %lu, Prec_b = %lu, Prec_c = %lu\nB = ",
mpfr_print_rnd_mode (rnd_mode),
MPFR_PREC (a), MPFR_PREC (b), MPFR_PREC (c));
mpfr_out_str (stderr, 16, 0, tb, MPFR_RNDN);
fprintf (stderr, "\nC = ");
mpfr_out_str (stderr, 16, 0, tc, MPFR_RNDN);
fprintf (stderr, "\nOldMul: ");
mpfr_out_str (stderr, 16, 0, ta, MPFR_RNDN);
fprintf (stderr, "\nNewMul: ");
mpfr_out_str (stderr, 16, 0, a, MPFR_RNDN);
fprintf (stderr, "\nNewInexact = %d | OldInexact = %d\n",
inexact1, inexact2);
MPFR_ASSERTN(0);
}
mpfr_clears (ta, tb, tc, (mpfr_ptr) 0);
return inexact1;
}
/* FastTwoSum: if EXP(x) >= EXP(y), u = o(x+y), v = o(u-x), w = o(y-v),
then x + y = u + w
thus if u = o(y-x), v = o(u+x), w = o(v-y), then y-x = u-w */
static void
check_two_sum (mpfr_prec_t p)
{
unsigned int x;
mpfr_t y, u, v, w;
mpfr_rnd_t rnd;
int inexact;
mpfr_inits2 (p, y, u, v, w, (mpfr_ptr) 0);
do
{
x = randlimb ();
}
while (x < 1);
mpfr_urandomb (y, RANDS);
rnd = MPFR_RNDN;
inexact = mpfr_sub_ui (u, y, x, rnd);
mpfr_add_ui (v, u, x, rnd);
mpfr_sub (w, v, y, rnd);
/* as u - (y-x) = w, we should have inexact and w of same sign */
if (((inexact == 0) && mpfr_cmp_ui (w, 0)) ||
((inexact > 0) && (mpfr_cmp_ui (w, 0) <= 0)) ||
((inexact < 0) && (mpfr_cmp_ui (w, 0) >= 0)))
{
printf ("Wrong inexact flag for prec=%u, rnd=%s\n",
(unsigned int) p, mpfr_print_rnd_mode (rnd));
printf ("x=%u\n", x);
printf ("y="); mpfr_print_binary(y); puts ("");
printf ("u="); mpfr_print_binary(u); puts ("");
printf ("v="); mpfr_print_binary(v); puts ("");
printf ("w="); mpfr_print_binary(w); puts ("");
printf ("inexact = %d\n", inexact);
exit (1);
}
mpfr_clears (y, u, v, w, (mpfr_ptr) 0);
}
/* glibc free() error or segmentation fault when configured
* with GMP 6.0.0 built with "--disable-alloca ABI=32".
* GCC's address sanitizer shows a heap-buffer-overflow.
* Fixed in r9369 (before the merge into the trunk). The problem was due
* to the fact that mpn functions do not accept a zero size argument, and
* since mpn_add_1 is here a macro in GMP, there's no assertion even when
* GMP was built with assertion checking (--enable-assert).
