text: /* Return arc hyperbole sine for double value, with the imaginary part
     of the result possibly adjusted for use in computing other
     functions.
     Copyright (C) 1997-2016 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 <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.  */
  
  __complex__ double
  __kernel_casinh (__complex__ double x, int adj)
  {
    __complex__ double res;
    double rx, ix;
    __complex__ double y;
  
    /* Avoid cancellation by reducing to the first quadrant.  */
    rx = fabs (__real__ x);
    ix = fabs (__imag__ x);
  
    if (rx >= 1.0 / DBL_EPSILON || ix >= 1.0 / DBL_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)
  	{
  	  double t = __real__ y;
  	  __real__ y = __copysign (__imag__ y, __imag__ x);
  	  __imag__ y = t;
  	}
  
        res = __clog (y);
        __real__ res += M_LN2;
      }
    else if (rx >= 0.5 && ix < DBL_EPSILON / 8.0)
      {
        double s = __ieee754_hypot (1.0, rx);
  
        __real__ res = __ieee754_log (rx + s);
        if (adj)
  	__imag__ res = __ieee754_atan2 (s, __imag__ x);
        else
  	__imag__ res = __ieee754_atan2 (ix, s);
      }
    else if (rx < DBL_EPSILON / 8.0 && ix >= 1.5)
      {
        double s = __ieee754_sqrt ((ix + 1.0) * (ix - 1.0));
  
        __real__ res = __ieee754_log (ix + s);
        if (adj)
  	__imag__ res = __ieee754_atan2 (rx, __copysign (s, __imag__ x));
        else
  	__imag__ res = __ieee754_atan2 (s, rx);
      }
    else if (ix > 1.0 && ix < 1.5 && rx < 0.5)
      {
        if (rx < DBL_EPSILON * DBL_EPSILON)
  	{
  	  double ix2m1 = (ix + 1.0) * (ix - 1.0);
  	  double s = __ieee754_sqrt (ix2m1);
  
  	  __real__ res = __log1p (2.0 * (ix2m1 + ix * s)) / 2.0;
  	  if (adj)
  	    __imag__ res = __ieee754_atan2 (rx, __copysign (s, __imag__ x));
  	  else
  	    __imag__ res = __ieee754_atan2 (s, rx);
  	}
        else
  	{
  	  double ix2m1 = (ix + 1.0) * (ix - 1.0);
  	  double rx2 = rx * rx;
  	  double f = rx2 * (2.0 + rx2 + 2.0 * ix * ix);
  	  double d = __ieee754_sqrt (ix2m1 * ix2m1 + f);
  	  double dp = d + ix2m1;
  	  double dm = f / dp;
  	  double r1 = __ieee754_sqrt ((dm + rx2) / 2.0);
  	  double r2 = rx * ix / r1;
  
  	  __real__ res = __log1p (rx2 + dp + 2.0 * (rx * r1 + ix * r2)) / 2.0;
  	  if (adj)
  	    __imag__ res = __ieee754_atan2 (rx + r1, __copysign (ix + r2,
  								 __imag__ x));
  	  else
  	    __imag__ res = __ieee754_atan2 (ix + r2, rx + r1);
  	}
      }
    else if (ix == 1.0 && rx < 0.5)
      {
        if (rx < DBL_EPSILON / 8.0)
  	{
  	  __real__ res = __log1p (2.0 * (rx + __ieee754_sqrt (rx))) / 2.0;
  	  if (adj)
  	    __imag__ res = __ieee754_atan2 (__ieee754_sqrt (rx),
  					    __copysign (1.0, __imag__ x));
  	  else
  	    __imag__ res = __ieee754_atan2 (1.0, __ieee754_sqrt (rx));
  	}
        else
  	{
  	  double d = rx * __ieee754_sqrt (4.0 + rx * rx);
  	  double s1 = __ieee754_sqrt ((d + rx * rx) / 2.0);
  	  double s2 = __ieee754_sqrt ((d - rx * rx) / 2.0);
  
  	  __real__ res = __log1p (rx * rx + d + 2.0 * (rx * s1 + s2)) / 2.0;
  	  if (adj)
  	    __imag__ res = __ieee754_atan2 (rx + s1, __copysign (1.0 + s2,
  								 __imag__ x));
  	  else
  	    __imag__ res = __ieee754_atan2 (1.0 + s2, rx + s1);
  	}
      }
    else if (ix < 1.0 && rx < 0.5)
      {
        if (ix >= DBL_EPSILON)
  	{
  	  if (rx < DBL_EPSILON * DBL_EPSILON)
  	    {
  	      double onemix2 = (1.0 + ix) * (1.0 - ix);
  	      double s = __ieee754_sqrt (onemix2);
  
  	      __real__ res = __log1p (2.0 * rx / s) / 2.0;
  	      if (adj)
  		__imag__ res = __ieee754_atan2 (s, __imag__ x);
  	      else
  		__imag__ res = __ieee754_atan2 (ix, s);
  	    }
  	  else
  	    {
  	      double onemix2 = (1.0 + ix) * (1.0 - ix);
  	      double rx2 = rx * rx;
  	      double f = rx2 * (2.0 + rx2 + 2.0 * ix * ix);
  	      double d = __ieee754_sqrt (onemix2 * onemix2 + f);
  	      double dp = d + onemix2;
  	      double dm = f / dp;
  	      double r1 = __ieee754_sqrt ((dp + rx2) / 2.0);
  	      double r2 = rx * ix / r1;
  
  	      __real__ res
  		= __log1p (rx2 + dm + 2.0 * (rx * r1 + ix * r2)) / 2.0;
  	      if (adj)
  		__imag__ res = __ieee754_atan2 (rx + r1,
  						__copysign (ix + r2,
  							    __imag__ x));
  	      else
  		__imag__ res = __ieee754_atan2 (ix + r2, rx + r1);
  	    }
  	}
        else
  	{
  	  double s = __ieee754_hypot (1.0, rx);
  
  	  __real__ res = __log1p (2.0 * rx * (rx + s)) / 2.0;
  	  if (adj)
  	    __imag__ res = __ieee754_atan2 (s, __imag__ x);
  	  else
  	    __imag__ res = __ieee754_atan2 (ix, s);
  	}
        math_check_force_underflow_nonneg (__real__ res);
      }
    else
      {
        __real__ y = (rx - ix) * (rx + ix) + 1.0;
        __imag__ y = 2.0 * rx * ix;
  
        y = __csqrt (y);
  
        __real__ y += rx;
        __imag__ y += ix;
  
        if (adj)
  	{
  	  double t = __real__ y;
  	  __real__ y = __copysign (__imag__ y, __imag__ x);
  	  __imag__ y = t;
  	}
  
        res = __clog (y);
      }
  
    /* Give results the correct sign for the original argument.  */
    __real__ res = __copysign (__real__ res, __real__ x);
    __imag__ res = __copysign (__imag__ res, (adj ? 1.0 : __imag__ x));
  
    return res;
  }
  