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    1 /* intprops.h -- properties of integer types
    2 
    3    Copyright (C) 2001-2019 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      || (1210 <= __IBMC__ && defined __IBM__TYPEOF__) \
   90      || (0x5110 <= __SUNPRO_C && !__STDC__))
   91 # define _GL_HAVE___TYPEOF__ 1
   92 #else
   93 # define _GL_HAVE___TYPEOF__ 0
   94 #endif
   95 
   96 /* Return 1 if the integer type or expression T might be signed.  Return 0
   97    if it is definitely unsigned.  This macro does not evaluate its argument,
   98    and expands to an integer constant expression.  */
   99 #if _GL_HAVE___TYPEOF__
  100 # define _GL_SIGNED_TYPE_OR_EXPR(t) TYPE_SIGNED (__typeof__ (t))
  101 #else
  102 # define _GL_SIGNED_TYPE_OR_EXPR(t) 1
  103 #endif
  104 
  105 /* Bound on length of the string representing an unsigned integer
  106    value representable in B bits.  log10 (2.0) < 146/485.  The
  107    smallest value of B where this bound is not tight is 2621.  */
  108 #define INT_BITS_STRLEN_BOUND(b) (((b) * 146 + 484) / 485)
  109 
  110 /* Bound on length of the string representing an integer type or expression T.
  111    Subtract 1 for the sign bit if T is signed, and then add 1 more for
  112    a minus sign if needed.
  113 
  114    Because _GL_SIGNED_TYPE_OR_EXPR sometimes returns 1 when its argument is
  115    unsigned, this macro may overestimate the true bound by one byte when
  116    applied to unsigned types of size 2, 4, 16, ... bytes.  */
  117 #define INT_STRLEN_BOUND(t)                                     \
  118   (INT_BITS_STRLEN_BOUND (TYPE_WIDTH (t) - _GL_SIGNED_TYPE_OR_EXPR (t)) \
  119    + _GL_SIGNED_TYPE_OR_EXPR (t))
  120 
  121 /* Bound on buffer size needed to represent an integer type or expression T,
  122    including the terminating null.  */
  123 #define INT_BUFSIZE_BOUND(t) (INT_STRLEN_BOUND (t) + 1)
  124 
  125 
  126 /* Range overflow checks.
  127 
  128    The INT_<op>_RANGE_OVERFLOW macros return 1 if the corresponding C
  129    operators might not yield numerically correct answers due to
  130    arithmetic overflow.  They do not rely on undefined or
  131    implementation-defined behavior.  Their implementations are simple
  132    and straightforward, but they are a bit harder to use than the
  133    INT_<op>_OVERFLOW macros described below.
  134 
  135    Example usage:
  136 
  137      long int i = ...;
  138      long int j = ...;
  139      if (INT_MULTIPLY_RANGE_OVERFLOW (i, j, LONG_MIN, LONG_MAX))
  140        printf ("multiply would overflow");
  141      else
  142        printf ("product is %ld", i * j);
  143 
  144    Restrictions on *_RANGE_OVERFLOW macros:
  145 
  146    These macros do not check for all possible numerical problems or
  147    undefined or unspecified behavior: they do not check for division
  148    by zero, for bad shift counts, or for shifting negative numbers.
  149 
  150    These macros may evaluate their arguments zero or multiple times,
  151    so the arguments should not have side effects.  The arithmetic
  152    arguments (including the MIN and MAX arguments) must be of the same
  153    integer type after the usual arithmetic conversions, and the type
  154    must have minimum value MIN and maximum MAX.  Unsigned types should
  155    use a zero MIN of the proper type.
  156 
  157    These macros are tuned for constant MIN and MAX.  For commutative
  158    operations such as A + B, they are also tuned for constant B.  */
  159 
  160 /* Return 1 if A + B would overflow in [MIN,MAX] arithmetic.
