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/* 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. T must not be a bit-field expression.
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)) - 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 || (4 <= __clang_major__) \
90 || (1210 <= __IBMC__ && defined __IBM__TYPEOF__) \
91 || (0x5110 <= __SUNPRO_C && !__STDC__))
92# define _GL_HAVE___TYPEOF__ 1
93#else
94# define _GL_HAVE___TYPEOF__ 0
95#endif
96
97/* Return 1 if the integer type or expression T might be signed. Return 0
98 if it is definitely unsigned. T must not be a bit-field expression.
99 This macro does not evaluate its argument, and expands to an
100 integer constant expression. */
101#if _GL_HAVE___TYPEOF__
102# define _GL_SIGNED_TYPE_OR_EXPR(t) TYPE_SIGNED (__typeof__ (t))
103#else
104# define _GL_SIGNED_TYPE_OR_EXPR(t) 1
105#endif
106
107/* Bound on length of the string representing an unsigned integer
108 value representable in B bits. log10 (2.0) < 146/485. The
109 smallest value of B where this bound is not tight is 2621. */
110#define INT_BITS_STRLEN_BOUND(b) (((b) * 146 + 484) / 485)
111
112/* Bound on length of the string representing an integer type or expression T.
113 T must not be a bit-field expression.
114
115 Subtract 1 for the sign bit if T is signed, and then add 1 more for
116 a minus sign if needed.
117
118 Because _GL_SIGNED_TYPE_OR_EXPR sometimes returns 1 when its argument is
119 unsigned, this macro may overestimate the true bound by one byte when
120 applied to unsigned types of size 2, 4, 16, ... bytes. */
121#define INT_STRLEN_BOUND(t) \
122 (INT_BITS_STRLEN_BOUND (TYPE_WIDTH (t) - _GL_SIGNED_TYPE_OR_EXPR (t)) \
123 + _GL_SIGNED_TYPE_OR_EXPR (t))
124
125/* Bound on buffer size needed to represent an integer type or expression T,
126 including the terminating null. T must not be a bit-field expression. */
127#define INT_BUFSIZE_BOUND(t) (INT_STRLEN_BOUND (t) + 1)
128
129
130/* Range overflow checks.
131
132 The INT_<op>_RANGE_OVERFLOW macros return 1 if the corresponding C
133 operators might not yield numerically correct answers due to
134 arithmetic overflow. They do not rely on undefined or
135 implementation-defined behavior. Their implementations are simple
136 and straightforward, but they are a bit harder to use than the
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 These macros are tuned for constant MIN and MAX. For commutative
162 operations such as A + B, they are also tuned for constant B. */
163
164/* Return 1 if A + B would overflow in [MIN,MAX] arithmetic.
165 See above for restrictions. */
166#define INT_ADD_RANGE_OVERFLOW(a, b, min, max) \
167 ((b) < 0 \
168 ? (a) < (min) - (b) \
169 : (max) - (b) < (a))
170
171/* Return 1 if A - B would overflow in [MIN,MAX] arithmetic.
172 See above for restrictions. */
173#define INT_SUBTRACT_RANGE_OVERFLOW(a, b, min, max) \
174 ((b) < 0 \
175 ? (max) + (b) < (a) \
176 : (a) < (min) + (b))
177
178/* Return 1 if - A would overflow in [MIN,MAX] arithmetic.
179 See above for restrictions. */
180#define INT_NEGATE_RANGE_OVERFLOW(a, min, max) \
181 ((min) < 0 \
182 ? (a) < - (max) \
183 : 0 < (a))
184
185/* Return 1 if A * B would overflow in [MIN,MAX] arithmetic.
