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1 /* intprops.h -- properties of integer types
3 Copyright (C) 2001-2017 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 General Public License as published
7 by the Free Software Foundation; either version 3 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 General Public License for more details.
15 You should have received a copy of the GNU General Public License
16 along with this program. If not, see <http://www.gnu.org/licenses/>. */
18 /* Written by Paul Eggert. */
20 #ifndef _GL_INTPROPS_H
21 #define _GL_INTPROPS_H
23 #include <limits.h>
24 #include <verify.h>
26 /* Return a value with the common real type of E and V and the value of V. */
27 #define _GL_INT_CONVERT(e, v) (0 * (e) + (v))
29 /* Act like _GL_INT_CONVERT (E, -V) but work around a bug in IRIX 6.5 cc; see
30 <http://lists.gnu.org/archive/html/bug-gnulib/2011-05/msg00406.html>. */
31 #define _GL_INT_NEGATE_CONVERT(e, v) (0 * (e) - (v))
33 /* The extra casts in the following macros work around compiler bugs,
34 e.g., in Cray C 5.0.3.0. */
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)
40 /* True if the real type T is signed. */
41 #define TYPE_SIGNED(t) (! ((t) 0 < (t) -1))
43 /* Return 1 if the real expression E, after promotion, has a
44 signed or floating type. */
45 #define EXPR_SIGNED(e) (_GL_INT_NEGATE_CONVERT (e, 1) < 0)
48 /* Minimum and maximum values for integer types and expressions. */
50 /* The width in bits of the integer type or expression T.
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 should not have side effects. */
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) + 0) - 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 As a sanity check, test the assumption for some signed types that
84 <limits.h> bounds. */
85 verify (TYPE_MINIMUM (signed char) == SCHAR_MIN);
86 verify (TYPE_MAXIMUM (signed char) == SCHAR_MAX);
87 verify (TYPE_MINIMUM (short int) == SHRT_MIN);
88 verify (TYPE_MAXIMUM (short int) == SHRT_MAX);
89 verify (TYPE_MINIMUM (int) == INT_MIN);
90 verify (TYPE_MAXIMUM (int) == INT_MAX);
91 verify (TYPE_MINIMUM (long int) == LONG_MIN);
92 verify (TYPE_MAXIMUM (long int) == LONG_MAX);
93 #ifdef LLONG_MAX
94 verify (TYPE_MINIMUM (long long int) == LLONG_MIN);
95 verify (TYPE_MAXIMUM (long long int) == LLONG_MAX);
96 #endif
97 /* Similarly, sanity-check one ISO/IEC TS 18661-1:2014 macro if defined. */
98 #ifdef UINT_WIDTH
99 verify (TYPE_WIDTH (unsigned int) == UINT_WIDTH);
100 #endif
102 /* Does the __typeof__ keyword work? This could be done by
103 'configure', but for now it's easier to do it by hand. */
104 #if (2 <= __GNUC__ \
105 || (1210 <= __IBMC__ && defined __IBM__TYPEOF__) \
106 || (0x5110 <= __SUNPRO_C && !__STDC__))
107 # define _GL_HAVE___TYPEOF__ 1
108 #else
109 # define _GL_HAVE___TYPEOF__ 0
110 #endif
112 /* Return 1 if the integer type or expression T might be signed. Return 0
113 if it is definitely unsigned. This macro does not evaluate its argument,
114 and expands to an integer constant expression. */
115 #if _GL_HAVE___TYPEOF__
116 # define _GL_SIGNED_TYPE_OR_EXPR(t) TYPE_SIGNED (__typeof__ (t))
117 #else
118 # define _GL_SIGNED_TYPE_OR_EXPR(t) 1
119 #endif
121 /* Bound on length of the string representing an unsigned integer
122 value representable in B bits. log10 (2.0) < 146/485. The
123 smallest value of B where this bound is not tight is 2621. */
124 #define INT_BITS_STRLEN_BOUND(b) (((b) * 146 + 484) / 485)
126 /* Bound on length of the string representing an integer type or expression T.
127 Subtract 1 for the sign bit if T is signed, and then add 1 more for
128 a minus sign if needed.
