| blob | d4a917f72a0689d528f3df586d0710c0e602fc58 |
1 /* intprops.h -- properties of integer types
3 Copyright (C) 2001-2022 Free Software Foundation, Inc.
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.
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.
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/>. */
19 #ifndef _GL_INTPROPS_H
20 #define _GL_INTPROPS_H
22 #include <limits.h>
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))
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))
32 /* The extra casts in the following macros work around compiler bugs,
33 e.g., in Cray C 5.0.3.0. */
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)
39 /* True if the real type T is signed. */
40 #define TYPE_SIGNED(t) (! ((t) 0 < (t) -1))
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)
47 /* Minimum and maximum values for integer types and expressions. */
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)
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)))
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)
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
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. */
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
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
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)
111 /* Bound on length of the string representing an integer type or expression T.
112 T must not be a bit-field expression.
114 Subtract 1 for the sign bit if T is signed, and then add 1 more for
115 a minus sign if needed.
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))
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)
129 /* Range overflow checks.
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.
139 Example usage:
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);
148 Restrictions on *_RANGE_OVERFLOW macros:
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.
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.
161 Because all arguments are subject to integer promotions, these
162 macros typically do not work on types narrower than 'int'.
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. */
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))
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))
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))
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)))
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))
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)
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))
230 /* True if __builtin_add_overflow (A, B, P) and __builtin_sub_overflow
231 (A, B, P) work when P is non-null. */
232 #ifdef __EDG__
233 /* EDG-based compilers like nvc 22.1 cannot add 64-bit signed to unsigned
234 <https://bugs.gnu.org/53256>. */
235 # define _GL_HAS_BUILTIN_ADD_OVERFLOW 0
236 #elif defined __has_builtin
237 # define _GL_HAS_BUILTIN_ADD_OVERFLOW __has_builtin (__builtin_add_overflow)
238 /* __builtin_{add,sub}_overflow exists but is not reliable in GCC 5.x and 6.x,
239 see <https://gcc.gnu.org/bugzilla/show_bug.cgi?id=98269>. */
240 #elif 7 <= __GNUC__
241 # define _GL_HAS_BUILTIN_ADD_OVERFLOW 1
242 #else
243 # define _GL_HAS_BUILTIN_ADD_OVERFLOW 0
244 #endif
246 /* True if __builtin_mul_overflow (A, B, P) works when P is non-null. */
247 #if defined __clang_major__ && __clang_major__ < 14
248 /* Work around Clang bug <https://bugs.llvm.org/show_bug.cgi?id=16404>. */
249 # define _GL_HAS_BUILTIN_MUL_OVERFLOW 0
250 #else
251 # define _GL_HAS_BUILTIN_MUL_OVERFLOW _GL_HAS_BUILTIN_ADD_OVERFLOW
252 #endif
254 /* True if __builtin_add_overflow_p (A, B, C) works, and similarly for
255 __builtin_sub_overflow_p and __builtin_mul_overflow_p. */
256 #ifdef __EDG__
257 /* In EDG-based compilers like ICC 2021.3 and earlier,
