1 /* intprops.h -- properties of integer types
2 
3    Copyright (C) 2001-2020 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 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.
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 General Public License for more details.
14 
15    You should have received a copy of the GNU 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 1 when its argument is
115    unsigned, 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) and __builtin_sub_overflow
224    (A, B, P) work when P is non-null.  */
225 #if 5 <= __GNUC__ && !defined __ICC
226 # define _GL_HAS_BUILTIN_ADD_OVERFLOW 1
227 #elif defined __has_builtin
228 # define _GL_HAS_BUILTIN_ADD_OVERFLOW __has_builtin (__builtin_add_overflow)
229 #else
230 # define _GL_HAS_BUILTIN_ADD_OVERFLOW 0
231 #endif
232 
233 /* True if __builtin_mul_overflow (A, B, P) works when P is non-null.  */
234 #ifdef __clang__
235 /* Work around Clang bug <https://bugs.llvm.org/show_bug.cgi?id=16404>.  */
236 # define _GL_HAS_BUILTIN_MUL_OVERFLOW 0
237 #else
238 # define _GL_HAS_BUILTIN_MUL_OVERFLOW _GL_HAS_BUILTIN_ADD_OVERFLOW
239 #endif
240 
241 /* True if __builtin_add_overflow_p (A, B, C) works, and similarly for
242    __builtin_mul_overflow_p and __builtin_mul_overflow_p.  */
243 #define _GL_HAS_BUILTIN_OVERFLOW_P (7 <= __GNUC__)
244 
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))
279 
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)
291 
292 /* Check for integer overflow, and report low order bits of answer.
293 
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 compute the low-order bits of the sum,
297    difference, and product of two C integers, and return 1 if these
298    low-order bits are not numerically correct.
299    These macros work correctly on all known practical hosts, and do not rely
300    on undefined behavior due to signed arithmetic overflow.
301 
302    Example usage, assuming A and B are long int:
303 
304      if (INT_MULTIPLY_OVERFLOW (a, b))
305        printf ("result would overflow\n");
306      else
307        printf ("result is %ld (no overflow)\n", a * b);
308 
309    Example usage with WRAPV flavor:
310 
311      long int result;
312      bool overflow = INT_MULTIPLY_WRAPV (a, b, &result);
313      printf ("result is %ld (%s)\n", result,
314              overflow ? "after overflow" : "no overflow");
315 
316    Restrictions on these macros:
317 
318    These macros do not check for all possible numerical problems or
319    undefined or unspecified behavior: they do not check for division
320    by zero, for bad shift counts, or for shifting negative numbers.
321 
322    These macros may evaluate their arguments zero or multiple times, so the
323    arguments should not have side effects.
324 
325    The WRAPV macros are not constant expressions.  They support only
326    +, binary -, and *.  Because the WRAPV macros convert the result,
327    they report overflow in different circumstances than the OVERFLOW
328    macros do.
329 
330    These macros are tuned for their last input argument being a constant.
331 
332    Return 1 if the integer expressions A * B, A - B, -A, A * B, A / B,
333    A % B, and A << B would overflow, respectively.  */
334 
335 #define INT_ADD_OVERFLOW(a, b) \
336   _GL_BINARY_OP_OVERFLOW (a, b, _GL_ADD_OVERFLOW)
337 #define INT_SUBTRACT_OVERFLOW(a, b) \
338   _GL_BINARY_OP_OVERFLOW (a, b, _GL_SUBTRACT_OVERFLOW)
339 #if _GL_HAS_BUILTIN_OVERFLOW_P
340 # define INT_NEGATE_OVERFLOW(a) INT_SUBTRACT_OVERFLOW (0, a)
341 #else
342 # define INT_NEGATE_OVERFLOW(a) \
343    INT_NEGATE_RANGE_OVERFLOW (a, _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
344 #endif
345 #define INT_MULTIPLY_OVERFLOW(a, b) \
346   _GL_BINARY_OP_OVERFLOW (a, b, _GL_MULTIPLY_OVERFLOW)
347 #define INT_DIVIDE_OVERFLOW(a, b) \
348   _GL_BINARY_OP_OVERFLOW (a, b, _GL_DIVIDE_OVERFLOW)
349 #define INT_REMAINDER_OVERFLOW(a, b) \
350   _GL_BINARY_OP_OVERFLOW (a, b, _GL_REMAINDER_OVERFLOW)
351 #define INT_LEFT_SHIFT_OVERFLOW(a, b) \
352   INT_LEFT_SHIFT_RANGE_OVERFLOW (a, b, \
353                                  _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
354 
355 /* Return 1 if the expression A <op> B would overflow,
356    where OP_RESULT_OVERFLOW (A, B, MIN, MAX) does the actual test,
357    assuming MIN and MAX are the minimum and maximum for the result type.
