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1 | /* intprops.h -- properties of integer types |
2 | ||
3 | Copyright (C) 2001-2005, 2009-2011 Free Software Foundation, Inc. | |
4 | ||
5 | This program is free software: you can redistribute it and/or modify | |
6 | it under the terms of the GNU General Public License as published by | |
7 | the Free Software Foundation; either version 3 of the License, or | |
8 | (at your option) any later version. | |
9 | ||
10 | This program is distributed in the hope that it will be useful, | |
11 | but WITHOUT ANY WARRANTY; without even the implied warranty of | |
12 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | |
13 | GNU General Public License for more details. | |
14 | ||
15 | You should have received a copy of the GNU General Public License | |
16 | along with this program. If not, see <http://www.gnu.org/licenses/>. */ | |
17 | ||
18 | /* Written by Paul Eggert. */ | |
19 | ||
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20 | #ifndef _GL_INTPROPS_H |
21 | #define _GL_INTPROPS_H | |
a451f14b | 22 | |
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23 | #include <limits.h> |
24 | ||
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25 | /* Return an integer value, converted to the same type as the integer |
26 | expression E after integer type promotion. V is the unconverted value. */ | |
842b28a0 | 27 | #define _GL_INT_CONVERT(e, v) (0 * (e) + (v)) |
a451f14b | 28 | |
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29 | /* Act like _GL_INT_CONVERT (E, -V) but work around a bug in IRIX 6.5 cc; see |
30 | <http://lists.gnu.org/archive/html/bug-gnulib/2011-05/msg00406.html>. */ | |
842b28a0 | 31 | #define _GL_INT_NEGATE_CONVERT(e, v) (0 * (e) - (v)) |
f518ae90 | 32 | |
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33 | /* The extra casts in the following macros work around compiler bugs, |
34 | e.g., in Cray C 5.0.3.0. */ | |
35 | ||
36 | /* True if the arithmetic type T is an integer type. bool counts as | |
37 | an integer. */ | |
1fc5f204 | 38 | #define TYPE_IS_INTEGER(t) ((t) 1.5 == 1) |
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39 | |
40 | /* True if negative values of the signed integer type T use two's | |
41 | complement, ones' complement, or signed magnitude representation, | |
42 | respectively. Much GNU code assumes two's complement, but some | |
43 | people like to be portable to all possible C hosts. */ | |
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44 | #define TYPE_TWOS_COMPLEMENT(t) ((t) ~ (t) 0 == (t) -1) |
45 | #define TYPE_ONES_COMPLEMENT(t) ((t) ~ (t) 0 == 0) | |
46 | #define TYPE_SIGNED_MAGNITUDE(t) ((t) ~ (t) 0 < (t) -1) | |
47 | ||
48 | /* True if the signed integer expression E uses two's complement. */ | |
49 | #define _GL_INT_TWOS_COMPLEMENT(e) (~ _GL_INT_CONVERT (e, 0) == -1) | |
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50 | |
51 | /* True if the arithmetic type T is signed. */ | |
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52 | #define TYPE_SIGNED(t) (! ((t) 0 < (t) -1)) |
53 | ||
54 | /* Return 1 if the integer expression E, after integer promotion, has | |
6a3e57bb | 55 | a signed type. */ |
f518ae90 | 56 | #define _GL_INT_SIGNED(e) (_GL_INT_NEGATE_CONVERT (e, 1) < 0) |
a451f14b | 57 | |
