intprops.h

Last change on this file was 3529, checked in by bird, 3 years ago
Imported grep 3.7 from grep-3.7.tar.gz (sha256: c22b0cf2d4f6bbe599c902387e8058990e1eee99aef333a203829e5fd3dbb342), applying minimal auto-props.
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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	/* 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 harder to use and may be less
137	efficient than the INT_<op>_WRAPV, INT_<op>_OK, and
138	INT_<op>_OVERFLOW macros described below.
139
140	Example usage:
141
142	long int i = ...;
143	long int j = ...;
144	if (INT_MULTIPLY_RANGE_OVERFLOW (i, j, LONG_MIN, LONG_MAX))
145	printf ("multiply would overflow");
146	else
147	printf ("product is %ld", i * j);
148
149	Restrictions on *_RANGE_OVERFLOW macros:
150
151	These macros do not check for all possible numerical problems or
152	undefined or unspecified behavior: they do not check for division
153	by zero, for bad shift counts, or for shifting negative numbers.
154
155	These macros may evaluate their arguments zero or multiple times,
156	so the arguments should not have side effects. The arithmetic
157	arguments (including the MIN and MAX arguments) must be of the same
158	integer type after the usual arithmetic conversions, and the type
159	must have minimum value MIN and maximum MAX. Unsigned types should
160	use a zero MIN of the proper type.
161
162	Because all arguments are subject to integer promotions, these
163	macros typically do not work on types narrower than 'int'.
164
165	These macros are tuned for constant MIN and MAX. For commutative
166	operations such as A + B, they are also tuned for constant B. */
167
168	/* Return 1 if A + B would overflow in [MIN,MAX] arithmetic.
169	See above for restrictions. */
170	#define INT_ADD_RANGE_OVERFLOW(a, b, min, max) \
171	((b) < 0 \
172	? (a) < (min) - (b) \
173	: (max) - (b) < (a))
174
175	/* Return 1 if A - B would overflow in [MIN,MAX] arithmetic.
176	See above for restrictions. */
177	#define INT_SUBTRACT_RANGE_OVERFLOW(a, b, min, max) \
178	((b) < 0 \
179	? (max) + (b) < (a) \
180	: (a) < (min) + (b))
181
182	/* Return 1 if - A would overflow in [MIN,MAX] arithmetic.
183	See above for restrictions. */
184	#define INT_NEGATE_RANGE_OVERFLOW(a, min, max) \
185	((min) < 0 \
186	? (a) < - (max) \
187	: 0 < (a))
188
189	/* Return 1 if A * B would overflow in [MIN,MAX] arithmetic.
190	See above for restrictions. Avoid && and \|\| as they tickle
191	bugs in Sun C 5.11 2010/08/13 and other compilers; see
192	<https://lists.gnu.org/r/bug-gnulib/2011-05/msg00401.html>. */
193	#define INT_MULTIPLY_RANGE_OVERFLOW(a, b, min, max) \
194	((b) < 0 \
195	? ((a) < 0 \
196	? (a) < (max) / (b) \
197	: (b) == -1 \
198	? 0 \
199	: (min) / (b) < (a)) \
200	: (b) == 0 \
201	? 0 \
202	: ((a) < 0 \
203	? (a) < (min) / (b) \
204	: (max) / (b) < (a)))
205
206	/* Return 1 if A / B would overflow in [MIN,MAX] arithmetic.
207	See above for restrictions. Do not check for division by zero. */
208	#define INT_DIVIDE_RANGE_OVERFLOW(a, b, min, max) \
209	((min) < 0 && (b) == -1 && (a) < - (max))
210
211	/* Return 1 if A % B would overflow in [MIN,MAX] arithmetic.
212	See above for restrictions. Do not check for division by zero.
213	Mathematically, % should never overflow, but on x86-like hosts
214	INT_MIN % -1 traps, and the C standard permits this, so treat this
215	as an overflow too. */
216	#define INT_REMAINDER_RANGE_OVERFLOW(a, b, min, max) \
217	INT_DIVIDE_RANGE_OVERFLOW (a, b, min, max)
218
219	/* Return 1 if A << B would overflow in [MIN,MAX] arithmetic.
