include/intprops.h

   1 /* intprops.h -- properties of integer types
   2
   3    Copyright (C) 2001-2020 Free Software Foundation, Inc.
   4
   5    This program is free software: you can redistribute it and/or modify it
   6    under the terms of the GNU Lesser General Public License as published
   7    by the Free Software Foundation; either version 2.1 of the License, or
   8    (at your option) any later version.
   9
  10    This program is distributed in the hope that it will be useful,
  11    but WITHOUT ANY WARRANTY; without even the implied warranty of
  12    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  13    GNU Lesser General Public License for more details.
  14
  15    You should have received a copy of the GNU Lesser General Public License
  16    along with this program.  If not, see <https://www.gnu.org/licenses/>.  */
  17
  18 /* Written by Paul Eggert.  */
  19
  20 #ifndef _GL_INTPROPS_H
  21 #define _GL_INTPROPS_H
  22
  23 #include <limits.h>
  24
  25 /* Return a value with the common real type of E and V and the value of V.
  26    Do not evaluate E.  */
  27 #define _GL_INT_CONVERT(e, v) ((1 ? 0 : (e)) + (v))
  28
  29 /* Act like _GL_INT_CONVERT (E, -V) but work around a bug in IRIX 6.5 cc; see
  30    <https://lists.gnu.org/r/bug-gnulib/2011-05/msg00406.html>.  */
  31 #define _GL_INT_NEGATE_CONVERT(e, v) ((1 ? 0 : (e)) - (v))
  32
  33 /* The extra casts in the following macros work around compiler bugs,
  34    e.g., in Cray C 5.0.3.0.  */
  35
  36 /* True if the arithmetic type T is an integer type.  bool counts as
  37    an integer.  */
  38 #define TYPE_IS_INTEGER(t) ((t) 1.5 == 1)
  39
  40 /* True if the real type T is signed.  */
  41 #define TYPE_SIGNED(t) (! ((t) 0 < (t) -1))
  42
  43 /* Return 1 if the real expression E, after promotion, has a
  44    signed or floating type.  Do not evaluate E.  */
  45 #define EXPR_SIGNED(e) (_GL_INT_NEGATE_CONVERT (e, 1) < 0)
  46
  47
  48 /* Minimum and maximum values for integer types and expressions.  */
  49
  50 /* The width in bits of the integer type or expression T.
  51    Do not evaluate T.
  52    Padding bits are not supported; this is checked at compile-time below.  */
  53 #define TYPE_WIDTH(t) (sizeof (t) * CHAR_BIT)
  54
  55 /* The maximum and minimum values for the integer type T.  */
  56 #define TYPE_MINIMUM(t) ((t) ~ TYPE_MAXIMUM (t))
  57 #define TYPE_MAXIMUM(t)                                                 \
  58   ((t) (! TYPE_SIGNED (t)                                               \
  59         ? (t) -1                                                        \
  60         : ((((t) 1 << (TYPE_WIDTH (t) - 2)) - 1) * 2 + 1)))
  61
  62 /* The maximum and minimum values for the type of the expression E,
  63    after integer promotion.  E is not evaluated.  */
  64 #define _GL_INT_MINIMUM(e)                                              \
  65   (EXPR_SIGNED (e)                                                      \
  66    ? ~ _GL_SIGNED_INT_MAXIMUM (e)                                       \
  67    : _GL_INT_CONVERT (e, 0))
  68 #define _GL_INT_MAXIMUM(e)                                              \
  69   (EXPR_SIGNED (e)                                                      \
  70    ? _GL_SIGNED_INT_MAXIMUM (e)                                         \
  71    : _GL_INT_NEGATE_CONVERT (e, 1))
  72 #define _GL_SIGNED_INT_MAXIMUM(e)                                       \
  73   (((_GL_INT_CONVERT (e, 1) << (TYPE_WIDTH ((e) + 0) - 2)) - 1) * 2 + 1)
  74
  75 /* Work around OpenVMS incompatibility with C99.  */
  76 #if !defined LLONG_MAX && defined __INT64_MAX
  77 # define LLONG_MAX __INT64_MAX
  78 # define LLONG_MIN __INT64_MIN
  79 #endif
  80
  81 /* This include file assumes that signed types are two's complement without
  82    padding bits; the above macros have undefined behavior otherwise.