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58 | |
59 | /* Minimum and maximum values for integer types and expressions. These | |
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60 | macros have undefined behavior if T is signed and has padding bits. |
61 | If this is a problem for you, please let us know how to fix it for | |
62 | your host. */ | |
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63 | |
64 | /* The maximum and minimum values for the integer type T. */ | |
65 | #define TYPE_MINIMUM(t) \ | |
66 | ((t) (! TYPE_SIGNED (t) \ | |
67 | ? (t) 0 \ | |
68 | : TYPE_SIGNED_MAGNITUDE (t) \ | |
69 | ? ~ (t) 0 \ | |
3de84ad9 | 70 | : ~ TYPE_MAXIMUM (t))) |
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71 | #define TYPE_MAXIMUM(t) \ |
72 | ((t) (! TYPE_SIGNED (t) \ | |
73 | ? (t) -1 \ | |
3de84ad9 | 74 | : ((((t) 1 << (sizeof (t) * CHAR_BIT - 2)) - 1) * 2 + 1))) |
a451f14b | 75 | |
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76 | /* The maximum and minimum values for the type of the expression E, |
77 | after integer promotion. E should not have side effects. */ | |
78 | #define _GL_INT_MINIMUM(e) \ | |
79 | (_GL_INT_SIGNED (e) \ | |
80 | ? - _GL_INT_TWOS_COMPLEMENT (e) - _GL_SIGNED_INT_MAXIMUM (e) \ | |
81 | : _GL_INT_CONVERT (e, 0)) | |
82 | #define _GL_INT_MAXIMUM(e) \ | |
83 | (_GL_INT_SIGNED (e) \ | |
84 | ? _GL_SIGNED_INT_MAXIMUM (e) \ | |
f518ae90 | 85 | : _GL_INT_NEGATE_CONVERT (e, 1)) |
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86 | #define _GL_SIGNED_INT_MAXIMUM(e) \ |
87 | (((_GL_INT_CONVERT (e, 1) << (sizeof ((e) + 0) * CHAR_BIT - 2)) - 1) * 2 + 1) | |
88 | ||
89 | ||
90 | /* Return 1 if the __typeof__ keyword works. This could be done by | |
91 | 'configure', but for now it's easier to do it by hand. */ | |
92 | #if 2 <= __GNUC__ || 0x5110 <= __SUNPRO_C | |
93 | # define _GL_HAVE___TYPEOF__ 1 | |
94 | #else | |
95 | # define _GL_HAVE___TYPEOF__ 0 | |
96 | #endif | |
97 | ||
98 | /* Return 1 if the integer type or expression T might be signed. Return 0 | |
99 | if it is definitely unsigned. This macro does not evaluate its argument, | |
100 | and expands to an integer constant expression. */ | |
101 | #if _GL_HAVE___TYPEOF__ | |
102 | # define _GL_SIGNED_TYPE_OR_EXPR(t) TYPE_SIGNED (__typeof__ (t)) | |
103 | #else | |
104 | # define _GL_SIGNED_TYPE_OR_EXPR(t) 1 | |
105 | #endif | |
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106 | |
107 | /* Bound on length of the string representing an unsigned integer | |
108 | value representable in B bits. log10 (2.0) < 146/485. The | |
109 | smallest value of B where this bound is not tight is 2621. */ | |
1fc5f204 | 110 | #define INT_BITS_STRLEN_BOUND(b) (((b) * 146 + 484) / 485) |
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111 | |
112 | /* Bound on length of the string representing an integer type or expression T. | |
113 | Subtract 1 for the sign bit if T is signed, and then add 1 more for | |
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114 | a minus sign if needed. |
115 | ||
116 | Because _GL_SIGNED_TYPE_OR_EXPR sometimes returns 0 when its argument is | |
117 | signed, this macro may overestimate the true bound by one byte when | |
118 | applied to unsigned types of size 2, 4, 16, ... bytes. */ | |
119 | #define INT_STRLEN_BOUND(t) \ | |
