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);
}
static void
check_set (void)
{
long int lo;
mpz_t mpz;
mpq_t mpq;
mpf_t mpf;
mpfr_t fr;
mpc_t x, z;
mpfr_prec_t prec;
mpz_init (mpz);
mpq_init (mpq);
mpf_init2 (mpf, 1000);
mpfr_init2 (fr, 1000);
mpc_init2 (x, 1000);
mpc_init2 (z, 1000);
mpz_set_ui (mpz, 0x4217);
mpq_set_si (mpq, -1, 0x4321);
mpf_set_q (mpf, mpq);
for (prec = 2; prec <= 1000; prec++)
{
unsigned long int u = (unsigned long int) prec;
mpc_set_prec (z, prec);
mpfr_set_prec (fr, prec);
lo = -prec;
mpfr_set_d (fr, 1.23456789, GMP_RNDN);
mpc_set_d (z, 1.23456789, MPC_RNDNN);
if (mpfr_cmp (MPC_RE(z), fr) != 0 || mpfr_cmp_si (MPC_IM(z), 0) != 0)
PRINT_ERROR ("mpc_set_d", prec, z);
#if defined _MPC_H_HAVE_COMPLEX
mpc_set_dc (z, I*1.23456789+1.23456789, MPC_RNDNN);
if (mpfr_cmp (MPC_RE(z), fr) != 0 || mpfr_cmp (MPC_IM(z), fr) != 0)
PRINT_ERROR ("mpc_set_c", prec, z);
#endif
mpc_set_ui (z, u, MPC_RNDNN);
if (mpfr_cmp_ui (MPC_RE(z), u) != 0
|| mpfr_cmp_ui (MPC_IM(z), 0) != 0)
PRINT_ERROR ("mpc_set_ui", prec, z);
mpc_set_d_d (z, 1.23456789, 1.23456789, MPC_RNDNN);
if (mpfr_cmp (MPC_RE(z), fr) != 0 || mpfr_cmp (MPC_IM(z), fr) != 0)
PRINT_ERROR ("mpc_set_d_d", prec, z);
mpc_set_si (z, lo, MPC_RNDNN);
if (mpfr_cmp_si (MPC_RE(z), lo) != 0 || mpfr_cmp_ui (MPC_IM(z), 0) != 0)
PRINT_ERROR ("mpc_set_si", prec, z);
mpfr_set_ld (fr, 1.23456789L, GMP_RNDN);
mpc_set_ld_ld (z, 1.23456789L, 1.23456789L, MPC_RNDNN);
if (mpfr_cmp (MPC_RE(z), fr) != 0 || mpfr_cmp (MPC_IM(z), fr) != 0)
PRINT_ERROR ("mpc_set_ld_ld", prec, z);
#if defined _MPC_H_HAVE_COMPLEX
mpc_set_ldc (z, I*1.23456789L+1.23456789L, MPC_RNDNN);
if (mpfr_cmp (MPC_RE(z), fr) != 0 || mpfr_cmp (MPC_IM(z), fr) != 0)
PRINT_ERROR ("mpc_set_lc", prec, z);
#endif
mpc_set_ui_ui (z, u, u, MPC_RNDNN);
if (mpfr_cmp_ui (MPC_RE(z), u) != 0
|| mpfr_cmp_ui (MPC_IM(z), u) != 0)
PRINT_ERROR ("mpc_set_ui_ui", prec, z);
mpc_set_ld (z, 1.23456789L, MPC_RNDNN);
mpfr_clear_flags ();
if (mpfr_cmp (MPC_RE(z), fr) != 0
|| mpfr_cmp_ui (MPC_IM(z), 0) != 0
|| mpfr_erangeflag_p())
PRINT_ERROR ("mpc_set_ld", prec, z);
mpc_set_prec (x, prec);
mpfr_set_ui(fr, 1, GMP_RNDN);
mpfr_div_ui(fr, fr, 3, GMP_RNDN);
