/* mpc_fma -- Fused multiply-add of three complex numbers

Copyright (C) 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 "mpc-impl.h"

/* return a bound on the precision needed to add or subtract x and y exactly */

static mpfr_prec_t

bound_prec_addsub (mpfr_srcptr x, mpfr_srcptr y)

{

  if (!mpfr_regular_p (x))

    return mpfr_get_prec (y);

  else if (!mpfr_regular_p (y))

    return mpfr_get_prec (x);

  else /* neither x nor y are NaN, Inf or zero */

    {

      mpfr_exp_t ex = mpfr_get_exp (x);

      mpfr_exp_t ey = mpfr_get_exp (y);

      mpfr_exp_t ulpx = ex - mpfr_get_prec (x);

      mpfr_exp_t ulpy = ey - mpfr_get_prec (y);

      return ((ex >= ey) ? ex : ey) + 1 - ((ulpx <= ulpy) ? ulpx : ulpy);

    }

}

/* r <- a*b+c */

int

mpc_fma_naive (mpc_ptr r, mpc_srcptr a, mpc_srcptr b, mpc_srcptr c, mpc_rnd_t rnd)

{

  mpfr_t rea_reb, rea_imb, ima_reb, ima_imb, tmp;

  mpfr_prec_t pre12, pre13, pre23, pim12, pim13, pim23;

  int inex_re, inex_im;

  mpfr_init2 (rea_reb, mpfr_get_prec (mpc_realref(a)) + mpfr_get_prec (mpc_realref(b)));

  mpfr_init2 (rea_imb, mpfr_get_prec (mpc_realref(a)) + mpfr_get_prec (mpc_imagref(b)));

  mpfr_init2 (ima_reb, mpfr_get_prec (mpc_imagref(a)) + mpfr_get_prec (mpc_realref(b)));

  mpfr_init2 (ima_imb, mpfr_get_prec (mpc_imagref(a)) + mpfr_get_prec (mpc_imagref(b)));

  mpfr_mul (rea_reb, mpc_realref(a), mpc_realref(b), GMP_RNDZ); /* exact */

  mpfr_mul (rea_imb, mpc_realref(a), mpc_imagref(b), GMP_RNDZ); /* exact */

  mpfr_mul (ima_reb, mpc_imagref(a), mpc_realref(b), GMP_RNDZ); /* exact */

  mpfr_mul (ima_imb, mpc_imagref(a), mpc_imagref(b), GMP_RNDZ); /* exact */

  /* Re(r) <- rea_reb - ima_imb + Re(c) */

  pre12 = bound_prec_addsub (rea_reb, ima_imb); /* bound on exact precision for

						   rea_reb - ima_imb */

  pre13 = bound_prec_addsub (rea_reb, mpc_realref(c));

  /* bound for rea_reb + Re(c) */

  pre23 = bound_prec_addsub (ima_imb, mpc_realref(c));

  /* bound for ima_imb - Re(c) */

  if (pre12 <= pre13 && pre12 <= pre23) /* (rea_reb - ima_imb) + Re(c) */

    {

      mpfr_init2 (tmp, pre12);

      mpfr_sub (tmp, rea_reb, ima_imb, GMP_RNDZ); /* exact */

      inex_re = mpfr_add (mpc_realref(r), tmp, mpc_realref(c), MPC_RND_RE(rnd));

      /* the only possible bad overlap is between r and c, but since we are

	 only touching the real part of both, it is ok */

    }

  else if (pre13 <= pre23) /* (rea_reb + Re(c)) - ima_imb */

    {

      mpfr_init2 (tmp, pre13);

      mpfr_add (tmp, rea_reb, mpc_realref(c), GMP_RNDZ); /* exact */

      inex_re = mpfr_sub (mpc_realref(r), tmp, ima_imb, MPC_RND_RE(rnd));

      /* the only possible bad overlap is between r and c, but since we are

	 only touching the real part of both, it is ok */

    }

  else /* rea_reb + (Re(c) - ima_imb) */

    {

      mpfr_init2 (tmp, pre23);

      mpfr_sub (tmp, mpc_realref(c), ima_imb, GMP_RNDZ); /* exact */

      inex_re = mpfr_add (mpc_realref(r), tmp, rea_reb, MPC_RND_RE(rnd));

      /* the only possible bad overlap is between r and c, but since we are

	 only touching the real part of both, it is ok */

    }

  /* Im(r) <- rea_imb + ima_reb + Im(c) */

  pim12 = bound_prec_addsub (rea_imb, ima_reb); /* bound on exact precision for

						   rea_imb + ima_reb */

  pim13 = bound_prec_addsub (rea_imb, mpc_imagref(c));

  /* bound for rea_imb + Im(c) */

  pim23 = bound_prec_addsub (ima_reb, mpc_imagref(c));

