1 /* Split a double into fraction and mantissa, for hexadecimal printf.
2    Copyright (C) 2007, 2009-2017 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 <https://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 
66 DOUBLE
FUNC(DOUBLE x,int * expptr)67 FUNC (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