mpfr_set(MPC_RE(x), fr, GMP_RNDN);
mpfr_set(MPC_IM(x), fr, GMP_RNDN);
mpc_set (z, x, MPC_RNDNN);
mpfr_clear_flags (); /* mpc_cmp set erange flag when an operand is a
NaN */
if (mpc_cmp (z, x) != 0 || mpfr_erangeflag_p())
{
printf ("Error in mpc_set for prec = %lu\n",
(unsigned long int) prec);
MPC_OUT(z);
MPC_OUT(x);
exit (1);
}
mpc_set_si_si (z, lo, lo, MPC_RNDNN);
if (mpfr_cmp_si (MPC_RE(z), lo) != 0
|| mpfr_cmp_si (MPC_IM(z), lo) != 0)
PRINT_ERROR ("mpc_set_si_si", prec, z);
mpc_set_fr (z, fr, MPC_RNDNN);
mpfr_clear_flags ();
if (mpfr_cmp (MPC_RE(z), fr) != 0
|| mpfr_cmp_ui (MPC_IM(z), 0) != 0
|| mpfr_erangeflag_p())
PRINT_ERROR ("mpc_set_fr", prec, z);
mpfr_set_z (fr, mpz, GMP_RNDN);
mpc_set_z_z (z, mpz, mpz, MPC_RNDNN);
mpfr_clear_flags ();
if (mpfr_cmp (MPC_RE(z), fr) != 0
|| mpfr_cmp (MPC_IM(z), fr) != 0
|| mpfr_erangeflag_p())
PRINT_ERROR ("mpc_set_z_z", prec, z);
mpc_set_fr_fr (z, fr, fr, MPC_RNDNN);
mpfr_clear_flags ();
if (mpfr_cmp (MPC_RE(z), fr) != 0
|| mpfr_cmp (MPC_IM(z), fr) != 0
|| mpfr_erangeflag_p())
PRINT_ERROR ("mpc_set_fr_fr", prec, z);
mpc_set_z (z, mpz, MPC_RNDNN);
mpfr_clear_flags ();
if (mpfr_cmp (MPC_RE(z), fr) != 0
|| mpfr_cmp_ui (MPC_IM(z), 0) != 0
|| mpfr_erangeflag_p())
PRINT_ERROR ("mpc_set_z", prec, z);
mpfr_set_q (fr, mpq, GMP_RNDN);
mpc_set_q_q (z, mpq, mpq, MPC_RNDNN);
mpfr_clear_flags ();
if (mpfr_cmp (MPC_RE(z), fr) != 0
|| mpfr_cmp (MPC_IM(z), fr) != 0
|| mpfr_erangeflag_p())
PRINT_ERROR ("mpc_set_q_q", prec, z);
mpc_set_ui_fr (z, u, fr, MPC_RNDNN);
mpfr_clear_flags ();
if (mpfr_cmp_ui (MPC_RE (z), u) != 0
|| mpfr_cmp (MPC_IM (z), fr) != 0
|| mpfr_erangeflag_p ())
PRINT_ERROR ("mpc_set_ui_fr", prec, z);
mpc_set_fr_ui (z, fr, u, MPC_RNDNN);
mpfr_clear_flags ();
if (mpfr_cmp (MPC_RE (z), fr) != 0
|| mpfr_cmp_ui (MPC_IM (z), u) != 0
|| mpfr_erangeflag_p())
PRINT_ERROR ("mpc_set_fr_ui", prec, z);
mpc_set_q (z, mpq, MPC_RNDNN);
mpfr_clear_flags ();
if (mpfr_cmp (MPC_RE(z), fr) != 0
|| mpfr_cmp_ui (MPC_IM(z), 0) != 0
|| mpfr_erangeflag_p())
PRINT_ERROR ("mpc_set_q", prec, z);
mpfr_set_f (fr, mpf, GMP_RNDN);
mpc_set_f_f (z, mpf, mpf, MPC_RNDNN);
mpfr_clear_flags ();
if (mpfr_cmp (MPC_RE(z), fr) != 0