220	See above for restrictions. Here, MIN and MAX are for A only, and B need
221	not be of the same type as the other arguments. The C standard says that
222	behavior is undefined for shifts unless 0 <= B < wordwidth, and that when
223	A is negative then A << B has undefined behavior and A >> B has
224	implementation-defined behavior, but do not check these other
225	restrictions. */
226	#define INT_LEFT_SHIFT_RANGE_OVERFLOW(a, b, min, max) \
227	((a) < 0 \
228	? (a) < (min) >> (b) \
229	: (max) >> (b) < (a))
230
231	/* True if __builtin_add_overflow (A, B, P) and __builtin_sub_overflow
232	(A, B, P) work when P is non-null. */
233	/* __builtin_{add,sub}_overflow exists but is not reliable in GCC 5.x and 6.x,
234	see <https://gcc.gnu.org/bugzilla/show_bug.cgi?id=98269>. */
235	#if 7 <= __GNUC__ && !defined __ICC
236	# define _GL_HAS_BUILTIN_ADD_OVERFLOW 1
237	#elif defined __has_builtin
238	# define _GL_HAS_BUILTIN_ADD_OVERFLOW __has_builtin (__builtin_add_overflow)
239	#else
240	# define _GL_HAS_BUILTIN_ADD_OVERFLOW 0
241	#endif
242
243	/* True if __builtin_mul_overflow (A, B, P) works when P is non-null. */
244	#ifdef __clang__
245	/* Work around Clang bug <https://bugs.llvm.org/show_bug.cgi?id=16404>. */
246	# define _GL_HAS_BUILTIN_MUL_OVERFLOW 0
247	#else
248	# define _GL_HAS_BUILTIN_MUL_OVERFLOW _GL_HAS_BUILTIN_ADD_OVERFLOW
249	#endif
250
251	/* True if __builtin_add_overflow_p (A, B, C) works, and similarly for
252	__builtin_sub_overflow_p and __builtin_mul_overflow_p. */
253	#if defined __clang__ \|\| defined __ICC
254	/* Clang 11 lacks __builtin_mul_overflow_p, and even if it did it
255	would presumably run afoul of Clang bug 16404. ICC 2021.1's
256	__builtin_add_overflow_p etc. are not treated as integral constant
257	expressions even when all arguments are. */
258	# define _GL_HAS_BUILTIN_OVERFLOW_P 0
259	#elif defined __has_builtin
260	# define _GL_HAS_BUILTIN_OVERFLOW_P __has_builtin (__builtin_mul_overflow_p)
261	#else
262	# define _GL_HAS_BUILTIN_OVERFLOW_P (7 <= __GNUC__)
263	#endif
264
265	/* The _GL*_OVERFLOW macros have the same restrictions as the
266	*_RANGE_OVERFLOW macros, except that they do not assume that operands
267	(e.g., A and B) have the same type as MIN and MAX. Instead, they assume
268	that the result (e.g., A + B) has that type. */
269	#if _GL_HAS_BUILTIN_OVERFLOW_P
270	# define _GL_ADD_OVERFLOW(a, b, min, max) \
271	__builtin_add_overflow_p (a, b, (__typeof__ ((a) + (b))) 0)
272	# define _GL_SUBTRACT_OVERFLOW(a, b, min, max) \
273	__builtin_sub_overflow_p (a, b, (__typeof__ ((a) - (b))) 0)
274	# define _GL_MULTIPLY_OVERFLOW(a, b, min, max) \
275	__builtin_mul_overflow_p (a, b, (__typeof__ ((a) * (b))) 0)
276	#else
277	# define _GL_ADD_OVERFLOW(a, b, min, max) \
278	((min) < 0 ? INT_ADD_RANGE_OVERFLOW (a, b, min, max) \
279	: (a) < 0 ? (b) <= (a) + (b) \
280	: (b) < 0 ? (a) <= (a) + (b) \
281	: (a) + (b) < (b))
282	# define _GL_SUBTRACT_OVERFLOW(a, b, min, max) \
283	((min) < 0 ? INT_SUBTRACT_RANGE_OVERFLOW (a, b, min, max) \
284	: (a) < 0 ? 1 \
285	: (b) < 0 ? (a) - (b) <= (a) \
286	: (a) < (b))
