/* mpc_div -- Divide two complex numbers.

Copyright (C) 2002, 2003, 2004, 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 "mpc-impl.h"

/* this routine deals with the case where w is zero */

static int

mpc_div_zero (mpc_ptr a, mpc_srcptr z, mpc_srcptr w, mpc_rnd_t rnd)

/* Assumes w==0, implementation according to C99 G.5.1.8 */

{

   int sign = MPFR_SIGNBIT (mpc_realref (w));

   mpfr_t infty;

   mpfr_init2 (infty, MPFR_PREC_MIN);

   mpfr_set_inf (infty, sign);

   mpfr_mul (mpc_realref (a), infty, mpc_realref (z), MPC_RND_RE (rnd));

   mpfr_mul (mpc_imagref (a), infty, mpc_imagref (z), MPC_RND_IM (rnd));

   mpfr_clear (infty);

   return MPC_INEX (0, 0); /* exact */

}

/* this routine deals with the case where z is infinite and w finite */

static int

mpc_div_inf_fin (mpc_ptr rop, mpc_srcptr z, mpc_srcptr w)

/* Assumes w finite and non-zero and z infinite; implementation

   according to C99 G.5.1.8                                     */

{

   int a, b, x, y;

   a = (mpfr_inf_p (mpc_realref (z)) ? MPFR_SIGNBIT (mpc_realref (z)) : 0);

   b = (mpfr_inf_p (mpc_imagref (z)) ? MPFR_SIGNBIT (mpc_imagref (z)) : 0);

   /* a is -1 if Re(z) = -Inf, 1 if Re(z) = +Inf, 0 if Re(z) is finite

      b is -1 if Im(z) = -Inf, 1 if Im(z) = +Inf, 0 if Im(z) is finite */

   /* x = MPC_MPFR_SIGN (a * mpc_realref (w) + b * mpc_imagref (w)) */

   /* y = MPC_MPFR_SIGN (b * mpc_realref (w) - a * mpc_imagref (w)) */

   if (a == 0 || b == 0) {

     /* only one of a or b can be zero, since z is infinite */

      x = a * MPC_MPFR_SIGN (mpc_realref (w)) + b * MPC_MPFR_SIGN (mpc_imagref (w));

      y = b * MPC_MPFR_SIGN (mpc_realref (w)) - a * MPC_MPFR_SIGN (mpc_imagref (w));

   }

   else {

      /* Both parts of z are infinite; x could be determined by sign

         considerations and comparisons. Since operations with non-finite

         numbers are not considered time-critical, we let mpfr do the work. */

      mpfr_t sign;

      mpfr_init2 (sign, 2);

      /* This is enough to determine the sign of sums and differences. */

      if (a == 1)

         if (b == 1) {

            mpfr_add (sign, mpc_realref (w), mpc_imagref (w), MPFR_RNDN);

            x = MPC_MPFR_SIGN (sign);

            mpfr_sub (sign, mpc_realref (w), mpc_imagref (w), MPFR_RNDN);

            y = MPC_MPFR_SIGN (sign);

         }

         else { /* b == -1 */

            mpfr_sub (sign, mpc_realref (w), mpc_imagref (w), MPFR_RNDN);

            x = MPC_MPFR_SIGN (sign);

            mpfr_add (sign, mpc_realref (w), mpc_imagref (w), MPFR_RNDN);

            y = -MPC_MPFR_SIGN (sign);

         }

      else /* a == -1 */

         if (b == 1) {

            mpfr_sub (sign, mpc_imagref (w), mpc_realref (w), MPFR_RNDN);

            x = MPC_MPFR_SIGN (sign);

            mpfr_add (sign, mpc_realref (w), mpc_imagref (w), MPFR_RNDN);

            y = MPC_MPFR_SIGN (sign);

         }

         else { /* b == -1 */

            mpfr_add (sign, mpc_realref (w), mpc_imagref (w), MPFR_RNDN);

            x = -MPC_MPFR_SIGN (sign);

            mpfr_sub (sign, mpc_imagref (w), mpc_realref (w), MPFR_RNDN);

            y = MPC_MPFR_SIGN (sign);

         }

      mpfr_clear (sign);

