code.delx.au - gnu-emacs/blob - 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 an integer value, converted to the same type as the integer
  26    expression E after integer type promotion.  V is the unconverted value.  */
  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 negative values of the signed integer type T use two's
  41    complement, ones' complement, or signed magnitude representation,
  42    respectively.  Much GNU code assumes two's complement, but some
  43    people like to be portable to all possible C hosts.  */
  44 #define TYPE_TWOS_COMPLEMENT(t) ((t) ~ (t) 0 == (t) -1)
  45 #define TYPE_ONES_COMPLEMENT(t) ((t) ~ (t) 0 == 0)
  46 #define TYPE_SIGNED_MAGNITUDE(t) ((t) ~ (t) 0 < (t) -1)
  47
  48 /* True if the signed integer expression E uses two's complement.  */
  49 #define _GL_INT_TWOS_COMPLEMENT(e) (~ _GL_INT_CONVERT (e, 0) == -1)
  50
  51 /* True if the arithmetic type T is signed.  */
  52 #define TYPE_SIGNED(t) (! ((t) 0 < (t) -1))
  53
  54 /* Return 1 if the integer expression E, after integer promotion, has
  55    a signed type.  */
  56 #define _GL_INT_SIGNED(e) (_GL_INT_NEGATE_CONVERT (e, 1) < 0)
  57
  58
  59 /* Minimum and maximum values for integer types and expressions.  These
  60    macros have undefined behavior if T is signed and has padding bits.
  61    If this is a problem for you, please let us know how to fix it for
  62    your host.  */
  63
  64 /* The maximum and minimum values for the integer type T.  */
  65 #define TYPE_MINIMUM(t)                                                 \
  66   ((t) (! TYPE_SIGNED (t)                                               \
  67         ? (t) 0                                                         \
  68         : TYPE_SIGNED_MAGNITUDE (t)                                     \
  69         ? ~ (t) 0                                                       \
  70         : ~ TYPE_MAXIMUM (t)))
  71 #define TYPE_MAXIMUM(t)                                                 \
  72   ((t) (! TYPE_SIGNED (t)                                               \
  73         ? (t) -1                                                        \
  74         : ((((t) 1 << (sizeof (t) * CHAR_BIT - 2)) - 1) * 2 + 1)))
  75
  76 /* The maximum and minimum values for the type of the expression E,
  77    after integer promotion.  E should not have side effects.  */
  78 #define _GL_INT_MINIMUM(e)                                              \
  79   (_GL_INT_SIGNED (e)                                                   \
  80    ? - _GL_INT_TWOS_COMPLEMENT (e) - _GL_SIGNED_INT_MAXIMUM (e)         \
  81    : _GL_INT_CONVERT (e, 0))
  82 #define _GL_INT_MAXIMUM(e)                                              \
  83   (_GL_INT_SIGNED (e)                                                   \
  84    ? _GL_SIGNED_INT_MAXIMUM (e)                                         \
  85    : _GL_INT_NEGATE_CONVERT (e, 1))
  86 #define _GL_SIGNED_INT_MAXIMUM(e)                                       \
  87   (((_GL_INT_CONVERT (e, 1) << (sizeof ((e) + 0) * CHAR_BIT - 2)) - 1) * 2 + 1)
  88
  89
  90 /* Return 1 if the __typeof__ keyword works.  This could be done by
  91    'configure', but for now it's easier to do it by hand.  */
  92 #if (2 <= __GNUC__ || defined __IBM__TYPEOF__ \
  93      || (0x5110 <= __SUNPRO_C && !__STDC__))
  94 # define _GL_HAVE___TYPEOF__ 1
  95 #else
  96 # define _GL_HAVE___TYPEOF__ 0
  97 #endif
  98
  99 /* Return 1 if the integer type or expression T might be signed.  Return 0
 100    if it is definitely unsigned.  This macro does not evaluate its argument,
 101    and expands to an integer constant expression.  */
 102 #if _GL_HAVE___TYPEOF__
 103 # define _GL_SIGNED_TYPE_OR_EXPR(t) TYPE_SIGNED (__typeof__ (t))
 104 #else
 105 # define _GL_SIGNED_TYPE_OR_EXPR(t) 1
 106 #endif
 107
 108 /* Bound on length of the string representing an unsigned integer
 109    value representable in B bits.  log10 (2.0) < 146/485.  The
 110    smallest value of B where this bound is not tight is 2621.  */
 111 #define INT_BITS_STRLEN_BOUND(b) (((b) * 146 + 484) / 485)
 112
 113 /* Bound on length of the string representing an integer type or expression T.