130 Because _GL_SIGNED_TYPE_OR_EXPR sometimes returns 0 when its argument is
131 signed, this macro may overestimate the true bound by one byte when
132 applied to unsigned types of size 2, 4, 16, ... bytes. */
133 #define INT_STRLEN_BOUND(t) \
134 (INT_BITS_STRLEN_BOUND (TYPE_WIDTH (t) - _GL_SIGNED_TYPE_OR_EXPR (t)) \
135 + _GL_SIGNED_TYPE_OR_EXPR (t))
137 /* Bound on buffer size needed to represent an integer type or expression T,
138 including the terminating null. */
139 #define INT_BUFSIZE_BOUND(t) (INT_STRLEN_BOUND (t) + 1)
142 /* Range overflow checks.
144 The INT_<op>_RANGE_OVERFLOW macros return 1 if the corresponding C
145 operators might not yield numerically correct answers due to
146 arithmetic overflow. They do not rely on undefined or
147 implementation-defined behavior. Their implementations are simple
148 and straightforward, but they are a bit harder to use than the
149 INT_<op>_OVERFLOW macros described below.
151 Example usage:
153 long int i = ...;
154 long int j = ...;
155 if (INT_MULTIPLY_RANGE_OVERFLOW (i, j, LONG_MIN, LONG_MAX))
156 printf ("multiply would overflow");
157 else
158 printf ("product is %ld", i * j);
160 Restrictions on *_RANGE_OVERFLOW macros:
162 These macros do not check for all possible numerical problems or
163 undefined or unspecified behavior: they do not check for division
164 by zero, for bad shift counts, or for shifting negative numbers.
166 These macros may evaluate their arguments zero or multiple times,
167 so the arguments should not have side effects. The arithmetic
168 arguments (including the MIN and MAX arguments) must be of the same
169 integer type after the usual arithmetic conversions, and the type
170 must have minimum value MIN and maximum MAX. Unsigned types should
171 use a zero MIN of the proper type.
173 These macros are tuned for constant MIN and MAX. For commutative
174 operations such as A + B, they are also tuned for constant B. */
176 /* Return 1 if A + B would overflow in [MIN,MAX] arithmetic.
177 See above for restrictions. */
178 #define INT_ADD_RANGE_OVERFLOW(a, b, min, max) \
179 ((b) < 0 \
180 ? (a) < (min) - (b) \
181 : (max) - (b) < (a))
183 /* Return 1 if A - B would overflow in [MIN,MAX] arithmetic.
184 See above for restrictions. */
185 #define INT_SUBTRACT_RANGE_OVERFLOW(a, b, min, max) \
186 ((b) < 0 \
187 ? (max) + (b) < (a) \
188 : (a) < (min) + (b))
190 /* Return 1 if - A would overflow in [MIN,MAX] arithmetic.
191 See above for restrictions. */
192 #define INT_NEGATE_RANGE_OVERFLOW(a, min, max) \
193 ((min) < 0 \
194 ? (a) < - (max) \
195 : 0 < (a))
197 /* Return 1 if A * B would overflow in [MIN,MAX] arithmetic.
198 See above for restrictions. Avoid && and || as they tickle
199 bugs in Sun C 5.11 2010/08/13 and other compilers; see
200 <http://lists.gnu.org/archive/html/bug-gnulib/2011-05/msg00401.html>. */
201 #define INT_MULTIPLY_RANGE_OVERFLOW(a, b, min, max) \
202 ((b) < 0 \
203 ? ((a) < 0 \
204 ? (a) < (max) / (b) \
205 : (b) == -1 \
206 ? 0 \
207 : (min) / (b) < (a)) \
208 : (b) == 0 \
209 ? 0 \
210 : ((a) < 0 \
211 ? (a) < (min) / (b) \
212 : (max) / (b) < (a)))
214 /* Return 1 if A / B would overflow in [MIN,MAX] arithmetic.
215 See above for restrictions. Do not check for division by zero. */
216 #define INT_DIVIDE_RANGE_OVERFLOW(a, b, min, max) \
217 ((min) < 0 && (b) == -1 && (a) < - (max))
219 /* Return 1 if A % B would overflow in [MIN,MAX] arithmetic.
220 See above for restrictions. Do not check for division by zero.
221 Mathematically, % should never overflow, but on x86-like hosts
222 INT_MIN % -1 traps, and the C standard permits this, so treat this
223 as an overflow too. */
224 #define INT_REMAINDER_RANGE_OVERFLOW(a, b, min, max) \
225 INT_DIVIDE_RANGE_OVERFLOW (a, b, min, max)
227 /* Return 1 if A << B would overflow in [MIN,MAX] arithmetic.
