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 #ifndef __has_builtin
  27 # define __has_builtin(x) 0
  28 #endif
  29
  30 /* Return a value with the common real type of E and V and the value of V.  */
  31 #define _GL_INT_CONVERT(e, v) (0 * (e) + (v))
  32
  33 /* Act like _GL_INT_CONVERT (E, -V) but work around a bug in IRIX 6.5 cc; see
  34    <http://lists.gnu.org/archive/html/bug-gnulib/2011-05/msg00406.html>.  */
  35 #define _GL_INT_NEGATE_CONVERT(e, v) (0 * (e) - (v))
  36
  37 /* The extra casts in the following macros work around compiler bugs,
  38    e.g., in Cray C 5.0.3.0.  */
  39
  40 /* True if the arithmetic type T is an integer type.  bool counts as
  41    an integer.  */
  42 #define TYPE_IS_INTEGER(t) ((t) 1.5 == 1)
  43
  44 /* True if the real type T is signed.  */
  45 #define TYPE_SIGNED(t) (! ((t) 0 < (t) -1))
  46
  47 /* Return 1 if the real expression E, after promotion, has a
  48    signed or floating type.  */
  49 #define EXPR_SIGNED(e) (_GL_INT_NEGATE_CONVERT (e, 1) < 0)
  50
  51
  52 /* Minimum and maximum values for integer types and expressions.  */
  53
  54 /* The maximum and minimum values for the integer type T.  */
  55 #define TYPE_MINIMUM(t) ((t) ~ TYPE_MAXIMUM (t))
  56 #define TYPE_MAXIMUM(t)                                                 \
  57   ((t) (! TYPE_SIGNED (t)                                               \
  58         ? (t) -1                                                        \
  59         : ((((t) 1 << (sizeof (t) * CHAR_BIT - 2)) - 1) * 2 + 1)))
  60
  61 /* The maximum and minimum values for the type of the expression E,
  62    after integer promotion.  E should not have side effects.  */
  63 #define _GL_INT_MINIMUM(e)                                              \
  64   (EXPR_SIGNED (e)                                                      \
  65    ? ~ _GL_SIGNED_INT_MAXIMUM (e)                                       \
  66    : _GL_INT_CONVERT (e, 0))
  67 #define _GL_INT_MAXIMUM(e)                                              \
  68   (EXPR_SIGNED (e)                                                      \
  69    ? _GL_SIGNED_INT_MAXIMUM (e)                                         \
  70    : _GL_INT_NEGATE_CONVERT (e, 1))
  71 #define _GL_SIGNED_INT_MAXIMUM(e)                                       \
  72   (((_GL_INT_CONVERT (e, 1) << (sizeof ((e) + 0) * CHAR_BIT - 2)) - 1) * 2 + 1)
  73
  74 /* Work around OpenVMS incompatibility with C99.  */
  75 #if !defined LLONG_MAX && defined __INT64_MAX
  76 # define LLONG_MAX __INT64_MAX
  77 # define LLONG_MIN __INT64_MIN
  78 #endif
  79
  80 /* This include file assumes that signed types are two's complement without
  81    padding bits; the above macros have undefined behavior otherwise.
