/* Bug found by Robert Bajema (regression in MPFR 2.3.0).
The cause is the underflow flag set before the mpfr_atan2 call. */
static void
atan2_bug_20071003 (void)
{
mpfr_t a, x, y, z;
mpfr_inits (a, x, y, z, (mpfr_ptr) 0);
mpfr_set_underflow ();
mpfr_set_str_binary (y,
"-0.10100110110100110111010110111111100110100010001110110E2");
mpfr_set_str_binary (x,
"0.10100101010110010100010010111000110110011110001011110E3");
mpfr_set_str_binary (z,
"-0.11101111001101101100111011001101000010010111101110110E-1");
mpfr_atan2 (a, y, x, MPFR_RNDN);
if (! mpfr_equal_p (a, z))
{
printf ("mpfr_atan2 fails on:\n");
printf (" y = ");
mpfr_dump (y);
printf (" x = ");
mpfr_dump (x);
printf ("Expected ");
mpfr_dump (z);
printf ("Got ");
mpfr_dump (a);
exit (1);
}
mpfr_clears (a, x, y, z, (mpfr_ptr) 0);
}
int
mpfr_check_range (mpfr_ptr x, mp_rnd_t rnd_mode)
{
if (MPFR_IS_FP(x) && MPFR_NOTZERO(x))
{ /* x is a non-zero FP */
mp_exp_t exp = MPFR_EXP(x);
if (exp < __mpfr_emin)
return mpfr_set_underflow(x, rnd_mode, MPFR_SIGN(x));
if (exp > __mpfr_emax)
return mpfr_set_overflow(x, rnd_mode, MPFR_SIGN(x));
}
return 0;
}
/* set f to the integer z */
int
mpfr_set_z (mpfr_ptr f, mpz_srcptr z, mp_rnd_t rnd_mode)
{
mp_size_t fn, zn, dif;
int k, sign_z, inex;
mp_limb_t *fp, *zp;
mp_exp_t exp;
MPFR_CLEAR_FLAGS (f); /* z cannot be NaN nor Inf */
sign_z = mpz_cmp_ui (z, 0);
if (sign_z == 0)
{
MPFR_SET_ZERO(f);
MPFR_SET_POS(f);
MPFR_RET(0);
}
fp = MPFR_MANT(f);
fn = 1 + (MPFR_PREC(f) - 1) / BITS_PER_MP_LIMB;
zn = ABS(SIZ(z));
dif = zn - fn;
zp = PTR(z);
count_leading_zeros(k, zp[zn-1]);
exp = (mp_prec_t) zn * BITS_PER_MP_LIMB - k;
/* The exponent will be exp or exp + 1 (due to rounding) */
if (exp > __mpfr_emax)
return mpfr_set_overflow(f, rnd_mode, sign_z);
if (exp + 1 < __mpfr_emin)
return mpfr_set_underflow(f, rnd_mode, sign_z);
if (MPFR_SIGN(f) * sign_z < 0)
MPFR_CHANGE_SIGN(f);
if (dif >= 0)
{
mp_limb_t cc;
int sh;
/* number has to be truncated */
if (k != 0)
{
mpn_lshift(fp, zp + dif, fn, k);
if (dif != 0)
fp[0] += zp[dif - 1] >> (BITS_PER_MP_LIMB - k);
}
static void
check_set (void)
{
mpfr_clear_flags ();
mpfr_set_overflow ();
MPFR_ASSERTN ((mpfr_overflow_p) ());
mpfr_set_underflow ();
MPFR_ASSERTN ((mpfr_underflow_p) ());
mpfr_set_nanflag ();
MPFR_ASSERTN ((mpfr_nanflag_p) ());
mpfr_set_inexflag ();
MPFR_ASSERTN ((mpfr_inexflag_p) ());
mpfr_set_erangeflag ();
MPFR_ASSERTN ((mpfr_erangeflag_p) ());
mpfr_clear_flags ();
}
int
mpfr_div_2ui (mpfr_ptr y, mpfr_srcptr x, unsigned long n, mp_rnd_t rnd_mode)
{
int inexact;
/* Most of the times, this function is called with y==x */
inexact = MPFR_UNLIKELY(y != x) ? mpfr_set (y, x, rnd_mode) : 0;
if (MPFR_LIKELY( MPFR_IS_PURE_FP(y)) )
{
/* n will have to be casted to long to make sure that the addition
and subtraction below (for overflow detection) are signed */
while (MPFR_UNLIKELY(n > LONG_MAX))
{
int inex2;
n -= LONG_MAX;
inex2 = mpfr_div_2ui(y, y, LONG_MAX, rnd_mode);
if (inex2)
return inex2; /* underflow */
}
/* MPFR_EMAX_MAX - (long) n is signed and doesn't lead to an integer
overflow; the first test useful so that the real test can't lead
to an integer overflow. */
{
mp_exp_t exp = MPFR_GET_EXP (y);
if (MPFR_UNLIKELY( __gmpfr_emin > MPFR_EMAX_MAX - (long) n ||
exp < __gmpfr_emin + (long) n) )
{
if (rnd_mode == GMP_RNDN &&
(__gmpfr_emin > MPFR_EMAX_MAX - (long) (n - 1) ||
exp < __gmpfr_emin + (long) (n - 1) ||
mpfr_powerof2_raw (y)))
rnd_mode = GMP_RNDZ;
return mpfr_set_underflow (y, rnd_mode, MPFR_SIGN(y));
}
MPFR_SET_EXP(y, exp - (long) n);
}
}
return inexact;
}
static void
test_set_underflow (void)
{
/* static to allow non-constant initialiers in r */
mpfr_t x, zero, min;
mpfr_ptr r[4];
int t[4] = { 1, -1, 1, -1 };
int i;
int s;
mpfr_inits (x, zero, min, (mpfr_ptr) 0);
mpfr_set_ui (zero, 0, GMP_RNDN);
mpfr_set_ui (min, 0, GMP_RNDN);
mpfr_nextabove (min);
r[0] = r[2] = min;
r[1] = r[3] = zero;
for (s = 1; s > 0; s = -1)
{
for (i = 0; i < GMP_RND_MAX ; i++)
{
int j;
int inex;
j = s < 0 && i > 1 ? 5 - i : i;
inex = mpfr_set_underflow (x, (mp_rnd_t) i, s);
if (mpfr_cmp (x, r[j]) || inex * t[j] <= 0)
{
printf ("Error in test_set_underflow, sign = %d,"
" rnd_mode = %s\n", s, mpfr_print_rnd_mode ((mp_rnd_t) i));
printf ("Got\n");
mpfr_out_str (stdout, 2, 0, x, GMP_RNDN);
printf (", inex = %d\ninstead of\n", inex);
mpfr_out_str (stdout, 2, 0, r[j], GMP_RNDN);
printf (", inex = %d\n", t[j]);
exit (1);
}
}
mpfr_neg (zero, zero, GMP_RNDN);
mpfr_neg (min, min, GMP_RNDN);
}
mpfr_clears (x, zero, min, (mpfr_ptr) 0);
}
int
mpfr_div_2si (mpfr_ptr y, mpfr_srcptr x, long int n, mp_rnd_t rnd_mode)
{
int inexact;
inexact = y != x ? mpfr_set (y, x, rnd_mode) : 0;
if (MPFR_IS_FP(y) && MPFR_NOTZERO(y))
{
if (n > 0 && (__mpfr_emin > MPFR_EMAX_MAX - n ||
MPFR_EXP(y) < __mpfr_emin + n))
return mpfr_set_underflow (y, rnd_mode, MPFR_SIGN(y));
if (n < 0 && (__mpfr_emax < MPFR_EMIN_MIN - n ||
MPFR_EXP(y) > __mpfr_emax + n))
return mpfr_set_overflow (y, rnd_mode, MPFR_SIGN(y));
MPFR_EXP(y) -= n;
}
return inexact;
}
/* Put in z the value of x^y, rounded according to 'rnd'.
