/* Split a double into fraction and mantissa.
   Copyright (C) 2007-2017 Free Software Foundation, Inc.

   This program is free software: you can redistribute it and/or
   modify it under the terms of either:

     * the GNU Lesser General Public License as published by the Free
       Software Foundation; either version 3 of the License, or (at your
       option) any later version.

   or

     * the GNU General Public License as published by the Free
       Software Foundation; either version 2 of the License, or (at your
       option) any later version.

   or both in parallel, as here.
   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;
}