lib/intprops.h

   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
  38 /* Minimum and maximum values for integer types and expressions.  */
  39
  40 /* The width in bits of the integer type or expression T.
  41    Do not evaluate T.  T must not be a bit-field expression.
  42    Padding bits are not supported; this is checked at compile-time below.  */
  43 #define TYPE_WIDTH(t) _GL_TYPE_WIDTH (t)
  44
  45 /* The maximum and minimum values for the integer type T.  */
  46 #define TYPE_MINIMUM(t) ((t) ~ TYPE_MAXIMUM (t))
  47 #define TYPE_MAXIMUM(t)                                                 \
  48   ((t) (! TYPE_SIGNED (t)                                               \
  49         ? (t) -1                                                        \
  50         : ((((t) 1 << (TYPE_WIDTH (t) - 2)) - 1) * 2 + 1)))
  51
  52 /* Bound on length of the string representing an unsigned integer
  53    value representable in B bits.  log10 (2.0) < 146/485.  The
  54    smallest value of B where this bound is not tight is 2621.  */
  55 #define INT_BITS_STRLEN_BOUND(b) (((b) * 146 + 484) / 485)
  56
  57 /* Bound on length of the string representing an integer type or expression T.
  58    T must not be a bit-field expression.
  59
  60    Subtract 1 for the sign bit if T is signed, and then add 1 more for
  61    a minus sign if needed.
  62
  63    Because _GL_SIGNED_TYPE_OR_EXPR sometimes returns 1 when its argument is
  64    unsigned, this macro may overestimate the true bound by one byte when
  65    applied to unsigned types of size 2, 4, 16, ... bytes.  */
  66 #define INT_STRLEN_BOUND(t)                                     \
  67   (INT_BITS_STRLEN_BOUND (TYPE_WIDTH (t) - _GL_SIGNED_TYPE_OR_EXPR (t)) \
  68    + _GL_SIGNED_TYPE_OR_EXPR (t))
  69
  70 /* Bound on buffer size needed to represent an integer type or expression T,
  71    including the terminating null.  T must not be a bit-field expression.  */
  72 #define INT_BUFSIZE_BOUND(t) (INT_STRLEN_BOUND (t) + 1)
  73
  74
  75 /* Range overflow checks.
  76
  77    The INT_<op>_RANGE_OVERFLOW macros return 1 if the corresponding C
  78    operators overflow arithmetically when given the same arguments.
  79    These macros do not rely on undefined or implementation-defined behavior.
  80    Although their implementations are simple and straightforward,
  81    they are harder to use and may be less efficient than the
  82    INT_<op>_WRAPV, INT_<op>_OK, and INT_<op>_OVERFLOW macros described below.
  83
  84    Example usage:
  85
  86      long int i = ...;
  87      long int j = ...;
  88      if (INT_MULTIPLY_RANGE_OVERFLOW (i, j, LONG_MIN, LONG_MAX))
  89        printf ("multiply would overflow");
  90      else
  91        printf ("product is %ld", i * j);
  92
  93    Restrictions on *_RANGE_OVERFLOW macros:
  94
  95    These macros do not check for all possible numerical problems or
  96    undefined or unspecified behavior: they do not check for division
  97    by zero, for bad shift counts, or for shifting negative numbers.
  98
  99    These macros may evaluate their arguments zero or multiple times,
 100    so the arguments should not have side effects.  The arithmetic
 101    arguments (including the MIN and MAX arguments) must be of the same
 102    integer type after the usual arithmetic conversions, and the type
 103    must have minimum value MIN and maximum MAX.  Unsigned types should
 104    use a zero MIN of the proper type.
 105
 106    Because all arguments are subject to integer promotions, these
 107    macros typically do not work on types narrower than 'int'.
 108
 109    These macros are tuned for constant MIN and MAX.  For commutative
 110    operations such as A + B, they are also tuned for constant B.  */
 111
 112 /* Return 1 if A + B would overflow in [MIN,MAX] arithmetic.
 113    See above for restrictions.  */
 114 #define INT_ADD_RANGE_OVERFLOW(a, b, min, max)          \
 115   ((b) < 0                                              \
 116    ? (a) < (min) - (b)                                  \
 117    : (max) - (b) < (a))
 118
 119 /* Return 1 if A - B would overflow in [MIN,MAX] arithmetic.