Return the inexact flag in [0, 10]. */
int
mpc_pow (mpc_ptr z, mpc_srcptr x, mpc_srcptr y, mpc_rnd_t rnd)
{
int ret = -2, loop, x_real, x_imag, y_real, z_real = 0, z_imag = 0;
mpc_t t, u;
mpfr_prec_t p, pr, pi, maxprec;
int saved_underflow, saved_overflow;
/* save the underflow or overflow flags from MPFR */
saved_underflow = mpfr_underflow_p ();
saved_overflow = mpfr_overflow_p ();
x_real = mpfr_zero_p (mpc_imagref(x));
y_real = mpfr_zero_p (mpc_imagref(y));
if (y_real && mpfr_zero_p (mpc_realref(y))) /* case y zero */
{
if (x_real && mpfr_zero_p (mpc_realref(x)))
{
/* we define 0^0 to be (1, +0) since the real part is
coherent with MPFR where 0^0 gives 1, and the sign of the
imaginary part cannot be determined */
mpc_set_ui_ui (z, 1, 0, MPC_RNDNN);
return 0;
}
else /* x^0 = 1 +/- i*0 even for x=NaN see algorithms.tex for the
sign of zero */
{
mpfr_t n;
int inex, cx1;
int sign_zi;
/* cx1 < 0 if |x| < 1
cx1 = 0 if |x| = 1
cx1 > 0 if |x| > 1
*/
mpfr_init (n);
inex = mpc_norm (n, x, MPFR_RNDN);
cx1 = mpfr_cmp_ui (n, 1);
if (cx1 == 0 && inex != 0)
cx1 = -inex;
sign_zi = (cx1 < 0 && mpfr_signbit (mpc_imagref (y)) == 0)
|| (cx1 == 0
&& mpfr_signbit (mpc_imagref (x)) != mpfr_signbit (mpc_realref (y)))
|| (cx1 > 0 && mpfr_signbit (mpc_imagref (y)));
/* warning: mpc_set_ui_ui does not set Im(z) to -0 if Im(rnd)=RNDD */
ret = mpc_set_ui_ui (z, 1, 0, rnd);
if (MPC_RND_IM (rnd) == MPFR_RNDD || sign_zi)
mpc_conj (z, z, MPC_RNDNN);
mpfr_clear (n);
return ret;
}
}
if (!mpc_fin_p (x) || !mpc_fin_p (y))
{
/* special values: exp(y*log(x)) */
mpc_init2 (u, 2);
mpc_log (u, x, MPC_RNDNN);
mpc_mul (u, u, y, MPC_RNDNN);
ret = mpc_exp (z, u, rnd);
mpc_clear (u);
goto end;
}
if (x_real) /* case x real */
{
if (mpfr_zero_p (mpc_realref(x))) /* x is zero */
{
/* special values: exp(y*log(x)) */
mpc_init2 (u, 2);
mpc_log (u, x, MPC_RNDNN);
mpc_mul (u, u, y, MPC_RNDNN);
ret = mpc_exp (z, u, rnd);
mpc_clear (u);
goto end;
}
/* Special case 1^y = 1 */
if (mpfr_cmp_ui (mpc_realref(x), 1) == 0)
{
int s1, s2;
s1 = mpfr_signbit (mpc_realref (y));
s2 = mpfr_signbit (mpc_imagref (x));
ret = mpc_set_ui (z, +1, rnd);
/* the sign of the zero imaginary part is known in some cases (see
algorithm.tex). In such cases we have
(x +s*0i)^(y+/-0i) = x^y + s*sign(y)*0i
where s = +/-1. We extend here this rule to fix the sign of the
zero part.
Note that the sign must also be set explicitly when rnd=RNDD
because mpfr_set_ui(z_i, 0, rnd) always sets z_i to +0.
*/
if (MPC_RND_IM (rnd) == MPFR_RNDD || s1 != s2)
mpc_conj (z, z, MPC_RNDNN);
goto end;
}
/* x^y is real when:
(a) x is real and y is integer
(b) x is real non-negative and y is real */
if (y_real && (mpfr_integer_p (mpc_realref(y)) ||
mpfr_cmp_ui (mpc_realref(x), 0) >= 0))
{
int s1, s2;
s1 = mpfr_signbit (mpc_realref (y));
s2 = mpfr_signbit (mpc_imagref (x));
ret = mpfr_pow (mpc_realref(z), mpc_realref(x), mpc_realref(y), MPC_RND_RE(rnd));
ret = MPC_INEX(ret, mpfr_set_ui (mpc_imagref(z), 0, MPC_RND_IM(rnd)));
/* the sign of the zero imaginary part is known in some cases
(see algorithm.tex). In such cases we have (x +s*0i)^(y+/-0i)
= x^y + s*sign(y)*0i where s = +/-1.
We extend here this rule to fix the sign of the zero part.
