lib/intprops-internal.h

   1 /* intprops-internal.h -- properties of integer types not visible to users
   2
   3    Copyright (C) 2001-2024 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 Lesser General Public License as published
   7    by the Free Software Foundation; either version 2.1 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 Lesser General Public License for more details.
  14
  15    You should have received a copy of the GNU Lesser General Public License
  16    along with this program.  If not, see <https://www.gnu.org/licenses/>.  */
  17
  18 #ifndef _GL_INTPROPS_INTERNAL_H
  19 #define _GL_INTPROPS_INTERNAL_H
  20
  21 #include <limits.h>
  22
  23 /* Pacify GCC 13.2 in some calls to _GL_EXPR_SIGNED.  */
  24 #if defined __GNUC__ && 4 < __GNUC__ + (3 <= __GNUC_MINOR__)
  25 # pragma GCC diagnostic ignored "-Wtype-limits"
  26 #endif
  27
  28 /* Return a value with the common real type of E and V and the value of V.
  29    Do not evaluate E.  */
  30 #define _GL_INT_CONVERT(e, v) ((1 ? 0 : (e)) + (v))
  31
  32 /* Act like _GL_INT_CONVERT (E, -V) but work around a bug in IRIX 6.5 cc; see
  33    <https://lists.gnu.org/r/bug-gnulib/2011-05/msg00406.html>.  */
  34 #define _GL_INT_NEGATE_CONVERT(e, v) ((1 ? 0 : (e)) - (v))
  35
  36 /* The extra casts in the following macros work around compiler bugs,
  37    e.g., in Cray C 5.0.3.0.  */
  38
  39 /* True if the real type T is signed.  */
  40 #define _GL_TYPE_SIGNED(t) (! ((t) 0 < (t) -1))
  41
  42 /* Return 1 if the real expression E, after promotion, has a
  43    signed or floating type.  Do not evaluate E.  */
  44 #define _GL_EXPR_SIGNED(e) (_GL_INT_NEGATE_CONVERT (e, 1) < 0)
  45
  46
  47 /* Minimum and maximum values for integer types and expressions.  */
  48
  49 /* The width in bits of the integer type or expression T.
  50    Do not evaluate T.  T must not be a bit-field expression.
  51    Padding bits are not supported; this is checked at compile-time below.  */
  52 #define _GL_TYPE_WIDTH(t) (sizeof (t) * CHAR_BIT)
  53
  54 /* The maximum and minimum values for the type of the expression E,
  55    after integer promotion.  E is not evaluated.  */
  56 #define _GL_INT_MINIMUM(e)                                              \
  57   (_GL_EXPR_SIGNED (e)                                                  \
  58    ? ~ _GL_SIGNED_INT_MAXIMUM (e)                                       \
  59    : _GL_INT_CONVERT (e, 0))
  60 #define _GL_INT_MAXIMUM(e)                                              \
  61   (_GL_EXPR_SIGNED (e)                                                  \
  62    ? _GL_SIGNED_INT_MAXIMUM (e)                                         \
  63    : _GL_INT_NEGATE_CONVERT (e, 1))
  64 #define _GL_SIGNED_INT_MAXIMUM(e)                                       \
  65   (((_GL_INT_CONVERT (e, 1) << (_GL_TYPE_WIDTH (+ (e)) - 2)) - 1) * 2 + 1)
  66
  67 /* Work around OpenVMS incompatibility with C99.  */
  68 #if !defined LLONG_MAX && defined __INT64_MAX
  69 # define LLONG_MAX __INT64_MAX
  70 # define LLONG_MIN __INT64_MIN
  71 #endif
  72
  73 /* This include file assumes that signed types are two's complement without
  74    padding bits; the above macros have undefined behavior otherwise.
  75    If this is a problem for you, please let us know how to fix it for your host.
  76    This assumption is tested by the intprops-tests module.  */
  77
  78 /* Does the __typeof__ keyword work?  This could be done by
  79    'configure', but for now it's easier to do it by hand.  */
  80 #if (2 <= __GNUC__ \
  81      || (4 <= __clang_major__) \
  82      || (1210 <= __IBMC__ && defined __IBM__TYPEOF__) \
  83      || (0x5110 <= __SUNPRO_C && !__STDC__))
  84 # define _GL_HAVE___TYPEOF__ 1
  85 #else
  86 # define _GL_HAVE___TYPEOF__ 0
  87 #endif
  88
  89 /* Return 1 if the integer type or expression T might be signed.  Return 0
  90    if it is definitely unsigned.  T must not be a bit-field expression.
