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1 /* intprops.h -- properties of integer types
2
3 Copyright (C) 2001-2021 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
19 #ifndef _GL_INTPROPS_H
20 #define _GL_INTPROPS_H
21
22 #include <limits.h>
23
24 /* Return a value with the common real type of E and V and the value of V.
25 Do not evaluate E. */
26 #define _GL_INT_CONVERT(e, v) ((1 ? 0 : (e)) + (v))
27
28 /* Act like _GL_INT_CONVERT (E, -V) but work around a bug in IRIX 6.5 cc; see
29 <https://lists.gnu.org/r/bug-gnulib/2011-05/msg00406.html>. */
30 #define _GL_INT_NEGATE_CONVERT(e, v) ((1 ? 0 : (e)) - (v))
31
32 /* The extra casts in the following macros work around compiler bugs,
33 e.g., in Cray C 5.0.3.0. */
34
35 /* True if the arithmetic type T is an integer type. bool counts as
36 an integer. */
37 #define TYPE_IS_INTEGER(t) ((t) 1.5 == 1)
38
39 /* True if the real type T is signed. */
40 #define TYPE_SIGNED(t) (! ((t) 0 < (t) -1))
41
42 /* Return 1 if the real expression E, after promotion, has a
43 signed or floating type. Do not evaluate E. */
44 #define EXPR_SIGNED(e) (_GL_INT_NEGATE_CONVERT (e, 1) < 0)
45
46
47 /* Minimum and maximum values for integer types and expressions. */
48
49 /* The width in bits of the integer type or expression T.
50 Do not evaluate T. T must not be a bit-field expression.
51 Padding bits are not supported; this is checked at compile-time below. */
52 #define TYPE_WIDTH(t) (sizeof (t) * CHAR_BIT)
53
54 /* The maximum and minimum values for the integer type T. */
55 #define TYPE_MINIMUM(t) ((t) ~ TYPE_MAXIMUM (t))
56 #define TYPE_MAXIMUM(t) \
57 ((t) (! TYPE_SIGNED (t) \
58 ? (t) -1 \
59 : ((((t) 1 << (TYPE_WIDTH (t) - 2)) - 1) * 2 + 1)))
60
61 /* The maximum and minimum values for the type of the expression E,
62 after integer promotion. E is not evaluated. */
63 #define _GL_INT_MINIMUM(e) \
64 (EXPR_SIGNED (e) \
65 ? ~ _GL_SIGNED_INT_MAXIMUM (e) \
66 : _GL_INT_CONVERT (e, 0))
67 #define _GL_INT_MAXIMUM(e) \
68 (EXPR_SIGNED (e) \
69 ? _GL_SIGNED_INT_MAXIMUM (e) \
70 : _GL_INT_NEGATE_CONVERT (e, 1))
71 #define _GL_SIGNED_INT_MAXIMUM(e) \
72 (((_GL_INT_CONVERT (e, 1) << (TYPE_WIDTH (+ (e)) - 2)) - 1) * 2 + 1)
73
74 /* Work around OpenVMS incompatibility with C99. */
75 #if !defined LLONG_MAX && defined __INT64_MAX
76 # define LLONG_MAX __INT64_MAX
77 # define LLONG_MIN __INT64_MIN
78 #endif
79
80 /* This include file assumes that signed types are two's complement without
81 padding bits; the above macros have undefined behavior otherwise.
82 If this is a problem for you, please let us know how to fix it for your host.
83 This assumption is tested by the intprops-tests module. */
84
85 /* Does the __typeof__ keyword work? This could be done by
86 'configure', but for now it's easier to do it by hand. */
87 #if (2 <= __GNUC__ \
88 || (4 <= __clang_major__) \
89 || (1210 <= __IBMC__ && defined __IBM__TYPEOF__) \
90 || (0x5110 <= __SUNPRO_C && !__STDC__))
91 # define _GL_HAVE___TYPEOF__ 1
92 #else
93 # define _GL_HAVE___TYPEOF__ 0
94 #endif
95
96 /* Return 1 if the integer type or expression T might be signed. Return 0
97 if it is definitely unsigned. T must not be a bit-field expression.
