aboutsummaryrefslogtreecommitdiff
path: root/include/intprops.h
blob: bc7e950a0eda45eb3386eea2f215bf46e0f0ca22 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
/* intprops.h -- properties of integer types

   Copyright (C) 2001-2019 Free Software Foundation, Inc.

   This program is free software: you can redistribute it and/or modify it
   under the terms of the GNU Lesser General Public License as published
   by the Free Software Foundation; either version 2.1 of the License, or
   (at your option) any later version.

   This program is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
   GNU Lesser General Public License for more details.

   You should have received a copy of the GNU Lesser General Public License
   along with this program.  If not, see <https://www.gnu.org/licenses/>.  */

/* Written by Paul Eggert.  */

#ifndef _GL_INTPROPS_H
#define _GL_INTPROPS_H

#include <limits.h>

/* Return a value with the common real type of E and V and the value of V.
   Do not evaluate E.  */
#define _GL_INT_CONVERT(e, v) ((1 ? 0 : (e)) + (v))

/* Act like _GL_INT_CONVERT (E, -V) but work around a bug in IRIX 6.5 cc; see
   <https://lists.gnu.org/r/bug-gnulib/2011-05/msg00406.html>.  */
#define _GL_INT_NEGATE_CONVERT(e, v) ((1 ? 0 : (e)) - (v))

/* The extra casts in the following macros work around compiler bugs,
   e.g., in Cray C 5.0.3.0.  */

/* True if the arithmetic type T is an integer type.  bool counts as
   an integer.  */
#define TYPE_IS_INTEGER(t) ((t) 1.5 == 1)

/* True if the real type T is signed.  */
#define TYPE_SIGNED(t) (! ((t) 0 < (t) -1))

/* Return 1 if the real expression E, after promotion, has a
   signed or floating type.  Do not evaluate E.  */
#define EXPR_SIGNED(e) (_GL_INT_NEGATE_CONVERT (e, 1) < 0)


/* Minimum and maximum values for integer types and expressions.  */

/* The width in bits of the integer type or expression T.
   Do not evaluate T.
   Padding bits are not supported; this is checked at compile-time below.  */
#define TYPE_WIDTH(t) (sizeof (t) * CHAR_BIT)

/* The maximum and minimum values for the integer type T.  */
#define TYPE_MINIMUM(t) ((t) ~ TYPE_MAXIMUM (t))
#define TYPE_MAXIMUM(t)                                                 \
  ((t) (! TYPE_SIGNED (t)                                               \
        ? (t) -1                                                        \
        : ((((t) 1 << (TYPE_WIDTH (t) - 2)) - 1) * 2 + 1)))

/* The maximum and minimum values for the type of the expression E,
   after integer promotion.  E is not evaluated.  */
#define _GL_INT_MINIMUM(e)                                              \
  (EXPR_SIGNED (e)                                                      \
   ? ~ _GL_SIGNED_INT_MAXIMUM (e)                                       \
   : _GL_INT_CONVERT (e, 0))
#define _GL_INT_MAXIMUM(e)                                              \
  (EXPR_SIGNED (e)                                                      \
   ? _GL_SIGNED_INT_MAXIMUM (e)                                         \
   : _GL_INT_NEGATE_CONVERT (e, 1))
#define _GL_SIGNED_INT_MAXIMUM(e)                                       \
  (((_GL_INT_CONVERT (e, 1) << (TYPE_WIDTH ((e) + 0) - 2)) - 1) * 2 + 1)

/* Work around OpenVMS incompatibility with C99.  */
#if !defined LLONG_MAX && defined __INT64_MAX
# define LLONG_MAX __INT64_MAX
# define LLONG_MIN __INT64_MIN
#endif

/* This include file assumes that signed types are two's complement without
   padding bits; the above macros have undefined behavior otherwise.
   If this is a problem for you, please let us know how to fix it for your host.
   This assumption is tested by the intprops-tests module.  */

/* Does the __typeof__ keyword work?  This could be done by
   'configure', but for now it's easier to do it by hand.  */
#if (2 <= __GNUC__ \
     || (1210 <= __IBMC__ && defined __IBM__TYPEOF__) \
     || (0x5110 <= __SUNPRO_C && !__STDC__))
# define _GL_HAVE___TYPEOF__ 1
#else
# define _GL_HAVE___TYPEOF__ 0
#endif

