lib/intprops.h

   1 /* intprops.h -- properties of integer types
   2
   3    Copyright (C) 2001-2019 Free Software Foundation, Inc.
   4
   5    This program is free software: you can redistribute it and/or modify it
   6    under the terms of the GNU Lesser General Public License as published
   7    by the Free Software Foundation; either version 2.1 of the License, or
   8    (at your option) any later version.
   9
  10    This program is distributed in the hope that it will be useful,
  11    but WITHOUT ANY WARRANTY; without even the implied warranty of
  12    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  13    GNU Lesser General Public License for more details.
  14
  15    You should have received a copy of the GNU Lesser General Public License
  16    along with this program.  If not, see <https://www.gnu.org/licenses/>.  */
  17
  18 /* Written by Paul Eggert.  */
  19
  20 #ifndef _GL_INTPROPS_H
  21 #define _GL_INTPROPS_H
  22
  23 #include <limits.h>
  24
  25 /* Return a value with the common real type of E and V and the value of V.
  26    Do not evaluate E.  */
  27 #define _GL_INT_CONVERT(e, v) ((1 ? 0 : (e)) + (v))
  28
  29 /* Act like _GL_INT_CONVERT (E, -V) but work around a bug in IRIX 6.5 cc; see
  30    <https://lists.gnu.org/r/bug-gnulib/2011-05/msg00406.html>.  */
  31 #define _GL_INT_NEGATE_CONVERT(e, v) ((1 ? 0 : (e)) - (v))
  32
  33 /* The extra casts in the following macros work around compiler bugs,
  34    e.g., in Cray C 5.0.3.0.  */
  35
  36 /* True if the arithmetic type T is an integer type.  bool counts as
  37    an integer.  */
  38 #define TYPE_IS_INTEGER(t) ((t) 1.5 == 1)
  39
  40 /* True if the real type T is signed.  */
  41 #define TYPE_SIGNED(t) (! ((t) 0 < (t) -1))
  42
  43 /* Return 1 if the real expression E, after promotion, has a
  44    signed or floating type.  Do not evaluate E.  */
  45 #define EXPR_SIGNED(e) (_GL_INT_NEGATE_CONVERT (e, 1) < 0)
  46
  47
  48 /* Minimum and maximum values for integer types and expressions.  */
  49
  50 /* The width in bits of the integer type or expression T.
  51    Do not evaluate T.
  52    Padding bits are not supported; this is checked at compile-time below.  */
  53 #define TYPE_WIDTH(t) (sizeof (t) * CHAR_BIT)
  54
  55 /* The maximum and minimum values for the integer type T.  */
  56 #define TYPE_MINIMUM(t) ((t) ~ TYPE_MAXIMUM (t))
  57 #define TYPE_MAXIMUM(t)                                                 \
  58   ((t) (! TYPE_SIGNED (t)                                               \
  59         ? (t) -1                                                        \
  60         : ((((t) 1 << (TYPE_WIDTH (t) - 2)) - 1) * 2 + 1)))
  61
  62 /* The maximum and minimum values for the type of the expression E,
  63    after integer promotion.  E is not evaluated.  */
  64 #define _GL_INT_MINIMUM(e)                                              \
  65   (EXPR_SIGNED (e)                                                      \
  66    ? ~ _GL_SIGNED_INT_MAXIMUM (e)                                       \
  67    : _GL_INT_CONVERT (e, 0))
  68 #define _GL_INT_MAXIMUM(e)                                              \
  69   (EXPR_SIGNED (e)                                                      \
  70    ? _GL_SIGNED_INT_MAXIMUM (e)                                         \
  71    : _GL_INT_NEGATE_CONVERT (e, 1))
  72 #define _GL_SIGNED_INT_MAXIMUM(e)                                       \
  73   (((_GL_INT_CONVERT (e, 1) << (TYPE_WIDTH ((e) + 0) - 2)) - 1) * 2 + 1)
  74
  75 /* Work around OpenVMS incompatibility with C99.  */
  76 #if !defined LLONG_MAX && defined __INT64_MAX
  77 # define LLONG_MAX __INT64_MAX
  78 # define LLONG_MIN __INT64_MIN
  79 #endif
  80
  81 /* This include file assumes that signed types are two's complement without
  82    padding bits; the above macros have undefined behavior otherwise.