Note that the sign must also be set explicitly when rnd=RNDD
because mpfr_set_ui(z_i, 0, rnd) always sets z_i to +0.
*/
if (MPC_RND_IM(rnd) == MPFR_RNDD || s1 != s2)
mpfr_neg (mpc_imagref(z), mpc_imagref(z), MPC_RND_IM(rnd));
goto end;
}
/* (-1)^(n+I*t) is real for n integer and t real */
if (mpfr_cmp_si (mpc_realref(x), -1) == 0 && mpfr_integer_p (mpc_realref(y)))
z_real = 1;
/* for x real, x^y is imaginary when:
(a) x is negative and y is half-an-integer
(b) x = -1 and Re(y) is half-an-integer
*/
if ((mpfr_cmp_ui (mpc_realref(x), 0) < 0) && is_odd (mpc_realref(y), 1)
&& (y_real || mpfr_cmp_si (mpc_realref(x), -1) == 0))
z_imag = 1;
}
else /* x non real */
/* I^(t*I) and (-I)^(t*I) are real for t real,
I^(n+t*I) and (-I)^(n+t*I) are real for n even and t real, and
I^(n+t*I) and (-I)^(n+t*I) are imaginary for n odd and t real
(s*I)^n is real for n even and imaginary for n odd */
if ((mpc_cmp_si_si (x, 0, 1) == 0 || mpc_cmp_si_si (x, 0, -1) == 0 ||
(mpfr_cmp_ui (mpc_realref(x), 0) == 0 && y_real)) &&
mpfr_integer_p (mpc_realref(y)))
{ /* x is I or -I, and Re(y) is an integer */
if (is_odd (mpc_realref(y), 0))
z_imag = 1; /* Re(y) odd: z is imaginary */
else
z_real = 1; /* Re(y) even: z is real */
}
else /* (t+/-t*I)^(2n) is imaginary for n odd and real for n even */
if (mpfr_cmpabs (mpc_realref(x), mpc_imagref(x)) == 0 && y_real &&
mpfr_integer_p (mpc_realref(y)) && is_odd (mpc_realref(y), 0) == 0)
{
if (is_odd (mpc_realref(y), -1)) /* y/2 is odd */
z_imag = 1;
else
z_real = 1;
}
pr = mpfr_get_prec (mpc_realref(z));
pi = mpfr_get_prec (mpc_imagref(z));
p = (pr > pi) ? pr : pi;
p += 12; /* experimentally, seems to give less than 10% of failures in
Ziv's strategy; probably wrong now since q is not computed */
if (p < 64)
p = 64;
mpc_init2 (u, p);
mpc_init2 (t, p);
pr += MPC_RND_RE(rnd) == MPFR_RNDN;
pi += MPC_RND_IM(rnd) == MPFR_RNDN;
maxprec = MPC_MAX_PREC (z);
x_imag = mpfr_zero_p (mpc_realref(x));
for (loop = 0;; loop++)
{
int ret_exp;
mpfr_exp_t dr, di;
mpfr_prec_t q;
mpc_log (t, x, MPC_RNDNN);
mpc_mul (t, t, y, MPC_RNDNN);
/* Compute q such that |Re (y log x)|, |Im (y log x)| < 2^q.
We recompute it at each loop since we might get different
bounds if the precision is not enough. */
q = mpfr_get_exp (mpc_realref(t)) > 0 ? mpfr_get_exp (mpc_realref(t)) : 0;
if (mpfr_get_exp (mpc_imagref(t)) > (mpfr_exp_t) q)
q = mpfr_get_exp (mpc_imagref(t));
mpfr_clear_overflow ();
mpfr_clear_underflow ();
ret_exp = mpc_exp (u, t, MPC_RNDNN);
if (mpfr_underflow_p () || mpfr_overflow_p ()) {
/* under- and overflow flags are set by mpc_exp */
mpc_set (z, u, MPC_RNDNN);
ret = ret_exp;
goto exact;
}
/* Since the error bound is global, we have to take into account the
exponent difference between the real and imaginary parts. We assume
either the real or the imaginary part of u is not zero.
*/
dr = mpfr_zero_p (mpc_realref(u)) ? mpfr_get_exp (mpc_imagref(u))
: mpfr_get_exp (mpc_realref(u));
di = mpfr_zero_p (mpc_imagref(u)) ? dr : mpfr_get_exp (mpc_imagref(u));
if (dr > di)
{
di = dr - di;
dr = 0;
}
else
{
dr = di - dr;
di = 0;
}
/* the term -3 takes into account the factor 4 in the complex error
(see algorithms.tex) plus one due to the exponent difference: if
z = a + I*b, where the relative error on z is at most 2^(-p), and
EXP(a) = EXP(b) + k, the relative error on b is at most 2^(k-p) */
if ((z_imag || (p > q + 3 + dr && mpfr_can_round (mpc_realref(u), p - q - 3 - dr, MPFR_RNDN, MPFR_RNDZ, pr))) &&
(z_real || (p > q + 3 + di && mpfr_can_round (mpc_imagref(u), p - q - 3 - di, MPFR_RNDN, MPFR_RNDZ, pi))))
break;
/* if Re(u) is not known to be zero, assume it is a normal number, i.e.,
neither zero, Inf or NaN, otherwise we might enter an infinite loop */
MPC_ASSERT (z_imag || mpfr_number_p (mpc_realref(u)));
/* idem for Im(u) */
MPC_ASSERT (z_real || mpfr_number_p (mpc_imagref(u)));
if (ret == -2) /* we did not yet call mpc_pow_exact, or it aborted
because intermediate computations had > maxprec bits */
{
/* check exact cases (see algorithms.tex) */
if (y_real)
{
maxprec *= 2;
ret = mpc_pow_exact (z, x, mpc_realref(y), rnd, maxprec);
if (ret != -1 && ret != -2)
goto exact;
}
p += dr + di + 64;
}
else
p += p / 2;
mpc_set_prec (t, p);
mpc_set_prec (u, p);
}
if (z_real)
{
/* When the result is real (see algorithm.tex for details),
Im(x^y) =
+ sign(imag(y))*0i, if |x| > 1
+ sign(imag(x))*sign(real(y))*0i, if |x| = 1
- sign(imag(y))*0i, if |x| < 1
*/
mpfr_t n;
