lib/intprops.h

   1 /* intprops.h -- properties of integer types
   2
   3    Copyright (C) 2001-2020 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 /* 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    Do not evaluate E.  */
  27 #define _GL_INT_CONVERT(e, v) ((1 ? 0 : (e)) + (v))
  28
  29 /* Act like _GL_INT_CONVERT (E, -V) but work around a bug in IRIX 6.5 cc; see
  30    <https://lists.gnu.org/r/bug-gnulib/2011-05/msg00406.html>.  */
  31 #define _GL_INT_NEGATE_CONVERT(e, v) ((1 ? 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.  Do not evaluate E.  */
  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    Do not evaluate T.
  52    Padding bits are not supported; this is checked at compile-time below.  */
  53 #define TYPE_WIDTH(t) (sizeof (t) * CHAR_BIT)
  54
  55 /* The maximum and minimum values for the integer type T.  */
  56 #define TYPE_MINIMUM(t) ((t) ~ TYPE_MAXIMUM (t))
  57 #define TYPE_MAXIMUM(t)                                                 \
  58   ((t) (! TYPE_SIGNED (t)                                               \
  59         ? (t) -1                                                        \
  60         : ((((t) 1 << (TYPE_WIDTH (t) - 2)) - 1) * 2 + 1)))
  61
  62 /* The maximum and minimum values for the type of the expression E,
  63    after integer promotion.  E is not evaluated.  */
  64 #define _GL_INT_MINIMUM(e)                                              \
  65   (EXPR_SIGNED (e)                                                      \
  66    ? ~ _GL_SIGNED_INT_MAXIMUM (e)                                       \
  67    : _GL_INT_CONVERT (e, 0))
  68 #define _GL_INT_MAXIMUM(e)                                              \
  69   (EXPR_SIGNED (e)                                                      \
  70    ? _GL_SIGNED_INT_MAXIMUM (e)                                         \
  71    : _GL_INT_NEGATE_CONVERT (e, 1))
  72 #define _GL_SIGNED_INT_MAXIMUM(e)                                       \
  73   (((_GL_INT_CONVERT (e, 1) << (TYPE_WIDTH ((e) + 0) - 2)) - 1) * 2 + 1)
  74
  75 /* Work around OpenVMS incompatibility with C99.  */
  76 #if !defined LLONG_MAX && defined __INT64_MAX
  77 # define LLONG_MAX __INT64_MAX
  78 # define LLONG_MIN __INT64_MIN
  79 #endif
  80
  81 /* This include file assumes that signed types are two's complement without
  82    padding bits; the above macros have undefined behavior otherwise.
  83    If this is a problem for you, please let us know how to fix it for your host.
  84    This assumption is tested by the intprops-tests module.  */
  85
  86 /* Does the __typeof__ keyword work?  This could be done by
  87    'configure', but for now it's easier to do it by hand.  */
  88 #if (2 <= __GNUC__ \
  89      || (4 <= __clang_major__) \
  90      || (1210 <= __IBMC__ && defined __IBM__TYPEOF__) \
  91      || (0x5110 <= __SUNPRO_C && !__STDC__))
  92 # define _GL_HAVE___TYPEOF__ 1
  93 #else
  94 # define _GL_HAVE___TYPEOF__ 0
  95 #endif
  96
  97 /* Return 1 if the integer type or expression T might be signed.  Return 0
  98    if it is definitely unsigned.  This macro does not evaluate its argument,
  99    and expands to an integer constant expression.  */
 100 #if _GL_HAVE___TYPEOF__
 101 # define _GL_SIGNED_TYPE_OR_EXPR(t) TYPE_SIGNED (__typeof__ (t))
 102 #else
 103 # define _GL_SIGNED_TYPE_OR_EXPR(t) 1
 104 #endif
 105
 106 /* Bound on length of the string representing an unsigned integer
 107    value representable in B bits.  log10 (2.0) < 146/485.  The
 108    smallest value of B where this bound is not tight is 2621.  */
 109 #define INT_BITS_STRLEN_BOUND(b) (((b) * 146 + 484) / 485)
 110
 111 /* Bound on length of the string representing an integer type or expression T.