  83    If this is a problem for you, please let us know how to fix it for your host.
  84    This assumption is tested by the intprops-tests module.  */
  85
  86 /* Does the __typeof__ keyword work?  This could be done by
  87    'configure', but for now it's easier to do it by hand.  */
  88 #if (2 <= __GNUC__ \
  89      || (1210 <= __IBMC__ && defined __IBM__TYPEOF__) \
  90      || (0x5110 <= __SUNPRO_C && !__STDC__))
  91 # define _GL_HAVE___TYPEOF__ 1
  92 #else
  93 # define _GL_HAVE___TYPEOF__ 0
  94 #endif
  95
  96 /* Return 1 if the integer type or expression T might be signed.  Return 0
  97    if it is definitely unsigned.  This macro does not evaluate its argument,
  98    and expands to an integer constant expression.  */
  99 #if _GL_HAVE___TYPEOF__
 100 # define _GL_SIGNED_TYPE_OR_EXPR(t) TYPE_SIGNED (__typeof__ (t))
 101 #else
 102 # define _GL_SIGNED_TYPE_OR_EXPR(t) 1
 103 #endif
 104
 105 /* Bound on length of the string representing an unsigned integer
 106    value representable in B bits.  log10 (2.0) < 146/485.  The
 107    smallest value of B where this bound is not tight is 2621.  */
 108 #define INT_BITS_STRLEN_BOUND(b) (((b) * 146 + 484) / 485)
 109
 110 /* Bound on length of the string representing an integer type or expression T.
 111    Subtract 1 for the sign bit if T is signed, and then add 1 more for
 112    a minus sign if needed.
 113
 114    Because _GL_SIGNED_TYPE_OR_EXPR sometimes returns 0 when its argument is
 115    signed, this macro may overestimate the true bound by one byte when
 116    applied to unsigned types of size 2, 4, 16, ... bytes.  */
 117 #define INT_STRLEN_BOUND(t)                                     \
 118   (INT_BITS_STRLEN_BOUND (TYPE_WIDTH (t) - _GL_SIGNED_TYPE_OR_EXPR (t)) \
 119    + _GL_SIGNED_TYPE_OR_EXPR (t))
 120
 121 /* Bound on buffer size needed to represent an integer type or expression T,
 122    including the terminating null.  */
 123 #define INT_BUFSIZE_BOUND(t) (INT_STRLEN_BOUND (t) + 1)
 124
 125
 126 /* Range overflow checks.
 127
 128    The INT_<op>_RANGE_OVERFLOW macros return 1 if the corresponding C
 129    operators might not yield numerically correct answers due to
 130    arithmetic overflow.  They do not rely on undefined or
 131    implementation-defined behavior.  Their implementations are simple
 132    and straightforward, but they are a bit harder to use than the
 133    INT_<op>_OVERFLOW macros described below.
 134
 135    Example usage:
 136
 137      long int i = ...;
 138      long int j = ...;
 139      if (INT_MULTIPLY_RANGE_OVERFLOW (i, j, LONG_MIN, LONG_MAX))
 140        printf ("multiply would overflow");
 141      else
 142        printf ("product is %ld", i * j);
 143
 144    Restrictions on *_RANGE_OVERFLOW macros:
 145
 146    These macros do not check for all possible numerical problems or
 147    undefined or unspecified behavior: they do not check for division
 148    by zero, for bad shift counts, or for shifting negative numbers.
 149
 150    These macros may evaluate their arguments zero or multiple times,
 151    so the arguments should not have side effects.  The arithmetic
 152    arguments (including the MIN and MAX arguments) must be of the same
 153    integer type after the usual arithmetic conversions, and the type
 154    must have minimum value MIN and maximum MAX.  Unsigned types should
 155    use a zero MIN of the proper type.
 156
 157    These macros are tuned for constant MIN and MAX.  For commutative
 158    operations such as A + B, they are also tuned for constant B.  */
 159
 160 /* Return 1 if A + B would overflow in [MIN,MAX] arithmetic.
