1/* intprops.h -- properties of integer types
2
3 Copyright (C) 2001-2020 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/* Written by Paul Eggert. */
19
20#ifndef _GL_INTPROPS_H
21#define _GL_INTPROPS_H
22
23#include <limits.h>
24
25/* Return a value with the common real type of E and V and the value of V.
26 Do not evaluate E. */
27#define _GL_INT_CONVERT(e, v) ((1 ? 0 : (e)) + (v))
28
29/* Act like _GL_INT_CONVERT (E, -V) but work around a bug in IRIX 6.5 cc; see
30 <https://lists.gnu.org/r/bug-gnulib/2011-05/msg00406.html>. */
31#define _GL_INT_NEGATE_CONVERT(e, v) ((1 ? 0 : (e)) - (v))
32
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. */
38#define TYPE_IS_INTEGER(t) ((t) 1.5 == 1)
39
40/* True if the real type T is signed. */
41#define TYPE_SIGNED(t) (! ((t) 0 < (t) -1))
42
43/* Return 1 if the real expression E, after promotion, has a
44 signed or floating type. Do not evaluate E. */
45#define EXPR_SIGNED(e) (_GL_INT_NEGATE_CONVERT (e, 1) < 0)
46
47
48/* Minimum and maximum values for integer types and expressions. */
49
50/* The width in bits of the integer type or expression T.
51 Do not evaluate T.
52 Padding bits are not supported; this is checked at compile-time below. */
53#define TYPE_WIDTH(t) (sizeof (t) * CHAR_BIT)
54
55/* The maximum and minimum values for the integer type T. */
56#define TYPE_MINIMUM(t) ((t) ~ TYPE_MAXIMUM (t))
57#define TYPE_MAXIMUM(t) \
58 ((t) (! TYPE_SIGNED (t) \
59 ? (t) -1 \
60 : ((((t) 1 << (TYPE_WIDTH (t) - 2)) - 1) * 2 + 1)))
61
62/* The maximum and minimum values for the type of the expression E,
63 after integer promotion. E is not evaluated. */
64#define _GL_INT_MINIMUM(e) \
65 (EXPR_SIGNED (e) \
66 ? ~ _GL_SIGNED_INT_MAXIMUM (e) \
67 : _GL_INT_CONVERT (e, 0))
68#define _GL_INT_MAXIMUM(e) \
69 (EXPR_SIGNED (e) \
70 ? _GL_SIGNED_INT_MAXIMUM (e) \
71 : _GL_INT_NEGATE_CONVERT (e, 1))
72#define _GL_SIGNED_INT_MAXIMUM(e) \
73 (((_GL_INT_CONVERT (e, 1) << (TYPE_WIDTH ((e) + 0) - 2)) - 1) * 2 + 1)
74
75/* Work around OpenVMS incompatibility with C99. */
76#if !defined LLONG_MAX && defined __INT64_MAX
77# define LLONG_MAX __INT64_MAX
78# define LLONG_MIN __INT64_MIN
79#endif
80
81/* This include file assumes that signed types are two's complement without
82 padding bits; the above macros have undefined behavior otherwise.
83 If this is a problem for you, please let us know how to fix it for your host.
84 This assumption is tested by the intprops-tests module. */
85
86/* Does the __typeof__ keyword work? This could be done by
87 'configure', but for now it's easier to do it by hand. */
88#if (2 <= __GNUC__ \
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. This macro does not evaluate its argument,
98 and expands to an integer constant expression. */
99#if _GL_HAVE___TYPEOF__
100# define _GL_SIGNED_TYPE_OR_EXPR(t) TYPE_SIGNED (__typeof__ (t))
101#else
102# define _GL_SIGNED_TYPE_OR_EXPR(t) 1
103#endif
104
105/* Bound on length of the string representing an unsigned integer
106 value representable in B bits. log10 (2.0) < 146/485. The
107 smallest value of B where this bound is not tight is 2621. */
108#define INT_BITS_STRLEN_BOUND(b) (((b) * 146 + 484) / 485)
109
110/* Bound on length of the string representing an integer type or expression T.
111 Subtract 1 for the sign bit if T is signed, and then add 1 more for
112 a minus sign if needed.