  83    If this is a problem for you, please let us know how to fix it for your host.
  84    This assumption is tested by the intprops-tests module.  */
  85
  86 /* Does the __typeof__ keyword work?  This could be done by
  87    'configure', but for now it's easier to do it by hand.  */
  88 #if (2 <= __GNUC__ \
  89      || (1210 <= __IBMC__ && defined __IBM__TYPEOF__) \
  90      || (0x5110 <= __SUNPRO_C && !__STDC__))
  91 # define _GL_HAVE___TYPEOF__ 1
  92 #else
  93 # define _GL_HAVE___TYPEOF__ 0
  94 #endif
  95
  96 /* Return 1 if the integer type or expression T might be signed.  Return 0
  97    if it is definitely unsigned.  This macro does not evaluate its argument,
  98    and expands to an integer constant expression.  */
  99 #if _GL_HAVE___TYPEOF__
 100 # define _GL_SIGNED_TYPE_OR_EXPR(t) TYPE_SIGNED (__typeof__ (t))
 101 #else
 102 # define _GL_SIGNED_TYPE_OR_EXPR(t) 1
 103 #endif
 104
 105 /* Bound on length of the string representing an unsigned integer
 106    value representable in B bits.  log10 (2.0) < 146/485.  The
 107    smallest value of B where this bound is not tight is 2621.  */
 108 #define INT_BITS_STRLEN_BOUND(b) (((b) * 146 + 484) / 485)
 109
 110 /* Bound on length of the string representing an integer type or expression T.
 111    Subtract 1 for the sign bit if T is signed, and then add 1 more for
 112    a minus sign if needed.
 113
 114    Because _GL_SIGNED_TYPE_OR_EXPR sometimes returns 1 when its argument is
 115    unsigned, this macro may overestimate the true bound by one byte when
 116    applied to unsigned types of size 2, 4, 16, ... bytes.  */
 117 #define INT_STRLEN_BOUND(t)                                     \
 118   (INT_BITS_STRLEN_BOUND (TYPE_WIDTH (t) - _GL_SIGNED_TYPE_OR_EXPR (t)) \
 119    + _GL_SIGNED_TYPE_OR_EXPR (t))
 120
 121 /* Bound on buffer size needed to represent an integer type or expression T,
 122    including the terminating null.  */
 123 #define INT_BUFSIZE_BOUND(t) (INT_STRLEN_BOUND (t) + 1)
 124
 125
 126 /* Range overflow checks.
 127
 128    The INT_<op>_RANGE_OVERFLOW macros return 1 if the corresponding C
 129    operators might not yield numerically correct answers due to
 130    arithmetic overflow.  They do not rely on undefined or
 131    implementation-defined behavior.  Their implementations are simple
 132    and straightforward, but they are a bit harder to use than the
 133    INT_<op>_OVERFLOW macros described below.
 134
 135    Example usage:
 136
 137      long int i = ...;
 138      long int j = ...;
 139      if (INT_MULTIPLY_RANGE_OVERFLOW (i, j, LONG_MIN, LONG_MAX))
 140        printf ("multiply would overflow");
 141      else
 142        printf ("product is %ld", i * j);
 143
 144    Restrictions on *_RANGE_OVERFLOW macros:
 145
 146    These macros do not check for all possible numerical problems or
 147    undefined or unspecified behavior: they do not check for division
 148    by zero, for bad shift counts, or for shifting negative numbers.
 149
 150    These macros may evaluate their arguments zero or multiple times,
 151    so the arguments should not have side effects.  The arithmetic
 152    arguments (including the MIN and MAX arguments) must be of the same
 153    integer type after the usual arithmetic conversions, and the type
 154    must have minimum value MIN and maximum MAX.  Unsigned types should
 155    use a zero MIN of the proper type.
 156
 157    These macros are tuned for constant MIN and MAX.  For commutative
 158    operations such as A + B, they are also tuned for constant B.  */
 159
 160 /* Return 1 if A + B would overflow in [MIN,MAX] arithmetic.