287	# define _GL_MULTIPLY_OVERFLOW(a, b, min, max) \
288	(((min) == 0 && (((a) < 0 && 0 < (b)) \|\| ((b) < 0 && 0 < (a)))) \
289	\|\| INT_MULTIPLY_RANGE_OVERFLOW (a, b, min, max))
290	#endif
291	#define _GL_DIVIDE_OVERFLOW(a, b, min, max) \
292	((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max) \
293	: (a) < 0 ? (b) <= (a) + (b) - 1 \
294	: (b) < 0 && (a) + (b) <= (a))
295	#define _GL_REMAINDER_OVERFLOW(a, b, min, max) \
296	((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max) \
297	: (a) < 0 ? (a) % (b) != ((max) - (b) + 1) % (b) \
298	: (b) < 0 && ! _GL_UNSIGNED_NEG_MULTIPLE (a, b, max))
299
300	/* Return a nonzero value if A is a mathematical multiple of B, where
301	A is unsigned, B is negative, and MAX is the maximum value of A's
302	type. A's type must be the same as (A % B)'s type. Normally (A %
303	-B == 0) suffices, but things get tricky if -B would overflow. */
304	#define _GL_UNSIGNED_NEG_MULTIPLE(a, b, max) \
305	(((b) < -_GL_SIGNED_INT_MAXIMUM (b) \
306	? (_GL_SIGNED_INT_MAXIMUM (b) == (max) \
307	? (a) \
308	: (a) % (_GL_INT_CONVERT (a, _GL_SIGNED_INT_MAXIMUM (b)) + 1)) \
309	: (a) % - (b)) \
310	== 0)
311
312	/* Check for integer overflow, and report low order bits of answer.
313
314	The INT_<op>_OVERFLOW macros return 1 if the corresponding C operators
315	might not yield numerically correct answers due to arithmetic overflow.
316	The INT_<op>_WRAPV macros compute the low-order bits of the sum,
317	difference, and product of two C integers, and return 1 if these
318	low-order bits are not numerically correct.
319	These macros work correctly on all known practical hosts, and do not rely
320	on undefined behavior due to signed arithmetic overflow.
321
322	Example usage, assuming A and B are long int:
323
324	if (INT_MULTIPLY_OVERFLOW (a, b))
325	printf ("result would overflow\n");
326	else
327	printf ("result is %ld (no overflow)\n", a * b);
328
329	Example usage with WRAPV flavor:
330
331	long int result;
332	bool overflow = INT_MULTIPLY_WRAPV (a, b, &result);
333	printf ("result is %ld (%s)\n", result,
334	overflow ? "after overflow" : "no overflow");
335
336	Restrictions on these macros:
337
338	These macros do not check for all possible numerical problems or
339	undefined or unspecified behavior: they do not check for division
340	by zero, for bad shift counts, or for shifting negative numbers.
341
342	These macros may evaluate their arguments zero or multiple times, so the
343	arguments should not have side effects.
344
345	The WRAPV macros are not constant expressions. They support only
346	+, binary -, and *.
347
348	Because the WRAPV macros convert the result, they report overflow
349	in different circumstances than the OVERFLOW macros do. For
350	example, in the typical case with 16-bit 'short' and 32-bit 'int',
351	if A, B and R are all of type 'short' then INT_ADD_OVERFLOW (A, B)
352	returns false because the addition cannot overflow after A and B
353	are converted to 'int', whereas INT_ADD_WRAPV (A, B, &R) returns
354	true or false depending on whether the sum fits into 'short'.