  82    If this is a problem for you, please let us know how to fix it for your host.
  83    As a sanity check, test the assumption for some signed types that
  84    <limits.h> bounds.  */
  85 verify (TYPE_MINIMUM (signed char) == SCHAR_MIN);
  86 verify (TYPE_MAXIMUM (signed char) == SCHAR_MAX);
  87 verify (TYPE_MINIMUM (short int) == SHRT_MIN);
  88 verify (TYPE_MAXIMUM (short int) == SHRT_MAX);
  89 verify (TYPE_MINIMUM (int) == INT_MIN);
  90 verify (TYPE_MAXIMUM (int) == INT_MAX);
  91 verify (TYPE_MINIMUM (long int) == LONG_MIN);
  92 verify (TYPE_MAXIMUM (long int) == LONG_MAX);
  93 #ifdef LLONG_MAX
  94 verify (TYPE_MINIMUM (long long int) == LLONG_MIN);
  95 verify (TYPE_MAXIMUM (long long int) == LLONG_MAX);
  96 #endif
  97
  98 /* Does the __typeof__ keyword work?  This could be done by
  99    'configure', but for now it's easier to do it by hand.  */
 100 #if (2 <= __GNUC__ || defined __IBM__TYPEOF__ \
 101      || (0x5110 <= __SUNPRO_C && !__STDC__))
 102 # define _GL_HAVE___TYPEOF__ 1
 103 #else
 104 # define _GL_HAVE___TYPEOF__ 0
 105 #endif
 106
 107 /* Return 1 if the integer type or expression T might be signed.  Return 0
 108    if it is definitely unsigned.  This macro does not evaluate its argument,
 109    and expands to an integer constant expression.  */
 110 #if _GL_HAVE___TYPEOF__
 111 # define _GL_SIGNED_TYPE_OR_EXPR(t) TYPE_SIGNED (__typeof__ (t))
 112 #else
 113 # define _GL_SIGNED_TYPE_OR_EXPR(t) 1
 114 #endif
 115
 116 /* Bound on length of the string representing an unsigned integer
 117    value representable in B bits.  log10 (2.0) < 146/485.  The
 118    smallest value of B where this bound is not tight is 2621.  */
 119 #define INT_BITS_STRLEN_BOUND(b) (((b) * 146 + 484) / 485)
 120
 121 /* Bound on length of the string representing an integer type or expression T.
 122    Subtract 1 for the sign bit if T is signed, and then add 1 more for
 123    a minus sign if needed.
 124
 125    Because _GL_SIGNED_TYPE_OR_EXPR sometimes returns 0 when its argument is
 126    signed, this macro may overestimate the true bound by one byte when
 127    applied to unsigned types of size 2, 4, 16, ... bytes.  */
 128 #define INT_STRLEN_BOUND(t)                                     \
 129   (INT_BITS_STRLEN_BOUND (sizeof (t) * CHAR_BIT                 \
 130                           - _GL_SIGNED_TYPE_OR_EXPR (t))        \
 131    + _GL_SIGNED_TYPE_OR_EXPR (t))
 132
 133 /* Bound on buffer size needed to represent an integer type or expression T,
 134    including the terminating null.  */
 135 #define INT_BUFSIZE_BOUND(t) (INT_STRLEN_BOUND (t) + 1)
 136
 137
 138 /* Range overflow checks.
 139
 140    The INT_<op>_RANGE_OVERFLOW macros return 1 if the corresponding C
 141    operators might not yield numerically correct answers due to
 142    arithmetic overflow.  They do not rely on undefined or
 143    implementation-defined behavior.  Their implementations are simple
 144    and straightforward, but they are a bit harder to use than the
 145    INT_<op>_OVERFLOW macros described below.
 146
 147    Example usage:
 148
 149      long int i = ...;
 150      long int j = ...;
 151      if (INT_MULTIPLY_RANGE_OVERFLOW (i, j, LONG_MIN, LONG_MAX))
 152        printf ("multiply would overflow");
 153      else
 154        printf ("product is %ld", i * j);
 155
 156    Restrictions on *_RANGE_OVERFLOW macros:
 157
 158    These macros do not check for all possible numerical problems or
 159    undefined or unspecified behavior: they do not check for division
 160    by zero, for bad shift counts, or for shifting negative numbers.
 161
 162    These macros may evaluate their arguments zero or multiple times,
 163    so the arguments should not have side effects.  The arithmetic
 164    arguments (including the MIN and MAX arguments) must be of the same
 165    integer type after the usual arithmetic conversions, and the type
 166    must have minimum value MIN and maximum MAX.  Unsigned types should
 167    use a zero MIN of the proper type.
 168
 169    These macros are tuned for constant MIN and MAX.  For commutative
 170    operations such as A + B, they are also tuned for constant B.  */
 171
 172 /* Return 1 if A + B would overflow in [MIN,MAX] arithmetic.