98 This macro does not evaluate its argument, and expands to an
99 integer constant expression. */
100 #if _GL_HAVE___TYPEOF__
101 # define _GL_SIGNED_TYPE_OR_EXPR(t) TYPE_SIGNED (__typeof__ (t))
102 #else
103 # define _GL_SIGNED_TYPE_OR_EXPR(t) 1
104 #endif
105
106 /* Bound on length of the string representing an unsigned integer
107 value representable in B bits. log10 (2.0) < 146/485. The
108 smallest value of B where this bound is not tight is 2621. */
109 #define INT_BITS_STRLEN_BOUND(b) (((b) * 146 + 484) / 485)
110
111 /* Bound on length of the string representing an integer type or expression T.
112 T must not be a bit-field expression.
113
114 Subtract 1 for the sign bit if T is signed, and then add 1 more for
115 a minus sign if needed.
116
117 Because _GL_SIGNED_TYPE_OR_EXPR sometimes returns 1 when its argument is
118 unsigned, this macro may overestimate the true bound by one byte when
119 applied to unsigned types of size 2, 4, 16, ... bytes. */
120 #define INT_STRLEN_BOUND(t) \
121 (INT_BITS_STRLEN_BOUND (TYPE_WIDTH (t) - _GL_SIGNED_TYPE_OR_EXPR (t)) \
122 + _GL_SIGNED_TYPE_OR_EXPR (t))
123
124 /* Bound on buffer size needed to represent an integer type or expression T,
125 including the terminating null. T must not be a bit-field expression. */
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 harder to use and may be less
136 efficient than the INT_<op>_WRAPV, INT_<op>_OK, and
137 INT_<op>_OVERFLOW macros described below.
138
139 Example usage:
140
141 long int i = ...;
142 long int j = ...;
143 if (INT_MULTIPLY_RANGE_OVERFLOW (i, j, LONG_MIN, LONG_MAX))
144 printf ("multiply would overflow");
145 else
146 printf ("product is %ld", i * j);
147
148 Restrictions on *_RANGE_OVERFLOW macros:
149
150 These macros do not check for all possible numerical problems or
151 undefined or unspecified behavior: they do not check for division
152 by zero, for bad shift counts, or for shifting negative numbers.
153
154 These macros may evaluate their arguments zero or multiple times,
155 so the arguments should not have side effects. The arithmetic
156 arguments (including the MIN and MAX arguments) must be of the same
157 integer type after the usual arithmetic conversions, and the type
158 must have minimum value MIN and maximum MAX. Unsigned types should
159 use a zero MIN of the proper type.
160
161 Because all arguments are subject to integer promotions, these
162 macros typically do not work on types narrower than 'int'.
163
164 These macros are tuned for constant MIN and MAX. For commutative
165 operations such as A + B, they are also tuned for constant B. */
166
167 /* Return 1 if A + B would overflow in [MIN,MAX] arithmetic.
168 See above for restrictions. */
169 #define INT_ADD_RANGE_OVERFLOW(a, b, min, max) \
170 ((b) < 0 \
171 ? (a) < (min) - (b) \
172 : (max) - (b) < (a))
173
174 /* Return 1 if A - B would overflow in [MIN,MAX] arithmetic.
175 See above for restrictions. */
176 #define INT_SUBTRACT_RANGE_OVERFLOW(a, b, min, max) \
177 ((b) < 0 \
178 ? (max) + (b) < (a) \
179 : (a) < (min) + (b))
180
181 /* Return 1 if - A would overflow in [MIN,MAX] arithmetic.
182 See above for restrictions. */
183 #define INT_NEGATE_RANGE_OVERFLOW(a, min, max) \
184 ((min) < 0 \
185 ? (a) < - (max) \
186 : 0 < (a))
187
188 /* Return 1 if A * B would overflow in [MIN,MAX] arithmetic.