/* Return 1 if the integer type or expression T might be signed.  Return 0
   if it is definitely unsigned.  This macro does not evaluate its argument,
   and expands to an integer constant expression.  */
#if _GL_HAVE___TYPEOF__
# define _GL_SIGNED_TYPE_OR_EXPR(t) TYPE_SIGNED (__typeof__ (t))
#else
# define _GL_SIGNED_TYPE_OR_EXPR(t) 1
#endif

/* Bound on length of the string representing an unsigned integer
   value representable in B bits.  log10 (2.0) < 146/485.  The
   smallest value of B where this bound is not tight is 2621.  */
#define INT_BITS_STRLEN_BOUND(b) (((b) * 146 + 484) / 485)

/* Bound on length of the string representing an integer type or expression T.
   Subtract 1 for the sign bit if T is signed, and then add 1 more for
   a minus sign if needed.

   Because _GL_SIGNED_TYPE_OR_EXPR sometimes returns 1 when its argument is
   unsigned, this macro may overestimate the true bound by one byte when
   applied to unsigned types of size 2, 4, 16, ... bytes.  */
#define INT_STRLEN_BOUND(t)                                     \
  (INT_BITS_STRLEN_BOUND (TYPE_WIDTH (t) - _GL_SIGNED_TYPE_OR_EXPR (t)) \
   + _GL_SIGNED_TYPE_OR_EXPR (t))

/* Bound on buffer size needed to represent an integer type or expression T,
   including the terminating null.  */
#define INT_BUFSIZE_BOUND(t) (INT_STRLEN_BOUND (t) + 1)


/* Range overflow checks.

   The INT_<op>_RANGE_OVERFLOW macros return 1 if the corresponding C
   operators might not yield numerically correct answers due to
   arithmetic overflow.  They do not rely on undefined or
   implementation-defined behavior.  Their implementations are simple
   and straightforward, but they are a bit harder to use than the
   INT_<op>_OVERFLOW macros described below.

   Example usage:

     long int i = ...;
     long int j = ...;
     if (INT_MULTIPLY_RANGE_OVERFLOW (i, j, LONG_MIN, LONG_MAX))
       printf ("multiply would overflow");
     else
       printf ("product is %ld", i * j);

   Restrictions on *_RANGE_OVERFLOW macros:

   These macros do not check for all possible numerical problems or
   undefined or unspecified behavior: they do not check for division
   by zero, for bad shift counts, or for shifting negative numbers.

   These macros may evaluate their arguments zero or multiple times,
   so the arguments should not have side effects.  The arithmetic
   arguments (including the MIN and MAX arguments) must be of the same
   integer type after the usual arithmetic conversions, and the type
   must have minimum value MIN and maximum MAX.  Unsigned types should
   use a zero MIN of the proper type.

   These macros are tuned for constant MIN and MAX.  For commutative
   operations such as A + B, they are also tuned for constant B.  */

/* Return 1 if A + B would overflow in [MIN,MAX] arithmetic.
   See above for restrictions.  */
#define INT_ADD_RANGE_OVERFLOW(a, b, min, max)          \
  ((b) < 0                                              \
   ? (a) < (min) - (b)                                  \
   : (max) - (b) < (a))

/* Return 1 if A - B would overflow in [MIN,MAX] arithmetic.
   See above for restrictions.  */
#define INT_SUBTRACT_RANGE_OVERFLOW(a, b, min, max)     \
  ((b) < 0                                              \
   ? (max) + (b) < (a)                                  \
   : (a) < (min) + (b))

/* Return 1 if - A would overflow in [MIN,MAX] arithmetic.
   See above for restrictions.  */
#define INT_NEGATE_RANGE_OVERFLOW(a, min, max)          \
  ((min) < 0                                            \
   ? (a) < - (max)                                      \
   : 0 < (a))