 120    See above for restrictions.  */
 121 #define INT_SUBTRACT_RANGE_OVERFLOW(a, b, min, max)     \
 122   ((b) < 0                                              \
 123    ? (max) + (b) < (a)                                  \
 124    : (a) < (min) + (b))
 125
 126 /* Return 1 if - A would overflow in [MIN,MAX] arithmetic.
 127    See above for restrictions.  */
 128 #define INT_NEGATE_RANGE_OVERFLOW(a, min, max)          \
 129   _GL_INT_NEGATE_RANGE_OVERFLOW (a, min, max)
 130
 131 /* Return 1 if A * B would overflow in [MIN,MAX] arithmetic.
 132    See above for restrictions.  Avoid && and || as they tickle
 133    bugs in Sun C 5.11 2010/08/13 and other compilers; see
 134    <https://lists.gnu.org/r/bug-gnulib/2011-05/msg00401.html>.  */
 135 #define INT_MULTIPLY_RANGE_OVERFLOW(a, b, min, max)     \
 136   ((b) < 0                                              \
 137    ? ((a) < 0                                           \
 138       ? (a) < (max) / (b)                               \
 139       : (b) == -1                                       \
 140       ? 0                                               \
 141       : (min) / (b) < (a))                              \
 142    : (b) == 0                                           \
 143    ? 0                                                  \
 144    : ((a) < 0                                           \
 145       ? (a) < (min) / (b)                               \
 146       : (max) / (b) < (a)))
 147
 148 /* Return 1 if A / B would overflow in [MIN,MAX] arithmetic.
 149    See above for restrictions.  Do not check for division by zero.  */
 150 #define INT_DIVIDE_RANGE_OVERFLOW(a, b, min, max)       \
 151   ((min) < 0 && (b) == -1 && (a) < - (max))
 152
 153 /* Return 1 if A % B would overflow in [MIN,MAX] arithmetic.
 154    See above for restrictions.  Do not check for division by zero.
 155    Mathematically, % should never overflow, but on x86-like hosts
 156    INT_MIN % -1 traps, and the C standard permits this, so treat this
 157    as an overflow too.  */
 158 #define INT_REMAINDER_RANGE_OVERFLOW(a, b, min, max)    \
 159   INT_DIVIDE_RANGE_OVERFLOW (a, b, min, max)
 160
 161 /* Return 1 if A << B would overflow in [MIN,MAX] arithmetic.
 162    See above for restrictions.  Here, MIN and MAX are for A only, and B need
 163    not be of the same type as the other arguments.  The C standard says that
 164    behavior is undefined for shifts unless 0 <= B < wordwidth, and that when
 165    A is negative then A << B has undefined behavior and A >> B has
 166    implementation-defined behavior, but do not check these other
 167    restrictions.  */
 168 #define INT_LEFT_SHIFT_RANGE_OVERFLOW(a, b, min, max)   \
 169   ((a) < 0                                              \
 170    ? (a) < (min) >> (b)                                 \
 171    : (max) >> (b) < (a))
 172
 173 /* The _GL*_OVERFLOW macros have the same restrictions as the
 174    *_RANGE_OVERFLOW macros, except that they do not assume that operands
 175    (e.g., A and B) have the same type as MIN and MAX.  Instead, they assume
 176    that the result (e.g., A + B) has that type.  */
 177 #if _GL_HAS_BUILTIN_OVERFLOW_P
 178 # define _GL_ADD_OVERFLOW(a, b, min, max)                               \
 179    __builtin_add_overflow_p (a, b, (__typeof__ ((a) + (b))) 0)
 180 # define _GL_SUBTRACT_OVERFLOW(a, b, min, max)                          \
 181    __builtin_sub_overflow_p (a, b, (__typeof__ ((a) - (b))) 0)
 182 # define _GL_MULTIPLY_OVERFLOW(a, b, min, max)                          \
 183    __builtin_mul_overflow_p (a, b, (__typeof__ ((a) * (b))) 0)
 184 #else
 185 # define _GL_ADD_OVERFLOW(a, b, min, max)                                \
 186    ((min) < 0 ? INT_ADD_RANGE_OVERFLOW (a, b, min, max)                  \
 187     : (a) < 0 ? (b) <= (a) + (b)                                         \
 188     : (b) < 0 ? (a) <= (a) + (b)                                         \
 189     : (a) + (b) < (b))