120 | (INT_BITS_STRLEN_BOUND (sizeof (t) * CHAR_BIT \ | |
121 | - _GL_SIGNED_TYPE_OR_EXPR (t)) \ | |
122 | + _GL_SIGNED_TYPE_OR_EXPR (t)) | |
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123 | |
124 | /* Bound on buffer size needed to represent an integer type or expression T, | |
125 | including the terminating null. */ | |
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126 | #define INT_BUFSIZE_BOUND(t) (INT_STRLEN_BOUND (t) + 1) |
127 | ||
128 | ||
129 | /* Range overflow checks. | |
130 | ||
131 | The INT_<op>_RANGE_OVERFLOW macros return 1 if the corresponding C | |
132 | operators might not yield numerically correct answers due to | |
133 | arithmetic overflow. They do not rely on undefined or | |
134 | implementation-defined behavior. Their implementations are simple | |
135 | and straightforward, but they are a bit harder to use than the | |
136 | INT_<op>_OVERFLOW macros described below. | |
137 | ||
138 | Example usage: | |
139 | ||
140 | long int i = ...; | |
141 | long int j = ...; | |
142 | if (INT_MULTIPLY_RANGE_OVERFLOW (i, j, LONG_MIN, LONG_MAX)) | |
143 | printf ("multiply would overflow"); | |
144 | else | |
145 | printf ("product is %ld", i * j); | |
146 | ||
147 | Restrictions on *_RANGE_OVERFLOW macros: | |
148 | ||
149 | These macros do not check for all possible numerical problems or | |
150 | undefined or unspecified behavior: they do not check for division | |
151 | by zero, for bad shift counts, or for shifting negative numbers. | |
152 | ||
153 | These macros may evaluate their arguments zero or multiple times, | |
154 | so the arguments should not have side effects. The arithmetic | |
155 | arguments (including the MIN and MAX arguments) must be of the same | |
156 | integer type after the usual arithmetic conversions, and the type | |
157 | must have minimum value MIN and maximum MAX. Unsigned types should | |
158 | use a zero MIN of the proper type. | |
159 | ||
160 | These macros are tuned for constant MIN and MAX. For commutative | |
161 | operations such as A + B, they are also tuned for constant B. */ | |
162 | ||
163 | /* Return 1 if A + B would overflow in [MIN,MAX] arithmetic. | |
164 | See above for restrictions. */ | |
165 | #define INT_ADD_RANGE_OVERFLOW(a, b, min, max) \ | |
166 | ((b) < 0 \ | |
167 | ? (a) < (min) - (b) \ | |
168 | : (max) - (b) < (a)) | |
169 | ||
170 | /* Return 1 if A - B would overflow in [MIN,MAX] arithmetic. | |
171 | See above for restrictions. */ | |
172 | #define INT_SUBTRACT_RANGE_OVERFLOW(a, b, min, max) \ | |
173 | ((b) < 0 \ | |
174 | ? (max) + (b) < (a) \ | |
175 | : (a) < (min) + (b)) | |
176 | ||
177 | /* Return 1 if - A would overflow in [MIN,MAX] arithmetic. | |
178 | See above for restrictions. */ | |
179 | #define INT_NEGATE_RANGE_OVERFLOW(a, min, max) \ | |
180 | ((min) < 0 \ | |
181 | ? (a) < - (max) \ | |
182 | : 0 < (a)) | |
183 | ||
184 | /* Return 1 if A * B would overflow in [MIN,MAX] arithmetic. | |
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185 | See above for restrictions. Avoid && and || as they tickle |
186 | bugs in Sun C 5.11 2010/08/13 and other compilers; see | |
187 | <http://lists.gnu.org/archive/html/bug-gnulib/2011-05/msg00401.html>. */ | |
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188 | #define INT_MULTIPLY_RANGE_OVERFLOW(a, b, min, max) \ |
