1 /* intprops.h -- properties of integer types
2 
3    Copyright (C) 2001-2022 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 
19 #ifndef _GL_INTPROPS_H
20 #define _GL_INTPROPS_H
21 
22 #include <limits.h>
23 
24 /* Return a value with the common real type of E and V and the value of V.
25    Do not evaluate E.  */
26 #define _GL_INT_CONVERT(e, v) ((1 ? 0 : (e)) + (v))
27 
28 /* Act like _GL_INT_CONVERT (E, -V) but work around a bug in IRIX 6.5 cc; see
29    <https://lists.gnu.org/r/bug-gnulib/2011-05/msg00406.html>.  */
30 #define _GL_INT_NEGATE_CONVERT(e, v) ((1 ? 0 : (e)) - (v))
31 
32 /* The extra casts in the following macros work around compiler bugs,
33    e.g., in Cray C 5.0.3.0.  */
34 
35 /* True if the arithmetic type T is an integer type.  bool counts as
36    an integer.  */
37 #define TYPE_IS_INTEGER(t) ((t) 1.5 == 1)
38 
39 /* True if the real type T is signed.  */
40 #define TYPE_SIGNED(t) (! ((t) 0 < (t) -1))
41 
42 /* Return 1 if the real expression E, after promotion, has a
43    signed or floating type.  Do not evaluate E.  */
44 #define EXPR_SIGNED(e) (_GL_INT_NEGATE_CONVERT (e, 1) < 0)
45 
46 
47 /* Minimum and maximum values for integer types and expressions.  */
48 
49 /* The width in bits of the integer type or expression T.
50    Do not evaluate T.  T must not be a bit-field expression.
51    Padding bits are not supported; this is checked at compile-time below.  */
52 #define TYPE_WIDTH(t) (sizeof (t) * CHAR_BIT)
53 
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)))
60 
61 /* The maximum and minimum values for the type of the expression E,
62    after integer promotion.  E is not evaluated.  */
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)) - 2)) - 1) * 2 + 1)
73 
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
79 
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    This assumption is tested by the intprops-tests module.  */
84 
85 /* Does the __typeof__ keyword work?  This could be done by
86    'configure', but for now it's easier to do it by hand.  */
87 #if (2 <= __GNUC__ \
88      || (4 <= __clang_major__) \
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.  T must not be a bit-field expression.
98    This macro does not evaluate its argument, and expands to an
99    integer constant expression.  */
100 #if _GL_HAVE___TYPEOF__
101 # define _GL_SIGNED_TYPE_OR_EXPR(t) TYPE_SIGNED (__typeof__ (t))
102 #else
103 # define _GL_SIGNED_TYPE_OR_EXPR(t) 1
104 #endif
105 
106 /* Bound on length of the string representing an unsigned integer
107    value representable in B bits.  log10 (2.0) < 146/485.  The
108    smallest value of B where this bound is not tight is 2621.  */
109 #define INT_BITS_STRLEN_BOUND(b) (((b) * 146 + 484) / 485)
110 
111 /* Bound on length of the string representing an integer type or expression T.
112    T must not be a bit-field expression.
113 
114    Subtract 1 for the sign bit if T is signed, and then add 1 more for
115    a minus sign if needed.
116 
117    Because _GL_SIGNED_TYPE_OR_EXPR sometimes returns 1 when its argument is
118    unsigned, this macro may overestimate the true bound by one byte when
119    applied to unsigned types of size 2, 4, 16, ... bytes.  */
120 #define INT_STRLEN_BOUND(t)                                     \
121   (INT_BITS_STRLEN_BOUND (TYPE_WIDTH (t) - _GL_SIGNED_TYPE_OR_EXPR (t)) \
122    + _GL_SIGNED_TYPE_OR_EXPR (t))
123 
124 /* Bound on buffer size needed to represent an integer type or expression T,
125    including the terminating null.  T must not be a bit-field expression.  */
126 #define INT_BUFSIZE_BOUND(t) (INT_STRLEN_BOUND (t) + 1)
127 
128 
129 /* Range overflow checks.