258 __builtin_add_overflow_p etc. are not treated as integral constant
259 expressions even when all arguments are. */
260 # define _GL_HAS_BUILTIN_OVERFLOW_P 0
261 #elif defined __has_builtin
262 # define _GL_HAS_BUILTIN_OVERFLOW_P __has_builtin (__builtin_mul_overflow_p)
263 #else
264 # define _GL_HAS_BUILTIN_OVERFLOW_P (7 <= __GNUC__)
265 #endif
267 /* The _GL*_OVERFLOW macros have the same restrictions as the
268 *_RANGE_OVERFLOW macros, except that they do not assume that operands
269 (e.g., A and B) have the same type as MIN and MAX. Instead, they assume
270 that the result (e.g., A + B) has that type. */
271 #if _GL_HAS_BUILTIN_OVERFLOW_P
272 # define _GL_ADD_OVERFLOW(a, b, min, max) \
273 __builtin_add_overflow_p (a, b, (__typeof__ ((a) + (b))) 0)
274 # define _GL_SUBTRACT_OVERFLOW(a, b, min, max) \
275 __builtin_sub_overflow_p (a, b, (__typeof__ ((a) - (b))) 0)
276 # define _GL_MULTIPLY_OVERFLOW(a, b, min, max) \
277 __builtin_mul_overflow_p (a, b, (__typeof__ ((a) * (b))) 0)
278 #else
279 # define _GL_ADD_OVERFLOW(a, b, min, max) \
280 ((min) < 0 ? INT_ADD_RANGE_OVERFLOW (a, b, min, max) \
281 : (a) < 0 ? (b) <= (a) + (b) \
282 : (b) < 0 ? (a) <= (a) + (b) \
283 : (a) + (b) < (b))
284 # define _GL_SUBTRACT_OVERFLOW(a, b, min, max) \
285 ((min) < 0 ? INT_SUBTRACT_RANGE_OVERFLOW (a, b, min, max) \
286 : (a) < 0 ? 1 \
287 : (b) < 0 ? (a) - (b) <= (a) \
288 : (a) < (b))
289 # define _GL_MULTIPLY_OVERFLOW(a, b, min, max) \
290 (((min) == 0 && (((a) < 0 && 0 < (b)) || ((b) < 0 && 0 < (a)))) \
291 || INT_MULTIPLY_RANGE_OVERFLOW (a, b, min, max))
292 #endif
293 #define _GL_DIVIDE_OVERFLOW(a, b, min, max) \
294 ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max) \
295 : (a) < 0 ? (b) <= (a) + (b) - 1 \
296 : (b) < 0 && (a) + (b) <= (a))
297 #define _GL_REMAINDER_OVERFLOW(a, b, min, max) \
298 ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max) \
299 : (a) < 0 ? (a) % (b) != ((max) - (b) + 1) % (b) \
300 : (b) < 0 && ! _GL_UNSIGNED_NEG_MULTIPLE (a, b, max))
302 /* Return a nonzero value if A is a mathematical multiple of B, where
303 A is unsigned, B is negative, and MAX is the maximum value of A's
304 type. A's type must be the same as (A % B)'s type. Normally (A %
305 -B == 0) suffices, but things get tricky if -B would overflow. */
306 #define _GL_UNSIGNED_NEG_MULTIPLE(a, b, max) \
307 (((b) < -_GL_SIGNED_INT_MAXIMUM (b) \
308 ? (_GL_SIGNED_INT_MAXIMUM (b) == (max) \
309 ? (a) \
310 : (a) % (_GL_INT_CONVERT (a, _GL_SIGNED_INT_MAXIMUM (b)) + 1)) \
311 : (a) % - (b)) \
312 == 0)
314 /* Check for integer overflow, and report low order bits of answer.
316 The INT_<op>_OVERFLOW macros return 1 if the corresponding C operators
317 might not yield numerically correct answers due to arithmetic overflow.
318 The INT_<op>_WRAPV macros compute the low-order bits of the sum,
319 difference, and product of two C integers, and return 1 if these
320 low-order bits are not numerically correct.
321 These macros work correctly on all known practical hosts, and do not rely
322 on undefined behavior due to signed arithmetic overflow.
324 Example usage, assuming A and B are long int:
326 if (INT_MULTIPLY_OVERFLOW (a, b))
327 printf ("result would overflow\n");
328 else
329 printf ("result is %ld (no overflow)\n", a * b);
331 Example usage with WRAPV flavor:
333 long int result;
334 bool overflow = INT_MULTIPLY_WRAPV (a, b, &result);
335 printf ("result is %ld (%s)\n", result,
336 overflow ? "after overflow" : "no overflow");
338 Restrictions on these macros:
340 These macros do not check for all possible numerical problems or
341 undefined or unspecified behavior: they do not check for division
342 by zero, for bad shift counts, or for shifting negative numbers.
344 These macros may evaluate their arguments zero or multiple times, so the
345 arguments should not have side effects.