  /* bound for ima_reb + Im(c) */

  if (pim12 <= pim13 && pim12 <= pim23) /* (rea_imb + ima_reb) + Im(c) */

    {

      mpfr_set_prec (tmp, pim12);

      mpfr_add (tmp, rea_imb, ima_reb, GMP_RNDZ); /* exact */

      inex_im = mpfr_add (mpc_imagref(r), tmp, mpc_imagref(c), MPC_RND_IM(rnd));

      /* the only possible bad overlap is between r and c, but since we are

	 only touching the imaginary part of both, it is ok */

    }

  else if (pim13 <= pim23) /* (rea_imb + Im(c)) + ima_reb */

    {

      mpfr_set_prec (tmp, pim13);

      mpfr_add (tmp, rea_imb, mpc_imagref(c), GMP_RNDZ); /* exact */

      inex_im = mpfr_add (mpc_imagref(r), tmp, ima_reb, MPC_RND_IM(rnd));

      /* the only possible bad overlap is between r and c, but since we are

	 only touching the imaginary part of both, it is ok */

    }

  else /* rea_imb + (Im(c) + ima_reb) */

    {

      mpfr_set_prec (tmp, pre23);

      mpfr_add (tmp, mpc_imagref(c), ima_reb, GMP_RNDZ); /* exact */

      inex_im = mpfr_add (mpc_imagref(r), tmp, rea_imb, MPC_RND_IM(rnd));

      /* the only possible bad overlap is between r and c, but since we are

	 only touching the imaginary part of both, it is ok */

    }

  mpfr_clear (rea_reb);

  mpfr_clear (rea_imb);

  mpfr_clear (ima_reb);

  mpfr_clear (ima_imb);

  mpfr_clear (tmp);

  return MPC_INEX(inex_re, inex_im);

}

/* The algorithm is as follows:

   - in a first pass, we use the target precision + some extra bits

   - if it fails, we add the number of cancelled bits when adding

     Re(a*b) and Re(c) [similarly for the imaginary part]

   - it is fails again, we call the mpc_fma_naive function, which also

     deals with the special cases */

int

mpc_fma (mpc_ptr r, mpc_srcptr a, mpc_srcptr b, mpc_srcptr c, mpc_rnd_t rnd)

{

  mpc_t ab;

  mpfr_prec_t pre, pim, wpre, wpim;

  mpfr_exp_t diffre, diffim;

  int i, inex = 0, okre = 0, okim = 0;

  if (mpc_fin_p (a) == 0 || mpc_fin_p (b) == 0 || mpc_fin_p (c) == 0)

    return mpc_fma_naive (r, a, b, c, rnd);

  pre = mpfr_get_prec (mpc_realref(r));

  pim = mpfr_get_prec (mpc_imagref(r));

  wpre = pre + mpc_ceil_log2 (pre) + 10;

  wpim = pim + mpc_ceil_log2 (pim) + 10;

  mpc_init3 (ab, wpre, wpim);

  for (i = 0; i < 2; ++i)

    {

      mpc_mul (ab, a, b, MPC_RNDZZ);

      if (mpfr_zero_p (mpc_realref(ab)) || mpfr_zero_p (mpc_imagref(ab)))

        break;

      diffre = mpfr_get_exp (mpc_realref(ab));

      diffim = mpfr_get_exp (mpc_imagref(ab));

      mpc_add (ab, ab, c, MPC_RNDZZ);

      if (mpfr_zero_p (mpc_realref(ab)) || mpfr_zero_p (mpc_imagref(ab)))

        break;

      diffre -= mpfr_get_exp (mpc_realref(ab));

      diffim -= mpfr_get_exp (mpc_imagref(ab));

      diffre = (diffre > 0 ? diffre + 1 : 1);

      diffim = (diffim > 0 ? diffim + 1 : 1);

      okre = diffre > (mpfr_exp_t) wpre ? 0 : mpfr_can_round (mpc_realref(ab),

                                 wpre - diffre, GMP_RNDN, GMP_RNDZ,

                                 pre + (MPC_RND_RE (rnd) == GMP_RNDN));

      okim = diffim > (mpfr_exp_t) wpim ? 0 : mpfr_can_round (mpc_imagref(ab),

                                 wpim - diffim, GMP_RNDN, GMP_RNDZ,

                                 pim + (MPC_RND_IM (rnd) == GMP_RNDN));

      if (okre && okim)

        {

          inex = mpc_set (r, ab, rnd);

          break;

        }

      if (i == 1)

        break;

      if (okre == 0 && diffre > 1)

        wpre += diffre;

      if (okim == 0 && diffim > 1)

        wpim += diffim;

      mpfr_set_prec (mpc_realref(ab), wpre);

      mpfr_set_prec (mpc_imagref(ab), wpim);

    }

  mpc_clear (ab);

  return okre && okim ? inex : mpc_fma_naive (r, a, b, c, rnd);

}