  161    See above for restrictions.  */
  162 #define INT_ADD_RANGE_OVERFLOW(a, b, min, max)          \
  163   ((b) < 0                                              \
  164    ? (a) < (min) - (b)                                  \
  165    : (max) - (b) < (a))
  166 
  167 /* Return 1 if A - B would overflow in [MIN,MAX] arithmetic.
  168    See above for restrictions.  */
  169 #define INT_SUBTRACT_RANGE_OVERFLOW(a, b, min, max)     \
  170   ((b) < 0                                              \
  171    ? (max) + (b) < (a)                                  \
  172    : (a) < (min) + (b))
  173 
  174 /* Return 1 if - A would overflow in [MIN,MAX] arithmetic.
  175    See above for restrictions.  */
  176 #define INT_NEGATE_RANGE_OVERFLOW(a, min, max)          \
  177   ((min) < 0                                            \
  178    ? (a) < - (max)                                      \
  179    : 0 < (a))
  180 
  181 /* Return 1 if A * B would overflow in [MIN,MAX] arithmetic.
  182    See above for restrictions.  Avoid && and || as they tickle
  183    bugs in Sun C 5.11 2010/08/13 and other compilers; see
  184    <https://lists.gnu.org/r/bug-gnulib/2011-05/msg00401.html>.  */
  185 #define INT_MULTIPLY_RANGE_OVERFLOW(a, b, min, max)     \
  186   ((b) < 0                                              \
  187    ? ((a) < 0                                           \
  188       ? (a) < (max) / (b)                               \
  189       : (b) == -1                                       \
  190       ? 0                                               \
  191       : (min) / (b) < (a))                              \
  192    : (b) == 0                                           \
  193    ? 0                                                  \
  194    : ((a) < 0                                           \
  195       ? (a) < (min) / (b)                               \
  196       : (max) / (b) < (a)))
  197 
  198 /* Return 1 if A / B would overflow in [MIN,MAX] arithmetic.
  199    See above for restrictions.  Do not check for division by zero.  */
  200 #define INT_DIVIDE_RANGE_OVERFLOW(a, b, min, max)       \
  201   ((min) < 0 && (b) == -1 && (a) < - (max))
  202 
  203 /* Return 1 if A % B would overflow in [MIN,MAX] arithmetic.
  204    See above for restrictions.  Do not check for division by zero.
  205    Mathematically, % should never overflow, but on x86-like hosts
  206    INT_MIN % -1 traps, and the C standard permits this, so treat this
  207    as an overflow too.  */
  208 #define INT_REMAINDER_RANGE_OVERFLOW(a, b, min, max)    \
  209   INT_DIVIDE_RANGE_OVERFLOW (a, b, min, max)
  210 
  211 /* Return 1 if A << B would overflow in [MIN,MAX] arithmetic.
  212    See above for restrictions.  Here, MIN and MAX are for A only, and B need
  213    not be of the same type as the other arguments.  The C standard says that
  214    behavior is undefined for shifts unless 0 <= B < wordwidth, and that when
  215    A is negative then A << B has undefined behavior and A >> B has
  216    implementation-defined behavior, but do not check these other
  217    restrictions.  */
  218 #define INT_LEFT_SHIFT_RANGE_OVERFLOW(a, b, min, max)   \
  219   ((a) < 0                                              \
  220    ? (a) < (min) >> (b)                                 \
  221    : (max) >> (b) < (a))
  222 
  223 /* True if __builtin_add_overflow (A, B, P) works when P is non-null.  */
  224 #if 5 <= __GNUC__ && !defined __ICC
  225 # define _GL_HAS_BUILTIN_OVERFLOW 1
  226 #else
  227 # define _GL_HAS_BUILTIN_OVERFLOW 0
  228 #endif
  229 
  230 /* True if __builtin_add_overflow_p (A, B, C) works.  */
  231 #define _GL_HAS_BUILTIN_OVERFLOW_P (7 <= __GNUC__)