358    Arguments should be free of side effects.  */
359 #define _GL_BINARY_OP_OVERFLOW(a, b, op_result_overflow)        \
360   op_result_overflow (a, b,                                     \
361                       _GL_INT_MINIMUM (_GL_INT_CONVERT (a, b)), \
362                       _GL_INT_MAXIMUM (_GL_INT_CONVERT (a, b)))
363 
364 /* Store the low-order bits of A + B, A - B, A * B, respectively, into *R.
365    Return 1 if the result overflows.  See above for restrictions.  */
366 #if _GL_HAS_BUILTIN_ADD_OVERFLOW
367 # define INT_ADD_WRAPV(a, b, r) __builtin_add_overflow (a, b, r)
368 # define INT_SUBTRACT_WRAPV(a, b, r) __builtin_sub_overflow (a, b, r)
369 #else
370 # define INT_ADD_WRAPV(a, b, r) \
371    _GL_INT_OP_WRAPV (a, b, r, +, _GL_INT_ADD_RANGE_OVERFLOW)
372 # define INT_SUBTRACT_WRAPV(a, b, r) \
373    _GL_INT_OP_WRAPV (a, b, r, -, _GL_INT_SUBTRACT_RANGE_OVERFLOW)
374 #endif
375 #if _GL_HAS_BUILTIN_MUL_OVERFLOW
376 # if (9 < __GNUC__ + (3 <= __GNUC_MINOR__) \
377       || (__GNUC__ == 8 && 4 <= __GNUC_MINOR__))
378 #  define INT_MULTIPLY_WRAPV(a, b, r) __builtin_mul_overflow (a, b, r)
379 # else
380    /* Work around GCC bug 91450.  */
381 #  define INT_MULTIPLY_WRAPV(a, b, r) \
382     ((!_GL_SIGNED_TYPE_OR_EXPR (*(r)) && EXPR_SIGNED (a) && EXPR_SIGNED (b) \
383       && _GL_INT_MULTIPLY_RANGE_OVERFLOW (a, b, 0, (__typeof__ (*(r))) -1)) \
384      ? ((void) __builtin_mul_overflow (a, b, r), 1) \
385      : __builtin_mul_overflow (a, b, r))
386 # endif
387 #else
388 # define INT_MULTIPLY_WRAPV(a, b, r) \
389    _GL_INT_OP_WRAPV (a, b, r, *, _GL_INT_MULTIPLY_RANGE_OVERFLOW)
390 #endif
391 
392 /* Nonzero if this compiler has GCC bug 68193 or Clang bug 25390.  See:
393    https://gcc.gnu.org/bugzilla/show_bug.cgi?id=68193
394    https://llvm.org/bugs/show_bug.cgi?id=25390
395    For now, assume all versions of GCC-like compilers generate bogus
396    warnings for _Generic.  This matters only for compilers that
397    lack relevant builtins.  */
398 #if __GNUC__
399 # define _GL__GENERIC_BOGUS 1
400 #else
401 # define _GL__GENERIC_BOGUS 0
402 #endif
403 
404 /* Store the low-order bits of A <op> B into *R, where OP specifies
405    the operation and OVERFLOW the overflow predicate.  Return 1 if the
406    result overflows.  See above for restrictions.  */
407 #if 201112 <= __STDC_VERSION__ && !_GL__GENERIC_BOGUS
408 # define _GL_INT_OP_WRAPV(a, b, r, op, overflow) \
409    (_Generic \
410     (*(r), \
411      signed char: \
412        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
413                         signed char, SCHAR_MIN, SCHAR_MAX), \
414      unsigned char: \
415        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
416                         unsigned char, 0, UCHAR_MAX), \
417      short int: \
418        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
419                         short int, SHRT_MIN, SHRT_MAX), \
420      unsigned short int: \
421        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
422                         unsigned short int, 0, USHRT_MAX), \
423      int: \
424        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
425                         int, INT_MIN, INT_MAX), \
426      unsigned int: \
427        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
428                         unsigned int, 0, UINT_MAX), \
429      long int: \
430        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
431                         long int, LONG_MIN, LONG_MAX), \
432      unsigned long int: \
433        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
434                         unsigned long int, 0, ULONG_MAX), \
435      long long int: \
436        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
437                         long long int, LLONG_MIN, LLONG_MAX), \
438      unsigned long long int: \
439        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
440                         unsigned long long int, 0, ULLONG_MAX)))
441 #else
442 /* Store the low-order bits of A <op> B into *R, where OP specifies
443    the operation and OVERFLOW the overflow predicate.  If *R is
444    signed, its type is ST with bounds SMIN..SMAX; otherwise its type
445    is UT with bounds U..UMAX.  ST and UT are narrower than int.
