/* Complex square root of a float type.

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

   This file is part of the GNU C Library.

   Based on an algorithm by Stephen L. Moshier <moshier@world.std.com>.

   Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.

   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>

CFLOAT

M_DECL_FUNC (__csqrt) (CFLOAT x)

{

  CFLOAT res;

  int rcls = fpclassify (__real__ x);

  int icls = fpclassify (__imag__ x);

  if (__glibc_unlikely (rcls <= FP_INFINITE || icls <= FP_INFINITE))

    {

      if (icls == FP_INFINITE)

	{

	  __real__ res = M_HUGE_VAL;

	  __imag__ res = __imag__ x;

	}

      else if (rcls == FP_INFINITE)

	{

	  if (__real__ x < 0)

	    {

	      __real__ res = icls == FP_NAN ? M_NAN : 0;

	      __imag__ res = M_COPYSIGN (M_HUGE_VAL, __imag__ x);

	    }

	  else

	    {

	      __real__ res = __real__ x;

	      __imag__ res = (icls == FP_NAN

			      ? M_NAN : M_COPYSIGN (0, __imag__ x));

	    }

	}

      else

	{

	  __real__ res = M_NAN;

	  __imag__ res = M_NAN;

	}

    }

  else

    {

      if (__glibc_unlikely (icls == FP_ZERO))

	{

	  if (__real__ x < 0)

	    {

	      __real__ res = 0;

	      __imag__ res = M_COPYSIGN (M_SQRT (-__real__ x), __imag__ x);

	    }

	  else

	    {

	      __real__ res = M_FABS (M_SQRT (__real__ x));

	      __imag__ res = M_COPYSIGN (0, __imag__ x);

	    }

	}

      else if (__glibc_unlikely (rcls == FP_ZERO))

	{

	  FLOAT r;

	  if (M_FABS (__imag__ x) >= 2 * M_MIN)

	    r = M_SQRT (M_LIT (0.5) * M_FABS (__imag__ x));

	  else

	    r = M_LIT (0.5) * M_SQRT (2 * M_FABS (__imag__ x));

	  __real__ res = r;

	  __imag__ res = M_COPYSIGN (r, __imag__ x);

	}

      else

	{

	  FLOAT d, r, s;

	  int scale = 0;

	  if (M_FABS (__real__ x) > M_MAX / 4)

	    {

	      scale = 1;

	      __real__ x = M_SCALBN (__real__ x, -2 * scale);

	      __imag__ x = M_SCALBN (__imag__ x, -2 * scale);

	    }

	  else if (M_FABS (__imag__ x) > M_MAX / 4)

	    {

	      scale = 1;

	      if (M_FABS (__real__ x) >= 4 * M_MIN)

		__real__ x = M_SCALBN (__real__ x, -2 * scale);

	      else

		__real__ x = 0;

	      __imag__ x = M_SCALBN (__imag__ x, -2 * scale);

	    }

	  else if (M_FABS (__real__ x) < 2 * M_MIN

		   && M_FABS (__imag__ x) < 2 * M_MIN)

	    {

	      scale = -((M_MANT_DIG + 1) / 2);

	      __real__ x = M_SCALBN (__real__ x, -2 * scale);

	      __imag__ x = M_SCALBN (__imag__ x, -2 * scale);

	    }

	  d = M_HYPOT (__real__ x, __imag__ x);

	  /* Use the identity   2  Re res  Im res = Im x

	     to avoid cancellation error in  d +/- Re x.  */

	  if (__real__ x > 0)

	    {

	      r = M_SQRT (M_LIT (0.5) * (d + __real__ x));

	      if (scale == 1 && M_FABS (__imag__ x) < 1)

		{

		  /* Avoid possible intermediate underflow.  */

		  s = __imag__ x / r;

		  r = M_SCALBN (r, scale);

		  scale = 0;

		}

	      else

		s = M_LIT (0.5) * (__imag__ x / r);

	    }

	  else

	    {

	      s = M_SQRT (M_LIT (0.5) * (d - __real__ x));

	      if (scale == 1 && M_FABS (__imag__ x) < 1)

		{

		  /* Avoid possible intermediate underflow.  */

		  r = M_FABS (__imag__ x / s);

		  s = M_SCALBN (s, scale);

		  scale = 0;

		}

	      else

		r = M_FABS (M_LIT (0.5) * (__imag__ x / s));

	    }

	  if (scale)

	    {

	      r = M_SCALBN (r, scale);

	      s = M_SCALBN (s, scale);

	    }

	  math_check_force_underflow (r);

	  math_check_force_underflow (s);

	  __real__ res = r;

	  __imag__ res = M_COPYSIGN (s, __imag__ x);

	}

    }

  return res;

}

declare_mgen_alias (__csqrt, csqrt)