include/intprops.h

   1 /* intprops.h -- properties of integer types
   2
   3    Copyright (C) 2001-2021 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.  T must not be a bit-field expression.
  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)) - 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      || (4 <= __clang_major__) \
  90      || (1210 <= __IBMC__ && defined __IBM__TYPEOF__) \
  91      || (0x5110 <= __SUNPRO_C && !__STDC__))
  92 # define _GL_HAVE___TYPEOF__ 1
  93 #else
  94 # define _GL_HAVE___TYPEOF__ 0
  95 #endif
  96
  97 /* Return 1 if the integer type or expression T might be signed.  Return 0
  98    if it is definitely unsigned.  T must not be a bit-field expression.
  99    This macro does not evaluate its argument, and expands to an
 100    integer constant expression.  */
 101 #if _GL_HAVE___TYPEOF__
 102 # define _GL_SIGNED_TYPE_OR_EXPR(t) TYPE_SIGNED (__typeof__ (t))
 103 #else
 104 # define _GL_SIGNED_TYPE_OR_EXPR(t) 1
 105 #endif
 106
 107 /* Bound on length of the string representing an unsigned integer
 108    value representable in B bits.  log10 (2.0) < 146/485.  The
 109    smallest value of B where this bound is not tight is 2621.  */
 110 #define INT_BITS_STRLEN_BOUND(b) (((b) * 146 + 484) / 485)
 111
 112 /* Bound on length of the string representing an integer type or expression T.
 113    T must not be a bit-field expression.
 114
 115    Subtract 1 for the sign bit if T is signed, and then add 1 more for
 116    a minus sign if needed.
 117
 118    Because _GL_SIGNED_TYPE_OR_EXPR sometimes returns 1 when its argument is
 119    unsigned, this macro may overestimate the true bound by one byte when
 120    applied to unsigned types of size 2, 4, 16, ... bytes.  */
 121 #define INT_STRLEN_BOUND(t)                                     \
 122   (INT_BITS_STRLEN_BOUND (TYPE_WIDTH (t) - _GL_SIGNED_TYPE_OR_EXPR (t)) \
 123    + _GL_SIGNED_TYPE_OR_EXPR (t))
 124
 125 /* Bound on buffer size needed to represent an integer type or expression T,
 126    including the terminating null.  T must not be a bit-field expression.  */
 127 #define INT_BUFSIZE_BOUND(t) (INT_STRLEN_BOUND (t) + 1)
 128
 129
 130 /* Range overflow checks.
 131
 132    The INT_<op>_RANGE_OVERFLOW macros return 1 if the corresponding C
 133    operators might not yield numerically correct answers due to
 134    arithmetic overflow.  They do not rely on undefined or
 135    implementation-defined behavior.  Their implementations are simple
 136    and straightforward, but they are a bit harder to use than the
 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    These macros are tuned for constant MIN and MAX.  For commutative
 162    operations such as A + B, they are also tuned for constant B.  */
 163
 164 /* Return 1 if A + B would overflow in [MIN,MAX] arithmetic.
 165    See above for restrictions.  */
 166 #define INT_ADD_RANGE_OVERFLOW(a, b, min, max)          \
 167   ((b) < 0                                              \
 168    ? (a) < (min) - (b)                                  \
 169    : (max) - (b) < (a))
 170
 171 /* Return 1 if A - B would overflow in [MIN,MAX] arithmetic.
 172    See above for restrictions.  */
 173 #define INT_SUBTRACT_RANGE_OVERFLOW(a, b, min, max)     \
 174   ((b) < 0                                              \
 175    ? (max) + (b) < (a)                                  \
 176    : (a) < (min) + (b))
 177
 178 /* Return 1 if - A would overflow in [MIN,MAX] arithmetic.
 179    See above for restrictions.  */
 180 #define INT_NEGATE_RANGE_OVERFLOW(a, min, max)          \
 181   ((min) < 0                                            \
 182    ? (a) < - (max)                                      \
 183    : 0 < (a))
 184
 185 /* Return 1 if A * B would overflow in [MIN,MAX] arithmetic.