/* Return 1 if A * B would overflow in [MIN,MAX] arithmetic.
   See above for restrictions.  Avoid && and || as they tickle
   bugs in Sun C 5.11 2010/08/13 and other compilers; see
   <https://lists.gnu.org/r/bug-gnulib/2011-05/msg00401.html>.  */
#define INT_MULTIPLY_RANGE_OVERFLOW(a, b, min, max)     \
  ((b) < 0                                              \
   ? ((a) < 0                                           \
      ? (a) < (max) / (b)                               \
      : (b) == -1                                       \
      ? 0                                               \
      : (min) / (b) < (a))                              \
   : (b) == 0                                           \
   ? 0                                                  \
   : ((a) < 0                                           \
      ? (a) < (min) / (b)                               \
      : (max) / (b) < (a)))

/* Return 1 if A / B would overflow in [MIN,MAX] arithmetic.
   See above for restrictions.  Do not check for division by zero.  */
#define INT_DIVIDE_RANGE_OVERFLOW(a, b, min, max)       \
  ((min) < 0 && (b) == -1 && (a) < - (max))

/* Return 1 if A % B would overflow in [MIN,MAX] arithmetic.
   See above for restrictions.  Do not check for division by zero.
   Mathematically, % should never overflow, but on x86-like hosts
   INT_MIN % -1 traps, and the C standard permits this, so treat this
   as an overflow too.  */
#define INT_REMAINDER_RANGE_OVERFLOW(a, b, min, max)    \
  INT_DIVIDE_RANGE_OVERFLOW (a, b, min, max)

/* Return 1 if A << B would overflow in [MIN,MAX] arithmetic.
   See above for restrictions.  Here, MIN and MAX are for A only, and B need
   not be of the same type as the other arguments.  The C standard says that
   behavior is undefined for shifts unless 0 <= B < wordwidth, and that when
   A is negative then A << B has undefined behavior and A >> B has
   implementation-defined behavior, but do not check these other
   restrictions.  */
#define INT_LEFT_SHIFT_RANGE_OVERFLOW(a, b, min, max)   \
  ((a) < 0                                              \
   ? (a) < (min) >> (b)                                 \
   : (max) >> (b) < (a))

/* True if __builtin_add_overflow (A, B, P) and __builtin_sub_overflow
   (A, B, P) work when P is non-null.  */
#if 5 <= __GNUC__ && !defined __ICC
# define _GL_HAS_BUILTIN_ADD_OVERFLOW 1
#elif defined __has_builtin
# define _GL_HAS_BUILTIN_ADD_OVERFLOW __has_builtin (__builtin_add_overflow)
#else
# define _GL_HAS_BUILTIN_ADD_OVERFLOW 0
#endif

/* True if __builtin_mul_overflow (A, B, P) works when P is non-null.  */
#ifdef __clang__
/* Work around Clang bug <https://bugs.llvm.org/show_bug.cgi?id=16404>.  */
# define _GL_HAS_BUILTIN_MUL_OVERFLOW 0
#else
# define _GL_HAS_BUILTIN_MUL_OVERFLOW _GL_HAS_BUILTIN_ADD_OVERFLOW
#endif

/* True if __builtin_add_overflow_p (A, B, C) works, and similarly for
   __builtin_mul_overflow_p and __builtin_mul_overflow_p.  */
#define _GL_HAS_BUILTIN_OVERFLOW_P (7 <= __GNUC__)