130 
131    The INT_<op>_RANGE_OVERFLOW macros return 1 if the corresponding C
132    operators might not yield numerically correct answers due to
133    arithmetic overflow.  They do not rely on undefined or
134    implementation-defined behavior.  Their implementations are simple
135    and straightforward, but they are harder to use and may be less
136    efficient than the INT_<op>_WRAPV, INT_<op>_OK, and
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    Because all arguments are subject to integer promotions, these
162    macros typically do not work on types narrower than 'int'.
163 
164    These macros are tuned for constant MIN and MAX.  For commutative
165    operations such as A + B, they are also tuned for constant B.  */
166 
167 /* Return 1 if A + B would overflow in [MIN,MAX] arithmetic.
168    See above for restrictions.  */
169 #define INT_ADD_RANGE_OVERFLOW(a, b, min, max)          \
170   ((b) < 0                                              \
171    ? (a) < (min) - (b)                                  \
172    : (max) - (b) < (a))
173 
174 /* Return 1 if A - B would overflow in [MIN,MAX] arithmetic.
175    See above for restrictions.  */
176 #define INT_SUBTRACT_RANGE_OVERFLOW(a, b, min, max)     \
177   ((b) < 0                                              \
178    ? (max) + (b) < (a)                                  \
179    : (a) < (min) + (b))
180 
181 /* Return 1 if - A would overflow in [MIN,MAX] arithmetic.
182    See above for restrictions.  */
183 #define INT_NEGATE_RANGE_OVERFLOW(a, min, max)          \
184   ((min) < 0                                            \
185    ? (a) < - (max)                                      \
186    : 0 < (a))
187 
188 /* Return 1 if A * B would overflow in [MIN,MAX] arithmetic.
189    See above for restrictions.  Avoid && and || as they tickle
190    bugs in Sun C 5.11 2010/08/13 and other compilers; see
191    <https://lists.gnu.org/r/bug-gnulib/2011-05/msg00401.html>.  */
192 #define INT_MULTIPLY_RANGE_OVERFLOW(a, b, min, max)     \
193   ((b) < 0                                              \
194    ? ((a) < 0                                           \
195       ? (a) < (max) / (b)                               \
196       : (b) == -1                                       \
197       ? 0                                               \
198       : (min) / (b) < (a))                              \
199    : (b) == 0                                           \
200    ? 0                                                  \
201    : ((a) < 0                                           \
202       ? (a) < (min) / (b)                               \
203       : (max) / (b) < (a)))
204 
205 /* Return 1 if A / B would overflow in [MIN,MAX] arithmetic.
206    See above for restrictions.  Do not check for division by zero.  */
207 #define INT_DIVIDE_RANGE_OVERFLOW(a, b, min, max)       \
208   ((min) < 0 && (b) == -1 && (a) < - (max))
209 
210 /* Return 1 if A % B would overflow in [MIN,MAX] arithmetic.
211    See above for restrictions.  Do not check for division by zero.
212    Mathematically, % should never overflow, but on x86-like hosts
213    INT_MIN % -1 traps, and the C standard permits this, so treat this
214    as an overflow too.  */
215 #define INT_REMAINDER_RANGE_OVERFLOW(a, b, min, max)    \
216   INT_DIVIDE_RANGE_OVERFLOW (a, b, min, max)
217 
218 /* Return 1 if A << B would overflow in [MIN,MAX] arithmetic.
