gsasl  1.10.0
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intprops.h
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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 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 */