 161    See above for restrictions.  */
 162 #define INT_ADD_RANGE_OVERFLOW(a, b, min, max)          \
 163   ((b) < 0                                              \
 164    ? (a) < (min) - (b)                                  \
 165    : (max) - (b) < (a))
 166
 167 /* Return 1 if A - B would overflow in [MIN,MAX] arithmetic.
 168    See above for restrictions.  */
 169 #define INT_SUBTRACT_RANGE_OVERFLOW(a, b, min, max)     \
 170   ((b) < 0                                              \
 171    ? (max) + (b) < (a)                                  \
 172    : (a) < (min) + (b))
 173
 174 /* Return 1 if - A would overflow in [MIN,MAX] arithmetic.
 175    See above for restrictions.  */
 176 #define INT_NEGATE_RANGE_OVERFLOW(a, min, max)          \
 177   ((min) < 0                                            \
 178    ? (a) < - (max)                                      \
 179    : 0 < (a))
 180
 181 /* Return 1 if A * B would overflow in [MIN,MAX] arithmetic.
 182    See above for restrictions.  Avoid && and || as they tickle
 183    bugs in Sun C 5.11 2010/08/13 and other compilers; see
 184    <https://lists.gnu.org/r/bug-gnulib/2011-05/msg00401.html>.  */
 185 #define INT_MULTIPLY_RANGE_OVERFLOW(a, b, min, max)     \
 186   ((b) < 0                                              \
 187    ? ((a) < 0                                           \
 188       ? (a) < (max) / (b)                               \
 189       : (b) == -1                                       \
 190       ? 0                                               \
 191       : (min) / (b) < (a))                              \
 192    : (b) == 0                                           \
 193    ? 0                                                  \
 194    : ((a) < 0                                           \
 195       ? (a) < (min) / (b)                               \
 196       : (max) / (b) < (a)))
 197
 198 /* Return 1 if A / B would overflow in [MIN,MAX] arithmetic.
 199    See above for restrictions.  Do not check for division by zero.  */
 200 #define INT_DIVIDE_RANGE_OVERFLOW(a, b, min, max)       \
 201   ((min) < 0 && (b) == -1 && (a) < - (max))
 202
 203 /* Return 1 if A % B would overflow in [MIN,MAX] arithmetic.
 204    See above for restrictions.  Do not check for division by zero.
 205    Mathematically, % should never overflow, but on x86-like hosts
 206    INT_MIN % -1 traps, and the C standard permits this, so treat this
 207    as an overflow too.  */
 208 #define INT_REMAINDER_RANGE_OVERFLOW(a, b, min, max)    \
 209   INT_DIVIDE_RANGE_OVERFLOW (a, b, min, max)
 210
 211 /* Return 1 if A << B would overflow in [MIN,MAX] arithmetic.
 212    See above for restrictions.  Here, MIN and MAX are for A only, and B need
 213    not be of the same type as the other arguments.  The C standard says that
 214    behavior is undefined for shifts unless 0 <= B < wordwidth, and that when
 215    A is negative then A << B has undefined behavior and A >> B has
 216    implementation-defined behavior, but do not check these other
 217    restrictions.  */
 218 #define INT_LEFT_SHIFT_RANGE_OVERFLOW(a, b, min, max)   \
 219   ((a) < 0                                              \
 220    ? (a) < (min) >> (b)                                 \
 221    : (max) >> (b) < (a))
 222
 223 /* True if __builtin_add_overflow (A, B, P) and __builtin_sub_overflow
 224    (A, B, P) work when P is non-null.  */
 225 #if 5 <= __GNUC__ && !defined __ICC
 226 # define _GL_HAS_BUILTIN_ADD_OVERFLOW 1
 227 #elif defined __has_builtin
 228 # define _GL_HAS_BUILTIN_ADD_OVERFLOW __has_builtin (__builtin_add_overflow)
 229 #else
 230 # define _GL_HAS_BUILTIN_ADD_OVERFLOW 0
