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- lib/intprops.h
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1 /* intprops.h -- properties of integer types
2
3 Copyright (C) 2001-2024 Free Software Foundation, Inc.
4
5 This program is free software: you can redistribute it and/or modify it
6 under the terms of the GNU Lesser General Public License as published
7 by the Free Software Foundation; either version 2.1 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 Lesser General Public License for more details.
14
15 You should have received a copy of the GNU Lesser General Public License
16 along with this program. If not, see <https://www.gnu.org/licenses/>. */
17
18 #ifndef _GL_INTPROPS_H
19 #define _GL_INTPROPS_H
20
21 #include "intprops-internal.h"
22
23 /* The extra casts in the following macros work around compiler bugs,
24 e.g., in Cray C 5.0.3.0. */
25
26 /* True if the arithmetic type T is an integer type. bool counts as
27 an integer. */
28 #define TYPE_IS_INTEGER(t) ((t) 1.5 == 1)
29
30 /* True if the real type T is signed. */
31 #define TYPE_SIGNED(t) _GL_TYPE_SIGNED (t)
32
33 /* Return 1 if the real expression E, after promotion, has a
34 signed or floating type. Do not evaluate E. */
35 #define EXPR_SIGNED(e) _GL_EXPR_SIGNED (e)
36
37 /* Minimum and maximum values for integer types and expressions. */
38
39 /* The width in bits of the integer type or expression T.
40 Do not evaluate T. T must not be a bit-field expression.
41 Padding bits are not supported; this is checked at compile-time below. */
42 #define TYPE_WIDTH(t) _GL_TYPE_WIDTH (t)
43
44 /* The maximum and minimum values for the integer type T. */
45 #define TYPE_MINIMUM(t) ((t) ~TYPE_MAXIMUM (t))
46 #define TYPE_MAXIMUM(t) \
47 ((t) (!TYPE_SIGNED (t) ? (t) - 1 : ((((t) 1 << (TYPE_WIDTH (t) - 2)) - 1) * 2 + 1)))
48
49 /* Bound on length of the string representing an unsigned integer
50 value representable in B bits. log10 (2.0) < 146/485. The
51 smallest value of B where this bound is not tight is 2621. */
52 #define INT_BITS_STRLEN_BOUND(b) (((b) * 146 + 484) / 485)
53
54 /* Bound on length of the string representing an integer type or expression T.
55 T must not be a bit-field expression.
56
57 Subtract 1 for the sign bit if T is signed, and then add 1 more for
58 a minus sign if needed.
59
60 Because _GL_SIGNED_TYPE_OR_EXPR sometimes returns 1 when its argument is
61 unsigned, this macro may overestimate the true bound by one byte when
62 applied to unsigned types of size 2, 4, 16, ... bytes. */
63 #define INT_STRLEN_BOUND(t) \
64 (INT_BITS_STRLEN_BOUND (TYPE_WIDTH (t) - _GL_SIGNED_TYPE_OR_EXPR (t)) \
65 + _GL_SIGNED_TYPE_OR_EXPR (t))
66
67 /* Bound on buffer size needed to represent an integer type or expression T,
68 including the terminating null. T must not be a bit-field expression. */
69 #define INT_BUFSIZE_BOUND(t) (INT_STRLEN_BOUND (t) + 1)
70
71 /* Range overflow checks.
72
73 The INT_<op>_RANGE_OVERFLOW macros return 1 if the corresponding C
74 operators overflow arithmetically when given the same arguments.
75 These macros do not rely on undefined or implementation-defined behavior.
76 Although their implementations are simple and straightforward,
77 they are harder to use and may be less efficient than the
78 INT_<op>_WRAPV, INT_<op>_OK, and INT_<op>_OVERFLOW macros described below.
79
80 Example usage:
81
82 long int i = ...;
83 long int j = ...;
84 if (INT_MULTIPLY_RANGE_OVERFLOW (i, j, LONG_MIN, LONG_MAX))
85 printf ("multiply would overflow");
86 else
87 printf ("product is %ld", i * j);
88
89 Restrictions on *_RANGE_OVERFLOW macros:
90
91 These macros do not check for all possible numerical problems or
92 undefined or unspecified behavior: they do not check for division
93 by zero, for bad shift counts, or for shifting negative numbers.
