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/* mpc_norm -- Square of the norm of a complex number.
Copyright (C) 2002, 2005, 2008, 2009, 2010, 2011 INRIA
This file is part of GNU MPC.
GNU MPC 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 3 of the License, or (at your
option) any later version.
GNU MPC 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 this program. If not, see http://www.gnu.org/licenses/ .
*/
#include "mpc-impl.h"
/* a <- norm(b) = b * conj(b)
(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)
{
int inexact;
/* handling of special values; consistent with abs in that
norm = abs^2; so norm (+-inf, xxx) = norm (xxx, +-inf) = +inf */
if (!mpc_fin_p (b))
return mpc_abs (a, b, rnd);
else if (mpfr_zero_p (MPC_RE (b))) {
if (mpfr_zero_p (MPC_IM (b)))
return mpfr_set_ui (a, 0, rnd); /* +0 */
else
return mpfr_sqr (a, MPC_IM (b), rnd);
}
else if (mpfr_zero_p (MPC_IM (b)))
return mpfr_sqr (a, MPC_RE (b), rnd); /* Re(b) <> 0 */
else /* everything finite and non-zero */ {
mpfr_t u, v, res;
mpfr_prec_t prec, prec_u, prec_v;
int loops;
const int max_loops = 2;
/* switch to exact squarings when loops==max_loops */
prec = mpfr_get_prec (a);
mpfr_init (u);
mpfr_init (v);
mpfr_init (res);
loops = 0;
mpfr_clear_underflow ();
mpfr_clear_overflow ();
do {
loops++;
prec += mpc_ceil_log2 (prec) + 3;
if (loops >= max_loops) {
prec_u = 2 * MPC_PREC_RE (b);
prec_v = 2 * MPC_PREC_IM (b);
}
else {
prec_u = MPC_MIN (prec, 2 * MPC_PREC_RE (b));
prec_v = MPC_MIN (prec, 2 * MPC_PREC_IM (b));
}
mpfr_set_prec (u, prec_u);
mpfr_set_prec (v, prec_v);
inexact = mpfr_sqr (u, MPC_RE(b), GMP_RNDD); /* err <= 1 ulp in prec */
inexact |= mpfr_sqr (v, MPC_IM(b), GMP_RNDD); /* err <= 1 ulp in prec */
/* If loops = max_loops, inexact should be 0 here, except in case
of underflow or overflow.
If loops < max_loops and inexact is zero, we can exit the
while-loop since it only remains to add u and v into a. */
if (inexact != 0)
{
mpfr_set_prec (res, prec);
mpfr_add (res, u, v, GMP_RNDD); /* err <= 3 ulp in prec */
}
} while (loops < max_loops && inexact != 0
&& !mpfr_can_round (res, prec - 2, GMP_RNDD, GMP_RNDU,
mpfr_get_prec (a) + (rnd == GMP_RNDN)));
if (inexact == 0) /* squarings were exact, nor underflow nor overflow */
inexact = mpfr_add (a, u, v, rnd);
/* if there was an overflow in Re(b)^2 or Im(b)^2 or their sum,
since the norm is larger, there is an overflow for the norm */
else if (mpfr_overflow_p ()) {
/* replace by "correctly rounded overflow" */
mpfr_set_ui (a, 1ul, GMP_RNDN);
inexact = mpfr_mul_2ui (a, a, mpfr_get_emax (), rnd);
}
else if (mpfr_underflow_p ()) {
/* necessarily one of the squarings did underflow (otherwise their
sum could not underflow), thus one of u, v is zero */
/* squarings were exact except for underflow */
inexact = mpfr_add (a, u, v, rnd);
if (!inexact) {
if (rnd == GMP_RNDN || rnd == GMP_RNDD || rnd == GMP_RNDZ)
inexact = -1;
else { /* rounding up */
mpfr_nextabove (a);
inexact = 1;
}
}
}
else /* no problems, ternary value due to mpfr_can_round trick */
inexact = mpfr_set (a, res, rnd);
mpfr_clear (u);
mpfr_clear (v);
mpfr_clear (res);
}
return inexact;
}
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