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/* mpc_sqr -- Square 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 <stdio.h> /* for MPC_ASSERT */
#include "mpc-impl.h"
int
mpc_sqr (mpc_ptr rop, mpc_srcptr op, mpc_rnd_t rnd)
{
int ok;
mpfr_t u, v;
mpfr_t x;
/* rop temporary variable to hold the real part of op,
needed in the case rop==op */
mpfr_prec_t prec;
int inex_re, inex_im, inexact;
mpfr_exp_t emin, emax;
/* special values: NaN and infinities */
if (!mpc_fin_p (op)) {
if (mpfr_nan_p (mpc_realref (op)) || mpfr_nan_p (mpc_imagref (op))) {
mpfr_set_nan (mpc_realref (rop));
mpfr_set_nan (mpc_imagref (rop));
}
else if (mpfr_inf_p (mpc_realref (op))) {
if (mpfr_inf_p (mpc_imagref (op))) {
mpfr_set_inf (mpc_imagref (rop),
MPFR_SIGN (mpc_realref (op)) * MPFR_SIGN (mpc_imagref (op)));
mpfr_set_nan (mpc_realref (rop));
}
else {
if (mpfr_zero_p (mpc_imagref (op)))
mpfr_set_nan (mpc_imagref (rop));
else
mpfr_set_inf (mpc_imagref (rop),
MPFR_SIGN (mpc_realref (op)) * MPFR_SIGN (mpc_imagref (op)));
mpfr_set_inf (mpc_realref (rop), +1);
}
}
else /* IM(op) is infinity, RE(op) is not */ {
if (mpfr_zero_p (mpc_realref (op)))
mpfr_set_nan (mpc_imagref (rop));
else
mpfr_set_inf (mpc_imagref (rop),
MPFR_SIGN (mpc_realref (op)) * MPFR_SIGN (mpc_imagref (op)));
mpfr_set_inf (mpc_realref (rop), -1);
}
return MPC_INEX (0, 0); /* exact */
}
prec = MPC_MAX_PREC(rop);
/* first check for real resp. purely imaginary number */
if (mpfr_zero_p (mpc_imagref(op)))
{
int same_sign = mpfr_signbit (mpc_realref (op)) == mpfr_signbit (mpc_imagref (op));
inex_re = mpfr_sqr (mpc_realref(rop), mpc_realref(op), MPC_RND_RE(rnd));
inex_im = mpfr_set_ui (mpc_imagref(rop), 0ul, GMP_RNDN);
if (!same_sign)
mpc_conj (rop, rop, MPC_RNDNN);
return MPC_INEX(inex_re, inex_im);
}
if (mpfr_zero_p (mpc_realref(op)))
{
int same_sign = mpfr_signbit (mpc_realref (op)) == mpfr_signbit (mpc_imagref (op));
inex_re = -mpfr_sqr (mpc_realref(rop), mpc_imagref(op), INV_RND (MPC_RND_RE(rnd)));
mpfr_neg (mpc_realref(rop), mpc_realref(rop), GMP_RNDN);
inex_im = mpfr_set_ui (mpc_imagref(rop), 0ul, GMP_RNDN);
if (!same_sign)
mpc_conj (rop, rop, MPC_RNDNN);
return MPC_INEX(inex_re, inex_im);
}
/* If the real and imaginary parts of the argument have very different */
/* exponents, it is not reasonable to use Karatsuba squaring; compute */
/* exactly with the standard formulae instead, even if this means an */
/* additional multiplication. */
if (SAFE_ABS (mpfr_exp_t,
mpfr_get_exp (mpc_realref (op)) - mpfr_get_exp (mpc_imagref (op)))
> (mpfr_exp_t) MPC_MAX_PREC (op) / 2)
{
mpfr_init2 (u, 2*MPC_PREC_RE (op));
mpfr_init2 (v, 2*MPC_PREC_IM (op));
mpfr_sqr (u, mpc_realref (op), GMP_RNDN);
mpfr_sqr (v, mpc_imagref (op), GMP_RNDN); /* both are exact */
inex_im = mpfr_mul (rop->im, op->re, op->im, MPC_RND_IM (rnd));
mpfr_mul_2exp (rop->im, rop->im, 1, GMP_RNDN);
inex_re = mpfr_sub (rop->re, u, v, MPC_RND_RE (rnd));
mpfr_clear (u);
mpfr_clear (v);
return MPC_INEX (inex_re, inex_im);
}
mpfr_init (u);
mpfr_init (v);
if (rop == op)
{
mpfr_init2 (x, MPC_PREC_RE (op));