228 See above for restrictions. Here, MIN and MAX are for A only, and B need
229 not be of the same type as the other arguments. The C standard says that
230 behavior is undefined for shifts unless 0 <= B < wordwidth, and that when
231 A is negative then A << B has undefined behavior and A >> B has
232 implementation-defined behavior, but do not check these other
233 restrictions. */
234 #define INT_LEFT_SHIFT_RANGE_OVERFLOW(a, b, min, max) \
235 ((a) < 0 \
236 ? (a) < (min) >> (b) \
237 : (max) >> (b) < (a))
239 /* True if __builtin_add_overflow (A, B, P) works when P is non-null. */
240 #define _GL_HAS_BUILTIN_OVERFLOW (5 <= __GNUC__)
242 /* True if __builtin_add_overflow_p (A, B, C) works. */
243 #define _GL_HAS_BUILTIN_OVERFLOW_P (7 <= __GNUC__)
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))
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)
292 /* Check for integer overflow, and report low order bits of answer.
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 also store the low-order bits of the answer.
297 These macros work correctly on all known practical hosts, and do not rely
298 on undefined behavior due to signed arithmetic overflow.
300 Example usage, assuming A and B are long int:
302 if (INT_MULTIPLY_OVERFLOW (a, b))
303 printf ("result would overflow\n");
304 else
305 printf ("result is %ld (no overflow)\n", a * b);
307 Example usage with WRAPV flavor:
309 long int result;
310 bool overflow = INT_MULTIPLY_WRAPV (a, b, &result);
311 printf ("result is %ld (%s)\n", result,
312 overflow ? "after overflow" : "no overflow");
314 Restrictions on these macros:
316 These macros do not check for all possible numerical problems or
317 undefined or unspecified behavior: they do not check for division
318 by zero, for bad shift counts, or for shifting negative numbers.
320 These macros may evaluate their arguments zero or multiple times, so the
321 arguments should not have side effects.
323 The WRAPV macros are not constant expressions. They support only
324 +, binary -, and *. The result type must be signed.
326 These macros are tuned for their last argument being a constant.
328 Return 1 if the integer expressions A * B, A - B, -A, A * B, A / B,
329 A % B, and A << B would overflow, respectively. */
331 #define INT_ADD_OVERFLOW(a, b) \
332 _GL_BINARY_OP_OVERFLOW (a, b, _GL_ADD_OVERFLOW)
333 #define INT_SUBTRACT_OVERFLOW(a, b) \
334 _GL_BINARY_OP_OVERFLOW (a, b, _GL_SUBTRACT_OVERFLOW)
335 #if _GL_HAS_BUILTIN_OVERFLOW_P
336 # define INT_NEGATE_OVERFLOW(a) INT_SUBTRACT_OVERFLOW (0, a)
337 #else
338 # define INT_NEGATE_OVERFLOW(a) \
339 INT_NEGATE_RANGE_OVERFLOW (a, _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
340 #endif
341 #define INT_MULTIPLY_OVERFLOW(a, b) \
342 _GL_BINARY_OP_OVERFLOW (a, b, _GL_MULTIPLY_OVERFLOW)
343 #define INT_DIVIDE_OVERFLOW(a, b) \
344 _GL_BINARY_OP_OVERFLOW (a, b, _GL_DIVIDE_OVERFLOW)
345 #define INT_REMAINDER_OVERFLOW(a, b) \
346 _GL_BINARY_OP_OVERFLOW (a, b, _GL_REMAINDER_OVERFLOW)
347 #define INT_LEFT_SHIFT_OVERFLOW(a, b) \
348 INT_LEFT_SHIFT_RANGE_OVERFLOW (a, b, \
349 _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
351 /* Return 1 if the expression A <op> B would overflow,
352 where OP_RESULT_OVERFLOW (A, B, MIN, MAX) does the actual test,
353 assuming MIN and MAX are the minimum and maximum for the result type.
354 Arguments should be free of side effects. */
355 #define _GL_BINARY_OP_OVERFLOW(a, b, op_result_overflow) \
356 op_result_overflow (a, b, \
357 _GL_INT_MINIMUM (0 * (b) + (a)), \
358 _GL_INT_MAXIMUM (0 * (b) + (a)))
360 /* Store the low-order bits of A + B, A - B, A * B, respectively, into *R.