189 | ((b) < 0 \ | |
190 | ? ((a) < 0 \ | |
191 | ? (a) < (max) / (b) \ | |
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192 | : (b) == -1 \ |
193 | ? 0 \ | |
194 | : (min) / (b) < (a)) \ | |
195 | : (b) == 0 \ | |
196 | ? 0 \ | |
197 | : ((a) < 0 \ | |
198 | ? (a) < (min) / (b) \ | |
199 | : (max) / (b) < (a))) | |
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200 | |
201 | /* Return 1 if A / B would overflow in [MIN,MAX] arithmetic. | |
202 | See above for restrictions. Do not check for division by zero. */ | |
203 | #define INT_DIVIDE_RANGE_OVERFLOW(a, b, min, max) \ | |
204 | ((min) < 0 && (b) == -1 && (a) < - (max)) | |
205 | ||
206 | /* Return 1 if A % B would overflow in [MIN,MAX] arithmetic. | |
207 | See above for restrictions. Do not check for division by zero. | |
208 | Mathematically, % should never overflow, but on x86-like hosts | |
209 | INT_MIN % -1 traps, and the C standard permits this, so treat this | |
210 | as an overflow too. */ | |
211 | #define INT_REMAINDER_RANGE_OVERFLOW(a, b, min, max) \ | |
212 | INT_DIVIDE_RANGE_OVERFLOW (a, b, min, max) | |
213 | ||
214 | /* Return 1 if A << B would overflow in [MIN,MAX] arithmetic. | |
215 | See above for restrictions. Here, MIN and MAX are for A only, and B need | |
216 | not be of the same type as the other arguments. The C standard says that | |
217 | behavior is undefined for shifts unless 0 <= B < wordwidth, and that when | |
218 | A is negative then A << B has undefined behavior and A >> B has | |
219 | implementation-defined behavior, but do not check these other | |
220 | restrictions. */ | |
221 | #define INT_LEFT_SHIFT_RANGE_OVERFLOW(a, b, min, max) \ | |
222 | ((a) < 0 \ | |
223 | ? (a) < (min) >> (b) \ | |
224 | : (max) >> (b) < (a)) | |
225 | ||
226 | ||
227 | /* The _GL*_OVERFLOW macros have the same restrictions as the | |
228 | *_RANGE_OVERFLOW macros, except that they do not assume that operands | |
229 | (e.g., A and B) have the same type as MIN and MAX. Instead, they assume | |
230 | that the result (e.g., A + B) has that type. */ | |
231 | #define _GL_ADD_OVERFLOW(a, b, min, max) \ | |
232 | ((min) < 0 ? INT_ADD_RANGE_OVERFLOW (a, b, min, max) \ | |
233 | : (a) < 0 ? (b) <= (a) + (b) \ | |
234 | : (b) < 0 ? (a) <= (a) + (b) \ | |
235 | : (a) + (b) < (b)) | |
236 | #define _GL_SUBTRACT_OVERFLOW(a, b, min, max) \ | |
237 | ((min) < 0 ? INT_SUBTRACT_RANGE_OVERFLOW (a, b, min, max) \ | |
238 | : (a) < 0 ? 1 \ | |
239 | : (b) < 0 ? (a) - (b) <= (a) \ | |
240 | : (a) < (b)) | |
241 | #define _GL_MULTIPLY_OVERFLOW(a, b, min, max) \ | |
242 | (((min) == 0 && (((a) < 0 && 0 < (b)) || ((b) < 0 && 0 < (a)))) \ | |
243 | || INT_MULTIPLY_RANGE_OVERFLOW (a, b, min, max)) | |
244 | #define _GL_DIVIDE_OVERFLOW(a, b, min, max) \ | |
f518ae90 | 245 | ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max) \ |
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246 | : (a) < 0 ? (b) <= (a) + (b) - 1 \ |
247 | : (b) < 0 && (a) + (b) <= (a)) | |
248 | #define _GL_REMAINDER_OVERFLOW(a, b, min, max) \ | |
f518ae90 | 249 | ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max) \ |
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250 | : (a) < 0 ? (a) % (b) != ((max) - (b) + 1) % (b) \ |
251 | : (b) < 0 && ! _GL_UNSIGNED_NEG_MULTIPLE (a, b, max)) | |
252 | ||