113
114 Because _GL_SIGNED_TYPE_OR_EXPR sometimes returns 1 when its argument is
115 unsigned, this macro may overestimate the true bound by one byte when
116 applied to unsigned types of size 2, 4, 16, ... bytes. */
117#define INT_STRLEN_BOUND(t) \
118 (INT_BITS_STRLEN_BOUND (TYPE_WIDTH (t) - _GL_SIGNED_TYPE_OR_EXPR (t)) \
119 + _GL_SIGNED_TYPE_OR_EXPR (t))
120
121/* Bound on buffer size needed to represent an integer type or expression T,
122 including the terminating null. */
123#define INT_BUFSIZE_BOUND(t) (INT_STRLEN_BOUND (t) + 1)
124
125
126/* Range overflow checks.
127
128 The INT_<op>_RANGE_OVERFLOW macros return 1 if the corresponding C
129 operators might not yield numerically correct answers due to
130 arithmetic overflow. They do not rely on undefined or
131 implementation-defined behavior. Their implementations are simple
132 and straightforward, but they are a bit harder to use than the
133 INT_<op>_OVERFLOW macros described below.
134
135 Example usage:
136
137 long int i = ...;
138 long int j = ...;
139 if (INT_MULTIPLY_RANGE_OVERFLOW (i, j, LONG_MIN, LONG_MAX))
140 printf ("multiply would overflow");
141 else
142 printf ("product is %ld", i * j);
143
144 Restrictions on *_RANGE_OVERFLOW macros:
145
146 These macros do not check for all possible numerical problems or
147 undefined or unspecified behavior: they do not check for division
148 by zero, for bad shift counts, or for shifting negative numbers.
149
150 These macros may evaluate their arguments zero or multiple times,
151 so the arguments should not have side effects. The arithmetic
152 arguments (including the MIN and MAX arguments) must be of the same
153 integer type after the usual arithmetic conversions, and the type
154 must have minimum value MIN and maximum MAX. Unsigned types should
155 use a zero MIN of the proper type.
156
157 These macros are tuned for constant MIN and MAX. For commutative
158 operations such as A + B, they are also tuned for constant B. */
159
160/* Return 1 if A + B would overflow in [MIN,MAX] arithmetic.
161 See above for restrictions. */
162#define INT_ADD_RANGE_OVERFLOW(a, b, min, max) \
163 ((b) < 0 \
164 ? (a) < (min) - (b) \
165 : (max) - (b) < (a))
166
167/* Return 1 if A - B would overflow in [MIN,MAX] arithmetic.
168 See above for restrictions. */
169#define INT_SUBTRACT_RANGE_OVERFLOW(a, b, min, max) \
170 ((b) < 0 \
171 ? (max) + (b) < (a) \
172 : (a) < (min) + (b))
173
174/* Return 1 if - A would overflow in [MIN,MAX] arithmetic.
175 See above for restrictions. */
176#define INT_NEGATE_RANGE_OVERFLOW(a, min, max) \
177 ((min) < 0 \
178 ? (a) < - (max) \
179 : 0 < (a))
180
181/* Return 1 if A * B would overflow in [MIN,MAX] arithmetic.
182 See above for restrictions. Avoid && and || as they tickle
183 bugs in Sun C 5.11 2010/08/13 and other compilers; see
184 <https://lists.gnu.org/r/bug-gnulib/2011-05/msg00401.html>. */
185#define INT_MULTIPLY_RANGE_OVERFLOW(a, b, min, max) \
186 ((b) < 0 \
187 ? ((a) < 0 \
188 ? (a) < (max) / (b) \
189 : (b) == -1 \
190 ? 0 \
191 : (min) / (b) < (a)) \
192 : (b) == 0 \
193 ? 0 \
194 : ((a) < 0 \
195 ? (a) < (min) / (b) \
196 : (max) / (b) < (a)))
197
198/* Return 1 if A / B would overflow in [MIN,MAX] arithmetic.
199 See above for restrictions. Do not check for division by zero. */
200#define INT_DIVIDE_RANGE_OVERFLOW(a, b, min, max) \
201 ((min) < 0 && (b) == -1 && (a) < - (max))
202
203/* Return 1 if A % B would overflow in [MIN,MAX] arithmetic.