 231 #endif
 232
 233 /* True if __builtin_mul_overflow (A, B, P) works when P is non-null.  */
 234 #ifdef __clang__
 235 /* Work around Clang bug <https://bugs.llvm.org/show_bug.cgi?id=16404>.  */
 236 # define _GL_HAS_BUILTIN_MUL_OVERFLOW 0
 237 #else
 238 # define _GL_HAS_BUILTIN_MUL_OVERFLOW _GL_HAS_BUILTIN_ADD_OVERFLOW
 239 #endif
 240
 241 /* True if __builtin_add_overflow_p (A, B, C) works, and similarly for
 242    __builtin_mul_overflow_p and __builtin_mul_overflow_p.  */
 243 #define _GL_HAS_BUILTIN_OVERFLOW_P (7 <= __GNUC__)
 244
 245 /* The _GL*_OVERFLOW macros have the same restrictions as the
 246    *_RANGE_OVERFLOW macros, except that they do not assume that operands
 247    (e.g., A and B) have the same type as MIN and MAX.  Instead, they assume
 248    that the result (e.g., A + B) has that type.  */
 249 #if _GL_HAS_BUILTIN_OVERFLOW_P
 250 # define _GL_ADD_OVERFLOW(a, b, min, max)                               \
 251    __builtin_add_overflow_p (a, b, (__typeof__ ((a) + (b))) 0)
 252 # define _GL_SUBTRACT_OVERFLOW(a, b, min, max)                          \
 253    __builtin_sub_overflow_p (a, b, (__typeof__ ((a) - (b))) 0)
 254 # define _GL_MULTIPLY_OVERFLOW(a, b, min, max)                          \
 255    __builtin_mul_overflow_p (a, b, (__typeof__ ((a) * (b))) 0)
 256 #else
 257 # define _GL_ADD_OVERFLOW(a, b, min, max)                                \
 258    ((min) < 0 ? INT_ADD_RANGE_OVERFLOW (a, b, min, max)                  \
 259     : (a) < 0 ? (b) <= (a) + (b)                                         \
 260     : (b) < 0 ? (a) <= (a) + (b)                                         \
 261     : (a) + (b) < (b))
 262 # define _GL_SUBTRACT_OVERFLOW(a, b, min, max)                           \
 263    ((min) < 0 ? INT_SUBTRACT_RANGE_OVERFLOW (a, b, min, max)             \
 264     : (a) < 0 ? 1                                                        \
 265     : (b) < 0 ? (a) - (b) <= (a)                                         \
 266     : (a) < (b))
 267 # define _GL_MULTIPLY_OVERFLOW(a, b, min, max)                           \
 268    (((min) == 0 && (((a) < 0 && 0 < (b)) || ((b) < 0 && 0 < (a))))       \
 269     || INT_MULTIPLY_RANGE_OVERFLOW (a, b, min, max))
 270 #endif
 271 #define _GL_DIVIDE_OVERFLOW(a, b, min, max)                             \
 272   ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max)  \
 273    : (a) < 0 ? (b) <= (a) + (b) - 1                                     \
 274    : (b) < 0 && (a) + (b) <= (a))
 275 #define _GL_REMAINDER_OVERFLOW(a, b, min, max)                          \
 276   ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max)  \
 277    : (a) < 0 ? (a) % (b) != ((max) - (b) + 1) % (b)                     \
 278    : (b) < 0 && ! _GL_UNSIGNED_NEG_MULTIPLE (a, b, max))
 279
 280 /* Return a nonzero value if A is a mathematical multiple of B, where
 281    A is unsigned, B is negative, and MAX is the maximum value of A's
 282    type.  A's type must be the same as (A % B)'s type.  Normally (A %
 283    -B == 0) suffices, but things get tricky if -B would overflow.  */
 284 #define _GL_UNSIGNED_NEG_MULTIPLE(a, b, max)                            \
 285   (((b) < -_GL_SIGNED_INT_MAXIMUM (b)                                   \
 286     ? (_GL_SIGNED_INT_MAXIMUM (b) == (max)                              \
 287        ? (a)                                                            \
 288        : (a) % (_GL_INT_CONVERT (a, _GL_SIGNED_INT_MAXIMUM (b)) + 1))   \
 289     : (a) % - (b))                                                      \
 290    == 0)
 291
 292 /* Check for integer overflow, and report low order bits of answer.