219    See above for restrictions.  Here, MIN and MAX are for A only, and B need
220    not be of the same type as the other arguments.  The C standard says that
221    behavior is undefined for shifts unless 0 <= B < wordwidth, and that when
222    A is negative then A << B has undefined behavior and A >> B has
223    implementation-defined behavior, but do not check these other
224    restrictions.  */
225 #define INT_LEFT_SHIFT_RANGE_OVERFLOW(a, b, min, max)   \
226   ((a) < 0                                              \
227    ? (a) < (min) >> (b)                                 \
228    : (max) >> (b) < (a))
229 
230 /* True if __builtin_add_overflow (A, B, P) and __builtin_sub_overflow
231    (A, B, P) work when P is non-null.  */
232 /* __builtin_{add,sub}_overflow exists but is not reliable in GCC 5.x and 6.x,
233    see <https://gcc.gnu.org/bugzilla/show_bug.cgi?id=98269>.  */
234 #if 7 <= __GNUC__ && !defined __ICC
235 # define _GL_HAS_BUILTIN_ADD_OVERFLOW 1
236 #elif defined __has_builtin
237 # define _GL_HAS_BUILTIN_ADD_OVERFLOW __has_builtin (__builtin_add_overflow)
238 #else
239 # define _GL_HAS_BUILTIN_ADD_OVERFLOW 0
240 #endif
241 
242 /* True if __builtin_mul_overflow (A, B, P) works when P is non-null.  */
243 #ifdef __clang__
244 /* Work around Clang bug <https://bugs.llvm.org/show_bug.cgi?id=16404>.  */
245 # define _GL_HAS_BUILTIN_MUL_OVERFLOW 0
246 #else
247 # define _GL_HAS_BUILTIN_MUL_OVERFLOW _GL_HAS_BUILTIN_ADD_OVERFLOW
248 #endif
249 
250 /* True if __builtin_add_overflow_p (A, B, C) works, and similarly for
251    __builtin_sub_overflow_p and __builtin_mul_overflow_p.  */
252 #if defined __clang__ || defined __ICC
253 /* Clang 11 lacks __builtin_mul_overflow_p, and even if it did it
254    would presumably run afoul of Clang bug 16404.  ICC 2021.1's
255    __builtin_add_overflow_p etc. are not treated as integral constant
256    expressions even when all arguments are.  */
257 # define _GL_HAS_BUILTIN_OVERFLOW_P 0
258 #elif defined __has_builtin
259 # define _GL_HAS_BUILTIN_OVERFLOW_P __has_builtin (__builtin_mul_overflow_p)
260 #else
261 # define _GL_HAS_BUILTIN_OVERFLOW_P (7 <= __GNUC__)
262 #endif
263 
264 /* The _GL*_OVERFLOW macros have the same restrictions as the
265    *_RANGE_OVERFLOW macros, except that they do not assume that operands
266    (e.g., A and B) have the same type as MIN and MAX.  Instead, they assume
267    that the result (e.g., A + B) has that type.  */
268 #if _GL_HAS_BUILTIN_OVERFLOW_P
269 # define _GL_ADD_OVERFLOW(a, b, min, max)                               \
270    __builtin_add_overflow_p (a, b, (__typeof__ ((a) + (b))) 0)
271 # define _GL_SUBTRACT_OVERFLOW(a, b, min, max)                          \
272    __builtin_sub_overflow_p (a, b, (__typeof__ ((a) - (b))) 0)
273 # define _GL_MULTIPLY_OVERFLOW(a, b, min, max)                          \
274    __builtin_mul_overflow_p (a, b, (__typeof__ ((a) * (b))) 0)
275 #else
276 # define _GL_ADD_OVERFLOW(a, b, min, max)                                \
277    ((min) < 0 ? INT_ADD_RANGE_OVERFLOW (a, b, min, max)                  \
278     : (a) < 0 ? (b) <= (a) + (b)                                         \
279     : (b) < 0 ? (a) <= (a) + (b)                                         \
280     : (a) + (b) < (b))
281 # define _GL_SUBTRACT_OVERFLOW(a, b, min, max)                           \
282    ((min) < 0 ? INT_SUBTRACT_RANGE_OVERFLOW (a, b, min, max)             \
283     : (a) < 0 ? 1                                                        \
284     : (b) < 0 ? (a) - (b) <= (a)                                         \
285     : (a) < (b))