 186    See above for restrictions.  Avoid && and || as they tickle
 187    bugs in Sun C 5.11 2010/08/13 and other compilers; see
 188    <https://lists.gnu.org/r/bug-gnulib/2011-05/msg00401.html>.  */
 189 #define INT_MULTIPLY_RANGE_OVERFLOW(a, b, min, max)     \
 190   ((b) < 0                                              \
 191    ? ((a) < 0                                           \
 192       ? (a) < (max) / (b)                               \
 193       : (b) == -1                                       \
 194       ? 0                                               \
 195       : (min) / (b) < (a))                              \
 196    : (b) == 0                                           \
 197    ? 0                                                  \
 198    : ((a) < 0                                           \
 199       ? (a) < (min) / (b)                               \
 200       : (max) / (b) < (a)))
 201
 202 /* Return 1 if A / B would overflow in [MIN,MAX] arithmetic.
 203    See above for restrictions.  Do not check for division by zero.  */
 204 #define INT_DIVIDE_RANGE_OVERFLOW(a, b, min, max)       \
 205   ((min) < 0 && (b) == -1 && (a) < - (max))
 206
 207 /* Return 1 if A % B would overflow in [MIN,MAX] arithmetic.
 208    See above for restrictions.  Do not check for division by zero.
 209    Mathematically, % should never overflow, but on x86-like hosts
 210    INT_MIN % -1 traps, and the C standard permits this, so treat this
 211    as an overflow too.  */
 212 #define INT_REMAINDER_RANGE_OVERFLOW(a, b, min, max)    \
 213   INT_DIVIDE_RANGE_OVERFLOW (a, b, min, max)
 214
 215 /* Return 1 if A << B would overflow in [MIN,MAX] arithmetic.
 216    See above for restrictions.  Here, MIN and MAX are for A only, and B need
 217    not be of the same type as the other arguments.  The C standard says that
 218    behavior is undefined for shifts unless 0 <= B < wordwidth, and that when
 219    A is negative then A << B has undefined behavior and A >> B has
 220    implementation-defined behavior, but do not check these other
 221    restrictions.  */
 222 #define INT_LEFT_SHIFT_RANGE_OVERFLOW(a, b, min, max)   \
 223   ((a) < 0                                              \
 224    ? (a) < (min) >> (b)                                 \
 225    : (max) >> (b) < (a))
 226
 227 /* True if __builtin_add_overflow (A, B, P) and __builtin_sub_overflow
 228    (A, B, P) work when P is non-null.  */
 229 /* __builtin_{add,sub}_overflow exists but is not reliable in GCC 5.x and 6.x,
 230    see <https://gcc.gnu.org/bugzilla/show_bug.cgi?id=98269>.  */
 231 #if 7 <= __GNUC__ && !defined __ICC
 232 # define _GL_HAS_BUILTIN_ADD_OVERFLOW 1
 233 #elif defined __has_builtin
 234 # define _GL_HAS_BUILTIN_ADD_OVERFLOW __has_builtin (__builtin_add_overflow)
 235 #else
 236 # define _GL_HAS_BUILTIN_ADD_OVERFLOW 0
 237 #endif
 238
 239 /* True if __builtin_mul_overflow (A, B, P) works when P is non-null.  */
 240 #ifdef __clang__
 241 /* Work around Clang bug <https://bugs.llvm.org/show_bug.cgi?id=16404>.  */
 242 # define _GL_HAS_BUILTIN_MUL_OVERFLOW 0
 243 #else
 244 # define _GL_HAS_BUILTIN_MUL_OVERFLOW _GL_HAS_BUILTIN_ADD_OVERFLOW
 245 #endif
 246
 247 /* True if __builtin_add_overflow_p (A, B, C) works, and similarly for
 248    __builtin_sub_overflow_p and __builtin_mul_overflow_p.  */
 249 #if defined __clang__ || defined __ICC
 250 /* Clang 11 lacks __builtin_mul_overflow_p, and even if it did it
 251    would presumably run afoul of Clang bug 16404.  ICC 2021.1's
 252    __builtin_add_overflow_p etc. are not treated as integral constant
 253    expressions even when all arguments are.  */
 254 # define _GL_HAS_BUILTIN_OVERFLOW_P 0
 255 #elif defined __has_builtin