   }

   if (x == 0)

      mpfr_set_nan (mpc_realref (rop));

   else

      mpfr_set_inf (mpc_realref (rop), x);

   if (y == 0)

      mpfr_set_nan (mpc_imagref (rop));

   else

      mpfr_set_inf (mpc_imagref (rop), y);

   return MPC_INEX (0, 0); /* exact */

}

/* this routine deals with the case where z if finite and w infinite */

static int

mpc_div_fin_inf (mpc_ptr rop, mpc_srcptr z, mpc_srcptr w)

/* Assumes z finite and w infinite; implementation according to

   C99 G.5.1.8                                                  */

{

   mpfr_t c, d, a, b, x, y, zero;

   mpfr_init2 (c, 2); /* needed to hold a signed zero, +1 or -1 */

   mpfr_init2 (d, 2);

   mpfr_init2 (x, 2);

   mpfr_init2 (y, 2);

   mpfr_init2 (zero, 2);

   mpfr_set_ui (zero, 0ul, MPFR_RNDN);

   mpfr_init2 (a, mpfr_get_prec (mpc_realref (z)));

   mpfr_init2 (b, mpfr_get_prec (mpc_imagref (z)));

   mpfr_set_ui (c, (mpfr_inf_p (mpc_realref (w)) ? 1 : 0), MPFR_RNDN);

   MPFR_COPYSIGN (c, c, mpc_realref (w), MPFR_RNDN);

   mpfr_set_ui (d, (mpfr_inf_p (mpc_imagref (w)) ? 1 : 0), MPFR_RNDN);

   MPFR_COPYSIGN (d, d, mpc_imagref (w), MPFR_RNDN);

   mpfr_mul (a, mpc_realref (z), c, MPFR_RNDN); /* exact */

   mpfr_mul (b, mpc_imagref (z), d, MPFR_RNDN);

   mpfr_add (x, a, b, MPFR_RNDN);

   mpfr_mul (b, mpc_imagref (z), c, MPFR_RNDN);

   mpfr_mul (a, mpc_realref (z), d, MPFR_RNDN);

   mpfr_sub (y, b, a, MPFR_RNDN);

   MPFR_COPYSIGN (mpc_realref (rop), zero, x, MPFR_RNDN);

   MPFR_COPYSIGN (mpc_imagref (rop), zero, y, MPFR_RNDN);

   mpfr_clear (c);

   mpfr_clear (d);

   mpfr_clear (x);

   mpfr_clear (y);

   mpfr_clear (zero);

   mpfr_clear (a);

   mpfr_clear (b);

   return MPC_INEX (0, 0); /* exact */

}

static int

mpc_div_real (mpc_ptr rop, mpc_srcptr z, mpc_srcptr w, mpc_rnd_t rnd)

/* Assumes z finite and w finite and non-zero, with imaginary part

   of w a signed zero.                                             */

{

   int inex_re, inex_im;

   /* save signs of operands in case there are overlaps */

   int zrs = MPFR_SIGNBIT (mpc_realref (z));

   int zis = MPFR_SIGNBIT (mpc_imagref (z));

   int wrs = MPFR_SIGNBIT (mpc_realref (w));

   int wis = MPFR_SIGNBIT (mpc_imagref (w));

   /* warning: rop may overlap with z,w so treat the imaginary part first */

   inex_im = mpfr_div (mpc_imagref(rop), mpc_imagref(z), mpc_realref(w), MPC_RND_IM(rnd));

   inex_re = mpfr_div (mpc_realref(rop), mpc_realref(z), mpc_realref(w), MPC_RND_RE(rnd));

   /* correct signs of zeroes if necessary, which does not affect the

      inexact flags                                                    */

   if (mpfr_zero_p (mpc_realref (rop)))

      mpfr_setsign (mpc_realref (rop), mpc_realref (rop), (zrs != wrs && zis != wis),

         MPFR_RNDN); /* exact */

   if (mpfr_zero_p (mpc_imagref (rop)))

      mpfr_setsign (mpc_imagref (rop), mpc_imagref (rop), (zis != wrs && zrs == wis),

         MPFR_RNDN);

   return MPC_INEX(inex_re, inex_im);

}

static int

mpc_div_imag (mpc_ptr rop, mpc_srcptr z, mpc_srcptr w, mpc_rnd_t rnd)

