lib/intprops.h

   1 /* intprops.h -- properties of integer types
   2
   3    Copyright (C) 2001-2005, 2009-2015 Free Software Foundation, Inc.
   4
   5    This program is free software: you can redistribute it and/or modify
   6    it under the terms of the GNU General Public License as published by
   7    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
  25 /* Return a value with the common real type of E and V and the value of V.  */
  26 #define _GL_INT_CONVERT(e, v) (0 * (e) + (v))
  27
  28 /* Act like _GL_INT_CONVERT (E, -V) but work around a bug in IRIX 6.5 cc; see
  29    <http://lists.gnu.org/archive/html/bug-gnulib/2011-05/msg00406.html>.  */
  30 #define _GL_INT_NEGATE_CONVERT(e, v) (0 * (e) - (v))
  31
  32 /* The extra casts in the following macros work around compiler bugs,
  33    e.g., in Cray C 5.0.3.0.  */
  34
  35 /* True if the arithmetic type T is an integer type.  bool counts as
  36    an integer.  */
  37 #define TYPE_IS_INTEGER(t) ((t) 1.5 == 1)
  38
  39 /* True if negative values of the signed integer type T use two's
  40    complement, ones' complement, or signed magnitude representation,
  41    respectively.  Much GNU code assumes two's complement, but some
  42    people like to be portable to all possible C hosts.  */
  43 #define TYPE_TWOS_COMPLEMENT(t) ((t) ~ (t) 0 == (t) -1)
  44 #define TYPE_ONES_COMPLEMENT(t) ((t) ~ (t) 0 == 0)
  45 #define TYPE_SIGNED_MAGNITUDE(t) ((t) ~ (t) 0 < (t) -1)
  46
  47 /* True if the signed integer expression E uses two's complement.  */
  48 #define _GL_INT_TWOS_COMPLEMENT(e) (~ _GL_INT_CONVERT (e, 0) == -1)
  49
  50 /* True if the real type T is signed.  */
  51 #define TYPE_SIGNED(t) (! ((t) 0 < (t) -1))
  52
  53 /* Return 1 if the real expression E, after promotion, has a
  54    signed or floating type.  */
  55 #define EXPR_SIGNED(e) (_GL_INT_NEGATE_CONVERT (e, 1) < 0)
  56
  57
  58 /* Minimum and maximum values for integer types and expressions.  These
  59    macros have undefined behavior if T is signed and has padding bits.
  60    If this is a problem for you, please let us know how to fix it for
  61    your host.  */
  62
  63 /* The maximum and minimum values for the integer type T.  */
  64 #define TYPE_MINIMUM(t)                                                 \
  65   ((t) (! TYPE_SIGNED (t)                                               \
  66         ? (t) 0                                                         \
  67         : TYPE_SIGNED_MAGNITUDE (t)                                     \
  68         ? ~ (t) 0                                                       \
  69         : ~ TYPE_MAXIMUM (t)))
  70 #define TYPE_MAXIMUM(t)                                                 \
  71   ((t) (! TYPE_SIGNED (t)                                               \
  72         ? (t) -1                                                        \
  73         : ((((t) 1 << (sizeof (t) * CHAR_BIT - 2)) - 1) * 2 + 1)))
  74
  75 /* The maximum and minimum values for the type of the expression E,
  76    after integer promotion.  E should not have side effects.  */
  77 #define _GL_INT_MINIMUM(e)                                              \
  78   (EXPR_SIGNED (e)                                                      \
  79    ? - _GL_INT_TWOS_COMPLEMENT (e) - _GL_SIGNED_INT_MAXIMUM (e)         \
  80    : _GL_INT_CONVERT (e, 0))
  81 #define _GL_INT_MAXIMUM(e)                                              \
  82   (EXPR_SIGNED (e)                                                      \
  83    ? _GL_SIGNED_INT_MAXIMUM (e)                                         \
  84    : _GL_INT_NEGATE_CONVERT (e, 1))
  85 #define _GL_SIGNED_INT_MAXIMUM(e)                                       \
  86   (((_GL_INT_CONVERT (e, 1) << (sizeof ((e) + 0) * CHAR_BIT - 2)) - 1) * 2 + 1)
  87
  88
  89 /* Return 1 if the __typeof__ keyword works.  This could be done by
  90    'configure', but for now it's easier to do it by hand.  */
  91 #if (2 <= __GNUC__ || defined __IBM__TYPEOF__ \
  92      || (0x5110 <= __SUNPRO_C && !__STDC__))
  93 # define _GL_HAVE___TYPEOF__ 1
  94 #else
  95 # define _GL_HAVE___TYPEOF__ 0
  96 #endif
  97
  98 /* Return 1 if the integer type or expression T might be signed.  Return 0
  99    if it is definitely unsigned.  This macro does not evaluate its argument,
 100    and expands to an 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    Subtract 1 for the sign bit if T is signed, and then add 1 more for
 114    a minus sign if needed.