 112    Subtract 1 for the sign bit if T is signed, and then add 1 more for
 113    a minus sign if needed.
 114
 115    Because _GL_SIGNED_TYPE_OR_EXPR sometimes returns 1 when its argument is
 116    unsigned, this macro may overestimate the true bound by one byte when
 117    applied to unsigned types of size 2, 4, 16, ... bytes.  */
 118 #define INT_STRLEN_BOUND(t)                                     \
 119   (INT_BITS_STRLEN_BOUND (TYPE_WIDTH (t) - _GL_SIGNED_TYPE_OR_EXPR (t)) \
 120    + _GL_SIGNED_TYPE_OR_EXPR (t))
 121
 122 /* Bound on buffer size needed to represent an integer type or expression T,
 123    including the terminating null.  */
 124 #define INT_BUFSIZE_BOUND(t) (INT_STRLEN_BOUND (t) + 1)
 125
 126
 127 /* Range overflow checks.
 128
 129    The INT_<op>_RANGE_OVERFLOW macros return 1 if the corresponding C
 130    operators might not yield numerically correct answers due to
 131    arithmetic overflow.  They do not rely on undefined or
 132    implementation-defined behavior.  Their implementations are simple
 133    and straightforward, but they are a bit harder to use than the
 134    INT_<op>_OVERFLOW macros described below.
 135
 136    Example usage:
 137
 138      long int i = ...;
 139      long int j = ...;
 140      if (INT_MULTIPLY_RANGE_OVERFLOW (i, j, LONG_MIN, LONG_MAX))
 141        printf ("multiply would overflow");
 142      else
 143        printf ("product is %ld", i * j);
 144
 145    Restrictions on *_RANGE_OVERFLOW macros:
 146
 147    These macros do not check for all possible numerical problems or
 148    undefined or unspecified behavior: they do not check for division
 149    by zero, for bad shift counts, or for shifting negative numbers.
 150
 151    These macros may evaluate their arguments zero or multiple times,
 152    so the arguments should not have side effects.  The arithmetic
 153    arguments (including the MIN and MAX arguments) must be of the same
 154    integer type after the usual arithmetic conversions, and the type
 155    must have minimum value MIN and maximum MAX.  Unsigned types should
 156    use a zero MIN of the proper type.
 157
 158    These macros are tuned for constant MIN and MAX.  For commutative
 159    operations such as A + B, they are also tuned for constant B.  */
 160
 161 /* Return 1 if A + B would overflow in [MIN,MAX] arithmetic.
 162    See above for restrictions.  */
 163 #define INT_ADD_RANGE_OVERFLOW(a, b, min, max)          \
 164   ((b) < 0                                              \
 165    ? (a) < (min) - (b)                                  \
 166    : (max) - (b) < (a))
 167
 168 /* Return 1 if A - B would overflow in [MIN,MAX] arithmetic.
 169    See above for restrictions.  */
 170 #define INT_SUBTRACT_RANGE_OVERFLOW(a, b, min, max)     \
 171   ((b) < 0                                              \
 172    ? (max) + (b) < (a)                                  \
 173    : (a) < (min) + (b))
 174
 175 /* Return 1 if - A would overflow in [MIN,MAX] arithmetic.
 176    See above for restrictions.  */
 177 #define INT_NEGATE_RANGE_OVERFLOW(a, min, max)          \
 178   ((min) < 0                                            \
 179    ? (a) < - (max)                                      \
 180    : 0 < (a))
 181
 182 /* Return 1 if A * B would overflow in [MIN,MAX] arithmetic.