 173    See above for restrictions.  */
 174 #define INT_ADD_RANGE_OVERFLOW(a, b, min, max)          \
 175   ((b) < 0                                              \
 176    ? (a) < (min) - (b)                                  \
 177    : (max) - (b) < (a))
 178
 179 /* Return 1 if A - B would overflow in [MIN,MAX] arithmetic.
 180    See above for restrictions.  */
 181 #define INT_SUBTRACT_RANGE_OVERFLOW(a, b, min, max)     \
 182   ((b) < 0                                              \
 183    ? (max) + (b) < (a)                                  \
 184    : (a) < (min) + (b))
 185
 186 /* Return 1 if - A would overflow in [MIN,MAX] arithmetic.
 187    See above for restrictions.  */
 188 #define INT_NEGATE_RANGE_OVERFLOW(a, min, max)          \
 189   ((min) < 0                                            \
 190    ? (a) < - (max)                                      \
 191    : 0 < (a))
 192
 193 /* Return 1 if A * B would overflow in [MIN,MAX] arithmetic.
 194    See above for restrictions.  Avoid && and || as they tickle
 195    bugs in Sun C 5.11 2010/08/13 and other compilers; see
 196    <http://lists.gnu.org/archive/html/bug-gnulib/2011-05/msg00401.html>.  */
 197 #define INT_MULTIPLY_RANGE_OVERFLOW(a, b, min, max)     \
 198   ((b) < 0                                              \
 199    ? ((a) < 0                                           \
 200       ? (a) < (max) / (b)                               \
 201       : (b) == -1                                       \
 202       ? 0                                               \
 203       : (min) / (b) < (a))                              \
 204    : (b) == 0                                           \
 205    ? 0                                                  \
 206    : ((a) < 0                                           \
 207       ? (a) < (min) / (b)                               \
 208       : (max) / (b) < (a)))
 209
 210 /* Return 1 if A / B would overflow in [MIN,MAX] arithmetic.
 211    See above for restrictions.  Do not check for division by zero.  */
 212 #define INT_DIVIDE_RANGE_OVERFLOW(a, b, min, max)       \
 213   ((min) < 0 && (b) == -1 && (a) < - (max))
 214
 215 /* Return 1 if A % B would overflow in [MIN,MAX] arithmetic.
 216    See above for restrictions.  Do not check for division by zero.
 217    Mathematically, % should never overflow, but on x86-like hosts
 218    INT_MIN % -1 traps, and the C standard permits this, so treat this
 219    as an overflow too.  */
 220 #define INT_REMAINDER_RANGE_OVERFLOW(a, b, min, max)    \
 221   INT_DIVIDE_RANGE_OVERFLOW (a, b, min, max)
 222
 223 /* Return 1 if A << B would overflow in [MIN,MAX] arithmetic.
 224    See above for restrictions.  Here, MIN and MAX are for A only, and B need
 225    not be of the same type as the other arguments.  The C standard says that
 226    behavior is undefined for shifts unless 0 <= B < wordwidth, and that when
 227    A is negative then A << B has undefined behavior and A >> B has
 228    implementation-defined behavior, but do not check these other
 229    restrictions.  */
 230 #define INT_LEFT_SHIFT_RANGE_OVERFLOW(a, b, min, max)   \
 231   ((a) < 0                                              \
 232    ? (a) < (min) >> (b)                                 \
 233    : (max) >> (b) < (a))
 234
 235 /* True if __builtin_add_overflow (A, B, P) works when P is non-null.  */
 236 #define _GL_HAS_BUILTIN_OVERFLOW \
 237   (5 <= __GNUC__ || __has_builtin (__builtin_add_overflow))
 238
 239 /* True if __builtin_add_overflow_p (A, B, C) works.  */
 240 #define _GL_HAS_BUILTIN_OVERFLOW_P \
 241   (7 <= __GNUC__ || __has_builtin (__builtin_add_overflow_p))
 242
 243 /* The _GL*_OVERFLOW macros have the same restrictions as the
 244    *_RANGE_OVERFLOW macros, except that they do not assume that operands
 245    (e.g., A and B) have the same type as MIN and MAX.  Instead, they assume
 246    that the result (e.g., A + B) has that type.  */
