intprops.h 14.2 KB
Newer Older
Paul Eggert's avatar
Paul Eggert committed
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
/* intprops.h -- properties of integer types

   Copyright (C) 2001-2005, 2009-2011 Free Software Foundation, Inc.

   This program is free software: you can redistribute it and/or modify
   it under the terms of the GNU General Public License as published by
   the Free Software Foundation; either version 3 of the License, or
   (at your option) any later version.

   This program is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
   GNU General Public License for more details.

   You should have received a copy of the GNU General Public License
   along with this program.  If not, see <http://www.gnu.org/licenses/>.  */

/* Written by Paul Eggert.  */

Paul Eggert's avatar
Paul Eggert committed
20 21
#ifndef _GL_INTPROPS_H
#define _GL_INTPROPS_H
Paul Eggert's avatar
Paul Eggert committed
22

Paul Eggert's avatar
Paul Eggert committed
23 24 25 26 27 28
#include <limits.h>

/* Return a integer value, converted to the same type as the integer
   expression E after integer type promotion.  V is the unconverted value.
   E should not have side effects.  */
#define _GL_INT_CONVERT(e, v) ((e) - (e) + (v))
Paul Eggert's avatar
Paul Eggert committed
29 30 31 32 33 34

/* The extra casts in the following macros work around compiler bugs,
   e.g., in Cray C 5.0.3.0.  */

/* True if the arithmetic type T is an integer type.  bool counts as
   an integer.  */
Paul Eggert's avatar
Paul Eggert committed
35
#define TYPE_IS_INTEGER(t) ((t) 1.5 == 1)
Paul Eggert's avatar
Paul Eggert committed
36 37 38 39 40

/* True if negative values of the signed integer type T use two's
   complement, ones' complement, or signed magnitude representation,
   respectively.  Much GNU code assumes two's complement, but some
   people like to be portable to all possible C hosts.  */
Paul Eggert's avatar
Paul Eggert committed
41 42 43 44 45 46
#define TYPE_TWOS_COMPLEMENT(t) ((t) ~ (t) 0 == (t) -1)
#define TYPE_ONES_COMPLEMENT(t) ((t) ~ (t) 0 == 0)
#define TYPE_SIGNED_MAGNITUDE(t) ((t) ~ (t) 0 < (t) -1)

/* True if the signed integer expression E uses two's complement.  */
#define _GL_INT_TWOS_COMPLEMENT(e) (~ _GL_INT_CONVERT (e, 0) == -1)
Paul Eggert's avatar
Paul Eggert committed
47 48

/* True if the arithmetic type T is signed.  */
Paul Eggert's avatar
Paul Eggert committed
49 50 51 52 53
#define TYPE_SIGNED(t) (! ((t) 0 < (t) -1))

/* Return 1 if the integer expression E, after integer promotion, has
   a signed type.  E should not have side effects.  */
#define _GL_INT_SIGNED(e) (_GL_INT_CONVERT (e, -1) < 0)
Paul Eggert's avatar
Paul Eggert committed
54

Paul Eggert's avatar
Paul Eggert committed
55 56

/* Minimum and maximum values for integer types and expressions.  These
Paul Eggert's avatar
Paul Eggert committed
57 58 59
   macros have undefined behavior if T is signed and has padding bits.
   If this is a problem for you, please let us know how to fix it for
   your host.  */
Paul Eggert's avatar
Paul Eggert committed
60 61 62 63 64 65 66

/* The maximum and minimum values for the integer type T.  */
#define TYPE_MINIMUM(t)                                                 \
  ((t) (! TYPE_SIGNED (t)                                               \
        ? (t) 0                                                         \
        : TYPE_SIGNED_MAGNITUDE (t)                                     \
        ? ~ (t) 0                                                       \
67
        : ~ TYPE_MAXIMUM (t)))
Paul Eggert's avatar
Paul Eggert committed
68 69 70
#define TYPE_MAXIMUM(t)                                                 \
  ((t) (! TYPE_SIGNED (t)                                               \
        ? (t) -1                                                        \
71
        : ((((t) 1 << (sizeof (t) * CHAR_BIT - 2)) - 1) * 2 + 1)))
Paul Eggert's avatar
Paul Eggert committed
72

Paul Eggert's avatar
Paul Eggert committed
73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102
/* The maximum and minimum values for the type of the expression E,
   after integer promotion.  E should not have side effects.  */
#define _GL_INT_MINIMUM(e)                                              \
  (_GL_INT_SIGNED (e)                                                   \
   ? - _GL_INT_TWOS_COMPLEMENT (e) - _GL_SIGNED_INT_MAXIMUM (e)         \
   : _GL_INT_CONVERT (e, 0))
#define _GL_INT_MAXIMUM(e)                                              \
  (_GL_INT_SIGNED (e)                                                   \
   ? _GL_SIGNED_INT_MAXIMUM (e)                                         \
   : _GL_INT_CONVERT (e, -1))
#define _GL_SIGNED_INT_MAXIMUM(e)                                       \
  (((_GL_INT_CONVERT (e, 1) << (sizeof ((e) + 0) * CHAR_BIT - 2)) - 1) * 2 + 1)