 190 # define _GL_SUBTRACT_OVERFLOW(a, b, min, max)                           \
 191    ((min) < 0 ? INT_SUBTRACT_RANGE_OVERFLOW (a, b, min, max)             \
 192     : (a) < 0 ? 1                                                        \
 193     : (b) < 0 ? (a) - (b) <= (a)                                         \
 194     : (a) < (b))
 195 # define _GL_MULTIPLY_OVERFLOW(a, b, min, max)                           \
 196    (((min) == 0 && (((a) < 0 && 0 < (b)) || ((b) < 0 && 0 < (a))))       \
 197     || INT_MULTIPLY_RANGE_OVERFLOW (a, b, min, max))
 198 #endif
 199 #define _GL_DIVIDE_OVERFLOW(a, b, min, max)                             \
 200   ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max)  \
 201    : (a) < 0 ? (b) <= (a) + (b) - 1                                     \
 202    : (b) < 0 && (a) + (b) <= (a))
 203 #define _GL_REMAINDER_OVERFLOW(a, b, min, max)                          \
 204   ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max)  \
 205    : (a) < 0 ? (a) % (b) != ((max) - (b) + 1) % (b)                     \
 206    : (b) < 0 && ! _GL_UNSIGNED_NEG_MULTIPLE (a, b, max))
 207
 208 /* Return a nonzero value if A is a mathematical multiple of B, where
 209    A is unsigned, B is negative, and MAX is the maximum value of A's
 210    type.  A's type must be the same as (A % B)'s type.  Normally (A %
 211    -B == 0) suffices, but things get tricky if -B would overflow.  */
 212 #define _GL_UNSIGNED_NEG_MULTIPLE(a, b, max)                            \
 213   (((b) < -_GL_SIGNED_INT_MAXIMUM (b)                                   \
 214     ? (_GL_SIGNED_INT_MAXIMUM (b) == (max)                              \
 215        ? (a)                                                            \
 216        : (a) % (_GL_INT_CONVERT (a, _GL_SIGNED_INT_MAXIMUM (b)) + 1))   \
 217     : (a) % - (b))                                                      \
 218    == 0)
 219
 220 /* Check for integer overflow, and report low order bits of answer.
 221
 222    The INT_<op>_OVERFLOW macros return 1 if the corresponding C operators
 223    might not yield numerically correct answers due to arithmetic overflow.
 224    The INT_<op>_WRAPV macros compute the low-order bits of the sum,
 225    difference, and product of two C integers, and return 1 if these
 226    low-order bits are not numerically correct.
 227    These macros work correctly on all known practical hosts, and do not rely
 228    on undefined behavior due to signed arithmetic overflow.
 229
 230    Example usage, assuming A and B are long int:
 231
 232      if (INT_MULTIPLY_OVERFLOW (a, b))
 233        printf ("result would overflow\n");
 234      else
 235        printf ("result is %ld (no overflow)\n", a * b);
 236
 237    Example usage with WRAPV flavor:
 238
 239      long int result;
 240      bool overflow = INT_MULTIPLY_WRAPV (a, b, &result);
 241      printf ("result is %ld (%s)\n", result,
 242              overflow ? "after overflow" : "no overflow");
 243
 244    Restrictions on these macros:
 245
 246    These macros do not check for all possible numerical problems or
 247    undefined or unspecified behavior: they do not check for division
 248    by zero, for bad shift counts, or for shifting negative numbers.
 249
 250    These macros may evaluate their arguments zero or multiple times, so the
 251    arguments should not have side effects.
 252
 253    The WRAPV macros are not constant expressions.  They support only
 254    +, binary -, and *.
 255
 256    Because the WRAPV macros convert the result, they report overflow
 257    in different circumstances than the OVERFLOW macros do.  For
 258    example, in the typical case with 16-bit 'short' and 32-bit 'int',
 259    if A, B and *R are all of type 'short' then INT_ADD_OVERFLOW (A, B)
 260    returns false because the addition cannot overflow after A and B
 261    are converted to 'int', whereas INT_ADD_WRAPV (A, B, R) returns
 262    true or false depending on whether the sum fits into 'short'.
