コード例 #1
0
ファイル: acosh.c プロジェクト: 119/aircam-openwrt
int
mpc_acosh (mpc_ptr rop, mpc_srcptr op, mpc_rnd_t rnd)
{
  /* acosh(z) =
      NaN + i*NaN, if z=0+i*NaN
     -i*acos(z), if sign(Im(z)) = -
      i*acos(z), if sign(Im(z)) = +
      http://functions.wolfram.com/ElementaryFunctions/ArcCosh/27/02/03/01/01/
  */
  mpc_t a;
  mpfr_t tmp;
  int inex;

  if (mpfr_zero_p (MPC_RE (op)) && mpfr_nan_p (MPC_IM (op)))
    {
      mpfr_set_nan (MPC_RE (rop));
      mpfr_set_nan (MPC_IM (rop));
      return 0;
    }
  
  /* Note reversal of precisions due to later multiplication by i or -i */
  mpc_init3 (a, MPC_PREC_IM(rop), MPC_PREC_RE(rop));

  if (mpfr_signbit (MPC_IM (op)))
    {
      inex = mpc_acos (a, op,
                       RNDC (INV_RND (MPC_RND_IM (rnd)), MPC_RND_RE (rnd)));

      /* change a to -i*a, i.e., -y+i*x to x+i*y */
      tmp[0] = MPC_RE (a)[0];
      MPC_RE (a)[0] = MPC_IM (a)[0];
      MPC_IM (a)[0] = tmp[0];
      MPFR_CHANGE_SIGN (MPC_IM (a));
      inex = MPC_INEX (MPC_INEX_IM (inex), -MPC_INEX_RE (inex));
    }
  else
    {
      inex = mpc_acos (a, op,
                       RNDC (MPC_RND_IM (rnd), INV_RND(MPC_RND_RE (rnd))));

      /* change a to i*a, i.e., y-i*x to x+i*y */
      tmp[0] = MPC_RE (a)[0];
      MPC_RE (a)[0] = MPC_IM (a)[0];
      MPC_IM (a)[0] = tmp[0];
      MPFR_CHANGE_SIGN (MPC_RE (a));
      inex = MPC_INEX (-MPC_INEX_IM (inex), MPC_INEX_RE (inex));
    }

  mpc_set (rop, a, rnd);

  mpc_clear (a);

  return inex;
}
コード例 #2
0
ファイル: asinh.c プロジェクト: 119/aircam-openwrt
int
mpc_asinh (mpc_ptr rop, mpc_srcptr op, mpc_rnd_t rnd)
{
  /* asinh(op) = -i*asin(i*op) */
  int inex;
  mpc_t z, a;
  mpfr_t tmp;

  /* z = i*op */
  MPC_RE (z)[0] = MPC_IM (op)[0];
  MPC_IM (z)[0] = MPC_RE (op)[0];
  MPFR_CHANGE_SIGN (MPC_RE (z));

  /* Note reversal of precisions due to later multiplication by -i */
  mpc_init3 (a, MPC_PREC_IM(rop), MPC_PREC_RE(rop));

  inex = mpc_asin (a, z,
                   RNDC (INV_RND (MPC_RND_IM (rnd)), MPC_RND_RE (rnd)));

  /* if a = asin(i*op) = x+i*y, and we want y-i*x */

  /* change a to -i*a */
  tmp[0] = MPC_RE (a)[0];
  MPC_RE (a)[0] = MPC_IM (a)[0];
  MPC_IM (a)[0] = tmp[0];
  MPFR_CHANGE_SIGN (MPC_IM (a));

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

  mpc_clear (a);

  return MPC_INEX (MPC_INEX_IM (inex), -MPC_INEX_RE (inex));
}
コード例 #3
0
ファイル: atanh.c プロジェクト: 119/aircam-openwrt
int
mpc_atanh (mpc_ptr rop, mpc_srcptr op, mpc_rnd_t rnd)
{
  /* atanh(op) = -i*atan(i*op) */
  int inex;
  mpfr_t tmp;
  mpc_t z, a;

  MPC_RE (z)[0] = MPC_IM (op)[0];
  MPC_IM (z)[0] = MPC_RE (op)[0];
  MPFR_CHANGE_SIGN (MPC_RE (z));

  /* Note reversal of precisions due to later multiplication by -i */
  mpc_init3 (a, MPC_PREC_IM(rop), MPC_PREC_RE(rop));

  inex = mpc_atan (a, z,
                   RNDC (INV_RND (MPC_RND_IM (rnd)), MPC_RND_RE (rnd)));

  /* change a to -i*a, i.e., x+i*y to y-i*x */
  tmp[0] = MPC_RE (a)[0];
  MPC_RE (a)[0] = MPC_IM (a)[0];
  MPC_IM (a)[0] = tmp[0];
  MPFR_CHANGE_SIGN (MPC_IM (a));

  mpc_set (rop, a, rnd);

  mpc_clear (a);

  return MPC_INEX (MPC_INEX_IM (inex), -MPC_INEX_RE (inex));
}
コード例 #4
0
/* set rop to
   -pi/2 if s < 0
   +pi/2 else
   rounded in the direction rnd
*/
int
set_pi_over_2 (mpfr_ptr rop, int s, mpfr_rnd_t rnd)
{
    int inex;

    inex = mpfr_const_pi (rop, s < 0 ? INV_RND (rnd) : rnd);
    mpfr_div_2ui (rop, rop, 1, GMP_RNDN);
    if (s < 0)
    {
        inex = -inex;
        mpfr_neg (rop, rop, GMP_RNDN);
    }

    return inex;
}
コード例 #5
0
ファイル: asin.c プロジェクト: Gwenio/DragonFlyBSD
int
mpc_asin (mpc_ptr rop, mpc_srcptr op, mpc_rnd_t rnd)
{
  mpfr_prec_t p, p_re, p_im, incr_p = 0;
  mpfr_rnd_t rnd_re, rnd_im;
  mpc_t z1;
  int inex;