 114    Subtract 1 for the sign bit if T is signed, and then add 1 more for
 115    a minus sign if needed.
 116
 117    Because _GL_SIGNED_TYPE_OR_EXPR sometimes returns 0 when its argument is
 118    signed, this macro may overestimate the true bound by one byte when
 119    applied to unsigned types of size 2, 4, 16, ... bytes.  */
 120 #define INT_STRLEN_BOUND(t)                                     \
 121   (INT_BITS_STRLEN_BOUND (sizeof (t) * CHAR_BIT                 \
 122                           - _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.  */
 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    <http://lists.gnu.org/archive/html/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
 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 #define _GL_ADD_OVERFLOW(a, b, min, max)                                \
 233   ((min) < 0 ? INT_ADD_RANGE_OVERFLOW (a, b, min, max)                  \
 234    : (a) < 0 ? (b) <= (a) + (b)                                         \
 235    : (b) < 0 ? (a) <= (a) + (b)                                         \
 236    : (a) + (b) < (b))
 237 #define _GL_SUBTRACT_OVERFLOW(a, b, min, max)                           \
 238   ((min) < 0 ? INT_SUBTRACT_RANGE_OVERFLOW (a, b, min, max)             \
 239    : (a) < 0 ? 1                                                        \
 240    : (b) < 0 ? (a) - (b) <= (a)                                         \
 241    : (a) < (b))
 242 #define _GL_MULTIPLY_OVERFLOW(a, b, min, max)                           \
 243   (((min) == 0 && (((a) < 0 && 0 < (b)) || ((b) < 0 && 0 < (a))))       \
 244    || INT_MULTIPLY_RANGE_OVERFLOW (a, b, min, max))
 245 #define _GL_DIVIDE_OVERFLOW(a, b, min, max)                             \
 246   ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max)  \
 247    : (a) < 0 ? (b) <= (a) + (b) - 1                                     \
 248    : (b) < 0 && (a) + (b) <= (a))
 249 #define _GL_REMAINDER_OVERFLOW(a, b, min, max)                          \
 250   ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max)  \
 251    : (a) < 0 ? (a) % (b) != ((max) - (b) + 1) % (b)                     \
 252    : (b) < 0 && ! _GL_UNSIGNED_NEG_MULTIPLE (a, b, max))
 253
 254 /* Return a nonzero value if A is a mathematical multiple of B, where
 255    A is unsigned, B is negative, and MAX is the maximum value of A's
 256    type.  A's type must be the same as (A % B)'s type.  Normally (A %
 257    -B == 0) suffices, but things get tricky if -B would overflow.  */
 258 #define _GL_UNSIGNED_NEG_MULTIPLE(a, b, max)                            \
 259   (((b) < -_GL_SIGNED_INT_MAXIMUM (b)                                   \
 260     ? (_GL_SIGNED_INT_MAXIMUM (b) == (max)                              \
 261        ? (a)                                                            \
 262        : (a) % (_GL_INT_CONVERT (a, _GL_SIGNED_INT_MAXIMUM (b)) + 1))   \
 263     : (a) % - (b))                                                      \
 264    == 0)
 265
 266 /* Check for integer overflow, and report low order bits of answer.
 267
 268    The INT_<op>_OVERFLOW macros return 1 if the corresponding C operators
 269    might not yield numerically correct answers due to arithmetic overflow.
 270    The INT_<op>_WRAPV macros also store the low-order bits of the answer.
 271    These macros work correctly on all known practical hosts, and do not rely
 272    on undefined behavior due to signed arithmetic overflow.
