lib/intprops.h

   1 /* intprops.h -- properties of integer types
   2
   3    Copyright (C) 2001-2016 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 General Public License as published
   7    by the Free Software Foundation; either version 3 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 General Public License for more details.
  14
  15    You should have received a copy of the GNU General Public License
  16    along with this program.  If not, see <http://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 #include <verify.h>
  25
  26 /* Return a value with the common real type of E and V and the value of V.  */
  27 #define _GL_INT_CONVERT(e, v) (0 * (e) + (v))
  28
  29 /* Act like _GL_INT_CONVERT (E, -V) but work around a bug in IRIX 6.5 cc; see
  30    <http://lists.gnu.org/archive/html/bug-gnulib/2011-05/msg00406.html>.  */
  31 #define _GL_INT_NEGATE_CONVERT(e, v) (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.  */
  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 maximum and minimum values for the integer type T.  */
  51 #define TYPE_MINIMUM(t) ((t) ~ TYPE_MAXIMUM (t))
  52 #define TYPE_MAXIMUM(t)                                                 \
  53   ((t) (! TYPE_SIGNED (t)                                               \
  54         ? (t) -1                                                        \
  55         : ((((t) 1 << (sizeof (t) * CHAR_BIT - 2)) - 1) * 2 + 1)))
  56
  57 /* The maximum and minimum values for the type of the expression E,
  58    after integer promotion.  E should not have side effects.  */
  59 #define _GL_INT_MINIMUM(e)                                              \
  60   (EXPR_SIGNED (e)                                                      \
  61    ? ~ _GL_SIGNED_INT_MAXIMUM (e)                                       \
  62    : _GL_INT_CONVERT (e, 0))
  63 #define _GL_INT_MAXIMUM(e)                                              \
  64   (EXPR_SIGNED (e)                                                      \
  65    ? _GL_SIGNED_INT_MAXIMUM (e)                                         \
  66    : _GL_INT_NEGATE_CONVERT (e, 1))
  67 #define _GL_SIGNED_INT_MAXIMUM(e)                                       \
  68   (((_GL_INT_CONVERT (e, 1) << (sizeof ((e) + 0) * CHAR_BIT - 2)) - 1) * 2 + 1)
  69
  70 /* This include file assumes that signed types are two's complement without
  71    padding bits; the above macros have undefined behavior otherwise.
  72    If this is a problem for you, please let us know how to fix it for your host.
  73    As a sanity check, test the assumption for some signed types that
  74    <limits.h> bounds.  */
  75 verify (TYPE_MINIMUM (signed char) == SCHAR_MIN);
  76 verify (TYPE_MAXIMUM (signed char) == SCHAR_MAX);
  77 verify (TYPE_MINIMUM (short int) == SHRT_MIN);
  78 verify (TYPE_MAXIMUM (short int) == SHRT_MAX);
  79 verify (TYPE_MINIMUM (int) == INT_MIN);
  80 verify (TYPE_MAXIMUM (int) == INT_MAX);
  81 verify (TYPE_MINIMUM (long int) == LONG_MIN);
  82 verify (TYPE_MAXIMUM (long int) == LONG_MAX);
  83 #ifdef LLONG_MAX
  84 verify (TYPE_MINIMUM (long long int) == LLONG_MIN);
  85 verify (TYPE_MAXIMUM (long long int) == LLONG_MAX);
  86 #endif
  87
  88 /* Does the __typeof__ keyword work?  This could be done by
  89    'configure', but for now it's easier to do it by hand.  */
  90 #if (2 <= __GNUC__ || 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.  This macro does not evaluate its argument,
  99    and expands to an integer constant expression.  */
 100 #if _GL_HAVE___TYPEOF__
 101 # define _GL_SIGNED_TYPE_OR_EXPR(t) TYPE_SIGNED (__typeof__ (t))
 102 #else
 103 # define _GL_SIGNED_TYPE_OR_EXPR(t) 1
 104 #endif
 105
 106 /* Bound on length of the string representing an unsigned integer
 107    value representable in B bits.  log10 (2.0) < 146/485.  The
 108    smallest value of B where this bound is not tight is 2621.  */
 109 #define INT_BITS_STRLEN_BOUND(b) (((b) * 146 + 484) / 485)
 110
 111 /* Bound on length of the string representing an integer type or expression T.
 112    Subtract 1 for the sign bit if T is signed, and then add 1 more for
 113    a minus sign if needed.