189 See above for restrictions. Avoid && and || as they tickle
190 bugs in Sun C 5.11 2010/08/13 and other compilers; see
191 <https://lists.gnu.org/r/bug-gnulib/2011-05/msg00401.html>. */
192 #define INT_MULTIPLY_RANGE_OVERFLOW(a, b, min, max) \
193 ((b) < 0 \
194 ? ((a) < 0 \
195 ? (a) < (max) / (b) \
196 : (b) == -1 \
197 ? 0 \
198 : (min) / (b) < (a)) \
199 : (b) == 0 \
200 ? 0 \
201 : ((a) < 0 \
202 ? (a) < (min) / (b) \
203 : (max) / (b) < (a)))
204
205 /* Return 1 if A / B would overflow in [MIN,MAX] arithmetic.
206 See above for restrictions. Do not check for division by zero. */
207 #define INT_DIVIDE_RANGE_OVERFLOW(a, b, min, max) \
208 ((min) < 0 && (b) == -1 && (a) < - (max))
209
210 /* Return 1 if A % B would overflow in [MIN,MAX] arithmetic.
211 See above for restrictions. Do not check for division by zero.
212 Mathematically, % should never overflow, but on x86-like hosts
213 INT_MIN % -1 traps, and the C standard permits this, so treat this
214 as an overflow too. */
215 #define INT_REMAINDER_RANGE_OVERFLOW(a, b, min, max) \
216 INT_DIVIDE_RANGE_OVERFLOW (a, b, min, max)
217
218 /* Return 1 if A << B would overflow in [MIN,MAX] arithmetic.
219 See above for restrictions. Here, MIN and MAX are for A only, and B need
220 not be of the same type as the other arguments. The C standard says that
221 behavior is undefined for shifts unless 0 <= B < wordwidth, and that when
222 A is negative then A << B has undefined behavior and A >> B has
223 implementation-defined behavior, but do not check these other
224 restrictions. */
225 #define INT_LEFT_SHIFT_RANGE_OVERFLOW(a, b, min, max) \
226 ((a) < 0 \
227 ? (a) < (min) >> (b) \
228 : (max) >> (b) < (a))
229
230 /* True if __builtin_add_overflow (A, B, P) and __builtin_sub_overflow
231 (A, B, P) work when P is non-null. */
232 #if defined __has_builtin
233 # define _GL_HAS_BUILTIN_ADD_OVERFLOW __has_builtin (__builtin_add_overflow)
234 /* __builtin_{add,sub}_overflow exists but is not reliable in GCC 5.x and 6.x,
235 see <https://gcc.gnu.org/bugzilla/show_bug.cgi?id=98269>. */
236 #elif 7 <= __GNUC__ && !defined __EDG__
237 # define _GL_HAS_BUILTIN_ADD_OVERFLOW 1
238 #else
239 # define _GL_HAS_BUILTIN_ADD_OVERFLOW 0
240 #endif
241
242 /* True if __builtin_mul_overflow (A, B, P) works when P is non-null. */
243 #if defined __clang_major_ && __clang_major__ < 14
244 /* Work around Clang bug <https://bugs.llvm.org/show_bug.cgi?id=16404>. */
245 # define _GL_HAS_BUILTIN_MUL_OVERFLOW 0
246 #else
247 # define _GL_HAS_BUILTIN_MUL_OVERFLOW _GL_HAS_BUILTIN_ADD_OVERFLOW
248 #endif
249
250 /* True if __builtin_add_overflow_p (A, B, C) works, and similarly for
251 __builtin_sub_overflow_p and __builtin_mul_overflow_p. */
252 #ifdef __EDG__
253 /* In EDG-based compilers like ICC 2021.3 and earlier,
254 __builtin_add_overflow_p etc. are not treated as integral constant
255 expressions even when all arguments are. */
256 # define _GL_HAS_BUILTIN_OVERFLOW_P 0
257 #elif defined __has_builtin
258 # define _GL_HAS_BUILTIN_OVERFLOW_P __has_builtin (__builtin_mul_overflow_p)
259 #else
260 # define _GL_HAS_BUILTIN_OVERFLOW_P (7 <= __GNUC__)
261 #endif
262
263 /* The _GL*_OVERFLOW macros have the same restrictions as the
264 *_RANGE_OVERFLOW macros, except that they do not assume that operands