355
356	These macros are tuned for their last input argument being a constant.
357
358	Return 1 if the integer expressions A * B, A - B, -A, A * B, A / B,
359	A % B, and A << B would overflow, respectively. */
360
361	#define INT_ADD_OVERFLOW(a, b) \
362	_GL_BINARY_OP_OVERFLOW (a, b, _GL_ADD_OVERFLOW)
363	#define INT_SUBTRACT_OVERFLOW(a, b) \
364	_GL_BINARY_OP_OVERFLOW (a, b, _GL_SUBTRACT_OVERFLOW)
365	#if _GL_HAS_BUILTIN_OVERFLOW_P
366	# define INT_NEGATE_OVERFLOW(a) INT_SUBTRACT_OVERFLOW (0, a)
367	#else
368	# define INT_NEGATE_OVERFLOW(a) \
369	INT_NEGATE_RANGE_OVERFLOW (a, _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
370	#endif
371	#define INT_MULTIPLY_OVERFLOW(a, b) \
372	_GL_BINARY_OP_OVERFLOW (a, b, _GL_MULTIPLY_OVERFLOW)
373	#define INT_DIVIDE_OVERFLOW(a, b) \
374	_GL_BINARY_OP_OVERFLOW (a, b, _GL_DIVIDE_OVERFLOW)
375	#define INT_REMAINDER_OVERFLOW(a, b) \
376	_GL_BINARY_OP_OVERFLOW (a, b, _GL_REMAINDER_OVERFLOW)
377	#define INT_LEFT_SHIFT_OVERFLOW(a, b) \
378	INT_LEFT_SHIFT_RANGE_OVERFLOW (a, b, \
379	_GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
380
381	/* Return 1 if the expression A <op> B would overflow,
382	where OP_RESULT_OVERFLOW (A, B, MIN, MAX) does the actual test,
383	assuming MIN and MAX are the minimum and maximum for the result type.
384	Arguments should be free of side effects. */
385	#define _GL_BINARY_OP_OVERFLOW(a, b, op_result_overflow) \
386	op_result_overflow (a, b, \
387	_GL_INT_MINIMUM (_GL_INT_CONVERT (a, b)), \
388	_GL_INT_MAXIMUM (_GL_INT_CONVERT (a, b)))
389
390	/* Store the low-order bits of A + B, A - B, A * B, respectively, into *R.
391	Return 1 if the result overflows. See above for restrictions. */
392	#if _GL_HAS_BUILTIN_ADD_OVERFLOW
393	# define INT_ADD_WRAPV(a, b, r) __builtin_add_overflow (a, b, r)
394	# define INT_SUBTRACT_WRAPV(a, b, r) __builtin_sub_overflow (a, b, r)
395	#else
396	# define INT_ADD_WRAPV(a, b, r) \
397	_GL_INT_OP_WRAPV (a, b, r, +, _GL_INT_ADD_RANGE_OVERFLOW)
398	# define INT_SUBTRACT_WRAPV(a, b, r) \
399	_GL_INT_OP_WRAPV (a, b, r, -, _GL_INT_SUBTRACT_RANGE_OVERFLOW)
400	#endif
401	#if _GL_HAS_BUILTIN_MUL_OVERFLOW
402	# if ((9 < __GNUC__ + (3 <= __GNUC_MINOR__) \
403	\|\| (__GNUC__ == 8 && 4 <= __GNUC_MINOR__)) \
404	&& !defined __ICC)
405	# define INT_MULTIPLY_WRAPV(a, b, r) __builtin_mul_overflow (a, b, r)
406	# else
407	/* Work around GCC bug 91450. */
408	# define INT_MULTIPLY_WRAPV(a, b, r) \
409	((!_GL_SIGNED_TYPE_OR_EXPR (*(r)) && EXPR_SIGNED (a) && EXPR_SIGNED (b) \
410	&& _GL_INT_MULTIPLY_RANGE_OVERFLOW (a, b, 0, (__typeof__ (*(r))) -1)) \
