gnulib/import/intprops.h

   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 #ifdef __EDG__
 233 /* EDG-based compilers like nvc 22.1 cannot add 64-bit signed to unsigned
 234    <https://bugs.gnu.org/53256>.  */
 235 # define _GL_HAS_BUILTIN_ADD_OVERFLOW 0
 236 #elif defined __has_builtin
 237 # define _GL_HAS_BUILTIN_ADD_OVERFLOW __has_builtin (__builtin_add_overflow)
 238 /* __builtin_{add,sub}_overflow exists but is not reliable in GCC 5.x and 6.x,
 239    see <https://gcc.gnu.org/bugzilla/show_bug.cgi?id=98269>.  */
 240 #elif 7 <= __GNUC__
 241 # define _GL_HAS_BUILTIN_ADD_OVERFLOW 1
 242 #else
 243 # define _GL_HAS_BUILTIN_ADD_OVERFLOW 0
 244 #endif
 245
 246 /* True if __builtin_mul_overflow (A, B, P) works when P is non-null.  */
 247 #if defined __clang_major__ && __clang_major__ < 14
 248 /* Work around Clang bug <https://bugs.llvm.org/show_bug.cgi?id=16404>.  */
 249 # define _GL_HAS_BUILTIN_MUL_OVERFLOW 0
 250 #else
 251 # define _GL_HAS_BUILTIN_MUL_OVERFLOW _GL_HAS_BUILTIN_ADD_OVERFLOW
 252 #endif
 253
 254 /* True if __builtin_add_overflow_p (A, B, C) works, and similarly for
 255    __builtin_sub_overflow_p and __builtin_mul_overflow_p.  */
 256 #ifdef __EDG__
 257 /* In EDG-based compilers like ICC 2021.3 and earlier,
 258    __builtin_add_overflow_p etc. are not treated as integral constant
 259    expressions even when all arguments are.  */
 260 # define _GL_HAS_BUILTIN_OVERFLOW_P 0
 261 #elif defined __has_builtin
 262 # define _GL_HAS_BUILTIN_OVERFLOW_P __has_builtin (__builtin_mul_overflow_p)
 263 #else
 264 # define _GL_HAS_BUILTIN_OVERFLOW_P (7 <= __GNUC__)
 265 #endif
 266
 267 /* The _GL*_OVERFLOW macros have the same restrictions as the
 268    *_RANGE_OVERFLOW macros, except that they do not assume that operands
 269    (e.g., A and B) have the same type as MIN and MAX.  Instead, they assume
 270    that the result (e.g., A + B) has that type.  */
 271 #if _GL_HAS_BUILTIN_OVERFLOW_P
 272 # define _GL_ADD_OVERFLOW(a, b, min, max)                               \
 273    __builtin_add_overflow_p (a, b, (__typeof__ ((a) + (b))) 0)
 274 # define _GL_SUBTRACT_OVERFLOW(a, b, min, max)                          \
 275    __builtin_sub_overflow_p (a, b, (__typeof__ ((a) - (b))) 0)
 276 # define _GL_MULTIPLY_OVERFLOW(a, b, min, max)                          \
 277    __builtin_mul_overflow_p (a, b, (__typeof__ ((a) * (b))) 0)
 278 #else
 279 # define _GL_ADD_OVERFLOW(a, b, min, max)                                \
 280    ((min) < 0 ? INT_ADD_RANGE_OVERFLOW (a, b, min, max)                  \
 281     : (a) < 0 ? (b) <= (a) + (b)                                         \
 282     : (b) < 0 ? (a) <= (a) + (b)                                         \
 283     : (a) + (b) < (b))
 284 # define _GL_SUBTRACT_OVERFLOW(a, b, min, max)                           \
 285    ((min) < 0 ? INT_SUBTRACT_RANGE_OVERFLOW (a, b, min, max)             \
 286     : (a) < 0 ? 1                                                        \
 287     : (b) < 0 ? (a) - (b) <= (a)                                         \
 288     : (a) < (b))
 289 # define _GL_MULTIPLY_OVERFLOW(a, b, min, max)                           \
 290    (((min) == 0 && (((a) < 0 && 0 < (b)) || ((b) < 0 && 0 < (a))))       \
 291     || INT_MULTIPLY_RANGE_OVERFLOW (a, b, min, max))
 292 #endif
 293 #define _GL_DIVIDE_OVERFLOW(a, b, min, max)                             \