  /* special values */
  if (mpfr_nan_p (mpc_realref (op)) || mpfr_nan_p (mpc_imagref (op)))
    {
      if (mpfr_inf_p (mpc_realref (op)) || mpfr_inf_p (mpc_imagref (op)))
        {
          mpfr_set_nan (mpc_realref (rop));
          mpfr_set_inf (mpc_imagref (rop), mpfr_signbit (mpc_imagref (op)) ? -1 : +1);
        }
      else if (mpfr_zero_p (mpc_realref (op)))
        {
          mpfr_set (mpc_realref (rop), mpc_realref (op), GMP_RNDN);
          mpfr_set_nan (mpc_imagref (rop));
        }
      else
        {
          mpfr_set_nan (mpc_realref (rop));
          mpfr_set_nan (mpc_imagref (rop));
        }

      return 0;
    }

  if (mpfr_inf_p (mpc_realref (op)) || mpfr_inf_p (mpc_imagref (op)))
    {
      int inex_re;
      if (mpfr_inf_p (mpc_realref (op)))
        {
          int inf_im = mpfr_inf_p (mpc_imagref (op));

          inex_re = set_pi_over_2 (mpc_realref (rop),
             (mpfr_signbit (mpc_realref (op)) ? -1 : 1), MPC_RND_RE (rnd));
          mpfr_set_inf (mpc_imagref (rop), (mpfr_signbit (mpc_imagref (op)) ? -1 : 1));

          if (inf_im)
            mpfr_div_2ui (mpc_realref (rop), mpc_realref (rop), 1, GMP_RNDN);
        }
      else
        {
          mpfr_set_zero (mpc_realref (rop), (mpfr_signbit (mpc_realref (op)) ? -1 : 1));
          inex_re = 0;
          mpfr_set_inf (mpc_imagref (rop), (mpfr_signbit (mpc_imagref (op)) ? -1 : 1));
        }

      return MPC_INEX (inex_re, 0);
    }

  /* pure real argument */
  if (mpfr_zero_p (mpc_imagref (op)))
    {
      int inex_re;
      int inex_im;
      int s_im;
      s_im = mpfr_signbit (mpc_imagref (op));

      if (mpfr_cmp_ui (mpc_realref (op), 1) > 0)
        {
          if (s_im)
            inex_im = -mpfr_acosh (mpc_imagref (rop), mpc_realref (op),
                                   INV_RND (MPC_RND_IM (rnd)));
          else
            inex_im = mpfr_acosh (mpc_imagref (rop), mpc_realref (op),
                                  MPC_RND_IM (rnd));
          inex_re = set_pi_over_2 (mpc_realref (rop),
             (mpfr_signbit (mpc_realref (op)) ? -1 : 1), MPC_RND_RE (rnd));
          if (s_im)
            mpc_conj (rop, rop, MPC_RNDNN);
        }
      else if (mpfr_cmp_si (mpc_realref (op), -1) < 0)
        {
          mpfr_t minus_op_re;
          minus_op_re[0] = mpc_realref (op)[0];
          MPFR_CHANGE_SIGN (minus_op_re);

          if (s_im)
            inex_im = -mpfr_acosh (mpc_imagref (rop), minus_op_re,
                                   INV_RND (MPC_RND_IM (rnd)));
          else
            inex_im = mpfr_acosh (mpc_imagref (rop), minus_op_re,
                                  MPC_RND_IM (rnd));
          inex_re = set_pi_over_2 (mpc_realref (rop),
             (mpfr_signbit (mpc_realref (op)) ? -1 : 1), MPC_RND_RE (rnd));
          if (s_im)
            mpc_conj (rop, rop, MPC_RNDNN);
        }
      else
        {
          inex_im = mpfr_set_ui (mpc_imagref (rop), 0, MPC_RND_IM (rnd));
          if (s_im)
            mpfr_neg (mpc_imagref (rop), mpc_imagref (rop), GMP_RNDN);
          inex_re = mpfr_asin (mpc_realref (rop), mpc_realref (op), MPC_RND_RE (rnd));
        }

      return MPC_INEX (inex_re, inex_im);
    }

  /* pure imaginary argument */
  if (mpfr_zero_p (mpc_realref (op)))
    {
      int inex_im;
      int s;
      s = mpfr_signbit (mpc_realref (op));
      mpfr_set_ui (mpc_realref (rop), 0, GMP_RNDN);
      if (s)
        mpfr_neg (mpc_realref (rop), mpc_realref (rop), GMP_RNDN);
      inex_im = mpfr_asinh (mpc_imagref (rop), mpc_imagref (op), MPC_RND_IM (rnd));

      return MPC_INEX (0, inex_im);
    }

  /* regular complex: asin(z) = -i*log(i*z+sqrt(1-z^2)) */
  p_re = mpfr_get_prec (mpc_realref(rop));
  p_im = mpfr_get_prec (mpc_imagref(rop));
  rnd_re = MPC_RND_RE(rnd);
  rnd_im = MPC_RND_IM(rnd);
  p = p_re >= p_im ? p_re : p_im;
  mpc_init2 (z1, p);
  while (1)
  {
    mpfr_exp_t ex, ey, err;

    p += mpc_ceil_log2 (p) + 3 + incr_p; /* incr_p is zero initially */
    incr_p = p / 2;
    mpfr_set_prec (mpc_realref(z1), p);
    mpfr_set_prec (mpc_imagref(z1), p);