 293
 294    The INT_<op>_OVERFLOW macros return 1 if the corresponding C operators
 295    might not yield numerically correct answers due to arithmetic overflow.
 296    The INT_<op>_WRAPV macros compute the low-order bits of the sum,
 297    difference, and product of two C integers, and return 1 if these
 298    low-order bits are not numerically correct.
 299    These macros work correctly on all known practical hosts, and do not rely
 300    on undefined behavior due to signed arithmetic overflow.
 301
 302    Example usage, assuming A and B are long int:
 303
 304      if (INT_MULTIPLY_OVERFLOW (a, b))
 305        printf ("result would overflow\n");
 306      else
 307        printf ("result is %ld (no overflow)\n", a * b);
 308
 309    Example usage with WRAPV flavor:
 310
 311      long int result;
 312      bool overflow = INT_MULTIPLY_WRAPV (a, b, &result);
 313      printf ("result is %ld (%s)\n", result,
 314              overflow ? "after overflow" : "no overflow");
 315
 316    Restrictions on these macros:
 317
 318    These macros do not check for all possible numerical problems or
 319    undefined or unspecified behavior: they do not check for division
 320    by zero, for bad shift counts, or for shifting negative numbers.
 321
 322    These macros may evaluate their arguments zero or multiple times, so the
 323    arguments should not have side effects.
 324
 325    The WRAPV macros are not constant expressions.  They support only
 326    +, binary -, and *.  Because the WRAPV macros convert the result,
 327    they report overflow in different circumstances than the OVERFLOW
 328    macros do.
 329
 330    These macros are tuned for their last input argument being a constant.
 331
 332    Return 1 if the integer expressions A * B, A - B, -A, A * B, A / B,
 333    A % B, and A << B would overflow, respectively.  */
 334
 335 #define INT_ADD_OVERFLOW(a, b) \
 336   _GL_BINARY_OP_OVERFLOW (a, b, _GL_ADD_OVERFLOW)
 337 #define INT_SUBTRACT_OVERFLOW(a, b) \
 338   _GL_BINARY_OP_OVERFLOW (a, b, _GL_SUBTRACT_OVERFLOW)
 339 #if _GL_HAS_BUILTIN_OVERFLOW_P
 340 # define INT_NEGATE_OVERFLOW(a) INT_SUBTRACT_OVERFLOW (0, a)
 341 #else
 342 # define INT_NEGATE_OVERFLOW(a) \
 343    INT_NEGATE_RANGE_OVERFLOW (a, _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
 344 #endif
 345 #define INT_MULTIPLY_OVERFLOW(a, b) \
 346   _GL_BINARY_OP_OVERFLOW (a, b, _GL_MULTIPLY_OVERFLOW)
 347 #define INT_DIVIDE_OVERFLOW(a, b) \
 348   _GL_BINARY_OP_OVERFLOW (a, b, _GL_DIVIDE_OVERFLOW)
 349 #define INT_REMAINDER_OVERFLOW(a, b) \
 350   _GL_BINARY_OP_OVERFLOW (a, b, _GL_REMAINDER_OVERFLOW)
 351 #define INT_LEFT_SHIFT_OVERFLOW(a, b) \
 352   INT_LEFT_SHIFT_RANGE_OVERFLOW (a, b, \
 353                                  _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
 354
 355 /* Return 1 if the expression A <op> B would overflow,
 356    where OP_RESULT_OVERFLOW (A, B, MIN, MAX) does the actual test,
 357    assuming MIN and MAX are the minimum and maximum for the result type.
 358    Arguments should be free of side effects.  */
 359 #define _GL_BINARY_OP_OVERFLOW(a, b, op_result_overflow)        \
 360   op_result_overflow (a, b,                                     \
 361                       _GL_INT_MINIMUM (_GL_INT_CONVERT (a, b)), \
 362                       _GL_INT_MAXIMUM (_GL_INT_CONVERT (a, b)))
 363
 364 /* Store the low-order bits of A + B, A - B, A * B, respectively, into *R.