411	? ((void) __builtin_mul_overflow (a, b, r), 1) \
412	: __builtin_mul_overflow (a, b, r))
413	# endif
414	#else
415	# define INT_MULTIPLY_WRAPV(a, b, r) \
416	_GL_INT_OP_WRAPV (a, b, r, *, _GL_INT_MULTIPLY_RANGE_OVERFLOW)
417	#endif
418
419	/* Nonzero if this compiler has GCC bug 68193 or Clang bug 25390. See:
420	https://gcc.gnu.org/bugzilla/show_bug.cgi?id=68193
421	https://llvm.org/bugs/show_bug.cgi?id=25390
422	For now, assume all versions of GCC-like compilers generate bogus
423	warnings for _Generic. This matters only for compilers that
424	lack relevant builtins. */
425	#if __GNUC__ \|\| defined __clang__
426	# define _GL__GENERIC_BOGUS 1
427	#else
428	# define _GL__GENERIC_BOGUS 0
429	#endif
430
431	/* Store the low-order bits of A <op> B into *R, where OP specifies
432	the operation and OVERFLOW the overflow predicate. Return 1 if the
433	result overflows. See above for restrictions. */
434	#if 201112 <= __STDC_VERSION__ && !_GL__GENERIC_BOGUS
435	# define _GL_INT_OP_WRAPV(a, b, r, op, overflow) \
436	(_Generic \
437	(*(r), \
438	signed char: \
439	_GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
440	signed char, SCHAR_MIN, SCHAR_MAX), \
441	unsigned char: \
442	_GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
443	unsigned char, 0, UCHAR_MAX), \
444	short int: \
445	_GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
446	short int, SHRT_MIN, SHRT_MAX), \
447	unsigned short int: \
448	_GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
449	unsigned short int, 0, USHRT_MAX), \
450	int: \
451	_GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
452	int, INT_MIN, INT_MAX), \
453	unsigned int: \
454	_GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
455	unsigned int, 0, UINT_MAX), \
456	long int: \
457	_GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
458	long int, LONG_MIN, LONG_MAX), \
459	unsigned long int: \
460	_GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
461	unsigned long int, 0, ULONG_MAX), \
462	long long int: \
463	_GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
464	long long int, LLONG_MIN, LLONG_MAX), \
465	unsigned long long int: \
466	_GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
467	unsigned long long int, 0, ULLONG_MAX)))
468	#else
469	/* Store the low-order bits of A <op> B into *R, where OP specifies
470	the operation and OVERFLOW the overflow predicate. If *R is
471	signed, its type is ST with bounds SMIN..SMAX; otherwise its type
472	is UT with bounds U..UMAX. ST and UT are narrower than int.