/* The _GL*_OVERFLOW macros have the same restrictions as the
   *_RANGE_OVERFLOW macros, except that they do not assume that operands
   (e.g., A and B) have the same type as MIN and MAX.  Instead, they assume
   that the result (e.g., A + B) has that type.  */
#if _GL_HAS_BUILTIN_OVERFLOW_P
# define _GL_ADD_OVERFLOW(a, b, min, max)                               \
   __builtin_add_overflow_p (a, b, (__typeof__ ((a) + (b))) 0)
# define _GL_SUBTRACT_OVERFLOW(a, b, min, max)                          \
   __builtin_sub_overflow_p (a, b, (__typeof__ ((a) - (b))) 0)
# define _GL_MULTIPLY_OVERFLOW(a, b, min, max)                          \
   __builtin_mul_overflow_p (a, b, (__typeof__ ((a) * (b))) 0)
#else
# define _GL_ADD_OVERFLOW(a, b, min, max)                                \
   ((min) < 0 ? INT_ADD_RANGE_OVERFLOW (a, b, min, max)                  \
    : (a) < 0 ? (b) <= (a) + (b)                                         \
    : (b) < 0 ? (a) <= (a) + (b)                                         \
    : (a) + (b) < (b))
# define _GL_SUBTRACT_OVERFLOW(a, b, min, max)                           \
   ((min) < 0 ? INT_SUBTRACT_RANGE_OVERFLOW (a, b, min, max)             \
    : (a) < 0 ? 1                                                        \
    : (b) < 0 ? (a) - (b) <= (a)                                         \
    : (a) < (b))
# define _GL_MULTIPLY_OVERFLOW(a, b, min, max)                           \
   (((min) == 0 && (((a) < 0 && 0 < (b)) || ((b) < 0 && 0 < (a))))       \
    || INT_MULTIPLY_RANGE_OVERFLOW (a, b, min, max))
#endif
#define _GL_DIVIDE_OVERFLOW(a, b, min, max)                             \
  ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max)  \
   : (a) < 0 ? (b) <= (a) + (b) - 1                                     \
   : (b) < 0 && (a) + (b) <= (a))
#define _GL_REMAINDER_OVERFLOW(a, b, min, max)                          \
  ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max)  \
   : (a) < 0 ? (a) % (b) != ((max) - (b) + 1) % (b)                     \
   : (b) < 0 && ! _GL_UNSIGNED_NEG_MULTIPLE (a, b, max))

/* Return a nonzero value if A is a mathematical multiple of B, where
   A is unsigned, B is negative, and MAX is the maximum value of A's
   type.  A's type must be the same as (A % B)'s type.  Normally (A %
   -B == 0) suffices, but things get tricky if -B would overflow.  */
#define _GL_UNSIGNED_NEG_MULTIPLE(a, b, max)                            \
  (((b) < -_GL_SIGNED_INT_MAXIMUM (b)                                   \
    ? (_GL_SIGNED_INT_MAXIMUM (b) == (max)                              \
       ? (a)                                                            \
       : (a) % (_GL_INT_CONVERT (a, _GL_SIGNED_INT_MAXIMUM (b)) + 1))   \
    : (a) % - (b))                                                      \
   == 0)

/* Check for integer overflow, and report low order bits of answer.

   The INT_<op>_OVERFLOW macros return 1 if the corresponding C operators
   might not yield numerically correct answers due to arithmetic overflow.
   The INT_<op>_WRAPV macros compute the low-order bits of the sum,
   difference, and product of two C integers, and return 1 if these
   low-order bits are not numerically correct.
   These macros work correctly on all known practical hosts, and do not rely
   on undefined behavior due to signed arithmetic overflow.

   Example usage, assuming A and B are long int:

     if (INT_MULTIPLY_OVERFLOW (a, b))
       printf ("result would overflow\n");
     else
       printf ("result is %ld (no overflow)\n", a * b);

   Example usage with WRAPV flavor:

     long int result;
     bool overflow = INT_MULTIPLY_WRAPV (a, b, &result);
     printf ("result is %ld (%s)\n", result,
             overflow ? "after overflow" : "no overflow");

   Restrictions on these macros:

   These macros do not check for all possible numerical problems or
   undefined or unspecified behavior: they do not check for division
   by zero, for bad shift counts, or for shifting negative numbers.

   These macros may evaluate their arguments zero or multiple times, so the
   arguments should not have side effects.

   The WRAPV macros are not constant expressions.  They support only
   +, binary -, and *.  Because the WRAPV macros convert the result,
   they report overflow in different circumstances than the OVERFLOW
   macros do.

   These macros are tuned for their last input argument being a constant.