 294   ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max)  \
 295    : (a) < 0 ? (b) <= (a) + (b) - 1                                     \
 296    : (b) < 0 && (a) + (b) <= (a))
 297 #define _GL_REMAINDER_OVERFLOW(a, b, min, max)                          \
 298   ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max)  \
 299    : (a) < 0 ? (a) % (b) != ((max) - (b) + 1) % (b)                     \
 300    : (b) < 0 && ! _GL_UNSIGNED_NEG_MULTIPLE (a, b, max))
 301
 302 /* Return a nonzero value if A is a mathematical multiple of B, where
 303    A is unsigned, B is negative, and MAX is the maximum value of A's
 304    type.  A's type must be the same as (A % B)'s type.  Normally (A %
 305    -B == 0) suffices, but things get tricky if -B would overflow.  */
 306 #define _GL_UNSIGNED_NEG_MULTIPLE(a, b, max)                            \
 307   (((b) < -_GL_SIGNED_INT_MAXIMUM (b)                                   \
 308     ? (_GL_SIGNED_INT_MAXIMUM (b) == (max)                              \
 309        ? (a)                                                            \
 310        : (a) % (_GL_INT_CONVERT (a, _GL_SIGNED_INT_MAXIMUM (b)) + 1))   \
 311     : (a) % - (b))                                                      \
 312    == 0)
 313
 314 /* Check for integer overflow, and report low order bits of answer.
 315
 316    The INT_<op>_OVERFLOW macros return 1 if the corresponding C operators
 317    might not yield numerically correct answers due to arithmetic overflow.
 318    The INT_<op>_WRAPV macros compute the low-order bits of the sum,
 319    difference, and product of two C integers, and return 1 if these
 320    low-order bits are not numerically correct.
 321    These macros work correctly on all known practical hosts, and do not rely
 322    on undefined behavior due to signed arithmetic overflow.
 323
 324    Example usage, assuming A and B are long int:
 325
 326      if (INT_MULTIPLY_OVERFLOW (a, b))
 327        printf ("result would overflow\n");
 328      else
 329        printf ("result is %ld (no overflow)\n", a * b);
 330
 331    Example usage with WRAPV flavor:
 332
 333      long int result;
 334      bool overflow = INT_MULTIPLY_WRAPV (a, b, &result);
 335      printf ("result is %ld (%s)\n", result,
 336              overflow ? "after overflow" : "no overflow");
 337
 338    Restrictions on these macros:
 339
 340    These macros do not check for all possible numerical problems or
 341    undefined or unspecified behavior: they do not check for division
 342    by zero, for bad shift counts, or for shifting negative numbers.
 343
 344    These macros may evaluate their arguments zero or multiple times, so the
 345    arguments should not have side effects.
 346
 347    The WRAPV macros are not constant expressions.  They support only
 348    +, binary -, and *.
 349
 350    Because the WRAPV macros convert the result, they report overflow
 351    in different circumstances than the OVERFLOW macros do.  For
 352    example, in the typical case with 16-bit 'short' and 32-bit 'int',
 353    if A, B and R are all of type 'short' then INT_ADD_OVERFLOW (A, B)
 354    returns false because the addition cannot overflow after A and B
 355    are converted to 'int', whereas INT_ADD_WRAPV (A, B, &R) returns
 356    true or false depending on whether the sum fits into 'short'.