 256 # define _GL_HAS_BUILTIN_OVERFLOW_P __has_builtin (__builtin_mul_overflow_p)
 257 #else
 258 # define _GL_HAS_BUILTIN_OVERFLOW_P (7 <= __GNUC__)
 259 #endif
 260
 261 /* The _GL*_OVERFLOW macros have the same restrictions as the
 262    *_RANGE_OVERFLOW macros, except that they do not assume that operands
 263    (e.g., A and B) have the same type as MIN and MAX.  Instead, they assume
 264    that the result (e.g., A + B) has that type.  */
 265 #if _GL_HAS_BUILTIN_OVERFLOW_P
 266 # define _GL_ADD_OVERFLOW(a, b, min, max)                               \
 267    __builtin_add_overflow_p (a, b, (__typeof__ ((a) + (b))) 0)
 268 # define _GL_SUBTRACT_OVERFLOW(a, b, min, max)                          \
 269    __builtin_sub_overflow_p (a, b, (__typeof__ ((a) - (b))) 0)
 270 # define _GL_MULTIPLY_OVERFLOW(a, b, min, max)                          \
 271    __builtin_mul_overflow_p (a, b, (__typeof__ ((a) * (b))) 0)
 272 #else
 273 # define _GL_ADD_OVERFLOW(a, b, min, max)                                \
 274    ((min) < 0 ? INT_ADD_RANGE_OVERFLOW (a, b, min, max)                  \
 275     : (a) < 0 ? (b) <= (a) + (b)                                         \
 276     : (b) < 0 ? (a) <= (a) + (b)                                         \
 277     : (a) + (b) < (b))
 278 # define _GL_SUBTRACT_OVERFLOW(a, b, min, max)                           \
 279    ((min) < 0 ? INT_SUBTRACT_RANGE_OVERFLOW (a, b, min, max)             \
 280     : (a) < 0 ? 1                                                        \
 281     : (b) < 0 ? (a) - (b) <= (a)                                         \
 282     : (a) < (b))
 283 # define _GL_MULTIPLY_OVERFLOW(a, b, min, max)                           \
 284    (((min) == 0 && (((a) < 0 && 0 < (b)) || ((b) < 0 && 0 < (a))))       \
 285     || INT_MULTIPLY_RANGE_OVERFLOW (a, b, min, max))
 286 #endif
 287 #define _GL_DIVIDE_OVERFLOW(a, b, min, max)                             \
 288   ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max)  \
 289    : (a) < 0 ? (b) <= (a) + (b) - 1                                     \
 290    : (b) < 0 && (a) + (b) <= (a))
 291 #define _GL_REMAINDER_OVERFLOW(a, b, min, max)                          \
 292   ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max)  \
 293    : (a) < 0 ? (a) % (b) != ((max) - (b) + 1) % (b)                     \
 294    : (b) < 0 && ! _GL_UNSIGNED_NEG_MULTIPLE (a, b, max))
 295
 296 /* Return a nonzero value if A is a mathematical multiple of B, where
 297    A is unsigned, B is negative, and MAX is the maximum value of A's
 298    type.  A's type must be the same as (A % B)'s type.  Normally (A %
 299    -B == 0) suffices, but things get tricky if -B would overflow.  */
 300 #define _GL_UNSIGNED_NEG_MULTIPLE(a, b, max)                            \
 301   (((b) < -_GL_SIGNED_INT_MAXIMUM (b)                                   \
 302     ? (_GL_SIGNED_INT_MAXIMUM (b) == (max)                              \
 303        ? (a)                                                            \
 304        : (a) % (_GL_INT_CONVERT (a, _GL_SIGNED_INT_MAXIMUM (b)) + 1))   \
 305     : (a) % - (b))                                                      \
 306    == 0)
 307
 308 /* Check for integer overflow, and report low order bits of answer.
 309
 310    The INT_<op>_OVERFLOW macros return 1 if the corresponding C operators
 311    might not yield numerically correct answers due to arithmetic overflow.
 312    The INT_<op>_WRAPV macros compute the low-order bits of the sum,
 313    difference, and product of two C integers, and return 1 if these
 314    low-order bits are not numerically correct.
 315    These macros work correctly on all known practical hosts, and do not rely
 316    on undefined behavior due to signed arithmetic overflow.