*/
static
void check_simple (void)
{
mpfr_t tab[3], r;
mpfr_ptr tabp[3];
int i;
mpfr_init2 (r, 16);
for (i = 0; i < 3; i++)
{
mpfr_init2 (tab[i], 16);
mpfr_set_ui (tab[i], 1, MPFR_RNDN);
tabp[i] = tab[i];
}
i = mpfr_sum (r, tabp, 3, MPFR_RNDN);
if (mpfr_cmp_ui (r, 3) || i != 0)
{
printf ("Error in check_simple\n");
exit (1);
}
mpfr_clears (tab[0], tab[1], tab[2], r, (mpfr_ptr) 0);
}
int
mpfr_exp (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd_mode)
{
mpfr_exp_t expx;
mpfr_prec_t precy;
int inexact;
MPFR_SAVE_EXPO_DECL (expo);
MPFR_LOG_FUNC (("x[%#R]=%R rnd=%d", x, x, rnd_mode),
("y[%#R]=%R inexact=%d", y, y, inexact));
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))
{
if (MPFR_IS_POS(x))
MPFR_SET_INF(y);
else
MPFR_SET_ZERO(y);
MPFR_SET_POS(y);
MPFR_RET(0);
}
else
{
MPFR_ASSERTD(MPFR_IS_ZERO(x));
return mpfr_set_ui (y, 1, rnd_mode);
}
}
/* First, let's detect most overflow and underflow cases. */
{
mpfr_t e, bound;
/* We must extended the exponent range and save the flags now. */
MPFR_SAVE_EXPO_MARK (expo);
mpfr_init2 (e, sizeof (mpfr_exp_t) * CHAR_BIT);
mpfr_init2 (bound, 32);
inexact = mpfr_set_exp_t (e, expo.saved_emax, MPFR_RNDN);
MPFR_ASSERTD (inexact == 0);
mpfr_const_log2 (bound, expo.saved_emax < 0 ? MPFR_RNDD : MPFR_RNDU);
mpfr_mul (bound, bound, e, MPFR_RNDU);
if (MPFR_UNLIKELY (mpfr_cmp (x, bound) >= 0))
{
/* x > log(2^emax), thus exp(x) > 2^emax */
mpfr_clears (e, bound, (mpfr_ptr) 0);
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_overflow (y, rnd_mode, 1);
}
inexact = mpfr_set_exp_t (e, expo.saved_emin, MPFR_RNDN);
MPFR_ASSERTD (inexact == 0);
inexact = mpfr_sub_ui (e, e, 2, MPFR_RNDN);
MPFR_ASSERTD (inexact == 0);
mpfr_const_log2 (bound, expo.saved_emin < 0 ? MPFR_RNDU : MPFR_RNDD);
mpfr_mul (bound, bound, e, MPFR_RNDD);
if (MPFR_UNLIKELY (mpfr_cmp (x, bound) <= 0))
{
/* x < log(2^(emin - 2)), thus exp(x) < 2^(emin - 2) */
mpfr_clears (e, bound, (mpfr_ptr) 0);
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_underflow (y, rnd_mode == MPFR_RNDN ? MPFR_RNDZ : rnd_mode,
1);
}
/* Other overflow/underflow cases must be detected
by the generic routines. */
mpfr_clears (e, bound, (mpfr_ptr) 0);
MPFR_SAVE_EXPO_FREE (expo);
}
expx = MPFR_GET_EXP (x);
precy = MPFR_PREC (y);
/* if x < 2^(-precy), then exp(x) i.e. gives 1 +/- 1 ulp(1) */
if (MPFR_UNLIKELY (expx < 0 && (mpfr_uexp_t) (-expx) > precy))
{
mpfr_exp_t emin = __gmpfr_emin;
mpfr_exp_t emax = __gmpfr_emax;
int signx = MPFR_SIGN (x);
MPFR_SET_POS (y);
if (MPFR_IS_NEG_SIGN (signx) && (rnd_mode == MPFR_RNDD ||
rnd_mode == MPFR_RNDZ))
{
__gmpfr_emin = 0;
__gmpfr_emax = 0;
mpfr_setmax (y, 0); /* y = 1 - epsilon */
inexact = -1;
}
else
{
__gmpfr_emin = 1;
__gmpfr_emax = 1;
mpfr_setmin (y, 1); /* y = 1 */