204 See above for restrictions. Do not check for division by zero.
205 Mathematically, % should never overflow, but on x86-like hosts
206 INT_MIN % -1 traps, and the C standard permits this, so treat this
207 as an overflow too. */
208#define INT_REMAINDER_RANGE_OVERFLOW(a, b, min, max) \
209 INT_DIVIDE_RANGE_OVERFLOW (a, b, min, max)
210
211/* Return 1 if A << B would overflow in [MIN,MAX] arithmetic.
212 See above for restrictions. Here, MIN and MAX are for A only, and B need
213 not be of the same type as the other arguments. The C standard says that
214 behavior is undefined for shifts unless 0 <= B < wordwidth, and that when
215 A is negative then A << B has undefined behavior and A >> B has
216 implementation-defined behavior, but do not check these other
217 restrictions. */
218#define INT_LEFT_SHIFT_RANGE_OVERFLOW(a, b, min, max) \
219 ((a) < 0 \
220 ? (a) < (min) >> (b) \
221 : (max) >> (b) < (a))
222
223/* True if __builtin_add_overflow (A, B, P) and __builtin_sub_overflow
224 (A, B, P) work when P is non-null. */
225#if 5 <= __GNUC__ && !defined __ICC
226# define _GL_HAS_BUILTIN_ADD_OVERFLOW 1
227#elif defined __has_builtin
228# define _GL_HAS_BUILTIN_ADD_OVERFLOW __has_builtin (__builtin_add_overflow)
229#else
230# define _GL_HAS_BUILTIN_ADD_OVERFLOW 0
231#endif
232
233/* True if __builtin_mul_overflow (A, B, P) works when P is non-null. */
234#ifdef __clang__
235/* Work around Clang bug <https://bugs.llvm.org/show_bug.cgi?id=16404>. */
236# define _GL_HAS_BUILTIN_MUL_OVERFLOW 0
237#else
238# define _GL_HAS_BUILTIN_MUL_OVERFLOW _GL_HAS_BUILTIN_ADD_OVERFLOW
239#endif
240
241/* True if __builtin_add_overflow_p (A, B, C) works, and similarly for
242 __builtin_mul_overflow_p and __builtin_mul_overflow_p. */
243#define _GL_HAS_BUILTIN_OVERFLOW_P (7 <= __GNUC__)
244
245/* The _GL*_OVERFLOW macros have the same restrictions as the
246 *_RANGE_OVERFLOW macros, except that they do not assume that operands
247 (e.g., A and B) have the same type as MIN and MAX. Instead, they assume
248 that the result (e.g., A + B) has that type. */
249#if _GL_HAS_BUILTIN_OVERFLOW_P
250# define _GL_ADD_OVERFLOW(a, b, min, max) \
251 __builtin_add_overflow_p (a, b, (__typeof__ ((a) + (b))) 0)
252# define _GL_SUBTRACT_OVERFLOW(a, b, min, max) \
253 __builtin_sub_overflow_p (a, b, (__typeof__ ((a) - (b))) 0)
254# define _GL_MULTIPLY_OVERFLOW(a, b, min, max) \
255 __builtin_mul_overflow_p (a, b, (__typeof__ ((a) * (b))) 0)
256#else
257# define _GL_ADD_OVERFLOW(a, b, min, max) \
258 ((min) < 0 ? INT_ADD_RANGE_OVERFLOW (a, b, min, max) \
259 : (a) < 0 ? (b) <= (a) + (b) \
260 : (b) < 0 ? (a) <= (a) + (b) \
261 : (a) + (b) < (b))
262# define _GL_SUBTRACT_OVERFLOW(a, b, min, max) \
263 ((min) < 0 ? INT_SUBTRACT_RANGE_OVERFLOW (a, b, min, max) \
264 : (a) < 0 ? 1 \
265 : (b) < 0 ? (a) - (b) <= (a) \
266 : (a) < (b))
267# define _GL_MULTIPLY_OVERFLOW(a, b, min, max) \
268 (((min) == 0 && (((a) < 0 && 0 < (b)) || ((b) < 0 && 0 < (a)))) \
269 || INT_MULTIPLY_RANGE_OVERFLOW (a, b, min, max))
270#endif
271#define _GL_DIVIDE_OVERFLOW(a, b, min, max) \
272 ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max) \
273 : (a) < 0 ? (b) <= (a) + (b) - 1 \
274 : (b) < 0 && (a) + (b) <= (a))
275#define _GL_REMAINDER_OVERFLOW(a, b, min, max) \
276 ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max) \
277 : (a) < 0 ? (a) % (b) != ((max) - (b) + 1) % (b) \
278 : (b) < 0 && ! _GL_UNSIGNED_NEG_MULTIPLE (a, b, max))
