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