1/* intprops.h -- properties of integer types
2
3 Copyright (C) 2001-2019 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 0 when its argument is
115 signed, 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) works when P is non-null. */
224#if 5 <= __GNUC__ && !defined __ICC
225# define _GL_HAS_BUILTIN_OVERFLOW 1
226#else
227# define _GL_HAS_BUILTIN_OVERFLOW 0
228#endif
229
230/* True if __builtin_add_overflow_p (A, B, C) works. */
231#define _GL_HAS_BUILTIN_OVERFLOW_P (7 <= __GNUC__)
232
233/* The _GL*_OVERFLOW macros have the same restrictions as the
234 *_RANGE_OVERFLOW macros, except that they do not assume that operands
235 (e.g., A and B) have the same type as MIN and MAX. Instead, they assume
236 that the result (e.g., A + B) has that type. */
237#if _GL_HAS_BUILTIN_OVERFLOW_P
238# define _GL_ADD_OVERFLOW(a, b, min, max) \
239 __builtin_add_overflow_p (a, b, (__typeof__ ((a) + (b))) 0)
240# define _GL_SUBTRACT_OVERFLOW(a, b, min, max) \
241 __builtin_sub_overflow_p (a, b, (__typeof__ ((a) - (b))) 0)
242# define _GL_MULTIPLY_OVERFLOW(a, b, min, max) \
243 __builtin_mul_overflow_p (a, b, (__typeof__ ((a) * (b))) 0)
244#else
245# define _GL_ADD_OVERFLOW(a, b, min, max) \
246 ((min) < 0 ? INT_ADD_RANGE_OVERFLOW (a, b, min, max) \
247 : (a) < 0 ? (b) <= (a) + (b) \
248 : (b) < 0 ? (a) <= (a) + (b) \
249 : (a) + (b) < (b))
250# define _GL_SUBTRACT_OVERFLOW(a, b, min, max) \
251 ((min) < 0 ? INT_SUBTRACT_RANGE_OVERFLOW (a, b, min, max) \
252 : (a) < 0 ? 1 \
253 : (b) < 0 ? (a) - (b) <= (a) \
254 : (a) < (b))
255# define _GL_MULTIPLY_OVERFLOW(a, b, min, max) \
256 (((min) == 0 && (((a) < 0 && 0 < (b)) || ((b) < 0 && 0 < (a)))) \
257 || INT_MULTIPLY_RANGE_OVERFLOW (a, b, min, max))
258#endif
259#define _GL_DIVIDE_OVERFLOW(a, b, min, max) \
260 ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max) \
261 : (a) < 0 ? (b) <= (a) + (b) - 1 \
262 : (b) < 0 && (a) + (b) <= (a))
263#define _GL_REMAINDER_OVERFLOW(a, b, min, max) \
264 ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max) \
265 : (a) < 0 ? (a) % (b) != ((max) - (b) + 1) % (b) \
266 : (b) < 0 && ! _GL_UNSIGNED_NEG_MULTIPLE (a, b, max))
267
268/* Return a nonzero value if A is a mathematical multiple of B, where
269 A is unsigned, B is negative, and MAX is the maximum value of A's
270 type. A's type must be the same as (A % B)'s type. Normally (A %
271 -B == 0) suffices, but things get tricky if -B would overflow. */
272#define _GL_UNSIGNED_NEG_MULTIPLE(a, b, max) \
273 (((b) < -_GL_SIGNED_INT_MAXIMUM (b) \
274 ? (_GL_SIGNED_INT_MAXIMUM (b) == (max) \
275 ? (a) \
276 : (a) % (_GL_INT_CONVERT (a, _GL_SIGNED_INT_MAXIMUM (b)) + 1)) \
277 : (a) % - (b)) \
278 == 0)
279
280/* Check for integer overflow, and report low order bits of answer.
281
282 The INT_<op>_OVERFLOW macros return 1 if the corresponding C operators
283 might not yield numerically correct answers due to arithmetic overflow.
284 The INT_<op>_WRAPV macros also store the low-order bits of the answer.
285 These macros work correctly on all known practical hosts, and do not rely
286 on undefined behavior due to signed arithmetic overflow.
