/* mpc_norm -- Square of the norm of a complex number.
Copyright (C) INRIA, 2002, 2005, 2008, 2009, 2010
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 "mpc-impl.h"
/* the rounding mode is mpfr_rnd_t here since we return an mpfr number */
int
mpc_norm (mpfr_ptr a, mpc_srcptr b, mpfr_rnd_t rnd)
{
mpfr_t u, v;
mpfr_prec_t prec;
int inexact, overflow, underflow;
prec = mpfr_get_prec (a);
/* handling of special values; consistent with abs in that
norm = abs^2; so norm (+-inf, nan) = norm (nan, +-inf) = +inf */
if ( (mpfr_nan_p (MPC_RE (b)) || mpfr_nan_p (MPC_IM (b)))
|| (mpfr_inf_p (MPC_RE (b)) || mpfr_inf_p (MPC_IM (b))))
return mpc_abs (a, b, rnd);
mpfr_init (u);
mpfr_init (v);
if (!mpfr_zero_p(MPC_RE(b)) && !mpfr_zero_p(MPC_IM(b)) &&
2 * SAFE_ABS (mpfr_exp_t,
mpfr_get_exp (MPC_RE (b)) - mpfr_get_exp (MPC_IM (b)))
> (mpfr_exp_t)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 * MPC_PREC_RE (b));
mpfr_set_prec (v, 2 * MPC_PREC_IM (b));
mpfr_sqr (u, MPC_RE (b), GMP_RNDN);
mpfr_sqr (v, MPC_IM (b), GMP_RNDN);
inexact = mpfr_add (a, u, v, rnd);
}
else if (mpfr_zero_p(MPC_RE(b)) && mpfr_zero_p(MPC_IM(b)))
{
inexact = mpfr_set_ui (a, 0, rnd);
}
else
{
do
{
prec += mpc_ceil_log2 (prec) + 3;
mpfr_set_prec (u, prec);
mpfr_set_prec (v, prec);
inexact = mpfr_sqr (u, MPC_RE(b), GMP_RNDN); /* err<=1/2ulp */
inexact |= mpfr_sqr (v, MPC_IM(b), GMP_RNDN); /* err<=1/2ulp*/
inexact |= mpfr_add (u, u, v, GMP_RNDN); /* err <= 3/2 ulps */
overflow = mpfr_inf_p (u);
underflow = mpfr_zero_p (u);
}
while (!overflow && !underflow && inexact &&
mpfr_can_round (u, prec - 2, GMP_RNDN, rnd, mpfr_get_prec (a)) == 0);
inexact |= mpfr_set (a, u, rnd);
if (overflow)
inexact = 1;
if (underflow)
inexact = -1;
}
mpfr_clear (u);
mpfr_clear (v);
return inexact;
}