/*

 * 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.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 <math_private.h>

typedef union {int64_t i[2]; long double x; double d[2]; } mynumber;

static const double

  t512 = 0x1p512,

  tm256 = 0x1p-256,

  two54 = 0x1p54,	/* 0x4350000000000000 */

  twom54 = 0x1p-54;	/* 0x3C90000000000000 */

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

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

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

/* root of x.                                                        */

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

long double __ieee754_sqrtl(long double x)

{

  static const long double big = 134217728.0, big1 = 134217729.0;

  long double t,s,i;

  mynumber a,c;

  uint64_t k, l;

  int64_t m, n;

  double d;

  a.x=x;

  k=a.i[0] & INT64_C(0x7fffffffffffffff);

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

  if (k>INT64_C(0x000fffff00000000) && k

    if (x < 0) return (big1-big1)/(big-big);

    l = (k&INT64_C(0x001fffffffffffff))|INT64_C(0x3fe0000000000000);

    if ((a.i[1] & INT64_C(0x7fffffffffffffff)) != 0) {

      n = (int64_t) ((l - k) * 2) >> 53;

      m = (a.i[1] >> 52) & 0x7ff;

      if (m == 0) {

	a.d[1] *= two54;

	m = ((a.i[1] >> 52) & 0x7ff) - 54;

      }

      m += n;

      if (m > 0)

	a.i[1] = (a.i[1] & INT64_C(0x800fffffffffffff)) | (m << 52);

      else if (m <= -54) {

	a.i[1] &= INT64_C(0x8000000000000000);

      } else {

	m += 54;

	a.i[1] = (a.i[1] & INT64_C(0x800fffffffffffff)) | (m << 52);

	a.d[1] *= twom54;

      }

    }

    a.i[0] = l;

    s = a.x;

    d = __ieee754_sqrt (a.d[0]);

    c.i[0] = INT64_C(0x2000000000000000)+((k&INT64_C(0x7fe0000000000000))>>1);

    c.i[1] = 0;

    i = d;

    t = 0.5L * (i + s / i);

    i = 0.5L * (t + s / t);

    return c.x * i;

  }

  else {

    if (k>=INT64_C(0x7ff0000000000000))

      /* sqrt (-Inf) = NaN, sqrt (NaN) = NaN, sqrt (+Inf) = +Inf.  */

      return x * x + x;

    if (x == 0) return x;

    if (x < 0) return (big1-big1)/(big-big);

    return tm256*__ieee754_sqrtl(x*t512);

  }

}

strong_alias (__ieee754_sqrtl, __sqrtl_finite)