/* mpfr_atan2 -- arc-tan 2 of a floating-point number

Copyright 2005 Free Software Foundation.

This file is part of the MPFR Library, and was contributed by Mathieu Dutour.

The MPFR Library 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 2.1 of the License, or (at your
option) any later version.

The MPFR Library 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 the MPFR Library; see the file COPYING.LIB.  If not, write to
the Free Software Foundation, Inc., 51 Franklin Place, Fifth Floor, Boston,
MA 02110-1301, USA. */

#define MPFR_NEED_LONGLONG_H
#include "mpfr-impl.h"

int
mpfr_atan2 (mpfr_ptr dest, mpfr_srcptr y, mpfr_srcptr x, mp_rnd_t rnd_mode)
{
  mpfr_t tmp, pi;
  int inexact;
  mp_prec_t prec;
  mp_exp_t e;
  MPFR_SAVE_EXPO_DECL (expo);
  MPFR_ZIV_DECL (loop);

  MPFR_LOG_FUNC (("y[%#R]=%R x[%#R]=%R rnd=%d", y, y, x, x, rnd_mode),
                 ("atan[%#R]=%R inexact=%d", dest, dest, inexact));

  /* Special cases */
  if (MPFR_ARE_SINGULAR (x, y))
    {
      /* atan2(0, 0) does not raise the "invalid" floating-point
         exception, nor does atan2(y, 0) raise the "divide-by-zero"
         floating-point exception.
         -- atan2(±0, -0) returns ±pi.313)
         -- atan2(±0, +0) returns ±0.
         -- atan2(±0, x) returns ±pi, for x < 0.
         -- atan2(±0, x) returns ±0, for x > 0.
         -- atan2(y, ±0) returns -pi/2 for y < 0.
         -- atan2(y, ±0) returns pi/2 for y > 0.
         -- atan2(±oo, -oo) returns ±3pi/4.
         -- atan2(±oo, +oo) returns ±pi/4.
         -- atan2(±oo, x) returns ±pi/2, for finite x.
         -- atan2(±y, -oo) returns ±pi, for finite y > 0.
         -- atan2(±y, +oo) returns ±0, for finite y > 0.
      */
      if (MPFR_IS_NAN (x) || MPFR_IS_NAN (y))
        {
          MPFR_SET_NAN (dest);
          MPFR_RET_NAN;
        }
      if (MPFR_IS_ZERO (y))
        {
          if (MPFR_IS_NEG (x)) /* +/- PI */
            {
            set_pi:
              if (MPFR_IS_NEG (y))
                {
                  inexact =  mpfr_const_pi (dest, MPFR_INVERT_RND (rnd_mode));
                  MPFR_CHANGE_SIGN (dest);
                  return -inexact;
                }
              else
                return mpfr_const_pi (dest, rnd_mode);
            }
          else /* +/- 0 */
            {
            set_zero:
              MPFR_SET_ZERO (dest);
              MPFR_SET_SAME_SIGN (dest, y);
              return 0;
            }
        }
      if (MPFR_IS_ZERO (x))
        {
        set_pi_2:
          if (MPFR_IS_NEG (y)) /* -PI/2 */
            {
              inexact = mpfr_const_pi (dest, MPFR_INVERT_RND(rnd_mode));
              MPFR_CHANGE_SIGN (dest);
              mpfr_div_2ui (dest, dest, 1, rnd_mode);
              return -inexact;
            }
          else /* PI/2 */
            {
              inexact = mpfr_const_pi (dest, rnd_mode);
              mpfr_div_2ui (dest, dest, 1, rnd_mode);
              return inexact;
            }
        }
      if (MPFR_IS_INF (y))
        {
          if (!MPFR_IS_INF (x)) /* +/- PI/2 */
            goto set_pi_2;
          else if (MPFR_IS_POS (x)) /* +/- PI/4 */
            {
              if (MPFR_IS_NEG (y))
                {
                  rnd_mode = MPFR_INVERT_RND (rnd_mode);
                  inexact = mpfr_const_pi (dest, rnd_mode);
                  MPFR_CHANGE_SIGN (dest);
                  mpfr_div_2ui (dest, dest, 2, rnd_mode);
                  return -inexact;
                }
              else
                {
                  inexact = mpfr_const_pi (dest, rnd_mode);
                  mpfr_div_2ui (dest, dest, 2, rnd_mode);
                  return inexact;
                }
            }
          else /* +/- 3*PI/4: Ugly since we have to round properly */
            {
              mpfr_t tmp;
              MPFR_ZIV_DECL (loop);
              mp_prec_t prec = MPFR_PREC (dest) + BITS_PER_MP_LIMB;