if (MPFR_IS_POS_SIGN (signx) && (rnd_mode == MPFR_RNDU ||
rnd_mode == MPFR_RNDA))
{
mp_size_t yn;
int sh;
yn = 1 + (MPFR_PREC(y) - 1) / GMP_NUMB_BITS;
sh = (mpfr_prec_t) yn * GMP_NUMB_BITS - MPFR_PREC(y);
MPFR_MANT(y)[0] += MPFR_LIMB_ONE << sh;
inexact = 1;
}
else
inexact = -MPFR_FROM_SIGN_TO_INT(signx);
}
__gmpfr_emin = emin;
__gmpfr_emax = emax;
}
else /* General case */
{
if (MPFR_UNLIKELY (precy >= MPFR_EXP_THRESHOLD))
/* mpfr_exp_3 saves the exponent range and flags itself, otherwise
the flag changes in mpfr_exp_3 are lost */
inexact = mpfr_exp_3 (y, x, rnd_mode); /* O(M(n) log(n)^2) */
else
{
MPFR_SAVE_EXPO_MARK (expo);
inexact = mpfr_exp_2 (y, x, rnd_mode); /* O(n^(1/3) M(n)) */
MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, __gmpfr_flags);
MPFR_SAVE_EXPO_FREE (expo);
}
}
return mpfr_check_range (y, inexact, rnd_mode);
}
static int
binary (void)
{
mpfr_t x;
mpfr_t z;
mpfr_inits2 (64, x, z, (mpfr_ptr) 0);
/* special */
mpfr_set_inf (x, 1);
check_sprintf (pinf_str, "%Rb", x);
mpfr_set_inf (x, -1);
check_sprintf (minf_str, "%Rb", x);
mpfr_set_nan (x);
check_sprintf (nan_str, "%Rb", x);
/* regular numbers */
mpfr_set_str (x, "1110010101.1001101", 2, MPFR_RNDN);
mpfr_set_ui (z, 0, MPFR_RNDN);
/* simplest case: right justified */
check_sprintf (" 1.1100101011001101p+9", "%25Rb", x);
check_sprintf (" 0p+0", "%25Rb", z);
/* sign or space, pad with leading zeros */
check_sprintf (" 0001.1100101011001101p+9", "% 025Rb", x);
check_sprintf (" 000000000000000000000p+0", "% 025Rb", z);
/* sign + or -, left justified */
check_sprintf ("+1.1100101011001101p+9 ", "%+-25Rb", x);
check_sprintf ("+0p+0 ", "%+-25Rb", z);
/* sign or space */
check_sprintf (" 1.110p+9", "% .3RNb", x);
check_sprintf (" 1.1101p+9", "% .4RNb", x);
check_sprintf (" 0.0000p+0", "% .4RNb", z);
/* sign + or -, decimal point, pad with leading zeros */
check_sprintf ("+00001.1p+9", "%0+#11.1RZb", x);
check_sprintf ("+0001.0p+10", "%0+#11.1RNb", x);
check_sprintf ("+000000.p+0", "%0+#11.0RNb", z);
/* pad with leading zero */
check_sprintf ("00001.1100101011001101p+9", "%025RDb", x);
/* sign or space, decimal point (unused), left justified */
check_sprintf (" 1.1p+9 ", "%- #11.1RDb", x);
check_sprintf (" 1.p+9 ", "%- #11.0RDb", x);
check_sprintf (" 1.p+10 ", "%- #11.0RUb", x);
check_sprintf (" 1.p+9 ", "%- #11.0RZb", x);
check_sprintf (" 1.p+10 ", "%- #11.0RYb", x);
check_sprintf (" 1.p+10 ", "%- #11.0RNb", x);
mpfr_mul_si (x, x, -1, MPFR_RNDD);
mpfr_mul_si (z, z, -1, MPFR_RNDD);
/* sign + or - */
check_sprintf (" -1.1p+9", "%+10.1RUb", x);
check_sprintf (" -0.0p+0", "%+10.1RUb", z);
/* precision 0 */
check_sprintf ("-1p+10", "%.0RNb", x);
check_sprintf ("-1p+10", "%.0RDb", x);
check_sprintf ("-1p+9", "%.0RUb", x);
check_sprintf ("-1p+9", "%.0RZb", x);
check_sprintf ("-1p+10", "%.0RYb", x);
