/*

 * IBM Accurate Mathematical Library

 * written by International Business Machines Corp.

 * Copyright (C) 2001-2018 Free Software Foundation, Inc.

 *

 * This program 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.

 *

 * This program 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 this program; if not, see <http://www.gnu.org/licenses/>.

 */

/*********************************************************************/

/* MODULE_NAME: uroot.c                                              */

/*                                                                   */

/* FUNCTION:    usqrt                                                */

/*                                                                   */

/* FILES NEEDED: dla.h endian.h mydefs.h                             */

/*               uroot.tbl                                           */

/*                                                                   */

/* An ultimate sqrt routine. Given an IEEE double machine number x   */

/* it computes the correctly rounded (to nearest) value of square    */

/* root of x.                                                        */

/* Assumption: Machine arithmetic operations are performed in        */

/* round to nearest mode of IEEE 754 standard.                       */

/*                                                                   */

/*********************************************************************/

#include "endian.h"

#include "mydefs.h"

#include <dla.h>

#include "MathLib.h"

#include "root.tbl"

#include <math-barriers.h>

#include <math_private.h>

/*********************************************************************/

/* An ultimate sqrt routine. Given an IEEE double machine number x   */

/* it computes the correctly rounded (to nearest) value of square    */

/* root of x.                                                        */

/*********************************************************************/

double

__ieee754_sqrt (double x)

{

  static const double

    rt0 = 9.99999999859990725855365213134618E-01,

    rt1 = 4.99999999495955425917856814202739E-01,

    rt2 = 3.75017500867345182581453026130850E-01,

    rt3 = 3.12523626554518656309172508769531E-01;

  static const double big = 134217728.0;

  double y, t, del, res, res1, hy, z, zz, p, hx, tx, ty, s;

  mynumber a, c = { { 0, 0 } };

  int4 k;

  a.x = x;

  k = a.i[HIGH_HALF];

  a.i[HIGH_HALF] = (k & 0x001fffff) | 0x3fe00000;

  t = inroot[(k & 0x001fffff) >> 14];

  s = a.x;

  /*----------------- 2^-1022  <= | x |< 2^1024  -----------------*/

  if (k > 0x000fffff && k < 0x7ff00000)

    {

      int rm = __fegetround ();

      fenv_t env;

      libc_feholdexcept_setround (&env, FE_TONEAREST);

      double ret;

      y = 1.0 - t * (t * s);

      t = t * (rt0 + y * (rt1 + y * (rt2 + y * rt3)));

      c.i[HIGH_HALF] = 0x20000000 + ((k & 0x7fe00000) >> 1);

      y = t * s;

      hy = (y + big) - big;

      del = 0.5 * t * ((s - hy * hy) - (y - hy) * (y + hy));

      res = y + del;

      if (res == (res + 1.002 * ((y - res) + del)))

	ret = res * c.x;

      else

	{

	  res1 = res + 1.5 * ((y - res) + del);

	  EMULV (res, res1, z, zz, p, hx, tx, hy, ty); /* (z+zz)=res*res1 */

	  res = ((((z - s) + zz) < 0) ? max (res, res1) :

					min (res, res1));

	  ret = res * c.x;

	}

      math_force_eval (ret);

      libc_fesetenv (&env;;

      double dret = x / ret;

      if (dret != ret)

	{

	  double force_inexact = 1.0 / 3.0;

	  math_force_eval (force_inexact);

	  /* The square root is inexact, ret is the round-to-nearest

	     value which may need adjusting for other rounding

	     modes.  */

	  switch (rm)

	    {

#ifdef FE_UPWARD

	    case FE_UPWARD:

	      if (dret > ret)

		ret = (res + 0x1p-1022) * c.x;

	      break;

#endif

#ifdef FE_DOWNWARD

	    case FE_DOWNWARD:

#endif

#ifdef FE_TOWARDZERO

	    case FE_TOWARDZERO:

#endif

#if defined FE_DOWNWARD || defined FE_TOWARDZERO

	      if (dret < ret)

		ret = (res - 0x1p-1022) * c.x;

	      break;

#endif

	    default:

	      break;

	    }

	}

      /* Otherwise (x / ret == ret), either the square root was exact or

         the division was inexact.  */

      return ret;

    }

  else

    {

      if ((k & 0x7ff00000) == 0x7ff00000)

	return x * x + x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf, sqrt(-inf)=sNaN */

      if (x == 0)

	return x;       /* sqrt(+0)=+0, sqrt(-0)=-0 */

      if (k < 0)

	return (x - x) / (x - x); /* sqrt(-ve)=sNaN */

      return 0x1p-256 * __ieee754_sqrt (x * 0x1p512);

    }

}

strong_alias (__ieee754_sqrt, __sqrt_finite)