 114
 115    Because _GL_SIGNED_TYPE_OR_EXPR sometimes returns 0 when its argument is
 116    signed, this macro may overestimate the true bound by one byte when
 117    applied to unsigned types of size 2, 4, 16, ... bytes.  */
 118 #define INT_STRLEN_BOUND(t)                                     \
 119   (INT_BITS_STRLEN_BOUND (sizeof (t) * CHAR_BIT                 \
 120                           - _GL_SIGNED_TYPE_OR_EXPR (t))        \
 121    + _GL_SIGNED_TYPE_OR_EXPR (t))
 122
 123 /* Bound on buffer size needed to represent an integer type or expression T,
 124    including the terminating null.  */
 125 #define INT_BUFSIZE_BOUND(t) (INT_STRLEN_BOUND (t) + 1)
 126
 127
 128 /* Range overflow checks.
 129
 130    The INT_<op>_RANGE_OVERFLOW macros return 1 if the corresponding C
 131    operators might not yield numerically correct answers due to
 132    arithmetic overflow.  They do not rely on undefined or
 133    implementation-defined behavior.  Their implementations are simple
 134    and straightforward, but they are a bit harder to use than the
 135    INT_<op>_OVERFLOW macros described below.
 136
 137    Example usage:
 138
 139      long int i = ...;
 140      long int j = ...;
 141      if (INT_MULTIPLY_RANGE_OVERFLOW (i, j, LONG_MIN, LONG_MAX))
 142        printf ("multiply would overflow");
 143      else
 144        printf ("product is %ld", i * j);
 145
 146    Restrictions on *_RANGE_OVERFLOW macros:
 147
 148    These macros do not check for all possible numerical problems or
 149    undefined or unspecified behavior: they do not check for division
 150    by zero, for bad shift counts, or for shifting negative numbers.
 151
 152    These macros may evaluate their arguments zero or multiple times,
 153    so the arguments should not have side effects.  The arithmetic
 154    arguments (including the MIN and MAX arguments) must be of the same
 155    integer type after the usual arithmetic conversions, and the type
 156    must have minimum value MIN and maximum MAX.  Unsigned types should
 157    use a zero MIN of the proper type.
 158
 159    These macros are tuned for constant MIN and MAX.  For commutative
 160    operations such as A + B, they are also tuned for constant B.  */
 161
 162 /* Return 1 if A + B would overflow in [MIN,MAX] arithmetic.
 163    See above for restrictions.  */
 164 #define INT_ADD_RANGE_OVERFLOW(a, b, min, max)          \
 165   ((b) < 0                                              \
 166    ? (a) < (min) - (b)                                  \
 167    : (max) - (b) < (a))
 168
 169 /* Return 1 if A - B would overflow in [MIN,MAX] arithmetic.
 170    See above for restrictions.  */
 171 #define INT_SUBTRACT_RANGE_OVERFLOW(a, b, min, max)     \
 172   ((b) < 0                                              \
 173    ? (max) + (b) < (a)                                  \
 174    : (a) < (min) + (b))
 175
 176 /* Return 1 if - A would overflow in [MIN,MAX] arithmetic.
 177    See above for restrictions.  */
 178 #define INT_NEGATE_RANGE_OVERFLOW(a, min, max)          \
 179   ((min) < 0                                            \
 180    ? (a) < - (max)                                      \
 181    : 0 < (a))
 182
 183 /* Return 1 if A * B would overflow in [MIN,MAX] arithmetic.
 184    See above for restrictions.  Avoid && and || as they tickle
 185    bugs in Sun C 5.11 2010/08/13 and other compilers; see
 186    <http://lists.gnu.org/archive/html/bug-gnulib/2011-05/msg00401.html>.  */
 187 #define INT_MULTIPLY_RANGE_OVERFLOW(a, b, min, max)     \
 188   ((b) < 0                                              \
 189    ? ((a) < 0                                           \
 190       ? (a) < (max) / (b)                               \
 191       : (b) == -1                                       \
 192       ? 0                                               \
 193       : (min) / (b) < (a))                              \
 194    : (b) == 0                                           \
 195    ? 0                                                  \
 196    : ((a) < 0                                           \
 197       ? (a) < (min) / (b)                               \
 198       : (max) / (b) < (a)))
 199
 200 /* Return 1 if A / B would overflow in [MIN,MAX] arithmetic.
 201    See above for restrictions.  Do not check for division by zero.  */
 202 #define INT_DIVIDE_RANGE_OVERFLOW(a, b, min, max)       \
 203   ((min) < 0 && (b) == -1 && (a) < - (max))
 204
 205 /* Return 1 if A % B would overflow in [MIN,MAX] arithmetic.