94
95 These macros may evaluate their arguments zero or multiple times,
96 so the arguments should not have side effects. The arithmetic
97 arguments (including the MIN and MAX arguments) must be of the same
98 integer type after the usual arithmetic conversions, and the type
99 must have minimum value MIN and maximum MAX. Unsigned types should
100 use a zero MIN of the proper type.
101
102 Because all arguments are subject to integer promotions, these
103 macros typically do not work on types narrower than 'int'.
104
105 These macros are tuned for constant MIN and MAX. For commutative
106 operations such as A + B, they are also tuned for constant B. */
107
108 /* Return 1 if A + B would overflow in [MIN,MAX] arithmetic.
109 See above for restrictions. */
110 #define INT_ADD_RANGE_OVERFLOW(a, b, min, max) ((b) < 0 ? (a) < (min) - (b) : (max) - (b) < (a))
111
112 /* Return 1 if A - B would overflow in [MIN,MAX] arithmetic.
113 See above for restrictions. */
114 #define INT_SUBTRACT_RANGE_OVERFLOW(a, b, min, max) \
115 ((b) < 0 ? (max) + (b) < (a) : (a) < (min) + (b))
116
117 /* Return 1 if - A would overflow in [MIN,MAX] arithmetic.
118 See above for restrictions. */
119 #define INT_NEGATE_RANGE_OVERFLOW(a, min, max) _GL_INT_NEGATE_RANGE_OVERFLOW (a, min, max)
120
121 /* Return 1 if A * B would overflow in [MIN,MAX] arithmetic.
122 See above for restrictions. Avoid && and || as they tickle
123 bugs in Sun C 5.11 2010/08/13 and other compilers; see
124 <https://lists.gnu.org/r/bug-gnulib/2011-05/msg00401.html>. */
125 #define INT_MULTIPLY_RANGE_OVERFLOW(a, b, min, max) \
126 ((b) < 0 ? ((a) < 0 ? (a) < (max) / (b) \
127 : (b) == -1 ? 0 \
128 : (min) / (b) < (a)) \
129 : (b) == 0 ? 0 \
130 : ((a) < 0 ? (a) < (min) / (b) : (max) / (b) < (a)))
131
132 /* Return 1 if A / B would overflow in [MIN,MAX] arithmetic.
133 See above for restrictions. Do not check for division by zero. */
134 #define INT_DIVIDE_RANGE_OVERFLOW(a, b, min, max) ((min) < 0 && (b) == -1 && (a) < -(max))
135
136 /* Return 1 if A % B would overflow in [MIN,MAX] arithmetic.
137 See above for restrictions. Do not check for division by zero.
138 Mathematically, % should never overflow, but on x86-like hosts
139 INT_MIN % -1 traps, and the C standard permits this, so treat this
140 as an overflow too. */
141 #define INT_REMAINDER_RANGE_OVERFLOW(a, b, min, max) INT_DIVIDE_RANGE_OVERFLOW (a, b, min, max)
142
143 /* Return 1 if A << B would overflow in [MIN,MAX] arithmetic.