 161    See above for restrictions.  */
 162 #define INT_ADD_RANGE_OVERFLOW(a, b, min, max)          \
 163   ((b) < 0                                              \
 164    ? (a) < (min) - (b)                                  \
 165    : (max) - (b) < (a))
 166
 167 /* Return 1 if A - B would overflow in [MIN,MAX] arithmetic.
 168    See above for restrictions.  */
 169 #define INT_SUBTRACT_RANGE_OVERFLOW(a, b, min, max)     \
 170   ((b) < 0                                              \
 171    ? (max) + (b) < (a)                                  \
 172    : (a) < (min) + (b))
 173
 174 /* Return 1 if - A would overflow in [MIN,MAX] arithmetic.
 175    See above for restrictions.  */
 176 #define INT_NEGATE_RANGE_OVERFLOW(a, min, max)          \
 177   ((min) < 0                                            \
 178    ? (a) < - (max)                                      \
 179    : 0 < (a))
 180
 181 /* Return 1 if A * B would overflow in [MIN,MAX] arithmetic.
 182    See above for restrictions.  Avoid && and || as they tickle
 183    bugs in Sun C 5.11 2010/08/13 and other compilers; see
 184    <https://lists.gnu.org/r/bug-gnulib/2011-05/msg00401.html>.  */
 185 #define INT_MULTIPLY_RANGE_OVERFLOW(a, b, min, max)     \
 186   ((b) < 0                                              \
 187    ? ((a) < 0                                           \
 188       ? (a) < (max) / (b)                               \
 189       : (b) == -1                                       \
 190       ? 0                                               \
 191       : (min) / (b) < (a))                              \
 192    : (b) == 0                                           \
 193    ? 0                                                  \
 194    : ((a) < 0                                           \
 195       ? (a) < (min) / (b)                               \
 196       : (max) / (b) < (a)))
 197
 198 /* Return 1 if A / B would overflow in [MIN,MAX] arithmetic.
 199    See above for restrictions.  Do not check for division by zero.  */
 200 #define INT_DIVIDE_RANGE_OVERFLOW(a, b, min, max)       \
 201   ((min) < 0 && (b) == -1 && (a) < - (max))
 202
 203 /* Return 1 if A % B would overflow in [MIN,MAX] arithmetic.
 204    See above for restrictions.  Do not check for division by zero.
 205    Mathematically, % should never overflow, but on x86-like hosts
 206    INT_MIN % -1 traps, and the C standard permits this, so treat this
 207    as an overflow too.  */
 208 #define INT_REMAINDER_RANGE_OVERFLOW(a, b, min, max)    \
 209   INT_DIVIDE_RANGE_OVERFLOW (a, b, min, max)
 210
 211 /* Return 1 if A << B would overflow in [MIN,MAX] arithmetic.
 212    See above for restrictions.  Here, MIN and MAX are for A only, and B need
 213    not be of the same type as the other arguments.  The C standard says that
 214    behavior is undefined for shifts unless 0 <= B < wordwidth, and that when
 215    A is negative then A << B has undefined behavior and A >> B has
 216    implementation-defined behavior, but do not check these other
 217    restrictions.  */
 218 #define INT_LEFT_SHIFT_RANGE_OVERFLOW(a, b, min, max)   \
 219   ((a) < 0                                              \
 220    ? (a) < (min) >> (b)                                 \
 221    : (max) >> (b) < (a))
 222
 223 /* True if __builtin_add_overflow (A, B, P) works when P is non-null.  */
 224 #if 5 <= __GNUC__ && !defined __ICC
 225 # define _GL_HAS_BUILTIN_OVERFLOW 1
 226 #else
 227 # define _GL_HAS_BUILTIN_OVERFLOW 0
 228 #endif
 229
 230 /* True if __builtin_add_overflow_p (A, B, C) works.  */
 231 #define _GL_HAS_BUILTIN_OVERFLOW_P (7 <= __GNUC__)
 232
 233 /* The _GL*_OVERFLOW macros have the same restrictions as the
 234    *_RANGE_OVERFLOW macros, except that they do not assume that operands
 235    (e.g., A and B) have the same type as MIN and MAX.  Instead, they assume
 236    that the result (e.g., A + B) has that type.  */
