root/lib/intprops.h

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   1 /* intprops.h -- properties of integer types
   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_H
  19 #define _GL_INTPROPS_H
  20 
  21 #include "intprops-internal.h"
  22 
  23 /* The extra casts in the following macros work around compiler bugs,
  24    e.g., in Cray C 5.0.3.0.  */
  25 
  26 /* True if the arithmetic type T is an integer type.  bool counts as
  27    an integer.  */
  28 #define TYPE_IS_INTEGER(t) ((t) 1.5 == 1)
  29 
  30 /* True if the real type T is signed.  */
  31 #define TYPE_SIGNED(t) _GL_TYPE_SIGNED (t)
  32 
  33 /* Return 1 if the real expression E, after promotion, has a
  34    signed or floating type.  Do not evaluate E.  */
  35 #define EXPR_SIGNED(e) _GL_EXPR_SIGNED (e)
  36 
  37 /* Minimum and maximum values for integer types and expressions.  */
  38 
  39 /* The width in bits of the integer type or expression T.
  40    Do not evaluate T.  T must not be a bit-field expression.
  41    Padding bits are not supported; this is checked at compile-time below.  */
  42 #define TYPE_WIDTH(t) _GL_TYPE_WIDTH (t)
  43 
  44 /* The maximum and minimum values for the integer type T.  */
  45 #define TYPE_MINIMUM(t) ((t) ~TYPE_MAXIMUM (t))
  46 #define TYPE_MAXIMUM(t)                                                                            \
  47     ((t) (!TYPE_SIGNED (t) ? (t) - 1 : ((((t) 1 << (TYPE_WIDTH (t) - 2)) - 1) * 2 + 1)))
  48 
  49 /* Bound on length of the string representing an unsigned integer
  50    value representable in B bits.  log10 (2.0) < 146/485.  The
  51    smallest value of B where this bound is not tight is 2621.  */
  52 #define INT_BITS_STRLEN_BOUND(b) (((b) * 146 + 484) / 485)
  53 
  54 /* Bound on length of the string representing an integer type or expression T.
  55    T must not be a bit-field expression.
  56 
  57    Subtract 1 for the sign bit if T is signed, and then add 1 more for
  58    a minus sign if needed.
  59 
  60    Because _GL_SIGNED_TYPE_OR_EXPR sometimes returns 1 when its argument is
  61    unsigned, this macro may overestimate the true bound by one byte when
  62    applied to unsigned types of size 2, 4, 16, ... bytes.  */
  63 #define INT_STRLEN_BOUND(t)                                                                        \
  64     (INT_BITS_STRLEN_BOUND (TYPE_WIDTH (t) - _GL_SIGNED_TYPE_OR_EXPR (t))                          \
  65      + _GL_SIGNED_TYPE_OR_EXPR (t))
  66 
  67 /* Bound on buffer size needed to represent an integer type or expression T,
  68    including the terminating null.  T must not be a bit-field expression.  */
  69 #define INT_BUFSIZE_BOUND(t) (INT_STRLEN_BOUND (t) + 1)
  70 
  71 /* Range overflow checks.
  72 
  73    The INT_<op>_RANGE_OVERFLOW macros return 1 if the corresponding C
  74    operators overflow arithmetically when given the same arguments.
  75    These macros do not rely on undefined or implementation-defined behavior.
  76    Although their implementations are simple and straightforward,
  77    they are harder to use and may be less efficient than the
  78    INT_<op>_WRAPV, INT_<op>_OK, and INT_<op>_OVERFLOW macros described below.
  79 
  80    Example usage:
  81 
  82      long int i = ...;
  83      long int j = ...;
  84      if (INT_MULTIPLY_RANGE_OVERFLOW (i, j, LONG_MIN, LONG_MAX))
  85        printf ("multiply would overflow");
  86      else
  87        printf ("product is %ld", i * j);
  88 
  89    Restrictions on *_RANGE_OVERFLOW macros:
  90 
  91    These macros do not check for all possible numerical problems or
  92    undefined or unspecified behavior: they do not check for division
  93    by zero, for bad shift counts, or for shifting negative numbers.
  94 
  95    These macros may evaluate their arguments zero or multiple times,
  96    so the arguments should not have side effects.  The arithmetic
  97    arguments (including the MIN and MAX arguments) must be of the same
  98    integer type after the usual arithmetic conversions, and the type
  99    must have minimum value MIN and maximum MAX.  Unsigned types should
 100    use a zero MIN of the proper type.
