/* Return arc hyperbolic sine for a complex float type, with the

   imaginary part of the result possibly adjusted for use in

   computing other functions.

   Copyright (C) 1997-2018 Free Software Foundation, Inc.

   This file is part of the GNU C Library.

   The GNU C 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 GNU C 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 GNU C Library; if not, see

   <http://www.gnu.org/licenses/>.  */

#include <complex.h>

#include <math.h>

#include <math_private.h>

#include <math-underflow.h>

#include <float.h>

/* Return the complex inverse hyperbolic sine of finite nonzero Z,

   with the imaginary part of the result subtracted from pi/2 if ADJ

   is nonzero.  */

CFLOAT

M_DECL_FUNC (__kernel_casinh) (CFLOAT x, int adj)

{

  CFLOAT res;

  FLOAT rx, ix;

  CFLOAT y;

  /* Avoid cancellation by reducing to the first quadrant.  */

  rx = M_FABS (__real__ x);

  ix = M_FABS (__imag__ x);

  if (rx >= 1 / M_EPSILON || ix >= 1 / M_EPSILON)

    {

      /* For large x in the first quadrant, x + csqrt (1 + x * x)

	 is sufficiently close to 2 * x to make no significant

	 difference to the result; avoid possible overflow from

	 the squaring and addition.  */

      __real__ y = rx;

      __imag__ y = ix;

      if (adj)

	{

	  FLOAT t = __real__ y;

	  __real__ y = M_COPYSIGN (__imag__ y, __imag__ x);

	  __imag__ y = t;

	}

      res = M_SUF (__clog) (y);

      __real__ res += (FLOAT) M_MLIT (M_LN2);

    }

  else if (rx >= M_LIT (0.5) && ix < M_EPSILON / 8)

    {

      FLOAT s = M_HYPOT (1, rx);

      __real__ res = M_LOG (rx + s);

      if (adj)

	__imag__ res = M_ATAN2 (s, __imag__ x);

      else

	__imag__ res = M_ATAN2 (ix, s);

    }

  else if (rx < M_EPSILON / 8 && ix >= M_LIT (1.5))

    {

      FLOAT s = M_SQRT ((ix + 1) * (ix - 1));

      __real__ res = M_LOG (ix + s);

      if (adj)

	__imag__ res = M_ATAN2 (rx, M_COPYSIGN (s, __imag__ x));

      else

	__imag__ res = M_ATAN2 (s, rx);

    }

  else if (ix > 1 && ix < M_LIT (1.5) && rx < M_LIT (0.5))

    {

      if (rx < M_EPSILON * M_EPSILON)

	{

	  FLOAT ix2m1 = (ix + 1) * (ix - 1);

	  FLOAT s = M_SQRT (ix2m1);

	  __real__ res = M_LOG1P (2 * (ix2m1 + ix * s)) / 2;

	  if (adj)

	    __imag__ res = M_ATAN2 (rx, M_COPYSIGN (s, __imag__ x));

	  else

	    __imag__ res = M_ATAN2 (s, rx);

	}

      else

	{

	  FLOAT ix2m1 = (ix + 1) * (ix - 1);

	  FLOAT rx2 = rx * rx;

	  FLOAT f = rx2 * (2 + rx2 + 2 * ix * ix);

	  FLOAT d = M_SQRT (ix2m1 * ix2m1 + f);

	  FLOAT dp = d + ix2m1;

	  FLOAT dm = f / dp;

	  FLOAT r1 = M_SQRT ((dm + rx2) / 2);

	  FLOAT r2 = rx * ix / r1;

	  __real__ res = M_LOG1P (rx2 + dp + 2 * (rx * r1 + ix * r2)) / 2;

	  if (adj)

	    __imag__ res = M_ATAN2 (rx + r1, M_COPYSIGN (ix + r2, __imag__ x));

	  else

	    __imag__ res = M_ATAN2 (ix + r2, rx + r1);

	}

    }

  else if (ix == 1 && rx < M_LIT (0.5))

    {

      if (rx < M_EPSILON / 8)

	{

	  __real__ res = M_LOG1P (2 * (rx + M_SQRT (rx))) / 2;

	  if (adj)

	    __imag__ res = M_ATAN2 (M_SQRT (rx), M_COPYSIGN (1, __imag__ x));

	  else

	    __imag__ res = M_ATAN2 (1, M_SQRT (rx));

	}

      else

	{

	  FLOAT d = rx * M_SQRT (4 + rx * rx);

	  FLOAT s1 = M_SQRT ((d + rx * rx) / 2);

	  FLOAT s2 = M_SQRT ((d - rx * rx) / 2);

	  __real__ res = M_LOG1P (rx * rx + d + 2 * (rx * s1 + s2)) / 2;

	  if (adj)

	    __imag__ res = M_ATAN2 (rx + s1, M_COPYSIGN (1 + s2, __imag__ x));

	  else

	    __imag__ res = M_ATAN2 (1 + s2, rx + s1);

	}

    }

  else if (ix < 1 && rx < M_LIT (0.5))

    {

      if (ix >= M_EPSILON)

	{

	  if (rx < M_EPSILON * M_EPSILON)

	    {

	      FLOAT onemix2 = (1 + ix) * (1 - ix);

	      FLOAT s = M_SQRT (onemix2);

	      __real__ res = M_LOG1P (2 * rx / s) / 2;

	      if (adj)

		__imag__ res = M_ATAN2 (s, __imag__ x);

	      else

		__imag__ res = M_ATAN2 (ix, s);

	    }

	  else

	    {

	      FLOAT onemix2 = (1 + ix) * (1 - ix);

	      FLOAT rx2 = rx * rx;

	      FLOAT f = rx2 * (2 + rx2 + 2 * ix * ix);

	      FLOAT d = M_SQRT (onemix2 * onemix2 + f);

	      FLOAT dp = d + onemix2;

	      FLOAT dm = f / dp;

	      FLOAT r1 = M_SQRT ((dp + rx2) / 2);

	      FLOAT r2 = rx * ix / r1;

	      __real__ res = M_LOG1P (rx2 + dm + 2 * (rx * r1 + ix * r2)) / 2;

	      if (adj)

		__imag__ res = M_ATAN2 (rx + r1, M_COPYSIGN (ix + r2,

							     __imag__ x));

	      else

		__imag__ res = M_ATAN2 (ix + r2, rx + r1);

	    }

	}

      else

	{

	  FLOAT s = M_HYPOT (1, rx);

	  __real__ res = M_LOG1P (2 * rx * (rx + s)) / 2;

	  if (adj)

	    __imag__ res = M_ATAN2 (s, __imag__ x);

	  else

	    __imag__ res = M_ATAN2 (ix, s);

	}

      math_check_force_underflow_nonneg (__real__ res);

    }

  else

    {

      __real__ y = (rx - ix) * (rx + ix) + 1;

      __imag__ y = 2 * rx * ix;

      y = M_SUF (__csqrt) (y);

      __real__ y += rx;

      __imag__ y += ix;

      if (adj)

	{

	  FLOAT t = __real__ y;

	  __real__ y = M_COPYSIGN (__imag__ y, __imag__ x);

	  __imag__ y = t;

	}

      res = M_SUF (__clog) (y);

    }

  /* Give results the correct sign for the original argument.  */

  __real__ res = M_COPYSIGN (__real__ res, __real__ x);

  __imag__ res = M_COPYSIGN (__imag__ res, (adj ? 1 : __imag__ x));

  return res;

}