 206    See above for restrictions.  Do not check for division by zero.
 207    Mathematically, % should never overflow, but on x86-like hosts
 208    INT_MIN % -1 traps, and the C standard permits this, so treat this
 209    as an overflow too.  */
 210 #define INT_REMAINDER_RANGE_OVERFLOW(a, b, min, max)    \
 211   INT_DIVIDE_RANGE_OVERFLOW (a, b, min, max)
 212
 213 /* Return 1 if A << B would overflow in [MIN,MAX] arithmetic.
 214    See above for restrictions.  Here, MIN and MAX are for A only, and B need
 215    not be of the same type as the other arguments.  The C standard says that
 216    behavior is undefined for shifts unless 0 <= B < wordwidth, and that when
 217    A is negative then A << B has undefined behavior and A >> B has
 218    implementation-defined behavior, but do not check these other
 219    restrictions.  */
 220 #define INT_LEFT_SHIFT_RANGE_OVERFLOW(a, b, min, max)   \
 221   ((a) < 0                                              \
 222    ? (a) < (min) >> (b)                                 \
 223    : (max) >> (b) < (a))
 224
 225 /* True if __builtin_add_overflow (A, B, P) works when P is null.  */
 226 #define _GL_HAS_BUILTIN_OVERFLOW_WITH_NULL (7 <= __GNUC__)
 227
 228 /* The _GL*_OVERFLOW macros have the same restrictions as the
 229    *_RANGE_OVERFLOW macros, except that they do not assume that operands
 230    (e.g., A and B) have the same type as MIN and MAX.  Instead, they assume
 231    that the result (e.g., A + B) has that type.  */
 232 #if _GL_HAS_BUILTIN_OVERFLOW_WITH_NULL
 233 # define _GL_ADD_OVERFLOW(a, b, min, max)
 234    __builtin_add_overflow (a, b, (__typeof__ ((a) + (b)) *) 0)
 235 # define _GL_SUBTRACT_OVERFLOW(a, b, min, max)
 236    __builtin_sub_overflow (a, b, (__typeof__ ((a) - (b)) *) 0)
 237 # define _GL_MULTIPLY_OVERFLOW(a, b, min, max)
 238    __builtin_mul_overflow (a, b, (__typeof__ ((a) * (b)) *) 0)
 239 #else
 240 # define _GL_ADD_OVERFLOW(a, b, min, max)                                \
 241    ((min) < 0 ? INT_ADD_RANGE_OVERFLOW (a, b, min, max)                  \
 242     : (a) < 0 ? (b) <= (a) + (b)                                         \
 243     : (b) < 0 ? (a) <= (a) + (b)                                         \
 244     : (a) + (b) < (b))
 245 # define _GL_SUBTRACT_OVERFLOW(a, b, min, max)                           \
 246    ((min) < 0 ? INT_SUBTRACT_RANGE_OVERFLOW (a, b, min, max)             \
 247     : (a) < 0 ? 1                                                        \
 248     : (b) < 0 ? (a) - (b) <= (a)                                         \
 249     : (a) < (b))
 250 # define _GL_MULTIPLY_OVERFLOW(a, b, min, max)                           \
 251    (((min) == 0 && (((a) < 0 && 0 < (b)) || ((b) < 0 && 0 < (a))))       \
 252     || INT_MULTIPLY_RANGE_OVERFLOW (a, b, min, max))
 253 #endif
 254 #define _GL_DIVIDE_OVERFLOW(a, b, min, max)                             \
 255   ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max)  \
 256    : (a) < 0 ? (b) <= (a) + (b) - 1                                     \
 257    : (b) < 0 && (a) + (b) <= (a))
 258 #define _GL_REMAINDER_OVERFLOW(a, b, min, max)                          \
 259   ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max)  \
 260    : (a) < 0 ? (a) % (b) != ((max) - (b) + 1) % (b)                     \
 261    : (b) < 0 && ! _GL_UNSIGNED_NEG_MULTIPLE (a, b, max))
 262
 263 /* Return a nonzero value if A is a mathematical multiple of B, where
 264    A is unsigned, B is negative, and MAX is the maximum value of A's
 265    type.  A's type must be the same as (A % B)'s type.  Normally (A %
 266    -B == 0) suffices, but things get tricky if -B would overflow.  */
 267 #define _GL_UNSIGNED_NEG_MULTIPLE(a, b, max)                            \
 268   (((b) < -_GL_SIGNED_INT_MAXIMUM (b)                                   \
 269     ? (_GL_SIGNED_INT_MAXIMUM (b) == (max)                              \
 270        ? (a)                                                            \
 271        : (a) % (_GL_INT_CONVERT (a, _GL_SIGNED_INT_MAXIMUM (b)) + 1))   \
 272     : (a) % - (b))                                                      \
 273    == 0)
 274
 275 /* Check for integer overflow, and report low order bits of answer.