265 (e.g., A and B) have the same type as MIN and MAX. Instead, they assume
266 that the result (e.g., A + B) has that type. */
267 #if _GL_HAS_BUILTIN_OVERFLOW_P
268 # define _GL_ADD_OVERFLOW(a, b, min, max) \
269 __builtin_add_overflow_p (a, b, (__typeof__ ((a) + (b))) 0)
270 # define _GL_SUBTRACT_OVERFLOW(a, b, min, max) \
271 __builtin_sub_overflow_p (a, b, (__typeof__ ((a) - (b))) 0)
272 # define _GL_MULTIPLY_OVERFLOW(a, b, min, max) \
273 __builtin_mul_overflow_p (a, b, (__typeof__ ((a) * (b))) 0)
274 #else
275 # define _GL_ADD_OVERFLOW(a, b, min, max) \
276 ((min) < 0 ? INT_ADD_RANGE_OVERFLOW (a, b, min, max) \
277 : (a) < 0 ? (b) <= (a) + (b) \
278 : (b) < 0 ? (a) <= (a) + (b) \
279 : (a) + (b) < (b))
280 # define _GL_SUBTRACT_OVERFLOW(a, b, min, max) \
281 ((min) < 0 ? INT_SUBTRACT_RANGE_OVERFLOW (a, b, min, max) \
282 : (a) < 0 ? 1 \
283 : (b) < 0 ? (a) - (b) <= (a) \
284 : (a) < (b))
285 # define _GL_MULTIPLY_OVERFLOW(a, b, min, max) \
286 (((min) == 0 && (((a) < 0 && 0 < (b)) || ((b) < 0 && 0 < (a)))) \
287 || INT_MULTIPLY_RANGE_OVERFLOW (a, b, min, max))
288 #endif
289 #define _GL_DIVIDE_OVERFLOW(a, b, min, max) \
290 ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max) \
291 : (a) < 0 ? (b) <= (a) + (b) - 1 \
292 : (b) < 0 && (a) + (b) <= (a))
293 #define _GL_REMAINDER_OVERFLOW(a, b, min, max) \
294 ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max) \
295 : (a) < 0 ? (a) % (b) != ((max) - (b) + 1) % (b) \
296 : (b) < 0 && ! _GL_UNSIGNED_NEG_MULTIPLE (a, b, max))
297
298 /* Return a nonzero value if A is a mathematical multiple of B, where
299 A is unsigned, B is negative, and MAX is the maximum value of A's
300 type. A's type must be the same as (A % B)'s type. Normally (A %
301 -B == 0) suffices, but things get tricky if -B would overflow. */
302 #define _GL_UNSIGNED_NEG_MULTIPLE(a, b, max) \
303 (((b) < -_GL_SIGNED_INT_MAXIMUM (b) \
304 ? (_GL_SIGNED_INT_MAXIMUM (b) == (max) \
305 ? (a) \
306 : (a) % (_GL_INT_CONVERT (a, _GL_SIGNED_INT_MAXIMUM (b)) + 1)) \
307 : (a) % - (b)) \
308 == 0)
309
310 /* Check for integer overflow, and report low order bits of answer.
311
312 The INT_<op>_OVERFLOW macros return 1 if the corresponding C operators
313 might not yield numerically correct answers due to arithmetic overflow.
314 The INT_<op>_WRAPV macros compute the low-order bits of the sum,
315 difference, and product of two C integers, and return 1 if these
316 low-order bits are not numerically correct.
317 These macros work correctly on all known practical hosts, and do not rely
318 on undefined behavior due to signed arithmetic overflow.
319
320 Example usage, assuming A and B are long int:
321
322 if (INT_MULTIPLY_OVERFLOW (a, b))
323 printf ("result would overflow\n");
324 else
325 printf ("result is %ld (no overflow)\n", a * b);
326
327 Example usage with WRAPV flavor:
328
329 long int result;
330 bool overflow = INT_MULTIPLY_WRAPV (a, b, &result);
331 printf ("result is %ld (%s)\n", result,
332 overflow ? "after overflow" : "no overflow");
333
334 Restrictions on these macros:
335
336 These macros do not check for all possible numerical problems or
337 undefined or unspecified behavior: they do not check for division
338 by zero, for bad shift counts, or for shifting negative numbers.
