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