 183    See above for restrictions.  Avoid && and || as they tickle
 184    bugs in Sun C 5.11 2010/08/13 and other compilers; see
 185    <https://lists.gnu.org/r/bug-gnulib/2011-05/msg00401.html>.  */
 186 #define INT_MULTIPLY_RANGE_OVERFLOW(a, b, min, max)     \
 187   ((b) < 0                                              \
 188    ? ((a) < 0                                           \
 189       ? (a) < (max) / (b)                               \
 190       : (b) == -1                                       \
 191       ? 0                                               \
 192       : (min) / (b) < (a))                              \
 193    : (b) == 0                                           \
 194    ? 0                                                  \
 195    : ((a) < 0                                           \
 196       ? (a) < (min) / (b)                               \
 197       : (max) / (b) < (a)))
 198
 199 /* Return 1 if A / B would overflow in [MIN,MAX] arithmetic.
 200    See above for restrictions.  Do not check for division by zero.  */
 201 #define INT_DIVIDE_RANGE_OVERFLOW(a, b, min, max)       \
 202   ((min) < 0 && (b) == -1 && (a) < - (max))
 203
 204 /* Return 1 if A % B would overflow in [MIN,MAX] arithmetic.
 205    See above for restrictions.  Do not check for division by zero.
 206    Mathematically, % should never overflow, but on x86-like hosts
 207    INT_MIN % -1 traps, and the C standard permits this, so treat this
 208    as an overflow too.  */
 209 #define INT_REMAINDER_RANGE_OVERFLOW(a, b, min, max)    \
 210   INT_DIVIDE_RANGE_OVERFLOW (a, b, min, max)
 211
 212 /* Return 1 if A << B would overflow in [MIN,MAX] arithmetic.
 213    See above for restrictions.  Here, MIN and MAX are for A only, and B need
 214    not be of the same type as the other arguments.  The C standard says that
 215    behavior is undefined for shifts unless 0 <= B < wordwidth, and that when
 216    A is negative then A << B has undefined behavior and A >> B has
 217    implementation-defined behavior, but do not check these other
 218    restrictions.  */
 219 #define INT_LEFT_SHIFT_RANGE_OVERFLOW(a, b, min, max)   \
 220   ((a) < 0                                              \
 221    ? (a) < (min) >> (b)                                 \
 222    : (max) >> (b) < (a))
 223
 224 /* True if __builtin_add_overflow (A, B, P) and __builtin_sub_overflow
 225    (A, B, P) work when P is non-null.  */
 226 #if 5 <= __GNUC__ && !defined __ICC
 227 # define _GL_HAS_BUILTIN_ADD_OVERFLOW 1
 228 #elif defined __has_builtin
 229 # define _GL_HAS_BUILTIN_ADD_OVERFLOW __has_builtin (__builtin_add_overflow)
 230 #else
 231 # define _GL_HAS_BUILTIN_ADD_OVERFLOW 0
 232 #endif
 233
 234 /* True if __builtin_mul_overflow (A, B, P) works when P is non-null.  */
 235 #ifdef __clang__
 236 /* Work around Clang bug <https://bugs.llvm.org/show_bug.cgi?id=16404>.  */
 237 # define _GL_HAS_BUILTIN_MUL_OVERFLOW 0
 238 #else
 239 # define _GL_HAS_BUILTIN_MUL_OVERFLOW _GL_HAS_BUILTIN_ADD_OVERFLOW
 240 #endif
 241
 242 /* True if __builtin_add_overflow_p (A, B, C) works, and similarly for
 243    __builtin_sub_overflow_p and __builtin_mul_overflow_p.  */
 244 #define _GL_HAS_BUILTIN_OVERFLOW_P (7 <= __GNUC__)
 245
 246 /* The _GL*_OVERFLOW macros have the same restrictions as the
 247    *_RANGE_OVERFLOW macros, except that they do not assume that operands