 357
 358    These macros are tuned for their last input argument being a constant.
 359
 360    Return 1 if the integer expressions A * B, A - B, -A, A * B, A / B,
 361    A % B, and A << B would overflow, respectively.  */
 362
 363 #define INT_ADD_OVERFLOW(a, b) \
 364   _GL_BINARY_OP_OVERFLOW (a, b, _GL_ADD_OVERFLOW)
 365 #define INT_SUBTRACT_OVERFLOW(a, b) \
 366   _GL_BINARY_OP_OVERFLOW (a, b, _GL_SUBTRACT_OVERFLOW)
 367 #if _GL_HAS_BUILTIN_OVERFLOW_P
 368 # define INT_NEGATE_OVERFLOW(a) INT_SUBTRACT_OVERFLOW (0, a)
 369 #else
 370 # define INT_NEGATE_OVERFLOW(a) \
 371    INT_NEGATE_RANGE_OVERFLOW (a, _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
 372 #endif
 373 #define INT_MULTIPLY_OVERFLOW(a, b) \
 374   _GL_BINARY_OP_OVERFLOW (a, b, _GL_MULTIPLY_OVERFLOW)
 375 #define INT_DIVIDE_OVERFLOW(a, b) \
 376   _GL_BINARY_OP_OVERFLOW (a, b, _GL_DIVIDE_OVERFLOW)
 377 #define INT_REMAINDER_OVERFLOW(a, b) \
 378   _GL_BINARY_OP_OVERFLOW (a, b, _GL_REMAINDER_OVERFLOW)
 379 #define INT_LEFT_SHIFT_OVERFLOW(a, b) \
 380   INT_LEFT_SHIFT_RANGE_OVERFLOW (a, b, \
 381                                  _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
 382
 383 /* Return 1 if the expression A <op> B would overflow,
 384    where OP_RESULT_OVERFLOW (A, B, MIN, MAX) does the actual test,
 385    assuming MIN and MAX are the minimum and maximum for the result type.
 386    Arguments should be free of side effects.  */
 387 #define _GL_BINARY_OP_OVERFLOW(a, b, op_result_overflow)        \
 388   op_result_overflow (a, b,                                     \
 389                       _GL_INT_MINIMUM (_GL_INT_CONVERT (a, b)), \
 390                       _GL_INT_MAXIMUM (_GL_INT_CONVERT (a, b)))
 391
 392 /* Store the low-order bits of A + B, A - B, A * B, respectively, into *R.
 393    Return 1 if the result overflows.  See above for restrictions.  */
 394 #if _GL_HAS_BUILTIN_ADD_OVERFLOW
 395 # define INT_ADD_WRAPV(a, b, r) __builtin_add_overflow (a, b, r)
 396 # define INT_SUBTRACT_WRAPV(a, b, r) __builtin_sub_overflow (a, b, r)
 397 #else
 398 # define INT_ADD_WRAPV(a, b, r) \
 399    _GL_INT_OP_WRAPV (a, b, r, +, _GL_INT_ADD_RANGE_OVERFLOW)
 400 # define INT_SUBTRACT_WRAPV(a, b, r) \
 401    _GL_INT_OP_WRAPV (a, b, r, -, _GL_INT_SUBTRACT_RANGE_OVERFLOW)
 402 #endif
 403 #if _GL_HAS_BUILTIN_MUL_OVERFLOW
 404 # if ((9 < __GNUC__ + (3 <= __GNUC_MINOR__) \
 405        || (__GNUC__ == 8 && 4 <= __GNUC_MINOR__)) \
 406       && !defined __EDG__)
 407 #  define INT_MULTIPLY_WRAPV(a, b, r) __builtin_mul_overflow (a, b, r)
 408 # else
 409    /* Work around GCC bug 91450.  */
 410 #  define INT_MULTIPLY_WRAPV(a, b, r) \
 411     ((!_GL_SIGNED_TYPE_OR_EXPR (*(r)) && EXPR_SIGNED (a) && EXPR_SIGNED (b) \
 412       && _GL_INT_MULTIPLY_RANGE_OVERFLOW (a, b, 0, (__typeof__ (*(r))) -1)) \
 413      ? ((void) __builtin_mul_overflow (a, b, r), 1) \
 414      : __builtin_mul_overflow (a, b, r))
 415 # endif
 416 #else
 417 # define INT_MULTIPLY_WRAPV(a, b, r) \
 418    _GL_INT_OP_WRAPV (a, b, r, *, _GL_INT_MULTIPLY_RANGE_OVERFLOW)
 419 #endif
 420
 421 /* Nonzero if this compiler has GCC bug 68193 or Clang bug 25390.  See:
 422    https://gcc.gnu.org/bugzilla/show_bug.cgi?id=68193
 423    https://llvm.org/bugs/show_bug.cgi?id=25390
 424    For now, assume all versions of GCC-like compilers generate bogus
 425    warnings for _Generic.  This matters only for compilers that
 426    lack relevant builtins.  */
 427 #if __GNUC__ || defined __clang__
 428 # define _GL__GENERIC_BOGUS 1
 429 #else
 430 # define _GL__GENERIC_BOGUS 0
 431 #endif