    /* z1 <- z^2 */
    mpc_sqr (z1, op, MPC_RNDNN);
    /* err(x) <= 1/2 ulp(x), err(y) <= 1/2 ulp(y) */
    /* z1 <- 1-z1 */
    ex = mpfr_get_exp (mpc_realref(z1));
    mpfr_ui_sub (mpc_realref(z1), 1, mpc_realref(z1), GMP_RNDN);
    mpfr_neg (mpc_imagref(z1), mpc_imagref(z1), GMP_RNDN);
    ex = ex - mpfr_get_exp (mpc_realref(z1));
    ex = (ex <= 0) ? 0 : ex;
    /* err(x) <= 2^ex * ulp(x) */
    ex = ex + mpfr_get_exp (mpc_realref(z1)) - p;
    /* err(x) <= 2^ex */
    ey = mpfr_get_exp (mpc_imagref(z1)) - p - 1;
    /* err(y) <= 2^ey */
    ex = (ex >= ey) ? ex : ey; /* err(x), err(y) <= 2^ex, i.e., the norm
                                  of the error is bounded by |h|<=2^(ex+1/2) */
    /* z1 <- sqrt(z1): if z1 = z + h, then sqrt(z1) = sqrt(z) + h/2/sqrt(t) */
    ey = mpfr_get_exp (mpc_realref(z1)) >= mpfr_get_exp (mpc_imagref(z1))
      ? mpfr_get_exp (mpc_realref(z1)) : mpfr_get_exp (mpc_imagref(z1));
    /* we have |z1| >= 2^(ey-1) thus 1/|z1| <= 2^(1-ey) */
    mpc_sqrt (z1, z1, MPC_RNDNN);
    ex = (2 * ex + 1) - 2 - (ey - 1); /* |h^2/4/|t| <= 2^ex */
    ex = (ex + 1) / 2; /* ceil(ex/2) */
    /* express ex in terms of ulp(z1) */
    ey = mpfr_get_exp (mpc_realref(z1)) <= mpfr_get_exp (mpc_imagref(z1))
      ? mpfr_get_exp (mpc_realref(z1)) : mpfr_get_exp (mpc_imagref(z1));
    ex = ex - ey + p;
    /* take into account the rounding error in the mpc_sqrt call */
    err = (ex <= 0) ? 1 : ex + 1;
    /* err(x) <= 2^err * ulp(x), err(y) <= 2^err * ulp(y) */
    /* z1 <- i*z + z1 */
    ex = mpfr_get_exp (mpc_realref(z1));
    ey = mpfr_get_exp (mpc_imagref(z1));
    mpfr_sub (mpc_realref(z1), mpc_realref(z1), mpc_imagref(op), GMP_RNDN);
    mpfr_add (mpc_imagref(z1), mpc_imagref(z1), mpc_realref(op), GMP_RNDN);
    if (mpfr_cmp_ui (mpc_realref(z1), 0) == 0 || mpfr_cmp_ui (mpc_imagref(z1), 0) == 0)
      continue;
    ex -= mpfr_get_exp (mpc_realref(z1)); /* cancellation in x */
    ey -= mpfr_get_exp (mpc_imagref(z1)); /* cancellation in y */
    ex = (ex >= ey) ? ex : ey; /* maximum cancellation */
    err += ex;
    err = (err <= 0) ? 1 : err + 1; /* rounding error in sub/add */
    /* z1 <- log(z1): if z1 = z + h, then log(z1) = log(z) + h/t with
       |t| >= min(|z1|,|z|) */
    ex = mpfr_get_exp (mpc_realref(z1));
    ey = mpfr_get_exp (mpc_imagref(z1));
    ex = (ex >= ey) ? ex : ey;
    err += ex - p; /* revert to absolute error <= 2^err */
    mpc_log (z1, z1, GMP_RNDN);
    err -= ex - 1; /* 1/|t| <= 1/|z| <= 2^(1-ex) */
    /* express err in terms of ulp(z1) */
    ey = mpfr_get_exp (mpc_realref(z1)) <= mpfr_get_exp (mpc_imagref(z1))
      ? mpfr_get_exp (mpc_realref(z1)) : mpfr_get_exp (mpc_imagref(z1));
    err = err - ey + p;
    /* take into account the rounding error in the mpc_log call */
    err = (err <= 0) ? 1 : err + 1;
    /* z1 <- -i*z1 */
    mpfr_swap (mpc_realref(z1), mpc_imagref(z1));
    mpfr_neg (mpc_imagref(z1), mpc_imagref(z1), GMP_RNDN);
    if (mpfr_can_round (mpc_realref(z1), p - err, GMP_RNDN, GMP_RNDZ,
                        p_re + (rnd_re == GMP_RNDN)) &&
        mpfr_can_round (mpc_imagref(z1), p - err, GMP_RNDN, GMP_RNDZ,
                        p_im + (rnd_im == GMP_RNDN)))
      break;
  }

  inex = mpc_set (rop, z1, rnd);
  mpc_clear (z1);

  return inex;
}
コード例 #6
0
ファイル: sqrt.c プロジェクト: 119/aircam-openwrt
int
mpc_sqrt (mpc_ptr a, mpc_srcptr b, mpc_rnd_t rnd)
{
  int ok_w, ok_t = 0;
  mpfr_t    w, t;
  mp_rnd_t  rnd_w, rnd_t;
  mp_prec_t prec_w, prec_t;
  /* the rounding mode and the precision required for w and t, which can */
  /* be either the real or the imaginary part of a */
  mp_prec_t prec;
  int inex_w, inex_t = 1, inex, loops = 0;
  /* comparison of the real/imaginary part of b with 0 */
  const int re_cmp = mpfr_cmp_ui (MPC_RE (b), 0);
  const int im_cmp = mpfr_cmp_ui (MPC_IM (b), 0);
  /* we need to know the sign of Im(b) when it is +/-0 */
  const int im_sgn = mpfr_signbit (MPC_IM (b)) == 0? 0 : -1;

  /* special values */
  /* sqrt(x +i*Inf) = +Inf +I*Inf, even if x = NaN */
  /* sqrt(x -i*Inf) = +Inf -I*Inf, even if x = NaN */
  if (mpfr_inf_p (MPC_IM (b)))
    {
      mpfr_set_inf (MPC_RE (a), +1);
      mpfr_set_inf (MPC_IM (a), im_sgn);
      return MPC_INEX (0, 0);
    }

  if (mpfr_inf_p (MPC_RE (b)))
    {
      if (mpfr_signbit (MPC_RE (b)))
        {
          if (mpfr_number_p (MPC_IM (b)))
            {
              /* sqrt(-Inf +i*y) = +0 +i*Inf, when y positive */
              /* sqrt(-Inf +i*y) = +0 -i*Inf, when y positive */
              mpfr_set_ui (MPC_RE (a), 0, GMP_RNDN);
              mpfr_set_inf (MPC_IM (a), im_sgn);
              return MPC_INEX (0, 0);
            }
          else
            {
              /* sqrt(-Inf +i*NaN) = NaN +/-i*Inf */
              mpfr_set_nan (MPC_RE (a));
              mpfr_set_inf (MPC_IM (a), im_sgn);
              return MPC_INEX (0, 0);
            }
        }
      else
        {
          if (mpfr_number_p (MPC_IM (b)))
            {
              /* sqrt(+Inf +i*y) = +Inf +i*0, when y positive */
              /* sqrt(+Inf +i*y) = +Inf -i*0, when y positive */
              mpfr_set_inf (MPC_RE (a), +1);
              mpfr_set_ui (MPC_IM (a), 0, GMP_RNDN);
              if (im_sgn)
                mpc_conj (a, a, MPC_RNDNN);
              return MPC_INEX (0, 0);
            }
          else
            {
              /* sqrt(+Inf -i*Inf) = +Inf -i*Inf */
              /* sqrt(+Inf +i*Inf) = +Inf +i*Inf */
              /* sqrt(+Inf +i*NaN) = +Inf +i*NaN */
              return mpc_set (a, b, rnd);
            }
        }
    }

  /* sqrt(x +i*NaN) = NaN +i*NaN, if x is not infinite */
  /* sqrt(NaN +i*y) = NaN +i*NaN, if y is not infinite */
  if (mpfr_nan_p (MPC_RE (b)) || mpfr_nan_p (MPC_IM (b)))
    {
      mpfr_set_nan (MPC_RE (a));
      mpfr_set_nan (MPC_IM (a));
      return MPC_INEX (0, 0);
    }