 101 
 102    Because all arguments are subject to integer promotions, these
 103    macros typically do not work on types narrower than 'int'.
 104 
 105    These macros are tuned for constant MIN and MAX.  For commutative
 106    operations such as A + B, they are also tuned for constant B.  */
 107 
 108 /* Return 1 if A + B would overflow in [MIN,MAX] arithmetic.
 109    See above for restrictions.  */
 110 #define INT_ADD_RANGE_OVERFLOW(a, b, min, max) ((b) < 0 ? (a) < (min) - (b) : (max) - (b) < (a))
 111 
 112 /* Return 1 if A - B would overflow in [MIN,MAX] arithmetic.
 113    See above for restrictions.  */
 114 #define INT_SUBTRACT_RANGE_OVERFLOW(a, b, min, max)                                                \
 115     ((b) < 0 ? (max) + (b) < (a) : (a) < (min) + (b))
 116 
 117 /* Return 1 if - A would overflow in [MIN,MAX] arithmetic.
 118    See above for restrictions.  */
 119 #define INT_NEGATE_RANGE_OVERFLOW(a, min, max) _GL_INT_NEGATE_RANGE_OVERFLOW (a, min, max)
 120 
 121 /* Return 1 if A * B would overflow in [MIN,MAX] arithmetic.
 122    See above for restrictions.  Avoid && and || as they tickle
 123    bugs in Sun C 5.11 2010/08/13 and other compilers; see
 124    <https://lists.gnu.org/r/bug-gnulib/2011-05/msg00401.html>.  */
 125 #define INT_MULTIPLY_RANGE_OVERFLOW(a, b, min, max)                                                \
 126     ((b) < 0        ? ((a) < 0         ? (a) < (max) / (b)                                         \
 127                            : (b) == -1 ? 0                                                         \
 128                                        : (min) / (b) < (a))                                        \
 129          : (b) == 0 ? 0                                                                            \
 130                     : ((a) < 0 ? (a) < (min) / (b) : (max) / (b) < (a)))
 131 
 132 /* Return 1 if A / B would overflow in [MIN,MAX] arithmetic.
 133    See above for restrictions.  Do not check for division by zero.  */
 134 #define INT_DIVIDE_RANGE_OVERFLOW(a, b, min, max) ((min) < 0 && (b) == -1 && (a) < -(max))
 135 
 136 /* Return 1 if A % B would overflow in [MIN,MAX] arithmetic.
 137    See above for restrictions.  Do not check for division by zero.
 138    Mathematically, % should never overflow, but on x86-like hosts
 139    INT_MIN % -1 traps, and the C standard permits this, so treat this
 140    as an overflow too.  */
 141 #define INT_REMAINDER_RANGE_OVERFLOW(a, b, min, max) INT_DIVIDE_RANGE_OVERFLOW (a, b, min, max)
 142 
 143 /* Return 1 if A << B would overflow in [MIN,MAX] arithmetic.
 144    See above for restrictions.  Here, MIN and MAX are for A only, and B need
 145    not be of the same type as the other arguments.  The C standard says that
 146    behavior is undefined for shifts unless 0 <= B < wordwidth, and that when
 147    A is negative then A << B has undefined behavior and A >> B has
 148    implementation-defined behavior, but do not check these other
 149    restrictions.  */
 150 #define INT_LEFT_SHIFT_RANGE_OVERFLOW(a, b, min, max)                                              \
 151     ((a) < 0 ? (a) < (min) >> (b) : (max) >> (b) < (a))
 152 
 153 /* The _GL*_OVERFLOW macros have the same restrictions as the
 154    *_RANGE_OVERFLOW macros, except that they do not assume that operands
 155    (e.g., A and B) have the same type as MIN and MAX.  Instead, they assume
 156    that the result (e.g., A + B) has that type.  */
 157 #if _GL_HAS_BUILTIN_OVERFLOW_P
 158 #    define _GL_ADD_OVERFLOW(a, b, min, max)                                                       \
 159         __builtin_add_overflow_p (a, b, (__typeof__ ((a) + (b))) 0)
 160 #    define _GL_SUBTRACT_OVERFLOW(a, b, min, max)                                                  \
 161         __builtin_sub_overflow_p (a, b, (__typeof__ ((a) - (b))) 0)
 162 #    define _GL_MULTIPLY_OVERFLOW(a, b, min, max)                                                  \
 163         __builtin_mul_overflow_p (a, b, (__typeof__ ((a) * (b))) 0)
 164 #else
 165 #    define _GL_ADD_OVERFLOW(a, b, min, max)                                                       \
 166         ((min) < 0     ? INT_ADD_RANGE_OVERFLOW (a, b, min, max)                                   \
 167              : (a) < 0 ? (b) <= (a) + (b)                                                          \
 168              : (b) < 0 ? (a) <= (a) + (b)                                                          \
 169                        : (a) + (b) < (b))
