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/* mpc_norm -- Square of the norm of a complex number.
Copyright (C) 2002, 2005 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 "gmp.h"
#include "mpfr.h"
#include "mpc.h"
#include "mpc-impl.h"
int
mpc_norm (mpfr_ptr a, mpc_srcptr b, mp_rnd_t rnd)
{
mpfr_t u, v;
mp_prec_t prec;
int inexact;
prec = MPFR_PREC(a);
mpfr_init (u);
mpfr_init (v);
if (2 * SAFE_ABS (mp_exp_t, MPFR_EXP (MPC_RE (b)) - MPFR_EXP (MPC_IM (b)))
> (unsigned int) prec)
/* If real and imaginary part have very different magnitudes, then the */
/* generic code increases the precision too much. Instead, compute the */
/* squarings _exactly_. */
{
mpfr_set_prec (u, 2 * MPFR_PREC (MPC_RE (b)));
mpfr_set_prec (v, 2 * MPFR_PREC (MPC_IM (b)));
mpfr_mul (u, MPC_RE (b), MPC_RE (b), GMP_RNDN);
mpfr_mul (v, MPC_IM (b), MPC_IM (b), GMP_RNDN);
inexact = mpfr_add (a, u, v, rnd);
}
else
{
do
{
prec += mpc_ceil_log2 (prec) + 3;
mpfr_set_prec (u, prec);
mpfr_set_prec (v, prec);
/* first compute norm(b)^2 */
inexact = mpfr_mul (u, MPC_RE(b), MPC_RE(b), GMP_RNDN); /* err<=1/2ulp */
inexact |= mpfr_mul (v, MPC_IM(b), MPC_IM(b), GMP_RNDN); /* err<=1/2ulp*/
inexact |= mpfr_add (u, u, v, GMP_RNDN); /* err <= 3/2 ulps */
}
while (inexact != 0 &&
mpfr_can_round (u, prec - 2, GMP_RNDN, rnd, MPFR_PREC(a)) == 0);
inexact |= mpfr_set (a, u, rnd);
}
mpfr_clear (u);
mpfr_clear (v);
return inexact;
}
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