  /* purely real */
  if (im_cmp == 0)
    {
      if (re_cmp == 0)
        {
          mpc_set_ui_ui (a, 0, 0, MPC_RNDNN);
          if (im_sgn)
            mpc_conj (a, a, MPC_RNDNN);
          return MPC_INEX (0, 0);
        }
      else if (re_cmp > 0)
        {
          inex_w = mpfr_sqrt (MPC_RE (a), MPC_RE (b), MPC_RND_RE (rnd));
          mpfr_set_ui (MPC_IM (a), 0, GMP_RNDN);
          if (im_sgn)
            mpc_conj (a, a, MPC_RNDNN);
          return MPC_INEX (inex_w, 0);
        }
      else
        {
          mpfr_init2 (w, MPFR_PREC (MPC_RE (b)));
          mpfr_neg (w, MPC_RE (b), GMP_RNDN);
          if (im_sgn)
            {
              inex_w = -mpfr_sqrt (MPC_IM (a), w, INV_RND (MPC_RND_IM (rnd)));
              mpfr_neg (MPC_IM (a), MPC_IM (a), GMP_RNDN);
            }
          else
            inex_w = mpfr_sqrt (MPC_IM (a), w, MPC_RND_IM (rnd));

          mpfr_set_ui (MPC_RE (a), 0, GMP_RNDN);
          mpfr_clear (w);
          return MPC_INEX (0, inex_w);
        }
    }

  /* purely imaginary */
  if (re_cmp == 0)
    {
      mpfr_t y;

      y[0] = MPC_IM (b)[0];
      /* If y/2 underflows, so does sqrt(y/2) */
      mpfr_div_2ui (y, y, 1, GMP_RNDN);
      if (im_cmp > 0)
        {
          inex_w = mpfr_sqrt (MPC_RE (a), y, MPC_RND_RE (rnd));
          inex_t = mpfr_sqrt (MPC_IM (a), y, MPC_RND_IM (rnd));
        }
      else
        {
          mpfr_neg (y, y, GMP_RNDN);
          inex_w = mpfr_sqrt (MPC_RE (a), y, MPC_RND_RE (rnd));
          inex_t = -mpfr_sqrt (MPC_IM (a), y, INV_RND (MPC_RND_IM (rnd)));
          mpfr_neg (MPC_IM (a), MPC_IM (a), GMP_RNDN);
        }
      return MPC_INEX (inex_w, inex_t);
    }

  prec = MPC_MAX_PREC(a);

  mpfr_init (w);
  mpfr_init (t);

  if (re_cmp >= 0)
    {
      rnd_w = MPC_RND_RE (rnd);
      prec_w = MPFR_PREC (MPC_RE (a));
      rnd_t = MPC_RND_IM(rnd);
      prec_t = MPFR_PREC (MPC_IM (a));
    }
  else
    {
      rnd_w = MPC_RND_IM(rnd);
      prec_w = MPFR_PREC (MPC_IM (a));
      rnd_t = MPC_RND_RE(rnd);
      prec_t = MPFR_PREC (MPC_RE (a));
      if (im_cmp < 0)
        {
          rnd_w = INV_RND(rnd_w);
          rnd_t = INV_RND(rnd_t);
        }
    }

  do
    {
      loops ++;
      prec += (loops <= 2) ? mpc_ceil_log2 (prec) + 4 : prec / 2;
      mpfr_set_prec (w, prec);
      mpfr_set_prec (t, prec);
      /* let b = x + iy */
      /* w = sqrt ((|x| + sqrt (x^2 + y^2)) / 2), rounded down */
      /* total error bounded by 3 ulps */
      inex_w = mpc_abs (w, b, GMP_RNDD);
      if (re_cmp < 0)
        inex_w |= mpfr_sub (w, w, MPC_RE (b), GMP_RNDD);
      else
        inex_w |= mpfr_add (w, w, MPC_RE (b), GMP_RNDD);
      inex_w |= mpfr_div_2ui (w, w, 1, GMP_RNDD);
      inex_w |= mpfr_sqrt (w, w, GMP_RNDD);

      ok_w = mpfr_can_round (w, (mp_exp_t) prec - 2, GMP_RNDD, GMP_RNDU,
                             prec_w + (rnd_w == GMP_RNDN));
      if (!inex_w || ok_w)
        {
          /* t = y / 2w, rounded away */
          /* total error bounded by 7 ulps */
          const mp_rnd_t r = im_sgn ? GMP_RNDD : GMP_RNDU;
          inex_t  = mpfr_div (t, MPC_IM (b), w, r);
          inex_t |= mpfr_div_2ui (t, t, 1, r);
          ok_t = mpfr_can_round (t, (mp_exp_t) prec - 3, r, GMP_RNDZ,
                                 prec_t + (rnd_t == GMP_RNDN));
          /* As for w; since t was rounded away, we check whether rounding to 0
             is possible. */
        }
    }
    while ((inex_w && !ok_w) || (inex_t && !ok_t));

  if (re_cmp > 0)
      inex = MPC_INEX (mpfr_set (MPC_RE (a), w, MPC_RND_RE(rnd)),
                       mpfr_set (MPC_IM (a), t, MPC_RND_IM(rnd)));
  else if (im_cmp > 0)
      inex = MPC_INEX (mpfr_set (MPC_RE(a), t, MPC_RND_RE(rnd)),
                       mpfr_set (MPC_IM(a), w, MPC_RND_IM(rnd)));
  else
      inex = MPC_INEX (mpfr_neg (MPC_RE (a), t, MPC_RND_RE(rnd)),
                       mpfr_neg (MPC_IM (a), w, MPC_RND_IM(rnd)));

  mpfr_clear (w);
  mpfr_clear (t);

  return inex;
}
コード例 #7
0
ファイル: sqr.c プロジェクト: BrianGladman/MPC
int
mpc_sqr (mpc_ptr rop, mpc_srcptr op, mpc_rnd_t rnd)
{
   int ok;
   mpfr_t u, v;
   mpfr_t x;
      /* 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;
   int saved_underflow;

   /* 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);

   /* 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, MPFR_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), MPFR_RNDN);
      inex_im = mpfr_set_ui (mpc_imagref(rop), 0ul, MPFR_RNDN);
      if (!same_sign)
        mpc_conj (rop, rop, MPC_RNDNN);
      return MPC_INEX(inex_re, inex_im);
   }

   if (rop == op)
   {
      mpfr_init2 (x, MPC_PREC_RE (op));
      mpfr_set (x, op->re, MPFR_RNDN);
   }
   else
      x [0] = op->re [0];
   /* From here on, use x instead of op->re and safely overwrite rop->re. */

   /* Compute real part of result. */
   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) {
      /* 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. Using the approach copied from mul, over-
         and underflows are also handled correctly. */

      inex_re = mpfr_fsss (rop->re, x, op->im, MPC_RND_RE (rnd));
   }
   else {
      /* Karatsuba squaring: we compute the real part as (x+y)*(x-y) and the
         imaginary part as 2*x*y, with a total of 2M instead of 2S+1M for the
         naive algorithm, which computes x^2-y^2 and 2*y*y */
      mpfr_init (u);
      mpfr_init (v);

      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 =   mpfr_add (u, x, mpc_imagref (op), MPFR_RNDA)
                   | mpfr_sub (v, x, mpc_imagref (op), MPFR_RNDA);