 115
 116    Because _GL_SIGNED_TYPE_OR_EXPR sometimes returns 0 when its argument is
 117    signed, this macro may overestimate the true bound by one byte when
 118    applied to unsigned types of size 2, 4, 16, ... bytes.  */
 119 #define INT_STRLEN_BOUND(t)                                     \
 120   (INT_BITS_STRLEN_BOUND (sizeof (t) * CHAR_BIT                 \
 121                           - _GL_SIGNED_TYPE_OR_EXPR (t))        \
 122    + _GL_SIGNED_TYPE_OR_EXPR (t))
 123
 124 /* Bound on buffer size needed to represent an integer type or expression T,
 125    including the terminating null.  */
 126 #define INT_BUFSIZE_BOUND(t) (INT_STRLEN_BOUND (t) + 1)
 127
 128
 129 /* Range overflow checks.
 130
 131    The INT_<op>_RANGE_OVERFLOW macros return 1 if the corresponding C
 132    operators might not yield numerically correct answers due to
 133    arithmetic overflow.  They do not rely on undefined or
 134    implementation-defined behavior.  Their implementations are simple
 135    and straightforward, but they are a bit harder to use than the
 136    INT_<op>_OVERFLOW macros described below.
 137
 138    Example usage:
 139
 140      long int i = ...;
 141      long int j = ...;
 142      if (INT_MULTIPLY_RANGE_OVERFLOW (i, j, LONG_MIN, LONG_MAX))
 143        printf ("multiply would overflow");
 144      else
 145        printf ("product is %ld", i * j);
 146
 147    Restrictions on *_RANGE_OVERFLOW macros:
 148
 149    These macros do not check for all possible numerical problems or
 150    undefined or unspecified behavior: they do not check for division
 151    by zero, for bad shift counts, or for shifting negative numbers.
 152
 153    These macros may evaluate their arguments zero or multiple times,
 154    so the arguments should not have side effects.  The arithmetic
 155    arguments (including the MIN and MAX arguments) must be of the same
 156    integer type after the usual arithmetic conversions, and the type
 157    must have minimum value MIN and maximum MAX.  Unsigned types should
 158    use a zero MIN of the proper type.
 159
 160    These macros are tuned for constant MIN and MAX.  For commutative
 161    operations such as A + B, they are also tuned for constant B.  */
 162
 163 /* Return 1 if A + B would overflow in [MIN,MAX] arithmetic.
 164    See above for restrictions.  */
 165 #define INT_ADD_RANGE_OVERFLOW(a, b, min, max)          \
 166   ((b) < 0                                              \
 167    ? (a) < (min) - (b)                                  \
 168    : (max) - (b) < (a))
 169
 170 /* Return 1 if A - B would overflow in [MIN,MAX] arithmetic.
 171    See above for restrictions.  */
 172 #define INT_SUBTRACT_RANGE_OVERFLOW(a, b, min, max)     \
 173   ((b) < 0                                              \
 174    ? (max) + (b) < (a)                                  \
 175    : (a) < (min) + (b))
 176
 177 /* Return 1 if - A would overflow in [MIN,MAX] arithmetic.
 178    See above for restrictions.  */
 179 #define INT_NEGATE_RANGE_OVERFLOW(a, min, max)          \
 180   ((min) < 0                                            \
 181    ? (a) < - (max)                                      \
 182    : 0 < (a))
 183
 184 /* Return 1 if A * B would overflow in [MIN,MAX] arithmetic.
 185    See above for restrictions.  Avoid && and || as they tickle
 186    bugs in Sun C 5.11 2010/08/13 and other compilers; see
 187    <http://lists.gnu.org/archive/html/bug-gnulib/2011-05/msg00401.html>.  */
 188 #define INT_MULTIPLY_RANGE_OVERFLOW(a, b, min, max)     \
 189   ((b) < 0                                              \
 190    ? ((a) < 0                                           \
 191       ? (a) < (max) / (b)                               \
 192       : (b) == -1                                       \
 193       ? 0                                               \
 194       : (min) / (b) < (a))                              \
 195    : (b) == 0                                           \
 196    ? 0                                                  \
 197    : ((a) < 0                                           \
 198       ? (a) < (min) / (b)                               \
 199       : (max) / (b) < (a)))
 200
 201 /* Return 1 if A / B would overflow in [MIN,MAX] arithmetic.
