lib/intprops.h

   1 /* intprops.h -- properties of integer types
   2
   3    Copyright (C) 2001-2017 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 width in bits of the integer type or expression T.
  51    Padding bits are not supported; this is checked at compile-time below.  */
  52 #define TYPE_WIDTH(t) (sizeof (t) * CHAR_BIT)
  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 << (TYPE_WIDTH (t) - 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) << (TYPE_WIDTH ((e) + 0) - 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 /* Similarly, sanity-check one ISO/IEC TS 18661-1:2014 macro if defined.  */
  98 #ifdef UINT_WIDTH
  99 verify (TYPE_WIDTH (unsigned int) == UINT_WIDTH);
 100 #endif
 101
 102 /* Does the __typeof__ keyword work?  This could be done by
 103    'configure', but for now it's easier to do it by hand.  */
 104 #if (2 <= __GNUC__ \
 105      || (1210 <= __IBMC__ && defined __IBM__TYPEOF__) \
 106      || (0x5110 <= __SUNPRO_C && !__STDC__))
 107 # define _GL_HAVE___TYPEOF__ 1
 108 #else
 109 # define _GL_HAVE___TYPEOF__ 0
 110 #endif
 111
 112 /* Return 1 if the integer type or expression T might be signed.  Return 0
 113    if it is definitely unsigned.  This macro does not evaluate its argument,
 114    and expands to an integer constant expression.  */
 115 #if _GL_HAVE___TYPEOF__
 116 # define _GL_SIGNED_TYPE_OR_EXPR(t) TYPE_SIGNED (__typeof__ (t))
 117 #else
 118 # define _GL_SIGNED_TYPE_OR_EXPR(t) 1
 119 #endif
 120
 121 /* Bound on length of the string representing an unsigned integer
 122    value representable in B bits.  log10 (2.0) < 146/485.  The
 123    smallest value of B where this bound is not tight is 2621.  */
 124 #define INT_BITS_STRLEN_BOUND(b) (((b) * 146 + 484) / 485)
 125
 126 /* Bound on length of the string representing an integer type or expression T.
 127    Subtract 1 for the sign bit if T is signed, and then add 1 more for
 128    a minus sign if needed.
 129
 130    Because _GL_SIGNED_TYPE_OR_EXPR sometimes returns 0 when its argument is
 131    signed, this macro may overestimate the true bound by one byte when
 132    applied to unsigned types of size 2, 4, 16, ... bytes.  */
 133 #define INT_STRLEN_BOUND(t)                                     \
 134   (INT_BITS_STRLEN_BOUND (TYPE_WIDTH (t) - _GL_SIGNED_TYPE_OR_EXPR (t)) \
 135    + _GL_SIGNED_TYPE_OR_EXPR (t))
 136
 137 /* Bound on buffer size needed to represent an integer type or expression T,
 138    including the terminating null.  */
 139 #define INT_BUFSIZE_BOUND(t) (INT_STRLEN_BOUND (t) + 1)
 140
 141
 142 /* Range overflow checks.
 143
 144    The INT_<op>_RANGE_OVERFLOW macros return 1 if the corresponding C
 145    operators might not yield numerically correct answers due to
 146    arithmetic overflow.  They do not rely on undefined or
 147    implementation-defined behavior.  Their implementations are simple
 148    and straightforward, but they are a bit harder to use than the
 149    INT_<op>_OVERFLOW macros described below.
 150
 151    Example usage:
 152
 153      long int i = ...;
 154      long int j = ...;
 155      if (INT_MULTIPLY_RANGE_OVERFLOW (i, j, LONG_MIN, LONG_MAX))
 156        printf ("multiply would overflow");
 157      else
 158        printf ("product is %ld", i * j);
 159
 160    Restrictions on *_RANGE_OVERFLOW macros:
 161
 162    These macros do not check for all possible numerical problems or
 163    undefined or unspecified behavior: they do not check for division
 164    by zero, for bad shift counts, or for shifting negative numbers.
 165
 166    These macros may evaluate their arguments zero or multiple times,
 167    so the arguments should not have side effects.  The arithmetic
 168    arguments (including the MIN and MAX arguments) must be of the same
 169    integer type after the usual arithmetic conversions, and the type
 170    must have minimum value MIN and maximum MAX.  Unsigned types should
 171    use a zero MIN of the proper type.