 273
 274    Example usage, assuming A and B are long int:
 275
 276      long int result = INT_MULTIPLY_WRAPV (a, b);
 277      printf ("result is %ld (%s)\n", result,
 278              INT_MULTIPLY_OVERFLOW (a, b) ? "after overflow" : "no overflow");
 279
 280    Example usage with WRAPV flavor:
 281
 282      long int result;
 283      bool overflow = INT_MULTIPLY_WRAPV (a, b, &result);
 284      printf ("result is %ld (%s)\n", result,
 285              overflow ? "after overflow" : "no overflow");
 286
 287    Restrictions on these macros:
 288
 289    These macros do not check for all possible numerical problems or
 290    undefined or unspecified behavior: they do not check for division
 291    by zero, for bad shift counts, or for shifting negative numbers.
 292
 293    These macros may evaluate their arguments zero or multiple times, so the
 294    arguments should not have side effects.
 295
 296    The WRAPV macros are not constant expressions.  They support only
 297    +, binary -, and *.  The result type must be signed.
 298
 299    These macros are tuned for their last argument being a constant.
 300
 301    Return 1 if the integer expressions A * B, A - B, -A, A * B, A / B,
 302    A % B, and A << B would overflow, respectively.  */
 303
 304 #define INT_ADD_OVERFLOW(a, b) \
 305   _GL_BINARY_OP_OVERFLOW (a, b, _GL_ADD_OVERFLOW)
 306 #define INT_SUBTRACT_OVERFLOW(a, b) \
 307   _GL_BINARY_OP_OVERFLOW (a, b, _GL_SUBTRACT_OVERFLOW)
 308 #define INT_NEGATE_OVERFLOW(a) \
 309   INT_NEGATE_RANGE_OVERFLOW (a, _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
 310 #define INT_MULTIPLY_OVERFLOW(a, b) \
 311   _GL_BINARY_OP_OVERFLOW (a, b, _GL_MULTIPLY_OVERFLOW)
 312 #define INT_DIVIDE_OVERFLOW(a, b) \
 313   _GL_BINARY_OP_OVERFLOW (a, b, _GL_DIVIDE_OVERFLOW)
 314 #define INT_REMAINDER_OVERFLOW(a, b) \
 315   _GL_BINARY_OP_OVERFLOW (a, b, _GL_REMAINDER_OVERFLOW)
 316 #define INT_LEFT_SHIFT_OVERFLOW(a, b) \
 317   INT_LEFT_SHIFT_RANGE_OVERFLOW (a, b, \
 318                                  _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
 319
 320 /* Return 1 if the expression A <op> B would overflow,
 321    where OP_RESULT_OVERFLOW (A, B, MIN, MAX) does the actual test,
 322    assuming MIN and MAX are the minimum and maximum for the result type.
 323    Arguments should be free of side effects.  */
 324 #define _GL_BINARY_OP_OVERFLOW(a, b, op_result_overflow)        \
 325   op_result_overflow (a, b,                                     \
 326                       _GL_INT_MINIMUM (0 * (b) + (a)),          \
 327                       _GL_INT_MAXIMUM (0 * (b) + (a)))
 328
 329 /* Compute A + B, A - B, A * B, respectively, storing the result into *R.
 330    Return 1 if the result overflows.  See above for restrictions.  */
 331 #define INT_ADD_WRAPV(a, b, r) \
 332   _GL_INT_OP_WRAPV (a, b, r, +, __builtin_add_overflow, INT_ADD_OVERFLOW)
 333 #define INT_SUBTRACT_WRAPV(a, b, r) \
 334   _GL_INT_OP_WRAPV (a, b, r, -, __builtin_sub_overflow, INT_SUBTRACT_OVERFLOW)
 335 #define INT_MULTIPLY_WRAPV(a, b, r) \
 336   _GL_INT_OP_WRAPV (a, b, r, *, __builtin_mul_overflow, INT_MULTIPLY_OVERFLOW)
 337
 338 #ifndef __has_builtin
 339 # define __has_builtin(x) 0
 340 #endif
 341
 342 /* Nonzero if this compiler has GCC bug 68193 or Clang bug 25390.  See:
 343    https://gcc.gnu.org/bugzilla/show_bug.cgi?id=68193
 344    https://llvm.org/bugs/show_bug.cgi?id=25390
 345    For now, assume all versions of GCC-like compilers generate bogus
 346    warnings for _Generic.  This matters only for older compilers that
 347    lack __builtin_add_overflow.  */
 348 #if __GNUC__
 349 # define _GL__GENERIC_BOGUS 1
 350 #else
 351 # define _GL__GENERIC_BOGUS 0
 352 #endif
 353
 354 /* Store A <op> B into *R, where OP specifies the operation.