 263
 264    These macros are tuned for their last input argument being a constant.
 265
 266    A, B, and *R should be integers; they need not be the same type,
 267    and they need not be all signed or all unsigned.
 268    However, none of the integer types should be bit-precise,
 269    and *R's type should not be char, bool, or an enumeration type.
 270
 271    Return 1 if the integer expressions A * B, A - B, -A, A * B, A / B,
 272    A % B, and A << B would overflow, respectively.  */
 273
 274 #define INT_ADD_OVERFLOW(a, b) \
 275   _GL_BINARY_OP_OVERFLOW (a, b, _GL_ADD_OVERFLOW)
 276 #define INT_SUBTRACT_OVERFLOW(a, b) \
 277   _GL_BINARY_OP_OVERFLOW (a, b, _GL_SUBTRACT_OVERFLOW)
 278 #define INT_NEGATE_OVERFLOW(a) _GL_INT_NEGATE_OVERFLOW (a)
 279 #define INT_MULTIPLY_OVERFLOW(a, b) \
 280   _GL_BINARY_OP_OVERFLOW (a, b, _GL_MULTIPLY_OVERFLOW)
 281 #define INT_DIVIDE_OVERFLOW(a, b) \
 282   _GL_BINARY_OP_OVERFLOW (a, b, _GL_DIVIDE_OVERFLOW)
 283 #define INT_REMAINDER_OVERFLOW(a, b) \
 284   _GL_BINARY_OP_OVERFLOW (a, b, _GL_REMAINDER_OVERFLOW)
 285 #define INT_LEFT_SHIFT_OVERFLOW(a, b) \
 286   INT_LEFT_SHIFT_RANGE_OVERFLOW (a, b, \
 287                                  _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
 288
 289 /* Return 1 if the expression A <op> B would overflow,
 290    where OP_RESULT_OVERFLOW (A, B, MIN, MAX) does the actual test,
 291    assuming MIN and MAX are the minimum and maximum for the result type.
 292    Arguments should be free of side effects.  */
 293 #define _GL_BINARY_OP_OVERFLOW(a, b, op_result_overflow)        \
 294   op_result_overflow (a, b,                                     \
 295                       _GL_INT_MINIMUM (_GL_INT_CONVERT (a, b)), \
 296                       _GL_INT_MAXIMUM (_GL_INT_CONVERT (a, b)))
 297
 298 /* Store the low-order bits of A + B, A - B, A * B, respectively, into *R.
 299    Return 1 if the result overflows.  See above for restrictions.  */
 300 #define INT_ADD_WRAPV(a, b, r) _GL_INT_ADD_WRAPV (a, b, r)
 301 #define INT_SUBTRACT_WRAPV(a, b, r) _GL_INT_SUBTRACT_WRAPV (a, b, r)
 302 #define INT_MULTIPLY_WRAPV(a, b, r) _GL_INT_MULTIPLY_WRAPV (a, b, r)
 303
 304 /* The following macros compute A + B, A - B, and A * B, respectively.
 305    If no overflow occurs, they set *R to the result and return 1;
 306    otherwise, they return 0 and may modify *R.
 307
 308    Example usage:
 309
 310      long int result;
 311      if (INT_ADD_OK (a, b, &result))
 312        printf ("result is %ld\n", result);
 313      else
 314        printf ("overflow\n");
 315
 316    A, B, and *R should be integers; they need not be the same type,
 317    and they need not be all signed or all unsigned.
 318    However, none of the integer types should be bit-precise,
 319    and *R's type should not be char, bool, or an enumeration type.
 320
 321    These macros work correctly on all known practical hosts, and do not rely
 322    on undefined behavior due to signed arithmetic overflow.
 323
 324    These macros are not constant expressions.
 325
 326    These macros may evaluate their arguments zero or multiple times, so the
 327    arguments should not have side effects.
 328
 329    These macros are tuned for B being a constant.  */
 330
 331 #define INT_ADD_OK(a, b, r) (! INT_ADD_WRAPV (a, b, r))
 332 #define INT_SUBTRACT_OK(a, b, r) (! INT_SUBTRACT_WRAPV (a, b, r))
 333 #define INT_MULTIPLY_OK(a, b, r) (! INT_MULTIPLY_WRAPV (a, b, r))
 334
 335 #endif /* _GL_INTPROPS_H */