int inex, cx1;
int sign_zi, sign_rex, sign_imx;
/* cx1 < 0 if |x| < 1
cx1 = 0 if |x| = 1
cx1 > 0 if |x| > 1
*/
sign_rex = mpfr_signbit (mpc_realref (x));
sign_imx = mpfr_signbit (mpc_imagref (x));
mpfr_init (n);
inex = mpc_norm (n, x, MPFR_RNDN);
cx1 = mpfr_cmp_ui (n, 1);
if (cx1 == 0 && inex != 0)
cx1 = -inex;
sign_zi = (cx1 < 0 && mpfr_signbit (mpc_imagref (y)) == 0)
|| (cx1 == 0 && sign_imx != mpfr_signbit (mpc_realref (y)))
|| (cx1 > 0 && mpfr_signbit (mpc_imagref (y)));
/* copy RE(y) to n since if z==y we will destroy Re(y) below */
mpfr_set_prec (n, mpfr_get_prec (mpc_realref (y)));
mpfr_set (n, mpc_realref (y), MPFR_RNDN);
ret = mpfr_set (mpc_realref(z), mpc_realref(u), MPC_RND_RE(rnd));
if (y_real && (x_real || x_imag))
{
/* FIXME: with y_real we assume Im(y) is really 0, which is the case
for example when y comes from pow_fr, but in case Im(y) is +0 or
-0, we might get different results */
mpfr_set_ui (mpc_imagref (z), 0, MPC_RND_IM (rnd));
fix_sign (z, sign_rex, sign_imx, n);
ret = MPC_INEX(ret, 0); /* imaginary part is exact */
}
else
{
ret = MPC_INEX (ret, mpfr_set_ui (mpc_imagref (z), 0, MPC_RND_IM (rnd)));
/* warning: mpfr_set_ui does not set Im(z) to -0 if Im(rnd) = RNDD */
if (MPC_RND_IM (rnd) == MPFR_RNDD || sign_zi)
mpc_conj (z, z, MPC_RNDNN);
}
mpfr_clear (n);
}
else if (z_imag)
{
ret = mpfr_set (mpc_imagref(z), mpc_imagref(u), MPC_RND_IM(rnd));
/* if z is imaginary and y real, then x cannot be real */
if (y_real && x_imag)
{
int sign_rex = mpfr_signbit (mpc_realref (x));
/* If z overlaps with y we set Re(z) before checking Re(y) below,
but in that case y=0, which was dealt with above. */
mpfr_set_ui (mpc_realref (z), 0, MPC_RND_RE (rnd));
/* Note: fix_sign only does something when y is an integer,
then necessarily y = 1 or 3 (mod 4), and in that case the
sign of Im(x) is irrelevant. */
fix_sign (z, sign_rex, 0, mpc_realref (y));
ret = MPC_INEX(0, ret);
}
else
ret = MPC_INEX(mpfr_set_ui (mpc_realref(z), 0, MPC_RND_RE(rnd)), ret);
}
else
ret = mpc_set (z, u, rnd);
exact:
mpc_clear (t);
mpc_clear (u);
/* restore underflow and overflow flags from MPFR */
if (saved_underflow)
mpfr_set_underflow ();
if (saved_overflow)
mpfr_set_overflow ();
end:
return ret;
}
int
mpc_sqr (mpc_ptr rop, mpc_srcptr op, mpc_rnd_t rnd)
{
int ok;
mpfr_t u, v;
mpfr_t x;
/* temporary variable to hold the real part of op,
needed in the case rop==op */
mpfr_prec_t prec;
int inex_re, inex_im, inexact;
mpfr_exp_t emin;
int saved_underflow;
/* special values: NaN and infinities */
if (!mpc_fin_p (op)) {
if (mpfr_nan_p (mpc_realref (op)) || mpfr_nan_p (mpc_imagref (op))) {
mpfr_set_nan (mpc_realref (rop));
mpfr_set_nan (mpc_imagref (rop));
}
else if (mpfr_inf_p (mpc_realref (op))) {
if (mpfr_inf_p (mpc_imagref (op))) {
mpfr_set_inf (mpc_imagref (rop),
MPFR_SIGN (mpc_realref (op)) * MPFR_SIGN (mpc_imagref (op)));
mpfr_set_nan (mpc_realref (rop));
}
else {
if (mpfr_zero_p (mpc_imagref (op)))
mpfr_set_nan (mpc_imagref (rop));
else
mpfr_set_inf (mpc_imagref (rop),
MPFR_SIGN (mpc_realref (op)) * MPFR_SIGN (mpc_imagref (op)));
mpfr_set_inf (mpc_realref (rop), +1);
}
}
else /* IM(op) is infinity, RE(op) is not */ {
if (mpfr_zero_p (mpc_realref (op)))
mpfr_set_nan (mpc_imagref (rop));
else
mpfr_set_inf (mpc_imagref (rop),
MPFR_SIGN (mpc_realref (op)) * MPFR_SIGN (mpc_imagref (op)));
mpfr_set_inf (mpc_realref (rop), -1);
}
return MPC_INEX (0, 0); /* exact */
}
prec = MPC_MAX_PREC(rop);
/* Check for real resp. purely imaginary number */
if (mpfr_zero_p (mpc_imagref(op))) {
int same_sign = mpfr_signbit (mpc_realref (op)) == mpfr_signbit (mpc_imagref (op));
inex_re = mpfr_sqr (mpc_realref(rop), mpc_realref(op), MPC_RND_RE(rnd));
inex_im = mpfr_set_ui (mpc_imagref(rop), 0ul, MPFR_RNDN);
if (!same_sign)
mpc_conj (rop, rop, MPC_RNDNN);
return MPC_INEX(inex_re, inex_im);
}
if (mpfr_zero_p (mpc_realref(op))) {
int same_sign = mpfr_signbit (mpc_realref (op)) == mpfr_signbit (mpc_imagref (op));
inex_re = -mpfr_sqr (mpc_realref(rop), mpc_imagref(op), INV_RND (MPC_RND_RE(rnd)));
mpfr_neg (mpc_realref(rop), mpc_realref(rop), MPFR_RNDN);
inex_im = mpfr_set_ui (mpc_imagref(rop), 0ul, MPFR_RNDN);
if (!same_sign)
mpc_conj (rop, rop, MPC_RNDNN);
return MPC_INEX(inex_re, inex_im);
}
if (rop == op)
{
mpfr_init2 (x, MPC_PREC_RE (op));
mpfr_set (x, op->re, MPFR_RNDN);
}
else
x [0] = op->re [0];
/* From here on, use x instead of op->re and safely overwrite rop->re. */
/* Compute real part of result. */