         /* 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, MPFR_RNDN);
            inex_re = 0;
            ok = 1;
         }
         else {
            inexact |= mpfr_mul (u, u, v, MPFR_RNDA); /* error 5 */
            if (mpfr_get_exp (u) == emin || mpfr_inf_p (u)) {
               /* under- or overflow */
               inex_re = mpfr_fsss (rop->re, x, op->im, MPC_RND_RE (rnd));
               ok = 1;
            }
            else {
               ok = (!inexact) | mpfr_can_round (u, prec - 3,
                     MPFR_RNDA, MPFR_RNDZ,
                     MPC_PREC_RE (rop) + (MPC_RND_RE (rnd) == MPFR_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;
               }
            }
         }
      }
      while (!ok);

      mpfr_clear (u);
      mpfr_clear (v);
   }

   saved_underflow = mpfr_underflow_p ();
   mpfr_clear_underflow ();
   inex_im = mpfr_mul (rop->im, x, op->im, MPC_RND_IM (rnd));
   if (!mpfr_underflow_p ())
      inex_im |= mpfr_mul_2ui (rop->im, rop->im, 1, MPC_RND_IM (rnd));
      /* We must not multiply by 2 if rop->im has been set to the smallest
         representable number. */
   if (saved_underflow)
      mpfr_set_underflow ();

   if (rop == op)
      mpfr_clear (x);

   return MPC_INEX (inex_re, inex_im);
}
コード例 #8
0
ファイル: log.c プロジェクト: Gwenio/DragonFlyBSD
int
mpc_log (mpc_ptr rop, mpc_srcptr op, mpc_rnd_t rnd){
   int ok, underflow = 0;
   mpfr_srcptr x, y;
   mpfr_t v, w;
   mpfr_prec_t prec;
   int loops;
   int re_cmp, im_cmp;
   int inex_re, inex_im;
   int err;
   mpfr_exp_t expw;
   int sgnw;

   /* special values: NaN and infinities */
   if (!mpc_fin_p (op)) {
      if (mpfr_nan_p (mpc_realref (op))) {
         if (mpfr_inf_p (mpc_imagref (op)))
            mpfr_set_inf (mpc_realref (rop), +1);
         else
            mpfr_set_nan (mpc_realref (rop));
         mpfr_set_nan (mpc_imagref (rop));
         inex_im = 0; /* Inf/NaN is exact */
      }
      else if (mpfr_nan_p (mpc_imagref (op))) {
         if (mpfr_inf_p (mpc_realref (op)))
            mpfr_set_inf (mpc_realref (rop), +1);
         else
            mpfr_set_nan (mpc_realref (rop));
         mpfr_set_nan (mpc_imagref (rop));
         inex_im = 0; /* Inf/NaN is exact */
      }
      else /* We have an infinity in at least one part. */ {
         inex_im = mpfr_atan2 (mpc_imagref (rop), mpc_imagref (op), mpc_realref (op),
                               MPC_RND_IM (rnd));
         mpfr_set_inf (mpc_realref (rop), +1);
      }
      return MPC_INEX(0, inex_im);
   }

   /* special cases: real and purely imaginary numbers */
   re_cmp = mpfr_cmp_ui (mpc_realref (op), 0);
   im_cmp = mpfr_cmp_ui (mpc_imagref (op), 0);
   if (im_cmp == 0) {
      if (re_cmp == 0) {
         inex_im = mpfr_atan2 (mpc_imagref (rop), mpc_imagref (op), mpc_realref (op),
                               MPC_RND_IM (rnd));
         mpfr_set_inf (mpc_realref (rop), -1);
         inex_re = 0; /* -Inf is exact */
      }
      else if (re_cmp > 0) {
         inex_re = mpfr_log (mpc_realref (rop), mpc_realref (op), MPC_RND_RE (rnd));
         inex_im = mpfr_set (mpc_imagref (rop), mpc_imagref (op), MPC_RND_IM (rnd));
      }
      else {
         /* op = x + 0*y; let w = -x = |x| */
         int negative_zero;
         mpfr_rnd_t rnd_im;

         negative_zero = mpfr_signbit (mpc_imagref (op));
         if (negative_zero)
            rnd_im = INV_RND (MPC_RND_IM (rnd));
         else
            rnd_im = MPC_RND_IM (rnd);
         w [0] = *mpc_realref (op);
         MPFR_CHANGE_SIGN (w);
         inex_re = mpfr_log (mpc_realref (rop), w, MPC_RND_RE (rnd));
         inex_im = mpfr_const_pi (mpc_imagref (rop), rnd_im);
         if (negative_zero) {
            mpc_conj (rop, rop, MPC_RNDNN);
            inex_im = -inex_im;
         }
      }
      return MPC_INEX(inex_re, inex_im);
   }
   else if (re_cmp == 0) {
      if (im_cmp > 0) {
         inex_re = mpfr_log (mpc_realref (rop), mpc_imagref (op), MPC_RND_RE (rnd));
         inex_im = mpfr_const_pi (mpc_imagref (rop), MPC_RND_IM (rnd));
         /* division by 2 does not change the ternary flag */
         mpfr_div_2ui (mpc_imagref (rop), mpc_imagref (rop), 1, GMP_RNDN);
      }
      else {
         w [0] = *mpc_imagref (op);
         MPFR_CHANGE_SIGN (w);
         inex_re = mpfr_log (mpc_realref (rop), w, MPC_RND_RE (rnd));
         inex_im = mpfr_const_pi (mpc_imagref (rop), INV_RND (MPC_RND_IM (rnd)));
         /* division by 2 does not change the ternary flag */
         mpfr_div_2ui (mpc_imagref (rop), mpc_imagref (rop), 1, GMP_RNDN);
         mpfr_neg (mpc_imagref (rop), mpc_imagref (rop), GMP_RNDN);
         inex_im = -inex_im; /* negate the ternary flag */
      }
      return MPC_INEX(inex_re, inex_im);
   }

   prec = MPC_PREC_RE(rop);
   mpfr_init2 (w, 2);
   /* let op = x + iy; log = 1/2 log (x^2 + y^2) + i atan2 (y, x)   */
   /* loop for the real part: 1/2 log (x^2 + y^2), fast, but unsafe */
   /* implementation                                                */
   ok = 0;
   for (loops = 1; !ok && loops <= 2; loops++) {
      prec += mpc_ceil_log2 (prec) + 4;
      mpfr_set_prec (w, prec);

      mpc_abs (w, op, GMP_RNDN);
         /* error 0.5 ulp */
      if (mpfr_inf_p (w))
         /* intermediate overflow; the logarithm may be representable.
            Intermediate underflow is impossible.                      */
         break;

      mpfr_log (w, w, GMP_RNDN);
         /* generic error of log: (2^(- exp(w)) + 0.5) ulp */