 317
 318    Example usage, assuming A and B are long int:
 319
 320      if (INT_MULTIPLY_OVERFLOW (a, b))
 321        printf ("result would overflow\n");
 322      else
 323        printf ("result is %ld (no overflow)\n", a * b);
 324
 325    Example usage with WRAPV flavor:
 326
 327      long int result;
 328      bool overflow = INT_MULTIPLY_WRAPV (a, b, &result);
 329      printf ("result is %ld (%s)\n", result,
 330              overflow ? "after overflow" : "no overflow");
 331
 332    Restrictions on these macros:
 333
 334    These macros do not check for all possible numerical problems or
 335    undefined or unspecified behavior: they do not check for division
 336    by zero, for bad shift counts, or for shifting negative numbers.
 337
 338    These macros may evaluate their arguments zero or multiple times, so the
 339    arguments should not have side effects.
 340
 341    The WRAPV macros are not constant expressions.  They support only
 342    +, binary -, and *.  Because the WRAPV macros convert the result,
 343    they report overflow in different circumstances than the OVERFLOW
 344    macros do.
 345
 346    These macros are tuned for their last input argument being a constant.
 347
 348    Return 1 if the integer expressions A * B, A - B, -A, A * B, A / B,
 349    A % B, and A << B would overflow, respectively.  */
 350
 351 #define INT_ADD_OVERFLOW(a, b) \
 352   _GL_BINARY_OP_OVERFLOW (a, b, _GL_ADD_OVERFLOW)
 353 #define INT_SUBTRACT_OVERFLOW(a, b) \
 354   _GL_BINARY_OP_OVERFLOW (a, b, _GL_SUBTRACT_OVERFLOW)
 355 #if _GL_HAS_BUILTIN_OVERFLOW_P
 356 # define INT_NEGATE_OVERFLOW(a) INT_SUBTRACT_OVERFLOW (0, a)
 357 #else
 358 # define INT_NEGATE_OVERFLOW(a) \
 359    INT_NEGATE_RANGE_OVERFLOW (a, _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
 360 #endif
 361 #define INT_MULTIPLY_OVERFLOW(a, b) \
 362   _GL_BINARY_OP_OVERFLOW (a, b, _GL_MULTIPLY_OVERFLOW)
 363 #define INT_DIVIDE_OVERFLOW(a, b) \
 364   _GL_BINARY_OP_OVERFLOW (a, b, _GL_DIVIDE_OVERFLOW)
 365 #define INT_REMAINDER_OVERFLOW(a, b) \
 366   _GL_BINARY_OP_OVERFLOW (a, b, _GL_REMAINDER_OVERFLOW)
 367 #define INT_LEFT_SHIFT_OVERFLOW(a, b) \
 368   INT_LEFT_SHIFT_RANGE_OVERFLOW (a, b, \
 369                                  _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
 370
 371 /* Return 1 if the expression A <op> B would overflow,
 372    where OP_RESULT_OVERFLOW (A, B, MIN, MAX) does the actual test,
 373    assuming MIN and MAX are the minimum and maximum for the result type.
 374    Arguments should be free of side effects.  */
 375 #define _GL_BINARY_OP_OVERFLOW(a, b, op_result_overflow)        \
 376   op_result_overflow (a, b,                                     \
 377                       _GL_INT_MINIMUM (_GL_INT_CONVERT (a, b)), \
 378                       _GL_INT_MAXIMUM (_GL_INT_CONVERT (a, b)))
 379
 380 /* Store the low-order bits of A + B, A - B, A * B, respectively, into *R.