if (SAFE_ABS (mpfr_exp_t,
mpfr_get_exp (mpc_realref (op)) - mpfr_get_exp (mpc_imagref (op)))
> (mpfr_exp_t) MPC_MAX_PREC (op) / 2) {
/* If the real and imaginary parts of the argument have very different
exponents, it is not reasonable to use Karatsuba squaring; compute
exactly with the standard formulae instead, even if this means an
additional multiplication. Using the approach copied from mul, over-
and underflows are also handled correctly. */
inex_re = mpfr_fsss (rop->re, x, op->im, MPC_RND_RE (rnd));
}
else {
/* Karatsuba squaring: we compute the real part as (x+y)*(x-y) and the
imaginary part as 2*x*y, with a total of 2M instead of 2S+1M for the
naive algorithm, which computes x^2-y^2 and 2*y*y */
mpfr_init (u);
mpfr_init (v);
emin = mpfr_get_emin ();
do
{
prec += mpc_ceil_log2 (prec) + 5;
mpfr_set_prec (u, prec);
mpfr_set_prec (v, prec);
/* Let op = x + iy. We need u = x+y and v = x-y, rounded away. */
/* The error is bounded above by 1 ulp. */
/* We first let inexact be 1 if the real part is not computed */
/* exactly and determine the sign later. */
inexact = mpfr_add (u, x, mpc_imagref (op), MPFR_RNDA)
| mpfr_sub (v, x, mpc_imagref (op), MPFR_RNDA);
/* compute the real part as u*v, rounded away */
/* determine also the sign of inex_re */
if (mpfr_sgn (u) == 0 || mpfr_sgn (v) == 0) {
/* as we have rounded away, the result is exact */
mpfr_set_ui (mpc_realref (rop), 0, MPFR_RNDN);
inex_re = 0;
ok = 1;
}
else {
inexact |= mpfr_mul (u, u, v, MPFR_RNDA); /* error 5 */
if (mpfr_get_exp (u) == emin || mpfr_inf_p (u)) {
/* under- or overflow */
inex_re = mpfr_fsss (rop->re, x, op->im, MPC_RND_RE (rnd));
ok = 1;
}
else {
ok = (!inexact) | mpfr_can_round (u, prec - 3,
MPFR_RNDA, MPFR_RNDZ,
MPC_PREC_RE (rop) + (MPC_RND_RE (rnd) == MPFR_RNDN));
if (ok) {
inex_re = mpfr_set (mpc_realref (rop), u, MPC_RND_RE (rnd));
if (inex_re == 0)
/* remember that u was already rounded */
inex_re = inexact;
}
}
}
}
while (!ok);
mpfr_clear (u);
mpfr_clear (v);
}
saved_underflow = mpfr_underflow_p ();
mpfr_clear_underflow ();
inex_im = mpfr_mul (rop->im, x, op->im, MPC_RND_IM (rnd));
if (!mpfr_underflow_p ())
inex_im |= mpfr_mul_2ui (rop->im, rop->im, 1, MPC_RND_IM (rnd));
/* We must not multiply by 2 if rop->im has been set to the smallest
representable number. */
if (saved_underflow)
mpfr_set_underflow ();
if (rop == op)
mpfr_clear (x);
return MPC_INEX (inex_re, inex_im);
}
int
mpc_div (mpc_ptr a, mpc_srcptr b, mpc_srcptr c, mpc_rnd_t rnd)
{
int ok_re = 0, ok_im = 0;
mpc_t res, c_conj;
mpfr_t q;
mpfr_prec_t prec;
int inex, inexact_prod, inexact_norm, inexact_re, inexact_im, loops = 0;
int underflow_norm, overflow_norm, underflow_prod, overflow_prod;
int underflow_re = 0, overflow_re = 0, underflow_im = 0, overflow_im = 0;
mpfr_rnd_t rnd_re = MPC_RND_RE (rnd), rnd_im = MPC_RND_IM (rnd);
int saved_underflow, saved_overflow;
int tmpsgn;
mpfr_exp_t e, emin, emax, emid; /* for scaling of exponents */
mpc_t b_scaled, c_scaled;
mpfr_t b_re, b_im, c_re, c_im;
/* According to the C standard G.3, there are three types of numbers: */
/* finite (both parts are usual real numbers; contains 0), infinite */
/* (at least one part is a real infinity) and all others; the latter */
/* are numbers containing a nan, but no infinity, and could reasonably */
/* be called nan. */
/* By G.5.1.4, infinite/finite=infinite; finite/infinite=0; */
/* all other divisions that are not finite/finite return nan+i*nan. */
/* Division by 0 could be handled by the following case of division by */
/* a real; we handle it separately instead. */
if (mpc_zero_p (c)) /* both Re(c) and Im(c) are zero */
return mpc_div_zero (a, b, c, rnd);
else if (mpc_inf_p (b) && mpc_fin_p (c)) /* either Re(b) or Im(b) is infinite
and both Re(c) and Im(c) are ordinary */
return mpc_div_inf_fin (a, b, c);
else if (mpc_fin_p (b) && mpc_inf_p (c))
return mpc_div_fin_inf (a, b, c);
else if (!mpc_fin_p (b) || !mpc_fin_p (c)) {
mpc_set_nan (a);
return MPC_INEX (0, 0);
}
else if (mpfr_zero_p(mpc_imagref(c)))
return mpc_div_real (a, b, c, rnd);
else if (mpfr_zero_p(mpc_realref(c)))
return mpc_div_imag (a, b, c, rnd);
prec = MPC_MAX_PREC(a);
mpc_init2 (res, 2);
mpfr_init (q);
/* compute scaling of exponents: none of Re(c) and Im(c) can be zero,
but one of Re(b) or Im(b) could be zero */
e = mpfr_get_exp (mpc_realref (c));
emin = emax = e;
e = mpfr_get_exp (mpc_imagref (c));
if (e > emax)
emax = e;
else if (e < emin)