   Return 1 if the integer expressions A * B, A - B, -A, A * B, A / B,
   A % B, and A << B would overflow, respectively.  */

#define INT_ADD_OVERFLOW(a, b) \
  _GL_BINARY_OP_OVERFLOW (a, b, _GL_ADD_OVERFLOW)
#define INT_SUBTRACT_OVERFLOW(a, b) \
  _GL_BINARY_OP_OVERFLOW (a, b, _GL_SUBTRACT_OVERFLOW)
#if _GL_HAS_BUILTIN_OVERFLOW_P
# define INT_NEGATE_OVERFLOW(a) INT_SUBTRACT_OVERFLOW (0, a)
#else
# define INT_NEGATE_OVERFLOW(a) \
   INT_NEGATE_RANGE_OVERFLOW (a, _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
#endif
#define INT_MULTIPLY_OVERFLOW(a, b) \
  _GL_BINARY_OP_OVERFLOW (a, b, _GL_MULTIPLY_OVERFLOW)
#define INT_DIVIDE_OVERFLOW(a, b) \
  _GL_BINARY_OP_OVERFLOW (a, b, _GL_DIVIDE_OVERFLOW)
#define INT_REMAINDER_OVERFLOW(a, b) \
  _GL_BINARY_OP_OVERFLOW (a, b, _GL_REMAINDER_OVERFLOW)
#define INT_LEFT_SHIFT_OVERFLOW(a, b) \
  INT_LEFT_SHIFT_RANGE_OVERFLOW (a, b, \
                                 _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))

/* Return 1 if the expression A <op> B would overflow,
   where OP_RESULT_OVERFLOW (A, B, MIN, MAX) does the actual test,
   assuming MIN and MAX are the minimum and maximum for the result type.
   Arguments should be free of side effects.  */
#define _GL_BINARY_OP_OVERFLOW(a, b, op_result_overflow)        \
  op_result_overflow (a, b,                                     \
                      _GL_INT_MINIMUM (_GL_INT_CONVERT (a, b)), \
                      _GL_INT_MAXIMUM (_GL_INT_CONVERT (a, b)))

/* Store the low-order bits of A + B, A - B, A * B, respectively, into *R.
   Return 1 if the result overflows.  See above for restrictions.  */
#if _GL_HAS_BUILTIN_ADD_OVERFLOW
# define INT_ADD_WRAPV(a, b, r) __builtin_add_overflow (a, b, r)
# define INT_SUBTRACT_WRAPV(a, b, r) __builtin_sub_overflow (a, b, r)
#else
# define INT_ADD_WRAPV(a, b, r) \
   _GL_INT_OP_WRAPV (a, b, r, +, _GL_INT_ADD_RANGE_OVERFLOW)
# define INT_SUBTRACT_WRAPV(a, b, r) \
   _GL_INT_OP_WRAPV (a, b, r, -, _GL_INT_SUBTRACT_RANGE_OVERFLOW)
#endif
#if _GL_HAS_BUILTIN_MUL_OVERFLOW
/* Work around GCC bug 91450.  */
# define INT_MULTIPLY_WRAPV(a, b, r) \
   ((!_GL_SIGNED_TYPE_OR_EXPR (*(r)) && EXPR_SIGNED (a) && EXPR_SIGNED (b) \
     && _GL_INT_MULTIPLY_RANGE_OVERFLOW (a, b, 0, (__typeof__ (*(r))) -1)) \
    ? ((void) __builtin_mul_overflow (a, b, r), 1) \
    : __builtin_mul_overflow (a, b, r))
#else
# define INT_MULTIPLY_WRAPV(a, b, r) \
   _GL_INT_OP_WRAPV (a, b, r, *, _GL_INT_MULTIPLY_RANGE_OVERFLOW)
#endif

/* Nonzero if this compiler has GCC bug 68193 or Clang bug 25390.  See:
   https://gcc.gnu.org/bugzilla/show_bug.cgi?id=68193
   https://llvm.org/bugs/show_bug.cgi?id=25390
   For now, assume all versions of GCC-like compilers generate bogus
   warnings for _Generic.  This matters only for compilers that
   lack relevant builtins.  */
#if __GNUC__
# define _GL__GENERIC_BOGUS 1
#else
# define _GL__GENERIC_BOGUS 0
#endif