 432
 433 /* Store the low-order bits of A <op> B into *R, where OP specifies
 434    the operation and OVERFLOW the overflow predicate.  Return 1 if the
 435    result overflows.  See above for restrictions.  */
 436 #if 201112 <= __STDC_VERSION__ && !_GL__GENERIC_BOGUS
 437 # define _GL_INT_OP_WRAPV(a, b, r, op, overflow) \
 438    (_Generic \
 439     (*(r), \
 440      signed char: \
 441        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 442                         signed char, SCHAR_MIN, SCHAR_MAX), \
 443      unsigned char: \
 444        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 445                         unsigned char, 0, UCHAR_MAX), \
 446      short int: \
 447        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 448                         short int, SHRT_MIN, SHRT_MAX), \
 449      unsigned short int: \
 450        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 451                         unsigned short int, 0, USHRT_MAX), \
 452      int: \
 453        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 454                         int, INT_MIN, INT_MAX), \
 455      unsigned int: \
 456        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 457                         unsigned int, 0, UINT_MAX), \
 458      long int: \
 459        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 460                         long int, LONG_MIN, LONG_MAX), \
 461      unsigned long int: \
 462        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 463                         unsigned long int, 0, ULONG_MAX), \
 464      long long int: \
 465        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
 466                         long long int, LLONG_MIN, LLONG_MAX), \
 467      unsigned long long int: \
 468        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
 469                         unsigned long long int, 0, ULLONG_MAX)))
 470 #else
 471 /* Store the low-order bits of A <op> B into *R, where OP specifies
 472    the operation and OVERFLOW the overflow predicate.  If *R is
 473    signed, its type is ST with bounds SMIN..SMAX; otherwise its type
 474    is UT with bounds U..UMAX.  ST and UT are narrower than int.
 475    Return 1 if the result overflows.  See above for restrictions.  */
 476 # if _GL_HAVE___TYPEOF__
 477 #  define _GL_INT_OP_WRAPV_SMALLISH(a,b,r,op,overflow,st,smin,smax,ut,umax) \
 478     (TYPE_SIGNED (__typeof__ (*(r))) \
 479      ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, st, smin, smax) \
 480      : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, ut, 0, umax))
 481 # else
 482 #  define _GL_INT_OP_WRAPV_SMALLISH(a,b,r,op,overflow,st,smin,smax,ut,umax) \
 483     (overflow (a, b, smin, smax) \
 484      ? (overflow (a, b, 0, umax) \
 485         ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st), 1) \
 486         : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st)) < 0) \
 487      : (overflow (a, b, 0, umax) \
 488         ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st)) >= 0 \
 489         : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st), 0)))
 490 # endif
 491
 492 # define _GL_INT_OP_WRAPV(a, b, r, op, overflow) \
 493    (sizeof *(r) == sizeof (signed char) \
 494     ? _GL_INT_OP_WRAPV_SMALLISH (a, b, r, op, overflow, \
 495                                  signed char, SCHAR_MIN, SCHAR_MAX, \
 496                                  unsigned char, UCHAR_MAX) \
 497     : sizeof *(r) == sizeof (short int) \
 498     ? _GL_INT_OP_WRAPV_SMALLISH (a, b, r, op, overflow, \