  91    This macro does not evaluate its argument, and expands to an
  92    integer constant expression.  */
  93 #if _GL_HAVE___TYPEOF__
  94 # define _GL_SIGNED_TYPE_OR_EXPR(t) _GL_TYPE_SIGNED (__typeof__ (t))
  95 #else
  96 # define _GL_SIGNED_TYPE_OR_EXPR(t) 1
  97 #endif
  98
  99 /* Return 1 if - A would overflow in [MIN,MAX] arithmetic.
 100    A should not have side effects, and A's type should be an
 101    integer with minimum value MIN and maximum MAX.  */
 102 #define _GL_INT_NEGATE_RANGE_OVERFLOW(a, min, max) \
 103   ((min) < 0 ? (a) < - (max) : 0 < (a))
 104
 105 /* True if __builtin_add_overflow (A, B, P) and __builtin_sub_overflow
 106    (A, B, P) work when P is non-null.  */
 107 #ifdef __EDG__
 108 /* EDG-based compilers like nvc 22.1 cannot add 64-bit signed to unsigned
 109    <https://bugs.gnu.org/53256>.  */
 110 # define _GL_HAS_BUILTIN_ADD_OVERFLOW 0
 111 #elif defined __has_builtin
 112 # define _GL_HAS_BUILTIN_ADD_OVERFLOW __has_builtin (__builtin_add_overflow)
 113 /* __builtin_{add,sub}_overflow exists but is not reliable in GCC 5.x and 6.x,
 114    see <https://gcc.gnu.org/bugzilla/show_bug.cgi?id=98269>.  */
 115 #elif 7 <= __GNUC__
 116 # define _GL_HAS_BUILTIN_ADD_OVERFLOW 1
 117 #else
 118 # define _GL_HAS_BUILTIN_ADD_OVERFLOW 0
 119 #endif
 120
 121 /* True if __builtin_mul_overflow (A, B, P) works when P is non-null.  */
 122 #if defined __clang_major__ && __clang_major__ < 14
 123 /* Work around Clang bug <https://bugs.llvm.org/show_bug.cgi?id=16404>.  */
 124 # define _GL_HAS_BUILTIN_MUL_OVERFLOW 0
 125 #else
 126 # define _GL_HAS_BUILTIN_MUL_OVERFLOW _GL_HAS_BUILTIN_ADD_OVERFLOW
 127 #endif
 128
 129 /* True if __builtin_add_overflow_p (A, B, C) works, and similarly for
 130    __builtin_sub_overflow_p and __builtin_mul_overflow_p.  */
 131 #ifdef __EDG__
 132 /* In EDG-based compilers like ICC 2021.3 and earlier,
 133    __builtin_add_overflow_p etc. are not treated as integral constant
 134    expressions even when all arguments are.  */
 135 # define _GL_HAS_BUILTIN_OVERFLOW_P 0
 136 #elif defined __has_builtin
 137 # define _GL_HAS_BUILTIN_OVERFLOW_P __has_builtin (__builtin_mul_overflow_p)
 138 #else
 139 # define _GL_HAS_BUILTIN_OVERFLOW_P (7 <= __GNUC__)
 140 #endif
 141
 142 #if (!defined _GL_STDCKDINT_H && 202311 <= __STDC_VERSION__ \
 143      && ! (_GL_HAS_BUILTIN_ADD_OVERFLOW && _GL_HAS_BUILTIN_MUL_OVERFLOW))
 144 # include <stdckdint.h>
 145 #endif
 146
 147 /* Store the low-order bits of A + B, A - B, A * B, respectively, into *R.