/* Assumes z finite and w finite and non-zero, with real part

   of w a signed zero.                                        */

{

   int inex_re, inex_im;

   int overlap = (rop == z) || (rop == w);

   int imag_z = mpfr_zero_p (mpc_realref (z));

   mpfr_t wloc;

   mpc_t tmprop;

   mpc_ptr dest = (overlap) ? tmprop : rop;

   /* save signs of operands in case there are overlaps */

   int zrs = MPFR_SIGNBIT (mpc_realref (z));

   int zis = MPFR_SIGNBIT (mpc_imagref (z));

   int wrs = MPFR_SIGNBIT (mpc_realref (w));

   int wis = MPFR_SIGNBIT (mpc_imagref (w));

   if (overlap)

      mpc_init3 (tmprop, MPC_PREC_RE (rop), MPC_PREC_IM (rop));

   wloc[0] = mpc_imagref(w)[0]; /* copies mpfr struct IM(w) into wloc */

   inex_re = mpfr_div (mpc_realref(dest), mpc_imagref(z), wloc, MPC_RND_RE(rnd));

   mpfr_neg (wloc, wloc, MPFR_RNDN);

   /* changes the sign only in wloc, not in w; no need to correct later */

   inex_im = mpfr_div (mpc_imagref(dest), mpc_realref(z), wloc, MPC_RND_IM(rnd));

   if (overlap) {

      /* Note: we could use mpc_swap here, but this might cause problems

         if rop and tmprop have been allocated using different methods, since

         it will swap the significands of rop and tmprop. See

         http://lists.gforge.inria.fr/pipermail/mpc-discuss/2009-August/000504.html */

      mpc_set (rop, tmprop, MPC_RNDNN); /* exact */

      mpc_clear (tmprop);

   }

   /* correct signs of zeroes if necessary, which does not affect the

      inexact flags                                                    */

   if (mpfr_zero_p (mpc_realref (rop)))

      mpfr_setsign (mpc_realref (rop), mpc_realref (rop), (zrs != wrs && zis != wis),

         MPFR_RNDN); /* exact */

   if (imag_z)

      mpfr_setsign (mpc_imagref (rop), mpc_imagref (rop), (zis != wrs && zrs == wis),

         MPFR_RNDN);

   return MPC_INEX(inex_re, inex_im);

}

int

mpc_div (mpc_ptr a, mpc_srcptr b, mpc_srcptr c, mpc_rnd_t rnd)

{

   int ok_re = 0, ok_im = 0;

   mpc_t res, c_conj;

   mpfr_t q;

   mpfr_prec_t prec;

   int inex, inexact_prod, inexact_norm, inexact_re, inexact_im, loops = 0;

   int underflow_norm, overflow_norm, underflow_prod, overflow_prod;

   int underflow_re = 0, overflow_re = 0, underflow_im = 0, overflow_im = 0;

   mpfr_rnd_t rnd_re = MPC_RND_RE (rnd), rnd_im = MPC_RND_IM (rnd);

   int saved_underflow, saved_overflow;

   int tmpsgn;

   /* According to the C standard G.3, there are three types of numbers:   */

   /* finite (both parts are usual real numbers; contains 0), infinite     */

   /* (at least one part is a real infinity) and all others; the latter    */

   /* are numbers containing a nan, but no infinity, and could reasonably  */

   /* be called nan.                                                       */

   /* By G.5.1.4, infinite/finite=infinite; finite/infinite=0;             */

   /* all other divisions that are not finite/finite return nan+i*nan.     */

   /* Division by 0 could be handled by the following case of division by  */

   /* a real; we handle it separately instead.                             */

   if (mpc_zero_p (c))

      return mpc_div_zero (a, b, c, rnd);

   else if (mpc_inf_p (b) && mpc_fin_p (c))

         return mpc_div_inf_fin (a, b, c);

   else if (mpc_fin_p (b) && mpc_inf_p (c))

         return mpc_div_fin_inf (a, b, c);

   else if (!mpc_fin_p (b) || !mpc_fin_p (c)) {

      mpc_set_nan (a);

      return MPC_INEX (0, 0);