 237 #if _GL_HAS_BUILTIN_OVERFLOW_P
 238 # define _GL_ADD_OVERFLOW(a, b, min, max)                               \
 239    __builtin_add_overflow_p (a, b, (__typeof__ ((a) + (b))) 0)
 240 # define _GL_SUBTRACT_OVERFLOW(a, b, min, max)                          \
 241    __builtin_sub_overflow_p (a, b, (__typeof__ ((a) - (b))) 0)
 242 # define _GL_MULTIPLY_OVERFLOW(a, b, min, max)                          \
 243    __builtin_mul_overflow_p (a, b, (__typeof__ ((a) * (b))) 0)
 244 #else
 245 # define _GL_ADD_OVERFLOW(a, b, min, max)                                \
 246    ((min) < 0 ? INT_ADD_RANGE_OVERFLOW (a, b, min, max)                  \
 247     : (a) < 0 ? (b) <= (a) + (b)                                         \
 248     : (b) < 0 ? (a) <= (a) + (b)                                         \
 249     : (a) + (b) < (b))
 250 # define _GL_SUBTRACT_OVERFLOW(a, b, min, max)                           \
 251    ((min) < 0 ? INT_SUBTRACT_RANGE_OVERFLOW (a, b, min, max)             \
 252     : (a) < 0 ? 1                                                        \
 253     : (b) < 0 ? (a) - (b) <= (a)                                         \
 254     : (a) < (b))
 255 # define _GL_MULTIPLY_OVERFLOW(a, b, min, max)                           \
 256    (((min) == 0 && (((a) < 0 && 0 < (b)) || ((b) < 0 && 0 < (a))))       \
 257     || INT_MULTIPLY_RANGE_OVERFLOW (a, b, min, max))
 258 #endif
 259 #define _GL_DIVIDE_OVERFLOW(a, b, min, max)                             \
 260   ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max)  \
 261    : (a) < 0 ? (b) <= (a) + (b) - 1                                     \
 262    : (b) < 0 && (a) + (b) <= (a))
 263 #define _GL_REMAINDER_OVERFLOW(a, b, min, max)                          \
 264   ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max)  \
 265    : (a) < 0 ? (a) % (b) != ((max) - (b) + 1) % (b)                     \
 266    : (b) < 0 && ! _GL_UNSIGNED_NEG_MULTIPLE (a, b, max))
 267
 268 /* Return a nonzero value if A is a mathematical multiple of B, where
 269    A is unsigned, B is negative, and MAX is the maximum value of A's
 270    type.  A's type must be the same as (A % B)'s type.  Normally (A %
 271    -B == 0) suffices, but things get tricky if -B would overflow.  */
 272 #define _GL_UNSIGNED_NEG_MULTIPLE(a, b, max)                            \
 273   (((b) < -_GL_SIGNED_INT_MAXIMUM (b)                                   \
 274     ? (_GL_SIGNED_INT_MAXIMUM (b) == (max)                              \
 275        ? (a)                                                            \
 276        : (a) % (_GL_INT_CONVERT (a, _GL_SIGNED_INT_MAXIMUM (b)) + 1))   \
 277     : (a) % - (b))                                                      \
 278    == 0)
 279
 280 /* Check for integer overflow, and report low order bits of answer.
 281
 282    The INT_<op>_OVERFLOW macros return 1 if the corresponding C operators
 283    might not yield numerically correct answers due to arithmetic overflow.
 284    The INT_<op>_WRAPV macros also store the low-order bits of the answer.
 285    These macros work correctly on all known practical hosts, and do not rely
 286    on undefined behavior due to signed arithmetic overflow.
 287
 288    Example usage, assuming A and B are long int:
 289
 290      if (INT_MULTIPLY_OVERFLOW (a, b))
 291        printf ("result would overflow\n");
 292      else
 293        printf ("result is %ld (no overflow)\n", a * b);
 294
 295    Example usage with WRAPV flavor:
 296
 297      long int result;
 298      bool overflow = INT_MULTIPLY_WRAPV (a, b, &result);
 299      printf ("result is %ld (%s)\n", result,
 300              overflow ? "after overflow" : "no overflow");
 301
 302    Restrictions on these macros:
 303
 304    These macros do not check for all possible numerical problems or
 305    undefined or unspecified behavior: they do not check for division
 306    by zero, for bad shift counts, or for shifting negative numbers.