144 See above for restrictions. Here, MIN and MAX are for A only, and B need
145 not be of the same type as the other arguments. The C standard says that
146 behavior is undefined for shifts unless 0 <= B < wordwidth, and that when
147 A is negative then A << B has undefined behavior and A >> B has
148 implementation-defined behavior, but do not check these other
149 restrictions. */
150 #define INT_LEFT_SHIFT_RANGE_OVERFLOW(a, b, min, max) \
151 ((a) < 0 ? (a) < (min) >> (b) : (max) >> (b) < (a))
152
153 /* The _GL*_OVERFLOW macros have the same restrictions as the
154 *_RANGE_OVERFLOW macros, except that they do not assume that operands
155 (e.g., A and B) have the same type as MIN and MAX. Instead, they assume
156 that the result (e.g., A + B) has that type. */
157 #if _GL_HAS_BUILTIN_OVERFLOW_P
158 # define _GL_ADD_OVERFLOW(a, b, min, max) \
159 __builtin_add_overflow_p (a, b, (__typeof__ ((a) + (b))) 0)
160 # define _GL_SUBTRACT_OVERFLOW(a, b, min, max) \
161 __builtin_sub_overflow_p (a, b, (__typeof__ ((a) - (b))) 0)
162 # define _GL_MULTIPLY_OVERFLOW(a, b, min, max) \
163 __builtin_mul_overflow_p (a, b, (__typeof__ ((a) * (b))) 0)
164 #else
165 # define _GL_ADD_OVERFLOW(a, b, min, max) \
166 ((min) < 0 ? INT_ADD_RANGE_OVERFLOW (a, b, min, max) \
167 : (a) < 0 ? (b) <= (a) + (b) \
168 : (b) < 0 ? (a) <= (a) + (b) \
169 : (a) + (b) < (b))
170 # define _GL_SUBTRACT_OVERFLOW(a, b, min, max) \
171 ((min) < 0 ? INT_SUBTRACT_RANGE_OVERFLOW (a, b, min, max) \
172 : (a) < 0 ? 1 \
173 : (b) < 0 ? (a) - (b) <= (a) \
174 : (a) < (b))
175 # define _GL_MULTIPLY_OVERFLOW(a, b, min, max) \
176 (((min) == 0 && (((a) < 0 && 0 < (b)) || ((b) < 0 && 0 < (a)))) \
177 || INT_MULTIPLY_RANGE_OVERFLOW (a, b, min, max))
178 #endif
179 #define _GL_DIVIDE_OVERFLOW(a, b, min, max) \
180 ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < -(max) \
181 : (a) < 0 ? (b) <= (a) + (b) - 1 \
182 : (b) < 0 && (a) + (b) <= (a))
183 #define _GL_REMAINDER_OVERFLOW(a, b, min, max) \
184 ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < -(max) \
185 : (a) < 0 ? (a) % (b) != ((max) - (b) + 1) % (b) \
186 : (b) < 0 && !_GL_UNSIGNED_NEG_MULTIPLE (a, b, max))
187
188 /* Return a nonzero value if A is a mathematical multiple of B, where
189 A is unsigned, B is negative, and MAX is the maximum value of A's
190 type. A's type must be the same as (A % B)'s type. Normally (A %
191 -B == 0) suffices, but things get tricky if -B would overflow. */
192 #define _GL_UNSIGNED_NEG_MULTIPLE(a, b, max) \
193 (((b) < -_GL_SIGNED_INT_MAXIMUM (b) \
194 ? (_GL_SIGNED_INT_MAXIMUM (b) == (max) \
195 ? (a) \
196 : (a) % (_GL_INT_CONVERT (a, _GL_SIGNED_INT_MAXIMUM (b)) + 1)) \
197 : (a) % -(b)) \
198 == 0)
199
200 /* Check for integer overflow, and report low order bits of answer.
201
202 The INT_<op>_OVERFLOW macros return 1 if the corresponding C operators
203 might not yield numerically correct answers due to arithmetic overflow.
204 The INT_<op>_WRAPV macros compute the low-order bits of the sum,
205 difference, and product of two C integers, and return 1 if these
206 low-order bits are not numerically correct.
207 These macros work correctly on all known practical hosts, and do not rely
208 on undefined behavior due to signed arithmetic overflow.
209
210 Example usage, assuming A and B are long int:
211
212 if (INT_MULTIPLY_OVERFLOW (a, b))
213 printf ("result would overflow\n");
214 else
215 printf ("result is %ld (no overflow)\n", a * b);
216
217 Example usage with WRAPV flavor:
218
219 long int result;
220 bool overflow = INT_MULTIPLY_WRAPV (a, b, &result);
221 printf ("result is %ld (%s)\n", result,
222 overflow ? "after overflow" : "no overflow");
223
224 Restrictions on these macros:
225
226 These macros do not check for all possible numerical problems or
227 undefined or unspecified behavior: they do not check for division
228 by zero, for bad shift counts, or for shifting negative numbers.
229
230 These macros may evaluate their arguments zero or multiple times, so the
231 arguments should not have side effects.
232
233 The WRAPV macros are not constant expressions. They support only
234 +, binary -, and *.