446    Return 1 if the result overflows.  See above for restrictions.  */
447 # if _GL_HAVE___TYPEOF__
448 #  define _GL_INT_OP_WRAPV_SMALLISH(a,b,r,op,overflow,st,smin,smax,ut,umax) \
449     (TYPE_SIGNED (__typeof__ (*(r))) \
450      ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, st, smin, smax) \
451      : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, ut, 0, umax))
452 # else
453 #  define _GL_INT_OP_WRAPV_SMALLISH(a,b,r,op,overflow,st,smin,smax,ut,umax) \
454     (overflow (a, b, smin, smax) \
455      ? (overflow (a, b, 0, umax) \
456         ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st), 1) \
457         : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st)) < 0) \
458      : (overflow (a, b, 0, umax) \
459         ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st)) >= 0 \
460         : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st), 0)))
461 # endif
462 
463 # define _GL_INT_OP_WRAPV(a, b, r, op, overflow) \
464    (sizeof *(r) == sizeof (signed char) \
465     ? _GL_INT_OP_WRAPV_SMALLISH (a, b, r, op, overflow, \
466                                  signed char, SCHAR_MIN, SCHAR_MAX, \
467                                  unsigned char, UCHAR_MAX) \
468     : sizeof *(r) == sizeof (short int) \
469     ? _GL_INT_OP_WRAPV_SMALLISH (a, b, r, op, overflow, \
470                                  short int, SHRT_MIN, SHRT_MAX, \
471                                  unsigned short int, USHRT_MAX) \
472     : sizeof *(r) == sizeof (int) \
473     ? (EXPR_SIGNED (*(r)) \
474        ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
475                           int, INT_MIN, INT_MAX) \
476        : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
477                           unsigned int, 0, UINT_MAX)) \
478     : _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow))
479 # ifdef LLONG_MAX
480 #  define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
481     (sizeof *(r) == sizeof (long int) \
482      ? (EXPR_SIGNED (*(r)) \
483         ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
484                            long int, LONG_MIN, LONG_MAX) \
485         : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
486                            unsigned long int, 0, ULONG_MAX)) \
487      : (EXPR_SIGNED (*(r)) \
488         ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
489                            long long int, LLONG_MIN, LLONG_MAX) \
490         : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
491                            unsigned long long int, 0, ULLONG_MAX)))
492 # else
493 #  define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
494     (EXPR_SIGNED (*(r)) \
495      ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
496                         long int, LONG_MIN, LONG_MAX) \
497      : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
498                         unsigned long int, 0, ULONG_MAX))
499 # endif
500 #endif
501 
502 /* Store the low-order bits of A <op> B into *R, where the operation
503    is given by OP.  Use the unsigned type UT for calculation to avoid
504    overflow problems.  *R's type is T, with extrema TMIN and TMAX.
505    T must be a signed integer type.  Return 1 if the result overflows.  */
506 #define _GL_INT_OP_CALC(a, b, r, op, overflow, ut, t, tmin, tmax) \
507   (overflow (a, b, tmin, tmax) \
508    ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 1) \
509    : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 0))
510 
511 /* Return the low-order bits of A <op> B, where the operation is given
512    by OP.  Use the unsigned type UT for calculation to avoid undefined
513    behavior on signed integer overflow, and convert the result to type T.