186 See above for restrictions. Avoid && and || as they tickle
187 bugs in Sun C 5.11 2010/08/13 and other compilers; see
188 <https://lists.gnu.org/r/bug-gnulib/2011-05/msg00401.html>. */
189#define INT_MULTIPLY_RANGE_OVERFLOW(a, b, min, max) \
190 ((b) < 0 \
191 ? ((a) < 0 \
192 ? (a) < (max) / (b) \
193 : (b) == -1 \
194 ? 0 \
195 : (min) / (b) < (a)) \
196 : (b) == 0 \
197 ? 0 \
198 : ((a) < 0 \
199 ? (a) < (min) / (b) \
200 : (max) / (b) < (a)))
201
202/* Return 1 if A / B would overflow in [MIN,MAX] arithmetic.
203 See above for restrictions. Do not check for division by zero. */
204#define INT_DIVIDE_RANGE_OVERFLOW(a, b, min, max) \
205 ((min) < 0 && (b) == -1 && (a) < - (max))
206
207/* Return 1 if A % B would overflow in [MIN,MAX] arithmetic.
208 See above for restrictions. Do not check for division by zero.
209 Mathematically, % should never overflow, but on x86-like hosts
210 INT_MIN % -1 traps, and the C standard permits this, so treat this
211 as an overflow too. */
212#define INT_REMAINDER_RANGE_OVERFLOW(a, b, min, max) \
213 INT_DIVIDE_RANGE_OVERFLOW (a, b, min, max)
214
215/* Return 1 if A << B would overflow in [MIN,MAX] arithmetic.
216 See above for restrictions. Here, MIN and MAX are for A only, and B need
217 not be of the same type as the other arguments. The C standard says that
218 behavior is undefined for shifts unless 0 <= B < wordwidth, and that when
219 A is negative then A << B has undefined behavior and A >> B has
220 implementation-defined behavior, but do not check these other
221 restrictions. */
222#define INT_LEFT_SHIFT_RANGE_OVERFLOW(a, b, min, max) \
223 ((a) < 0 \
224 ? (a) < (min) >> (b) \
225 : (max) >> (b) < (a))
226
227/* True if __builtin_add_overflow (A, B, P) and __builtin_sub_overflow
228 (A, B, P) work when P is non-null. */
229/* __builtin_{add,sub}_overflow exists but is not reliable in GCC 5.x and 6.x,
230 see <https://gcc.gnu.org/bugzilla/show_bug.cgi?id=98269>. */
231#if 7 <= __GNUC__ && !defined __ICC
232# define _GL_HAS_BUILTIN_ADD_OVERFLOW 1
233#elif defined __has_builtin
234# define _GL_HAS_BUILTIN_ADD_OVERFLOW __has_builtin (__builtin_add_overflow)
235#else
236# define _GL_HAS_BUILTIN_ADD_OVERFLOW 0
237#endif
238
239/* True if __builtin_mul_overflow (A, B, P) works when P is non-null. */
240#ifdef __clang__
241/* Work around Clang bug <https://bugs.llvm.org/show_bug.cgi?id=16404>. */
242# define _GL_HAS_BUILTIN_MUL_OVERFLOW 0
243#else
244# define _GL_HAS_BUILTIN_MUL_OVERFLOW _GL_HAS_BUILTIN_ADD_OVERFLOW
245#endif
246
247/* True if __builtin_add_overflow_p (A, B, C) works, and similarly for
248 __builtin_sub_overflow_p and __builtin_mul_overflow_p. */
249#if defined __clang__ || defined __ICC
250/* Clang 11 lacks __builtin_mul_overflow_p, and even if it did it
251 would presumably run afoul of Clang bug 16404. ICC 2021.1's
252 __builtin_add_overflow_p etc. are not treated as integral constant
253 expressions even when all arguments are. */
254# define _GL_HAS_BUILTIN_OVERFLOW_P 0
255#elif defined __has_builtin
256# define _GL_HAS_BUILTIN_OVERFLOW_P __has_builtin (__builtin_mul_overflow_p)
257#else
258# define _GL_HAS_BUILTIN_OVERFLOW_P (7 <= __GNUC__)
259#endif
260
261/* The _GL*_OVERFLOW macros have the same restrictions as the
262 *_RANGE_OVERFLOW macros, except that they do not assume that operands