 307
 308    These macros may evaluate their arguments zero or multiple times, so the
 309    arguments should not have side effects.
 310
 311    The WRAPV macros are not constant expressions.  They support only
 312    +, binary -, and *.  The result type must be signed.
 313
 314    These macros are tuned for their last argument being a constant.
 315
 316    Return 1 if the integer expressions A * B, A - B, -A, A * B, A / B,
 317    A % B, and A << B would overflow, respectively.  */
 318
 319 #define INT_ADD_OVERFLOW(a, b) \
 320   _GL_BINARY_OP_OVERFLOW (a, b, _GL_ADD_OVERFLOW)
 321 #define INT_SUBTRACT_OVERFLOW(a, b) \
 322   _GL_BINARY_OP_OVERFLOW (a, b, _GL_SUBTRACT_OVERFLOW)
 323 #if _GL_HAS_BUILTIN_OVERFLOW_P
 324 # define INT_NEGATE_OVERFLOW(a) INT_SUBTRACT_OVERFLOW (0, a)
 325 #else
 326 # define INT_NEGATE_OVERFLOW(a) \
 327    INT_NEGATE_RANGE_OVERFLOW (a, _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
 328 #endif
 329 #define INT_MULTIPLY_OVERFLOW(a, b) \
 330   _GL_BINARY_OP_OVERFLOW (a, b, _GL_MULTIPLY_OVERFLOW)
 331 #define INT_DIVIDE_OVERFLOW(a, b) \
 332   _GL_BINARY_OP_OVERFLOW (a, b, _GL_DIVIDE_OVERFLOW)
 333 #define INT_REMAINDER_OVERFLOW(a, b) \
 334   _GL_BINARY_OP_OVERFLOW (a, b, _GL_REMAINDER_OVERFLOW)
 335 #define INT_LEFT_SHIFT_OVERFLOW(a, b) \
 336   INT_LEFT_SHIFT_RANGE_OVERFLOW (a, b, \
 337                                  _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
 338
 339 /* Return 1 if the expression A <op> B would overflow,
 340    where OP_RESULT_OVERFLOW (A, B, MIN, MAX) does the actual test,
 341    assuming MIN and MAX are the minimum and maximum for the result type.
 342    Arguments should be free of side effects.  */
 343 #define _GL_BINARY_OP_OVERFLOW(a, b, op_result_overflow)        \
 344   op_result_overflow (a, b,                                     \
 345                       _GL_INT_MINIMUM (_GL_INT_CONVERT (a, b)), \
 346                       _GL_INT_MAXIMUM (_GL_INT_CONVERT (a, b)))
 347
 348 /* Store the low-order bits of A + B, A - B, A * B, respectively, into *R.
 349    Return 1 if the result overflows.  See above for restrictions.  */
 350 #define INT_ADD_WRAPV(a, b, r) \
 351   _GL_INT_OP_WRAPV (a, b, r, +, __builtin_add_overflow, INT_ADD_OVERFLOW)
 352 #define INT_SUBTRACT_WRAPV(a, b, r) \
 353   _GL_INT_OP_WRAPV (a, b, r, -, __builtin_sub_overflow, INT_SUBTRACT_OVERFLOW)
 354 #define INT_MULTIPLY_WRAPV(a, b, r) \
 355   _GL_INT_OP_WRAPV (a, b, r, *, __builtin_mul_overflow, INT_MULTIPLY_OVERFLOW)
 356
 357 /* Nonzero if this compiler has GCC bug 68193 or Clang bug 25390.  See:
 358    https://gcc.gnu.org/bugzilla/show_bug.cgi?id=68193
 359    https://llvm.org/bugs/show_bug.cgi?id=25390
 360    For now, assume all versions of GCC-like compilers generate bogus
 361    warnings for _Generic.  This matters only for older compilers that
 362    lack __builtin_add_overflow.  */
 363 #if __GNUC__
 364 # define _GL__GENERIC_BOGUS 1
 365 #else
 366 # define _GL__GENERIC_BOGUS 0
 367 #endif
 368
 369 /* Store the low-order bits of A <op> B into *R, where OP specifies
 370    the operation.  BUILTIN is the builtin operation, and OVERFLOW the
 371    overflow predicate.  Return 1 if the result overflows.  See above
 372    for restrictions.  */
 373 #if _GL_HAS_BUILTIN_OVERFLOW
 374 # define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) builtin (a, b, r)
 375 #elif 201112 <= __STDC_VERSION__ && !_GL__GENERIC_BOGUS
 376 # define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) \
 377    (_Generic \
 378     (*(r), \
 379      signed char: \
 380        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 381                         signed char, SCHAR_MIN, SCHAR_MAX), \
 382      short int: \
 383        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 384                         short int, SHRT_MIN, SHRT_MAX), \
