/* mpc_norm -- Square of the norm of a complex number.

Copyright (C) 2002, 2005, 2008, 2009, 2010, 2011, 2012 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"

/* 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;

   int saved_underflow, saved_overflow;

   /* 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_realref (b))) {

      if (mpfr_zero_p (mpc_imagref (b)))

         return mpfr_set_ui (a, 0, rnd); /* +0 */

      else

         return mpfr_sqr (a, mpc_imagref (b), rnd);

   }

   else if (mpfr_zero_p (mpc_imagref (b)))

     return mpfr_sqr (a, mpc_realref (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);

      /* save the underflow or overflow flags from MPFR */

      saved_underflow = mpfr_underflow_p ();

      saved_overflow = mpfr_overflow_p ();

      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_realref(b), MPFR_RNDD); /* err <= 1 ulp in prec */

         inexact |= mpfr_sqr (v, mpc_imagref(b), MPFR_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) {

             mpfr_set_prec (res, prec);

             mpfr_add (res, u, v, MPFR_RNDD); /* err <= 3 ulp in prec */

         }

      } while (loops < max_loops && inexact != 0

               && !mpfr_can_round (res, prec - 2, MPFR_RNDD, MPFR_RNDU,

                                   mpfr_get_prec (a) + (rnd == MPFR_RNDN)));

      if (!inexact)

         /* squarings were exact, neither 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, MPFR_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. */

         mpfr_exp_t emin = mpfr_get_emin ();

         /* Now either both u and v are zero, or u is zero and v exact,

            or v is zero and u exact.

            In the latter case, Im(b)^2 < 2^(emin-1).

            If ulp(u) >= 2^(emin+1) and norm(b) is not exactly

            representable at the target precision, then rounding u+Im(b)^2

            is equivalent to rounding u+2^(emin-1).

            For instance, if exp(u)>0 and the target precision is smaller

            than about |emin|, the norm is not representable. To make the

            scaling in the "else" case work without underflow, we test

            whether exp(u) is larger than a small negative number instead.

            The second case is handled analogously.                        */

         if (!mpfr_zero_p (u)

             && mpfr_get_exp (u) - 2 * (mpfr_exp_t) prec_u > emin

             && mpfr_get_exp (u) > -10) {

               mpfr_set_prec (v, MPFR_PREC_MIN);

               mpfr_set_ui_2exp (v, 1, emin - 1, MPFR_RNDZ);

               inexact = mpfr_add (a, u, v, rnd);

         }

         else if (!mpfr_zero_p (v)

             && mpfr_get_exp (v) - 2 * (mpfr_exp_t) prec_v > emin

             && mpfr_get_exp (v) > -10) {

               mpfr_set_prec (u, MPFR_PREC_MIN);

               mpfr_set_ui_2exp (u, 1, emin - 1, MPFR_RNDZ);

               inexact = mpfr_add (a, u, v, rnd);

         }

         else {

            unsigned long int scale, exp_re, exp_im;

            int inex_underflow;

            /* scale the input to an average exponent close to 0 */

            exp_re = (unsigned long int) (-mpfr_get_exp (mpc_realref (b)));

            exp_im = (unsigned long int) (-mpfr_get_exp (mpc_imagref (b)));

            scale = exp_re / 2 + exp_im / 2 + (exp_re % 2 + exp_im % 2) / 2;

               /* (exp_re + exp_im) / 2, computed in a way avoiding

                  integer overflow                                  */

            if (mpfr_zero_p (u)) {

               /* recompute the scaled value exactly */

               mpfr_mul_2ui (u, mpc_realref (b), scale, MPFR_RNDN);

               mpfr_sqr (u, u, MPFR_RNDN);

            }

            else /* just scale */

               mpfr_mul_2ui (u, u, 2*scale, MPFR_RNDN);

            if (mpfr_zero_p (v)) {

               mpfr_mul_2ui (v, mpc_imagref (b), scale, MPFR_RNDN);

               mpfr_sqr (v, v, MPFR_RNDN);

            }

            else

               mpfr_mul_2ui (v, v, 2*scale, MPFR_RNDN);

            inexact = mpfr_add (a, u, v, rnd);

            mpfr_clear_underflow ();

            inex_underflow = mpfr_div_2ui (a, a, 2*scale, rnd);

            if (mpfr_underflow_p ())

               inexact = inex_underflow;

         }

      }

      else /* no problems, ternary value due to mpfr_can_round trick */

         inexact = mpfr_set (a, res, rnd);

      /* restore underflow and overflow flags from MPFR */

      if (saved_underflow)

        mpfr_set_underflow ();

      if (saved_overflow)

        mpfr_set_overflow ();

      mpfr_clear (u);

      mpfr_clear (v);

      mpfr_clear (res);

   }

   return inexact;

}