 247 #if _GL_HAS_BUILTIN_OVERFLOW_P
 248 # define _GL_ADD_OVERFLOW(a, b, min, max)                               \
 249    __builtin_add_overflow_p (a, b, (__typeof__ ((a) + (b))) 0)
 250 # define _GL_SUBTRACT_OVERFLOW(a, b, min, max)                          \
 251    __builtin_sub_overflow_p (a, b, (__typeof__ ((a) - (b))) 0)
 252 # define _GL_MULTIPLY_OVERFLOW(a, b, min, max)                          \
 253    __builtin_mul_overflow_p (a, b, (__typeof__ ((a) * (b))) 0)
 254 #else
 255 # define _GL_ADD_OVERFLOW(a, b, min, max)                                \
 256    ((min) < 0 ? INT_ADD_RANGE_OVERFLOW (a, b, min, max)                  \
 257     : (a) < 0 ? (b) <= (a) + (b)                                         \
 258     : (b) < 0 ? (a) <= (a) + (b)                                         \
 259     : (a) + (b) < (b))
 260 # define _GL_SUBTRACT_OVERFLOW(a, b, min, max)                           \
 261    ((min) < 0 ? INT_SUBTRACT_RANGE_OVERFLOW (a, b, min, max)             \
 262     : (a) < 0 ? 1                                                        \
 263     : (b) < 0 ? (a) - (b) <= (a)                                         \
 264     : (a) < (b))
 265 # define _GL_MULTIPLY_OVERFLOW(a, b, min, max)                           \
 266    (((min) == 0 && (((a) < 0 && 0 < (b)) || ((b) < 0 && 0 < (a))))       \
 267     || INT_MULTIPLY_RANGE_OVERFLOW (a, b, min, max))
 268 #endif
 269 #define _GL_DIVIDE_OVERFLOW(a, b, min, max)                             \
 270   ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max)  \
 271    : (a) < 0 ? (b) <= (a) + (b) - 1                                     \
 272    : (b) < 0 && (a) + (b) <= (a))
 273 #define _GL_REMAINDER_OVERFLOW(a, b, min, max)                          \
 274   ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max)  \
 275    : (a) < 0 ? (a) % (b) != ((max) - (b) + 1) % (b)                     \
 276    : (b) < 0 && ! _GL_UNSIGNED_NEG_MULTIPLE (a, b, max))
 277
 278 /* Return a nonzero value if A is a mathematical multiple of B, where
 279    A is unsigned, B is negative, and MAX is the maximum value of A's
 280    type.  A's type must be the same as (A % B)'s type.  Normally (A %
 281    -B == 0) suffices, but things get tricky if -B would overflow.  */
 282 #define _GL_UNSIGNED_NEG_MULTIPLE(a, b, max)                            \
 283   (((b) < -_GL_SIGNED_INT_MAXIMUM (b)                                   \
 284     ? (_GL_SIGNED_INT_MAXIMUM (b) == (max)                              \
 285        ? (a)                                                            \
 286        : (a) % (_GL_INT_CONVERT (a, _GL_SIGNED_INT_MAXIMUM (b)) + 1))   \
 287     : (a) % - (b))                                                      \
 288    == 0)
 289
 290 /* Check for integer overflow, and report low order bits of answer.
 291
 292    The INT_<op>_OVERFLOW macros return 1 if the corresponding C operators
 293    might not yield numerically correct answers due to arithmetic overflow.
 294    The INT_<op>_WRAPV macros also store the low-order bits of the answer.
 295    These macros work correctly on all known practical hosts, and do not rely
 296    on undefined behavior due to signed arithmetic overflow.
 297
 298    Example usage, assuming A and B are long int:
 299
 300      if (INT_MULTIPLY_OVERFLOW (a, b))
 301        printf ("result would overflow\n");
 302      else
 303        printf ("result is %ld (no overflow)\n", a * b);
 304
 305    Example usage with WRAPV flavor:
 306
 307      long int result;
 308      bool overflow = INT_MULTIPLY_WRAPV (a, b, &result);
 309      printf ("result is %ld (%s)\n", result,
 310              overflow ? "after overflow" : "no overflow");
 311
 312    Restrictions on these macros:
 313
 314    These macros do not check for all possible numerical problems or
 315    undefined or unspecified behavior: they do not check for division
 316    by zero, for bad shift counts, or for shifting negative numbers.
