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/* mpc_abs -- Absolute value of a complex number.
Copyright (C) 2002, 2004, 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_abs_basic (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_init2 (u, 2*prec);
mpfr_init2 (v, 2*prec);
do
{
prec += mpc_ceil_log2 (prec) + 3;
mpfr_set_prec (u, prec);
mpfr_set_prec (v, prec);
/* first compute norm(b)^2 */
inexact = mpfr_sqr (u, MPC_RE(b), GMP_RNDU); /* err<=1ulp */
inexact |= mpfr_sqr (v, MPC_IM(b), GMP_RNDU); /* err<=1ulp*/
inexact |= mpfr_add (u, u, v, GMP_RNDU); /* err <= 3 ulps */
inexact |= mpfr_sqrt (u, u, GMP_RNDU); /* err <= 4 ulps */
}
while (inexact != 0 &&
mpfr_can_round (u, prec - 2, GMP_RNDU, rnd, MPFR_PREC(a)) == 0);
inexact |= mpfr_set (a, u, rnd);
mpfr_clear (u);
mpfr_clear (v);
return inexact;
}
int
mpc_abs (mpfr_ptr a, mpc_srcptr b, mp_rnd_t rnd)
/* a more sophisticated version treating special cases separately */
{
mpfr_t u, v;
mp_prec_t prec;
int inexact;
if (MPFR_IS_ZERO (MPC_RE (b)))
return mpfr_abs (a, MPC_IM (b), rnd);
else if (MPFR_IS_ZERO (MPC_IM (b)))
return mpfr_abs (a, MPC_RE (b), rnd);
prec = MPFR_PREC(a);
if (prec >= MPFR_PREC (MPC_RE (b))
&& 2 * (MPFR_EXP (MPC_RE (b)) - MPFR_EXP (MPC_IM (b)) - 1) >
(signed long) prec)
/* try to detect the case that the imaginary part is negligible;
this is the case, independently of the rounding mode, whenever
setting the result to the real part is exact, and the imaginary
part contributes less than 1/2 ulp */
{
mpfr_abs (a, MPC_RE (b), GMP_RNDN); /* exact */
if (rnd == GMP_RNDU)
{
mpfr_add_one_ulp (a, GMP_RNDN);
return 1;
}
else
return -1;
}
else if (prec >= MPFR_PREC (MPC_IM (b))
&& 2 * (MPFR_EXP (MPC_IM (b)) - MPFR_EXP (MPC_RE (b)) - 1) >
(signed long) prec)
{
mpfr_abs (a, MPC_IM (b), GMP_RNDN); /* exact */
if (rnd == GMP_RNDU)
{
mpfr_add_one_ulp (a, GMP_RNDN);
return 1;
}
else
return -1;
}
mpfr_init2 (u, 2*prec);
mpfr_init2 (v, 2*prec);
do
{
prec += mpc_ceil_log2 (prec) + 3;
mpfr_set_prec (u, prec);
mpfr_set_prec (v, prec);
if (4*(MPFR_EXP(MPC_RE(b)) - MPFR_EXP(MPC_IM(b))) > (signed long) prec)
/* |Re (b)| >> |Im (b)|, use the Taylor series sqrt (a^2 + b^2)
= |a| + b^2 / (2 |a|) - e with 0 <= e <= 1 ulp of the target;
so we round towards infinity */
{
inexact = 1;
mpfr_sqr (u, MPC_IM (b), GMP_RNDU); /* err <= 1 ulp */
if (MPFR_SIGN (MPC_RE (b)) > 0)
{
mpfr_div (u, u, MPC_RE (b), GMP_RNDU); /* err <= 3 ulp */
mpfr_div_2ui (u, u, 1, GMP_RNDU);
mpfr_add (u, u, MPC_RE (b), GMP_RNDU); /* err <= 4 ulp */
}
else
{
mpfr_div (u, u, MPC_RE (b), GMP_RNDD);
mpfr_div_2ui (u, u, 1, GMP_RNDD);
mpfr_add (u, u, MPC_RE (b), GMP_RNDD);
mpfr_neg (u, u, GMP_RNDU);
}
/* err <= 5 ulps (one for Taylor approximation) */
}
else if (4*(MPFR_EXP(MPC_IM(b)) - MPFR_EXP(MPC_RE(b))) >
(signed long) prec)
{
inexact = 1;
mpfr_sqr (u, MPC_RE (b), GMP_RNDU);
if (MPFR_SIGN (MPC_IM (b)) > 0)
{
mpfr_div (u, u, MPC_IM (b), GMP_RNDU);
mpfr_div_2ui (u, u, 1, GMP_RNDU);
mpfr_add (u, u, MPC_IM (b), GMP_RNDU);
}
else
{
mpfr_div (u, u, MPC_IM (b), GMP_RNDD);
mpfr_div_2ui (u, u, 1, GMP_RNDD);
mpfr_add (u, u, MPC_IM (b), GMP_RNDD);
mpfr_neg (u, u, GMP_RNDU);
}
}
else
{
/* first compute norm(b)^2 */
inexact = mpfr_sqr (u, MPC_RE(b), GMP_RNDU); /* err<=1ulp */
inexact |= mpfr_sqr (v, MPC_IM(b), GMP_RNDU); /* err<=1ulp*/
inexact |= mpfr_add (u, u, v, GMP_RNDU); /* err <= 3 ulps */
inexact |= mpfr_sqrt (u, u, GMP_RNDU); /* err <= 4 ulps */
}
}
while (inexact != 0 &&
mpfr_can_round (u, prec - 3, GMP_RNDU, rnd, MPFR_PREC(a)) == 0);
inexact |= mpfr_set (a, u, rnd);
mpfr_clear (u);
mpfr_clear (v);
return inexact;
}
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