              mpfr_init2 (tmp, prec);
              MPFR_ZIV_INIT (loop, prec);
              for (;;)
                {
                  mpfr_const_pi (tmp, GMP_RNDN);
                  mpfr_mul_ui (tmp, tmp, 3, GMP_RNDN); /* Error <= 2  */
                  mpfr_div_2ui (tmp, tmp, 2, GMP_RNDN);
                  if (mpfr_round_p (MPFR_MANT (tmp), MPFR_LIMB_SIZE (tmp),
                                    MPFR_PREC (tmp)-2,
                                    MPFR_PREC (dest) + (rnd_mode == GMP_RNDN)))
                    break;
                  MPFR_ZIV_NEXT (loop, prec);
                  mpfr_set_prec (tmp, prec);
                }
              MPFR_ZIV_FREE (loop);
              if (MPFR_IS_NEG (y))
                MPFR_CHANGE_SIGN (tmp);
              inexact = mpfr_set (dest, tmp, rnd_mode);
              mpfr_clear (tmp);
              return inexact;
            }
        }
      MPFR_ASSERTD (MPFR_IS_INF (x));
      if (MPFR_IS_NEG (x))
        goto set_pi;
      else
        goto set_zero;
    }
  MPFR_SAVE_EXPO_MARK (expo);

  /* Set up initial prec */
  prec = MPFR_PREC (dest) + 3 + MPFR_INT_CEIL_LOG2 (MPFR_PREC (dest));
  mpfr_init2 (tmp, prec);

  MPFR_ZIV_INIT (loop, prec);
  if (MPFR_IS_POS (x))
    /* use atan2(y,x) = atan(y/x) */
    for (;;)
      {
        mpfr_div (tmp, y, x, GMP_RNDN);   /* Error <= ulp (tmp) */
        mpfr_atan (tmp, tmp, GMP_RNDN);   /* Error <= 2*ulp (tmp) since
                                             abs(D(arctan)) <= 1 */
        /*FIXME: Error <= ulp(tmp) ? */
        if (MPFR_LIKELY (MPFR_CAN_ROUND (tmp, prec - 2, MPFR_PREC (dest),
                                         rnd_mode)))
          break;
        MPFR_ZIV_NEXT (loop, prec);
        mpfr_set_prec (tmp, prec);
      }
  else /* x < 0 */
    /*  Use sign(y)*(PI - atan (|y/x|)) */
    {
      mpfr_init2 (pi, prec);
      for (;;)
        {
          mpfr_div (tmp, y, x, GMP_RNDN);   /* Error <= ulp (tmp) */
          MPFR_SET_POS (tmp);               /* no error */
          mpfr_atan (tmp, tmp, GMP_RNDN);   /* Error <= 2*ulp (tmp) since
                                               abs(D(arctan)) <= 1 */
          mpfr_const_pi (pi, GMP_RNDN);     /* Error <= ulp(pi) /2 */
          e = MPFR_GET_EXP (tmp);
          mpfr_sub (tmp, pi, tmp, GMP_RNDN);          /* see above */
          if (MPFR_IS_NEG (y))
            MPFR_CHANGE_SIGN (tmp);
          /* Error(tmp) <= (1/2+2^(EXP(pi)-EXP(tmp)-1)+2^(e-EXP(tmp)+1))*ulp
                        <= 2^(MAX (MAX (EXP(PI)-EXP(tmp)-1, e-EXP(tmp)+1),
                                        -1)+2)*ulp(tmp) */
          e = MAX (MAX (MPFR_GET_EXP (pi)-MPFR_GET_EXP (tmp) - 1,
                        e - MPFR_GET_EXP (tmp) + 1), -1) + 2;
          if (MPFR_LIKELY (MPFR_CAN_ROUND (tmp, prec - e, MPFR_PREC (dest),
                                           rnd_mode)))
            break;
          MPFR_ZIV_NEXT (loop, prec);
          mpfr_set_prec (tmp, prec);
          mpfr_set_prec (pi, prec);
        }
      mpfr_clear (pi);
    }
  MPFR_ZIV_FREE (loop);

  inexact = mpfr_set (dest, tmp, rnd_mode);
  mpfr_clear (tmp);
  MPFR_SAVE_EXPO_FREE (expo);
  return mpfr_check_range (dest, inexact, rnd_mode);
}