263 (e.g., A and B) have the same type as MIN and MAX. Instead, they assume
264 that the result (e.g., A + B) has that type. */
265#if _GL_HAS_BUILTIN_OVERFLOW_P
266# define _GL_ADD_OVERFLOW(a, b, min, max) \
267 __builtin_add_overflow_p (a, b, (__typeof__ ((a) + (b))) 0)
268# define _GL_SUBTRACT_OVERFLOW(a, b, min, max) \
269 __builtin_sub_overflow_p (a, b, (__typeof__ ((a) - (b))) 0)
270# define _GL_MULTIPLY_OVERFLOW(a, b, min, max) \
271 __builtin_mul_overflow_p (a, b, (__typeof__ ((a) * (b))) 0)
272#else
273# define _GL_ADD_OVERFLOW(a, b, min, max) \
274 ((min) < 0 ? INT_ADD_RANGE_OVERFLOW (a, b, min, max) \
275 : (a) < 0 ? (b) <= (a) + (b) \
276 : (b) < 0 ? (a) <= (a) + (b) \
277 : (a) + (b) < (b))
278# define _GL_SUBTRACT_OVERFLOW(a, b, min, max) \
279 ((min) < 0 ? INT_SUBTRACT_RANGE_OVERFLOW (a, b, min, max) \
280 : (a) < 0 ? 1 \
281 : (b) < 0 ? (a) - (b) <= (a) \
282 : (a) < (b))
283# define _GL_MULTIPLY_OVERFLOW(a, b, min, max) \
284 (((min) == 0 && (((a) < 0 && 0 < (b)) || ((b) < 0 && 0 < (a)))) \
285 || INT_MULTIPLY_RANGE_OVERFLOW (a, b, min, max))
286#endif
287#define _GL_DIVIDE_OVERFLOW(a, b, min, max) \
288 ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max) \
289 : (a) < 0 ? (b) <= (a) + (b) - 1 \
290 : (b) < 0 && (a) + (b) <= (a))
291#define _GL_REMAINDER_OVERFLOW(a, b, min, max) \
292 ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max) \
293 : (a) < 0 ? (a) % (b) != ((max) - (b) + 1) % (b) \
294 : (b) < 0 && ! _GL_UNSIGNED_NEG_MULTIPLE (a, b, max))
295
296/* Return a nonzero value if A is a mathematical multiple of B, where
297 A is unsigned, B is negative, and MAX is the maximum value of A's
298 type. A's type must be the same as (A % B)'s type. Normally (A %
299 -B == 0) suffices, but things get tricky if -B would overflow. */
300#define _GL_UNSIGNED_NEG_MULTIPLE(a, b, max) \
301 (((b) < -_GL_SIGNED_INT_MAXIMUM (b) \
302 ? (_GL_SIGNED_INT_MAXIMUM (b) == (max) \
303 ? (a) \
304 : (a) % (_GL_INT_CONVERT (a, _GL_SIGNED_INT_MAXIMUM (b)) + 1)) \
305 : (a) % - (b)) \
306 == 0)
307
308/* Check for integer overflow, and report low order bits of answer.
309
310 The INT_<op>_OVERFLOW macros return 1 if the corresponding C operators
311 might not yield numerically correct answers due to arithmetic overflow.
312 The INT_<op>_WRAPV macros compute the low-order bits of the sum,
313 difference, and product of two C integers, and return 1 if these
314 low-order bits are not numerically correct.
315 These macros work correctly on all known practical hosts, and do not rely
316 on undefined behavior due to signed arithmetic overflow.
317
318 Example usage, assuming A and B are long int:
319
320 if (INT_MULTIPLY_OVERFLOW (a, b))
321 printf ("result would overflow\n");
322 else
323 printf ("result is %ld (no overflow)\n", a * b);
324
325 Example usage with WRAPV flavor:
326
327 long int result;
328 bool overflow = INT_MULTIPLY_WRAPV (a, b, &result);
329 printf ("result is %ld (%s)\n", result,
330 overflow ? "after overflow" : "no overflow");
331
332 Restrictions on these macros:
333
334 These macros do not check for all possible numerical problems or
335 undefined or unspecified behavior: they do not check for division
336 by zero, for bad shift counts, or for shifting negative numbers.