 317
 318    These macros may evaluate their arguments zero or multiple times, so the
 319    arguments should not have side effects.
 320
 321    The WRAPV macros are not constant expressions.  They support only
 322    +, binary -, and *.  The result type must be signed.
 323
 324    These macros are tuned for their last argument being a constant.
 325
 326    Return 1 if the integer expressions A * B, A - B, -A, A * B, A / B,
 327    A % B, and A << B would overflow, respectively.  */
 328
 329 #define INT_ADD_OVERFLOW(a, b) \
 330   _GL_BINARY_OP_OVERFLOW (a, b, _GL_ADD_OVERFLOW)
 331 #define INT_SUBTRACT_OVERFLOW(a, b) \
 332   _GL_BINARY_OP_OVERFLOW (a, b, _GL_SUBTRACT_OVERFLOW)
 333 #if _GL_HAS_BUILTIN_OVERFLOW_P
 334 # define INT_NEGATE_OVERFLOW(a) INT_SUBTRACT_OVERFLOW (0, a)
 335 #else
 336 # define INT_NEGATE_OVERFLOW(a) \
 337    INT_NEGATE_RANGE_OVERFLOW (a, _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
 338 #endif
 339 #define INT_MULTIPLY_OVERFLOW(a, b) \
 340   _GL_BINARY_OP_OVERFLOW (a, b, _GL_MULTIPLY_OVERFLOW)
 341 #define INT_DIVIDE_OVERFLOW(a, b) \
 342   _GL_BINARY_OP_OVERFLOW (a, b, _GL_DIVIDE_OVERFLOW)
 343 #define INT_REMAINDER_OVERFLOW(a, b) \
 344   _GL_BINARY_OP_OVERFLOW (a, b, _GL_REMAINDER_OVERFLOW)
 345 #define INT_LEFT_SHIFT_OVERFLOW(a, b) \
 346   INT_LEFT_SHIFT_RANGE_OVERFLOW (a, b, \
 347                                  _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
 348
 349 /* Return 1 if the expression A <op> B would overflow,
 350    where OP_RESULT_OVERFLOW (A, B, MIN, MAX) does the actual test,
 351    assuming MIN and MAX are the minimum and maximum for the result type.
 352    Arguments should be free of side effects.  */
 353 #define _GL_BINARY_OP_OVERFLOW(a, b, op_result_overflow)        \
 354   op_result_overflow (a, b,                                     \
 355                       _GL_INT_MINIMUM (0 * (b) + (a)),          \
 356                       _GL_INT_MAXIMUM (0 * (b) + (a)))
 357
 358 /* Store the low-order bits of A + B, A - B, A * B, respectively, into *R.