 381    Return 1 if the result overflows.  See above for restrictions.  */
 382 #if _GL_HAS_BUILTIN_ADD_OVERFLOW
 383 # define INT_ADD_WRAPV(a, b, r) __builtin_add_overflow (a, b, r)
 384 # define INT_SUBTRACT_WRAPV(a, b, r) __builtin_sub_overflow (a, b, r)
 385 #else
 386 # define INT_ADD_WRAPV(a, b, r) \
 387    _GL_INT_OP_WRAPV (a, b, r, +, _GL_INT_ADD_RANGE_OVERFLOW)
 388 # define INT_SUBTRACT_WRAPV(a, b, r) \
 389    _GL_INT_OP_WRAPV (a, b, r, -, _GL_INT_SUBTRACT_RANGE_OVERFLOW)
 390 #endif
 391 #if _GL_HAS_BUILTIN_MUL_OVERFLOW
 392 # if ((9 < __GNUC__ + (3 <= __GNUC_MINOR__) \
 393        || (__GNUC__ == 8 && 4 <= __GNUC_MINOR__)) \
 394       && !defined __ICC)
 395 #  define INT_MULTIPLY_WRAPV(a, b, r) __builtin_mul_overflow (a, b, r)
 396 # else
 397    /* Work around GCC bug 91450.  */
 398 #  define INT_MULTIPLY_WRAPV(a, b, r) \
 399     ((!_GL_SIGNED_TYPE_OR_EXPR (*(r)) && EXPR_SIGNED (a) && EXPR_SIGNED (b) \
 400       && _GL_INT_MULTIPLY_RANGE_OVERFLOW (a, b, 0, (__typeof__ (*(r))) -1)) \
 401      ? ((void) __builtin_mul_overflow (a, b, r), 1) \
 402      : __builtin_mul_overflow (a, b, r))
 403 # endif
 404 #else
 405 # define INT_MULTIPLY_WRAPV(a, b, r) \
 406    _GL_INT_OP_WRAPV (a, b, r, *, _GL_INT_MULTIPLY_RANGE_OVERFLOW)
 407 #endif
 408
 409 /* Nonzero if this compiler has GCC bug 68193 or Clang bug 25390.  See:
 410    https://gcc.gnu.org/bugzilla/show_bug.cgi?id=68193
 411    https://llvm.org/bugs/show_bug.cgi?id=25390
 412    For now, assume all versions of GCC-like compilers generate bogus
 413    warnings for _Generic.  This matters only for compilers that
 414    lack relevant builtins.  */
 415 #if __GNUC__ || defined __clang__
 416 # define _GL__GENERIC_BOGUS 1
 417 #else
 418 # define _GL__GENERIC_BOGUS 0
 419 #endif
 420
 421 /* Store the low-order bits of A <op> B into *R, where OP specifies
 422    the operation and OVERFLOW the overflow predicate.  Return 1 if the
 423    result overflows.  See above for restrictions.  */
 424 #if 201112 <= __STDC_VERSION__ && !_GL__GENERIC_BOGUS
 425 # define _GL_INT_OP_WRAPV(a, b, r, op, overflow) \
 426    (_Generic \
 427     (*(r), \
 428      signed char: \
 429        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 430                         signed char, SCHAR_MIN, SCHAR_MAX), \
 431      unsigned char: \
 432        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 433                         unsigned char, 0, UCHAR_MAX), \
 434      short int: \
 435        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 436                         short int, SHRT_MIN, SHRT_MAX), \
 437      unsigned short int: \
 438        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 439                         unsigned short int, 0, USHRT_MAX), \
 440      int: \
 441        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 442                         int, INT_MIN, INT_MAX), \
 443      unsigned int: \
 444        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 445                         unsigned int, 0, UINT_MAX), \
 446      long int: \
 447        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 448                         long int, LONG_MIN, LONG_MAX), \
 449      unsigned long int: \
 450        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 451                         unsigned long int, 0, ULONG_MAX), \
 452      long long int: \
 453        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
 454                         long long int, LLONG_MIN, LLONG_MAX), \
 455      unsigned long long int: \
 456        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
 457                         unsigned long long int, 0, ULLONG_MAX)))
 458 #else
 459 /* Store the low-order bits of A <op> B into *R, where OP specifies
 460    the operation and OVERFLOW the overflow predicate.  If *R is
 461    signed, its type is ST with bounds SMIN..SMAX; otherwise its type
 462    is UT with bounds U..UMAX.  ST and UT are narrower than int.
