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/* mpc_sqr -- Square a complex number.
Copyright (C) 2002 Free Software Foundation, Inc.
This file is part of the MPC Library.
The MPC Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 2.1 of the License, or (at your
option) any later version.
The MPC Library is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
License for more details.
You should have received a copy of the GNU Lesser General Public License
along with the MPC Library; see the file COPYING.LIB. If not, write to
the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
MA 02111-1307, USA. */
#include "gmp.h"
#include "mpfr.h"
#include "mpc.h"
#include "mpc-impl.h"
#define INV_RND(r) \
(((r) == GMP_RNDU) ? GMP_RNDD : (((r) == GMP_RNDD) ? GMP_RNDU : (r)))
int
mpc_sqr (mpc_ptr a, mpc_srcptr b, mp_rnd_t rnd)
{
int ok;
mpfr_t u, v;
mpfr_t x;
/* a temporary variable to hold the real part of b,
needed in the case a==b */
mp_prec_t prec;
int inex_re, inex_im, inexact;
prec = MPC_MAX_PREC(a);
/* first check for real resp. purely imaginary number */
if (MPFR_IS_ZERO (MPC_IM(b)))
{
inex_re = mpfr_mul (MPC_RE(a), MPC_RE(b), MPC_RE(b), MPC_RND_RE(rnd));
inex_im = mpfr_set_ui (MPC_IM(a), 0, GMP_RNDN);
return MPC_INEX(inex_re, inex_im);
}
if (MPFR_IS_ZERO (MPC_RE(b)))
{
inex_re = -mpfr_mul (MPC_RE(a), MPC_IM(b), MPC_IM(b),
INV_RND (MPC_RND_RE(rnd)));
mpfr_neg (MPC_RE(a), MPC_RE(a), GMP_RNDN);
inex_im = mpfr_set_ui (MPC_IM(a), 0, GMP_RNDN);
return MPC_INEX(inex_re, inex_im);
}
mpfr_init (u);
mpfr_init (v);
if (a == b)
{
mpfr_init2 (x, MPFR_PREC (b->re));
mpfr_set (x, b->re, GMP_RNDN);
}
else
x [0] = b->re [0];
do
{
prec += _mpfr_ceil_log2 ((double) prec) + 5;
mpfr_set_prec (u, prec);
mpfr_set_prec (v, prec);
/* Let b = x + iy. We need u = x+y and v = x-y, rounded away. */
/* As this is not implemented in mpfr, we round towards zero and */
/* add one ulp if the result is not exact. 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 = 0;
if (mpfr_add (u, x, MPC_IM (b), GMP_RNDZ))
/* we have to use x here instead of MPC_RE (b), as MPC_RE (a)
may be modified later in the attempt to assign u to it */
{
mpfr_add_one_ulp (u, GMP_RNDN);
inexact = 1;
}
if (mpfr_sub (v, x, MPC_IM (b), GMP_RNDZ))
{
mpfr_add_one_ulp (v, GMP_RNDN);
inexact = 1;
}
/* 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 (u, 0, GMP_RNDN);
mpfr_set_ui (MPC_RE (a), 0, GMP_RNDN);
inex_re = 0;
ok = 1;
}
else if (mpfr_sgn (u) * mpfr_sgn (v) > 0)
{
inexact |= mpfr_mul (u, u, v, GMP_RNDU); /* error 5 */
ok = !inexact | mpfr_can_round (u, prec - 3, GMP_RNDU,
MPC_RND_RE (rnd), MPFR_PREC (MPC_RE (a)));
if (ok)
{
inex_re = mpfr_set (MPC_RE (a), u, MPC_RND_RE (rnd));
if (inex_re == 0)
/* remember that u was already rounded */
inex_re = inexact;
/* even if rounding did work, we might not know whether the
result is too large, too small or exact */
else if (inexact && MPC_RND_RE (rnd) == GMP_RNDN
&& inex_re < 0
&& !mpfr_can_round (u, prec - 3, GMP_RNDU, GMP_RNDU,
MPFR_PREC (MPC_RE (a))))
ok = 0;
}
}
else
{
inexact |= mpfr_mul (u, u, v, GMP_RNDD); /* error 5 */
ok = !inexact | mpfr_can_round (u, prec - 3, GMP_RNDD,
MPC_RND_RE (rnd), MPFR_PREC (MPC_RE (a)));
if (ok)
{
inex_re = mpfr_set (MPC_RE (a), u, MPC_RND_RE (rnd));
if (inex_re == 0)
inex_re = inexact;
/* even if rounding did work, we might not know whether the
result is too large, too small or exact */
else if (inexact && MPC_RND_RE (rnd) == GMP_RNDN
&& inex_re > 0
&& !mpfr_can_round (u, prec - 3, GMP_RNDD, GMP_RNDD,
MPFR_PREC (MPC_RE (a))))
ok = 0;
}
}
}
while (!ok);
/* compute the imaginary part as 2*x*y, which is always possible */
inex_im = mpfr_mul (MPC_IM (a), x, MPC_IM (b),
MPC_RND_IM (rnd));
MPFR_EXP (MPC_IM (a))++;
mpfr_clear (u);
mpfr_clear (v);
if (a == b)
mpfr_clear (x);
return MPC_INEX (inex_re, inex_im);
}
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