 359    Return 1 if the result overflows.  See above for restrictions.  */
 360 #define INT_ADD_WRAPV(a, b, r) \
 361   _GL_INT_OP_WRAPV (a, b, r, +, __builtin_add_overflow, INT_ADD_OVERFLOW)
 362 #define INT_SUBTRACT_WRAPV(a, b, r) \
 363   _GL_INT_OP_WRAPV (a, b, r, -, __builtin_sub_overflow, INT_SUBTRACT_OVERFLOW)
 364 #define INT_MULTIPLY_WRAPV(a, b, r) \
 365   _GL_INT_OP_WRAPV (a, b, r, *, __builtin_mul_overflow, INT_MULTIPLY_OVERFLOW)
 366
 367 /* Nonzero if this compiler has GCC bug 68193 or Clang bug 25390.  See:
 368    https://gcc.gnu.org/bugzilla/show_bug.cgi?id=68193
 369    https://llvm.org/bugs/show_bug.cgi?id=25390
 370    For now, assume all versions of GCC-like compilers generate bogus
 371    warnings for _Generic.  This matters only for older compilers that
 372    lack __builtin_add_overflow.  */
 373 #if __GNUC__
 374 # define _GL__GENERIC_BOGUS 1
 375 #else
 376 # define _GL__GENERIC_BOGUS 0
 377 #endif
 378
 379 /* Store the low-order bits of A <op> B into *R, where OP specifies
 380    the operation.  BUILTIN is the builtin operation, and OVERFLOW the
 381    overflow predicate.  Return 1 if the result overflows.  See above
 382    for restrictions.  */
 383 #if _GL_HAS_BUILTIN_OVERFLOW
 384 # define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) builtin (a, b, r)
 385 #elif 201112 <= __STDC_VERSION__ && !_GL__GENERIC_BOGUS
 386 # define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) \
 387    (_Generic \
 388     (*(r), \
 389      signed char: \
 390        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned char, \
 391                         signed char, SCHAR_MIN, SCHAR_MAX), \
 392      short int: \
 393        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned short int, \
 394                         short int, SHRT_MIN, SHRT_MAX), \
 395      int: \
 396        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 397                         int, INT_MIN, INT_MAX), \
 398      long int: \
 399        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 400                         long int, LONG_MIN, LONG_MAX), \
 401      long long int: \
 402        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
 403                         long long int, LLONG_MIN, LLONG_MAX)))
 404 #else
 405 # define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) \
 406    (sizeof *(r) == sizeof (signed char) \
 407     ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned char, \
 408                        signed char, SCHAR_MIN, SCHAR_MAX) \
 409     : sizeof *(r) == sizeof (short int) \
 410     ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned short int, \
 411                        short int, SHRT_MIN, SHRT_MAX) \
 412     : sizeof *(r) == sizeof (int) \
 413     ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 414                        int, INT_MIN, INT_MAX) \
 415     : _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow))
 416 # ifdef LLONG_MAX
 417 #  define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
 418     (sizeof *(r) == sizeof (long int) \
 419      ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 420                         long int, LONG_MIN, LONG_MAX) \
 421      : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
 422                         long long int, LLONG_MIN, LLONG_MAX))
 423 # else
 424 #  define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
 425     _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 426                      long int, LONG_MIN, LONG_MAX)
 427 # endif
 428 #endif
 429
 430 /* Store the low-order bits of A <op> B into *R, where the operation
 431    is given by OP.  Use the unsigned type UT for calculation to avoid
 432    overflow problems.  *R's type is T, with extremal values TMIN and
 433    TMAX.  T must be a signed integer type.  Return 1 if the result
 434    overflows.  */
 435 #define _GL_INT_OP_CALC(a, b, r, op, overflow, ut, t, tmin, tmax) \
 436   (sizeof ((a) op (b)) < sizeof (t) \
 437    ? _GL_INT_OP_CALC1 ((t) (a), (t) (b), r, op, overflow, ut, t, tmin, tmax) \
 438    : _GL_INT_OP_CALC1 (a, b, r, op, overflow, ut, t, tmin, tmax))
 439 #define _GL_INT_OP_CALC1(a, b, r, op, overflow, ut, t, tmin, tmax) \
 440   ((overflow (a, b) \
 441     || (EXPR_SIGNED ((a) op (b)) && ((a) op (b)) < (tmin)) \
 442     || (tmax) < ((a) op (b))) \
 443    ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t, tmin, tmax), 1) \
 444    : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t, tmin, tmax), 0))
 445
 446 /* Return A <op> B, where the operation is given by OP.  Use the
 447    unsigned type UT for calculation to avoid overflow problems.
 448    Convert the result to type T without overflow by subtracting TMIN
 449    from large values before converting, and adding it afterwards.
 450    Compilers can optimize all the operations except OP.  */
 451 #define _GL_INT_OP_WRAPV_VIA_UNSIGNED(a, b, op, ut, t, tmin, tmax) \
 452   (((ut) (a) op (ut) (b)) <= (tmax) \
 453    ? (t) ((ut) (a) op (ut) (b)) \
 454    : ((t) (((ut) (a) op (ut) (b)) - (tmin)) + (tmin)))
 455
 456 #endif /* _GL_INTPROPS_H */