 463    Return 1 if the result overflows.  See above for restrictions.  */
 464 # if _GL_HAVE___TYPEOF__
 465 #  define _GL_INT_OP_WRAPV_SMALLISH(a,b,r,op,overflow,st,smin,smax,ut,umax) \
 466     (TYPE_SIGNED (__typeof__ (*(r))) \
 467      ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, st, smin, smax) \
 468      : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, ut, 0, umax))
 469 # else
 470 #  define _GL_INT_OP_WRAPV_SMALLISH(a,b,r,op,overflow,st,smin,smax,ut,umax) \
 471     (overflow (a, b, smin, smax) \
 472      ? (overflow (a, b, 0, umax) \
 473         ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st), 1) \
 474         : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st)) < 0) \
 475      : (overflow (a, b, 0, umax) \
 476         ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st)) >= 0 \
 477         : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st), 0)))
 478 # endif
 479
 480 # define _GL_INT_OP_WRAPV(a, b, r, op, overflow) \
 481    (sizeof *(r) == sizeof (signed char) \
 482     ? _GL_INT_OP_WRAPV_SMALLISH (a, b, r, op, overflow, \
 483                                  signed char, SCHAR_MIN, SCHAR_MAX, \
 484                                  unsigned char, UCHAR_MAX) \
 485     : sizeof *(r) == sizeof (short int) \
 486     ? _GL_INT_OP_WRAPV_SMALLISH (a, b, r, op, overflow, \
 487                                  short int, SHRT_MIN, SHRT_MAX, \
 488                                  unsigned short int, USHRT_MAX) \
 489     : sizeof *(r) == sizeof (int) \
 490     ? (EXPR_SIGNED (*(r)) \
 491        ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 492                           int, INT_MIN, INT_MAX) \
 493        : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 494                           unsigned int, 0, UINT_MAX)) \
 495     : _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow))
 496 # ifdef LLONG_MAX
 497 #  define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
 498     (sizeof *(r) == sizeof (long int) \
 499      ? (EXPR_SIGNED (*(r)) \
 500         ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 501                            long int, LONG_MIN, LONG_MAX) \
 502         : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 503                            unsigned long int, 0, ULONG_MAX)) \
 504      : (EXPR_SIGNED (*(r)) \
 505         ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
 506                            long long int, LLONG_MIN, LLONG_MAX) \
 507         : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
 508                            unsigned long long int, 0, ULLONG_MAX)))
 509 # else
 510 #  define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
 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 # endif
 517 #endif
 518
 519 /* Store the low-order bits of A <op> B into *R, where the operation
 520    is given by OP.  Use the unsigned type UT for calculation to avoid
 521    overflow problems.  *R's type is T, with extrema TMIN and TMAX.
 522    T must be a signed integer type.  Return 1 if the result overflows.  */
 523 #define _GL_INT_OP_CALC(a, b, r, op, overflow, ut, t, tmin, tmax) \
 524   (overflow (a, b, tmin, tmax) \
 525    ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 1) \
 526    : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 0))
 527
 528 /* Return the low-order bits of A <op> B, where the operation is given
 529    by OP.  Use the unsigned type UT for calculation to avoid undefined
 530    behavior on signed integer overflow, and convert the result to type T.
 531    UT is at least as wide as T and is no narrower than unsigned int,
 532    T is two's complement, and there is no padding or trap representations.
 533    Assume that converting UT to T yields the low-order bits, as is
 534    done in all known two's-complement C compilers.  E.g., see:
 535    https://gcc.gnu.org/onlinedocs/gcc/Integers-implementation.html
 536
 537    According to the C standard, converting UT to T yields an
 538    implementation-defined result or signal for values outside T's
 539    range.  However, code that works around this theoretical problem
 540    runs afoul of a compiler bug in Oracle Studio 12.3 x86.  See:
 541    https://lists.gnu.org/r/bug-gnulib/2017-04/msg00049.html
 542    As the compiler bug is real, don't try to work around the
 543    theoretical problem.  */
 544
 545 #define _GL_INT_OP_WRAPV_VIA_UNSIGNED(a, b, op, ut, t) \
 546   ((t) ((ut) (a) op (ut) (b)))
 547
 548 /* Return true if the numeric values A + B, A - B, A * B fall outside
 549    the range TMIN..TMAX.  Arguments should be integer expressions
 550    without side effects.  TMIN should be signed and nonpositive.