 499                                  short int, SHRT_MIN, SHRT_MAX, \
 500                                  unsigned short int, USHRT_MAX) \
 501     : sizeof *(r) == sizeof (int) \
 502     ? (EXPR_SIGNED (*(r)) \
 503        ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 504                           int, INT_MIN, INT_MAX) \
 505        : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 506                           unsigned int, 0, UINT_MAX)) \
 507     : _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow))
 508 # ifdef LLONG_MAX
 509 #  define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
 510     (sizeof *(r) == sizeof (long int) \
 511      ? (EXPR_SIGNED (*(r)) \
 512         ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 513                            long int, LONG_MIN, LONG_MAX) \
 514         : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 515                            unsigned long int, 0, ULONG_MAX)) \
 516      : (EXPR_SIGNED (*(r)) \
 517         ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
 518                            long long int, LLONG_MIN, LLONG_MAX) \
 519         : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
 520                            unsigned long long int, 0, ULLONG_MAX)))
 521 # else
 522 #  define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
 523     (EXPR_SIGNED (*(r)) \
 524      ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 525                         long int, LONG_MIN, LONG_MAX) \
 526      : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 527                         unsigned long int, 0, ULONG_MAX))
 528 # endif
 529 #endif
 530
 531 /* Store the low-order bits of A <op> B into *R, where the operation
 532    is given by OP.  Use the unsigned type UT for calculation to avoid
 533    overflow problems.  *R's type is T, with extrema TMIN and TMAX.
 534    T must be a signed integer type.  Return 1 if the result overflows.  */
 535 #define _GL_INT_OP_CALC(a, b, r, op, overflow, ut, t, tmin, tmax) \
 536   (overflow (a, b, tmin, tmax) \
 537    ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 1) \
 538    : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 0))
 539
 540 /* Return the low-order bits of A <op> B, where the operation is given
 541    by OP.  Use the unsigned type UT for calculation to avoid undefined
 542    behavior on signed integer overflow, and convert the result to type T.
 543    UT is at least as wide as T and is no narrower than unsigned int,
 544    T is two's complement, and there is no padding or trap representations.
 545    Assume that converting UT to T yields the low-order bits, as is
 546    done in all known two's-complement C compilers.  E.g., see:
 547    https://gcc.gnu.org/onlinedocs/gcc/Integers-implementation.html
 548
 549    According to the C standard, converting UT to T yields an
 550    implementation-defined result or signal for values outside T's
 551    range.  However, code that works around this theoretical problem
 552    runs afoul of a compiler bug in Oracle Studio 12.3 x86.  See:
 553    https://lists.gnu.org/r/bug-gnulib/2017-04/msg00049.html
 554    As the compiler bug is real, don't try to work around the
 555    theoretical problem.  */
 556
 557 #define _GL_INT_OP_WRAPV_VIA_UNSIGNED(a, b, op, ut, t) \
 558   ((t) ((ut) (a) op (ut) (b)))
 559
 560 /* Return true if the numeric values A + B, A - B, A * B fall outside
 561    the range TMIN..TMAX.  Arguments should be integer expressions
 562    without side effects.  TMIN should be signed and nonpositive.