347 The WRAPV macros are not constant expressions. They support only
348 +, binary -, and *.
350 Because the WRAPV macros convert the result, they report overflow
351 in different circumstances than the OVERFLOW macros do. For
352 example, in the typical case with 16-bit 'short' and 32-bit 'int',
353 if A, B and R are all of type 'short' then INT_ADD_OVERFLOW (A, B)
354 returns false because the addition cannot overflow after A and B
355 are converted to 'int', whereas INT_ADD_WRAPV (A, B, &R) returns
356 true or false depending on whether the sum fits into 'short'.
358 These macros are tuned for their last input argument being a constant.
360 Return 1 if the integer expressions A * B, A - B, -A, A * B, A / B,
361 A % B, and A << B would overflow, respectively. */
363 #define INT_ADD_OVERFLOW(a, b) \
364 _GL_BINARY_OP_OVERFLOW (a, b, _GL_ADD_OVERFLOW)
365 #define INT_SUBTRACT_OVERFLOW(a, b) \
366 _GL_BINARY_OP_OVERFLOW (a, b, _GL_SUBTRACT_OVERFLOW)
367 #if _GL_HAS_BUILTIN_OVERFLOW_P
368 # define INT_NEGATE_OVERFLOW(a) INT_SUBTRACT_OVERFLOW (0, a)
369 #else
370 # define INT_NEGATE_OVERFLOW(a) \
371 INT_NEGATE_RANGE_OVERFLOW (a, _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
372 #endif
373 #define INT_MULTIPLY_OVERFLOW(a, b) \
374 _GL_BINARY_OP_OVERFLOW (a, b, _GL_MULTIPLY_OVERFLOW)
375 #define INT_DIVIDE_OVERFLOW(a, b) \
376 _GL_BINARY_OP_OVERFLOW (a, b, _GL_DIVIDE_OVERFLOW)
377 #define INT_REMAINDER_OVERFLOW(a, b) \
378 _GL_BINARY_OP_OVERFLOW (a, b, _GL_REMAINDER_OVERFLOW)
379 #define INT_LEFT_SHIFT_OVERFLOW(a, b) \
380 INT_LEFT_SHIFT_RANGE_OVERFLOW (a, b, \
381 _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
383 /* Return 1 if the expression A <op> B would overflow,
384 where OP_RESULT_OVERFLOW (A, B, MIN, MAX) does the actual test,
385 assuming MIN and MAX are the minimum and maximum for the result type.
386 Arguments should be free of side effects. */
387 #define _GL_BINARY_OP_OVERFLOW(a, b, op_result_overflow) \
388 op_result_overflow (a, b, \
389 _GL_INT_MINIMUM (_GL_INT_CONVERT (a, b)), \
390 _GL_INT_MAXIMUM (_GL_INT_CONVERT (a, b)))
392 /* Store the low-order bits of A + B, A - B, A * B, respectively, into *R.