 551    TMAX should be positive, and should be signed unless TMIN is zero.  */
 552 #define _GL_INT_ADD_RANGE_OVERFLOW(a, b, tmin, tmax) \
 553   ((b) < 0 \
 554    ? (((tmin) \
 555        ? ((EXPR_SIGNED (_GL_INT_CONVERT (a, (tmin) - (b))) || (b) < (tmin)) \
 556           && (a) < (tmin) - (b)) \
 557        : (a) <= -1 - (b)) \
 558       || ((EXPR_SIGNED (a) ? 0 <= (a) : (tmax) < (a)) && (tmax) < (a) + (b))) \
 559    : (a) < 0 \
 560    ? (((tmin) \
 561        ? ((EXPR_SIGNED (_GL_INT_CONVERT (b, (tmin) - (a))) || (a) < (tmin)) \
 562           && (b) < (tmin) - (a)) \
 563        : (b) <= -1 - (a)) \
 564       || ((EXPR_SIGNED (_GL_INT_CONVERT (a, b)) || (tmax) < (b)) \
 565           && (tmax) < (a) + (b))) \
 566    : (tmax) < (b) || (tmax) - (b) < (a))
 567 #define _GL_INT_SUBTRACT_RANGE_OVERFLOW(a, b, tmin, tmax) \
 568   (((a) < 0) == ((b) < 0) \
 569    ? ((a) < (b) \
 570       ? !(tmin) || -1 - (tmin) < (b) - (a) - 1 \
 571       : (tmax) < (a) - (b)) \
 572    : (a) < 0 \
 573    ? ((!EXPR_SIGNED (_GL_INT_CONVERT ((a) - (tmin), b)) && (a) - (tmin) < 0) \
 574       || (a) - (tmin) < (b)) \
 575    : ((! (EXPR_SIGNED (_GL_INT_CONVERT (tmax, b)) \
 576           && EXPR_SIGNED (_GL_INT_CONVERT ((tmax) + (b), a))) \
 577        && (tmax) <= -1 - (b)) \
 578       || (tmax) + (b) < (a)))
 579 #define _GL_INT_MULTIPLY_RANGE_OVERFLOW(a, b, tmin, tmax) \
 580   ((b) < 0 \
 581    ? ((a) < 0 \
 582       ? (EXPR_SIGNED (_GL_INT_CONVERT (tmax, b)) \
 583          ? (a) < (tmax) / (b) \
 584          : ((INT_NEGATE_OVERFLOW (b) \
 585              ? _GL_INT_CONVERT (b, tmax) >> (TYPE_WIDTH (+ (b)) - 1) \
 586              : (tmax) / -(b)) \
 587             <= -1 - (a))) \
 588       : INT_NEGATE_OVERFLOW (_GL_INT_CONVERT (b, tmin)) && (b) == -1 \
 589       ? (EXPR_SIGNED (a) \
 590          ? 0 < (a) + (tmin) \
 591          : 0 < (a) && -1 - (tmin) < (a) - 1) \
 592       : (tmin) / (b) < (a)) \
 593    : (b) == 0 \
 594    ? 0 \
 595    : ((a) < 0 \
 596       ? (INT_NEGATE_OVERFLOW (_GL_INT_CONVERT (a, tmin)) && (a) == -1 \
 597          ? (EXPR_SIGNED (b) ? 0 < (b) + (tmin) : -1 - (tmin) < (b) - 1) \
 598          : (tmin) / (a) < (b)) \
 599       : (tmax) / (b) < (a)))
 600
 601 /* The following macros compute A + B, A - B, and A * B, respectively.
 602    If no overflow occurs, they set *R to the result and return 1;
 603    otherwise, they return 0 and may modify *R.
 604
 605    Example usage:
 606
 607      long int result;
 608      if (INT_ADD_OK (a, b, &result))
 609        printf ("result is %ld\n", result);
 610      else
 611        printf ("overflow\n");
 612
 613    A, B, and *R should be integers; they need not be the same type,
 614    and they need not be all signed or all unsigned.
 615
 616    These macros work correctly on all known practical hosts, and do not rely
 617    on undefined behavior due to signed arithmetic overflow.
 618
 619    These macros are not constant expressions.
 620
 621    These macros may evaluate their arguments zero or multiple times, so the
 622    arguments should not have side effects.
 623
 624    These macros are tuned for B being a constant.  */
 625
 626 #define INT_ADD_OK(a, b, r) ! INT_ADD_WRAPV (a, b, r)
 627 #define INT_SUBTRACT_OK(a, b, r) ! INT_SUBTRACT_WRAPV (a, b, r)
 628 #define INT_MULTIPLY_OK(a, b, r) ! INT_MULTIPLY_WRAPV (a, b, r)
 629
 630 #endif /* _GL_INTPROPS_H */