 172
 173    These macros are tuned for constant MIN and MAX.  For commutative
 174    operations such as A + B, they are also tuned for constant B.  */
 175
 176 /* Return 1 if A + B would overflow in [MIN,MAX] arithmetic.
 177    See above for restrictions.  */
 178 #define INT_ADD_RANGE_OVERFLOW(a, b, min, max)          \
 179   ((b) < 0                                              \
 180    ? (a) < (min) - (b)                                  \
 181    : (max) - (b) < (a))
 182
 183 /* Return 1 if A - B would overflow in [MIN,MAX] arithmetic.
 184    See above for restrictions.  */
 185 #define INT_SUBTRACT_RANGE_OVERFLOW(a, b, min, max)     \
 186   ((b) < 0                                              \
 187    ? (max) + (b) < (a)                                  \
 188    : (a) < (min) + (b))
 189
 190 /* Return 1 if - A would overflow in [MIN,MAX] arithmetic.
 191    See above for restrictions.  */
 192 #define INT_NEGATE_RANGE_OVERFLOW(a, min, max)          \
 193   ((min) < 0                                            \
 194    ? (a) < - (max)                                      \
 195    : 0 < (a))
 196
 197 /* Return 1 if A * B would overflow in [MIN,MAX] arithmetic.
 198    See above for restrictions.  Avoid && and || as they tickle
 199    bugs in Sun C 5.11 2010/08/13 and other compilers; see
 200    <http://lists.gnu.org/archive/html/bug-gnulib/2011-05/msg00401.html>.  */
 201 #define INT_MULTIPLY_RANGE_OVERFLOW(a, b, min, max)     \
 202   ((b) < 0                                              \
 203    ? ((a) < 0                                           \
 204       ? (a) < (max) / (b)                               \
 205       : (b) == -1                                       \
 206       ? 0                                               \
 207       : (min) / (b) < (a))                              \
 208    : (b) == 0                                           \
 209    ? 0                                                  \
 210    : ((a) < 0                                           \
 211       ? (a) < (min) / (b)                               \
 212       : (max) / (b) < (a)))
 213
 214 /* Return 1 if A / B would overflow in [MIN,MAX] arithmetic.
 215    See above for restrictions.  Do not check for division by zero.  */
 216 #define INT_DIVIDE_RANGE_OVERFLOW(a, b, min, max)       \
 217   ((min) < 0 && (b) == -1 && (a) < - (max))
 218
 219 /* Return 1 if A % B would overflow in [MIN,MAX] arithmetic.
 220    See above for restrictions.  Do not check for division by zero.
 221    Mathematically, % should never overflow, but on x86-like hosts
 222    INT_MIN % -1 traps, and the C standard permits this, so treat this
 223    as an overflow too.  */
 224 #define INT_REMAINDER_RANGE_OVERFLOW(a, b, min, max)    \
 225   INT_DIVIDE_RANGE_OVERFLOW (a, b, min, max)
 226
 227 /* Return 1 if A << B would overflow in [MIN,MAX] arithmetic.