279
280/* Return a nonzero value if A is a mathematical multiple of B, where
281 A is unsigned, B is negative, and MAX is the maximum value of A's
282 type. A's type must be the same as (A % B)'s type. Normally (A %
283 -B == 0) suffices, but things get tricky if -B would overflow. */
284#define _GL_UNSIGNED_NEG_MULTIPLE(a, b, max) \
285 (((b) < -_GL_SIGNED_INT_MAXIMUM (b) \
286 ? (_GL_SIGNED_INT_MAXIMUM (b) == (max) \
287 ? (a) \
288 : (a) % (_GL_INT_CONVERT (a, _GL_SIGNED_INT_MAXIMUM (b)) + 1)) \
289 : (a) % - (b)) \
290 == 0)
291
292/* Check for integer overflow, and report low order bits of answer.
293
294 The INT_<op>_OVERFLOW macros return 1 if the corresponding C operators
295 might not yield numerically correct answers due to arithmetic overflow.
296 The INT_<op>_WRAPV macros compute the low-order bits of the sum,
297 difference, and product of two C integers, and return 1 if these
298 low-order bits are not numerically correct.
299 These macros work correctly on all known practical hosts, and do not rely
300 on undefined behavior due to signed arithmetic overflow.
301
302 Example usage, assuming A and B are long int:
303
304 if (INT_MULTIPLY_OVERFLOW (a, b))
305 printf ("result would overflow\n");
306 else
307 printf ("result is %ld (no overflow)\n", a * b);
308
309 Example usage with WRAPV flavor:
310
311 long int result;
312 bool overflow = INT_MULTIPLY_WRAPV (a, b, &result);
313 printf ("result is %ld (%s)\n", result,
314 overflow ? "after overflow" : "no overflow");
315
316 Restrictions on these macros:
317
318 These macros do not check for all possible numerical problems or
319 undefined or unspecified behavior: they do not check for division
320 by zero, for bad shift counts, or for shifting negative numbers.
321
322 These macros may evaluate their arguments zero or multiple times, so the
323 arguments should not have side effects.
324
325 The WRAPV macros are not constant expressions. They support only
326 +, binary -, and *. Because the WRAPV macros convert the result,
327 they report overflow in different circumstances than the OVERFLOW
328 macros do.
329
330 These macros are tuned for their last input argument being a constant.
331
332 Return 1 if the integer expressions A * B, A - B, -A, A * B, A / B,
333 A % B, and A << B would overflow, respectively. */
334
335#define INT_ADD_OVERFLOW(a, b) \
336 _GL_BINARY_OP_OVERFLOW (a, b, _GL_ADD_OVERFLOW)
337#define INT_SUBTRACT_OVERFLOW(a, b) \
338 _GL_BINARY_OP_OVERFLOW (a, b, _GL_SUBTRACT_OVERFLOW)
339#if _GL_HAS_BUILTIN_OVERFLOW_P
340# define INT_NEGATE_OVERFLOW(a) INT_SUBTRACT_OVERFLOW (0, a)
341#else
342# define INT_NEGATE_OVERFLOW(a) \
343 INT_NEGATE_RANGE_OVERFLOW (a, _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
344#endif
345#define INT_MULTIPLY_OVERFLOW(a, b) \
346 _GL_BINARY_OP_OVERFLOW (a, b, _GL_MULTIPLY_OVERFLOW)
347#define INT_DIVIDE_OVERFLOW(a, b) \
348 _GL_BINARY_OP_OVERFLOW (a, b, _GL_DIVIDE_OVERFLOW)
349#define INT_REMAINDER_OVERFLOW(a, b) \
350 _GL_BINARY_OP_OVERFLOW (a, b, _GL_REMAINDER_OVERFLOW)
351#define INT_LEFT_SHIFT_OVERFLOW(a, b) \
352 INT_LEFT_SHIFT_RANGE_OVERFLOW (a, b, \
353 _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
354
355/* Return 1 if the expression A <op> B would overflow,
356 where OP_RESULT_OVERFLOW (A, B, MIN, MAX) does the actual test,
357 assuming MIN and MAX are the minimum and maximum for the result type.