473	Return 1 if the result overflows. See above for restrictions. */
474	# if _GL_HAVE___TYPEOF__
475	# define _GL_INT_OP_WRAPV_SMALLISH(a,b,r,op,overflow,st,smin,smax,ut,umax) \
476	(TYPE_SIGNED (__typeof__ (*(r))) \
477	? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, st, smin, smax) \
478	: _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, ut, 0, umax))
479	# else
480	# define _GL_INT_OP_WRAPV_SMALLISH(a,b,r,op,overflow,st,smin,smax,ut,umax) \
481	(overflow (a, b, smin, smax) \
482	? (overflow (a, b, 0, umax) \
483	? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st), 1) \
484	: (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st)) < 0) \
485	: (overflow (a, b, 0, umax) \
486	? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st)) >= 0 \
487	: (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st), 0)))
488	# endif
489
490	# define _GL_INT_OP_WRAPV(a, b, r, op, overflow) \
491	(sizeof *(r) == sizeof (signed char) \
492	? _GL_INT_OP_WRAPV_SMALLISH (a, b, r, op, overflow, \
493	signed char, SCHAR_MIN, SCHAR_MAX, \
494	unsigned char, UCHAR_MAX) \
495	: sizeof *(r) == sizeof (short int) \
496	? _GL_INT_OP_WRAPV_SMALLISH (a, b, r, op, overflow, \
497	short int, SHRT_MIN, SHRT_MAX, \
498	unsigned short int, USHRT_MAX) \
499	: sizeof *(r) == sizeof (int) \
500	? (EXPR_SIGNED (*(r)) \
501	? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
502	int, INT_MIN, INT_MAX) \
503	: _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
504	unsigned int, 0, UINT_MAX)) \
505	: _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow))
506	# ifdef LLONG_MAX
507	# define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
508	(sizeof *(r) == sizeof (long int) \
509	? (EXPR_SIGNED (*(r)) \
510	? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
511	long int, LONG_MIN, LONG_MAX) \
512	: _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
513	unsigned long int, 0, ULONG_MAX)) \
514	: (EXPR_SIGNED (*(r)) \
515	? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
516	long long int, LLONG_MIN, LLONG_MAX) \
517	: _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
518	unsigned long long int, 0, ULLONG_MAX)))
519	# else
520	# define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
521	(EXPR_SIGNED (*(r)) \
522	? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
523	long int, LONG_MIN, LONG_MAX) \
524	: _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
525	unsigned long int, 0, ULONG_MAX))
526	# endif
527	#endif
528
529	/* Store the low-order bits of A <op> B into *R, where the operation
530	is given by OP. Use the unsigned type UT for calculation to avoid
531	overflow problems. *R's type is T, with extrema TMIN and TMAX.
532	T must be a signed integer type. Return 1 if the result overflows. */
533	#define _GL_INT_OP_CALC(a, b, r, op, overflow, ut, t, tmin, tmax) \
534	(overflow (a, b, tmin, tmax) \
535	? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 1) \
536	: (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 0))
537
538	/* Return the low-order bits of A <op> B, where the operation is given
539	by OP. Use the unsigned type UT for calculation to avoid undefined
540	behavior on signed integer overflow, and convert the result to type T.
541	UT is at least as wide as T and is no narrower than unsigned int,
542	T is two's complement, and there is no padding or trap representations.
543	Assume that converting UT to T yields the low-order bits, as is
544	done in all known two's-complement C compilers. E.g., see:
545	https://gcc.gnu.org/onlinedocs/gcc/Integers-implementation.html
546
547	According to the C standard, converting UT to T yields an
548	implementation-defined result or signal for values outside T's
549	range. However, code that works around this theoretical problem
550	runs afoul of a compiler bug in Oracle Studio 12.3 x86. See:
551	https://lists.gnu.org/r/bug-gnulib/2017-04/msg00049.html
552	As the compiler bug is real, don't try to work around the
553	theoretical problem. */
554
555	#define _GL_INT_OP_WRAPV_VIA_UNSIGNED(a, b, op, ut, t) \
556	((t) ((ut) (a) op (ut) (b)))
557
558	/* Return true if the numeric values A + B, A - B, A * B fall outside
559	the range TMIN..TMAX. Arguments should be integer expressions
560	without side effects. TMIN should be signed and nonpositive.