 228    See above for restrictions.  Here, MIN and MAX are for A only, and B need
 229    not be of the same type as the other arguments.  The C standard says that
 230    behavior is undefined for shifts unless 0 <= B < wordwidth, and that when
 231    A is negative then A << B has undefined behavior and A >> B has
 232    implementation-defined behavior, but do not check these other
 233    restrictions.  */
 234 #define INT_LEFT_SHIFT_RANGE_OVERFLOW(a, b, min, max)   \
 235   ((a) < 0                                              \
 236    ? (a) < (min) >> (b)                                 \
 237    : (max) >> (b) < (a))
 238
 239 /* True if __builtin_add_overflow (A, B, P) works when P is non-null.  */
 240 #define _GL_HAS_BUILTIN_OVERFLOW (5 <= __GNUC__)
 241
 242 /* True if __builtin_add_overflow_p (A, B, C) works.  */
 243 #define _GL_HAS_BUILTIN_OVERFLOW_P (7 <= __GNUC__)
 244
 245 /* The _GL*_OVERFLOW macros have the same restrictions as the
 246    *_RANGE_OVERFLOW macros, except that they do not assume that operands
 247    (e.g., A and B) have the same type as MIN and MAX.  Instead, they assume
 248    that the result (e.g., A + B) has that type.  */
 249 #if _GL_HAS_BUILTIN_OVERFLOW_P
 250 # define _GL_ADD_OVERFLOW(a, b, min, max)                               \
 251    __builtin_add_overflow_p (a, b, (__typeof__ ((a) + (b))) 0)
 252 # define _GL_SUBTRACT_OVERFLOW(a, b, min, max)                          \
 253    __builtin_sub_overflow_p (a, b, (__typeof__ ((a) - (b))) 0)
 254 # define _GL_MULTIPLY_OVERFLOW(a, b, min, max)                          \
 255    __builtin_mul_overflow_p (a, b, (__typeof__ ((a) * (b))) 0)
 256 #else
 257 # define _GL_ADD_OVERFLOW(a, b, min, max)                                \
 258    ((min) < 0 ? INT_ADD_RANGE_OVERFLOW (a, b, min, max)                  \
 259     : (a) < 0 ? (b) <= (a) + (b)                                         \
 260     : (b) < 0 ? (a) <= (a) + (b)                                         \
 261     : (a) + (b) < (b))
 262 # define _GL_SUBTRACT_OVERFLOW(a, b, min, max)                           \
 263    ((min) < 0 ? INT_SUBTRACT_RANGE_OVERFLOW (a, b, min, max)             \
 264     : (a) < 0 ? 1                                                        \
 265     : (b) < 0 ? (a) - (b) <= (a)                                         \
 266     : (a) < (b))
 267 # define _GL_MULTIPLY_OVERFLOW(a, b, min, max)                           \
 268    (((min) == 0 && (((a) < 0 && 0 < (b)) || ((b) < 0 && 0 < (a))))       \
 269     || INT_MULTIPLY_RANGE_OVERFLOW (a, b, min, max))
 270 #endif
 271 #define _GL_DIVIDE_OVERFLOW(a, b, min, max)                             \
 272   ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max)  \
 273    : (a) < 0 ? (b) <= (a) + (b) - 1                                     \
 274    : (b) < 0 && (a) + (b) <= (a))
 275 #define _GL_REMAINDER_OVERFLOW(a, b, min, max)                          \
 276   ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max)  \
 277    : (a) < 0 ? (a) % (b) != ((max) - (b) + 1) % (b)                     \
 278    : (b) < 0 && ! _GL_UNSIGNED_NEG_MULTIPLE (a, b, max))
 279
 280 /* Return a nonzero value if A is a mathematical multiple of B, where
 281    A is unsigned, B is negative, and MAX is the maximum value of A's
 282    type.  A's type must be the same as (A % B)'s type.  Normally (A %
 283    -B == 0) suffices, but things get tricky if -B would overflow.  */
 284 #define _GL_UNSIGNED_NEG_MULTIPLE(a, b, max)                            \
 285   (((b) < -_GL_SIGNED_INT_MAXIMUM (b)                                   \
 286     ? (_GL_SIGNED_INT_MAXIMUM (b) == (max)                              \
 287        ? (a)                                                            \
 288        : (a) % (_GL_INT_CONVERT (a, _GL_SIGNED_INT_MAXIMUM (b)) + 1))   \
 289     : (a) % - (b))                                                      \
 290    == 0)
 291
 292 /* Check for integer overflow, and report low order bits of answer.
 293
 294    The INT_<op>_OVERFLOW macros return 1 if the corresponding C operators
 295    might not yield numerically correct answers due to arithmetic overflow.
 296    The INT_<op>_WRAPV macros also store the low-order bits of the answer.
 297    These macros work correctly on all known practical hosts, and do not rely
 298    on undefined behavior due to signed arithmetic overflow.