287
288 Example usage, assuming A and B are long int:
289
290 if (INT_MULTIPLY_OVERFLOW (a, b))
291 printf ("result would overflow\n");
292 else
293 printf ("result is %ld (no overflow)\n", a * b);
294
295 Example usage with WRAPV flavor:
296
297 long int result;
298 bool overflow = INT_MULTIPLY_WRAPV (a, b, &result);
299 printf ("result is %ld (%s)\n", result,
300 overflow ? "after overflow" : "no overflow");
301
302 Restrictions on these macros:
303
304 These macros do not check for all possible numerical problems or
305 undefined or unspecified behavior: they do not check for division
306 by zero, for bad shift counts, or for shifting negative numbers.
307
308 These macros may evaluate their arguments zero or multiple times, so the
309 arguments should not have side effects.
310
311 The WRAPV macros are not constant expressions. They support only
312 +, binary -, and *. The result type must be signed.
313
314 These macros are tuned for their last argument being a constant.
315
316 Return 1 if the integer expressions A * B, A - B, -A, A * B, A / B,
317 A % B, and A << B would overflow, respectively. */
318
319#define INT_ADD_OVERFLOW(a, b) \
320 _GL_BINARY_OP_OVERFLOW (a, b, _GL_ADD_OVERFLOW)
321#define INT_SUBTRACT_OVERFLOW(a, b) \
322 _GL_BINARY_OP_OVERFLOW (a, b, _GL_SUBTRACT_OVERFLOW)
323#if _GL_HAS_BUILTIN_OVERFLOW_P
324# define INT_NEGATE_OVERFLOW(a) INT_SUBTRACT_OVERFLOW (0, a)
325#else
326# define INT_NEGATE_OVERFLOW(a) \
327 INT_NEGATE_RANGE_OVERFLOW (a, _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
328#endif
329#define INT_MULTIPLY_OVERFLOW(a, b) \
330 _GL_BINARY_OP_OVERFLOW (a, b, _GL_MULTIPLY_OVERFLOW)
331#define INT_DIVIDE_OVERFLOW(a, b) \
332 _GL_BINARY_OP_OVERFLOW (a, b, _GL_DIVIDE_OVERFLOW)
333#define INT_REMAINDER_OVERFLOW(a, b) \
334 _GL_BINARY_OP_OVERFLOW (a, b, _GL_REMAINDER_OVERFLOW)
335#define INT_LEFT_SHIFT_OVERFLOW(a, b) \
336 INT_LEFT_SHIFT_RANGE_OVERFLOW (a, b, \
337 _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
338
339/* Return 1 if the expression A <op> B would overflow,
340 where OP_RESULT_OVERFLOW (A, B, MIN, MAX) does the actual test,
341 assuming MIN and MAX are the minimum and maximum for the result type.
342 Arguments should be free of side effects. */
343#define _GL_BINARY_OP_OVERFLOW(a, b, op_result_overflow) \
344 op_result_overflow (a, b, \
345 _GL_INT_MINIMUM (_GL_INT_CONVERT (a, b)), \
346 _GL_INT_MAXIMUM (_GL_INT_CONVERT (a, b)))
347
348/* Store the low-order bits of A + B, A - B, A * B, respectively, into *R.