339
340 These macros may evaluate their arguments zero or multiple times, so the
341 arguments should not have side effects.
342
343 The WRAPV macros are not constant expressions. They support only
344 +, binary -, and *.
345
346 Because the WRAPV macros convert the result, they report overflow
347 in different circumstances than the OVERFLOW macros do. For
348 example, in the typical case with 16-bit 'short' and 32-bit 'int',
349 if A, B and R are all of type 'short' then INT_ADD_OVERFLOW (A, B)
350 returns false because the addition cannot overflow after A and B
351 are converted to 'int', whereas INT_ADD_WRAPV (A, B, &R) returns
352 true or false depending on whether the sum fits into 'short'.
353
354 These macros are tuned for their last input argument being a constant.
355
356 Return 1 if the integer expressions A * B, A - B, -A, A * B, A / B,
357 A % B, and A << B would overflow, respectively. */
358
359 #define INT_ADD_OVERFLOW(a, b) \
360 _GL_BINARY_OP_OVERFLOW (a, b, _GL_ADD_OVERFLOW)
361 #define INT_SUBTRACT_OVERFLOW(a, b) \
362 _GL_BINARY_OP_OVERFLOW (a, b, _GL_SUBTRACT_OVERFLOW)
363 #if _GL_HAS_BUILTIN_OVERFLOW_P
364 # define INT_NEGATE_OVERFLOW(a) INT_SUBTRACT_OVERFLOW (0, a)
365 #else
366 # define INT_NEGATE_OVERFLOW(a) \
367 INT_NEGATE_RANGE_OVERFLOW (a, _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
368 #endif
369 #define INT_MULTIPLY_OVERFLOW(a, b) \
370 _GL_BINARY_OP_OVERFLOW (a, b, _GL_MULTIPLY_OVERFLOW)
371 #define INT_DIVIDE_OVERFLOW(a, b) \
372 _GL_BINARY_OP_OVERFLOW (a, b, _GL_DIVIDE_OVERFLOW)
373 #define INT_REMAINDER_OVERFLOW(a, b) \
374 _GL_BINARY_OP_OVERFLOW (a, b, _GL_REMAINDER_OVERFLOW)
375 #define INT_LEFT_SHIFT_OVERFLOW(a, b) \
376 INT_LEFT_SHIFT_RANGE_OVERFLOW (a, b, \
377 _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
378
379 /* Return 1 if the expression A <op> B would overflow,
380 where OP_RESULT_OVERFLOW (A, B, MIN, MAX) does the actual test,
381 assuming MIN and MAX are the minimum and maximum for the result type.
382 Arguments should be free of side effects. */
383 #define _GL_BINARY_OP_OVERFLOW(a, b, op_result_overflow) \
384 op_result_overflow (a, b, \
385 _GL_INT_MINIMUM (_GL_INT_CONVERT (a, b)), \
386 _GL_INT_MAXIMUM (_GL_INT_CONVERT (a, b)))
387
388 /* Store the low-order bits of A + B, A - B, A * B, respectively, into *R.
