include/intprops.h

   1 /* intprops.h -- properties of integer types
   2
   3    Copyright (C) 2001-2024 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 */