  232 
  233 /* The _GL*_OVERFLOW macros have the same restrictions as the
  234    *_RANGE_OVERFLOW macros, except that they do not assume that operands
  235    (e.g., A and B) have the same type as MIN and MAX.  Instead, they assume
  236    that the result (e.g., A + B) has that type.  */
  237 #if _GL_HAS_BUILTIN_OVERFLOW_P
  238 # define _GL_ADD_OVERFLOW(a, b, min, max)                               \
  239    __builtin_add_overflow_p (a, b, (__typeof__ ((a) + (b))) 0)
  240 # define _GL_SUBTRACT_OVERFLOW(a, b, min, max)                          \
  241    __builtin_sub_overflow_p (a, b, (__typeof__ ((a) - (b))) 0)
  242 # define _GL_MULTIPLY_OVERFLOW(a, b, min, max)                          \
  243    __builtin_mul_overflow_p (a, b, (__typeof__ ((a) * (b))) 0)
  244 #else
  245 # define _GL_ADD_OVERFLOW(a, b, min, max)                                \
  246    ((min) < 0 ? INT_ADD_RANGE_OVERFLOW (a, b, min, max)                  \
  247     : (a) < 0 ? (b) <= (a) + (b)                                         \
  248     : (b) < 0 ? (a) <= (a) + (b)                                         \
  249     : (a) + (b) < (b))
  250 # define _GL_SUBTRACT_OVERFLOW(a, b, min, max)                           \
  251    ((min) < 0 ? INT_SUBTRACT_RANGE_OVERFLOW (a, b, min, max)             \
  252     : (a) < 0 ? 1                                                        \
  253     : (b) < 0 ? (a) - (b) <= (a)                                         \
  254     : (a) < (b))
  255 # define _GL_MULTIPLY_OVERFLOW(a, b, min, max)                           \
  256    (((min) == 0 && (((a) < 0 && 0 < (b)) || ((b) < 0 && 0 < (a))))       \
  257     || INT_MULTIPLY_RANGE_OVERFLOW (a, b, min, max))
  258 #endif
  259 #define _GL_DIVIDE_OVERFLOW(a, b, min, max)                             \
  260   ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max)  \
  261    : (a) < 0 ? (b) <= (a) + (b) - 1                                     \
  262    : (b) < 0 && (a) + (b) <= (a))
  263 #define _GL_REMAINDER_OVERFLOW(a, b, min, max)                          \
  264   ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max)  \
  265    : (a) < 0 ? (a) % (b) != ((max) - (b) + 1) % (b)                     \
  266    : (b) < 0 && ! _GL_UNSIGNED_NEG_MULTIPLE (a, b, max))
  267 
  268 /* Return a nonzero value if A is a mathematical multiple of B, where
  269    A is unsigned, B is negative, and MAX is the maximum value of A's
  270    type.  A's type must be the same as (A % B)'s type.  Normally (A %
  271    -B == 0) suffices, but things get tricky if -B would overflow.  */
  272 #define _GL_UNSIGNED_NEG_MULTIPLE(a, b, max)                            \
  273   (((b) < -_GL_SIGNED_INT_MAXIMUM (b)                                   \
  274     ? (_GL_SIGNED_INT_MAXIMUM (b) == (max)                              \
  275        ? (a)                                                            \
  276        : (a) % (_GL_INT_CONVERT (a, _GL_SIGNED_INT_MAXIMUM (b)) + 1))   \
  277     : (a) % - (b))                                                      \
  278    == 0)
  279 
  280 /* Check for integer overflow, and report low order bits of answer.
  281 
  282    The INT_<op>_OVERFLOW macros return 1 if the corresponding C operators
  283    might not yield numerically correct answers due to arithmetic overflow.
  284    The INT_<op>_WRAPV macros compute the low-order bits of the sum,
  285    difference, and product of two C integers, and return 1 if these
  286    low-order bits are not numerically correct.
  287    These macros work correctly on all known practical hosts, and do not rely
  288    on undefined behavior due to signed arithmetic overflow.