393 Return 1 if the result overflows. See above for restrictions. */
394 #if _GL_HAS_BUILTIN_ADD_OVERFLOW
395 # define INT_ADD_WRAPV(a, b, r) __builtin_add_overflow (a, b, r)
396 # define INT_SUBTRACT_WRAPV(a, b, r) __builtin_sub_overflow (a, b, r)
397 #else
398 # define INT_ADD_WRAPV(a, b, r) \
399 _GL_INT_OP_WRAPV (a, b, r, +, _GL_INT_ADD_RANGE_OVERFLOW)
400 # define INT_SUBTRACT_WRAPV(a, b, r) \
401 _GL_INT_OP_WRAPV (a, b, r, -, _GL_INT_SUBTRACT_RANGE_OVERFLOW)
402 #endif
403 #if _GL_HAS_BUILTIN_MUL_OVERFLOW
404 # if ((9 < __GNUC__ + (3 <= __GNUC_MINOR__) \
405 || (__GNUC__ == 8 && 4 <= __GNUC_MINOR__)) \
406 && !defined __EDG__)
407 # define INT_MULTIPLY_WRAPV(a, b, r) __builtin_mul_overflow (a, b, r)
408 # else
409 /* Work around GCC bug 91450. */
410 # define INT_MULTIPLY_WRAPV(a, b, r) \
411 ((!_GL_SIGNED_TYPE_OR_EXPR (*(r)) && EXPR_SIGNED (a) && EXPR_SIGNED (b) \
412 && _GL_INT_MULTIPLY_RANGE_OVERFLOW (a, b, 0, (__typeof__ (*(r))) -1)) \
413 ? ((void) __builtin_mul_overflow (a, b, r), 1) \
414 : __builtin_mul_overflow (a, b, r))
415 # endif
416 #else
417 # define INT_MULTIPLY_WRAPV(a, b, r) \
418 _GL_INT_OP_WRAPV (a, b, r, *, _GL_INT_MULTIPLY_RANGE_OVERFLOW)
419 #endif
421 /* Nonzero if this compiler has GCC bug 68193 or Clang bug 25390. See:
422 https://gcc.gnu.org/bugzilla/show_bug.cgi?id=68193
423 https://llvm.org/bugs/show_bug.cgi?id=25390
424 For now, assume all versions of GCC-like compilers generate bogus
425 warnings for _Generic. This matters only for compilers that
426 lack relevant builtins. */
427 #if __GNUC__ || defined __clang__
428 # define _GL__GENERIC_BOGUS 1
429 #else
430 # define _GL__GENERIC_BOGUS 0
431 #endif
433 /* Store the low-order bits of A <op> B into *R, where OP specifies
434 the operation and OVERFLOW the overflow predicate. Return 1 if the
435 result overflows. See above for restrictions. */
436 #if 201112 <= __STDC_VERSION__ && !_GL__GENERIC_BOGUS
437 # define _GL_INT_OP_WRAPV(a, b, r, op, overflow) \
438 (_Generic \
439 (*(r), \
440 signed char: \
441 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
442 signed char, SCHAR_MIN, SCHAR_MAX), \
443 unsigned char: \
444 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
445 unsigned char, 0, UCHAR_MAX), \
446 short int: \
447 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
448 short int, SHRT_MIN, SHRT_MAX), \
449 unsigned short int: \
450 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
451 unsigned short int, 0, USHRT_MAX), \
452 int: \
453 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
454 int, INT_MIN, INT_MAX), \
455 unsigned int: \
456 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
457 unsigned int, 0, UINT_MAX), \
458 long int: \
459 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
460 long int, LONG_MIN, LONG_MAX), \
461 unsigned long int: \
462 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
463 unsigned long int, 0, ULONG_MAX), \
464 long long int: \
465 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
466 long long int, LLONG_MIN, LLONG_MAX), \
467 unsigned long long int: \
468 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
469 unsigned long long int, 0, ULLONG_MAX)))
470 #else
471 /* Store the low-order bits of A <op> B into *R, where OP specifies
472 the operation and OVERFLOW the overflow predicate. If *R is
473 signed, its type is ST with bounds SMIN..SMAX; otherwise its type
474 is UT with bounds U..UMAX. ST and UT are narrower than int.