337
338 These macros may evaluate their arguments zero or multiple times, so the
339 arguments should not have side effects.
340
341 The WRAPV macros are not constant expressions. They support only
342 +, binary -, and *. Because the WRAPV macros convert the result,
343 they report overflow in different circumstances than the OVERFLOW
344 macros do.
345
346 These macros are tuned for their last input argument being a constant.
347
348 Return 1 if the integer expressions A * B, A - B, -A, A * B, A / B,
349 A % B, and A << B would overflow, respectively. */
350
351#define INT_ADD_OVERFLOW(a, b) \
352 _GL_BINARY_OP_OVERFLOW (a, b, _GL_ADD_OVERFLOW)
353#define INT_SUBTRACT_OVERFLOW(a, b) \
354 _GL_BINARY_OP_OVERFLOW (a, b, _GL_SUBTRACT_OVERFLOW)
355#if _GL_HAS_BUILTIN_OVERFLOW_P
356# define INT_NEGATE_OVERFLOW(a) INT_SUBTRACT_OVERFLOW (0, a)
357#else
358# define INT_NEGATE_OVERFLOW(a) \
359 INT_NEGATE_RANGE_OVERFLOW (a, _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
360#endif
361#define INT_MULTIPLY_OVERFLOW(a, b) \
362 _GL_BINARY_OP_OVERFLOW (a, b, _GL_MULTIPLY_OVERFLOW)
363#define INT_DIVIDE_OVERFLOW(a, b) \
364 _GL_BINARY_OP_OVERFLOW (a, b, _GL_DIVIDE_OVERFLOW)
365#define INT_REMAINDER_OVERFLOW(a, b) \
366 _GL_BINARY_OP_OVERFLOW (a, b, _GL_REMAINDER_OVERFLOW)
367#define INT_LEFT_SHIFT_OVERFLOW(a, b) \
368 INT_LEFT_SHIFT_RANGE_OVERFLOW (a, b, \
369 _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
370
371/* Return 1 if the expression A <op> B would overflow,
372 where OP_RESULT_OVERFLOW (A, B, MIN, MAX) does the actual test,
373 assuming MIN and MAX are the minimum and maximum for the result type.
374 Arguments should be free of side effects. */
375#define _GL_BINARY_OP_OVERFLOW(a, b, op_result_overflow) \
376 op_result_overflow (a, b, \
377 _GL_INT_MINIMUM (_GL_INT_CONVERT (a, b)), \
378 _GL_INT_MAXIMUM (_GL_INT_CONVERT (a, b)))
379
380/* Store the low-order bits of A + B, A - B, A * B, respectively, into *R.