emin = e;
if (!mpfr_zero_p (mpc_realref (b)))
{
e = mpfr_get_exp (mpc_realref (b));
if (e > emax)
emax = e;
else if (e < emin)
emin = e;
}
if (!mpfr_zero_p (mpc_imagref (b)))
{
e = mpfr_get_exp (mpc_imagref (b));
if (e > emax)
emax = e;
else if (e < emin)
emin = e;
}
/* all input exponents are in [emin, emax] */
emid = emin / 2 + emax / 2;
/* scale the inputs */
b_re[0] = mpc_realref (b)[0];
if (!mpfr_zero_p (mpc_realref (b)))
MPFR_EXP(b_re) = MPFR_EXP(mpc_realref (b)) - emid;
b_im[0] = mpc_imagref (b)[0];
if (!mpfr_zero_p (mpc_imagref (b)))
MPFR_EXP(b_im) = MPFR_EXP(mpc_imagref (b)) - emid;
c_re[0] = mpc_realref (c)[0];
MPFR_EXP(c_re) = MPFR_EXP(mpc_realref (c)) - emid;
c_im[0] = mpc_imagref (c)[0];
MPFR_EXP(c_im) = MPFR_EXP(mpc_imagref (c)) - emid;
/* create the scaled inputs without allocating new memory */
mpc_realref (b_scaled)[0] = b_re[0];
mpc_imagref (b_scaled)[0] = b_im[0];
mpc_realref (c_scaled)[0] = c_re[0];
mpc_imagref (c_scaled)[0] = c_im[0];
/* create the conjugate of c in c_conj without allocating new memory */
mpc_realref (c_conj)[0] = mpc_realref (c_scaled)[0];
mpc_imagref (c_conj)[0] = mpc_imagref (c_scaled)[0];
MPFR_CHANGE_SIGN (mpc_imagref (c_conj));
/* save the underflow or overflow flags from MPFR */
saved_underflow = mpfr_underflow_p ();
saved_overflow = mpfr_overflow_p ();
do {
loops ++;
prec += loops <= 2 ? mpc_ceil_log2 (prec) + 5 : prec / 2;
mpc_set_prec (res, prec);
mpfr_set_prec (q, prec);
/* first compute norm(c_scaled) */
mpfr_clear_underflow ();
mpfr_clear_overflow ();
inexact_norm = mpc_norm (q, c_scaled, MPFR_RNDU);
underflow_norm = mpfr_underflow_p ();
overflow_norm = mpfr_overflow_p ();
if (underflow_norm)
mpfr_set_ui (q, 0ul, MPFR_RNDN);
/* to obtain divisions by 0 later on */
/* now compute b_scaled*conjugate(c_scaled) */
mpfr_clear_underflow ();
mpfr_clear_overflow ();
inexact_prod = mpc_mul (res, b_scaled, c_conj, MPC_RNDZZ);
inexact_re = MPC_INEX_RE (inexact_prod);
inexact_im = MPC_INEX_IM (inexact_prod);
underflow_prod = mpfr_underflow_p ();
overflow_prod = mpfr_overflow_p ();
/* unfortunately, does not distinguish between under-/overflow
in real or imaginary parts
hopefully, the side-effects of mpc_mul do indeed raise the
mpfr exceptions */
if (overflow_prod) {
/* FIXME: in case overflow_norm is also true, the code below is wrong,
since the after division by the norm, we might end up with finite
real and/or imaginary parts. A workaround would be to scale the
inputs (in case the exponents are within the same range). */
int isinf = 0;
/* determine if the real part of res is the maximum or the minimum
representable number */
tmpsgn = mpfr_sgn (mpc_realref(res));
if (tmpsgn > 0)
{
mpfr_nextabove (mpc_realref(res));
isinf = mpfr_inf_p (mpc_realref(res));
mpfr_nextbelow (mpc_realref(res));
}
else if (tmpsgn < 0)
{
mpfr_nextbelow (mpc_realref(res));
isinf = mpfr_inf_p (mpc_realref(res));
mpfr_nextabove (mpc_realref(res));
}
if (isinf)
{
mpfr_set_inf (mpc_realref(res), tmpsgn);
overflow_re = 1;
}
/* same for the imaginary part */
tmpsgn = mpfr_sgn (mpc_imagref(res));
isinf = 0;
if (tmpsgn > 0)
{
mpfr_nextabove (mpc_imagref(res));
isinf = mpfr_inf_p (mpc_imagref(res));
mpfr_nextbelow (mpc_imagref(res));
}
else if (tmpsgn < 0)
{
mpfr_nextbelow (mpc_imagref(res));
isinf = mpfr_inf_p (mpc_imagref(res));
mpfr_nextabove (mpc_imagref(res));
}
if (isinf)
{
mpfr_set_inf (mpc_imagref(res), tmpsgn);
overflow_im = 1;
}
mpc_set (a, res, rnd);
goto end;
}
/* divide the product by the norm */
if (inexact_norm == 0 && (inexact_re == 0 || inexact_im == 0)) {
/* The division has good chances to be exact in at least one part. */
/* Since this can cause problems when not rounding to the nearest, */
/* we use the division code of mpfr, which handles the situation. */
mpfr_clear_underflow ();
mpfr_clear_overflow ();
inexact_re |= mpfr_div (mpc_realref (res), mpc_realref (res), q, MPFR_RNDZ);
underflow_re = mpfr_underflow_p ();
overflow_re = mpfr_overflow_p ();
ok_re = !inexact_re || underflow_re || overflow_re
|| mpfr_can_round (mpc_realref (res), prec - 4, MPFR_RNDN,
MPFR_RNDZ, MPC_PREC_RE(a) + (rnd_re == MPFR_RNDN));
if (ok_re) /* compute imaginary part */ {
mpfr_clear_underflow ();
mpfr_clear_overflow ();
inexact_im |= mpfr_div (mpc_imagref (res), mpc_imagref (res), q, MPFR_RNDZ);
underflow_im = mpfr_underflow_p ();
overflow_im = mpfr_overflow_p ();
ok_im = !inexact_im || underflow_im || overflow_im