 170 #    define _GL_SUBTRACT_OVERFLOW(a, b, min, max)                                                  \
 171         ((min) < 0     ? INT_SUBTRACT_RANGE_OVERFLOW (a, b, min, max)                              \
 172              : (a) < 0 ? 1                                                                         \
 173              : (b) < 0 ? (a) - (b) <= (a)                                                          \
 174                        : (a) < (b))
 175 #    define _GL_MULTIPLY_OVERFLOW(a, b, min, max)                                                  \
 176         (((min) == 0 && (((a) < 0 && 0 < (b)) || ((b) < 0 && 0 < (a))))                            \
 177          || INT_MULTIPLY_RANGE_OVERFLOW (a, b, min, max))
 178 #endif
 179 #define _GL_DIVIDE_OVERFLOW(a, b, min, max)                                                        \
 180     ((min) < 0     ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < -(max)                        \
 181          : (a) < 0 ? (b) <= (a) + (b) - 1                                                          \
 182                    : (b) < 0 && (a) + (b) <= (a))
 183 #define _GL_REMAINDER_OVERFLOW(a, b, min, max)                                                     \
 184     ((min) < 0     ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < -(max)                        \
 185          : (a) < 0 ? (a) % (b) != ((max) - (b) + 1) % (b)                                          \
 186                    : (b) < 0 && !_GL_UNSIGNED_NEG_MULTIPLE (a, b, max))
 187 
 188 /* Return a nonzero value if A is a mathematical multiple of B, where
 189    A is unsigned, B is negative, and MAX is the maximum value of A's
 190    type.  A's type must be the same as (A % B)'s type.  Normally (A %
 191    -B == 0) suffices, but things get tricky if -B would overflow.  */
 192 #define _GL_UNSIGNED_NEG_MULTIPLE(a, b, max)                                                       \
 193     (((b) < -_GL_SIGNED_INT_MAXIMUM (b)                                                            \
 194           ? (_GL_SIGNED_INT_MAXIMUM (b) == (max)                                                   \
 195                  ? (a)                                                                             \
 196                  : (a) % (_GL_INT_CONVERT (a, _GL_SIGNED_INT_MAXIMUM (b)) + 1))                    \
 197           : (a) % -(b))                                                                            \
 198      == 0)
 199 
 200 /* Check for integer overflow, and report low order bits of answer.
 201 
 202    The INT_<op>_OVERFLOW macros return 1 if the corresponding C operators
 203    might not yield numerically correct answers due to arithmetic overflow.
 204    The INT_<op>_WRAPV macros compute the low-order bits of the sum,
 205    difference, and product of two C integers, and return 1 if these
 206    low-order bits are not numerically correct.
 207    These macros work correctly on all known practical hosts, and do not rely
 208    on undefined behavior due to signed arithmetic overflow.
 209 
 210    Example usage, assuming A and B are long int:
 211 
 212      if (INT_MULTIPLY_OVERFLOW (a, b))
 213        printf ("result would overflow\n");
 214      else
 215        printf ("result is %ld (no overflow)\n", a * b);
 216 
 217    Example usage with WRAPV flavor:
 218 
 219      long int result;
 220      bool overflow = INT_MULTIPLY_WRAPV (a, b, &result);
 221      printf ("result is %ld (%s)\n", result,
 222              overflow ? "after overflow" : "no overflow");
 223 
 224    Restrictions on these macros:
 225 
 226    These macros do not check for all possible numerical problems or
 227    undefined or unspecified behavior: they do not check for division
 228    by zero, for bad shift counts, or for shifting negative numbers.
 229 
 230    These macros may evaluate their arguments zero or multiple times, so the
 231    arguments should not have side effects.
 232 
 233    The WRAPV macros are not constant expressions.  They support only
 234    +, binary -, and *.
 235 
 236    Because the WRAPV macros convert the result, they report overflow
 237    in different circumstances than the OVERFLOW macros do.  For
 238    example, in the typical case with 16-bit 'short' and 32-bit 'int',
 239    if A, B and *R are all of type 'short' then INT_ADD_OVERFLOW (A, B)
 240    returns false because the addition cannot overflow after A and B
 241    are converted to 'int', whereas INT_ADD_WRAPV (A, B, R) returns
 242    true or false depending on whether the sum fits into 'short'.