 148    Return 1 if the result overflows.  Arguments should not have side
 149    effects and A, B and *R can be of any integer type other than char,
 150    bool, a bit-precise integer type, or an enumeration type.  */
 151 #if _GL_HAS_BUILTIN_ADD_OVERFLOW
 152 # define _GL_INT_ADD_WRAPV(a, b, r) __builtin_add_overflow (a, b, r)
 153 # define _GL_INT_SUBTRACT_WRAPV(a, b, r) __builtin_sub_overflow (a, b, r)
 154 #elif defined ckd_add && defined ckd_sub && !defined _GL_STDCKDINT_H
 155 # define _GL_INT_ADD_WRAPV(a, b, r) ckd_add (r, + (a), + (b))
 156 # define _GL_INT_SUBTRACT_WRAPV(a, b, r) ckd_sub (r, + (a), + (b))
 157 #else
 158 # define _GL_INT_ADD_WRAPV(a, b, r) \
 159    _GL_INT_OP_WRAPV (a, b, r, +, _GL_INT_ADD_RANGE_OVERFLOW)
 160 # define _GL_INT_SUBTRACT_WRAPV(a, b, r) \
 161    _GL_INT_OP_WRAPV (a, b, r, -, _GL_INT_SUBTRACT_RANGE_OVERFLOW)
 162 #endif
 163 #if _GL_HAS_BUILTIN_MUL_OVERFLOW
 164 # if ((9 < __GNUC__ + (3 <= __GNUC_MINOR__) \
 165        || (__GNUC__ == 8 && 4 <= __GNUC_MINOR__)) \
 166       && !defined __EDG__)
 167 #  define _GL_INT_MULTIPLY_WRAPV(a, b, r) __builtin_mul_overflow (a, b, r)
 168 # else
 169    /* Work around GCC bug 91450.  */
 170 #  define _GL_INT_MULTIPLY_WRAPV(a, b, r) \
 171     ((!_GL_SIGNED_TYPE_OR_EXPR (*(r)) && _GL_EXPR_SIGNED (a) && _GL_EXPR_SIGNED (b) \
 172       && _GL_INT_MULTIPLY_RANGE_OVERFLOW (a, b, \
 173                                           (__typeof__ (*(r))) 0, \
 174                                           (__typeof__ (*(r))) -1)) \
 175      ? ((void) __builtin_mul_overflow (a, b, r), 1) \
 176      : __builtin_mul_overflow (a, b, r))
 177 # endif
 178 #elif defined ckd_mul && !defined _GL_STDCKDINT_H
 179 # define _GL_INT_MULTIPLY_WRAPV(a, b, r) ckd_mul (r, + (a), + (b))
 180 #else
 181 # define _GL_INT_MULTIPLY_WRAPV(a, b, r) \
 182    _GL_INT_OP_WRAPV (a, b, r, *, _GL_INT_MULTIPLY_RANGE_OVERFLOW)
 183 #endif
 184
 185 /* Nonzero if this compiler has GCC bug 68193 or Clang bug 25390.  See:
 186    https://gcc.gnu.org/bugzilla/show_bug.cgi?id=68193
 187    https://llvm.org/bugs/show_bug.cgi?id=25390
 188    For now, assume all versions of GCC-like compilers generate bogus
 189    warnings for _Generic.  This matters only for compilers that
 190    lack relevant builtins.  */
 191 #if __GNUC__ || defined __clang__
 192 # define _GL__GENERIC_BOGUS 1
 193 #else
 194 # define _GL__GENERIC_BOGUS 0
 195 #endif
 196
 197 /* Store the low-order bits of A <op> B into *R, where OP specifies
 198    the operation and OVERFLOW the overflow predicate.  Return 1 if the
 199    result overflows.  Arguments should not have side effects,
 200    and A, B and *R can be of any integer type other than char, bool, a
 201    bit-precise integer type, or an enumeration type.  */
 202 #if 201112 <= __STDC_VERSION__ && !_GL__GENERIC_BOGUS
 203 # define _GL_INT_OP_WRAPV(a, b, r, op, overflow) \
 204    (_Generic \
 205     (*(r), \
 206      signed char: \
 207        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 208                         signed char, SCHAR_MIN, SCHAR_MAX), \
 209      unsigned char: \
 210        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 211                         unsigned char, 0, UCHAR_MAX), \
 212      short int: \
 213        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 214                         short int, SHRT_MIN, SHRT_MAX), \
 215      unsigned short int: \
 216        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 217                         unsigned short int, 0, USHRT_MAX), \
 218      int: \
 219        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 220                         int, INT_MIN, INT_MAX), \
 221      unsigned int: \
 222        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 223                         unsigned int, 0, UINT_MAX), \
 224      long int: \
 225        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 226                         long int, LONG_MIN, LONG_MAX), \
 227      unsigned long int: \
 228        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 229                         unsigned long int, 0, ULONG_MAX), \
 230      long long int: \
 231        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
 232                         long long int, LLONG_MIN, LLONG_MAX), \
 233      unsigned long long int: \
 234        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
 235                         unsigned long long int, 0, ULLONG_MAX)))
 236 #else
 237 /* Store the low-order bits of A <op> B into *R, where OP specifies
 238    the operation and OVERFLOW the overflow predicate.  If *R is
 239    signed, its type is ST with bounds SMIN..SMAX; otherwise its type
 240    is UT with bounds U..UMAX.  ST and UT are narrower than int.