 365    Return 1 if the result overflows.  See above for restrictions.  */
 366 #if _GL_HAS_BUILTIN_ADD_OVERFLOW
 367 # define INT_ADD_WRAPV(a, b, r) __builtin_add_overflow (a, b, r)
 368 # define INT_SUBTRACT_WRAPV(a, b, r) __builtin_sub_overflow (a, b, r)
 369 #else
 370 # define INT_ADD_WRAPV(a, b, r) \
 371    _GL_INT_OP_WRAPV (a, b, r, +, _GL_INT_ADD_RANGE_OVERFLOW)
 372 # define INT_SUBTRACT_WRAPV(a, b, r) \
 373    _GL_INT_OP_WRAPV (a, b, r, -, _GL_INT_SUBTRACT_RANGE_OVERFLOW)
 374 #endif
 375 #if _GL_HAS_BUILTIN_MUL_OVERFLOW
 376 # if (9 < __GNUC__ + (3 <= __GNUC_MINOR__) \
 377       || (__GNUC__ == 8 && 4 <= __GNUC_MINOR__))
 378 #  define INT_MULTIPLY_WRAPV(a, b, r) __builtin_mul_overflow (a, b, r)
 379 # else
 380    /* Work around GCC bug 91450.  */
 381 #  define INT_MULTIPLY_WRAPV(a, b, r) \
 382     ((!_GL_SIGNED_TYPE_OR_EXPR (*(r)) && EXPR_SIGNED (a) && EXPR_SIGNED (b) \
 383       && _GL_INT_MULTIPLY_RANGE_OVERFLOW (a, b, 0, (__typeof__ (*(r))) -1)) \
 384      ? ((void) __builtin_mul_overflow (a, b, r), 1) \
 385      : __builtin_mul_overflow (a, b, r))
 386 # endif
 387 #else
 388 # define INT_MULTIPLY_WRAPV(a, b, r) \
 389    _GL_INT_OP_WRAPV (a, b, r, *, _GL_INT_MULTIPLY_RANGE_OVERFLOW)
 390 #endif
 391
 392 /* Nonzero if this compiler has GCC bug 68193 or Clang bug 25390.  See:
 393    https://gcc.gnu.org/bugzilla/show_bug.cgi?id=68193
 394    https://llvm.org/bugs/show_bug.cgi?id=25390
 395    For now, assume all versions of GCC-like compilers generate bogus
 396    warnings for _Generic.  This matters only for compilers that
 397    lack relevant builtins.  */
 398 #if __GNUC__
 399 # define _GL__GENERIC_BOGUS 1
 400 #else
 401 # define _GL__GENERIC_BOGUS 0
 402 #endif
 403
 404 /* Store the low-order bits of A <op> B into *R, where OP specifies
 405    the operation and OVERFLOW the overflow predicate.  Return 1 if the
 406    result overflows.  See above for restrictions.  */
 407 #if 201112 <= __STDC_VERSION__ && !_GL__GENERIC_BOGUS
 408 # define _GL_INT_OP_WRAPV(a, b, r, op, overflow) \
 409    (_Generic \
 410     (*(r), \
 411      signed char: \
 412        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 413                         signed char, SCHAR_MIN, SCHAR_MAX), \
 414      unsigned char: \
 415        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 416                         unsigned char, 0, UCHAR_MAX), \
 417      short int: \
 418        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 419                         short int, SHRT_MIN, SHRT_MAX), \
 420      unsigned short int: \
 421        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 422                         unsigned short int, 0, USHRT_MAX), \
 423      int: \
 424        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 425                         int, INT_MIN, INT_MAX), \
 426      unsigned int: \
 427        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 428                         unsigned int, 0, UINT_MAX), \
 429      long int: \
 430        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 431                         long int, LONG_MIN, LONG_MAX), \
 432      unsigned long int: \
 433        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 434                         unsigned long int, 0, ULONG_MAX), \
 435      long long int: \
 436        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
 437                         long long int, LLONG_MIN, LLONG_MAX), \
 438      unsigned long long int: \
 439        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
 440                         unsigned long long int, 0, ULLONG_MAX)))
 441 #else
 442 /* Store the low-order bits of A <op> B into *R, where OP specifies
 443    the operation and OVERFLOW the overflow predicate.  If *R is
 444    signed, its type is ST with bounds SMIN..SMAX; otherwise its type
 445    is UT with bounds U..UMAX.  ST and UT are narrower than int.