 299
 300    Example usage, assuming A and B are long int:
 301
 302      if (INT_MULTIPLY_OVERFLOW (a, b))
 303        printf ("result would overflow\n");
 304      else
 305        printf ("result is %ld (no overflow)\n", a * b);
 306
 307    Example usage with WRAPV flavor:
 308
 309      long int result;
 310      bool overflow = INT_MULTIPLY_WRAPV (a, b, &result);
 311      printf ("result is %ld (%s)\n", result,
 312              overflow ? "after overflow" : "no overflow");
 313
 314    Restrictions on these macros:
 315
 316    These macros do not check for all possible numerical problems or
 317    undefined or unspecified behavior: they do not check for division
 318    by zero, for bad shift counts, or for shifting negative numbers.
 319
 320    These macros may evaluate their arguments zero or multiple times, so the
 321    arguments should not have side effects.
 322
 323    The WRAPV macros are not constant expressions.  They support only
 324    +, binary -, and *.  The result type must be signed.
 325
 326    These macros are tuned for their last argument being a constant.
 327
 328    Return 1 if the integer expressions A * B, A - B, -A, A * B, A / B,
 329    A % B, and A << B would overflow, respectively.  */
 330
 331 #define INT_ADD_OVERFLOW(a, b) \
 332   _GL_BINARY_OP_OVERFLOW (a, b, _GL_ADD_OVERFLOW)
 333 #define INT_SUBTRACT_OVERFLOW(a, b) \
 334   _GL_BINARY_OP_OVERFLOW (a, b, _GL_SUBTRACT_OVERFLOW)
 335 #if _GL_HAS_BUILTIN_OVERFLOW_P
 336 # define INT_NEGATE_OVERFLOW(a) INT_SUBTRACT_OVERFLOW (0, a)
 337 #else
 338 # define INT_NEGATE_OVERFLOW(a) \
 339    INT_NEGATE_RANGE_OVERFLOW (a, _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
 340 #endif
 341 #define INT_MULTIPLY_OVERFLOW(a, b) \
 342   _GL_BINARY_OP_OVERFLOW (a, b, _GL_MULTIPLY_OVERFLOW)
 343 #define INT_DIVIDE_OVERFLOW(a, b) \
 344   _GL_BINARY_OP_OVERFLOW (a, b, _GL_DIVIDE_OVERFLOW)
 345 #define INT_REMAINDER_OVERFLOW(a, b) \
 346   _GL_BINARY_OP_OVERFLOW (a, b, _GL_REMAINDER_OVERFLOW)
 347 #define INT_LEFT_SHIFT_OVERFLOW(a, b) \
 348   INT_LEFT_SHIFT_RANGE_OVERFLOW (a, b, \
 349                                  _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
 350
 351 /* Return 1 if the expression A <op> B would overflow,
 352    where OP_RESULT_OVERFLOW (A, B, MIN, MAX) does the actual test,
 353    assuming MIN and MAX are the minimum and maximum for the result type.
 354    Arguments should be free of side effects.  */
 355 #define _GL_BINARY_OP_OVERFLOW(a, b, op_result_overflow)        \
 356   op_result_overflow (a, b,                                     \
 357                       _GL_INT_MINIMUM (0 * (b) + (a)),          \
 358                       _GL_INT_MAXIMUM (0 * (b) + (a)))
 359
 360 /* Store the low-order bits of A + B, A - B, A * B, respectively, into *R.