|| mpfr_can_round (mpc_imagref (res), prec - 4, MPFR_RNDN,
MPFR_RNDZ, MPC_PREC_IM(a) + (rnd_im == MPFR_RNDN));
}
}
else {
/* The division is inexact, so for efficiency reasons we invert q */
/* only once and multiply by the inverse. */
if (mpfr_ui_div (q, 1ul, q, MPFR_RNDZ) || inexact_norm) {
/* if 1/q is inexact, the approximations of the real and
imaginary part below will be inexact, unless RE(res)
or IM(res) is zero */
inexact_re |= !mpfr_zero_p (mpc_realref (res));
inexact_im |= !mpfr_zero_p (mpc_imagref (res));
}
mpfr_clear_underflow ();
mpfr_clear_overflow ();
inexact_re |= mpfr_mul (mpc_realref (res), mpc_realref (res), q, MPFR_RNDZ);
underflow_re = mpfr_underflow_p ();
overflow_re = mpfr_overflow_p ();
ok_re = !inexact_re || underflow_re || overflow_re
|| mpfr_can_round (mpc_realref (res), prec - 4, MPFR_RNDN,
MPFR_RNDZ, MPC_PREC_RE(a) + (rnd_re == MPFR_RNDN));
if (ok_re) /* compute imaginary part */ {
mpfr_clear_underflow ();
mpfr_clear_overflow ();
inexact_im |= mpfr_mul (mpc_imagref (res), mpc_imagref (res), q, MPFR_RNDZ);
underflow_im = mpfr_underflow_p ();
overflow_im = mpfr_overflow_p ();
ok_im = !inexact_im || underflow_im || overflow_im
|| mpfr_can_round (mpc_imagref (res), prec - 4, MPFR_RNDN,
MPFR_RNDZ, MPC_PREC_IM(a) + (rnd_im == MPFR_RNDN));
}
}
} while ((!ok_re || !ok_im) && !underflow_norm && !overflow_norm
&& !underflow_prod && !overflow_prod);
inex = mpc_set (a, res, rnd);
inexact_re = MPC_INEX_RE (inex);
inexact_im = MPC_INEX_IM (inex);
end:
/* fix values and inexact flags in case of overflow/underflow */
/* FIXME: heuristic, certainly does not cover all cases */
if (overflow_re || (underflow_norm && !underflow_prod)) {
mpfr_set_inf (mpc_realref (a), mpfr_sgn (mpc_realref (res)));
inexact_re = mpfr_sgn (mpc_realref (res));
}
else if (underflow_re || (overflow_norm && !overflow_prod)) {
inexact_re = mpfr_signbit (mpc_realref (res)) ? 1 : -1;
mpfr_set_zero (mpc_realref (a), -inexact_re);
}
if (overflow_im || (underflow_norm && !underflow_prod)) {
mpfr_set_inf (mpc_imagref (a), mpfr_sgn (mpc_imagref (res)));
inexact_im = mpfr_sgn (mpc_imagref (res));
}
else if (underflow_im || (overflow_norm && !overflow_prod)) {
inexact_im = mpfr_signbit (mpc_imagref (res)) ? 1 : -1;
mpfr_set_zero (mpc_imagref (a), -inexact_im);
}
mpc_clear (res);
mpfr_clear (q);
/* restore underflow and overflow flags from MPFR */
if (saved_underflow)
mpfr_set_underflow ();
if (saved_overflow)
mpfr_set_overflow ();
return MPC_INEX (inexact_re, inexact_im);
}
int
mpc_exp (mpc_ptr rop, mpc_srcptr op, mpc_rnd_t rnd)
{
mpfr_t x, y, z;
mpfr_prec_t prec;
int ok = 0;
int inex_re, inex_im;
int saved_underflow, saved_overflow;
/* special values */
if (mpfr_nan_p (mpc_realref (op)) || mpfr_nan_p (mpc_imagref (op)))
/* NaNs
exp(nan +i*y) = nan -i*0 if y = -0,
nan +i*0 if y = +0,
nan +i*nan otherwise
exp(x+i*nan) = +/-0 +/-i*0 if x=-inf,
+/-inf +i*nan if x=+inf,
nan +i*nan otherwise */
{
if (mpfr_zero_p (mpc_imagref (op)))
return mpc_set (rop, op, MPC_RNDNN);
if (mpfr_inf_p (mpc_realref (op)))
{
if (mpfr_signbit (mpc_realref (op)))
return mpc_set_ui_ui (rop, 0, 0, MPC_RNDNN);
else
{
mpfr_set_inf (mpc_realref (rop), +1);
mpfr_set_nan (mpc_imagref (rop));
return MPC_INEX(0, 0); /* Inf/NaN are exact */
}
}
mpfr_set_nan (mpc_realref (rop));
mpfr_set_nan (mpc_imagref (rop));
return MPC_INEX(0, 0); /* NaN is exact */
}
if (mpfr_zero_p (mpc_imagref(op)))
/* special case when the input is real
exp(x-i*0) = exp(x) -i*0, even if x is NaN
exp(x+i*0) = exp(x) +i*0, even if x is NaN */
{
inex_re = mpfr_exp (mpc_realref(rop), mpc_realref(op), MPC_RND_RE(rnd));
inex_im = mpfr_set (mpc_imagref(rop), mpc_imagref(op), MPC_RND_IM(rnd));
return MPC_INEX(inex_re, inex_im);
}
if (mpfr_zero_p (mpc_realref (op)))
/* special case when the input is imaginary */
{
inex_re = mpfr_cos (mpc_realref (rop), mpc_imagref (op), MPC_RND_RE(rnd));
inex_im = mpfr_sin (mpc_imagref (rop), mpc_imagref (op), MPC_RND_IM(rnd));
return MPC_INEX(inex_re, inex_im);
}
if (mpfr_inf_p (mpc_realref (op)))
/* real part is an infinity,
exp(-inf +i*y) = 0*(cos y +i*sin y)
exp(+inf +i*y) = +/-inf +i*nan if y = +/-inf
+inf*(cos y +i*sin y) if 0 < |y| < inf */
{
mpfr_t n;
mpfr_init2 (n, 2);
if (mpfr_signbit (mpc_realref (op)))
mpfr_set_ui (n, 0, GMP_RNDN);
else
mpfr_set_inf (n, +1);
if (mpfr_inf_p (mpc_imagref (op)))
{
inex_re = mpfr_set (mpc_realref (rop), n, GMP_RNDN);
if (mpfr_signbit (mpc_realref (op)))