 241    Return 1 if the result overflows.  Arguments should not have side
 242    effects, and A, B and *R can be of any integer type other than
 243    char, bool, a bit-precise integer type, or an enumeration type.  */
 244 # if _GL_HAVE___TYPEOF__
 245 #  define _GL_INT_OP_WRAPV_SMALLISH(a,b,r,op,overflow,st,smin,smax,ut,umax) \
 246     (_GL_TYPE_SIGNED (__typeof__ (*(r))) \
 247      ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, st, smin, smax) \
 248      : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, ut, 0, umax))
 249 # else
 250 #  define _GL_INT_OP_WRAPV_SMALLISH(a,b,r,op,overflow,st,smin,smax,ut,umax) \
 251     (overflow (a, b, smin, smax) \
 252      ? (overflow (a, b, 0, umax) \
 253         ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st), 1) \
 254         : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st)) < 0) \
 255      : (overflow (a, b, 0, umax) \
 256         ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st)) >= 0 \
 257         : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st), 0)))
 258 # endif
 259
 260 # define _GL_INT_OP_WRAPV(a, b, r, op, overflow) \
 261    (sizeof *(r) == sizeof (signed char) \
 262     ? _GL_INT_OP_WRAPV_SMALLISH (a, b, r, op, overflow, \
 263                                  signed char, SCHAR_MIN, SCHAR_MAX, \
 264                                  unsigned char, UCHAR_MAX) \
 265     : sizeof *(r) == sizeof (short int) \
 266     ? _GL_INT_OP_WRAPV_SMALLISH (a, b, r, op, overflow, \
 267                                  short int, SHRT_MIN, SHRT_MAX, \
 268                                  unsigned short int, USHRT_MAX) \
 269     : sizeof *(r) == sizeof (int) \
 270     ? (_GL_EXPR_SIGNED (*(r)) \
 271        ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 272                           int, INT_MIN, INT_MAX) \
 273        : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 274                           unsigned int, 0, UINT_MAX)) \
 275     : _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow))
 276 # ifdef LLONG_MAX
 277 #  define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
 278     (sizeof *(r) == sizeof (long int) \
 279      ? (_GL_EXPR_SIGNED (*(r)) \
 280         ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 281                            long int, LONG_MIN, LONG_MAX) \
 282         : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 283                            unsigned long int, 0, ULONG_MAX)) \
 284      : (_GL_EXPR_SIGNED (*(r)) \
 285         ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
 286                            long long int, LLONG_MIN, LLONG_MAX) \
 287         : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
 288                            unsigned long long int, 0, ULLONG_MAX)))
 289 # else
 290 #  define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
 291     (_GL_EXPR_SIGNED (*(r)) \
 292      ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 293                         long int, LONG_MIN, LONG_MAX) \
 294      : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 295                         unsigned long int, 0, ULONG_MAX))
 296 # endif
 297 #endif
 298
 299 /* Store the low-order bits of A <op> B into *R, where the operation
 300    is given by OP.  Use the unsigned type UT for calculation to avoid
 301    overflow problems.  *R's type is T, with extrema TMIN and TMAX.
 302    T can be any signed integer type other than char, bool, a
 303    bit-precise integer type, or an enumeration type.
 304    Return 1 if the result overflows.  */
 305 #define _GL_INT_OP_CALC(a, b, r, op, overflow, ut, t, tmin, tmax) \
 306   (overflow (a, b, tmin, tmax) \
 307    ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 1) \
 308    : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 0))
 309
 310 /* Return 1 if the integer expressions A - B and -A would overflow,
 311    respectively.  Arguments should not have side effects,
 312    and can be any signed integer type other than char, bool, a
 313    bit-precise integer type, or an enumeration type.
 314    These macros are tuned for their last input argument being a constant.  */
 315
 316 #if _GL_HAS_BUILTIN_OVERFLOW_P
 317 # define _GL_INT_NEGATE_OVERFLOW(a) \
 318    __builtin_sub_overflow_p (0, a, (__typeof__ (- (a))) 0)
 319 #else
 320 # define _GL_INT_NEGATE_OVERFLOW(a) \
 321    _GL_INT_NEGATE_RANGE_OVERFLOW (a, _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
 322 #endif
 323
 324 /* Return the low-order bits of A <op> B, where the operation is given
 325    by OP.  Use the unsigned type UT for calculation to avoid undefined
 326    behavior on signed integer overflow, and convert the result to type T.