 563    TMAX should be positive, and should be signed unless TMIN is zero.  */
 564 #define _GL_INT_ADD_RANGE_OVERFLOW(a, b, tmin, tmax) \
 565   ((b) < 0 \
 566    ? (((tmin) \
 567        ? ((EXPR_SIGNED (_GL_INT_CONVERT (a, (tmin) - (b))) || (b) < (tmin)) \
 568           && (a) < (tmin) - (b)) \
 569        : (a) <= -1 - (b)) \
 570       || ((EXPR_SIGNED (a) ? 0 <= (a) : (tmax) < (a)) && (tmax) < (a) + (b))) \
 571    : (a) < 0 \
 572    ? (((tmin) \
 573        ? ((EXPR_SIGNED (_GL_INT_CONVERT (b, (tmin) - (a))) || (a) < (tmin)) \
 574           && (b) < (tmin) - (a)) \
 575        : (b) <= -1 - (a)) \
 576       || ((EXPR_SIGNED (_GL_INT_CONVERT (a, b)) || (tmax) < (b)) \
 577           && (tmax) < (a) + (b))) \
 578    : (tmax) < (b) || (tmax) - (b) < (a))
 579 #define _GL_INT_SUBTRACT_RANGE_OVERFLOW(a, b, tmin, tmax) \
 580   (((a) < 0) == ((b) < 0) \
 581    ? ((a) < (b) \
 582       ? !(tmin) || -1 - (tmin) < (b) - (a) - 1 \
 583       : (tmax) < (a) - (b)) \
 584    : (a) < 0 \
 585    ? ((!EXPR_SIGNED (_GL_INT_CONVERT ((a) - (tmin), b)) && (a) - (tmin) < 0) \
 586       || (a) - (tmin) < (b)) \
 587    : ((! (EXPR_SIGNED (_GL_INT_CONVERT (tmax, b)) \
 588           && EXPR_SIGNED (_GL_INT_CONVERT ((tmax) + (b), a))) \
 589        && (tmax) <= -1 - (b)) \
 590       || (tmax) + (b) < (a)))
 591 #define _GL_INT_MULTIPLY_RANGE_OVERFLOW(a, b, tmin, tmax) \
 592   ((b) < 0 \
 593    ? ((a) < 0 \
 594       ? (EXPR_SIGNED (_GL_INT_CONVERT (tmax, b)) \
 595          ? (a) < (tmax) / (b) \
 596          : ((INT_NEGATE_OVERFLOW (b) \
 597              ? _GL_INT_CONVERT (b, tmax) >> (TYPE_WIDTH (+ (b)) - 1) \
 598              : (tmax) / -(b)) \
 599             <= -1 - (a))) \
 600       : INT_NEGATE_OVERFLOW (_GL_INT_CONVERT (b, tmin)) && (b) == -1 \
 601       ? (EXPR_SIGNED (a) \
 602          ? 0 < (a) + (tmin) \
 603          : 0 < (a) && -1 - (tmin) < (a) - 1) \
 604       : (tmin) / (b) < (a)) \
 605    : (b) == 0 \
 606    ? 0 \
 607    : ((a) < 0 \
 608       ? (INT_NEGATE_OVERFLOW (_GL_INT_CONVERT (a, tmin)) && (a) == -1 \
 609          ? (EXPR_SIGNED (b) ? 0 < (b) + (tmin) : -1 - (tmin) < (b) - 1) \
 610          : (tmin) / (a) < (b)) \
 611       : (tmax) / (b) < (a)))
 612
 613 /* The following macros compute A + B, A - B, and A * B, respectively.
 614    If no overflow occurs, they set *R to the result and return 1;
 615    otherwise, they return 0 and may modify *R.
 616
 617    Example usage:
 618
 619      long int result;
 620      if (INT_ADD_OK (a, b, &result))
 621        printf ("result is %ld\n", result);
 622      else
 623        printf ("overflow\n");
 624
 625    A, B, and *R should be integers; they need not be the same type,
 626    and they need not be all signed or all unsigned.
 627
 628    These macros work correctly on all known practical hosts, and do not rely
 629    on undefined behavior due to signed arithmetic overflow.
 630
 631    These macros are not constant expressions.
 632
 633    These macros may evaluate their arguments zero or multiple times, so the
 634    arguments should not have side effects.
 635
 636    These macros are tuned for B being a constant.  */
 637
 638 #define INT_ADD_OK(a, b, r) ! INT_ADD_WRAPV (a, b, r)
 639 #define INT_SUBTRACT_OK(a, b, r) ! INT_SUBTRACT_WRAPV (a, b, r)
 640 #define INT_MULTIPLY_OK(a, b, r) ! INT_MULTIPLY_WRAPV (a, b, r)
 641
 642 #endif /* _GL_INTPROPS_H */