 361    Return 1 if the result overflows.  See above for restrictions.  */
 362 #define INT_ADD_WRAPV(a, b, r) \
 363   _GL_INT_OP_WRAPV (a, b, r, +, __builtin_add_overflow, INT_ADD_OVERFLOW)
 364 #define INT_SUBTRACT_WRAPV(a, b, r) \
 365   _GL_INT_OP_WRAPV (a, b, r, -, __builtin_sub_overflow, INT_SUBTRACT_OVERFLOW)
 366 #define INT_MULTIPLY_WRAPV(a, b, r) \
 367   _GL_INT_OP_WRAPV (a, b, r, *, __builtin_mul_overflow, INT_MULTIPLY_OVERFLOW)
 368
 369 /* Nonzero if this compiler has GCC bug 68193 or Clang bug 25390.  See:
 370    https://gcc.gnu.org/bugzilla/show_bug.cgi?id=68193
 371    https://llvm.org/bugs/show_bug.cgi?id=25390
 372    For now, assume all versions of GCC-like compilers generate bogus
 373    warnings for _Generic.  This matters only for older compilers that
 374    lack __builtin_add_overflow.  */
 375 #if __GNUC__
 376 # define _GL__GENERIC_BOGUS 1
 377 #else
 378 # define _GL__GENERIC_BOGUS 0
 379 #endif
 380
 381 /* Store the low-order bits of A <op> B into *R, where OP specifies
 382    the operation.  BUILTIN is the builtin operation, and OVERFLOW the
 383    overflow predicate.  Return 1 if the result overflows.  See above
 384    for restrictions.  */
 385 #if _GL_HAS_BUILTIN_OVERFLOW
 386 # define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) builtin (a, b, r)
 387 #elif 201112 <= __STDC_VERSION__ && !_GL__GENERIC_BOGUS
 388 # define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) \
 389    (_Generic \
 390     (*(r), \
 391      signed char: \
 392        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned char, \
 393                         signed char, SCHAR_MIN, SCHAR_MAX), \
 394      short int: \
 395        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned short int, \
 396                         short int, SHRT_MIN, SHRT_MAX), \
 397      int: \
 398        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 399                         int, INT_MIN, INT_MAX), \
 400      long int: \
 401        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 402                         long int, LONG_MIN, LONG_MAX), \
 403      long long int: \
 404        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
 405                         long long int, LLONG_MIN, LLONG_MAX)))
 406 #else
 407 # define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) \
 408    (sizeof *(r) == sizeof (signed char) \
 409     ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned char, \
 410                        signed char, SCHAR_MIN, SCHAR_MAX) \
 411     : sizeof *(r) == sizeof (short int) \
 412     ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned short int, \
 413                        short int, SHRT_MIN, SHRT_MAX) \
 414     : sizeof *(r) == sizeof (int) \
 415     ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 416                        int, INT_MIN, INT_MAX) \
 417     : _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow))
 418 # ifdef LLONG_MAX
 419 #  define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
 420     (sizeof *(r) == sizeof (long int) \
 421      ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 422                         long int, LONG_MIN, LONG_MAX) \
 423      : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
 424                         long long int, LLONG_MIN, LLONG_MAX))
 425 # else
 426 #  define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
 427     _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 428                      long int, LONG_MIN, LONG_MAX)
 429 # endif
 430 #endif
 431
 432 /* Store the low-order bits of A <op> B into *R, where the operation
 433    is given by OP.  Use the unsigned type UT for calculation to avoid
 434    overflow problems.  *R's type is T, with extremal values TMIN and
 435    TMAX.  T must be a signed integer type.  Return 1 if the result
 436    overflows.  */
 437 #define _GL_INT_OP_CALC(a, b, r, op, overflow, ut, t, tmin, tmax) \
 438   (sizeof ((a) op (b)) < sizeof (t) \
 439    ? _GL_INT_OP_CALC1 ((t) (a), (t) (b), r, op, overflow, ut, t, tmin, tmax) \
 440    : _GL_INT_OP_CALC1 (a, b, r, op, overflow, ut, t, tmin, tmax))
 441 #define _GL_INT_OP_CALC1(a, b, r, op, overflow, ut, t, tmin, tmax) \
 442   ((overflow (a, b) \
 443     || (EXPR_SIGNED ((a) op (b)) && ((a) op (b)) < (tmin)) \
 444     || (tmax) < ((a) op (b))) \
 445    ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t, tmin, tmax), 1) \
 446    : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t, tmin, tmax), 0))
 447
 448 /* Return A <op> B, where the operation is given by OP.  Use the
 449    unsigned type UT for calculation to avoid overflow problems.
 450    Convert the result to type T without overflow by subtracting TMIN
 451    from large values before converting, and adding it afterwards.
 452    Compilers can optimize all the operations except OP.  */
 453 #define _GL_INT_OP_WRAPV_VIA_UNSIGNED(a, b, op, ut, t, tmin, tmax) \
 454   (((ut) (a) op (ut) (b)) <= (tmax) \
 455    ? (t) ((ut) (a) op (ut) (b)) \
 456    : ((t) (((ut) (a) op (ut) (b)) - (tmin)) + (tmin)))
 457
 458 #endif /* _GL_INTPROPS_H */