 248    (e.g., A and B) have the same type as MIN and MAX.  Instead, they assume
 249    that the result (e.g., A + B) has that type.  */
 250 #if _GL_HAS_BUILTIN_OVERFLOW_P
 251 # define _GL_ADD_OVERFLOW(a, b, min, max)                               \
 252    __builtin_add_overflow_p (a, b, (__typeof__ ((a) + (b))) 0)
 253 # define _GL_SUBTRACT_OVERFLOW(a, b, min, max)                          \
 254    __builtin_sub_overflow_p (a, b, (__typeof__ ((a) - (b))) 0)
 255 # define _GL_MULTIPLY_OVERFLOW(a, b, min, max)                          \
 256    __builtin_mul_overflow_p (a, b, (__typeof__ ((a) * (b))) 0)
 257 #else
 258 # define _GL_ADD_OVERFLOW(a, b, min, max)                                \
 259    ((min) < 0 ? INT_ADD_RANGE_OVERFLOW (a, b, min, max)                  \
 260     : (a) < 0 ? (b) <= (a) + (b)                                         \
 261     : (b) < 0 ? (a) <= (a) + (b)                                         \
 262     : (a) + (b) < (b))
 263 # define _GL_SUBTRACT_OVERFLOW(a, b, min, max)                           \
 264    ((min) < 0 ? INT_SUBTRACT_RANGE_OVERFLOW (a, b, min, max)             \
 265     : (a) < 0 ? 1                                                        \
 266     : (b) < 0 ? (a) - (b) <= (a)                                         \
 267     : (a) < (b))
 268 # define _GL_MULTIPLY_OVERFLOW(a, b, min, max)                           \
 269    (((min) == 0 && (((a) < 0 && 0 < (b)) || ((b) < 0 && 0 < (a))))       \
 270     || INT_MULTIPLY_RANGE_OVERFLOW (a, b, min, max))
 271 #endif
 272 #define _GL_DIVIDE_OVERFLOW(a, b, min, max)                             \
 273   ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max)  \
 274    : (a) < 0 ? (b) <= (a) + (b) - 1                                     \
 275    : (b) < 0 && (a) + (b) <= (a))
 276 #define _GL_REMAINDER_OVERFLOW(a, b, min, max)                          \
 277   ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max)  \
 278    : (a) < 0 ? (a) % (b) != ((max) - (b) + 1) % (b)                     \
 279    : (b) < 0 && ! _GL_UNSIGNED_NEG_MULTIPLE (a, b, max))
 280
 281 /* Return a nonzero value if A is a mathematical multiple of B, where
 282    A is unsigned, B is negative, and MAX is the maximum value of A's
 283    type.  A's type must be the same as (A % B)'s type.  Normally (A %
 284    -B == 0) suffices, but things get tricky if -B would overflow.  */
 285 #define _GL_UNSIGNED_NEG_MULTIPLE(a, b, max)                            \
 286   (((b) < -_GL_SIGNED_INT_MAXIMUM (b)                                   \
 287     ? (_GL_SIGNED_INT_MAXIMUM (b) == (max)                              \
 288        ? (a)                                                            \
 289        : (a) % (_GL_INT_CONVERT (a, _GL_SIGNED_INT_MAXIMUM (b)) + 1))   \
 290     : (a) % - (b))                                                      \
 291    == 0)
 292
 293 /* Check for integer overflow, and report low order bits of answer.
 294
 295    The INT_<op>_OVERFLOW macros return 1 if the corresponding C operators
 296    might not yield numerically correct answers due to arithmetic overflow.
 297    The INT_<op>_WRAPV macros compute the low-order bits of the sum,
 298    difference, and product of two C integers, and return 1 if these
 299    low-order bits are not numerically correct.
 300    These macros work correctly on all known practical hosts, and do not rely
 301    on undefined behavior due to signed arithmetic overflow.