      if (mpfr_zero_p (w))
         /* impossible to round, switch to second algorithm */
         break;

      err = MPC_MAX (-mpfr_get_exp (w), 0) + 1;
         /* number of lost digits */
      ok = mpfr_can_round (w, prec - err, GMP_RNDN, GMP_RNDZ,
         mpfr_get_prec (mpc_realref (rop)) + (MPC_RND_RE (rnd) == GMP_RNDN));
   }

   if (!ok) {
      prec = MPC_PREC_RE(rop);
      mpfr_init2 (v, 2);
      /* compute 1/2 log (x^2 + y^2) = log |x| + 1/2 * log (1 + (y/x)^2)
            if |x| >= |y|; otherwise, exchange x and y                   */
      if (mpfr_cmpabs (mpc_realref (op), mpc_imagref (op)) >= 0) {
         x = mpc_realref (op);
         y = mpc_imagref (op);
      }
      else {
         x = mpc_imagref (op);
         y = mpc_realref (op);
      }

      do {
         prec += mpc_ceil_log2 (prec) + 4;
         mpfr_set_prec (v, prec);
         mpfr_set_prec (w, prec);

         mpfr_div (v, y, x, GMP_RNDD); /* error 1 ulp */
         mpfr_sqr (v, v, GMP_RNDD);
            /* generic error of multiplication:
               1 + 2*1*(2+1*2^(1-prec)) <= 5.0625 since prec >= 6 */
         mpfr_log1p (v, v, GMP_RNDD);
            /* error 1 + 4*5.0625 = 21.25 , see algorithms.tex */
         mpfr_div_2ui (v, v, 1, GMP_RNDD);
            /* If the result is 0, then there has been an underflow somewhere. */

         mpfr_abs (w, x, GMP_RNDN); /* exact */
         mpfr_log (w, w, GMP_RNDN); /* error 0.5 ulp */
         expw = mpfr_get_exp (w);
         sgnw = mpfr_signbit (w);

         mpfr_add (w, w, v, GMP_RNDN);
         if (!sgnw) /* v is positive, so no cancellation;
                       error 22.25 ulp; error counts lost bits */
            err = 5;
         else
            err =   MPC_MAX (5 + mpfr_get_exp (v),
                  /* 21.25 ulp (v) rewritten in ulp (result, now in w) */
                           -1 + expw             - mpfr_get_exp (w)
                  /* 0.5 ulp (previous w), rewritten in ulp (result) */
                  ) + 2;

         /* handle one special case: |x|=1, and (y/x)^2 underflows;
            then 1/2*log(x^2+y^2) \approx 1/2*y^2 also underflows.  */
         if (   (mpfr_cmp_si (x, -1) == 0 || mpfr_cmp_ui (x, 1) == 0)
             && mpfr_zero_p (w))
            underflow = 1;

      } while (!underflow &&
               !mpfr_can_round (w, prec - err, GMP_RNDN, GMP_RNDZ,
               mpfr_get_prec (mpc_realref (rop)) + (MPC_RND_RE (rnd) == GMP_RNDN)));
      mpfr_clear (v);
   }

   /* imaginary part */
   inex_im = mpfr_atan2 (mpc_imagref (rop), mpc_imagref (op), mpc_realref (op),
                         MPC_RND_IM (rnd));

   /* set the real part; cannot be done before if rop==op */
   if (underflow)
      /* create underflow in result */
      inex_re = mpfr_set_ui_2exp (mpc_realref (rop), 1,
                                  mpfr_get_emin_min () - 2, MPC_RND_RE (rnd));
   else
      inex_re = mpfr_set (mpc_realref (rop), w, MPC_RND_RE (rnd));
   mpfr_clear (w);
   return MPC_INEX(inex_re, inex_im);
}
コード例 #9
0
ファイル: rootofunity.c プロジェクト: BrianGladman/MPC
/* put in rop the value of exp(2*i*pi*k/n) rounded according to rnd */
int
mpc_rootofunity (mpc_ptr rop, unsigned long n, unsigned long k, mpc_rnd_t rnd)
{
   unsigned long g;
   mpq_t kn;
   mpfr_t t, s, c;
   mpfr_prec_t prec;
   int inex_re, inex_im;
   mpfr_rnd_t rnd_re, rnd_im;

   if (n == 0) {
      /* Compute exp (0 + i*inf). */
      mpfr_set_nan (mpc_realref (rop));
      mpfr_set_nan (mpc_imagref (rop));
      return MPC_INEX (0, 0);
   }

   /* Eliminate common denominator. */
   k %= n;
   g = gcd (k, n);
   k /= g;
   n /= g;

