/* Split a double into fraction and mantissa.

   Copyright (C) 2007-2018 Free Software Foundation, Inc.

   This program is free software: you can redistribute it and/or modify

   it under the terms of the GNU General Public License as published by

   the Free Software Foundation; either version 3 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 General Public License for more details.

   You should have received a copy of the GNU General Public License

   along with this program.  If not, see <https://www.gnu.org/licenses/>.  */

/* Written by Paolo Bonzini <bonzini@gnu.org>, 2003, and

   Bruno Haible <bruno@clisp.org>, 2007.  */

#if ! defined USE_LONG_DOUBLE

# include <config.h>

#endif

/* Specification.  */

#include <math.h>

#include <float.h>

#ifdef USE_LONG_DOUBLE

# include "isnanl-nolibm.h"

# include "fpucw.h"

#else

# include "isnand-nolibm.h"

#endif

/* This file assumes FLT_RADIX = 2.  If FLT_RADIX is a power of 2 greater

   than 2, or not even a power of 2, some rounding errors can occur, so that

   then the returned mantissa is only guaranteed to be <= 1.0, not < 1.0.  */

#ifdef USE_LONG_DOUBLE

# define FUNC frexpl

# define DOUBLE long double

# define ISNAN isnanl

# define DECL_ROUNDING DECL_LONG_DOUBLE_ROUNDING

# define BEGIN_ROUNDING() BEGIN_LONG_DOUBLE_ROUNDING ()

# define END_ROUNDING() END_LONG_DOUBLE_ROUNDING ()

# define L_(literal) literal##L

#else

# define FUNC frexp

# define DOUBLE double

# define ISNAN isnand

# define DECL_ROUNDING

# define BEGIN_ROUNDING()

# define END_ROUNDING()

# define L_(literal) literal

#endif

DOUBLE

FUNC (DOUBLE x, int *expptr)

{

  int sign;

  int exponent;

  DECL_ROUNDING

  /* Test for NaN, infinity, and zero.  */

  if (ISNAN (x) || x + x == x)

    {

      *expptr = 0;

      return x;

    }

  sign = 0;

  if (x < 0)

    {

      x = - x;

      sign = -1;

    }

  BEGIN_ROUNDING ();

  {

    /* Since the exponent is an 'int', it fits in 64 bits.  Therefore the

       loops are executed no more than 64 times.  */

    DOUBLE pow2[64]; /* pow2[i] = 2^2^i */

    DOUBLE powh[64]; /* powh[i] = 2^-2^i */

    int i;

    exponent = 0;

    if (x >= L_(1.0))

      {

        /* A positive exponent.  */

        DOUBLE pow2_i; /* = pow2[i] */

        DOUBLE powh_i; /* = powh[i] */

        /* Invariants: pow2_i = 2^2^i, powh_i = 2^-2^i,

           x * 2^exponent = argument, x >= 1.0.  */

        for (i = 0, pow2_i = L_(2.0), powh_i = L_(0.5);

             ;

             i++, pow2_i = pow2_i * pow2_i, powh_i = powh_i * powh_i)

          {

            if (x >= pow2_i)

              {

                exponent += (1 << i);

                x *= powh_i;

              }

            else

              break;

            pow2[i] = pow2_i;

            powh[i] = powh_i;

          }

        /* Avoid making x too small, as it could become a denormalized

           number and thus lose precision.  */

        while (i > 0 && x < pow2[i - 1])

          {

            i--;

            powh_i = powh[i];

          }

        exponent += (1 << i);

        x *= powh_i;

        /* Here 2^-2^i <= x < 1.0.  */

      }

    else

      {

        /* A negative or zero exponent.  */

        DOUBLE pow2_i; /* = pow2[i] */

        DOUBLE powh_i; /* = powh[i] */

        /* Invariants: pow2_i = 2^2^i, powh_i = 2^-2^i,

           x * 2^exponent = argument, x < 1.0.  */

        for (i = 0, pow2_i = L_(2.0), powh_i = L_(0.5);

             ;

             i++, pow2_i = pow2_i * pow2_i, powh_i = powh_i * powh_i)

          {

            if (x < powh_i)

              {

                exponent -= (1 << i);

                x *= pow2_i;

              }

            else

              break;

            pow2[i] = pow2_i;

            powh[i] = powh_i;

          }

        /* Here 2^-2^i <= x < 1.0.  */

      }

    /* Invariants: x * 2^exponent = argument, and 2^-2^i <= x < 1.0.  */

    while (i > 0)

      {

        i--;

        if (x < powh[i])

          {

            exponent -= (1 << i);

            x *= pow2[i];

          }

      }

    /* Here 0.5 <= x < 1.0.  */

  }

  if (sign < 0)

    x = - x;

  END_ROUNDING ();

  *expptr = exponent;

  return x;

}