361 Return 1 if the result overflows. See above for restrictions. */
362 #define INT_ADD_WRAPV(a, b, r) \
363 _GL_INT_OP_WRAPV (a, b, r, +, __builtin_add_overflow, INT_ADD_OVERFLOW)
364 #define INT_SUBTRACT_WRAPV(a, b, r) \
365 _GL_INT_OP_WRAPV (a, b, r, -, __builtin_sub_overflow, INT_SUBTRACT_OVERFLOW)
366 #define INT_MULTIPLY_WRAPV(a, b, r) \
367 _GL_INT_OP_WRAPV (a, b, r, *, __builtin_mul_overflow, INT_MULTIPLY_OVERFLOW)
369 /* Nonzero if this compiler has GCC bug 68193 or Clang bug 25390. See:
370 https://gcc.gnu.org/bugzilla/show_bug.cgi?id=68193
371 https://llvm.org/bugs/show_bug.cgi?id=25390
372 For now, assume all versions of GCC-like compilers generate bogus
373 warnings for _Generic. This matters only for older compilers that
374 lack __builtin_add_overflow. */
375 #if __GNUC__
376 # define _GL__GENERIC_BOGUS 1
377 #else
378 # define _GL__GENERIC_BOGUS 0
379 #endif
381 /* Store the low-order bits of A <op> B into *R, where OP specifies
382 the operation. BUILTIN is the builtin operation, and OVERFLOW the
383 overflow predicate. Return 1 if the result overflows. See above
384 for restrictions. */
385 #if _GL_HAS_BUILTIN_OVERFLOW
386 # define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) builtin (a, b, r)
387 #elif 201112 <= __STDC_VERSION__ && !_GL__GENERIC_BOGUS
388 # define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) \
389 (_Generic \
390 (*(r), \
391 signed char: \
392 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned char, \
393 signed char, SCHAR_MIN, SCHAR_MAX), \
394 short int: \
395 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned short int, \
396 short int, SHRT_MIN, SHRT_MAX), \
397 int: \
398 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
399 int, INT_MIN, INT_MAX), \
400 long int: \
401 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
402 long int, LONG_MIN, LONG_MAX), \
403 long long int: \
404 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
405 long long int, LLONG_MIN, LLONG_MAX)))
406 #else
407 # define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) \
408 (sizeof *(r) == sizeof (signed char) \
409 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned char, \
410 signed char, SCHAR_MIN, SCHAR_MAX) \
411 : sizeof *(r) == sizeof (short int) \
412 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned short int, \
413 short int, SHRT_MIN, SHRT_MAX) \
414 : sizeof *(r) == sizeof (int) \
415 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
416 int, INT_MIN, INT_MAX) \
417 : _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow))
418 # ifdef LLONG_MAX
419 # define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
420 (sizeof *(r) == sizeof (long int) \
421 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
422 long int, LONG_MIN, LONG_MAX) \
423 : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
424 long long int, LLONG_MIN, LLONG_MAX))
425 # else
426 # define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
427 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
428 long int, LONG_MIN, LONG_MAX)
429 # endif
430 #endif
432 /* Store the low-order bits of A <op> B into *R, where the operation
433 is given by OP. Use the unsigned type UT for calculation to avoid
434 overflow problems. *R's type is T, with extremal values TMIN and
435 TMAX. T must be a signed integer type. Return 1 if the result
436 overflows. */
437 #define _GL_INT_OP_CALC(a, b, r, op, overflow, ut, t, tmin, tmax) \
438 (sizeof ((a) op (b)) < sizeof (t) \
439 ? _GL_INT_OP_CALC1 ((t) (a), (t) (b), r, op, overflow, ut, t, tmin, tmax) \
440 : _GL_INT_OP_CALC1 (a, b, r, op, overflow, ut, t, tmin, tmax))
441 #define _GL_INT_OP_CALC1(a, b, r, op, overflow, ut, t, tmin, tmax) \
442 ((overflow (a, b) \
443 || (EXPR_SIGNED ((a) op (b)) && ((a) op (b)) < (tmin)) \
444 || (tmax) < ((a) op (b))) \
445 ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t, tmin, tmax), 1) \
446 : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t, tmin, tmax), 0))
448 /* Return A <op> B, where the operation is given by OP. Use the
449 unsigned type UT for calculation to avoid overflow problems.
450 Convert the result to type T without overflow by subtracting TMIN
451 from large values before converting, and adding it afterwards.
452 Compilers can optimize all the operations except OP. */
453 #define _GL_INT_OP_WRAPV_VIA_UNSIGNED(a, b, op, ut, t, tmin, tmax) \
454 (((ut) (a) op (ut) (b)) <= (tmax) \
455 ? (t) ((ut) (a) op (ut) (b)) \
456 : ((t) (((ut) (a) op (ut) (b)) - (tmin)) + (tmin)))
458 #endif /* _GL_INTPROPS_H */