/* round to next base power */
check_sprintf ("-1.0p+10", "%.1RNb", x);
check_sprintf ("-1.0p+10", "%.1RDb", x);
check_sprintf ("-1.0p+10", "%.1RYb", x);
/* do not round to next base power */
check_sprintf ("-1.1p+9", "%.1RUb", x);
check_sprintf ("-1.1p+9", "%.1RZb", x);
/* rounding bit is zero */
check_sprintf ("-1.11p+9", "%.2RNb", x);
/* tie case in round to nearest mode */
check_sprintf ("-1.1100101011001101p+9", "%.16RNb", x);
/* trailing zeros in fractional part */
check_sprintf ("-1.110010101100110100000000000000p+9", "%.30RNb", x);
mpfr_clears (x, z, (mpfr_ptr) 0);
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
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);
}
static void
check_cmp (int argc, char *argv[])
{
mpfr_t x, y;
int n, k;
mpfr_inits2 (53, x, y, (mpfr_ptr) 0);
mpfr_set_ui(x, 1, MPFR_RNDN);
(mpfr_abs) (x, x, MPFR_RNDN);
if (mpfr_cmp_ui (x, 1))
{
printf ("Error in mpfr_abs(1.0)\n");
exit (1);
}
mpfr_set_si(x, -1, MPFR_RNDN);
mpfr_abs(x, x, MPFR_RNDN);
if (mpfr_cmp_ui (x, 1))
{
printf ("Error in mpfr_abs(1.0)\n");
exit (1);
}
mpfr_set_si(x, -1, MPFR_RNDN);
mpfr_abs(x, x, MPFR_RNDN);
if (mpfr_cmp_ui (x, 1))
{
printf ("Error in mpfr_abs(-1.0)\n");
exit (1);
}
mpfr_set_inf (x, 1);
mpfr_abs (x, x, MPFR_RNDN);
if (!mpfr_inf_p(x) || (mpfr_sgn(x) <= 0))
{
printf ("Error in mpfr_abs(Inf).\n");
exit (1);
}
mpfr_set_inf (x, -1);
mpfr_abs (x, x, MPFR_RNDN);
if (!mpfr_inf_p(x) || (mpfr_sgn(x) <= 0))
{
printf ("Error in mpfr_abs(-Inf).\n");
exit (1);
}
MPFR_SET_NAN(x);
mpfr_abs (x, x, MPFR_RNDN);
if (!MPFR_IS_NAN(x))
{
printf ("Error in mpfr_abs(NAN).\n");
exit (1);
}
n = (argc==1) ? 25000 : atoi(argv[1]);
for (k = 1; k <= n; k++)
{
mpfr_rnd_t rnd;
int sign = SIGN_RAND ();
mpfr_urandomb (x, RANDS);
MPFR_SET_SIGN (x, sign);
rnd = RND_RAND ();
mpfr_abs (y, x, rnd);
MPFR_SET_POS (x);
if (mpfr_cmp (x, y))
{
printf ("Mismatch for sign=%d and x=", sign);
mpfr_print_binary (x);
printf ("\nResults=");
mpfr_print_binary (y);
putchar ('\n');
exit (1);
}
}
mpfr_clears (x, y, (mpfr_ptr) 0);
}
int
main (void)
{
int j, k;
mpfr_t x, y, z, t, y2, z2, t2;
tests_start_mpfr ();
mpfr_inits2 (SIZEX, x, y, z, t, y2, z2, t2, (mpfr_ptr) 0);
mpfr_set_str1 (x, "0.5");
mpfr_ceil(y, x);
if (mpfr_cmp_ui (y, 1))
{
printf ("Error in mpfr_ceil for x=0.5: expected 1.0, got ");
mpfr_print_binary(y);
putchar('\n');
exit (1);
}
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_ceil(y, x);
if (mpfr_cmp_ui(y,0))
{
printf ("Error in mpfr_ceil for x=0.0: expected 0.0, got ");
mpfr_print_binary(y);
putchar('\n');
exit (1);
}
mpfr_set_ui (x, 1, MPFR_RNDN);
mpfr_ceil(y, x);
if (mpfr_cmp_ui(y,1))
{
printf ("Error in mpfr_ceil for x=1.0: expected 1.0, got ");
mpfr_print_binary(y);
putchar('\n');
exit (1);
}
for (j=0;j<1000;j++)