 202    See above for restrictions.  Do not check for division by zero.  */
 203 #define INT_DIVIDE_RANGE_OVERFLOW(a, b, min, max)       \
 204   ((min) < 0 && (b) == -1 && (a) < - (max))
 205
 206 /* Return 1 if A % B would overflow in [MIN,MAX] arithmetic.
 207    See above for restrictions.  Do not check for division by zero.
 208    Mathematically, % should never overflow, but on x86-like hosts
 209    INT_MIN % -1 traps, and the C standard permits this, so treat this
 210    as an overflow too.  */
 211 #define INT_REMAINDER_RANGE_OVERFLOW(a, b, min, max)    \
 212   INT_DIVIDE_RANGE_OVERFLOW (a, b, min, max)
 213
 214 /* Return 1 if A << B would overflow in [MIN,MAX] arithmetic.
 215    See above for restrictions.  Here, MIN and MAX are for A only, and B need
 216    not be of the same type as the other arguments.  The C standard says that
 217    behavior is undefined for shifts unless 0 <= B < wordwidth, and that when
 218    A is negative then A << B has undefined behavior and A >> B has
 219    implementation-defined behavior, but do not check these other
 220    restrictions.  */
 221 #define INT_LEFT_SHIFT_RANGE_OVERFLOW(a, b, min, max)   \
 222   ((a) < 0                                              \
 223    ? (a) < (min) >> (b)                                 \
 224    : (max) >> (b) < (a))
 225
 226
 227 /* The _GL*_OVERFLOW macros have the same restrictions as the
 228    *_RANGE_OVERFLOW macros, except that they do not assume that operands
 229    (e.g., A and B) have the same type as MIN and MAX.  Instead, they assume
 230    that the result (e.g., A + B) has that type.  */
 231 #define _GL_ADD_OVERFLOW(a, b, min, max)                                \
 232   ((min) < 0 ? INT_ADD_RANGE_OVERFLOW (a, b, min, max)                  \
 233    : (a) < 0 ? (b) <= (a) + (b)                                         \
 234    : (b) < 0 ? (a) <= (a) + (b)                                         \
 235    : (a) + (b) < (b))
 236 #define _GL_SUBTRACT_OVERFLOW(a, b, min, max)                           \
 237   ((min) < 0 ? INT_SUBTRACT_RANGE_OVERFLOW (a, b, min, max)             \
 238    : (a) < 0 ? 1                                                        \
 239    : (b) < 0 ? (a) - (b) <= (a)                                         \
 240    : (a) < (b))
 241 #define _GL_MULTIPLY_OVERFLOW(a, b, min, max)                           \
 242   (((min) == 0 && (((a) < 0 && 0 < (b)) || ((b) < 0 && 0 < (a))))       \
 243    || INT_MULTIPLY_RANGE_OVERFLOW (a, b, min, max))
 244 #define _GL_DIVIDE_OVERFLOW(a, b, min, max)                             \
 245   ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max)  \
 246    : (a) < 0 ? (b) <= (a) + (b) - 1                                     \
 247    : (b) < 0 && (a) + (b) <= (a))
 248 #define _GL_REMAINDER_OVERFLOW(a, b, min, max)                          \
 249   ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max)  \
 250    : (a) < 0 ? (a) % (b) != ((max) - (b) + 1) % (b)                     \
 251    : (b) < 0 && ! _GL_UNSIGNED_NEG_MULTIPLE (a, b, max))
 252
 253 /* Return a nonzero value if A is a mathematical multiple of B, where
 254    A is unsigned, B is negative, and MAX is the maximum value of A's
 255    type.  A's type must be the same as (A % B)'s type.  Normally (A %
 256    -B == 0) suffices, but things get tricky if -B would overflow.  */
 257 #define _GL_UNSIGNED_NEG_MULTIPLE(a, b, max)                            \
 258   (((b) < -_GL_SIGNED_INT_MAXIMUM (b)                                   \
 259     ? (_GL_SIGNED_INT_MAXIMUM (b) == (max)                              \
 260        ? (a)                                                            \
 261        : (a) % (_GL_INT_CONVERT (a, _GL_SIGNED_INT_MAXIMUM (b)) + 1))   \
 262     : (a) % - (b))                                                      \
 263    == 0)
 264
 265 /* Check for integer overflow, and report low order bits of answer.