|| mpfr_cmp (MPC_IM(z), fr) != 0
|| mpfr_erangeflag_p())
PRINT_ERROR ("mpc_set_f_f", prec, z);
mpc_set_f (z, mpf, MPC_RNDNN);
mpfr_clear_flags ();
if (mpfr_cmp (MPC_RE(z), fr) != 0
|| mpfr_cmp_ui (MPC_IM(z), 0) != 0
|| mpfr_erangeflag_p())
PRINT_ERROR ("mpc_set_f", prec, z);
mpc_set_f_si (z, mpf, lo, MPC_RNDNN);
mpfr_clear_flags ();
if (mpfr_cmp (MPC_RE (z), fr) != 0
|| mpfr_cmp_si (MPC_IM (z), lo) != 0
|| mpfr_erangeflag_p ())
PRINT_ERROR ("mpc_set_f", prec, z);
mpc_set_nan (z);
if (!mpfr_nan_p (MPC_RE(z)) || !mpfr_nan_p (MPC_IM(z)))
PRINT_ERROR ("mpc_set_nan", prec, z);
#ifdef _MPC_H_HAVE_INTMAX_T
{
uintmax_t uim = (uintmax_t) prec;
intmax_t im = (intmax_t) prec;
mpc_set_uj (z, uim, MPC_RNDNN);
if (mpfr_cmp_ui (MPC_RE(z), u) != 0
|| mpfr_cmp_ui (MPC_IM(z), 0) != 0)
PRINT_ERROR ("mpc_set_uj", prec, z);
mpc_set_sj (z, im, MPC_RNDNN);
if (mpfr_cmp_ui (MPC_RE(z), u) != 0
|| mpfr_cmp_ui (MPC_IM(z), 0) != 0)
PRINT_ERROR ("mpc_set_sj (1)", prec, z);
mpc_set_uj_uj (z, uim, uim, MPC_RNDNN);
if (mpfr_cmp_ui (MPC_RE(z), u) != 0
|| mpfr_cmp_ui (MPC_IM(z), u) != 0)
PRINT_ERROR ("mpc_set_uj_uj", prec, z);
mpc_set_sj_sj (z, im, im, MPC_RNDNN);
if (mpfr_cmp_ui (MPC_RE(z), u) != 0
|| mpfr_cmp_ui (MPC_IM(z), u) != 0)
PRINT_ERROR ("mpc_set_sj_sj (1)", prec, z);
im = LONG_MAX;
if (sizeof (intmax_t) == 2 * sizeof (unsigned long))
im = 2 * im * im + 4 * im + 1; /* gives 2^(2n-1)-1 from 2^(n-1)-1 */
mpc_set_sj (z, im, MPC_RNDNN);
if (mpfr_get_sj (MPC_RE(z), GMP_RNDN) != im ||
mpfr_cmp_ui (MPC_IM(z), 0) != 0)
PRINT_ERROR ("mpc_set_sj (2)", im, z);
mpc_set_sj_sj (z, im, im, MPC_RNDNN);
if (mpfr_get_sj (MPC_RE(z), GMP_RNDN) != im ||
mpfr_get_sj (MPC_IM(z), GMP_RNDN) != im)
PRINT_ERROR ("mpc_set_sj_sj (2)", im, z);
}
#endif /* _MPC_H_HAVE_INTMAX_T */
#if defined _MPC_H_HAVE_COMPLEX
{
double _Complex c = 1.0 - 2.0*I;
long double _Complex lc = c;
mpc_set_dc (z, c, MPC_RNDNN);
if (mpc_get_dc (z, MPC_RNDNN) != c)
PRINT_ERROR ("mpc_get_c", prec, z);
mpc_set_ldc (z, lc, MPC_RNDNN);
if (mpc_get_ldc (z, MPC_RNDNN) != lc)
PRINT_ERROR ("mpc_get_lc", prec, z);
}
#endif
}
mpz_clear (mpz);
mpq_clear (mpq);
mpf_clear (mpf);
mpfr_clear (fr);
mpc_clear (x);
mpc_clear (z);
}