389 Return 1 if the result overflows. See above for restrictions. */
390 #if _GL_HAS_BUILTIN_ADD_OVERFLOW
391 # define INT_ADD_WRAPV(a, b, r) __builtin_add_overflow (a, b, r)
392 # define INT_SUBTRACT_WRAPV(a, b, r) __builtin_sub_overflow (a, b, r)
393 #else
394 # define INT_ADD_WRAPV(a, b, r) \
395 _GL_INT_OP_WRAPV (a, b, r, +, _GL_INT_ADD_RANGE_OVERFLOW)
396 # define INT_SUBTRACT_WRAPV(a, b, r) \
397 _GL_INT_OP_WRAPV (a, b, r, -, _GL_INT_SUBTRACT_RANGE_OVERFLOW)
398 #endif
399 #if _GL_HAS_BUILTIN_MUL_OVERFLOW
400 # if ((9 < __GNUC__ + (3 <= __GNUC_MINOR__) \
401 || (__GNUC__ == 8 && 4 <= __GNUC_MINOR__)) \
402 && !defined __EDG__)
403 # define INT_MULTIPLY_WRAPV(a, b, r) __builtin_mul_overflow (a, b, r)
404 # else
405 /* Work around GCC bug 91450. */
406 # define INT_MULTIPLY_WRAPV(a, b, r) \
407 ((!_GL_SIGNED_TYPE_OR_EXPR (*(r)) && EXPR_SIGNED (a) && EXPR_SIGNED (b) \
408 && _GL_INT_MULTIPLY_RANGE_OVERFLOW (a, b, 0, (__typeof__ (*(r))) -1)) \
409 ? ((void) __builtin_mul_overflow (a, b, r), 1) \
410 : __builtin_mul_overflow (a, b, r))
411 # endif
412 #else
413 # define INT_MULTIPLY_WRAPV(a, b, r) \
414 _GL_INT_OP_WRAPV (a, b, r, *, _GL_INT_MULTIPLY_RANGE_OVERFLOW)
415 #endif
416
417 /* Nonzero if this compiler has GCC bug 68193 or Clang bug 25390. See:
418 https://gcc.gnu.org/bugzilla/show_bug.cgi?id=68193
419 https://llvm.org/bugs/show_bug.cgi?id=25390
420 For now, assume all versions of GCC-like compilers generate bogus
421 warnings for _Generic. This matters only for compilers that
422 lack relevant builtins. */
423 #if __GNUC__ || defined __clang__
424 # define _GL__GENERIC_BOGUS 1
425 #else
426 # define _GL__GENERIC_BOGUS 0
427 #endif
428
429 /* Store the low-order bits of A <op> B into *R, where OP specifies
430 the operation and OVERFLOW the overflow predicate. Return 1 if the
431 result overflows. See above for restrictions. */
432 #if 201112 <= __STDC_VERSION__ && !_GL__GENERIC_BOGUS
433 # define _GL_INT_OP_WRAPV(a, b, r, op, overflow) \
434 (_Generic \
435 (*(r), \
436 signed char: \
437 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
438 signed char, SCHAR_MIN, SCHAR_MAX), \
439 unsigned char: \
440 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
441 unsigned char, 0, UCHAR_MAX), \
442 short int: \
443 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
444 short int, SHRT_MIN, SHRT_MAX), \
445 unsigned short int: \
446 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
447 unsigned short int, 0, USHRT_MAX), \
448 int: \
449 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
450 int, INT_MIN, INT_MAX), \
451 unsigned int: \
452 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
453 unsigned int, 0, UINT_MAX), \
454 long int: \
455 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
456 long int, LONG_MIN, LONG_MAX), \
457 unsigned long int: \
458 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
459 unsigned long int, 0, ULONG_MAX), \
460 long long int: \
461 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
462 long long int, LLONG_MIN, LLONG_MAX), \
463 unsigned long long int: \
464 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
465 unsigned long long int, 0, ULLONG_MAX)))
466 #else
467 /* Store the low-order bits of A <op> B into *R, where OP specifies
468 the operation and OVERFLOW the overflow predicate. If *R is
469 signed, its type is ST with bounds SMIN..SMAX; otherwise its type
470 is UT with bounds U..UMAX. ST and UT are narrower than int.