 266
 267    The INT_<op>_OVERFLOW macros return 1 if the corresponding C operators
 268    might not yield numerically correct answers due to arithmetic overflow.
 269    The INT_<op>_WRAPV macros also store the low-order bits of the answer.
 270    These macros work correctly on all known practical hosts, and do not rely
 271    on undefined behavior due to signed arithmetic overflow.
 272
 273    Example usage, assuming A and B are long int:
 274
 275      long int result = INT_MULTIPLY_WRAPV (a, b);
 276      printf ("result is %ld (%s)\n", result,
 277              INT_MULTIPLY_OVERFLOW (a, b) ? "after overflow" : "no overflow");
 278
 279    Example usage with WRAPV flavor:
 280
 281      long int result;
 282      bool overflow = INT_MULTIPLY_WRAPV (a, b, &result);
 283      printf ("result is %ld (%s)\n", result,
 284              overflow ? "after overflow" : "no overflow");
 285
 286    Restrictions on these macros:
 287
 288    These macros do not check for all possible numerical problems or
 289    undefined or unspecified behavior: they do not check for division
 290    by zero, for bad shift counts, or for shifting negative numbers.
 291
 292    These macros may evaluate their arguments zero or multiple times, so the
 293    arguments should not have side effects.
 294
 295    The WRAPV macros are not constant expressions.  They support only
 296    +, binary -, and *.  The result type must be signed.
 297
 298    These macros are tuned for their last argument being a constant.
 299
 300    Return 1 if the integer expressions A * B, A - B, -A, A * B, A / B,
 301    A % B, and A << B would overflow, respectively.  */
 302
 303 #define INT_ADD_OVERFLOW(a, b) \
 304   _GL_BINARY_OP_OVERFLOW (a, b, _GL_ADD_OVERFLOW)
 305 #define INT_SUBTRACT_OVERFLOW(a, b) \
 306   _GL_BINARY_OP_OVERFLOW (a, b, _GL_SUBTRACT_OVERFLOW)
 307 #define INT_NEGATE_OVERFLOW(a) \
 308   INT_NEGATE_RANGE_OVERFLOW (a, _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
 309 #define INT_MULTIPLY_OVERFLOW(a, b) \
 310   _GL_BINARY_OP_OVERFLOW (a, b, _GL_MULTIPLY_OVERFLOW)
 311 #define INT_DIVIDE_OVERFLOW(a, b) \
 312   _GL_BINARY_OP_OVERFLOW (a, b, _GL_DIVIDE_OVERFLOW)
 313 #define INT_REMAINDER_OVERFLOW(a, b) \
 314   _GL_BINARY_OP_OVERFLOW (a, b, _GL_REMAINDER_OVERFLOW)
 315 #define INT_LEFT_SHIFT_OVERFLOW(a, b) \
 316   INT_LEFT_SHIFT_RANGE_OVERFLOW (a, b, \
 317                                  _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
 318
 319 /* Return 1 if the expression A <op> B would overflow,
 320    where OP_RESULT_OVERFLOW (A, B, MIN, MAX) does the actual test,
 321    assuming MIN and MAX are the minimum and maximum for the result type.
 322    Arguments should be free of side effects.  */
 323 #define _GL_BINARY_OP_OVERFLOW(a, b, op_result_overflow)        \
 324   op_result_overflow (a, b,                                     \
 325                       _GL_INT_MINIMUM (0 * (b) + (a)),          \
 326                       _GL_INT_MAXIMUM (0 * (b) + (a)))
 327
 328 /* Compute A + B, A - B, A * B, respectively, storing the result into *R.
 329    Return 1 if the result overflows.  See above for restrictions.  */
 330 #define INT_ADD_WRAPV(a, b, r) \
 331   _GL_INT_OP_WRAPV (a, b, r, +, __builtin_add_overflow, INT_ADD_OVERFLOW)
 332 #define INT_SUBTRACT_WRAPV(a, b, r) \
 333   _GL_INT_OP_WRAPV (a, b, r, -, __builtin_sub_overflow, INT_SUBTRACT_OVERFLOW)
 334 #define INT_MULTIPLY_WRAPV(a, b, r) \
 335   _GL_INT_OP_WRAPV (a, b, r, *, __builtin_mul_overflow, INT_MULTIPLY_OVERFLOW)
 336
 337 #ifndef __has_builtin
 338 # define __has_builtin(x) 0
 339 #endif
 340
 341 /* Nonzero if this compiler has GCC bug 68193 or Clang bug 25390.  See:
 342    https://gcc.gnu.org/bugzilla/show_bug.cgi?id=68193
 343    https://llvm.org/bugs/show_bug.cgi?id=25390
 344    For now, assume all versions of GCC-like compilers generate bogus
 345    warnings for _Generic.  This matters only for older compilers that
 346    lack __builtin_add_overflow.  */
 347 #if __GNUC__
 348 # define _GL__GENERIC_BOGUS 1
 349 #else
 350 # define _GL__GENERIC_BOGUS 0
 351 #endif
 352
 353 /* Store A <op> B into *R, where OP specifies the operation.