358 Arguments should be free of side effects. */
359#define _GL_BINARY_OP_OVERFLOW(a, b, op_result_overflow) \
360 op_result_overflow (a, b, \
361 _GL_INT_MINIMUM (_GL_INT_CONVERT (a, b)), \
362 _GL_INT_MAXIMUM (_GL_INT_CONVERT (a, b)))
363
364/* Store the low-order bits of A + B, A - B, A * B, respectively, into *R.
365 Return 1 if the result overflows. See above for restrictions. */
366#if _GL_HAS_BUILTIN_ADD_OVERFLOW
367# define INT_ADD_WRAPV(a, b, r) __builtin_add_overflow (a, b, r)
368# define INT_SUBTRACT_WRAPV(a, b, r) __builtin_sub_overflow (a, b, r)
369#else
370# define INT_ADD_WRAPV(a, b, r) \
371 _GL_INT_OP_WRAPV (a, b, r, +, _GL_INT_ADD_RANGE_OVERFLOW)
372# define INT_SUBTRACT_WRAPV(a, b, r) \
373 _GL_INT_OP_WRAPV (a, b, r, -, _GL_INT_SUBTRACT_RANGE_OVERFLOW)
374#endif
375#if _GL_HAS_BUILTIN_MUL_OVERFLOW
376/* Work around GCC bug 91450. */
377# define INT_MULTIPLY_WRAPV(a, b, r) \
378 ((!_GL_SIGNED_TYPE_OR_EXPR (*(r)) && EXPR_SIGNED (a) && EXPR_SIGNED (b) \
379 && _GL_INT_MULTIPLY_RANGE_OVERFLOW (a, b, 0, (__typeof__ (*(r))) -1)) \
380 ? ((void) __builtin_mul_overflow (a, b, r), 1) \
381 : __builtin_mul_overflow (a, b, r))
382#else
383# define INT_MULTIPLY_WRAPV(a, b, r) \
384 _GL_INT_OP_WRAPV (a, b, r, *, _GL_INT_MULTIPLY_RANGE_OVERFLOW)
385#endif
386
387/* Nonzero if this compiler has GCC bug 68193 or Clang bug 25390. See:
388 https://gcc.gnu.org/bugzilla/show_bug.cgi?id=68193
389 https://llvm.org/bugs/show_bug.cgi?id=25390
390 For now, assume all versions of GCC-like compilers generate bogus
391 warnings for _Generic. This matters only for compilers that
392 lack relevant builtins. */
393#if __GNUC__
394# define _GL__GENERIC_BOGUS 1
395#else
396# define _GL__GENERIC_BOGUS 0
397#endif
398
399/* Store the low-order bits of A <op> B into *R, where OP specifies
400 the operation and OVERFLOW the overflow predicate. Return 1 if the
401 result overflows. See above for restrictions. */
402#if 201112 <= __STDC_VERSION__ && !_GL__GENERIC_BOGUS
403# define _GL_INT_OP_WRAPV(a, b, r, op, overflow) \
404 (_Generic \
405 (*(r), \
406 signed char: \
407 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
408 signed char, SCHAR_MIN, SCHAR_MAX), \
409 unsigned char: \
410 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
411 unsigned char, 0, UCHAR_MAX), \
412 short int: \
413 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
414 short int, SHRT_MIN, SHRT_MAX), \
415 unsigned short int: \
416 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
417 unsigned short int, 0, USHRT_MAX), \
418 int: \
419 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
420 int, INT_MIN, INT_MAX), \
421 unsigned int: \
422 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
423 unsigned int, 0, UINT_MAX), \
424 long int: \
425 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
426 long int, LONG_MIN, LONG_MAX), \
427 unsigned long int: \
428 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
429 unsigned long int, 0, ULONG_MAX), \
430 long long int: \
431 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
432 long long int, LLONG_MIN, LLONG_MAX), \
433 unsigned long long int: \
434 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
435 unsigned long long int, 0, ULLONG_MAX)))
436#else
437/* Store the low-order bits of A <op> B into *R, where OP specifies
438 the operation and OVERFLOW the overflow predicate. If *R is
439 signed, its type is ST with bounds SMIN..SMAX; otherwise its type
440 is UT with bounds U..UMAX. ST and UT are narrower than int.