 302
 303    Example usage, assuming A and B are long int:
 304
 305      if (INT_MULTIPLY_OVERFLOW (a, b))
 306        printf ("result would overflow\n");
 307      else
 308        printf ("result is %ld (no overflow)\n", a * b);
 309
 310    Example usage with WRAPV flavor:
 311
 312      long int result;
 313      bool overflow = INT_MULTIPLY_WRAPV (a, b, &result);
 314      printf ("result is %ld (%s)\n", result,
 315              overflow ? "after overflow" : "no overflow");
 316
 317    Restrictions on these macros:
 318
 319    These macros do not check for all possible numerical problems or
 320    undefined or unspecified behavior: they do not check for division
 321    by zero, for bad shift counts, or for shifting negative numbers.
 322
 323    These macros may evaluate their arguments zero or multiple times, so the
 324    arguments should not have side effects.
 325
 326    The WRAPV macros are not constant expressions.  They support only
 327    +, binary -, and *.  Because the WRAPV macros convert the result,
 328    they report overflow in different circumstances than the OVERFLOW
 329    macros do.
 330
 331    These macros are tuned for their last input argument being a constant.
 332
 333    Return 1 if the integer expressions A * B, A - B, -A, A * B, A / B,
 334    A % B, and A << B would overflow, respectively.  */
 335
 336 #define INT_ADD_OVERFLOW(a, b) \
 337   _GL_BINARY_OP_OVERFLOW (a, b, _GL_ADD_OVERFLOW)
 338 #define INT_SUBTRACT_OVERFLOW(a, b) \
 339   _GL_BINARY_OP_OVERFLOW (a, b, _GL_SUBTRACT_OVERFLOW)
 340 #if _GL_HAS_BUILTIN_OVERFLOW_P
 341 # define INT_NEGATE_OVERFLOW(a) INT_SUBTRACT_OVERFLOW (0, a)
 342 #else
 343 # define INT_NEGATE_OVERFLOW(a) \
 344    INT_NEGATE_RANGE_OVERFLOW (a, _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
 345 #endif
 346 #define INT_MULTIPLY_OVERFLOW(a, b) \
 347   _GL_BINARY_OP_OVERFLOW (a, b, _GL_MULTIPLY_OVERFLOW)
 348 #define INT_DIVIDE_OVERFLOW(a, b) \
 349   _GL_BINARY_OP_OVERFLOW (a, b, _GL_DIVIDE_OVERFLOW)
 350 #define INT_REMAINDER_OVERFLOW(a, b) \
 351   _GL_BINARY_OP_OVERFLOW (a, b, _GL_REMAINDER_OVERFLOW)
 352 #define INT_LEFT_SHIFT_OVERFLOW(a, b) \
 353   INT_LEFT_SHIFT_RANGE_OVERFLOW (a, b, \
 354                                  _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
 355
 356 /* Return 1 if the expression A <op> B would overflow,
 357    where OP_RESULT_OVERFLOW (A, B, MIN, MAX) does the actual test,
 358    assuming MIN and MAX are the minimum and maximum for the result type.
 359    Arguments should be free of side effects.  */
 360 #define _GL_BINARY_OP_OVERFLOW(a, b, op_result_overflow)        \
 361   op_result_overflow (a, b,                                     \
 362                       _GL_INT_MINIMUM (_GL_INT_CONVERT (a, b)), \
 363                       _GL_INT_MAXIMUM (_GL_INT_CONVERT (a, b)))
 364
 365 /* Store the low-order bits of A + B, A - B, A * B, respectively, into *R.