  289 
  290    Example usage, assuming A and B are long int:
  291 
  292      if (INT_MULTIPLY_OVERFLOW (a, b))
  293        printf ("result would overflow\n");
  294      else
  295        printf ("result is %ld (no overflow)\n", a * b);
  296 
  297    Example usage with WRAPV flavor:
  298 
  299      long int result;
  300      bool overflow = INT_MULTIPLY_WRAPV (a, b, &result);
  301      printf ("result is %ld (%s)\n", result,
  302              overflow ? "after overflow" : "no overflow");
  303 
  304    Restrictions on these macros:
  305 
  306    These macros do not check for all possible numerical problems or
  307    undefined or unspecified behavior: they do not check for division
  308    by zero, for bad shift counts, or for shifting negative numbers.
  309 
  310    These macros may evaluate their arguments zero or multiple times, so the
  311    arguments should not have side effects.
  312 
  313    The WRAPV macros are not constant expressions.  They support only
  314    +, binary -, and *.  Because the WRAPV macros convert the result,
  315    they report overflow in different circumstances than the OVERFLOW
  316    macros do.
  317 
  318    These macros are tuned for their last input argument being a constant.
  319 
  320    Return 1 if the integer expressions A * B, A - B, -A, A * B, A / B,
  321    A % B, and A << B would overflow, respectively.  */
  322 
  323 #define INT_ADD_OVERFLOW(a, b) \
  324   _GL_BINARY_OP_OVERFLOW (a, b, _GL_ADD_OVERFLOW)
  325 #define INT_SUBTRACT_OVERFLOW(a, b) \
  326   _GL_BINARY_OP_OVERFLOW (a, b, _GL_SUBTRACT_OVERFLOW)
  327 #if _GL_HAS_BUILTIN_OVERFLOW_P
  328 # define INT_NEGATE_OVERFLOW(a) INT_SUBTRACT_OVERFLOW (0, a)
  329 #else
  330 # define INT_NEGATE_OVERFLOW(a) \
  331    INT_NEGATE_RANGE_OVERFLOW (a, _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
  332 #endif
  333 #define INT_MULTIPLY_OVERFLOW(a, b) \
  334   _GL_BINARY_OP_OVERFLOW (a, b, _GL_MULTIPLY_OVERFLOW)
  335 #define INT_DIVIDE_OVERFLOW(a, b) \
  336   _GL_BINARY_OP_OVERFLOW (a, b, _GL_DIVIDE_OVERFLOW)
  337 #define INT_REMAINDER_OVERFLOW(a, b) \
  338   _GL_BINARY_OP_OVERFLOW (a, b, _GL_REMAINDER_OVERFLOW)
  339 #define INT_LEFT_SHIFT_OVERFLOW(a, b) \
  340   INT_LEFT_SHIFT_RANGE_OVERFLOW (a, b, \
  341                                  _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
  342 
  343 /* Return 1 if the expression A <op> B would overflow,
  344    where OP_RESULT_OVERFLOW (A, B, MIN, MAX) does the actual test,
  345    assuming MIN and MAX are the minimum and maximum for the result type.
  346    Arguments should be free of side effects.  */
  347 #define _GL_BINARY_OP_OVERFLOW(a, b, op_result_overflow)        \
  348   op_result_overflow (a, b,                                     \
  349                       _GL_INT_MINIMUM (_GL_INT_CONVERT (a, b)), \
  350                       _GL_INT_MAXIMUM (_GL_INT_CONVERT (a, b)))
  351 
  352 /* Store the low-order bits of A + B, A - B, A * B, respectively, into *R.