381 Return 1 if the result overflows. See above for restrictions. */
382#if _GL_HAS_BUILTIN_ADD_OVERFLOW
383# define INT_ADD_WRAPV(a, b, r) __builtin_add_overflow (a, b, r)
384# define INT_SUBTRACT_WRAPV(a, b, r) __builtin_sub_overflow (a, b, r)
385#else
386# define INT_ADD_WRAPV(a, b, r) \
387 _GL_INT_OP_WRAPV (a, b, r, +, _GL_INT_ADD_RANGE_OVERFLOW)
388# define INT_SUBTRACT_WRAPV(a, b, r) \
389 _GL_INT_OP_WRAPV (a, b, r, -, _GL_INT_SUBTRACT_RANGE_OVERFLOW)
390#endif
391#if _GL_HAS_BUILTIN_MUL_OVERFLOW
392# if ((9 < __GNUC__ + (3 <= __GNUC_MINOR__) \
393 || (__GNUC__ == 8 && 4 <= __GNUC_MINOR__)) \
394 && !defined __ICC)
395# define INT_MULTIPLY_WRAPV(a, b, r) __builtin_mul_overflow (a, b, r)
396# else
397 /* Work around GCC bug 91450. */
398# define INT_MULTIPLY_WRAPV(a, b, r) \
399 ((!_GL_SIGNED_TYPE_OR_EXPR (*(r)) && EXPR_SIGNED (a) && EXPR_SIGNED (b) \
400 && _GL_INT_MULTIPLY_RANGE_OVERFLOW (a, b, 0, (__typeof__ (*(r))) -1)) \
401 ? ((void) __builtin_mul_overflow (a, b, r), 1) \
402 : __builtin_mul_overflow (a, b, r))
403# endif
404#else
405# define INT_MULTIPLY_WRAPV(a, b, r) \
406 _GL_INT_OP_WRAPV (a, b, r, *, _GL_INT_MULTIPLY_RANGE_OVERFLOW)
407#endif
408
409/* Nonzero if this compiler has GCC bug 68193 or Clang bug 25390. See:
410 https://gcc.gnu.org/bugzilla/show_bug.cgi?id=68193
411 https://llvm.org/bugs/show_bug.cgi?id=25390
412 For now, assume all versions of GCC-like compilers generate bogus
413 warnings for _Generic. This matters only for compilers that
414 lack relevant builtins. */
415#if __GNUC__ || defined __clang__
416# define _GL__GENERIC_BOGUS 1
417#else
418# define _GL__GENERIC_BOGUS 0
419#endif
420
421/* Store the low-order bits of A <op> B into *R, where OP specifies
422 the operation and OVERFLOW the overflow predicate. Return 1 if the
423 result overflows. See above for restrictions. */
424#if 201112 <= __STDC_VERSION__ && !_GL__GENERIC_BOGUS
425# define _GL_INT_OP_WRAPV(a, b, r, op, overflow) \
426 (_Generic \
427 (*(r), \
428 signed char: \
429 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
430 signed char, SCHAR_MIN, SCHAR_MAX), \
431 unsigned char: \
432 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
433 unsigned char, 0, UCHAR_MAX), \
434 short int: \
435 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
436 short int, SHRT_MIN, SHRT_MAX), \
437 unsigned short int: \
438 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
439 unsigned short int, 0, USHRT_MAX), \
440 int: \
441 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
442 int, INT_MIN, INT_MAX), \
443 unsigned int: \
444 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
445 unsigned int, 0, UINT_MAX), \
446 long int: \
447 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
448 long int, LONG_MIN, LONG_MAX), \
449 unsigned long int: \
450 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
451 unsigned long int, 0, ULONG_MAX), \
452 long long int: \
453 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
454 long long int, LLONG_MIN, LLONG_MAX), \
455 unsigned long long int: \
456 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
457 unsigned long long int, 0, ULLONG_MAX)))
458#else
459/* Store the low-order bits of A <op> B into *R, where OP specifies
460 the operation and OVERFLOW the overflow predicate. If *R is
461 signed, its type is ST with bounds SMIN..SMAX; otherwise its type
462 is UT with bounds U..UMAX. ST and UT are narrower than int.