 446    Return 1 if the result overflows.  See above for restrictions.  */
 447 # if _GL_HAVE___TYPEOF__
 448 #  define _GL_INT_OP_WRAPV_SMALLISH(a,b,r,op,overflow,st,smin,smax,ut,umax) \
 449     (TYPE_SIGNED (__typeof__ (*(r))) \
 450      ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, st, smin, smax) \
 451      : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, ut, 0, umax))
 452 # else
 453 #  define _GL_INT_OP_WRAPV_SMALLISH(a,b,r,op,overflow,st,smin,smax,ut,umax) \
 454     (overflow (a, b, smin, smax) \
 455      ? (overflow (a, b, 0, umax) \
 456         ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st), 1) \
 457         : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st)) < 0) \
 458      : (overflow (a, b, 0, umax) \
 459         ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st)) >= 0 \
 460         : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st), 0)))
 461 # endif
 462
 463 # define _GL_INT_OP_WRAPV(a, b, r, op, overflow) \
 464    (sizeof *(r) == sizeof (signed char) \
 465     ? _GL_INT_OP_WRAPV_SMALLISH (a, b, r, op, overflow, \
 466                                  signed char, SCHAR_MIN, SCHAR_MAX, \
 467                                  unsigned char, UCHAR_MAX) \
 468     : sizeof *(r) == sizeof (short int) \
 469     ? _GL_INT_OP_WRAPV_SMALLISH (a, b, r, op, overflow, \
 470                                  short int, SHRT_MIN, SHRT_MAX, \
 471                                  unsigned short int, USHRT_MAX) \
 472     : sizeof *(r) == sizeof (int) \
 473     ? (EXPR_SIGNED (*(r)) \
 474        ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 475                           int, INT_MIN, INT_MAX) \
 476        : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 477                           unsigned int, 0, UINT_MAX)) \
 478     : _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow))
 479 # ifdef LLONG_MAX
 480 #  define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
 481     (sizeof *(r) == sizeof (long int) \
 482      ? (EXPR_SIGNED (*(r)) \
 483         ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 484                            long int, LONG_MIN, LONG_MAX) \
 485         : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 486                            unsigned long int, 0, ULONG_MAX)) \
 487      : (EXPR_SIGNED (*(r)) \
 488         ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
 489                            long long int, LLONG_MIN, LLONG_MAX) \
 490         : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
 491                            unsigned long long int, 0, ULLONG_MAX)))
 492 # else
 493 #  define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
 494     (EXPR_SIGNED (*(r)) \
 495      ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 496                         long int, LONG_MIN, LONG_MAX) \
 497      : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 498                         unsigned long int, 0, ULONG_MAX))
 499 # endif
 500 #endif
 501
 502 /* Store the low-order bits of A <op> B into *R, where the operation
 503    is given by OP.  Use the unsigned type UT for calculation to avoid
 504    overflow problems.  *R's type is T, with extrema TMIN and TMAX.
 505    T must be a signed integer type.  Return 1 if the result overflows.  */
 506 #define _GL_INT_OP_CALC(a, b, r, op, overflow, ut, t, tmin, tmax) \
 507   (overflow (a, b, tmin, tmax) \
 508    ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 1) \
 509    : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 0))
 510
 511 /* Return the low-order bits of A <op> B, where the operation is given
 512    by OP.  Use the unsigned type UT for calculation to avoid undefined
 513    behavior on signed integer overflow, and convert the result to type T.