 354    BUILTIN is the builtin operation, and OVERFLOW the overflow predicate.
 355    See above for restrictions.  */
 356 #if 5 <= __GNUC__ || __has_builtin (__builtin_add_overflow)
 357 # define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) builtin (a, b, r)
 358 #elif 201112 <= __STDC_VERSION__ && !_GL__GENERIC_BOGUS
 359 # define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) \
 360    (_Generic \
 361     (*(r), \
 362      signed char: \
 363        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned char, \
 364                         signed char, SCHAR_MIN, SCHAR_MAX), \
 365      short int: \
 366        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned short int, \
 367                         short int, SHRT_MIN, SHRT_MAX), \
 368      int: \
 369        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 370                         int, INT_MIN, INT_MAX), \
 371      long int: \
 372        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 373                         long int, LONG_MIN, LONG_MAX), \
 374      long long int: \
 375        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
 376                         long long int, LLONG_MIN, LLONG_MAX)))
 377 #else
 378 # define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) \
 379    (sizeof *(r) == sizeof (signed char) \
 380     ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned char, \
 381                        signed char, SCHAR_MIN, SCHAR_MAX) \
 382     : sizeof *(r) == sizeof (short int) \
 383     ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned short int, \
 384                        short int, SHRT_MIN, SHRT_MAX) \
 385     : sizeof *(r) == sizeof (int) \
 386     ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 387                        int, INT_MIN, INT_MAX) \
 388     : _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow))
 389 # ifdef LLONG_MAX
 390 #  define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
 391     (sizeof *(r) == sizeof (long int) \
 392      ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 393                         long int, LONG_MIN, LONG_MAX) \
 394      : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
 395                         long long int, LLONG_MIN, LLONG_MAX))
 396 # else
 397 #  define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
 398     _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 399                      long int, LONG_MIN, LONG_MAX))
 400 # endif
 401 #endif
 402
 403 /* Store the low-order bits of A <op> B into *R, where the operation
 404    is given by OP.  Use the unsigned type UT for calculation to avoid
 405    overflow problems.  *R's type is T, with extremal values TMIN and
 406    TMAX.  T must be a signed integer type.  */
 407 #define _GL_INT_OP_CALC(a, b, r, op, overflow, ut, t, tmin, tmax) \
 408   (sizeof ((a) op (b)) < sizeof (t) \
 409    ? _GL_INT_OP_CALC1 ((t) (a), (t) (b), r, op, overflow, ut, t, tmin, tmax) \
 410    : _GL_INT_OP_CALC1 (a, b, r, op, overflow, ut, t, tmin, tmax))
 411 #define _GL_INT_OP_CALC1(a, b, r, op, overflow, ut, t, tmin, tmax) \
 412   ((overflow (a, b) \
 413     || (EXPR_SIGNED ((a) op (b)) && ((a) op (b)) < (tmin)) \
 414     || (tmax) < ((a) op (b))) \
 415    ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t, tmin, tmax), 1) \
 416    : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t, tmin, tmax), 0))
 417
 418 /* Return A <op> B, where the operation is given by OP.  Use the
 419    unsigned type UT for calculation to avoid overflow problems.
 420    Convert the result to type T without overflow by subtracting TMIN
 421    from large values before converting, and adding it afterwards.
 422    Compilers can optimize all the operations except OP.  */
 423 #define _GL_INT_OP_WRAPV_VIA_UNSIGNED(a, b, op, ut, t, tmin, tmax) \
 424   (((ut) (a) op (ut) (b)) <= (tmax) \
 425    ? (t) ((ut) (a) op (ut) (b)) \
 426    : ((t) (((ut) (a) op (ut) (b)) - (tmin)) + (tmin)))
 427
 428 #endif /* _GL_INTPROPS_H */