463 Return 1 if the result overflows. See above for restrictions. */
464# if _GL_HAVE___TYPEOF__
465# define _GL_INT_OP_WRAPV_SMALLISH(a,b,r,op,overflow,st,smin,smax,ut,umax) \
466 (TYPE_SIGNED (__typeof__ (*(r))) \
467 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, st, smin, smax) \
468 : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, ut, 0, umax))
469# else
470# define _GL_INT_OP_WRAPV_SMALLISH(a,b,r,op,overflow,st,smin,smax,ut,umax) \
471 (overflow (a, b, smin, smax) \
472 ? (overflow (a, b, 0, umax) \
473 ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st), 1) \
474 : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st)) < 0) \
475 : (overflow (a, b, 0, umax) \
476 ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st)) >= 0 \
477 : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st), 0)))
478# endif
479
480# define _GL_INT_OP_WRAPV(a, b, r, op, overflow) \
481 (sizeof *(r) == sizeof (signed char) \
482 ? _GL_INT_OP_WRAPV_SMALLISH (a, b, r, op, overflow, \
483 signed char, SCHAR_MIN, SCHAR_MAX, \
484 unsigned char, UCHAR_MAX) \
485 : sizeof *(r) == sizeof (short int) \
486 ? _GL_INT_OP_WRAPV_SMALLISH (a, b, r, op, overflow, \
487 short int, SHRT_MIN, SHRT_MAX, \
488 unsigned short int, USHRT_MAX) \
489 : sizeof *(r) == sizeof (int) \
490 ? (EXPR_SIGNED (*(r)) \
491 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
492 int, INT_MIN, INT_MAX) \
493 : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
494 unsigned int, 0, UINT_MAX)) \
495 : _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow))
496# ifdef LLONG_MAX
497# define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
498 (sizeof *(r) == sizeof (long int) \
499 ? (EXPR_SIGNED (*(r)) \
500 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
501 long int, LONG_MIN, LONG_MAX) \
502 : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
503 unsigned long int, 0, ULONG_MAX)) \
504 : (EXPR_SIGNED (*(r)) \
505 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
506 long long int, LLONG_MIN, LLONG_MAX) \
507 : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
508 unsigned long long int, 0, ULLONG_MAX)))
509# else
510# define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
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# endif
517#endif
518
519/* Store the low-order bits of A <op> B into *R, where the operation
520 is given by OP. Use the unsigned type UT for calculation to avoid
521 overflow problems. *R's type is T, with extrema TMIN and TMAX.
522 T must be a signed integer type. Return 1 if the result overflows. */
523#define _GL_INT_OP_CALC(a, b, r, op, overflow, ut, t, tmin, tmax) \
524 (overflow (a, b, tmin, tmax) \
525 ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 1) \
526 : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 0))
527
528/* Return the low-order bits of A <op> B, where the operation is given
529 by OP. Use the unsigned type UT for calculation to avoid undefined
530 behavior on signed integer overflow, and convert the result to type T.
531 UT is at least as wide as T and is no narrower than unsigned int,
532 T is two's complement, and there is no padding or trap representations.
533 Assume that converting UT to T yields the low-order bits, as is
534 done in all known two's-complement C compilers. E.g., see:
535 https://gcc.gnu.org/onlinedocs/gcc/Integers-implementation.html
536
537 According to the C standard, converting UT to T yields an
538 implementation-defined result or signal for values outside T's
539 range. However, code that works around this theoretical problem
540 runs afoul of a compiler bug in Oracle Studio 12.3 x86. See:
541 https://lists.gnu.org/r/bug-gnulib/2017-04/msg00049.html
542 As the compiler bug is real, don't try to work around the
543 theoretical problem. */
544
545#define _GL_INT_OP_WRAPV_VIA_UNSIGNED(a, b, op, ut, t) \
546 ((t) ((ut) (a) op (ut) (b)))
547
548/* Return true if the numeric values A + B, A - B, A * B fall outside
549 the range TMIN..TMAX. Arguments should be integer expressions
550 without side effects. TMIN should be signed and nonpositive.