286 # define _GL_MULTIPLY_OVERFLOW(a, b, min, max)                           \
287    (((min) == 0 && (((a) < 0 && 0 < (b)) || ((b) < 0 && 0 < (a))))       \
288     || INT_MULTIPLY_RANGE_OVERFLOW (a, b, min, max))
289 #endif
290 #define _GL_DIVIDE_OVERFLOW(a, b, min, max)                             \
291   ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max)  \
292    : (a) < 0 ? (b) <= (a) + (b) - 1                                     \
293    : (b) < 0 && (a) + (b) <= (a))
294 #define _GL_REMAINDER_OVERFLOW(a, b, min, max)                          \
295   ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max)  \
296    : (a) < 0 ? (a) % (b) != ((max) - (b) + 1) % (b)                     \
297    : (b) < 0 && ! _GL_UNSIGNED_NEG_MULTIPLE (a, b, max))
298 
299 /* Return a nonzero value if A is a mathematical multiple of B, where
300    A is unsigned, B is negative, and MAX is the maximum value of A's
301    type.  A's type must be the same as (A % B)'s type.  Normally (A %
302    -B == 0) suffices, but things get tricky if -B would overflow.  */
303 #define _GL_UNSIGNED_NEG_MULTIPLE(a, b, max)                            \
304   (((b) < -_GL_SIGNED_INT_MAXIMUM (b)                                   \
305     ? (_GL_SIGNED_INT_MAXIMUM (b) == (max)                              \
306        ? (a)                                                            \
307        : (a) % (_GL_INT_CONVERT (a, _GL_SIGNED_INT_MAXIMUM (b)) + 1))   \
308     : (a) % - (b))                                                      \
309    == 0)
310 
311 /* Check for integer overflow, and report low order bits of answer.
312 
313    The INT_<op>_OVERFLOW macros return 1 if the corresponding C operators
314    might not yield numerically correct answers due to arithmetic overflow.
315    The INT_<op>_WRAPV macros compute the low-order bits of the sum,
316    difference, and product of two C integers, and return 1 if these
317    low-order bits are not numerically correct.
318    These macros work correctly on all known practical hosts, and do not rely
319    on undefined behavior due to signed arithmetic overflow.
320 
321    Example usage, assuming A and B are long int:
322 
323      if (INT_MULTIPLY_OVERFLOW (a, b))
324        printf ("result would overflow\n");
325      else
326        printf ("result is %ld (no overflow)\n", a * b);
327 
328    Example usage with WRAPV flavor:
329 
330      long int result;
331      bool overflow = INT_MULTIPLY_WRAPV (a, b, &result);
332      printf ("result is %ld (%s)\n", result,
333              overflow ? "after overflow" : "no overflow");
334 
335    Restrictions on these macros:
336 
337    These macros do not check for all possible numerical problems or
338    undefined or unspecified behavior: they do not check for division
339    by zero, for bad shift counts, or for shifting negative numbers.
340 
341    These macros may evaluate their arguments zero or multiple times, so the
342    arguments should not have side effects.
343 
344    The WRAPV macros are not constant expressions.  They support only
345    +, binary -, and *.
346 
347    Because the WRAPV macros convert the result, they report overflow
348    in different circumstances than the OVERFLOW macros do.  For
349    example, in the typical case with 16-bit 'short' and 32-bit 'int',
350    if A, B and R are all of type 'short' then INT_ADD_OVERFLOW (A, B)
351    returns false because the addition cannot overflow after A and B
352    are converted to 'int', whereas INT_ADD_WRAPV (A, B, &R) returns
353    true or false depending on whether the sum fits into 'short'.