514    UT is at least as wide as T and is no narrower than unsigned int,
515    T is two's complement, and there is no padding or trap representations.
516    Assume that converting UT to T yields the low-order bits, as is
517    done in all known two's-complement C compilers.  E.g., see:
518    https://gcc.gnu.org/onlinedocs/gcc/Integers-implementation.html
519 
520    According to the C standard, converting UT to T yields an
521    implementation-defined result or signal for values outside T's
522    range.  However, code that works around this theoretical problem
523    runs afoul of a compiler bug in Oracle Studio 12.3 x86.  See:
524    https://lists.gnu.org/r/bug-gnulib/2017-04/msg00049.html
525    As the compiler bug is real, don't try to work around the
526    theoretical problem.  */
527 
528 #define _GL_INT_OP_WRAPV_VIA_UNSIGNED(a, b, op, ut, t) \
529   ((t) ((ut) (a) op (ut) (b)))
530 
531 /* Return true if the numeric values A + B, A - B, A * B fall outside
532    the range TMIN..TMAX.  Arguments should be integer expressions
533    without side effects.  TMIN should be signed and nonpositive.
534    TMAX should be positive, and should be signed unless TMIN is zero.  */
535 #define _GL_INT_ADD_RANGE_OVERFLOW(a, b, tmin, tmax) \
536   ((b) < 0 \
537    ? (((tmin) \
538        ? ((EXPR_SIGNED (_GL_INT_CONVERT (a, (tmin) - (b))) || (b) < (tmin)) \
539           && (a) < (tmin) - (b)) \
540        : (a) <= -1 - (b)) \
541       || ((EXPR_SIGNED (a) ? 0 <= (a) : (tmax) < (a)) && (tmax) < (a) + (b))) \
542    : (a) < 0 \
543    ? (((tmin) \
544        ? ((EXPR_SIGNED (_GL_INT_CONVERT (b, (tmin) - (a))) || (a) < (tmin)) \
545           && (b) < (tmin) - (a)) \
546        : (b) <= -1 - (a)) \
547       || ((EXPR_SIGNED (_GL_INT_CONVERT (a, b)) || (tmax) < (b)) \
548           && (tmax) < (a) + (b))) \
549    : (tmax) < (b) || (tmax) - (b) < (a))
550 #define _GL_INT_SUBTRACT_RANGE_OVERFLOW(a, b, tmin, tmax) \
551   (((a) < 0) == ((b) < 0) \
552    ? ((a) < (b) \
553       ? !(tmin) || -1 - (tmin) < (b) - (a) - 1 \
554       : (tmax) < (a) - (b)) \
555    : (a) < 0 \
556    ? ((!EXPR_SIGNED (_GL_INT_CONVERT ((a) - (tmin), b)) && (a) - (tmin) < 0) \
557       || (a) - (tmin) < (b)) \
558    : ((! (EXPR_SIGNED (_GL_INT_CONVERT (tmax, b)) \
559           && EXPR_SIGNED (_GL_INT_CONVERT ((tmax) + (b), a))) \
560        && (tmax) <= -1 - (b)) \
561       || (tmax) + (b) < (a)))
562 #define _GL_INT_MULTIPLY_RANGE_OVERFLOW(a, b, tmin, tmax) \
563   ((b) < 0 \
564    ? ((a) < 0 \
565       ? (EXPR_SIGNED (_GL_INT_CONVERT (tmax, b)) \
566          ? (a) < (tmax) / (b) \
567          : ((INT_NEGATE_OVERFLOW (b) \
568              ? _GL_INT_CONVERT (b, tmax) >> (TYPE_WIDTH (b) - 1) \
569              : (tmax) / -(b)) \
570             <= -1 - (a))) \
571       : INT_NEGATE_OVERFLOW (_GL_INT_CONVERT (b, tmin)) && (b) == -1 \
572       ? (EXPR_SIGNED (a) \
573          ? 0 < (a) + (tmin) \
574          : 0 < (a) && -1 - (tmin) < (a) - 1) \
575       : (tmin) / (b) < (a)) \
576    : (b) == 0 \
577    ? 0 \
578    : ((a) < 0 \
579       ? (INT_NEGATE_OVERFLOW (_GL_INT_CONVERT (a, tmin)) && (a) == -1 \
580          ? (EXPR_SIGNED (b) ? 0 < (b) + (tmin) : -1 - (tmin) < (b) - 1) \
581          : (tmin) / (a) < (b)) \
582       : (tmax) / (b) < (a)))
583 
584 #endif /* _GL_INTPROPS_H */
585