1 /* Split a double into fraction and mantissa, for hexadecimal printf.
2 Copyright (C) 2007, 2009-2019 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 Lesser General Public License as published by
6 the Free Software Foundation; either version 2.1 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 Lesser General Public License for more details.
13
14 You should have received a copy of the GNU Lesser 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 <gnulib_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
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 }