354 
355    These macros are tuned for their last input argument being a constant.
356 
357    Return 1 if the integer expressions A * B, A - B, -A, A * B, A / B,
358    A % B, and A << B would overflow, respectively.  */
359 
360 #define INT_ADD_OVERFLOW(a, b) \
361   _GL_BINARY_OP_OVERFLOW (a, b, _GL_ADD_OVERFLOW)
362 #define INT_SUBTRACT_OVERFLOW(a, b) \
363   _GL_BINARY_OP_OVERFLOW (a, b, _GL_SUBTRACT_OVERFLOW)
364 #if _GL_HAS_BUILTIN_OVERFLOW_P
365 # define INT_NEGATE_OVERFLOW(a) INT_SUBTRACT_OVERFLOW (0, a)
366 #else
367 # define INT_NEGATE_OVERFLOW(a) \
368    INT_NEGATE_RANGE_OVERFLOW (a, _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
369 #endif
370 #define INT_MULTIPLY_OVERFLOW(a, b) \
371   _GL_BINARY_OP_OVERFLOW (a, b, _GL_MULTIPLY_OVERFLOW)
372 #define INT_DIVIDE_OVERFLOW(a, b) \
373   _GL_BINARY_OP_OVERFLOW (a, b, _GL_DIVIDE_OVERFLOW)
374 #define INT_REMAINDER_OVERFLOW(a, b) \
375   _GL_BINARY_OP_OVERFLOW (a, b, _GL_REMAINDER_OVERFLOW)
376 #define INT_LEFT_SHIFT_OVERFLOW(a, b) \
377   INT_LEFT_SHIFT_RANGE_OVERFLOW (a, b, \
378                                  _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
379 
380 /* Return 1 if the expression A <op> B would overflow,
381    where OP_RESULT_OVERFLOW (A, B, MIN, MAX) does the actual test,
382    assuming MIN and MAX are the minimum and maximum for the result type.
383    Arguments should be free of side effects.  */
384 #define _GL_BINARY_OP_OVERFLOW(a, b, op_result_overflow)        \
385   op_result_overflow (a, b,                                     \
386                       _GL_INT_MINIMUM (_GL_INT_CONVERT (a, b)), \
387                       _GL_INT_MAXIMUM (_GL_INT_CONVERT (a, b)))
388 
389 /* Store the low-order bits of A + B, A - B, A * B, respectively, into *R.
390    Return 1 if the result overflows.  See above for restrictions.  */
391 #if _GL_HAS_BUILTIN_ADD_OVERFLOW
392 # define INT_ADD_WRAPV(a, b, r) __builtin_add_overflow (a, b, r)
393 # define INT_SUBTRACT_WRAPV(a, b, r) __builtin_sub_overflow (a, b, r)
394 #else
395 # define INT_ADD_WRAPV(a, b, r) \
396    _GL_INT_OP_WRAPV (a, b, r, +, _GL_INT_ADD_RANGE_OVERFLOW)
397 # define INT_SUBTRACT_WRAPV(a, b, r) \
398    _GL_INT_OP_WRAPV (a, b, r, -, _GL_INT_SUBTRACT_RANGE_OVERFLOW)
399 #endif
400 #if _GL_HAS_BUILTIN_MUL_OVERFLOW
401 # if ((9 < __GNUC__ + (3 <= __GNUC_MINOR__) \
402        || (__GNUC__ == 8 && 4 <= __GNUC_MINOR__)) \
403       && !defined __ICC)
404 #  define INT_MULTIPLY_WRAPV(a, b, r) __builtin_mul_overflow (a, b, r)
405 # else
406    /* Work around GCC bug 91450.  */
407 #  define INT_MULTIPLY_WRAPV(a, b, r) \
408     ((!_GL_SIGNED_TYPE_OR_EXPR (*(r)) && EXPR_SIGNED (a) && EXPR_SIGNED (b) \
409       && _GL_INT_MULTIPLY_RANGE_OVERFLOW (a, b, 0, (__typeof__ (*(r))) -1)) \
410      ? ((void) __builtin_mul_overflow (a, b, r), 1) \
411      : __builtin_mul_overflow (a, b, r))
412 # endif
413 #else
414 # define INT_MULTIPLY_WRAPV(a, b, r) \
415    _GL_INT_OP_WRAPV (a, b, r, *, _GL_INT_MULTIPLY_RANGE_OVERFLOW)
416 #endif
417 
418 /* Nonzero if this compiler has GCC bug 68193 or Clang bug 25390.  See:
419    https://gcc.gnu.org/bugzilla/show_bug.cgi?id=68193
420    https://llvm.org/bugs/show_bug.cgi?id=25390
421    For now, assume all versions of GCC-like compilers generate bogus
422    warnings for _Generic.  This matters only for compilers that
423    lack relevant builtins.  */
424 #if __GNUC__ || defined __clang__
425 # define _GL__GENERIC_BOGUS 1
426 #else
427 # define _GL__GENERIC_BOGUS 0
428 #endif
429 
