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/* mpc_sqrt -- Take the square root of a complex number.
Copyright (C) 2002 Andreas Enge, Paul Zimmermann
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 <stdio.h>
#include "gmp.h"
#include "mpfr.h"
#include "mpc.h"
#include "mpc-impl.h"
int
mpc_sqrt (mpc_ptr a, mpc_srcptr b, mp_rnd_t rnd)
{
int ok=0;
mpfr_t w, t;
mp_rnd_t rnd_w, rnd_t;
mp_prec_t prec_w, prec_t;
/* the rounding mode and the precision required for w and t, which can */
/* be either the real or the imaginary part of a */
int re_cmp, im_cmp;
/* comparison of the real/imaginary part of b with 0 */
mp_prec_t prec;
int inexact;
im_cmp = mpfr_cmp_ui (MPC_IM (b), 0);
re_cmp = mpfr_cmp_ui (MPC_RE (b), 0);
if (im_cmp == 0)
{
if (re_cmp == 0)
{
mpc_set_ui_ui (a, 0, 0, MPC_RNDNN);
return 0;
}
else if (re_cmp > 0)
{
inexact = mpfr_sqrt (MPC_RE (a), MPC_RE (b), MPC_RND_RE (rnd));
mpfr_set_ui (MPC_IM (a), 0, GMP_RNDN);
return inexact;
}
else
{
mpfr_init2 (w, MPFR_PREC (MPC_RE (b)));
inexact = mpfr_neg (w, MPC_RE (b), GMP_RNDN);
inexact = mpfr_sqrt (MPC_IM (a), w, MPC_RND_IM (rnd));
mpfr_set_ui (MPC_RE (a), 0, GMP_RNDN);
mpfr_clear (w);
return inexact;
}
}
prec = MPC_MAX_PREC(a);
mpfr_init (w);
mpfr_init (t);
if (re_cmp >= 0)
{
rnd_w = MPC_RND_RE (rnd);
prec_w = MPFR_PREC (MPC_RE (a));
rnd_t = MPC_RND_IM(rnd);
prec_t = MPFR_PREC (MPC_IM (a));
}
else
{
rnd_w = MPC_RND_IM(rnd);
prec_w = MPFR_PREC (MPC_IM (a));
rnd_t = MPC_RND_RE(rnd);
prec_t = MPFR_PREC (MPC_RE (a));
if (im_cmp < 0)
{
if (rnd_w == GMP_RNDD)
rnd_w = GMP_RNDU;
else if (rnd_w == GMP_RNDU)
rnd_w = GMP_RNDD;
if (rnd_t == GMP_RNDD)
rnd_t = GMP_RNDU;
if (rnd_t == GMP_RNDU)
rnd_t = GMP_RNDD;
}
}
do
{
prec += _mpfr_ceil_log2 ((double) prec) + 4;
mpfr_set_prec (w, prec);
mpfr_set_prec (t, prec);
/* let b = x + iy */
/* w = sqrt ((|x| + sqrt (x^2 + y^2)) / 2), rounded down */
/* total error bounded by 3 ulps */
inexact = mpc_abs (w, b, GMP_RNDD);
if (re_cmp < 0)
inexact |= mpfr_sub (w, w, MPC_RE (b), GMP_RNDD);
else
inexact |= mpfr_add (w, w, MPC_RE (b), GMP_RNDD);
inexact |= mpfr_div_2ui (w, w, 1, GMP_RNDD);
inexact |= mpfr_sqrt (w, w, GMP_RNDD);
ok = mpfr_can_round (w, prec - 2, GMP_RNDD, rnd_w, prec_w);
if (ok)
{
/* t = y / 2w, rounded up */
/* total error bounded by 7 ulps */
inexact |= mpfr_div (t, MPC_IM (b), w, GMP_RNDU);
inexact |= mpfr_div_2ui (t, t, 1, GMP_RNDU);
ok = mpfr_can_round (t, prec - 3, GMP_RNDU, rnd_t, prec_t);
}
}
while (inexact != 0 && ok == 0);
if (re_cmp > 0)
{
inexact |= mpfr_set (MPC_RE (a), w, rnd_w);
inexact |= mpfr_set (MPC_IM (a), t, rnd_t);
}
else
{
inexact |= mpfr_set (MPC_RE(a), t, MPC_RND_RE(rnd));
inexact |= mpfr_set (MPC_IM(a), w, MPC_RND_IM(rnd));
if (im_cmp < 0)
{
inexact |= mpfr_neg (MPC_RE (a), MPC_RE (a), MPC_RND_RE (rnd));
inexact |= mpfr_neg (MPC_IM (a), MPC_IM (a), MPC_RND_IM (rnd));
}
}
mpfr_clear (w);
mpfr_clear (t);
return inexact;
}
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