235
236 Because the WRAPV macros convert the result, they report overflow
237 in different circumstances than the OVERFLOW macros do. For
238 example, in the typical case with 16-bit 'short' and 32-bit 'int',
239 if A, B and *R are all of type 'short' then INT_ADD_OVERFLOW (A, B)
240 returns false because the addition cannot overflow after A and B
241 are converted to 'int', whereas INT_ADD_WRAPV (A, B, R) returns
242 true or false depending on whether the sum fits into 'short'.
243
244 These macros are tuned for their last input argument being a constant.
245
246 A, B, and *R should be integers; they need not be the same type,
247 and they need not be all signed or all unsigned.
248 However, none of the integer types should be bit-precise,
249 and *R's type should not be char, bool, or an enumeration type.
250
251 Return 1 if the integer expressions A * B, A - B, -A, A * B, A / B,
252 A % B, and A << B would overflow, respectively. */
253
254 #define INT_ADD_OVERFLOW(a, b) _GL_BINARY_OP_OVERFLOW (a, b, _GL_ADD_OVERFLOW)
255 #define INT_SUBTRACT_OVERFLOW(a, b) _GL_BINARY_OP_OVERFLOW (a, b, _GL_SUBTRACT_OVERFLOW)
256 #define INT_NEGATE_OVERFLOW(a) _GL_INT_NEGATE_OVERFLOW (a)
257 #define INT_MULTIPLY_OVERFLOW(a, b) _GL_BINARY_OP_OVERFLOW (a, b, _GL_MULTIPLY_OVERFLOW)
258 #define INT_DIVIDE_OVERFLOW(a, b) _GL_BINARY_OP_OVERFLOW (a, b, _GL_DIVIDE_OVERFLOW)
259 #define INT_REMAINDER_OVERFLOW(a, b) _GL_BINARY_OP_OVERFLOW (a, b, _GL_REMAINDER_OVERFLOW)
260 #define INT_LEFT_SHIFT_OVERFLOW(a, b) \
261 INT_LEFT_SHIFT_RANGE_OVERFLOW (a, b, _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
262
263 /* Return 1 if the expression A <op> B would overflow,
264 where OP_RESULT_OVERFLOW (A, B, MIN, MAX) does the actual test,
265 assuming MIN and MAX are the minimum and maximum for the result type.
266 Arguments should be free of side effects. */
267 #define _GL_BINARY_OP_OVERFLOW(a, b, op_result_overflow) \
268 op_result_overflow (a, b, _GL_INT_MINIMUM (_GL_INT_CONVERT (a, b)), \
269 _GL_INT_MAXIMUM (_GL_INT_CONVERT (a, b)))
270
271 /* Store the low-order bits of A + B, A - B, A * B, respectively, into *R.
272 Return 1 if the result overflows. See above for restrictions. */
273 #define INT_ADD_WRAPV(a, b, r) _GL_INT_ADD_WRAPV (a, b, r)
274 #define INT_SUBTRACT_WRAPV(a, b, r) _GL_INT_SUBTRACT_WRAPV (a, b, r)
275 #define INT_MULTIPLY_WRAPV(a, b, r) _GL_INT_MULTIPLY_WRAPV (a, b, r)
276
277 /* The following macros compute A + B, A - B, and A * B, respectively.
278 If no overflow occurs, they set *R to the result and return 1;
279 otherwise, they return 0 and may modify *R.
280
281 Example usage:
282
283 long int result;
284 if (INT_ADD_OK (a, b, &result))
285 printf ("result is %ld\n", result);
286 else
287 printf ("overflow\n");
288
289 A, B, and *R should be integers; they need not be the same type,
290 and they need not be all signed or all unsigned.
291 However, none of the integer types should be bit-precise,
292 and *R's type should not be char, bool, or an enumeration type.
293
294 These macros work correctly on all known practical hosts, and do not rely
295 on undefined behavior due to signed arithmetic overflow.
296
297 These macros are not constant expressions.
298
299 These macros may evaluate their arguments zero or multiple times, so the
300 arguments should not have side effects.
301
302 These macros are tuned for B being a constant. */
303
304 #define INT_ADD_OK(a, b, r) (!INT_ADD_WRAPV (a, b, r))
305 #define INT_SUBTRACT_OK(a, b, r) (!INT_SUBTRACT_WRAPV (a, b, r))
306 #define INT_MULTIPLY_OK(a, b, r) (!INT_MULTIPLY_WRAPV (a, b, r))
307
308 #endif
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