/* Store the low-order bits of A <op> B into *R, where OP specifies
   the operation and OVERFLOW the overflow predicate.  Return 1 if the
   result overflows.  See above for restrictions.  */
#if 201112 <= __STDC_VERSION__ && !_GL__GENERIC_BOGUS
# define _GL_INT_OP_WRAPV(a, b, r, op, overflow) \
   (_Generic \
    (*(r), \
     signed char: \
       _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
                        signed char, SCHAR_MIN, SCHAR_MAX), \
     unsigned char: \
       _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
                        unsigned char, 0, UCHAR_MAX), \
     short int: \
       _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
                        short int, SHRT_MIN, SHRT_MAX), \
     unsigned short int: \
       _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
                        unsigned short int, 0, USHRT_MAX), \
     int: \
       _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
                        int, INT_MIN, INT_MAX), \
     unsigned int: \
       _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
                        unsigned int, 0, UINT_MAX), \
     long int: \
       _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
                        long int, LONG_MIN, LONG_MAX), \
     unsigned long int: \
       _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
                        unsigned long int, 0, ULONG_MAX), \
     long long int: \
       _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
                        long long int, LLONG_MIN, LLONG_MAX), \
     unsigned long long int: \
       _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
                        unsigned long long int, 0, ULLONG_MAX)))
#else
/* Store the low-order bits of A <op> B into *R, where OP specifies
   the operation and OVERFLOW the overflow predicate.  If *R is
   signed, its type is ST with bounds SMIN..SMAX; otherwise its type
   is UT with bounds U..UMAX.  ST and UT are narrower than int.
   Return 1 if the result overflows.  See above for restrictions.  */
# if _GL_HAVE___TYPEOF__
#  define _GL_INT_OP_WRAPV_SMALLISH(a,b,r,op,overflow,st,smin,smax,ut,umax) \
    (TYPE_SIGNED (__typeof__ (*(r))) \
     ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, st, smin, smax) \
     : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, ut, 0, umax))
# else
#  define _GL_INT_OP_WRAPV_SMALLISH(a,b,r,op,overflow,st,smin,smax,ut,umax) \
    (overflow (a, b, smin, smax) \
     ? (overflow (a, b, 0, umax) \
        ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st), 1) \
        : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st)) < 0) \
     : (overflow (a, b, 0, umax) \
        ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st)) >= 0 \
        : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st), 0)))
# endif

# define _GL_INT_OP_WRAPV(a, b, r, op, overflow) \
   (sizeof *(r) == sizeof (signed char) \
    ? _GL_INT_OP_WRAPV_SMALLISH (a, b, r, op, overflow, \
                                 signed char, SCHAR_MIN, SCHAR_MAX, \
                                 unsigned char, UCHAR_MAX) \
    : sizeof *(r) == sizeof (short int) \
    ? _GL_INT_OP_WRAPV_SMALLISH (a, b, r, op, overflow, \
                                 short int, SHRT_MIN, SHRT_MAX, \
                                 unsigned short int, USHRT_MAX) \
    : sizeof *(r) == sizeof (int) \
    ? (EXPR_SIGNED (*(r)) \
       ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
                          int, INT_MIN, INT_MAX) \
       : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
                          unsigned int, 0, UINT_MAX)) \
    : _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow))
# ifdef LLONG_MAX
#  define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
    (sizeof *(r) == sizeof (long int) \
     ? (EXPR_SIGNED (*(r)) \
        ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
                           long int, LONG_MIN, LONG_MAX) \
        : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
                           unsigned long int, 0, ULONG_MAX)) \
     : (EXPR_SIGNED (*(r)) \
        ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
                           long long int, LLONG_MIN, LLONG_MAX) \
        : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
                           unsigned long long int, 0, ULLONG_MAX)))
# else
#  define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
    (EXPR_SIGNED (*(r)) \
     ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
                        long int, LONG_MIN, LONG_MAX) \
     : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
                        unsigned long int, 0, ULONG_MAX))
# endif
#endif

/* Store the low-order bits of A <op> B into *R, where the operation
   is given by OP.  Use the unsigned type UT for calculation to avoid
   overflow problems.  *R's type is T, with extrema TMIN and TMAX.
   T must be a signed integer type.  Return 1 if the result overflows.  */
#define _GL_INT_OP_CALC(a, b, r, op, overflow, ut, t, tmin, tmax) \
  (overflow (a, b, tmin, tmax) \
   ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 1) \
   : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 0))

/* Return the low-order bits of A <op> B, where the operation is given
   by OP.  Use the unsigned type UT for calculation to avoid undefined
   behavior on signed integer overflow, and convert the result to type T.
   UT is at least as wide as T and is no narrower than unsigned int,
   T is two's complement, and there is no padding or trap representations.
   Assume that converting UT to T yields the low-order bits, as is
   done in all known two's-complement C compilers.  E.g., see:
   https://gcc.gnu.org/onlinedocs/gcc/Integers-implementation.html

