/* Split a double into fraction and mantissa, for hexadecimal printf.

   Copyright (C) 2007, 2009-2018 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/>.  */

#if ! defined USE_LONG_DOUBLE

# include <config.h>

#endif

/* Specification.  */

#ifdef USE_LONG_DOUBLE

# include "printf-frexpl.h"

#else

# include "printf-frexp.h"

#endif

#include <float.h>

#include <math.h>

#ifdef USE_LONG_DOUBLE

# include "fpucw.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 <= 2.0, not < 2.0.  */

#ifdef USE_LONG_DOUBLE

# define FUNC printf_frexpl

# define DOUBLE long double

# define MIN_EXP LDBL_MIN_EXP

# if HAVE_FREXPL_IN_LIBC && HAVE_LDEXPL_IN_LIBC

#  define USE_FREXP_LDEXP

#  define FREXP frexpl

#  define LDEXP ldexpl

# endif

# 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 printf_frexp

# define DOUBLE double

# define MIN_EXP DBL_MIN_EXP

# if HAVE_FREXP_IN_LIBC && HAVE_LDEXP_IN_LIBC

#  define USE_FREXP_LDEXP

#  define FREXP frexp

#  define LDEXP ldexp

# endif

# define DECL_ROUNDING

# define BEGIN_ROUNDING()

# define END_ROUNDING()

# define L_(literal) literal

#endif

DOUBLE

FUNC (DOUBLE x, int *expptr)

{

  int exponent;

  DECL_ROUNDING

  BEGIN_ROUNDING ();

#ifdef USE_FREXP_LDEXP

  /* frexp and ldexp are usually faster than the loop below.  */

  x = FREXP (x, &exponent);

  x = x + x;

  exponent -= 1;

  if (exponent < MIN_EXP - 1)

    {

      x = LDEXP (x, exponent - (MIN_EXP - 1));

      exponent = MIN_EXP - 1;

    }

#else

  {

    /* 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 nonnegative 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;

            }

        }

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

      }

    else

      {

        /* A negative 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, exponent >= MIN_EXP - 1.  */

          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 (exponent - (1 << i) < MIN_EXP - 1)

                break;

              exponent -= (1 << i);

              x *= pow2_i;

              if (x >= L_(1.0))

                break;

              pow2[i] = pow2_i;

              powh[i] = powh_i;

            }

        }

        /* Here either x < 1.0 and exponent - 2^i < MIN_EXP - 1 <= exponent,

           or 1.0 <= x < 2^2^i and exponent >= MIN_EXP - 1.  */

        if (x < L_(1.0))

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

             exponent - 2^i < MIN_EXP - 1 <= exponent.  */

          while (i > 0)

            {

              i--;

              if (exponent - (1 << i) >= MIN_EXP - 1)

                {

                  exponent -= (1 << i);

                  x *= pow2[i];

                  if (x >= L_(1.0))

                    break;

                }

            }

        /* Here either x < 1.0 and exponent = MIN_EXP - 1,

           or 1.0 <= x < 2^2^i and exponent >= MIN_EXP - 1.  */

      }

    /* Invariants: x * 2^exponent = argument, and

       either x < 1.0 and exponent = MIN_EXP - 1,

       or 1.0 <= x < 2^2^i and exponent >= MIN_EXP - 1.  */

    while (i > 0)

      {

        i--;

        if (x >= pow2[i])

          {

            exponent += (1 << i);

            x *= powh[i];

          }

      }

    /* Here either x < 1.0 and exponent = MIN_EXP - 1,

       or 1.0 <= x < 2.0 and exponent >= MIN_EXP - 1.  */

  }

#endif

  END_ROUNDING ();

  *expptr = exponent;

  return x;

}