475 Return 1 if the result overflows. See above for restrictions. */
476 # if _GL_HAVE___TYPEOF__
477 # define _GL_INT_OP_WRAPV_SMALLISH(a,b,r,op,overflow,st,smin,smax,ut,umax) \
478 (TYPE_SIGNED (__typeof__ (*(r))) \
479 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, st, smin, smax) \
480 : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, ut, 0, umax))
481 # else
482 # define _GL_INT_OP_WRAPV_SMALLISH(a,b,r,op,overflow,st,smin,smax,ut,umax) \
483 (overflow (a, b, smin, smax) \
484 ? (overflow (a, b, 0, umax) \
485 ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st), 1) \
486 : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st)) < 0) \
487 : (overflow (a, b, 0, umax) \
488 ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st)) >= 0 \
489 : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st), 0)))
490 # endif
492 # define _GL_INT_OP_WRAPV(a, b, r, op, overflow) \
493 (sizeof *(r) == sizeof (signed char) \
494 ? _GL_INT_OP_WRAPV_SMALLISH (a, b, r, op, overflow, \
495 signed char, SCHAR_MIN, SCHAR_MAX, \
496 unsigned char, UCHAR_MAX) \
497 : sizeof *(r) == sizeof (short int) \
498 ? _GL_INT_OP_WRAPV_SMALLISH (a, b, r, op, overflow, \
499 short int, SHRT_MIN, SHRT_MAX, \
500 unsigned short int, USHRT_MAX) \
501 : sizeof *(r) == sizeof (int) \
502 ? (EXPR_SIGNED (*(r)) \
503 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
504 int, INT_MIN, INT_MAX) \
505 : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
506 unsigned int, 0, UINT_MAX)) \
507 : _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow))
508 # ifdef LLONG_MAX
509 # define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
510 (sizeof *(r) == sizeof (long int) \
511 ? (EXPR_SIGNED (*(r)) \
512 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
513 long int, LONG_MIN, LONG_MAX) \
514 : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
515 unsigned long int, 0, ULONG_MAX)) \
516 : (EXPR_SIGNED (*(r)) \
517 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
518 long long int, LLONG_MIN, LLONG_MAX) \
519 : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
520 unsigned long long int, 0, ULLONG_MAX)))
521 # else
522 # define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
523 (EXPR_SIGNED (*(r)) \
524 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
525 long int, LONG_MIN, LONG_MAX) \
526 : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
527 unsigned long int, 0, ULONG_MAX))
528 # endif
529 #endif
531 /* Store the low-order bits of A <op> B into *R, where the operation
532 is given by OP. Use the unsigned type UT for calculation to avoid
533 overflow problems. *R's type is T, with extrema TMIN and TMAX.
534 T must be a signed integer type. Return 1 if the result overflows. */
535 #define _GL_INT_OP_CALC(a, b, r, op, overflow, ut, t, tmin, tmax) \
536 (overflow (a, b, tmin, tmax) \
537 ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 1) \
538 : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 0))
540 /* Return the low-order bits of A <op> B, where the operation is given
541 by OP. Use the unsigned type UT for calculation to avoid undefined
542 behavior on signed integer overflow, and convert the result to type T.
543 UT is at least as wide as T and is no narrower than unsigned int,
544 T is two's complement, and there is no padding or trap representations.
545 Assume that converting UT to T yields the low-order bits, as is
546 done in all known two's-complement C compilers. E.g., see:
547 https://gcc.gnu.org/onlinedocs/gcc/Integers-implementation.html
549 According to the C standard, converting UT to T yields an
550 implementation-defined result or signal for values outside T's
551 range. However, code that works around this theoretical problem
552 runs afoul of a compiler bug in Oracle Studio 12.3 x86. See:
553 https://lists.gnu.org/r/bug-gnulib/2017-04/msg00049.html
554 As the compiler bug is real, don't try to work around the
555 theoretical problem. */
557 #define _GL_INT_OP_WRAPV_VIA_UNSIGNED(a, b, op, ut, t) \
558 ((t) ((ut) (a) op (ut) (b)))
560 /* Return true if the numeric values A + B, A - B, A * B fall outside
561 the range TMIN..TMAX. Arguments should be integer expressions
562 without side effects. TMIN should be signed and nonpositive.