430 /* Store the low-order bits of A <op> B into *R, where OP specifies
431    the operation and OVERFLOW the overflow predicate.  Return 1 if the
432    result overflows.  See above for restrictions.  */
433 #if 201112 <= __STDC_VERSION__ && !_GL__GENERIC_BOGUS
434 # define _GL_INT_OP_WRAPV(a, b, r, op, overflow) \
435    (_Generic \
436     (*(r), \
437      signed char: \
438        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
439                         signed char, SCHAR_MIN, SCHAR_MAX), \
440      unsigned char: \
441        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
442                         unsigned char, 0, UCHAR_MAX), \
443      short int: \
444        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
445                         short int, SHRT_MIN, SHRT_MAX), \
446      unsigned short int: \
447        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
448                         unsigned short int, 0, USHRT_MAX), \
449      int: \
450        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
451                         int, INT_MIN, INT_MAX), \
452      unsigned int: \
453        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
454                         unsigned int, 0, UINT_MAX), \
455      long int: \
456        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
457                         long int, LONG_MIN, LONG_MAX), \
458      unsigned long int: \
459        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
460                         unsigned long int, 0, ULONG_MAX), \
461      long long int: \
462        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
463                         long long int, LLONG_MIN, LLONG_MAX), \
464      unsigned long long int: \
465        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
466                         unsigned long long int, 0, ULLONG_MAX)))
467 #else
468 /* Store the low-order bits of A <op> B into *R, where OP specifies
469    the operation and OVERFLOW the overflow predicate.  If *R is
470    signed, its type is ST with bounds SMIN..SMAX; otherwise its type
471    is UT with bounds U..UMAX.  ST and UT are narrower than int.
472    Return 1 if the result overflows.  See above for restrictions.  */
473 # if _GL_HAVE___TYPEOF__
474 #  define _GL_INT_OP_WRAPV_SMALLISH(a,b,r,op,overflow,st,smin,smax,ut,umax) \
475     (TYPE_SIGNED (__typeof__ (*(r))) \
476      ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, st, smin, smax) \
477      : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, ut, 0, umax))
478 # else
479 #  define _GL_INT_OP_WRAPV_SMALLISH(a,b,r,op,overflow,st,smin,smax,ut,umax) \
480     (overflow (a, b, smin, smax) \
481      ? (overflow (a, b, 0, umax) \
482         ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st), 1) \
483         : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st)) < 0) \
484      : (overflow (a, b, 0, umax) \
485         ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st)) >= 0 \
486         : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st), 0)))
487 # endif
488 
489 # define _GL_INT_OP_WRAPV(a, b, r, op, overflow) \
490    (sizeof *(r) == sizeof (signed char) \
491     ? _GL_INT_OP_WRAPV_SMALLISH (a, b, r, op, overflow, \
492                                  signed char, SCHAR_MIN, SCHAR_MAX, \
493                                  unsigned char, UCHAR_MAX) \
494     : sizeof *(r) == sizeof (short int) \
495     ? _GL_INT_OP_WRAPV_SMALLISH (a, b, r, op, overflow, \