inex_im = mpfr_set (mpc_imagref (rop), n, GMP_RNDN);
else
{
mpfr_set_nan (mpc_imagref (rop));
inex_im = 0; /* NaN is exact */
}
}
else
{
mpfr_t c, s;
mpfr_init2 (c, 2);
mpfr_init2 (s, 2);
mpfr_sin_cos (s, c, mpc_imagref (op), GMP_RNDN);
inex_re = mpfr_copysign (mpc_realref (rop), n, c, GMP_RNDN);
inex_im = mpfr_copysign (mpc_imagref (rop), n, s, GMP_RNDN);
mpfr_clear (s);
mpfr_clear (c);
}
mpfr_clear (n);
return MPC_INEX(inex_re, inex_im);
}
if (mpfr_inf_p (mpc_imagref (op)))
/* real part is finite non-zero number, imaginary part is an infinity */
{
mpfr_set_nan (mpc_realref (rop));
mpfr_set_nan (mpc_imagref (rop));
return MPC_INEX(0, 0); /* NaN is exact */
}
/* from now on, both parts of op are regular numbers */
prec = MPC_MAX_PREC(rop)
+ MPC_MAX (MPC_MAX (-mpfr_get_exp (mpc_realref (op)), 0),
-mpfr_get_exp (mpc_imagref (op)));
/* When op is close to 0, then exp is close to 1+Re(op), while
cos is close to 1-Im(op); to decide on the ternary value of exp*cos,
we need a high enough precision so that none of exp or cos is
computed as 1. */
mpfr_init2 (x, 2);
mpfr_init2 (y, 2);
mpfr_init2 (z, 2);
/* save the underflow or overflow flags from MPFR */
saved_underflow = mpfr_underflow_p ();
saved_overflow = mpfr_overflow_p ();
do
{
prec += mpc_ceil_log2 (prec) + 5;
mpfr_set_prec (x, prec);
mpfr_set_prec (y, prec);
mpfr_set_prec (z, prec);
/* FIXME: x may overflow so x.y does overflow too, while Re(exp(op))
could be represented in the precision of rop. */
mpfr_clear_overflow ();
mpfr_clear_underflow ();
mpfr_exp (x, mpc_realref(op), GMP_RNDN); /* error <= 0.5ulp */
mpfr_sin_cos (z, y, mpc_imagref(op), GMP_RNDN); /* errors <= 0.5ulp */
mpfr_mul (y, y, x, GMP_RNDN); /* error <= 2ulp */
ok = mpfr_overflow_p () || mpfr_zero_p (x)
|| mpfr_can_round (y, prec - 2, GMP_RNDN, GMP_RNDZ,
MPC_PREC_RE(rop) + (MPC_RND_RE(rnd) == GMP_RNDN));
if (ok) /* compute imaginary part */
{
mpfr_mul (z, z, x, GMP_RNDN);
ok = mpfr_overflow_p () || mpfr_zero_p (x)
|| mpfr_can_round (z, prec - 2, GMP_RNDN, GMP_RNDZ,
MPC_PREC_IM(rop) + (MPC_RND_IM(rnd) == GMP_RNDN));
}
}
while (ok == 0);
inex_re = mpfr_set (mpc_realref(rop), y, MPC_RND_RE(rnd));
inex_im = mpfr_set (mpc_imagref(rop), z, MPC_RND_IM(rnd));
if (mpfr_overflow_p ()) {
/* overflow in real exponential, inex is sign of infinite result */
inex_re = mpfr_sgn (y);
inex_im = mpfr_sgn (z);
}
else if (mpfr_underflow_p ()) {
/* underflow in real exponential, inex is opposite of sign of 0 result */
inex_re = (mpfr_signbit (y) ? +1 : -1);
inex_im = (mpfr_signbit (z) ? +1 : -1);
}
mpfr_clear (x);
mpfr_clear (y);
mpfr_clear (z);
/* restore underflow and overflow flags from MPFR */
if (saved_underflow)
mpfr_set_underflow ();
if (saved_overflow)
mpfr_set_overflow ();
return MPC_INEX(inex_re, inex_im);
}
static void
check_set (void)
{
mpfr_clear_flags ();
mpfr_set_overflow ();
MPFR_ASSERTN ((mpfr_overflow_p) ());
mpfr_set_underflow ();
MPFR_ASSERTN ((mpfr_underflow_p) ());
mpfr_set_divby0 ();
MPFR_ASSERTN ((mpfr_divby0_p) ());
mpfr_set_nanflag ();
MPFR_ASSERTN ((mpfr_nanflag_p) ());
mpfr_set_inexflag ();
MPFR_ASSERTN ((mpfr_inexflag_p) ());
mpfr_set_erangeflag ();
MPFR_ASSERTN ((mpfr_erangeflag_p) ());
MPFR_ASSERTN (__gmpfr_flags == MPFR_FLAGS_ALL);
mpfr_clear_overflow ();
MPFR_ASSERTN (! (mpfr_overflow_p) ());
mpfr_clear_underflow ();
MPFR_ASSERTN (! (mpfr_underflow_p) ());
mpfr_clear_divby0 ();
MPFR_ASSERTN (! (mpfr_divby0_p) ());
mpfr_clear_nanflag ();
MPFR_ASSERTN (! (mpfr_nanflag_p) ());
mpfr_clear_inexflag ();
MPFR_ASSERTN (! (mpfr_inexflag_p) ());
mpfr_clear_erangeflag ();
MPFR_ASSERTN (! (mpfr_erangeflag_p) ());
MPFR_ASSERTN (__gmpfr_flags == 0);
(mpfr_set_overflow) ();
MPFR_ASSERTN (mpfr_overflow_p ());
(mpfr_set_underflow) ();
MPFR_ASSERTN (mpfr_underflow_p ());
(mpfr_set_divby0) ();
MPFR_ASSERTN (mpfr_divby0_p ());
(mpfr_set_nanflag) ();
MPFR_ASSERTN (mpfr_nanflag_p ());
(mpfr_set_inexflag) ();
MPFR_ASSERTN (mpfr_inexflag_p ());
(mpfr_set_erangeflag) ();
MPFR_ASSERTN (mpfr_erangeflag_p ());
MPFR_ASSERTN (__gmpfr_flags == MPFR_FLAGS_ALL);
(mpfr_clear_overflow) ();
MPFR_ASSERTN (! mpfr_overflow_p ());
(mpfr_clear_underflow) ();
MPFR_ASSERTN (! mpfr_underflow_p ());
(mpfr_clear_divby0) ();
MPFR_ASSERTN (! mpfr_divby0_p ());
(mpfr_clear_nanflag) ();
MPFR_ASSERTN (! mpfr_nanflag_p ());
(mpfr_clear_inexflag) ();
MPFR_ASSERTN (! mpfr_inexflag_p ());
(mpfr_clear_erangeflag) ();
MPFR_ASSERTN (! mpfr_erangeflag_p ());
MPFR_ASSERTN (__gmpfr_flags == 0);
}