  353    Return 1 if the result overflows.  See above for restrictions.  */
  354 #define INT_ADD_WRAPV(a, b, r) \
  355   _GL_INT_OP_WRAPV (a, b, r, +, __builtin_add_overflow, \
  356                     _GL_INT_ADD_RANGE_OVERFLOW)
  357 #define INT_SUBTRACT_WRAPV(a, b, r) \
  358   _GL_INT_OP_WRAPV (a, b, r, -, __builtin_sub_overflow, \
  359                     _GL_INT_SUBTRACT_RANGE_OVERFLOW)
  360 #define INT_MULTIPLY_WRAPV(a, b, r) \
  361    _GL_INT_OP_WRAPV (a, b, r, *, _GL_BUILTIN_MUL_OVERFLOW, \
  362                      _GL_INT_MULTIPLY_RANGE_OVERFLOW)
  363 
  364 /* Like __builtin_mul_overflow, but work around GCC bug 91450.  */
  365 #define _GL_BUILTIN_MUL_OVERFLOW(a, b, r) \
  366   ((!_GL_SIGNED_TYPE_OR_EXPR (*(r)) && EXPR_SIGNED (a) && EXPR_SIGNED (b) \
  367     && _GL_INT_MULTIPLY_RANGE_OVERFLOW (a, b, 0, (__typeof__ (*(r))) -1)) \
  368    ? ((void) __builtin_mul_overflow (a, b, r), 1) \
  369    : __builtin_mul_overflow (a, b, r))
  370 
  371 /* Nonzero if this compiler has GCC bug 68193 or Clang bug 25390.  See:
  372    https://gcc.gnu.org/bugzilla/show_bug.cgi?id=68193
  373    https://llvm.org/bugs/show_bug.cgi?id=25390
  374    For now, assume all versions of GCC-like compilers generate bogus
  375    warnings for _Generic.  This matters only for older compilers that
  376    lack __builtin_add_overflow.  */
  377 #if __GNUC__
  378 # define _GL__GENERIC_BOGUS 1
  379 #else
  380 # define _GL__GENERIC_BOGUS 0
  381 #endif
  382 
  383 /* Store the low-order bits of A <op> B into *R, where OP specifies
  384    the operation.  BUILTIN is the builtin operation, and OVERFLOW the
  385    overflow predicate.  Return 1 if the result overflows.  See above
  386    for restrictions.  */
  387 #if _GL_HAS_BUILTIN_OVERFLOW
  388 # define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) builtin (a, b, r)
  389 #elif 201112 <= __STDC_VERSION__ && !_GL__GENERIC_BOGUS
  390 # define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) \
  391    (_Generic \
  392     (*(r), \
  393      signed char: \
  394        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
  395                         signed char, SCHAR_MIN, SCHAR_MAX), \
  396      unsigned char: \
  397        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
  398                         unsigned char, 0, UCHAR_MAX), \
  399      short int: \
  400        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
  401                         short int, SHRT_MIN, SHRT_MAX), \
  402      unsigned short int: \
  403        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
  404                         unsigned short int, 0, USHRT_MAX), \
  405      int: \
  406        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
  407                         int, INT_MIN, INT_MAX), \
  408      unsigned int: \
  409        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
  410                         unsigned int, 0, UINT_MAX), \
  411      long int: \
  412        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
  413                         long int, LONG_MIN, LONG_MAX), \
  414      unsigned long int: \
  415        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
  416                         unsigned long int, 0, ULONG_MAX), \
  417      long long int: \
  418        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
  419                         long long int, LLONG_MIN, LLONG_MAX), \
  420      unsigned long long int: \
  421        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
  422                         unsigned long long int, 0, ULLONG_MAX)))
  423 #else
  424 /* Store the low-order bits of A <op> B into *R, where OP specifies
  425    the operation and OVERFLOW the overflow predicate.  If *R is
  426    signed, its type is ST with bounds SMIN..SMAX; otherwise its type
  427    is UT with bounds U..UMAX.  ST and UT are narrower than int.