471 Return 1 if the result overflows. See above for restrictions. */
472 # if _GL_HAVE___TYPEOF__
473 # define _GL_INT_OP_WRAPV_SMALLISH(a,b,r,op,overflow,st,smin,smax,ut,umax) \
474 (TYPE_SIGNED (__typeof__ (*(r))) \
475 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, st, smin, smax) \
476 : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, ut, 0, umax))
477 # else
478 # define _GL_INT_OP_WRAPV_SMALLISH(a,b,r,op,overflow,st,smin,smax,ut,umax) \
479 (overflow (a, b, smin, smax) \
480 ? (overflow (a, b, 0, umax) \
481 ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st), 1) \
482 : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st)) < 0) \
483 : (overflow (a, b, 0, umax) \
484 ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st)) >= 0 \
485 : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st), 0)))
486 # endif
487
488 # define _GL_INT_OP_WRAPV(a, b, r, op, overflow) \
489 (sizeof *(r) == sizeof (signed char) \
490 ? _GL_INT_OP_WRAPV_SMALLISH (a, b, r, op, overflow, \
491 signed char, SCHAR_MIN, SCHAR_MAX, \
492 unsigned char, UCHAR_MAX) \
493 : sizeof *(r) == sizeof (short int) \
494 ? _GL_INT_OP_WRAPV_SMALLISH (a, b, r, op, overflow, \
495 short int, SHRT_MIN, SHRT_MAX, \
496 unsigned short int, USHRT_MAX) \
497 : sizeof *(r) == sizeof (int) \
498 ? (EXPR_SIGNED (*(r)) \
499 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
500 int, INT_MIN, INT_MAX) \
501 : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
502 unsigned int, 0, UINT_MAX)) \
503 : _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow))
504 # ifdef LLONG_MAX
505 # define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
506 (sizeof *(r) == sizeof (long int) \
507 ? (EXPR_SIGNED (*(r)) \
508 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
509 long int, LONG_MIN, LONG_MAX) \
510 : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
511 unsigned long int, 0, ULONG_MAX)) \
512 : (EXPR_SIGNED (*(r)) \
513 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
514 long long int, LLONG_MIN, LLONG_MAX) \
515 : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
516 unsigned long long int, 0, ULLONG_MAX)))
517 # else
518 # define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
519 (EXPR_SIGNED (*(r)) \
520 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
521 long int, LONG_MIN, LONG_MAX) \
522 : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
523 unsigned long int, 0, ULONG_MAX))
524 # endif
525 #endif
526
527 /* Store the low-order bits of A <op> B into *R, where the operation
528 is given by OP. Use the unsigned type UT for calculation to avoid
529 overflow problems. *R's type is T, with extrema TMIN and TMAX.
530 T must be a signed integer type. Return 1 if the result overflows. */
531 #define _GL_INT_OP_CALC(a, b, r, op, overflow, ut, t, tmin, tmax) \
532 (overflow (a, b, tmin, tmax) \
533 ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 1) \
534 : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 0))
535
536 /* Return the low-order bits of A <op> B, where the operation is given
537 by OP. Use the unsigned type UT for calculation to avoid undefined
538 behavior on signed integer overflow, and convert the result to type T.
539 UT is at least as wide as T and is no narrower than unsigned int,
540 T is two's complement, and there is no padding or trap representations.
541 Assume that converting UT to T yields the low-order bits, as is
542 done in all known two's-complement C compilers. E.g., see:
543 https://gcc.gnu.org/onlinedocs/gcc/Integers-implementation.html
544
545 According to the C standard, converting UT to T yields an
546 implementation-defined result or signal for values outside T's
547 range. However, code that works around this theoretical problem
548 runs afoul of a compiler bug in Oracle Studio 12.3 x86. See:
549 https://lists.gnu.org/r/bug-gnulib/2017-04/msg00049.html
550 As the compiler bug is real, don't try to work around the
551 theoretical problem. */
552
553 #define _GL_INT_OP_WRAPV_VIA_UNSIGNED(a, b, op, ut, t) \
554 ((t) ((ut) (a) op (ut) (b)))
555
556 /* Return true if the numeric values A + B, A - B, A * B fall outside
557 the range TMIN..TMAX. Arguments should be integer expressions
558 without side effects. TMIN should be signed and nonpositive.