   }

   else if (mpfr_zero_p(mpc_imagref(c)))

      return mpc_div_real (a, b, c, rnd);

   else if (mpfr_zero_p(mpc_realref(c)))

      return mpc_div_imag (a, b, c, rnd);

   prec = MPC_MAX_PREC(a);

   mpc_init2 (res, 2);

   mpfr_init (q);

   /* create the conjugate of c in c_conj without allocating new memory */

   mpc_realref (c_conj)[0] = mpc_realref (c)[0];

   mpc_imagref (c_conj)[0] = mpc_imagref (c)[0];

   MPFR_CHANGE_SIGN (mpc_imagref (c_conj));

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

   saved_underflow = mpfr_underflow_p ();

   saved_overflow = mpfr_overflow_p ();

   do {

      loops ++;

      prec += loops <= 2 ? mpc_ceil_log2 (prec) + 5 : prec / 2;

      mpc_set_prec (res, prec);

      mpfr_set_prec (q, prec);

      /* first compute norm(c) */

      mpfr_clear_underflow ();

      mpfr_clear_overflow ();

      inexact_norm = mpc_norm (q, c, MPFR_RNDU);

      underflow_norm = mpfr_underflow_p ();

      overflow_norm = mpfr_overflow_p ();

      if (underflow_norm)

         mpfr_set_ui (q, 0ul, MPFR_RNDN);

         /* to obtain divisions by 0 later on */

      /* now compute b*conjugate(c) */

      mpfr_clear_underflow ();

      mpfr_clear_overflow ();

      inexact_prod = mpc_mul (res, b, c_conj, MPC_RNDZZ);

      inexact_re = MPC_INEX_RE (inexact_prod);

      inexact_im = MPC_INEX_IM (inexact_prod);

      underflow_prod = mpfr_underflow_p ();

      overflow_prod = mpfr_overflow_p ();

         /* unfortunately, does not distinguish between under-/overflow

            in real or imaginary parts

            hopefully, the side-effects of mpc_mul do indeed raise the

            mpfr exceptions */

      if (overflow_prod) {

         int isinf = 0;

         tmpsgn = mpfr_sgn (mpc_realref(res));

         if (tmpsgn > 0)

           {

             mpfr_nextabove (mpc_realref(res));

             isinf = mpfr_inf_p (mpc_realref(res));

             mpfr_nextbelow (mpc_realref(res));

           }

         else if (tmpsgn < 0)

           {

             mpfr_nextbelow (mpc_realref(res));

             isinf = mpfr_inf_p (mpc_realref(res));

             mpfr_nextabove (mpc_realref(res));

           }

         if (isinf)

           {

             mpfr_set_inf (mpc_realref(res), tmpsgn);

             overflow_re = 1;

           }

         tmpsgn = mpfr_sgn (mpc_imagref(res));

         isinf = 0;

         if (tmpsgn > 0)

           {

             mpfr_nextabove (mpc_imagref(res));

             isinf = mpfr_inf_p (mpc_imagref(res));

             mpfr_nextbelow (mpc_imagref(res));

           }

         else if (tmpsgn < 0)

           {

             mpfr_nextbelow (mpc_imagref(res));

             isinf = mpfr_inf_p (mpc_imagref(res));

             mpfr_nextabove (mpc_imagref(res));

           }

         if (isinf)

           {

             mpfr_set_inf (mpc_imagref(res), tmpsgn);

             overflow_im = 1;

           }

         mpc_set (a, res, rnd);

         goto end;

      }

      /* divide the product by the norm */

      if (inexact_norm == 0 && (inexact_re == 0 || inexact_im == 0)) {

         /* The division has good chances to be exact in at least one part.  */

         /* Since this can cause problems when not rounding to the nearest,  */

         /* we use the division code of mpfr, which handles the situation.   */

         mpfr_clear_underflow ();

         mpfr_clear_overflow ();

         inexact_re |= mpfr_div (mpc_realref (res), mpc_realref (res), q, MPFR_RNDZ);

         underflow_re = mpfr_underflow_p ();

         overflow_re = mpfr_overflow_p ();

         ok_re = !inexact_re || underflow_re || overflow_re

                 || mpfr_can_round (mpc_realref (res), prec - 4, MPFR_RNDN,

                    MPFR_RNDZ, MPC_PREC_RE(a) + (rnd_re == MPFR_RNDN));