mpfr_set (x, op->re, GMP_RNDN);
}
else
x [0] = op->re [0];
emax = mpfr_get_emax ();
emin = mpfr_get_emin ();
do
{
prec += mpc_ceil_log2 (prec) + 5;
mpfr_set_prec (u, prec);
mpfr_set_prec (v, prec);
/* Let op = x + iy. We need u = x+y and v = x-y, rounded away. */
/* The error is bounded above by 1 ulp. */
/* We first let inexact be 1 if the real part is not computed */
/* exactly and determine the sign later. */
inexact = ROUND_AWAY (mpfr_add (u, x, mpc_imagref (op), MPFR_RNDA), u)
| ROUND_AWAY (mpfr_sub (v, x, mpc_imagref (op), MPFR_RNDA), v);
/* compute the real part as u*v, rounded away */
/* determine also the sign of inex_re */
if (mpfr_sgn (u) == 0 || mpfr_sgn (v) == 0)
{
/* as we have rounded away, the result is exact */
mpfr_set_ui (mpc_realref (rop), 0, GMP_RNDN);
inex_re = 0;
ok = 1;
}
else if (mpfr_sgn (u) * mpfr_sgn (v) > 0)
{
inexact |= mpfr_mul (u, u, v, GMP_RNDU); /* error 5 */
/* checks that no overflow nor underflow occurs: since u*v > 0
and we round up, an overflow will give +Inf, but an underflow
will give 0.5*2^emin */
MPC_ASSERT (mpfr_get_exp (u) != emin);
if (mpfr_inf_p (u))
{
/* let mpc_realref(rop) be a "correctly rounded overflow" */
inex_re = mpfr_set_ui_2exp (mpc_realref (rop), 1, emax, MPC_RND_RE (rnd));
break;
}
ok = (!inexact) | mpfr_can_round (u, prec - 3, GMP_RNDU, GMP_RNDZ,
MPC_PREC_RE (rop) + (MPC_RND_RE (rnd) == GMP_RNDN));
if (ok)
{
inex_re = mpfr_set (mpc_realref (rop), u, MPC_RND_RE (rnd));
if (inex_re == 0)
/* remember that u was already rounded */
inex_re = inexact;
}
}
else
{
inexact |= mpfr_mul (u, u, v, GMP_RNDD); /* error 5 */
/* checks that no overflow occurs: since u*v < 0 and we round down,
an overflow will give -Inf */
MPC_ASSERT (mpfr_inf_p (u) == 0);
/* if an underflow happens (i.e., u = -0.5*2^emin since we round
away from zero), the result will be an underflow */
if (mpfr_get_exp (u) == emin)
{
mpfr_rnd_t rnd_re = MPC_RND_RE (rnd);
if (rnd_re == GMP_RNDZ || rnd_re == GMP_RNDN ||
rnd_re == GMP_RNDU)
{
mpfr_set_ui (mpc_realref (rop), 0, rnd_re);
inex_re = 1;
}
else /* round down or away from zero */ {
mpfr_set (mpc_realref (rop), u, rnd_re);
inex_re = -1;
}
break;
}
ok = (!inexact) | mpfr_can_round (u, prec - 3, GMP_RNDD, GMP_RNDZ,
MPC_PREC_RE (rop) + (MPC_RND_RE (rnd) == GMP_RNDN));
if (ok)
{
inex_re = mpfr_set (mpc_realref (rop), u, MPC_RND_RE (rnd));
if (inex_re == 0)
inex_re = inexact;
}
}
}
while (!ok);
/* compute the imaginary part as 2*x*y, which is always possible */
if (mpfr_get_exp (x) + mpfr_get_exp(mpc_imagref (op)) <= emin + 1)
{
mpfr_mul_2ui (x, x, 1, GMP_RNDN);
inex_im = mpfr_mul (mpc_imagref (rop), x, mpc_imagref (op), MPC_RND_IM (rnd));
}
else
{
inex_im = mpfr_mul (mpc_imagref (rop), x, mpc_imagref (op), MPC_RND_IM (rnd));
/* checks that no underflow occurs (an overflow can occur here) */
MPC_ASSERT (mpfr_zero_p (mpc_imagref (rop)) == 0);
mpfr_mul_2ui (mpc_imagref (rop), mpc_imagref (rop), 1, GMP_RNDN);
}
mpfr_clear (u);
mpfr_clear (v);
if (rop == op)
mpfr_clear (x);
return MPC_INEX (inex_re, inex_im);
}
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