496                                  short int, SHRT_MIN, SHRT_MAX, \
497                                  unsigned short int, USHRT_MAX) \
498     : sizeof *(r) == sizeof (int) \
499     ? (EXPR_SIGNED (*(r)) \
500        ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
501                           int, INT_MIN, INT_MAX) \
502        : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
503                           unsigned int, 0, UINT_MAX)) \
504     : _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow))
505 # ifdef LLONG_MAX
506 #  define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
507     (sizeof *(r) == sizeof (long int) \
508      ? (EXPR_SIGNED (*(r)) \
509         ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
510                            long int, LONG_MIN, LONG_MAX) \
511         : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
512                            unsigned long int, 0, ULONG_MAX)) \
513      : (EXPR_SIGNED (*(r)) \
514         ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
515                            long long int, LLONG_MIN, LLONG_MAX) \
516         : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
517                            unsigned long long int, 0, ULLONG_MAX)))
518 # else
519 #  define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
520     (EXPR_SIGNED (*(r)) \
521      ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
522                         long int, LONG_MIN, LONG_MAX) \
523      : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
524                         unsigned long int, 0, ULONG_MAX))
525 # endif
526 #endif
527 
528 /* Store the low-order bits of A <op> B into *R, where the operation
529    is given by OP.  Use the unsigned type UT for calculation to avoid
530    overflow problems.  *R's type is T, with extrema TMIN and TMAX.
531    T must be a signed integer type.  Return 1 if the result overflows.  */
532 #define _GL_INT_OP_CALC(a, b, r, op, overflow, ut, t, tmin, tmax) \
533   (overflow (a, b, tmin, tmax) \
534    ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 1) \
535    : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 0))
536 
537 /* Return the low-order bits of A <op> B, where the operation is given
538    by OP.  Use the unsigned type UT for calculation to avoid undefined
539    behavior on signed integer overflow, and convert the result to type T.
540    UT is at least as wide as T and is no narrower than unsigned int,
541    T is two's complement, and there is no padding or trap representations.
542    Assume that converting UT to T yields the low-order bits, as is
543    done in all known two's-complement C compilers.  E.g., see:
544    https://gcc.gnu.org/onlinedocs/gcc/Integers-implementation.html
545 
546    According to the C standard, converting UT to T yields an
547    implementation-defined result or signal for values outside T's
548    range.  However, code that works around this theoretical problem
549    runs afoul of a compiler bug in Oracle Studio 12.3 x86.  See:
550    https://lists.gnu.org/r/bug-gnulib/2017-04/msg00049.html
551    As the compiler bug is real, don't try to work around the
552    theoretical problem.  */
553 
554 #define _GL_INT_OP_WRAPV_VIA_UNSIGNED(a, b, op, ut, t) \
555   ((t) ((ut) (a) op (ut) (b)))
556 
557 /* Return true if the numeric values A + B, A - B, A * B fall outside
558    the range TMIN..TMAX.  Arguments should be integer expressions
559    without side effects.  TMIN should be signed and nonpositive.
