+
−/* Split a double into fraction and mantissa, for hexadecimal printf.
+
−   Copyright (C) 2007, 2009-2013 Free Software Foundation, Inc.
+
−
+
−   This program is free software: you can redistribute it and/or modify
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−   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,
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−   but WITHOUT ANY WARRANTY; without even the implied warranty of
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−   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
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−   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 <http://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
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−
+
−/* This file assumes FLT_RADIX = 2.  If FLT_RADIX is a power of 2 greater
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−   than 2, or not even a power of 2, some rounding errors can occur, so that
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−   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
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−# if HAVE_FREXPL_IN_LIBC && HAVE_LDEXPL_IN_LIBC
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−#  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
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−# define DOUBLE double
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−# define MIN_EXP DBL_MIN_EXP
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−# if HAVE_FREXP_IN_LIBC && HAVE_LDEXP_IN_LIBC
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−#  define USE_FREXP_LDEXP
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−#  define FREXP frexp
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−#  define LDEXP ldexp
+
−# endif
+
−# define DECL_ROUNDING
+
−# define BEGIN_ROUNDING()
+
−# define END_ROUNDING()
+
−# define L_(literal) literal
+
−#endif
+
−
+
−DOUBLE
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−FUNC (DOUBLE x, int *expptr)
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−{
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−  int exponent;
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−  DECL_ROUNDING
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−
+
−  BEGIN_ROUNDING ();
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−
+
−#ifdef USE_FREXP_LDEXP
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−  /* frexp and ldexp are usually faster than the loop below.  */
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−  x = FREXP (x, &exponent);
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−
+
−  x = x + x;
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−  exponent -= 1;
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−
+
−  if (exponent < MIN_EXP - 1)
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−    {
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−      x = LDEXP (x, exponent - (MIN_EXP - 1));
+
−      exponent = MIN_EXP - 1;
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−    }
+
−#else
+
−  {
+
−    /* Since the exponent is an 'int', it fits in 64 bits.  Therefore the
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−       loops are executed no more than 64 times.  */
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−    DOUBLE pow2[64]; /* pow2[i] = 2^2^i */
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−    DOUBLE powh[64]; /* powh[i] = 2^-2^i */
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−    int i;
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−
+
−    exponent = 0;
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−    if (x >= L_(1.0))
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−      {
+
−        /* A nonnegative exponent.  */
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−        {
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−          DOUBLE pow2_i; /* = pow2[i] */
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−          DOUBLE powh_i; /* = powh[i] */
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−
+
−          /* Invariants: pow2_i = 2^2^i, powh_i = 2^-2^i,
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−             x * 2^exponent = argument, x >= 1.0.  */
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−          for (i = 0, pow2_i = L_(2.0), powh_i = L_(0.5);
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−               ;
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−               i++, pow2_i = pow2_i * pow2_i, powh_i = powh_i * powh_i)
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−            {
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−              if (x >= pow2_i)
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−                {
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−                  exponent += (1 << i);
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−                  x *= powh_i;
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−                }
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−              else
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−                break;
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−
+
−              pow2[i] = pow2_i;
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−              powh[i] = powh_i;
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−            }
+
−        }
+
−        /* Here 1.0 <= x < 2^2^i.  */
+
−      }
+
−    else
+
−      {
+
−        /* A negative exponent.  */
+
−        {
+
−          DOUBLE pow2_i; /* = pow2[i] */
+
−          DOUBLE powh_i; /* = powh[i] */
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−
+
−          /* Invariants: pow2_i = 2^2^i, powh_i = 2^-2^i,
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−             x * 2^exponent = argument, x < 1.0, exponent >= MIN_EXP - 1.  */
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−          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)
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−                break;
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−
+
−              exponent -= (1 << i);
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−              x *= pow2_i;
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−              if (x >= L_(1.0))
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−                break;
+
−
+
−              pow2[i] = pow2_i;
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−              powh[i] = powh_i;
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−            }
+
−        }
+
−        /* Here either x < 1.0 and exponent - 2^i < MIN_EXP - 1 <= exponent,
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−           or 1.0 <= x < 2^2^i and exponent >= MIN_EXP - 1.  */
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−
+
−        if (x < L_(1.0))
+
−          /* Invariants: x * 2^exponent = argument, x < 1.0 and
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−             exponent - 2^i < MIN_EXP - 1 <= exponent.  */
+
−          while (i > 0)
+
−            {
+
−              i--;
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−              if (exponent - (1 << i) >= MIN_EXP - 1)
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−                {
+
−                  exponent -= (1 << i);
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−                  x *= pow2[i];
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−                  if (x >= L_(1.0))
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−                    break;
+
−                }
+
−            }
+
−
+
−        /* Here either x < 1.0 and exponent = MIN_EXP - 1,
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−           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,
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−       or 1.0 <= x < 2.0 and exponent >= MIN_EXP - 1.  */
+
−  }
+
−#endif
+
−
+
−  END_ROUNDING ();
+
−
+
−  *expptr = exponent;
+
−  return x;
+
−}