559 TMAX should be positive, and should be signed unless TMIN is zero. */
560 #define _GL_INT_ADD_RANGE_OVERFLOW(a, b, tmin, tmax) \
561 ((b) < 0 \
562 ? (((tmin) \
563 ? ((EXPR_SIGNED (_GL_INT_CONVERT (a, (tmin) - (b))) || (b) < (tmin)) \
564 && (a) < (tmin) - (b)) \
565 : (a) <= -1 - (b)) \
566 || ((EXPR_SIGNED (a) ? 0 <= (a) : (tmax) < (a)) && (tmax) < (a) + (b))) \
567 : (a) < 0 \
568 ? (((tmin) \
569 ? ((EXPR_SIGNED (_GL_INT_CONVERT (b, (tmin) - (a))) || (a) < (tmin)) \
570 && (b) < (tmin) - (a)) \
571 : (b) <= -1 - (a)) \
572 || ((EXPR_SIGNED (_GL_INT_CONVERT (a, b)) || (tmax) < (b)) \
573 && (tmax) < (a) + (b))) \
574 : (tmax) < (b) || (tmax) - (b) < (a))
575 #define _GL_INT_SUBTRACT_RANGE_OVERFLOW(a, b, tmin, tmax) \
576 (((a) < 0) == ((b) < 0) \
577 ? ((a) < (b) \
578 ? !(tmin) || -1 - (tmin) < (b) - (a) - 1 \
579 : (tmax) < (a) - (b)) \
580 : (a) < 0 \
581 ? ((!EXPR_SIGNED (_GL_INT_CONVERT ((a) - (tmin), b)) && (a) - (tmin) < 0) \
582 || (a) - (tmin) < (b)) \
583 : ((! (EXPR_SIGNED (_GL_INT_CONVERT (tmax, b)) \
584 && EXPR_SIGNED (_GL_INT_CONVERT ((tmax) + (b), a))) \
585 && (tmax) <= -1 - (b)) \
586 || (tmax) + (b) < (a)))
587 #define _GL_INT_MULTIPLY_RANGE_OVERFLOW(a, b, tmin, tmax) \
588 ((b) < 0 \
589 ? ((a) < 0 \
590 ? (EXPR_SIGNED (_GL_INT_CONVERT (tmax, b)) \
591 ? (a) < (tmax) / (b) \
592 : ((INT_NEGATE_OVERFLOW (b) \
593 ? _GL_INT_CONVERT (b, tmax) >> (TYPE_WIDTH (+ (b)) - 1) \
594 : (tmax) / -(b)) \
595 <= -1 - (a))) \
596 : INT_NEGATE_OVERFLOW (_GL_INT_CONVERT (b, tmin)) && (b) == -1 \
597 ? (EXPR_SIGNED (a) \
598 ? 0 < (a) + (tmin) \
599 : 0 < (a) && -1 - (tmin) < (a) - 1) \
600 : (tmin) / (b) < (a)) \
601 : (b) == 0 \
602 ? 0 \
603 : ((a) < 0 \
604 ? (INT_NEGATE_OVERFLOW (_GL_INT_CONVERT (a, tmin)) && (a) == -1 \
605 ? (EXPR_SIGNED (b) ? 0 < (b) + (tmin) : -1 - (tmin) < (b) - 1) \
606 : (tmin) / (a) < (b)) \
607 : (tmax) / (b) < (a)))
608
609 /* The following macros compute A + B, A - B, and A * B, respectively.
610 If no overflow occurs, they set *R to the result and return 1;
611 otherwise, they return 0 and may modify *R.
612
613 Example usage:
614
615 long int result;
616 if (INT_ADD_OK (a, b, &result))
617 printf ("result is %ld\n", result);
618 else
619 printf ("overflow\n");
620
621 A, B, and *R should be integers; they need not be the same type,
622 and they need not be all signed or all unsigned.
623
624 These macros work correctly on all known practical hosts, and do not rely
625 on undefined behavior due to signed arithmetic overflow.
626
627 These macros are not constant expressions.
628
629 These macros may evaluate their arguments zero or multiple times, so the
630 arguments should not have side effects.
631
632 These macros are tuned for B being a constant. */
633
634 #define INT_ADD_OK(a, b, r) ! INT_ADD_WRAPV (a, b, r)
635 #define INT_SUBTRACT_OK(a, b, r) ! INT_SUBTRACT_WRAPV (a, b, r)
636 #define INT_MULTIPLY_OK(a, b, r) ! INT_MULTIPLY_WRAPV (a, b, r)
637
638 #endif /* _GL_INTPROPS_H */
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