551 TMAX should be positive, and should be signed unless TMIN is zero. */
552#define _GL_INT_ADD_RANGE_OVERFLOW(a, b, tmin, tmax) \
553 ((b) < 0 \
554 ? (((tmin) \
555 ? ((EXPR_SIGNED (_GL_INT_CONVERT (a, (tmin) - (b))) || (b) < (tmin)) \
556 && (a) < (tmin) - (b)) \
557 : (a) <= -1 - (b)) \
558 || ((EXPR_SIGNED (a) ? 0 <= (a) : (tmax) < (a)) && (tmax) < (a) + (b))) \
559 : (a) < 0 \
560 ? (((tmin) \
561 ? ((EXPR_SIGNED (_GL_INT_CONVERT (b, (tmin) - (a))) || (a) < (tmin)) \
562 && (b) < (tmin) - (a)) \
563 : (b) <= -1 - (a)) \
564 || ((EXPR_SIGNED (_GL_INT_CONVERT (a, b)) || (tmax) < (b)) \
565 && (tmax) < (a) + (b))) \
566 : (tmax) < (b) || (tmax) - (b) < (a))
567#define _GL_INT_SUBTRACT_RANGE_OVERFLOW(a, b, tmin, tmax) \
568 (((a) < 0) == ((b) < 0) \
569 ? ((a) < (b) \
570 ? !(tmin) || -1 - (tmin) < (b) - (a) - 1 \
571 : (tmax) < (a) - (b)) \
572 : (a) < 0 \
573 ? ((!EXPR_SIGNED (_GL_INT_CONVERT ((a) - (tmin), b)) && (a) - (tmin) < 0) \
574 || (a) - (tmin) < (b)) \
575 : ((! (EXPR_SIGNED (_GL_INT_CONVERT (tmax, b)) \
576 && EXPR_SIGNED (_GL_INT_CONVERT ((tmax) + (b), a))) \
577 && (tmax) <= -1 - (b)) \
578 || (tmax) + (b) < (a)))
579#define _GL_INT_MULTIPLY_RANGE_OVERFLOW(a, b, tmin, tmax) \
580 ((b) < 0 \
581 ? ((a) < 0 \
582 ? (EXPR_SIGNED (_GL_INT_CONVERT (tmax, b)) \
583 ? (a) < (tmax) / (b) \
584 : ((INT_NEGATE_OVERFLOW (b) \
585 ? _GL_INT_CONVERT (b, tmax) >> (TYPE_WIDTH (+ (b)) - 1) \
586 : (tmax) / -(b)) \
587 <= -1 - (a))) \
588 : INT_NEGATE_OVERFLOW (_GL_INT_CONVERT (b, tmin)) && (b) == -1 \
589 ? (EXPR_SIGNED (a) \
590 ? 0 < (a) + (tmin) \
591 : 0 < (a) && -1 - (tmin) < (a) - 1) \
592 : (tmin) / (b) < (a)) \
593 : (b) == 0 \
594 ? 0 \
595 : ((a) < 0 \
596 ? (INT_NEGATE_OVERFLOW (_GL_INT_CONVERT (a, tmin)) && (a) == -1 \
597 ? (EXPR_SIGNED (b) ? 0 < (b) + (tmin) : -1 - (tmin) < (b) - 1) \
598 : (tmin) / (a) < (b)) \
599 : (tmax) / (b) < (a)))
600
601/* The following macros compute A + B, A - B, and A * B, respectively.
602 If no overflow occurs, they set *R to the result and return 1;
603 otherwise, they return 0 and may modify *R.
604
605 Example usage:
606
607 long int result;
608 if (INT_ADD_OK (a, b, &result))
609 printf ("result is %ld\n", result);
610 else
611 printf ("overflow\n");
612
613 A, B, and *R should be integers; they need not be the same type,
614 and they need not be all signed or all unsigned.
615
616 These macros work correctly on all known practical hosts, and do not rely
617 on undefined behavior due to signed arithmetic overflow.
618
619 These macros are not constant expressions.
620
621 These macros may evaluate their arguments zero or multiple times, so the
622 arguments should not have side effects.
623
624 These macros are tuned for B being a constant. */
625
626#define INT_ADD_OK(a, b, r) ! INT_ADD_WRAPV (a, b, r)
627#define INT_SUBTRACT_OK(a, b, r) ! INT_SUBTRACT_WRAPV (a, b, r)
628#define INT_MULTIPLY_OK(a, b, r) ! INT_MULTIPLY_WRAPV (a, b, r)
629
630#endif /* _GL_INTPROPS_H */
631