  428    Return 1 if the result overflows.  See above for restrictions.  */
  429 # if _GL_HAVE___TYPEOF__
  430 #  define _GL_INT_OP_WRAPV_SMALLISH(a,b,r,op,overflow,st,smin,smax,ut,umax) \
  431     (TYPE_SIGNED (__typeof__ (*(r))) \
  432      ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, st, smin, smax) \
  433      : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, ut, 0, umax))
  434 # else
  435 #  define _GL_INT_OP_WRAPV_SMALLISH(a,b,r,op,overflow,st,smin,smax,ut,umax) \
  436     (overflow (a, b, smin, smax) \
  437      ? (overflow (a, b, 0, umax) \
  438         ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st), 1) \
  439         : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st)) < 0) \
  440      : (overflow (a, b, 0, umax) \
  441         ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st)) >= 0 \
  442         : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st), 0)))
  443 # endif
  444 
  445 # define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) \
  446    (sizeof *(r) == sizeof (signed char) \
  447     ? _GL_INT_OP_WRAPV_SMALLISH (a, b, r, op, overflow, \
  448                                  signed char, SCHAR_MIN, SCHAR_MAX, \
  449                                  unsigned char, UCHAR_MAX) \
  450     : sizeof *(r) == sizeof (short int) \
  451     ? _GL_INT_OP_WRAPV_SMALLISH (a, b, r, op, overflow, \
  452                                  short int, SHRT_MIN, SHRT_MAX, \
  453                                  unsigned short int, USHRT_MAX) \
  454     : sizeof *(r) == sizeof (int) \
  455     ? (EXPR_SIGNED (*(r)) \
  456        ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
  457                           int, INT_MIN, INT_MAX) \
  458        : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
  459                           unsigned int, 0, UINT_MAX)) \
  460     : _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow))
  461 # ifdef LLONG_MAX
  462 #  define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
  463     (sizeof *(r) == sizeof (long int) \
  464      ? (EXPR_SIGNED (*(r)) \
  465         ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
  466                            long int, LONG_MIN, LONG_MAX) \
  467         : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
  468                            unsigned long int, 0, ULONG_MAX)) \
  469      : (EXPR_SIGNED (*(r)) \
  470         ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
  471                            long long int, LLONG_MIN, LLONG_MAX) \
  472         : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
  473                            unsigned long long int, 0, ULLONG_MAX)))
  474 # else
  475 #  define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
  476     (EXPR_SIGNED (*(r)) \
  477      ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
  478                         long int, LONG_MIN, LONG_MAX) \
  479      : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
  480                         unsigned long int, 0, ULONG_MAX))
  481 # endif
  482 #endif
  483 
  484 /* Store the low-order bits of A <op> B into *R, where the operation
  485    is given by OP.  Use the unsigned type UT for calculation to avoid
  486    overflow problems.  *R's type is T, with extrema TMIN and TMAX.
  487    T must be a signed integer type.  Return 1 if the result overflows.  */
  488 #define _GL_INT_OP_CALC(a, b, r, op, overflow, ut, t, tmin, tmax) \
  489   (overflow (a, b, tmin, tmax) \
  490    ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 1) \
  491    : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 0))
  492 
  493 /* Return the low-order bits of A <op> B, where the operation is given
  494    by OP.  Use the unsigned type UT for calculation to avoid undefined
  495    behavior on signed integer overflow, and convert the result to type T.
  496    UT is at least as wide as T and is no narrower than unsigned int,
  497    T is two's complement, and there is no padding or trap representations.
  498    Assume that converting UT to T yields the low-order bits, as is
  499    done in all known two's-complement C compilers.  E.g., see:
  500    https://gcc.gnu.org/onlinedocs/gcc/Integers-implementation.html
  501 
  502    According to the C standard, converting UT to T yields an
  503    implementation-defined result or signal for values outside T's
  504    range.  However, code that works around this theoretical problem
  505    runs afoul of a compiler bug in Oracle Studio 12.3 x86.  See:
  506    https://lists.gnu.org/r/bug-gnulib/2017-04/msg00049.html
  507    As the compiler bug is real, don't try to work around the
  508    theoretical problem.  */
  509 
  510 #define _GL_INT_OP_WRAPV_VIA_UNSIGNED(a, b, op, ut, t) \
  511   ((t) ((ut) (a) op (ut) (b)))
  512 
  513 /* Return true if the numeric values A + B, A - B, A * B fall outside
  514    the range TMIN..TMAX.  Arguments should be integer expressions
  515    without side effects.  TMIN should be signed and nonpositive.