 385      int: \
 386        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 387                         int, INT_MIN, INT_MAX), \
 388      long int: \
 389        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 390                         long int, LONG_MIN, LONG_MAX), \
 391      long long int: \
 392        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
 393                         long long int, LLONG_MIN, LLONG_MAX)))
 394 #else
 395 # define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) \
 396    (sizeof *(r) == sizeof (signed char) \
 397     ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 398                        signed char, SCHAR_MIN, SCHAR_MAX) \
 399     : sizeof *(r) == sizeof (short int) \
 400     ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 401                        short int, SHRT_MIN, SHRT_MAX) \
 402     : sizeof *(r) == sizeof (int) \
 403     ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 404                        int, INT_MIN, INT_MAX) \
 405     : _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow))
 406 # ifdef LLONG_MAX
 407 #  define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
 408     (sizeof *(r) == sizeof (long int) \
 409      ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 410                         long int, LONG_MIN, LONG_MAX) \
 411      : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
 412                         long long int, LLONG_MIN, LLONG_MAX))
 413 # else
 414 #  define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
 415     _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 416                      long int, LONG_MIN, LONG_MAX)
 417 # endif
 418 #endif
 419
 420 /* Store the low-order bits of A <op> B into *R, where the operation
 421    is given by OP.  Use the unsigned type UT for calculation to avoid
 422    overflow problems.  *R's type is T, with extrema TMIN and TMAX.
 423    T must be a signed integer type.  Return 1 if the result overflows.  */
 424 #define _GL_INT_OP_CALC(a, b, r, op, overflow, ut, t, tmin, tmax) \
 425   (sizeof ((a) op (b)) < sizeof (t) \
 426    ? _GL_INT_OP_CALC1 ((t) (a), (t) (b), r, op, overflow, ut, t, tmin, tmax) \
 427    : _GL_INT_OP_CALC1 (a, b, r, op, overflow, ut, t, tmin, tmax))
 428 #define _GL_INT_OP_CALC1(a, b, r, op, overflow, ut, t, tmin, tmax) \
 429   ((overflow (a, b) \
 430     || (EXPR_SIGNED ((a) op (b)) && ((a) op (b)) < (tmin)) \
 431     || (tmax) < ((a) op (b))) \
 432    ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 1) \
 433    : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 0))
 434
 435 /* Return the low-order bits of A <op> B, where the operation is given
 436    by OP.  Use the unsigned type UT for calculation to avoid undefined
 437    behavior on signed integer overflow, and convert the result to type T.
 438    UT is at least as wide as T and is no narrower than unsigned int,
 439    T is two's complement, and there is no padding or trap representations.
 440    Assume that converting UT to T yields the low-order bits, as is
 441    done in all known two's-complement C compilers.  E.g., see:
 442    https://gcc.gnu.org/onlinedocs/gcc/Integers-implementation.html
 443
 444    According to the C standard, converting UT to T yields an
 445    implementation-defined result or signal for values outside T's
 446    range.  However, code that works around this theoretical problem
 447    runs afoul of a compiler bug in Oracle Studio 12.3 x86.  See:
 448    https://lists.gnu.org/r/bug-gnulib/2017-04/msg00049.html
 449    As the compiler bug is real, don't try to work around the
 450    theoretical problem.  */
 451
 452 #define _GL_INT_OP_WRAPV_VIA_UNSIGNED(a, b, op, ut, t) \
 453   ((t) ((ut) (a) op (ut) (b)))
 454
 455 #endif /* _GL_INTPROPS_H */