 366    Return 1 if the result overflows.  See above for restrictions.  */
 367 #if _GL_HAS_BUILTIN_ADD_OVERFLOW
 368 # define INT_ADD_WRAPV(a, b, r) __builtin_add_overflow (a, b, r)
 369 # define INT_SUBTRACT_WRAPV(a, b, r) __builtin_sub_overflow (a, b, r)
 370 #else
 371 # define INT_ADD_WRAPV(a, b, r) \
 372    _GL_INT_OP_WRAPV (a, b, r, +, _GL_INT_ADD_RANGE_OVERFLOW)
 373 # define INT_SUBTRACT_WRAPV(a, b, r) \
 374    _GL_INT_OP_WRAPV (a, b, r, -, _GL_INT_SUBTRACT_RANGE_OVERFLOW)
 375 #endif
 376 #if _GL_HAS_BUILTIN_MUL_OVERFLOW
 377 # if (9 < __GNUC__ + (3 <= __GNUC_MINOR__) \
 378       || (__GNUC__ == 8 && 4 <= __GNUC_MINOR__))
 379 #  define INT_MULTIPLY_WRAPV(a, b, r) __builtin_mul_overflow (a, b, r)
 380 # else
 381    /* Work around GCC bug 91450.  */
 382 #  define INT_MULTIPLY_WRAPV(a, b, r) \
 383     ((!_GL_SIGNED_TYPE_OR_EXPR (*(r)) && EXPR_SIGNED (a) && EXPR_SIGNED (b) \
 384       && _GL_INT_MULTIPLY_RANGE_OVERFLOW (a, b, 0, (__typeof__ (*(r))) -1)) \
 385      ? ((void) __builtin_mul_overflow (a, b, r), 1) \
 386      : __builtin_mul_overflow (a, b, r))
 387 # endif
 388 #else
 389 # define INT_MULTIPLY_WRAPV(a, b, r) \
 390    _GL_INT_OP_WRAPV (a, b, r, *, _GL_INT_MULTIPLY_RANGE_OVERFLOW)
 391 #endif
 392
 393 /* Nonzero if this compiler has GCC bug 68193 or Clang bug 25390.  See:
 394    https://gcc.gnu.org/bugzilla/show_bug.cgi?id=68193
 395    https://llvm.org/bugs/show_bug.cgi?id=25390
 396    For now, assume all versions of GCC-like compilers generate bogus
 397    warnings for _Generic.  This matters only for compilers that
 398    lack relevant builtins.  */
 399 #if __GNUC__ || defined __clang__
 400 # define _GL__GENERIC_BOGUS 1
 401 #else
 402 # define _GL__GENERIC_BOGUS 0
 403 #endif
 404
 405 /* Store the low-order bits of A <op> B into *R, where OP specifies
 406    the operation and OVERFLOW the overflow predicate.  Return 1 if the
 407    result overflows.  See above for restrictions.  */
 408 #if 201112 <= __STDC_VERSION__ && !_GL__GENERIC_BOGUS
 409 # define _GL_INT_OP_WRAPV(a, b, r, op, overflow) \
 410    (_Generic \
 411     (*(r), \
 412      signed char: \
 413        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 414                         signed char, SCHAR_MIN, SCHAR_MAX), \
 415      unsigned char: \
 416        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 417                         unsigned char, 0, UCHAR_MAX), \
 418      short int: \
 419        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 420                         short int, SHRT_MIN, SHRT_MAX), \
 421      unsigned short int: \
 422        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 423                         unsigned short int, 0, USHRT_MAX), \
 424      int: \
 425        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 426                         int, INT_MIN, INT_MAX), \
 427      unsigned int: \
 428        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 429                         unsigned int, 0, UINT_MAX), \
 430      long int: \
 431        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 432                         long int, LONG_MIN, LONG_MAX), \
 433      unsigned long int: \
 434        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 435                         unsigned long int, 0, ULONG_MAX), \
 436      long long int: \
 437        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
 438                         long long int, LLONG_MIN, LLONG_MAX), \
 439      unsigned long long int: \
 440        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
 441                         unsigned long long int, 0, ULLONG_MAX)))
 442 #else
 443 /* Store the low-order bits of A <op> B into *R, where OP specifies
 444    the operation and OVERFLOW the overflow predicate.  If *R is
 445    signed, its type is ST with bounds SMIN..SMAX; otherwise its type
 446    is UT with bounds U..UMAX.  ST and UT are narrower than int.