253 | /* Return a nonzero value if A is a mathematical multiple of B, where | |
254 | A is unsigned, B is negative, and MAX is the maximum value of A's | |
255 | type. A's type must be the same as (A % B)'s type. Normally (A % | |
256 | -B == 0) suffices, but things get tricky if -B would overflow. */ | |
257 | #define _GL_UNSIGNED_NEG_MULTIPLE(a, b, max) \ | |
258 | (((b) < -_GL_SIGNED_INT_MAXIMUM (b) \ | |
259 | ? (_GL_SIGNED_INT_MAXIMUM (b) == (max) \ | |
260 | ? (a) \ | |
261 | : (a) % (_GL_INT_CONVERT (a, _GL_SIGNED_INT_MAXIMUM (b)) + 1)) \ | |
262 | : (a) % - (b)) \ | |
263 | == 0) | |
264 | ||
265 | ||
266 | /* Integer overflow checks. | |
267 | ||
268 | The INT_<op>_OVERFLOW macros return 1 if the corresponding C operators | |
269 | might not yield numerically correct answers due to arithmetic overflow. | |
270 | They work correctly on all known practical hosts, and do not rely | |
271 | on undefined behavior due to signed arithmetic overflow. | |
272 | ||
273 | Example usage: | |
274 | ||
275 | long int i = ...; | |
276 | long int j = ...; | |
277 | if (INT_MULTIPLY_OVERFLOW (i, j)) | |
278 | printf ("multiply would overflow"); | |
279 | else | |
280 | printf ("product is %ld", i * j); | |
281 | ||
282 | These macros do not check for all possible numerical problems or | |
283 | undefined or unspecified behavior: they do not check for division | |
284 | by zero, for bad shift counts, or for shifting negative numbers. | |
285 | ||
286 | These macros may evaluate their arguments zero or multiple times, so the | |
287 | arguments should not have side effects. | |
288 | ||
289 | These macros are tuned for their last argument being a constant. | |
290 | ||
291 | Return 1 if the integer expressions A * B, A - B, -A, A * B, A / B, | |
292 | A % B, and A << B would overflow, respectively. */ | |
293 | ||
294 | #define INT_ADD_OVERFLOW(a, b) \ | |
295 | _GL_BINARY_OP_OVERFLOW (a, b, _GL_ADD_OVERFLOW) | |
296 | #define INT_SUBTRACT_OVERFLOW(a, b) \ | |
297 | _GL_BINARY_OP_OVERFLOW (a, b, _GL_SUBTRACT_OVERFLOW) | |
298 | #define INT_NEGATE_OVERFLOW(a) \ | |
299 | INT_NEGATE_RANGE_OVERFLOW (a, _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a)) | |
300 | #define INT_MULTIPLY_OVERFLOW(a, b) \ | |
301 | _GL_BINARY_OP_OVERFLOW (a, b, _GL_MULTIPLY_OVERFLOW) | |
302 | #define INT_DIVIDE_OVERFLOW(a, b) \ | |
303 | _GL_BINARY_OP_OVERFLOW (a, b, _GL_DIVIDE_OVERFLOW) | |
304 | #define INT_REMAINDER_OVERFLOW(a, b) \ | |
305 | _GL_BINARY_OP_OVERFLOW (a, b, _GL_REMAINDER_OVERFLOW) | |
306 | #define INT_LEFT_SHIFT_OVERFLOW(a, b) \ | |
307 | INT_LEFT_SHIFT_RANGE_OVERFLOW (a, b, \ | |
308 | _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a)) | |
309 | ||
310 | /* Return 1 if the expression A <op> B would overflow, | |
311 | where OP_RESULT_OVERFLOW (A, B, MIN, MAX) does the actual test, | |
312 | assuming MIN and MAX are the minimum and maximum for the result type. | |
f518ae90 | 313 | Arguments should be free of side effects. */ |
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314 | #define _GL_BINARY_OP_OVERFLOW(a, b, op_result_overflow) \ |
315 | op_result_overflow (a, b, \ | |
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316 | _GL_INT_MINIMUM (0 * (b) + (a)), \ |
317 | _GL_INT_MAXIMUM (0 * (b) + (a))) | |
a451f14b | 318 | |
1fc5f204 | 319 | #endif /* _GL_INTPROPS_H */ |