   /* Now 0 <= k < n and gcd(k,n)=1. */

   /* We assume that only n=1, 2, 3, 4, 6 and 12 may yield exact results
      and treat them separately; n=8 is also treated here for efficiency
      reasons. */
   if (n == 1)
     {
       /* necessarily k=0 thus we want exp(0)=1 */
       MPC_ASSERT (k == 0);
       return mpc_set_ui_ui (rop, 1, 0, rnd);
     }
   else if (n == 2)
     {
       /* since gcd(k,n)=1, necessarily k=1, thus we want exp(i*pi)=-1 */
       MPC_ASSERT (k == 1);
       return mpc_set_si_si (rop, -1, 0, rnd);
     }
   else if (n == 4)
     {
       /* since gcd(k,n)=1, necessarily k=1 or k=3, thus we want
          exp(2*i*pi/4)=i or exp(2*i*pi*3/4)=-i */
       MPC_ASSERT (k == 1 || k == 3);
       if (k == 1)
         return mpc_set_ui_ui (rop, 0, 1, rnd);
       else
         return mpc_set_si_si (rop, 0, -1, rnd);
     }
   else if (n == 3 || n == 6)
     {
       MPC_ASSERT ((n == 3 && (k == 1 || k == 2)) ||
                   (n == 6 && (k == 1 || k == 5)));
       /* for n=3, necessarily k=1 or k=2: -1/2+/-1/2*sqrt(3)*i;
          for n=6, necessarily k=1 or k=5: 1/2+/-1/2*sqrt(3)*i */
       inex_re = mpfr_set_si (mpc_realref (rop), (n == 3 ? -1 : 1),
                              MPC_RND_RE (rnd));
       /* inverse the rounding mode for -sqrt(3)/2 for zeta_3^2 and zeta_6^5 */
       rnd_im = MPC_RND_IM (rnd);
       if (k != 1)
         rnd_im = INV_RND (rnd_im);
       inex_im = mpfr_sqrt_ui (mpc_imagref (rop), 3, rnd_im);
       mpc_div_2ui (rop, rop, 1, MPC_RNDNN);
       if (k != 1)
         {
           mpfr_neg (mpc_imagref (rop), mpc_imagref (rop), MPFR_RNDN);
           inex_im = -inex_im;
         }
       return MPC_INEX (inex_re, inex_im);
     }
   else if (n == 12)
     {
       /* necessarily k=1, 5, 7, 11:
          k=1: 1/2*sqrt(3) + 1/2*I
          k=5: -1/2*sqrt(3) + 1/2*I
          k=7: -1/2*sqrt(3) - 1/2*I
          k=11: 1/2*sqrt(3) - 1/2*I */
       MPC_ASSERT (k == 1 || k == 5 || k == 7 || k == 11);
       /* inverse the rounding mode for -sqrt(3)/2 for zeta_12^5 and zeta_12^7 */
       rnd_re = MPC_RND_RE (rnd);
       if (k == 5 || k == 7)
         rnd_re = INV_RND (rnd_re);
       inex_re = mpfr_sqrt_ui (mpc_realref (rop), 3, rnd_re);
       inex_im = mpfr_set_si (mpc_imagref (rop), k < 6 ? 1 : -1,
                              MPC_RND_IM (rnd));
       mpc_div_2ui (rop, rop, 1, MPC_RNDNN);
       if (k == 5 || k == 7)
         {
           mpfr_neg (mpc_realref (rop), mpc_realref (rop), MPFR_RNDN);
           inex_re = -inex_re;
         }
       return MPC_INEX (inex_re, inex_im);
     }
   else if (n == 8)
     {
       /* k=1, 3, 5 or 7:
          k=1: (1/2*I + 1/2)*sqrt(2)
          k=3: (1/2*I - 1/2)*sqrt(2)
          k=5: -(1/2*I + 1/2)*sqrt(2)
          k=7: -(1/2*I - 1/2)*sqrt(2) */
       MPC_ASSERT (k == 1 || k == 3 || k == 5 || k == 7);
       rnd_re = MPC_RND_RE (rnd);
       if (k == 3 || k == 5)
         rnd_re = INV_RND (rnd_re);
       rnd_im = MPC_RND_IM (rnd);
       if (k > 4)
         rnd_im = INV_RND (rnd_im);
       inex_re = mpfr_sqrt_ui (mpc_realref (rop), 2, rnd_re);
       inex_im = mpfr_sqrt_ui (mpc_imagref (rop), 2, rnd_im);
       mpc_div_2ui (rop, rop, 1, MPC_RNDNN);
       if (k == 3 || k == 5)
         {
           mpfr_neg (mpc_realref (rop), mpc_realref (rop), MPFR_RNDN);
           inex_re = -inex_re;
         }
       if (k > 4)
         {
           mpfr_neg (mpc_imagref (rop), mpc_imagref (rop), MPFR_RNDN);
           inex_im = -inex_im;
         }
       return MPC_INEX (inex_re, inex_im);
     }

   prec = MPC_MAX_PREC(rop);

   /* For the error analysis justifying the following algorithm,
      see algorithms.tex. */
   mpfr_init2 (t, 67);
   mpfr_init2 (s, 67);
   mpfr_init2 (c, 67);
   mpq_init (kn);
   mpq_set_ui (kn, k, n);
   mpq_mul_2exp (kn, kn, 1); /* kn=2*k/n < 2 */

   do {
      prec += mpc_ceil_log2 (prec) + 5; /* prec >= 6 */

      mpfr_set_prec (t, prec);
      mpfr_set_prec (s, prec);
      mpfr_set_prec (c, prec);

      mpfr_const_pi (t, MPFR_RNDN);
      mpfr_mul_q (t, t, kn, MPFR_RNDN);
      mpfr_sin_cos (s, c, t, MPFR_RNDN);
   }
   while (   !mpfr_can_round (c, prec - (4 - mpfr_get_exp (c)),
                 MPFR_RNDN, MPFR_RNDZ,
                 MPC_PREC_RE(rop) + (MPC_RND_RE(rnd) == MPFR_RNDN))
          || !mpfr_can_round (s, prec - (4 - mpfr_get_exp (s)),
                 MPFR_RNDN, MPFR_RNDZ,
                 MPC_PREC_IM(rop) + (MPC_RND_IM(rnd) == MPFR_RNDN)));

   inex_re = mpfr_set (mpc_realref(rop), c, MPC_RND_RE(rnd));
   inex_im = mpfr_set (mpc_imagref(rop), s, MPC_RND_IM(rnd));

   mpfr_clear (t);
   mpfr_clear (s);
   mpfr_clear (c);
   mpq_clear (kn);

   return MPC_INEX(inex_re, inex_im);
}
コード例 #10
0
ファイル: acos.c プロジェクト: Gwenio/DragonFlyBSD
int
mpc_acos (mpc_ptr rop, mpc_srcptr op, mpc_rnd_t rnd)
{
  int inex_re, inex_im, inex;
  mpfr_prec_t p_re, p_im, p;
  mpc_t z1;
  mpfr_t pi_over_2;
  mpfr_exp_t e1, e2;
  mpfr_rnd_t rnd_im;
  mpc_rnd_t rnd1;

  inex_re = 0;
  inex_im = 0;

  /* special values */
  if (mpfr_nan_p (mpc_realref (op)) || mpfr_nan_p (mpc_imagref (op)))
    {
      if (mpfr_inf_p (mpc_realref (op)) || mpfr_inf_p (mpc_imagref (op)))
        {
          mpfr_set_inf (mpc_imagref (rop), mpfr_signbit (mpc_imagref (op)) ? +1 : -1);
          mpfr_set_nan (mpc_realref (rop));
        }
      else if (mpfr_zero_p (mpc_realref (op)))
        {
          inex_re = set_pi_over_2 (mpc_realref (rop), +1, MPC_RND_RE (rnd));
          mpfr_set_nan (mpc_imagref (rop));
        }
      else
        {
          mpfr_set_nan (mpc_realref (rop));
          mpfr_set_nan (mpc_imagref (rop));
        }

      return MPC_INEX (inex_re, 0);
    }

  if (mpfr_inf_p (mpc_realref (op)) || mpfr_inf_p (mpc_imagref (op)))
    {
      if (mpfr_inf_p (mpc_realref (op)))
        {
          if (mpfr_inf_p (mpc_imagref (op)))
            {
              if (mpfr_sgn (mpc_realref (op)) > 0)
                {
                  inex_re =
                    set_pi_over_2 (mpc_realref (rop), +1, MPC_RND_RE (rnd));
                  mpfr_div_2ui (mpc_realref (rop), mpc_realref (rop), 1, GMP_RNDN);
                }
              else
                {