  516    TMAX should be positive, and should be signed unless TMIN is zero.  */
  517 #define _GL_INT_ADD_RANGE_OVERFLOW(a, b, tmin, tmax) \
  518   ((b) < 0 \
  519    ? (((tmin) \
  520        ? ((EXPR_SIGNED (_GL_INT_CONVERT (a, (tmin) - (b))) || (b) < (tmin)) \
  521           && (a) < (tmin) - (b)) \
  522        : (a) <= -1 - (b)) \
  523       || ((EXPR_SIGNED (a) ? 0 <= (a) : (tmax) < (a)) && (tmax) < (a) + (b))) \
  524    : (a) < 0 \
  525    ? (((tmin) \
  526        ? ((EXPR_SIGNED (_GL_INT_CONVERT (b, (tmin) - (a))) || (a) < (tmin)) \
  527           && (b) < (tmin) - (a)) \
  528        : (b) <= -1 - (a)) \
  529       || ((EXPR_SIGNED (_GL_INT_CONVERT (a, b)) || (tmax) < (b)) \
  530           && (tmax) < (a) + (b))) \
  531    : (tmax) < (b) || (tmax) - (b) < (a))
  532 #define _GL_INT_SUBTRACT_RANGE_OVERFLOW(a, b, tmin, tmax) \
  533   (((a) < 0) == ((b) < 0) \
  534    ? ((a) < (b) \
  535       ? !(tmin) || -1 - (tmin) < (b) - (a) - 1 \
  536       : (tmax) < (a) - (b)) \
  537    : (a) < 0 \
  538    ? ((!EXPR_SIGNED (_GL_INT_CONVERT ((a) - (tmin), b)) && (a) - (tmin) < 0) \
  539       || (a) - (tmin) < (b)) \
  540    : ((! (EXPR_SIGNED (_GL_INT_CONVERT (tmax, b)) \
  541           && EXPR_SIGNED (_GL_INT_CONVERT ((tmax) + (b), a))) \
  542        && (tmax) <= -1 - (b)) \
  543       || (tmax) + (b) < (a)))
  544 #define _GL_INT_MULTIPLY_RANGE_OVERFLOW(a, b, tmin, tmax) \
  545   ((b) < 0 \
  546    ? ((a) < 0 \
  547       ? (EXPR_SIGNED (_GL_INT_CONVERT (tmax, b)) \
  548          ? (a) < (tmax) / (b) \
  549          : ((INT_NEGATE_OVERFLOW (b) \
  550              ? _GL_INT_CONVERT (b, tmax) >> (TYPE_WIDTH (b) - 1) \
  551              : (tmax) / -(b)) \
  552             <= -1 - (a))) \
  553       : INT_NEGATE_OVERFLOW (_GL_INT_CONVERT (b, tmin)) && (b) == -1 \
  554       ? (EXPR_SIGNED (a) \
  555          ? 0 < (a) + (tmin) \
  556          : 0 < (a) && -1 - (tmin) < (a) - 1) \
  557       : (tmin) / (b) < (a)) \
  558    : (b) == 0 \
  559    ? 0 \
  560    : ((a) < 0 \
  561       ? (INT_NEGATE_OVERFLOW (_GL_INT_CONVERT (a, tmin)) && (a) == -1 \
  562          ? (EXPR_SIGNED (b) ? 0 < (b) + (tmin) : -1 - (tmin) < (b) - 1) \
  563          : (tmin) / (a) < (b)) \
  564       : (tmax) / (b) < (a)))
  565 
  566 #endif /* _GL_INTPROPS_H */