 276
 277    The INT_<op>_OVERFLOW macros return 1 if the corresponding C operators
 278    might not yield numerically correct answers due to arithmetic overflow.
 279    The INT_<op>_WRAPV macros also store the low-order bits of the answer.
 280    These macros work correctly on all known practical hosts, and do not rely
 281    on undefined behavior due to signed arithmetic overflow.
 282
 283    Example usage, assuming A and B are long int:
 284
 285      if (INT_MULTIPLY_OVERFLOW (a, b))
 286        printf ("result would overflow\n");
 287      else
 288        printf ("result is %ld (no overflow)\n", a * b);
 289
 290    Example usage with WRAPV flavor:
 291
 292      long int result;
 293      bool overflow = INT_MULTIPLY_WRAPV (a, b, &result);
 294      printf ("result is %ld (%s)\n", result,
 295              overflow ? "after overflow" : "no overflow");
 296
 297    Restrictions on these macros:
 298
 299    These macros do not check for all possible numerical problems or
 300    undefined or unspecified behavior: they do not check for division
 301    by zero, for bad shift counts, or for shifting negative numbers.
 302
 303    These macros may evaluate their arguments zero or multiple times, so the
 304    arguments should not have side effects.
 305
 306    The WRAPV macros are not constant expressions.  They support only
 307    +, binary -, and *.  The result type must be signed.
 308
 309    These macros are tuned for their last argument being a constant.
 310
 311    Return 1 if the integer expressions A * B, A - B, -A, A * B, A / B,
 312    A % B, and A << B would overflow, respectively.  */
 313
 314 #define INT_ADD_OVERFLOW(a, b) \
 315   _GL_BINARY_OP_OVERFLOW (a, b, _GL_ADD_OVERFLOW)
 316 #define INT_SUBTRACT_OVERFLOW(a, b) \
 317   _GL_BINARY_OP_OVERFLOW (a, b, _GL_SUBTRACT_OVERFLOW)
 318 #if _GL_HAS_BUILTIN_OVERFLOW_WITH_NULL
 319 # define INT_NEGATE_OVERFLOW(a) INT_SUBTRACT_OVERFLOW (0, a)
 320 #else
 321 # define INT_NEGATE_OVERFLOW(a) \
 322    INT_NEGATE_RANGE_OVERFLOW (a, _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
 323 #endif
 324 #define INT_MULTIPLY_OVERFLOW(a, b) \
 325   _GL_BINARY_OP_OVERFLOW (a, b, _GL_MULTIPLY_OVERFLOW)
 326 #define INT_DIVIDE_OVERFLOW(a, b) \
 327   _GL_BINARY_OP_OVERFLOW (a, b, _GL_DIVIDE_OVERFLOW)
 328 #define INT_REMAINDER_OVERFLOW(a, b) \
 329   _GL_BINARY_OP_OVERFLOW (a, b, _GL_REMAINDER_OVERFLOW)
 330 #define INT_LEFT_SHIFT_OVERFLOW(a, b) \
 331   INT_LEFT_SHIFT_RANGE_OVERFLOW (a, b, \
 332                                  _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
 333
 334 /* Return 1 if the expression A <op> B would overflow,
 335    where OP_RESULT_OVERFLOW (A, B, MIN, MAX) does the actual test,
 336    assuming MIN and MAX are the minimum and maximum for the result type.
 337    Arguments should be free of side effects.  */
 338 #define _GL_BINARY_OP_OVERFLOW(a, b, op_result_overflow)        \
 339   op_result_overflow (a, b,                                     \
 340                       _GL_INT_MINIMUM (0 * (b) + (a)),          \
 341                       _GL_INT_MAXIMUM (0 * (b) + (a)))
 342
 343 /* Store the low-order bits of A + B, A - B, A * B, respectively, into *R.