441 Return 1 if the result overflows. See above for restrictions. */
442# if _GL_HAVE___TYPEOF__
443# define _GL_INT_OP_WRAPV_SMALLISH(a,b,r,op,overflow,st,smin,smax,ut,umax) \
444 (TYPE_SIGNED (__typeof__ (*(r))) \
445 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, st, smin, smax) \
446 : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, ut, 0, umax))
447# else
448# define _GL_INT_OP_WRAPV_SMALLISH(a,b,r,op,overflow,st,smin,smax,ut,umax) \
449 (overflow (a, b, smin, smax) \
450 ? (overflow (a, b, 0, umax) \
451 ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st), 1) \
452 : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st)) < 0) \
453 : (overflow (a, b, 0, umax) \
454 ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st)) >= 0 \
455 : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st), 0)))
456# endif
457
458# define _GL_INT_OP_WRAPV(a, b, r, op, overflow) \
459 (sizeof *(r) == sizeof (signed char) \
460 ? _GL_INT_OP_WRAPV_SMALLISH (a, b, r, op, overflow, \
461 signed char, SCHAR_MIN, SCHAR_MAX, \
462 unsigned char, UCHAR_MAX) \
463 : sizeof *(r) == sizeof (short int) \
464 ? _GL_INT_OP_WRAPV_SMALLISH (a, b, r, op, overflow, \
465 short int, SHRT_MIN, SHRT_MAX, \
466 unsigned short int, USHRT_MAX) \
467 : sizeof *(r) == sizeof (int) \
468 ? (EXPR_SIGNED (*(r)) \
469 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
470 int, INT_MIN, INT_MAX) \
471 : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
472 unsigned int, 0, UINT_MAX)) \
473 : _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow))
474# ifdef LLONG_MAX
475# define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
476 (sizeof *(r) == sizeof (long int) \
477 ? (EXPR_SIGNED (*(r)) \
478 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
479 long int, LONG_MIN, LONG_MAX) \
480 : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
481 unsigned long int, 0, ULONG_MAX)) \
482 : (EXPR_SIGNED (*(r)) \
483 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
484 long long int, LLONG_MIN, LLONG_MAX) \
485 : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
486 unsigned long long int, 0, ULLONG_MAX)))
487# else
488# define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
489 (EXPR_SIGNED (*(r)) \
490 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
491 long int, LONG_MIN, LONG_MAX) \
492 : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
493 unsigned long int, 0, ULONG_MAX))
494# endif
495#endif
496
497/* Store the low-order bits of A <op> B into *R, where the operation
498 is given by OP. Use the unsigned type UT for calculation to avoid
499 overflow problems. *R's type is T, with extrema TMIN and TMAX.
500 T must be a signed integer type. Return 1 if the result overflows. */
501#define _GL_INT_OP_CALC(a, b, r, op, overflow, ut, t, tmin, tmax) \
502 (overflow (a, b, tmin, tmax) \
503 ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 1) \
504 : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 0))
505
506/* Return the low-order bits of A <op> B, where the operation is given
507 by OP. Use the unsigned type UT for calculation to avoid undefined
508 behavior on signed integer overflow, and convert the result to type T.