563 TMAX should be positive, and should be signed unless TMIN is zero. */
564 #define _GL_INT_ADD_RANGE_OVERFLOW(a, b, tmin, tmax) \
565 ((b) < 0 \
566 ? (((tmin) \
567 ? ((EXPR_SIGNED (_GL_INT_CONVERT (a, (tmin) - (b))) || (b) < (tmin)) \
568 && (a) < (tmin) - (b)) \
569 : (a) <= -1 - (b)) \
570 || ((EXPR_SIGNED (a) ? 0 <= (a) : (tmax) < (a)) && (tmax) < (a) + (b))) \
571 : (a) < 0 \
572 ? (((tmin) \
573 ? ((EXPR_SIGNED (_GL_INT_CONVERT (b, (tmin) - (a))) || (a) < (tmin)) \
574 && (b) < (tmin) - (a)) \
575 : (b) <= -1 - (a)) \
576 || ((EXPR_SIGNED (_GL_INT_CONVERT (a, b)) || (tmax) < (b)) \
577 && (tmax) < (a) + (b))) \
578 : (tmax) < (b) || (tmax) - (b) < (a))
579 #define _GL_INT_SUBTRACT_RANGE_OVERFLOW(a, b, tmin, tmax) \
580 (((a) < 0) == ((b) < 0) \
581 ? ((a) < (b) \
582 ? !(tmin) || -1 - (tmin) < (b) - (a) - 1 \
583 : (tmax) < (a) - (b)) \
584 : (a) < 0 \
585 ? ((!EXPR_SIGNED (_GL_INT_CONVERT ((a) - (tmin), b)) && (a) - (tmin) < 0) \
586 || (a) - (tmin) < (b)) \
587 : ((! (EXPR_SIGNED (_GL_INT_CONVERT (tmax, b)) \
588 && EXPR_SIGNED (_GL_INT_CONVERT ((tmax) + (b), a))) \
589 && (tmax) <= -1 - (b)) \
590 || (tmax) + (b) < (a)))
591 #define _GL_INT_MULTIPLY_RANGE_OVERFLOW(a, b, tmin, tmax) \
592 ((b) < 0 \
593 ? ((a) < 0 \
594 ? (EXPR_SIGNED (_GL_INT_CONVERT (tmax, b)) \
595 ? (a) < (tmax) / (b) \
596 : ((INT_NEGATE_OVERFLOW (b) \
597 ? _GL_INT_CONVERT (b, tmax) >> (TYPE_WIDTH (+ (b)) - 1) \
598 : (tmax) / -(b)) \
599 <= -1 - (a))) \
600 : INT_NEGATE_OVERFLOW (_GL_INT_CONVERT (b, tmin)) && (b) == -1 \
601 ? (EXPR_SIGNED (a) \
602 ? 0 < (a) + (tmin) \
603 : 0 < (a) && -1 - (tmin) < (a) - 1) \
604 : (tmin) / (b) < (a)) \
605 : (b) == 0 \
606 ? 0 \
607 : ((a) < 0 \
608 ? (INT_NEGATE_OVERFLOW (_GL_INT_CONVERT (a, tmin)) && (a) == -1 \
609 ? (EXPR_SIGNED (b) ? 0 < (b) + (tmin) : -1 - (tmin) < (b) - 1) \
610 : (tmin) / (a) < (b)) \
611 : (tmax) / (b) < (a)))
613 /* The following macros compute A + B, A - B, and A * B, respectively.
614 If no overflow occurs, they set *R to the result and return 1;
615 otherwise, they return 0 and may modify *R.
617 Example usage:
619 long int result;
620 if (INT_ADD_OK (a, b, &result))
621 printf ("result is %ld\n", result);
622 else
623 printf ("overflow\n");
625 A, B, and *R should be integers; they need not be the same type,
626 and they need not be all signed or all unsigned.
628 These macros work correctly on all known practical hosts, and do not rely
629 on undefined behavior due to signed arithmetic overflow.
631 These macros are not constant expressions.
633 These macros may evaluate their arguments zero or multiple times, so the
634 arguments should not have side effects.
636 These macros are tuned for B being a constant. */
638 #define INT_ADD_OK(a, b, r) ! INT_ADD_WRAPV (a, b, r)
639 #define INT_SUBTRACT_OK(a, b, r) ! INT_SUBTRACT_WRAPV (a, b, r)
640 #define INT_MULTIPLY_OK(a, b, r) ! INT_MULTIPLY_WRAPV (a, b, r)