{
mpfr_urandomb (x, RANDS);
MPFR_EXP (x) = 2;
for (k = 2; k <= SIZEX; k++)
{
mpfr_set_prec(y, k);
mpfr_set_prec(y2, k);
mpfr_set_prec(z, k);
mpfr_set_prec(z2, k);
mpfr_set_prec(t, k);
mpfr_set_prec(t2, k);
mpfr_floor(y, x);
mpfr_set(y2, x, MPFR_RNDD);
mpfr_trunc(z, x);
mpfr_set(z2, x, MPFR_RNDZ);
mpfr_ceil(t, x);
mpfr_set(t2, x, MPFR_RNDU);
if (!mpfr_eq(y, y2, k))
{
printf("Error in floor, x = "); mpfr_print_binary(x);
printf("\n");
printf("floor(x) = "); mpfr_print_binary(y);
printf("\n");
printf("round(x, RNDD) = "); mpfr_print_binary(y2);
printf("\n");
exit(1);
}
if (!mpfr_eq(z, z2, k))
{
printf("Error in trunc, x = "); mpfr_print_binary(x);
printf("\n");
printf("trunc(x) = "); mpfr_print_binary(z);
printf("\n");
printf("round(x, RNDZ) = "); mpfr_print_binary(z2);
printf("\n");
exit(1);
}
if (!mpfr_eq(y, y2, k))
{
printf("Error in ceil, x = "); mpfr_print_binary(x);
printf("\n");
printf("ceil(x) = "); mpfr_print_binary(t);
printf("\n");
printf("round(x, RNDU) = "); mpfr_print_binary(t2);
printf("\n");
exit(1);
}
MPFR_EXP(x)++;
}
}
mpfr_clears (x, y, z, t, y2, z2, t2, (mpfr_ptr) 0);
tests_end_mpfr ();
return 0;
}
static void
check4 (const char *as, const char *bs, mpfr_rnd_t rnd_mode,
const char *res, int inex)
{
mpfr_t ta, tb, tc, tres;
mpfr_exp_t emin, emax;
int i;
emin = mpfr_get_emin ();
emax = mpfr_get_emax ();
mpfr_inits2 (53, ta, tb, tc, tres, (mpfr_ptr) 0);
for (i = 0; i <= 2; i++)
{
unsigned int expflags, newflags;
int inex2;
mpfr_set_str1 (ta, as);
mpfr_set_str1 (tb, bs);
mpfr_set_str1 (tc, res);
if (i > 0)
{
mpfr_exp_t ea, eb, ec, e0;
set_emin (MPFR_EMIN_MIN);
set_emax (MPFR_EMAX_MAX);
ea = mpfr_get_exp (ta);
eb = mpfr_get_exp (tb);
ec = mpfr_get_exp (tc);
e0 = i == 1 ? __gmpfr_emin : __gmpfr_emax;
if ((i == 1 && ea < eb) || (i == 2 && ea > eb))
{
mpfr_set_exp (ta, e0);
mpfr_set_exp (tb, e0 + (eb - ea));
mpfr_set_exp (tc, e0 + (ec - ea));
}
else
{
mpfr_set_exp (ta, e0 + (ea - eb));
mpfr_set_exp (tb, e0);
mpfr_set_exp (tc, e0 + (ec - eb));
}
}
__gmpfr_flags = expflags =
(randlimb () & 1) ? MPFR_FLAGS_ALL ^ MPFR_FLAGS_ERANGE : 0;
inex2 = mpfr_agm (tres, ta, tb, rnd_mode);
newflags = __gmpfr_flags;
expflags |= MPFR_FLAGS_INEXACT;
if (SIGN (inex2) != inex || newflags != expflags ||
! mpfr_equal_p (tres, tc))
{
printf ("mpfr_agm failed in rnd_mode=%s for\n",
mpfr_print_rnd_mode (rnd_mode));
printf (" a = ");
mpfr_out_str (stdout, 10, 0, ta, MPFR_RNDN);
printf ("\n");
printf (" b = ");
mpfr_out_str (stdout, 10, 0, tb, MPFR_RNDN);
printf ("\n");
printf ("expected inex = %d, flags = %u,\n"
" ", inex, expflags);
mpfr_dump (tc);
printf ("got inex = %d, flags = %u,\n"
" ", inex2, newflags);
mpfr_dump (tres);
exit (1);
}
set_emin (emin);
set_emax (emax);
}
mpfr_clears (ta, tb, tc, tres, (mpfr_ptr) 0);
}