561	TMAX should be positive, and should be signed unless TMIN is zero. */
562	#define _GL_INT_ADD_RANGE_OVERFLOW(a, b, tmin, tmax) \
563	((b) < 0 \
564	? (((tmin) \
565	? ((EXPR_SIGNED (_GL_INT_CONVERT (a, (tmin) - (b))) \|\| (b) < (tmin)) \
566	&& (a) < (tmin) - (b)) \
567	: (a) <= -1 - (b)) \
568	\|\| ((EXPR_SIGNED (a) ? 0 <= (a) : (tmax) < (a)) && (tmax) < (a) + (b))) \
569	: (a) < 0 \
570	? (((tmin) \
571	? ((EXPR_SIGNED (_GL_INT_CONVERT (b, (tmin) - (a))) \|\| (a) < (tmin)) \
572	&& (b) < (tmin) - (a)) \
573	: (b) <= -1 - (a)) \
574	\|\| ((EXPR_SIGNED (_GL_INT_CONVERT (a, b)) \|\| (tmax) < (b)) \
575	&& (tmax) < (a) + (b))) \
576	: (tmax) < (b) \|\| (tmax) - (b) < (a))
577	#define _GL_INT_SUBTRACT_RANGE_OVERFLOW(a, b, tmin, tmax) \
578	(((a) < 0) == ((b) < 0) \
579	? ((a) < (b) \
580	? !(tmin) \|\| -1 - (tmin) < (b) - (a) - 1 \
581	: (tmax) < (a) - (b)) \
582	: (a) < 0 \
583	? ((!EXPR_SIGNED (_GL_INT_CONVERT ((a) - (tmin), b)) && (a) - (tmin) < 0) \
584	\|\| (a) - (tmin) < (b)) \
585	: ((! (EXPR_SIGNED (_GL_INT_CONVERT (tmax, b)) \
586	&& EXPR_SIGNED (_GL_INT_CONVERT ((tmax) + (b), a))) \
587	&& (tmax) <= -1 - (b)) \
588	\|\| (tmax) + (b) < (a)))
589	#define _GL_INT_MULTIPLY_RANGE_OVERFLOW(a, b, tmin, tmax) \
590	((b) < 0 \
591	? ((a) < 0 \
592	? (EXPR_SIGNED (_GL_INT_CONVERT (tmax, b)) \
593	? (a) < (tmax) / (b) \
594	: ((INT_NEGATE_OVERFLOW (b) \
595	? _GL_INT_CONVERT (b, tmax) >> (TYPE_WIDTH (+ (b)) - 1) \
596	: (tmax) / -(b)) \
597	<= -1 - (a))) \
598	: INT_NEGATE_OVERFLOW (_GL_INT_CONVERT (b, tmin)) && (b) == -1 \
599	? (EXPR_SIGNED (a) \
600	? 0 < (a) + (tmin) \
601	: 0 < (a) && -1 - (tmin) < (a) - 1) \
602	: (tmin) / (b) < (a)) \
603	: (b) == 0 \
604	? 0 \
605	: ((a) < 0 \
606	? (INT_NEGATE_OVERFLOW (_GL_INT_CONVERT (a, tmin)) && (a) == -1 \
607	? (EXPR_SIGNED (b) ? 0 < (b) + (tmin) : -1 - (tmin) < (b) - 1) \
608	: (tmin) / (a) < (b)) \
609	: (tmax) / (b) < (a)))
610
611	/* The following macros compute A + B, A - B, and A * B, respectively.
612	If no overflow occurs, they set *R to the result and return 1;
613	otherwise, they return 0 and may modify *R.
614
615	Example usage:
616
617	long int result;
618	if (INT_ADD_OK (a, b, &result))
619	printf ("result is %ld\n", result);
620	else
621	printf ("overflow\n");
622
623	A, B, and *R should be integers; they need not be the same type,
624	and they need not be all signed or all unsigned.
625
626	These macros work correctly on all known practical hosts, and do not rely
627	on undefined behavior due to signed arithmetic overflow.
628
629	These macros are not constant expressions.
630
631	These macros may evaluate their arguments zero or multiple times, so the
632	arguments should not have side effects.
633
634	These macros are tuned for B being a constant. */
635
636	#define INT_ADD_OK(a, b, r) ! INT_ADD_WRAPV (a, b, r)
637	#define INT_SUBTRACT_OK(a, b, r) ! INT_SUBTRACT_WRAPV (a, b, r)
638	#define INT_MULTIPLY_OK(a, b, r) ! INT_MULTIPLY_WRAPV (a, b, r)
639
640	#endif /* _GL_INTPROPS_H */

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