 355    BUILTIN is the builtin operation, and OVERFLOW the overflow predicate.
 356    See above for restrictions.  */
 357 #if 5 <= __GNUC__ || __has_builtin (__builtin_add_oveflow)
 358 # define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) builtin (a, b, r)
 359 #elif 201112 <= __STDC_VERSION__ && !_GL__GENERIC_BOGUS
 360 # define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) \
 361    (_Generic \
 362     (*(r), \
 363      signed char: \
 364        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned char, \
 365                         signed char, SCHAR_MIN, SCHAR_MAX), \
 366      short int: \
 367        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned short int, \
 368                         short int, SHRT_MIN, SHRT_MAX), \
 369      int: \
 370        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 371                         int, INT_MIN, INT_MAX), \
 372      long int: \
 373        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 374                         long int, LONG_MIN, LONG_MAX), \
 375      long long int: \
 376        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
 377                         long long int, LLONG_MIN, LLONG_MAX)))
 378 #else
 379 # define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) \
 380    (sizeof *(r) == sizeof (signed char) \
 381     ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned char, \
 382                        signed char, SCHAR_MIN, SCHAR_MAX) \
 383     : sizeof *(r) == sizeof (short int) \
 384     ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned short int, \
 385                        short int, SHRT_MIN, SHRT_MAX) \
 386     : sizeof *(r) == sizeof (int) \
 387     ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 388                        int, INT_MIN, INT_MAX) \
 389     : _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow))
 390 # ifdef LLONG_MAX
 391 #  define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
 392     (sizeof *(r) == sizeof (long int) \
 393      ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 394                         long int, LONG_MIN, LONG_MAX) \
 395      : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
 396                         long long int, LLONG_MIN, LLONG_MAX))
 397 # else
 398 #  define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
 399     _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 400                      long int, LONG_MIN, LONG_MAX))
 401 # endif
 402 #endif
 403
 404 /* Store the low-order bits of A <op> B into *R, where the operation
 405    is given by OP.  Use the unsigned type UT for calculation to avoid
 406    overflow problems.  *R's type is T, with extremal values TMIN and
 407    TMAX.  T must be a signed integer type.  */
 408 #define _GL_INT_OP_CALC(a, b, r, op, overflow, ut, t, tmin, tmax) \
 409   (sizeof ((a) op (b)) < sizeof (t) \
 410    ? _GL_INT_OP_CALC1 ((t) (a), (t) (b), r, op, overflow, ut, t, tmin, tmax) \
 411    : _GL_INT_OP_CALC1 (a, b, r, op, overflow, ut, t, tmin, tmax))
 412 #define _GL_INT_OP_CALC1(a, b, r, op, overflow, ut, t, tmin, tmax) \
 413   ((overflow (a, b) \
 414     || (_GL_INT_SIGNED ((a) op (b)) && ((a) op (b)) < (tmin)) \
 415     || (tmax) < ((a) op (b))) \
 416    ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t, tmin, tmax), 1) \
 417    : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t, tmin, tmax), 0))
 418
 419 /* Return A <op> B, where the operation is given by OP.  Use the
 420    unsigned type UT for calculation to avoid overflow problems.
 421    Convert the result to type T without overflow by subtracting TMIN
 422    from large values before converting, and adding it afterwards.
 423    Compilers can optimize all the operations except OP.  */
 424 #define _GL_INT_OP_WRAPV_VIA_UNSIGNED(a, b, op, ut, t, tmin, tmax) \
 425   (((ut) (a) op (ut) (b)) <= (tmax) \
 426    ? (t) ((ut) (a) op (ut) (b)) \
 427    : ((t) (((ut) (a) op (ut) (b)) - (tmin)) + (tmin)))
 428
 429 #endif /* _GL_INTPROPS_H */