509 UT is at least as wide as T and is no narrower than unsigned int,
510 T is two's complement, and there is no padding or trap representations.
511 Assume that converting UT to T yields the low-order bits, as is
512 done in all known two's-complement C compilers. E.g., see:
513 https://gcc.gnu.org/onlinedocs/gcc/Integers-implementation.html
514
515 According to the C standard, converting UT to T yields an
516 implementation-defined result or signal for values outside T's
517 range. However, code that works around this theoretical problem
518 runs afoul of a compiler bug in Oracle Studio 12.3 x86. See:
519 https://lists.gnu.org/r/bug-gnulib/2017-04/msg00049.html
520 As the compiler bug is real, don't try to work around the
521 theoretical problem. */
522
523#define _GL_INT_OP_WRAPV_VIA_UNSIGNED(a, b, op, ut, t) \
524 ((t) ((ut) (a) op (ut) (b)))
525
526/* Return true if the numeric values A + B, A - B, A * B fall outside
527 the range TMIN..TMAX. Arguments should be integer expressions
528 without side effects. TMIN should be signed and nonpositive.
529 TMAX should be positive, and should be signed unless TMIN is zero. */
530#define _GL_INT_ADD_RANGE_OVERFLOW(a, b, tmin, tmax) \
531 ((b) < 0 \
532 ? (((tmin) \
533 ? ((EXPR_SIGNED (_GL_INT_CONVERT (a, (tmin) - (b))) || (b) < (tmin)) \
534 && (a) < (tmin) - (b)) \
535 : (a) <= -1 - (b)) \
536 || ((EXPR_SIGNED (a) ? 0 <= (a) : (tmax) < (a)) && (tmax) < (a) + (b))) \
537 : (a) < 0 \
538 ? (((tmin) \
539 ? ((EXPR_SIGNED (_GL_INT_CONVERT (b, (tmin) - (a))) || (a) < (tmin)) \
540 && (b) < (tmin) - (a)) \
541 : (b) <= -1 - (a)) \
542 || ((EXPR_SIGNED (_GL_INT_CONVERT (a, b)) || (tmax) < (b)) \
543 && (tmax) < (a) + (b))) \
544 : (tmax) < (b) || (tmax) - (b) < (a))
545#define _GL_INT_SUBTRACT_RANGE_OVERFLOW(a, b, tmin, tmax) \
546 (((a) < 0) == ((b) < 0) \
547 ? ((a) < (b) \
548 ? !(tmin) || -1 - (tmin) < (b) - (a) - 1 \
549 : (tmax) < (a) - (b)) \
550 : (a) < 0 \
551 ? ((!EXPR_SIGNED (_GL_INT_CONVERT ((a) - (tmin), b)) && (a) - (tmin) < 0) \
552 || (a) - (tmin) < (b)) \
553 : ((! (EXPR_SIGNED (_GL_INT_CONVERT (tmax, b)) \
554 && EXPR_SIGNED (_GL_INT_CONVERT ((tmax) + (b), a))) \
555 && (tmax) <= -1 - (b)) \
556 || (tmax) + (b) < (a)))
557#define _GL_INT_MULTIPLY_RANGE_OVERFLOW(a, b, tmin, tmax) \
558 ((b) < 0 \
559 ? ((a) < 0 \
560 ? (EXPR_SIGNED (_GL_INT_CONVERT (tmax, b)) \
561 ? (a) < (tmax) / (b) \
562 : ((INT_NEGATE_OVERFLOW (b) \
563 ? _GL_INT_CONVERT (b, tmax) >> (TYPE_WIDTH (b) - 1) \
564 : (tmax) / -(b)) \
565 <= -1 - (a))) \
566 : INT_NEGATE_OVERFLOW (_GL_INT_CONVERT (b, tmin)) && (b) == -1 \
567 ? (EXPR_SIGNED (a) \
568 ? 0 < (a) + (tmin) \
569 : 0 < (a) && -1 - (tmin) < (a) - 1) \
570 : (tmin) / (b) < (a)) \
571 : (b) == 0 \
572 ? 0 \
573 : ((a) < 0 \
574 ? (INT_NEGATE_OVERFLOW (_GL_INT_CONVERT (a, tmin)) && (a) == -1 \
575 ? (EXPR_SIGNED (b) ? 0 < (b) + (tmin) : -1 - (tmin) < (b) - 1) \
576 : (tmin) / (a) < (b)) \
577 : (tmax) / (b) < (a)))
578
579#endif /* _GL_INTPROPS_H */
580