         if (ok_re) /* compute imaginary part */ {

            mpfr_clear_underflow ();

            mpfr_clear_overflow ();

            inexact_im |= mpfr_div (mpc_imagref (res), mpc_imagref (res), q, MPFR_RNDZ);

            underflow_im = mpfr_underflow_p ();

            overflow_im = mpfr_overflow_p ();

            ok_im = !inexact_im || underflow_im || overflow_im

                    || mpfr_can_round (mpc_imagref (res), prec - 4, MPFR_RNDN,

                       MPFR_RNDZ, MPC_PREC_IM(a) + (rnd_im == MPFR_RNDN));

         }

      }

      else {

         /* The division is inexact, so for efficiency reasons we invert q */

         /* only once and multiply by the inverse. */

         if (mpfr_ui_div (q, 1ul, q, MPFR_RNDZ) || inexact_norm) {

             /* if 1/q is inexact, the approximations of the real and

                imaginary part below will be inexact, unless RE(res)

                or IM(res) is zero */

             inexact_re |= !mpfr_zero_p (mpc_realref (res));

             inexact_im |= !mpfr_zero_p (mpc_imagref (res));

         }

         mpfr_clear_underflow ();

         mpfr_clear_overflow ();

         inexact_re |= mpfr_mul (mpc_realref (res), mpc_realref (res), q, MPFR_RNDZ);

         underflow_re = mpfr_underflow_p ();

         overflow_re = mpfr_overflow_p ();

         ok_re = !inexact_re || underflow_re || overflow_re

                 || mpfr_can_round (mpc_realref (res), prec - 4, MPFR_RNDN,

                    MPFR_RNDZ, MPC_PREC_RE(a) + (rnd_re == MPFR_RNDN));

         if (ok_re) /* compute imaginary part */ {

            mpfr_clear_underflow ();

            mpfr_clear_overflow ();

            inexact_im |= mpfr_mul (mpc_imagref (res), mpc_imagref (res), q, MPFR_RNDZ);

            underflow_im = mpfr_underflow_p ();

            overflow_im = mpfr_overflow_p ();

            ok_im = !inexact_im || underflow_im || overflow_im

                    || mpfr_can_round (mpc_imagref (res), prec - 4, MPFR_RNDN,

                       MPFR_RNDZ, MPC_PREC_IM(a) + (rnd_im == MPFR_RNDN));

         }

      }

   } while ((!ok_re || !ok_im) && !underflow_norm && !overflow_norm

                               && !underflow_prod && !overflow_prod);

   inex = mpc_set (a, res, rnd);

   inexact_re = MPC_INEX_RE (inex);

   inexact_im = MPC_INEX_IM (inex);

 end:

   /* fix values and inexact flags in case of overflow/underflow */

   /* FIXME: heuristic, certainly does not cover all cases */

   if (overflow_re || (underflow_norm && !underflow_prod)) {

      mpfr_set_inf (mpc_realref (a), mpfr_sgn (mpc_realref (res)));

      inexact_re = mpfr_sgn (mpc_realref (res));

   }

   else if (underflow_re || (overflow_norm && !overflow_prod)) {

      inexact_re = mpfr_signbit (mpc_realref (res)) ? 1 : -1;

      mpfr_set_zero (mpc_realref (a), -inexact_re);

   }

   if (overflow_im || (underflow_norm && !underflow_prod)) {

      mpfr_set_inf (mpc_imagref (a), mpfr_sgn (mpc_imagref (res)));

      inexact_im = mpfr_sgn (mpc_imagref (res));

   }

   else if (underflow_im || (overflow_norm && !overflow_prod)) {

      inexact_im = mpfr_signbit (mpc_imagref (res)) ? 1 : -1;

      mpfr_set_zero (mpc_imagref (a), -inexact_im);

   }

   mpc_clear (res);

   mpfr_clear (q);

   /* restore underflow and overflow flags from MPFR */

   if (saved_underflow)

     mpfr_set_underflow ();

   if (saved_overflow)

     mpfr_set_overflow ();

   return MPC_INEX (inexact_re, inexact_im);

}