1/* Split a double into fraction and mantissa, for hexadecimal printf.
2   Copyright (C) 2007, 2009-2012 Free Software Foundation, Inc.
3
4   This program is free software: you can redistribute it and/or modify
5   it under the terms of the GNU General Public License as published by
6   the Free Software Foundation; either version 3 of the License, or
7   (at your option) any later version.
8
9   This program is distributed in the hope that it will be useful,
10   but WITHOUT ANY WARRANTY; without even the implied warranty of
11   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
12   GNU General Public License for more details.
13
14   You should have received a copy of the GNU General Public License
15   along with this program.  If not, see <http://www.gnu.org/licenses/>.  */
16
17#if ! defined USE_LONG_DOUBLE
18# include <config.h>
19#endif
20
21/* Specification.  */
22#ifdef USE_LONG_DOUBLE
23# include "printf-frexpl.h"
24#else
25# include "printf-frexp.h"
26#endif
27
28#include <float.h>
29#include <math.h>
30#ifdef USE_LONG_DOUBLE
31# include "fpucw.h"
32#endif
33
34/* This file assumes FLT_RADIX = 2.  If FLT_RADIX is a power of 2 greater
35   than 2, or not even a power of 2, some rounding errors can occur, so that
36   then the returned mantissa is only guaranteed to be <= 2.0, not < 2.0.  */
37
38#ifdef USE_LONG_DOUBLE
39# define FUNC printf_frexpl
40# define DOUBLE long double
41# define MIN_EXP LDBL_MIN_EXP
42# if HAVE_FREXPL_IN_LIBC && HAVE_LDEXPL_IN_LIBC
43#  define USE_FREXP_LDEXP
44#  define FREXP frexpl
45#  define LDEXP ldexpl
46# endif
47# define DECL_ROUNDING DECL_LONG_DOUBLE_ROUNDING
48# define BEGIN_ROUNDING() BEGIN_LONG_DOUBLE_ROUNDING ()
49# define END_ROUNDING() END_LONG_DOUBLE_ROUNDING ()
50# define L_(literal) literal##L
51#else
52# define FUNC printf_frexp
53# define DOUBLE double
54# define MIN_EXP DBL_MIN_EXP
55# if HAVE_FREXP_IN_LIBC && HAVE_LDEXP_IN_LIBC
56#  define USE_FREXP_LDEXP
57#  define FREXP frexp
58#  define LDEXP ldexp
59# endif
60# define DECL_ROUNDING
61# define BEGIN_ROUNDING()
62# define END_ROUNDING()
63# define L_(literal) literal
64#endif
65
66DOUBLE
67FUNC (DOUBLE x, int *expptr)
68{
69  int exponent;
70  DECL_ROUNDING
71
72  BEGIN_ROUNDING ();
73
74#ifdef USE_FREXP_LDEXP
75  /* frexp and ldexp are usually faster than the loop below.  */
76  x = FREXP (x, &exponent);
77
78  x = x + x;
79  exponent -= 1;
80
81  if (exponent < MIN_EXP - 1)
82    {
83      x = LDEXP (x, exponent - (MIN_EXP - 1));
84      exponent = MIN_EXP - 1;
85    }
86#else
87  {
88    /* Since the exponent is an 'int', it fits in 64 bits.  Therefore the
89       loops are executed no more than 64 times.  */
90    DOUBLE pow2[64]; /* pow2[i] = 2^2^i */
91    DOUBLE powh[64]; /* powh[i] = 2^-2^i */
92    int i;
93
94    exponent = 0;
95    if (x >= L_(1.0))
96      {
97        /* A nonnegative exponent.  */
98        {
99          DOUBLE pow2_i; /* = pow2[i] */
100          DOUBLE powh_i; /* = powh[i] */
101
102          /* Invariants: pow2_i = 2^2^i, powh_i = 2^-2^i,
103             x * 2^exponent = argument, x >= 1.0.  */
104          for (i = 0, pow2_i = L_(2.0), powh_i = L_(0.5);
105               ;
106               i++, pow2_i = pow2_i * pow2_i, powh_i = powh_i * powh_i)
107            {
108              if (x >= pow2_i)
109                {
110                  exponent += (1 << i);
111                  x *= powh_i;
112                }
113              else
114                break;
115
116              pow2[i] = pow2_i;
117              powh[i] = powh_i;
118            }
119        }
120        /* Here 1.0 <= x < 2^2^i.  */
121      }
122    else
123      {
124        /* A negative exponent.  */
125        {
126          DOUBLE pow2_i; /* = pow2[i] */
127          DOUBLE powh_i; /* = powh[i] */
128
129          /* Invariants: pow2_i = 2^2^i, powh_i = 2^-2^i,
130             x * 2^exponent = argument, x < 1.0, exponent >= MIN_EXP - 1.  */
131          for (i = 0, pow2_i = L_(2.0), powh_i = L_(0.5);
132               ;
133               i++, pow2_i = pow2_i * pow2_i, powh_i = powh_i * powh_i)
134            {
135              if (exponent - (1 << i) < MIN_EXP - 1)
136                break;
137
138              exponent -= (1 << i);
139              x *= pow2_i;
140              if (x >= L_(1.0))
141                break;
142
143              pow2[i] = pow2_i;
144              powh[i] = powh_i;
145            }
146        }
147        /* Here either x < 1.0 and exponent - 2^i < MIN_EXP - 1 <= exponent,
148           or 1.0 <= x < 2^2^i and exponent >= MIN_EXP - 1.  */
149
150        if (x < L_(1.0))
151          /* Invariants: x * 2^exponent = argument, x < 1.0 and
152             exponent - 2^i < MIN_EXP - 1 <= exponent.  */
153          while (i > 0)
154            {
155              i--;
156              if (exponent - (1 << i) >= MIN_EXP - 1)
157                {
158                  exponent -= (1 << i);
159                  x *= pow2[i];
160                  if (x >= L_(1.0))
161                    break;
162                }
163            }
164
165        /* Here either x < 1.0 and exponent = MIN_EXP - 1,
166           or 1.0 <= x < 2^2^i and exponent >= MIN_EXP - 1.  */
167      }
168
169    /* Invariants: x * 2^exponent = argument, and
170       either x < 1.0 and exponent = MIN_EXP - 1,
171       or 1.0 <= x < 2^2^i and exponent >= MIN_EXP - 1.  */
172    while (i > 0)
173      {
174        i--;
175        if (x >= pow2[i])
176          {
177            exponent += (1 << i);
178            x *= powh[i];
179          }
180      }
181    /* Here either x < 1.0 and exponent = MIN_EXP - 1,
182       or 1.0 <= x < 2.0 and exponent >= MIN_EXP - 1.  */
183  }
184#endif
185
186  END_ROUNDING ();
187
188  *expptr = exponent;
189  return x;
190}
191