   According to the C standard, converting UT to T yields an
   implementation-defined result or signal for values outside T's
   range.  However, code that works around this theoretical problem
   runs afoul of a compiler bug in Oracle Studio 12.3 x86.  See:
   https://lists.gnu.org/r/bug-gnulib/2017-04/msg00049.html
   As the compiler bug is real, don't try to work around the
   theoretical problem.  */

#define _GL_INT_OP_WRAPV_VIA_UNSIGNED(a, b, op, ut, t) \
  ((t) ((ut) (a) op (ut) (b)))

/* Return true if the numeric values A + B, A - B, A * B fall outside
   the range TMIN..TMAX.  Arguments should be integer expressions
   without side effects.  TMIN should be signed and nonpositive.
   TMAX should be positive, and should be signed unless TMIN is zero.  */
#define _GL_INT_ADD_RANGE_OVERFLOW(a, b, tmin, tmax) \
  ((b) < 0 \
   ? (((tmin) \
       ? ((EXPR_SIGNED (_GL_INT_CONVERT (a, (tmin) - (b))) || (b) < (tmin)) \
          && (a) < (tmin) - (b)) \
       : (a) <= -1 - (b)) \
      || ((EXPR_SIGNED (a) ? 0 <= (a) : (tmax) < (a)) && (tmax) < (a) + (b))) \
   : (a) < 0 \
   ? (((tmin) \
       ? ((EXPR_SIGNED (_GL_INT_CONVERT (b, (tmin) - (a))) || (a) < (tmin)) \
          && (b) < (tmin) - (a)) \
       : (b) <= -1 - (a)) \
      || ((EXPR_SIGNED (_GL_INT_CONVERT (a, b)) || (tmax) < (b)) \
          && (tmax) < (a) + (b))) \
   : (tmax) < (b) || (tmax) - (b) < (a))
#define _GL_INT_SUBTRACT_RANGE_OVERFLOW(a, b, tmin, tmax) \
  (((a) < 0) == ((b) < 0) \
   ? ((a) < (b) \
      ? !(tmin) || -1 - (tmin) < (b) - (a) - 1 \
      : (tmax) < (a) - (b)) \
   : (a) < 0 \
   ? ((!EXPR_SIGNED (_GL_INT_CONVERT ((a) - (tmin), b)) && (a) - (tmin) < 0) \
      || (a) - (tmin) < (b)) \
   : ((! (EXPR_SIGNED (_GL_INT_CONVERT (tmax, b)) \
          && EXPR_SIGNED (_GL_INT_CONVERT ((tmax) + (b), a))) \
       && (tmax) <= -1 - (b)) \
      || (tmax) + (b) < (a)))
#define _GL_INT_MULTIPLY_RANGE_OVERFLOW(a, b, tmin, tmax) \
  ((b) < 0 \
   ? ((a) < 0 \
      ? (EXPR_SIGNED (_GL_INT_CONVERT (tmax, b)) \
         ? (a) < (tmax) / (b) \
         : ((INT_NEGATE_OVERFLOW (b) \
             ? _GL_INT_CONVERT (b, tmax) >> (TYPE_WIDTH (b) - 1) \
             : (tmax) / -(b)) \
            <= -1 - (a))) \
      : INT_NEGATE_OVERFLOW (_GL_INT_CONVERT (b, tmin)) && (b) == -1 \
      ? (EXPR_SIGNED (a) \
         ? 0 < (a) + (tmin) \
         : 0 < (a) && -1 - (tmin) < (a) - 1) \
      : (tmin) / (b) < (a)) \
   : (b) == 0 \
   ? 0 \
   : ((a) < 0 \
      ? (INT_NEGATE_OVERFLOW (_GL_INT_CONVERT (a, tmin)) && (a) == -1 \
         ? (EXPR_SIGNED (b) ? 0 < (b) + (tmin) : -1 - (tmin) < (b) - 1) \
         : (tmin) / (a) < (b)) \
      : (tmax) / (b) < (a)))

#endif /* _GL_INTPROPS_H */