 447    Return 1 if the result overflows.  See above for restrictions.  */
 448 # if _GL_HAVE___TYPEOF__
 449 #  define _GL_INT_OP_WRAPV_SMALLISH(a,b,r,op,overflow,st,smin,smax,ut,umax) \
 450     (TYPE_SIGNED (__typeof__ (*(r))) \
 451      ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, st, smin, smax) \
 452      : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, ut, 0, umax))
 453 # else
 454 #  define _GL_INT_OP_WRAPV_SMALLISH(a,b,r,op,overflow,st,smin,smax,ut,umax) \
 455     (overflow (a, b, smin, smax) \
 456      ? (overflow (a, b, 0, umax) \
 457         ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st), 1) \
 458         : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st)) < 0) \
 459      : (overflow (a, b, 0, umax) \
 460         ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st)) >= 0 \
 461         : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st), 0)))
 462 # endif
 463
 464 # define _GL_INT_OP_WRAPV(a, b, r, op, overflow) \
 465    (sizeof *(r) == sizeof (signed char) \
 466     ? _GL_INT_OP_WRAPV_SMALLISH (a, b, r, op, overflow, \
 467                                  signed char, SCHAR_MIN, SCHAR_MAX, \
 468                                  unsigned char, UCHAR_MAX) \
 469     : sizeof *(r) == sizeof (short int) \
 470     ? _GL_INT_OP_WRAPV_SMALLISH (a, b, r, op, overflow, \
 471                                  short int, SHRT_MIN, SHRT_MAX, \
 472                                  unsigned short int, USHRT_MAX) \
 473     : sizeof *(r) == sizeof (int) \
 474     ? (EXPR_SIGNED (*(r)) \
 475        ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 476                           int, INT_MIN, INT_MAX) \
 477        : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 478                           unsigned int, 0, UINT_MAX)) \
 479     : _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow))
 480 # ifdef LLONG_MAX
 481 #  define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
 482     (sizeof *(r) == sizeof (long int) \
 483      ? (EXPR_SIGNED (*(r)) \
 484         ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 485                            long int, LONG_MIN, LONG_MAX) \
 486         : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 487                            unsigned long int, 0, ULONG_MAX)) \
 488      : (EXPR_SIGNED (*(r)) \
 489         ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
 490                            long long int, LLONG_MIN, LLONG_MAX) \
 491         : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
 492                            unsigned long long int, 0, ULLONG_MAX)))
 493 # else
 494 #  define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
 495     (EXPR_SIGNED (*(r)) \
 496      ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 497                         long int, LONG_MIN, LONG_MAX) \
 498      : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 499                         unsigned long int, 0, ULONG_MAX))
 500 # endif
 501 #endif
 502
 503 /* Store the low-order bits of A <op> B into *R, where the operation
 504    is given by OP.  Use the unsigned type UT for calculation to avoid
 505    overflow problems.  *R's type is T, with extrema TMIN and TMAX.
 506    T must be a signed integer type.  Return 1 if the result overflows.  */
 507 #define _GL_INT_OP_CALC(a, b, r, op, overflow, ut, t, tmin, tmax) \
 508   (overflow (a, b, tmin, tmax) \
 509    ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 1) \
 510    : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 0))
 511
 512 /* Return the low-order bits of A <op> B, where the operation is given
 513    by OP.  Use the unsigned type UT for calculation to avoid undefined
 514    behavior on signed integer overflow, and convert the result to type T.
 515    UT is at least as wide as T and is no narrower than unsigned int,
 516    T is two's complement, and there is no padding or trap representations.
 517    Assume that converting UT to T yields the low-order bits, as is
 518    done in all known two's-complement C compilers.  E.g., see:
 519    https://gcc.gnu.org/onlinedocs/gcc/Integers-implementation.html
 520
 521    According to the C standard, converting UT to T yields an
 522    implementation-defined result or signal for values outside T's
 523    range.  However, code that works around this theoretical problem
 524    runs afoul of a compiler bug in Oracle Studio 12.3 x86.  See:
 525    https://lists.gnu.org/r/bug-gnulib/2017-04/msg00049.html
 526    As the compiler bug is real, don't try to work around the
 527    theoretical problem.  */
 528
 529 #define _GL_INT_OP_WRAPV_VIA_UNSIGNED(a, b, op, ut, t) \
 530   ((t) ((ut) (a) op (ut) (b)))
 531
 532 /* Return true if the numeric values A + B, A - B, A * B fall outside
 533    the range TMIN..TMAX.  Arguments should be integer expressions
 534    without side effects.  TMIN should be signed and nonpositive.
