int
mpfi_sech (mpfi_ptr a, mpfi_srcptr b)
{
mpfr_t tmp;
int inexact_left, inexact_right, inexact=0;
if ( MPFI_NAN_P (b) ) {
mpfr_set_nan (&(a->left));
mpfr_set_nan (&(a->right));
MPFR_RET_NAN;
}
if ( MPFI_IS_NONNEG (b) ) {
mpfr_init2 (tmp, mpfr_get_prec (&(a->left)));
inexact_left = mpfr_sech (tmp, &(b->right), MPFI_RNDD);
inexact_right = mpfr_sech (&(a->right), &(b->left), MPFI_RNDU);
mpfr_set (&(a->left), tmp, MPFI_RNDD); /* exact */
mpfr_clear (tmp);
}
else if ( MPFI_HAS_ZERO (b) ) {
mpfr_init2 (tmp, mpfr_get_prec (&(b->left)));
mpfr_neg (tmp, &(b->left), MPFI_RNDD); /* exact */
if (mpfr_cmp (tmp, &(b->right)) > 0)
inexact_left = mpfr_sech (&(a->left), tmp, MPFI_RNDD);
else
inexact_left = mpfr_sech (&(a->left), &(b->right), MPFI_RNDD);
inexact_right = mpfr_set_ui (&(a->right), 1, MPFI_RNDU);
mpfr_clear (tmp);
}
else { /* b <= 0 */
inexact_left = mpfr_sech (&(a->left), &(b->left), MPFI_RNDD);
inexact_right = mpfr_sech (&(a->right), &(b->right), MPFI_RNDU);
}
/* do not allow +0 as upper bound */
if (mpfr_zero_p (&(a->right)) && !mpfr_signbit (&(a->right))) {
mpfr_neg (&(a->right), &(a->right), MPFI_RNDD);
}
if (inexact_left)
inexact += 1;
if (inexact_right)
inexact += 2;
return inexact;
}
static void
overflowed_sech0 (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. */
/* and if emax < 0, 1 - eps is not representable either. */
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_sech (x, x, (mpfr_rnd_t) rnd);
if ((i == 0 || emax < 0 || rnd == MPFR_RNDN || rnd == MPFR_RNDU) &&
! mpfr_overflow_p ())
{
printf ("Error in overflowed_sech0 (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_sech0 (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_sech0 (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_sech0 (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_sech0 (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);
}
static void
check_specials (void)
{
mpfr_t x, y;
mpfr_init2 (x, 123L);
mpfr_init2 (y, 123L);
mpfr_set_nan (x);
mpfr_sech (y, x, MPFR_RNDN);
if (! mpfr_nan_p (y))
{
printf ("Error: sech(NaN) != NaN\n");
exit (1);
}
mpfr_set_inf (x, 1);
mpfr_sech (y, x, MPFR_RNDN);
if (! (MPFR_IS_ZERO (y) && MPFR_SIGN (y) > 0))
{
printf ("Error: sech(+Inf) != +0\n");
exit (1);
}
mpfr_set_inf (x, -1);
mpfr_sech (y, x, MPFR_RNDN);
if (! (MPFR_IS_ZERO (y) && MPFR_SIGN (y) > 0))
{
printf ("Error: sech(-Inf) != +0\n");
exit (1);
}
/* sec(+/-0) = 1 */
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_sech (y, x, MPFR_RNDN);
if (mpfr_cmp_ui (y, 1))
{
printf ("Error: sech(+0) != 1\n");
exit (1);
}
mpfr_neg (x, x, MPFR_RNDN);
mpfr_sech (y, x, MPFR_RNDN);
if (mpfr_cmp_ui (y, 1))
{
printf ("Error: sech(-0) != 1\n");
exit (1);
}
/* check huge x */
mpfr_set_str (x, "8e8", 10, MPFR_RNDN);
mpfr_sech (y, x, MPFR_RNDN);
if (! (mpfr_zero_p (y) && MPFR_SIGN (y) > 0))
{
printf ("Error: sech(8e8) != +0\n");
exit (1);
}
mpfr_set_str (x, "-8e8", 10, MPFR_RNDN);
mpfr_sech (y, x, MPFR_RNDN);
if (! (mpfr_zero_p (y) && MPFR_SIGN (y) > 0))
{
printf ("Error: sech(-8e8) != +0\n");
exit (1);
}
mpfr_clear (x);
mpfr_clear (y);
}