 514    UT is at least as wide as T and is no narrower than unsigned int,
 515    T is two's complement, and there is no padding or trap representations.
 516    Assume that converting UT to T yields the low-order bits, as is
 517    done in all known two's-complement C compilers.  E.g., see:
 518    https://gcc.gnu.org/onlinedocs/gcc/Integers-implementation.html
 519
 520    According to the C standard, converting UT to T yields an
 521    implementation-defined result or signal for values outside T's
 522    range.  However, code that works around this theoretical problem
 523    runs afoul of a compiler bug in Oracle Studio 12.3 x86.  See:
 524    https://lists.gnu.org/r/bug-gnulib/2017-04/msg00049.html
 525    As the compiler bug is real, don't try to work around the
 526    theoretical problem.  */
 527
 528 #define _GL_INT_OP_WRAPV_VIA_UNSIGNED(a, b, op, ut, t) \
 529   ((t) ((ut) (a) op (ut) (b)))
 530
 531 /* Return true if the numeric values A + B, A - B, A * B fall outside
 532    the range TMIN..TMAX.  Arguments should be integer expressions
 533    without side effects.  TMIN should be signed and nonpositive.
 534    TMAX should be positive, and should be signed unless TMIN is zero.  */
 535 #define _GL_INT_ADD_RANGE_OVERFLOW(a, b, tmin, tmax) \
 536   ((b) < 0 \
 537    ? (((tmin) \
 538        ? ((EXPR_SIGNED (_GL_INT_CONVERT (a, (tmin) - (b))) || (b) < (tmin)) \
 539           && (a) < (tmin) - (b)) \
 540        : (a) <= -1 - (b)) \
 541       || ((EXPR_SIGNED (a) ? 0 <= (a) : (tmax) < (a)) && (tmax) < (a) + (b))) \
 542    : (a) < 0 \
 543    ? (((tmin) \
 544        ? ((EXPR_SIGNED (_GL_INT_CONVERT (b, (tmin) - (a))) || (a) < (tmin)) \
 545           && (b) < (tmin) - (a)) \
 546        : (b) <= -1 - (a)) \
 547       || ((EXPR_SIGNED (_GL_INT_CONVERT (a, b)) || (tmax) < (b)) \
 548           && (tmax) < (a) + (b))) \
 549    : (tmax) < (b) || (tmax) - (b) < (a))
 550 #define _GL_INT_SUBTRACT_RANGE_OVERFLOW(a, b, tmin, tmax) \
 551   (((a) < 0) == ((b) < 0) \
 552    ? ((a) < (b) \
 553       ? !(tmin) || -1 - (tmin) < (b) - (a) - 1 \
 554       : (tmax) < (a) - (b)) \
 555    : (a) < 0 \
 556    ? ((!EXPR_SIGNED (_GL_INT_CONVERT ((a) - (tmin), b)) && (a) - (tmin) < 0) \
 557       || (a) - (tmin) < (b)) \
 558    : ((! (EXPR_SIGNED (_GL_INT_CONVERT (tmax, b)) \
 559           && EXPR_SIGNED (_GL_INT_CONVERT ((tmax) + (b), a))) \
 560        && (tmax) <= -1 - (b)) \
 561       || (tmax) + (b) < (a)))
 562 #define _GL_INT_MULTIPLY_RANGE_OVERFLOW(a, b, tmin, tmax) \
 563   ((b) < 0 \
 564    ? ((a) < 0 \
 565       ? (EXPR_SIGNED (_GL_INT_CONVERT (tmax, b)) \
 566          ? (a) < (tmax) / (b) \
 567          : ((INT_NEGATE_OVERFLOW (b) \
 568              ? _GL_INT_CONVERT (b, tmax) >> (TYPE_WIDTH (b) - 1) \
 569              : (tmax) / -(b)) \
 570             <= -1 - (a))) \
 571       : INT_NEGATE_OVERFLOW (_GL_INT_CONVERT (b, tmin)) && (b) == -1 \
 572       ? (EXPR_SIGNED (a) \
 573          ? 0 < (a) + (tmin) \
 574          : 0 < (a) && -1 - (tmin) < (a) - 1) \
 575       : (tmin) / (b) < (a)) \
 576    : (b) == 0 \
 577    ? 0 \
 578    : ((a) < 0 \
 579       ? (INT_NEGATE_OVERFLOW (_GL_INT_CONVERT (a, tmin)) && (a) == -1 \
 580          ? (EXPR_SIGNED (b) ? 0 < (b) + (tmin) : -1 - (tmin) < (b) - 1) \
 581          : (tmin) / (a) < (b)) \
 582       : (tmax) / (b) < (a)))
 583
 584 #endif /* _GL_INTPROPS_H */