 535    TMAX should be positive, and should be signed unless TMIN is zero.  */
 536 #define _GL_INT_ADD_RANGE_OVERFLOW(a, b, tmin, tmax) \
 537   ((b) < 0 \
 538    ? (((tmin) \
 539        ? ((EXPR_SIGNED (_GL_INT_CONVERT (a, (tmin) - (b))) || (b) < (tmin)) \
 540           && (a) < (tmin) - (b)) \
 541        : (a) <= -1 - (b)) \
 542       || ((EXPR_SIGNED (a) ? 0 <= (a) : (tmax) < (a)) && (tmax) < (a) + (b))) \
 543    : (a) < 0 \
 544    ? (((tmin) \
 545        ? ((EXPR_SIGNED (_GL_INT_CONVERT (b, (tmin) - (a))) || (a) < (tmin)) \
 546           && (b) < (tmin) - (a)) \
 547        : (b) <= -1 - (a)) \
 548       || ((EXPR_SIGNED (_GL_INT_CONVERT (a, b)) || (tmax) < (b)) \
 549           && (tmax) < (a) + (b))) \
 550    : (tmax) < (b) || (tmax) - (b) < (a))
 551 #define _GL_INT_SUBTRACT_RANGE_OVERFLOW(a, b, tmin, tmax) \
 552   (((a) < 0) == ((b) < 0) \
 553    ? ((a) < (b) \
 554       ? !(tmin) || -1 - (tmin) < (b) - (a) - 1 \
 555       : (tmax) < (a) - (b)) \
 556    : (a) < 0 \
 557    ? ((!EXPR_SIGNED (_GL_INT_CONVERT ((a) - (tmin), b)) && (a) - (tmin) < 0) \
 558       || (a) - (tmin) < (b)) \
 559    : ((! (EXPR_SIGNED (_GL_INT_CONVERT (tmax, b)) \
 560           && EXPR_SIGNED (_GL_INT_CONVERT ((tmax) + (b), a))) \
 561        && (tmax) <= -1 - (b)) \
 562       || (tmax) + (b) < (a)))
 563 #define _GL_INT_MULTIPLY_RANGE_OVERFLOW(a, b, tmin, tmax) \
 564   ((b) < 0 \
 565    ? ((a) < 0 \
 566       ? (EXPR_SIGNED (_GL_INT_CONVERT (tmax, b)) \
 567          ? (a) < (tmax) / (b) \
 568          : ((INT_NEGATE_OVERFLOW (b) \
 569              ? _GL_INT_CONVERT (b, tmax) >> (TYPE_WIDTH (b) - 1) \
 570              : (tmax) / -(b)) \
 571             <= -1 - (a))) \
 572       : INT_NEGATE_OVERFLOW (_GL_INT_CONVERT (b, tmin)) && (b) == -1 \
 573       ? (EXPR_SIGNED (a) \
 574          ? 0 < (a) + (tmin) \
 575          : 0 < (a) && -1 - (tmin) < (a) - 1) \
 576       : (tmin) / (b) < (a)) \
 577    : (b) == 0 \
 578    ? 0 \
 579    : ((a) < 0 \
 580       ? (INT_NEGATE_OVERFLOW (_GL_INT_CONVERT (a, tmin)) && (a) == -1 \
 581          ? (EXPR_SIGNED (b) ? 0 < (b) + (tmin) : -1 - (tmin) < (b) - 1) \
 582          : (tmin) / (a) < (b)) \
 583       : (tmax) / (b) < (a)))
 584
 585 #endif /* _GL_INTPROPS_H */