 243 
 244    These macros are tuned for their last input argument being a constant.
 245 
 246    A, B, and *R should be integers; they need not be the same type,
 247    and they need not be all signed or all unsigned.
 248    However, none of the integer types should be bit-precise,
 249    and *R's type should not be char, bool, or an enumeration type.
 250 
 251    Return 1 if the integer expressions A * B, A - B, -A, A * B, A / B,
 252    A % B, and A << B would overflow, respectively.  */
 253 
 254 #define INT_ADD_OVERFLOW(a, b)       _GL_BINARY_OP_OVERFLOW (a, b, _GL_ADD_OVERFLOW)
 255 #define INT_SUBTRACT_OVERFLOW(a, b)  _GL_BINARY_OP_OVERFLOW (a, b, _GL_SUBTRACT_OVERFLOW)
 256 #define INT_NEGATE_OVERFLOW(a)       _GL_INT_NEGATE_OVERFLOW (a)
 257 #define INT_MULTIPLY_OVERFLOW(a, b)  _GL_BINARY_OP_OVERFLOW (a, b, _GL_MULTIPLY_OVERFLOW)
 258 #define INT_DIVIDE_OVERFLOW(a, b)    _GL_BINARY_OP_OVERFLOW (a, b, _GL_DIVIDE_OVERFLOW)
 259 #define INT_REMAINDER_OVERFLOW(a, b) _GL_BINARY_OP_OVERFLOW (a, b, _GL_REMAINDER_OVERFLOW)
 260 #define INT_LEFT_SHIFT_OVERFLOW(a, b)                                                              \
 261     INT_LEFT_SHIFT_RANGE_OVERFLOW (a, b, _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
 262 
 263 /* Return 1 if the expression A <op> B would overflow,
 264    where OP_RESULT_OVERFLOW (A, B, MIN, MAX) does the actual test,
 265    assuming MIN and MAX are the minimum and maximum for the result type.
 266    Arguments should be free of side effects.  */
 267 #define _GL_BINARY_OP_OVERFLOW(a, b, op_result_overflow)                                           \
 268     op_result_overflow (a, b, _GL_INT_MINIMUM (_GL_INT_CONVERT (a, b)),                            \
 269                         _GL_INT_MAXIMUM (_GL_INT_CONVERT (a, b)))
 270 
 271 /* Store the low-order bits of A + B, A - B, A * B, respectively, into *R.
 272    Return 1 if the result overflows.  See above for restrictions.  */
 273 #define INT_ADD_WRAPV(a, b, r)      _GL_INT_ADD_WRAPV (a, b, r)
 274 #define INT_SUBTRACT_WRAPV(a, b, r) _GL_INT_SUBTRACT_WRAPV (a, b, r)
 275 #define INT_MULTIPLY_WRAPV(a, b, r) _GL_INT_MULTIPLY_WRAPV (a, b, r)
 276 
 277 /* The following macros compute A + B, A - B, and A * B, respectively.
 278    If no overflow occurs, they set *R to the result and return 1;
 279    otherwise, they return 0 and may modify *R.
 280 
 281    Example usage:
 282 
 283      long int result;
 284      if (INT_ADD_OK (a, b, &result))
 285        printf ("result is %ld\n", result);
 286      else
 287        printf ("overflow\n");
 288 
 289    A, B, and *R should be integers; they need not be the same type,
 290    and they need not be all signed or all unsigned.
 291    However, none of the integer types should be bit-precise,
 292    and *R's type should not be char, bool, or an enumeration type.
 293 
 294    These macros work correctly on all known practical hosts, and do not rely
 295    on undefined behavior due to signed arithmetic overflow.
 296 
 297    These macros are not constant expressions.
 298 
 299    These macros may evaluate their arguments zero or multiple times, so the
 300    arguments should not have side effects.
 301 
 302    These macros are tuned for B being a constant.  */
 303 
 304 #define INT_ADD_OK(a, b, r)      (!INT_ADD_WRAPV (a, b, r))
 305 #define INT_SUBTRACT_OK(a, b, r) (!INT_SUBTRACT_WRAPV (a, b, r))
 306 #define INT_MULTIPLY_OK(a, b, r) (!INT_MULTIPLY_WRAPV (a, b, r))
 307 
 308 #endif

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