 344    Return 1 if the result overflows.  See above for restrictions.  */
 345 #define INT_ADD_WRAPV(a, b, r) \
 346   _GL_INT_OP_WRAPV (a, b, r, +, __builtin_add_overflow, INT_ADD_OVERFLOW)
 347 #define INT_SUBTRACT_WRAPV(a, b, r) \
 348   _GL_INT_OP_WRAPV (a, b, r, -, __builtin_sub_overflow, INT_SUBTRACT_OVERFLOW)
 349 #define INT_MULTIPLY_WRAPV(a, b, r) \
 350   _GL_INT_OP_WRAPV (a, b, r, *, __builtin_mul_overflow, INT_MULTIPLY_OVERFLOW)
 351
 352 #ifndef __has_builtin
 353 # define __has_builtin(x) 0
 354 #endif
 355
 356 /* Nonzero if this compiler has GCC bug 68193 or Clang bug 25390.  See:
 357    https://gcc.gnu.org/bugzilla/show_bug.cgi?id=68193
 358    https://llvm.org/bugs/show_bug.cgi?id=25390
 359    For now, assume all versions of GCC-like compilers generate bogus
 360    warnings for _Generic.  This matters only for older compilers that
 361    lack __builtin_add_overflow.  */
 362 #if __GNUC__
 363 # define _GL__GENERIC_BOGUS 1
 364 #else
 365 # define _GL__GENERIC_BOGUS 0
 366 #endif
 367
 368 /* Store the low-order bits of A <op> B into *R, where OP specifies
 369    the operation.  BUILTIN is the builtin operation, and OVERFLOW the
 370    overflow predicate.  Return 1 if the result overflows.  See above
 371    for restrictions.  */
 372 #if 5 <= __GNUC__ || __has_builtin (__builtin_add_overflow)
 373 # define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) builtin (a, b, r)
 374 #elif 201112 <= __STDC_VERSION__ && !_GL__GENERIC_BOGUS
 375 # define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) \
 376    (_Generic \
 377     (*(r), \
 378      signed char: \
 379        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned char, \
 380                         signed char, SCHAR_MIN, SCHAR_MAX), \
 381      short int: \
 382        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned short int, \
 383                         short int, SHRT_MIN, SHRT_MAX), \
 384      int: \
 385        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 386                         int, INT_MIN, INT_MAX), \
 387      long int: \
 388        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 389                         long int, LONG_MIN, LONG_MAX), \
 390      long long int: \
 391        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
 392                         long long int, LLONG_MIN, LLONG_MAX)))
 393 #else
 394 # define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) \
 395    (sizeof *(r) == sizeof (signed char) \
 396     ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned char, \
 397                        signed char, SCHAR_MIN, SCHAR_MAX) \
 398     : sizeof *(r) == sizeof (short int) \
 399     ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned short int, \
 400                        short int, SHRT_MIN, SHRT_MAX) \
 401     : sizeof *(r) == sizeof (int) \
 402     ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 403                        int, INT_MIN, INT_MAX) \
 404     : _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow))
 405 # ifdef LLONG_MAX
 406 #  define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
 407     (sizeof *(r) == sizeof (long int) \
 408      ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 409                         long int, LONG_MIN, LONG_MAX) \
 410      : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
 411                         long long int, LLONG_MIN, LLONG_MAX))
 412 # else
 413 #  define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
 414     _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 415                      long int, LONG_MIN, LONG_MAX))
 416 # endif
 417 #endif
 418
 419 /* Store the low-order bits of A <op> B into *R, where the operation
 420    is given by OP.  Use the unsigned type UT for calculation to avoid
 421    overflow problems.  *R's type is T, with extremal values TMIN and
 422    TMAX.  T must be a signed integer type.  Return 1 if the result
 423    overflows.  */
 424 #define _GL_INT_OP_CALC(a, b, r, op, overflow, ut, t, tmin, tmax) \
 425   (sizeof ((a) op (b)) < sizeof (t) \
 426    ? _GL_INT_OP_CALC1 ((t) (a), (t) (b), r, op, overflow, ut, t, tmin, tmax) \
 427    : _GL_INT_OP_CALC1 (a, b, r, op, overflow, ut, t, tmin, tmax))
 428 #define _GL_INT_OP_CALC1(a, b, r, op, overflow, ut, t, tmin, tmax) \
 429   ((overflow (a, b) \
 430     || (EXPR_SIGNED ((a) op (b)) && ((a) op (b)) < (tmin)) \
 431     || (tmax) < ((a) op (b))) \
 432    ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t, tmin, tmax), 1) \
 433    : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t, tmin, tmax), 0))
 434
 435 /* Return A <op> B, where the operation is given by OP.  Use the
 436    unsigned type UT for calculation to avoid overflow problems.
 437    Convert the result to type T without overflow by subtracting TMIN
 438    from large values before converting, and adding it afterwards.
 439    Compilers can optimize all the operations except OP.  */
 440 #define _GL_INT_OP_WRAPV_VIA_UNSIGNED(a, b, op, ut, t, tmin, tmax) \
 441   (((ut) (a) op (ut) (b)) <= (tmax) \
 442    ? (t) ((ut) (a) op (ut) (b)) \
 443    : ((t) (((ut) (a) op (ut) (b)) - (tmin)) + (tmin)))
 444
 445 #endif /* _GL_INTPROPS_H */