560    TMAX should be positive, and should be signed unless TMIN is zero.  */
561 #define _GL_INT_ADD_RANGE_OVERFLOW(a, b, tmin, tmax) \
562   ((b) < 0 \
563    ? (((tmin) \
564        ? ((EXPR_SIGNED (_GL_INT_CONVERT (a, (tmin) - (b))) || (b) < (tmin)) \
565           && (a) < (tmin) - (b)) \
566        : (a) <= -1 - (b)) \
567       || ((EXPR_SIGNED (a) ? 0 <= (a) : (tmax) < (a)) && (tmax) < (a) + (b))) \
568    : (a) < 0 \
569    ? (((tmin) \
570        ? ((EXPR_SIGNED (_GL_INT_CONVERT (b, (tmin) - (a))) || (a) < (tmin)) \
571           && (b) < (tmin) - (a)) \
572        : (b) <= -1 - (a)) \
573       || ((EXPR_SIGNED (_GL_INT_CONVERT (a, b)) || (tmax) < (b)) \
574           && (tmax) < (a) + (b))) \
575    : (tmax) < (b) || (tmax) - (b) < (a))
576 #define _GL_INT_SUBTRACT_RANGE_OVERFLOW(a, b, tmin, tmax) \
577   (((a) < 0) == ((b) < 0) \
578    ? ((a) < (b) \
579       ? !(tmin) || -1 - (tmin) < (b) - (a) - 1 \
580       : (tmax) < (a) - (b)) \
581    : (a) < 0 \
582    ? ((!EXPR_SIGNED (_GL_INT_CONVERT ((a) - (tmin), b)) && (a) - (tmin) < 0) \
583       || (a) - (tmin) < (b)) \
584    : ((! (EXPR_SIGNED (_GL_INT_CONVERT (tmax, b)) \
585           && EXPR_SIGNED (_GL_INT_CONVERT ((tmax) + (b), a))) \
586        && (tmax) <= -1 - (b)) \
587       || (tmax) + (b) < (a)))
588 #define _GL_INT_MULTIPLY_RANGE_OVERFLOW(a, b, tmin, tmax) \
589   ((b) < 0 \
590    ? ((a) < 0 \
591       ? (EXPR_SIGNED (_GL_INT_CONVERT (tmax, b)) \
592          ? (a) < (tmax) / (b) \
593          : ((INT_NEGATE_OVERFLOW (b) \
594              ? _GL_INT_CONVERT (b, tmax) >> (TYPE_WIDTH (+ (b)) - 1) \
595              : (tmax) / -(b)) \
596             <= -1 - (a))) \
597       : INT_NEGATE_OVERFLOW (_GL_INT_CONVERT (b, tmin)) && (b) == -1 \
598       ? (EXPR_SIGNED (a) \
599          ? 0 < (a) + (tmin) \
600          : 0 < (a) && -1 - (tmin) < (a) - 1) \
601       : (tmin) / (b) < (a)) \
602    : (b) == 0 \
603    ? 0 \
604    : ((a) < 0 \
605       ? (INT_NEGATE_OVERFLOW (_GL_INT_CONVERT (a, tmin)) && (a) == -1 \
606          ? (EXPR_SIGNED (b) ? 0 < (b) + (tmin) : -1 - (tmin) < (b) - 1) \
607          : (tmin) / (a) < (b)) \
608       : (tmax) / (b) < (a)))
609 
610 /* The following macros compute A + B, A - B, and A * B, respectively.
611    If no overflow occurs, they set *R to the result and return 1;
612    otherwise, they return 0 and may modify *R.
613 
614    Example usage:
615 
616      long int result;
617      if (INT_ADD_OK (a, b, &result))
618        printf ("result is %ld\n", result);
619      else
620        printf ("overflow\n");
621 
622    A, B, and *R should be integers; they need not be the same type,
623    and they need not be all signed or all unsigned.
624 
625    These macros work correctly on all known practical hosts, and do not rely
626    on undefined behavior due to signed arithmetic overflow.
627 
628    These macros are not constant expressions.
629 
630    These macros may evaluate their arguments zero or multiple times, so the
631    arguments should not have side effects.
632 
633    These macros are tuned for B being a constant.  */
634 
635 #define INT_ADD_OK(a, b, r) ! INT_ADD_WRAPV (a, b, r)
636 #define INT_SUBTRACT_OK(a, b, r) ! INT_SUBTRACT_WRAPV (a, b, r)
637 #define INT_MULTIPLY_OK(a, b, r) ! INT_MULTIPLY_WRAPV (a, b, r)
638 
639 #endif /* _GL_INTPROPS_H */
640