                  /* the real part of the result is 3*pi/4
                     a = o(pi)  error(a) < 1 ulp(a)
                     b = o(3*a) error(b) < 2 ulp(b)
                     c = b/4    exact
                     thus 1 bit is lost */
                  mpfr_t x;
                  mpfr_prec_t prec;
                  int ok;
                  mpfr_init (x);
                  prec = mpfr_get_prec (mpc_realref (rop));
                  p = prec;

                  do
                    {
                      p += mpc_ceil_log2 (p);
                      mpfr_set_prec (x, p);
                      mpfr_const_pi (x, GMP_RNDD);
                      mpfr_mul_ui (x, x, 3, GMP_RNDD);
                      ok =
                        mpfr_can_round (x, p - 1, GMP_RNDD, MPC_RND_RE (rnd),
                                        prec+(MPC_RND_RE (rnd) == GMP_RNDN));

                    } while (ok == 0);
                  inex_re =
                    mpfr_div_2ui (mpc_realref (rop), x, 2, MPC_RND_RE (rnd));
                  mpfr_clear (x);
                }
            }
          else
            {
              if (mpfr_sgn (mpc_realref (op)) > 0)
                mpfr_set_ui (mpc_realref (rop), 0, GMP_RNDN);
              else
                inex_re = mpfr_const_pi (mpc_realref (rop), MPC_RND_RE (rnd));
            }
        }
      else
        inex_re = set_pi_over_2 (mpc_realref (rop), +1, MPC_RND_RE (rnd));

      mpfr_set_inf (mpc_imagref (rop), mpfr_signbit (mpc_imagref (op)) ? +1 : -1);

      return MPC_INEX (inex_re, 0);
    }

  /* pure real argument */
  if (mpfr_zero_p (mpc_imagref (op)))
    {
      int s_im;
      s_im = mpfr_signbit (mpc_imagref (op));

      if (mpfr_cmp_ui (mpc_realref (op), 1) > 0)
        {
          if (s_im)
            inex_im = mpfr_acosh (mpc_imagref (rop), mpc_realref (op),
                                  MPC_RND_IM (rnd));
          else
            inex_im = -mpfr_acosh (mpc_imagref (rop), mpc_realref (op),
                                   INV_RND (MPC_RND_IM (rnd)));

          mpfr_set_ui (mpc_realref (rop), 0, GMP_RNDN);
        }
      else if (mpfr_cmp_si (mpc_realref (op), -1) < 0)
        {
          mpfr_t minus_op_re;
          minus_op_re[0] = mpc_realref (op)[0];
          MPFR_CHANGE_SIGN (minus_op_re);

          if (s_im)
            inex_im = mpfr_acosh (mpc_imagref (rop), minus_op_re,
                                  MPC_RND_IM (rnd));
          else
            inex_im = -mpfr_acosh (mpc_imagref (rop), minus_op_re,
                                   INV_RND (MPC_RND_IM (rnd)));
          inex_re = mpfr_const_pi (mpc_realref (rop), MPC_RND_RE (rnd));
        }
      else
        {
          inex_re = mpfr_acos (mpc_realref (rop), mpc_realref (op), MPC_RND_RE (rnd));
          mpfr_set_ui (mpc_imagref (rop), 0, MPC_RND_IM (rnd));
        }

      if (!s_im)
        mpc_conj (rop, rop, MPC_RNDNN);

      return MPC_INEX (inex_re, inex_im);
    }

  /* pure imaginary argument */
  if (mpfr_zero_p (mpc_realref (op)))
    {
      inex_re = set_pi_over_2 (mpc_realref (rop), +1, MPC_RND_RE (rnd));
      inex_im = -mpfr_asinh (mpc_imagref (rop), mpc_imagref (op),
                             INV_RND (MPC_RND_IM (rnd)));
      mpc_conj (rop,rop, MPC_RNDNN);

      return MPC_INEX (inex_re, inex_im);
    }

  /* regular complex argument: acos(z) = Pi/2 - asin(z) */
  p_re = mpfr_get_prec (mpc_realref(rop));
  p_im = mpfr_get_prec (mpc_imagref(rop));
  p = p_re;
  mpc_init3 (z1, p, p_im); /* we round directly the imaginary part to p_im,
                              with rounding mode opposite to rnd_im */
  rnd_im = MPC_RND_IM(rnd);
  /* the imaginary part of asin(z) has the same sign as Im(z), thus if
     Im(z) > 0 and rnd_im = RNDZ, we want to round the Im(asin(z)) to -Inf
     so that -Im(asin(z)) is rounded to zero */
  if (rnd_im == GMP_RNDZ)
    rnd_im = mpfr_sgn (mpc_imagref(op)) > 0 ? GMP_RNDD : GMP_RNDU;
  else
    rnd_im = rnd_im == GMP_RNDU ? GMP_RNDD
      : rnd_im == GMP_RNDD ? GMP_RNDU
      : rnd_im; /* both RNDZ and RNDA map to themselves for -asin(z) */
  rnd1 = MPC_RND (GMP_RNDN, rnd_im);
  mpfr_init2 (pi_over_2, p);
  for (;;)
    {
      p += mpc_ceil_log2 (p) + 3;

      mpfr_set_prec (mpc_realref(z1), p);
      mpfr_set_prec (pi_over_2, p);

      set_pi_over_2 (pi_over_2, +1, GMP_RNDN);
      e1 = 1; /* Exp(pi_over_2) */
      inex = mpc_asin (z1, op, rnd1); /* asin(z) */
      MPC_ASSERT (mpfr_sgn (mpc_imagref(z1)) * mpfr_sgn (mpc_imagref(op)) > 0);
      inex_im = MPC_INEX_IM(inex); /* inex_im is in {-1, 0, 1} */
      e2 = mpfr_get_exp (mpc_realref(z1));
      mpfr_sub (mpc_realref(z1), pi_over_2, mpc_realref(z1), GMP_RNDN);
      if (!mpfr_zero_p (mpc_realref(z1)))
        {
          /* the error on x=Re(z1) is bounded by 1/2 ulp(x) + 2^(e1-p-1) +
             2^(e2-p-1) */
          e1 = e1 >= e2 ? e1 + 1 : e2 + 1;
          /* the error on x is bounded by 1/2 ulp(x) + 2^(e1-p-1) */
          e1 -= mpfr_get_exp (mpc_realref(z1));
          /* the error on x is bounded by 1/2 ulp(x) [1 + 2^e1] */
          e1 = e1 <= 0 ? 0 : e1;
          /* the error on x is bounded by 2^e1 * ulp(x) */
          mpfr_neg (mpc_imagref(z1), mpc_imagref(z1), GMP_RNDN); /* exact */
          inex_im = -inex_im;
          if (mpfr_can_round (mpc_realref(z1), p - e1, GMP_RNDN, GMP_RNDZ,
                              p_re + (MPC_RND_RE(rnd) == GMP_RNDN)))
            break;
        }
    }
  inex = mpc_set (rop, z1, rnd);
  inex_re = MPC_INEX_RE(inex);
  mpc_clear (z1);
  mpfr_clear (pi_over_2);

  return MPC_INEX(inex_re, inex_im);
}