349 Return 1 if the result overflows. See above for restrictions. */
350#define INT_ADD_WRAPV(a, b, r) \
351 _GL_INT_OP_WRAPV (a, b, r, +, __builtin_add_overflow, INT_ADD_OVERFLOW)
352#define INT_SUBTRACT_WRAPV(a, b, r) \
353 _GL_INT_OP_WRAPV (a, b, r, -, __builtin_sub_overflow, INT_SUBTRACT_OVERFLOW)
354#define INT_MULTIPLY_WRAPV(a, b, r) \
355 _GL_INT_OP_WRAPV (a, b, r, *, __builtin_mul_overflow, INT_MULTIPLY_OVERFLOW)
356
357/* Nonzero if this compiler has GCC bug 68193 or Clang bug 25390. See:
358 https://gcc.gnu.org/bugzilla/show_bug.cgi?id=68193
359 https://llvm.org/bugs/show_bug.cgi?id=25390
360 For now, assume all versions of GCC-like compilers generate bogus
361 warnings for _Generic. This matters only for older compilers that
362 lack __builtin_add_overflow. */
363#if __GNUC__
364# define _GL__GENERIC_BOGUS 1
365#else
366# define _GL__GENERIC_BOGUS 0
367#endif
368
369/* Store the low-order bits of A <op> B into *R, where OP specifies
370 the operation. BUILTIN is the builtin operation, and OVERFLOW the
371 overflow predicate. Return 1 if the result overflows. See above
372 for restrictions. */
373#if _GL_HAS_BUILTIN_OVERFLOW
374# define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) builtin (a, b, r)
375#elif 201112 <= __STDC_VERSION__ && !_GL__GENERIC_BOGUS
376# define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) \
377 (_Generic \
378 (*(r), \
379 signed char: \
380 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
381 signed char, SCHAR_MIN, SCHAR_MAX), \
382 short int: \
383 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
384 short int, SHRT_MIN, SHRT_MAX), \
385 int: \
386 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
387 int, INT_MIN, INT_MAX), \
388 long int: \
389 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
390 long int, LONG_MIN, LONG_MAX), \
391 long long int: \
392 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
393 long long int, LLONG_MIN, LLONG_MAX)))
394#else
395# define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) \
396 (sizeof *(r) == sizeof (signed char) \
397 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
398 signed char, SCHAR_MIN, SCHAR_MAX) \
399 : sizeof *(r) == sizeof (short int) \
400 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
401 short int, SHRT_MIN, SHRT_MAX) \
402 : sizeof *(r) == sizeof (int) \
403 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
404 int, INT_MIN, INT_MAX) \
405 : _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow))
406# ifdef LLONG_MAX
407# define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
408 (sizeof *(r) == sizeof (long int) \
409 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
410 long int, LONG_MIN, LONG_MAX) \
411 : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
412 long long int, LLONG_MIN, LLONG_MAX))
413# else
414# define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
415 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
416 long int, LONG_MIN, LONG_MAX)
417# endif
418#endif
419
420/* Store the low-order bits of A <op> B into *R, where the operation
421 is given by OP. Use the unsigned type UT for calculation to avoid
422 overflow problems. *R's type is T, with extrema TMIN and TMAX.
423 T must be a signed integer type. Return 1 if the result overflows. */
424#define _GL_INT_OP_CALC(a, b, r, op, overflow, ut, t, tmin, tmax) \
425 (sizeof ((a) op (b)) < sizeof (t) \
426 ? _GL_INT_OP_CALC1 ((t) (a), (t) (b), r, op, overflow, ut, t, tmin, tmax) \
427 : _GL_INT_OP_CALC1 (a, b, r, op, overflow, ut, t, tmin, tmax))
428#define _GL_INT_OP_CALC1(a, b, r, op, overflow, ut, t, tmin, tmax) \
429 ((overflow (a, b) \
430 || (EXPR_SIGNED ((a) op (b)) && ((a) op (b)) < (tmin)) \
431 || (tmax) < ((a) op (b))) \
432 ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 1) \
433 : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 0))
434
435/* Return the low-order bits of A <op> B, where the operation is given
436 by OP. Use the unsigned type UT for calculation to avoid undefined
437 behavior on signed integer overflow, and convert the result to type T.
438 UT is at least as wide as T and is no narrower than unsigned int,
439 T is two's complement, and there is no padding or trap representations.
440 Assume that converting UT to T yields the low-order bits, as is
441 done in all known two's-complement C compilers. E.g., see:
442 https://gcc.gnu.org/onlinedocs/gcc/Integers-implementation.html
443
444 According to the C standard, converting UT to T yields an
445 implementation-defined result or signal for values outside T's
446 range. However, code that works around this theoretical problem
447 runs afoul of a compiler bug in Oracle Studio 12.3 x86. See:
448 https://lists.gnu.org/r/bug-gnulib/2017-04/msg00049.html
449 As the compiler bug is real, don't try to work around the
450 theoretical problem. */
451
452#define _GL_INT_OP_WRAPV_VIA_UNSIGNED(a, b, op, ut, t) \
453 ((t) ((ut) (a) op (ut) (b)))
454
455#endif /* _GL_INTPROPS_H */
456