 327    UT is at least as wide as T and is no narrower than unsigned int,
 328    T is two's complement, and there is no padding or trap representations.
 329    Assume that converting UT to T yields the low-order bits, as is
 330    done in all known two's-complement C compilers.  E.g., see:
 331    https://gcc.gnu.org/onlinedocs/gcc/Integers-implementation.html
 332
 333    According to the C standard, converting UT to T yields an
 334    implementation-defined result or signal for values outside T's
 335    range.  However, code that works around this theoretical problem
 336    runs afoul of a compiler bug in Oracle Studio 12.3 x86.  See:
 337    https://lists.gnu.org/r/bug-gnulib/2017-04/msg00049.html
 338    As the compiler bug is real, don't try to work around the
 339    theoretical problem.  */
 340
 341 #define _GL_INT_OP_WRAPV_VIA_UNSIGNED(a, b, op, ut, t) \
 342   ((t) ((ut) (a) op (ut) (b)))
 343
 344 /* Return true if the numeric values A + B, A - B, A * B fall outside
 345    the range TMIN..TMAX.  Arguments should not have side effects
 346    and can be any integer type other than char, bool,
 347    a bit-precise integer type, or an enumeration type.
 348    TMIN should be signed and nonpositive.
 349    TMAX should be positive, and should be signed unless TMIN is zero.  */
 350 #define _GL_INT_ADD_RANGE_OVERFLOW(a, b, tmin, tmax) \
 351   ((b) < 0 \
 352    ? (((tmin) \
 353        ? ((_GL_EXPR_SIGNED (_GL_INT_CONVERT (a, (tmin) - (b))) || (b) < (tmin)) \
 354           && (a) < (tmin) - (b)) \
 355        : (a) <= -1 - (b)) \
 356       || ((_GL_EXPR_SIGNED (a) ? 0 <= (a) : (tmax) < (a)) && (tmax) < (a) + (b))) \
 357    : (a) < 0 \
 358    ? (((tmin) \
 359        ? ((_GL_EXPR_SIGNED (_GL_INT_CONVERT (b, (tmin) - (a))) || (a) < (tmin)) \
 360           && (b) < (tmin) - (a)) \
 361        : (b) <= -1 - (a)) \
 362       || ((_GL_EXPR_SIGNED (_GL_INT_CONVERT (a, b)) || (tmax) < (b)) \
 363           && (tmax) < (a) + (b))) \
 364    : (tmax) < (b) || (tmax) - (b) < (a))
 365 #define _GL_INT_SUBTRACT_RANGE_OVERFLOW(a, b, tmin, tmax) \
 366   (((a) < 0) == ((b) < 0) \
 367    ? ((a) < (b) \
 368       ? !(tmin) || -1 - (tmin) < (b) - (a) - 1 \
 369       : (tmax) < (a) - (b)) \
 370    : (a) < 0 \
 371    ? ((!_GL_EXPR_SIGNED (_GL_INT_CONVERT ((a) - (tmin), b)) && (a) - (tmin) < 0) \
 372       || (a) - (tmin) < (b)) \
 373    : ((! (_GL_EXPR_SIGNED (_GL_INT_CONVERT (tmax, b)) \
 374           && _GL_EXPR_SIGNED (_GL_INT_CONVERT ((tmax) + (b), a))) \
 375        && (tmax) <= -1 - (b)) \
 376       || (tmax) + (b) < (a)))
 377 #define _GL_INT_MULTIPLY_RANGE_OVERFLOW(a, b, tmin, tmax) \
 378   ((b) < 0 \
 379    ? ((a) < 0 \
 380       ? (_GL_EXPR_SIGNED (_GL_INT_CONVERT (tmax, b)) \
 381          ? (a) < (tmax) / (b) \
 382          : ((_GL_INT_NEGATE_OVERFLOW (b) \
 383              ? _GL_INT_CONVERT (b, tmax) >> (_GL_TYPE_WIDTH (+ (b)) - 1) \
 384              : (tmax) / -(b)) \
 385             <= -1 - (a))) \
 386       : _GL_INT_NEGATE_OVERFLOW (_GL_INT_CONVERT (b, tmin)) && (b) == -1 \
 387       ? (_GL_EXPR_SIGNED (a) \
 388          ? 0 < (a) + (tmin) \
 389          : 0 < (a) && -1 - (tmin) < (a) - 1) \
 390       : (tmin) / (b) < (a)) \
 391    : (b) == 0 \
 392    ? 0 \
 393    : ((a) < 0 \
 394       ? (_GL_INT_NEGATE_OVERFLOW (_GL_INT_CONVERT (a, tmin)) && (a) == -1 \
 395          ? (_GL_EXPR_SIGNED (b) ? 0 < (b) + (tmin) : -1 - (tmin) < (b) - 1) \
 396          : (tmin) / (a) < (b)) \
 397       : (tmax) / (b) < (a)))
 398
 399 #endif /* _GL_INTPROPS_INTERNAL_H */