/* Return 1 if the __typeof__ keyword works.  This could be done by
   'configure', but for now it's easier to do it by hand.  */
#if 2 <= __GNUC__ || 0x5110 <= __SUNPRO_C
# define _GL_HAVE___TYPEOF__ 1
#else
# define _GL_HAVE___TYPEOF__ 0
#endif

/* Return 1 if the integer type or expression T might be signed.  Return 0
   if it is definitely unsigned.  This macro does not evaluate its argument,
   and expands to an integer constant expression.  */
#if _GL_HAVE___TYPEOF__
# define _GL_SIGNED_TYPE_OR_EXPR(t) TYPE_SIGNED (__typeof__ (t))
#else
# define _GL_SIGNED_TYPE_OR_EXPR(t) 1
#endif
Paul Eggert's avatar
Paul Eggert committed
103 104 105 106

/* Bound on length of the string representing an unsigned integer
   value representable in B bits.  log10 (2.0) < 146/485.  The
   smallest value of B where this bound is not tight is 2621.  */
Paul Eggert's avatar
Paul Eggert committed
107
#define INT_BITS_STRLEN_BOUND(b) (((b) * 146 + 484) / 485)
Paul Eggert's avatar
Paul Eggert committed
108 109 110

/* Bound on length of the string representing an integer type or expression T.
   Subtract 1 for the sign bit if T is signed, and then add 1 more for
Paul Eggert's avatar
Paul Eggert committed
111 112 113 114 115 116 117 118 119
   a minus sign if needed.

   Because _GL_SIGNED_TYPE_OR_EXPR sometimes returns 0 when its argument is
   signed, this macro may overestimate the true bound by one byte when
   applied to unsigned types of size 2, 4, 16, ... bytes.  */
#define INT_STRLEN_BOUND(t)                                     \
  (INT_BITS_STRLEN_BOUND (sizeof (t) * CHAR_BIT                 \
                          - _GL_SIGNED_TYPE_OR_EXPR (t))        \
   + _GL_SIGNED_TYPE_OR_EXPR (t))
Paul Eggert's avatar
Paul Eggert committed
120 121 122

/* Bound on buffer size needed to represent an integer type or expression T,
   including the terminating null.  */
Paul Eggert's avatar
Paul Eggert committed
123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312
#define INT_BUFSIZE_BOUND(t) (INT_STRLEN_BOUND (t) + 1)


/* Range overflow checks.

   The INT_<op>_RANGE_OVERFLOW macros return 1 if the corresponding C
   operators might not yield numerically correct answers due to
   arithmetic overflow.  They do not rely on undefined or
   implementation-defined behavior.  Their implementations are simple
   and straightforward, but they are a bit harder to use than the
   INT_<op>_OVERFLOW macros described below.

   Example usage:

     long int i = ...;
     long int j = ...;
     if (INT_MULTIPLY_RANGE_OVERFLOW (i, j, LONG_MIN, LONG_MAX))
       printf ("multiply would overflow");
     else
       printf ("product is %ld", i * j);

   Restrictions on *_RANGE_OVERFLOW macros:

   These macros do not check for all possible numerical problems or
   undefined or unspecified behavior: they do not check for division
   by zero, for bad shift counts, or for shifting negative numbers.

   These macros may evaluate their arguments zero or multiple times,
   so the arguments should not have side effects.  The arithmetic
   arguments (including the MIN and MAX arguments) must be of the same
   integer type after the usual arithmetic conversions, and the type
   must have minimum value MIN and maximum MAX.  Unsigned types should
   use a zero MIN of the proper type.

   These macros are tuned for constant MIN and MAX.  For commutative
   operations such as A + B, they are also tuned for constant B.  */

/* Return 1 if A + B would overflow in [MIN,MAX] arithmetic.
   See above for restrictions.  */
#define INT_ADD_RANGE_OVERFLOW(a, b, min, max)          \
  ((b) < 0                                              \
   ? (a) < (min) - (b)                                  \
   : (max) - (b) < (a))

/* Return 1 if A - B would overflow in [MIN,MAX] arithmetic.
   See above for restrictions.  */
#define INT_SUBTRACT_RANGE_OVERFLOW(a, b, min, max)     \
  ((b) < 0                                              \
   ? (max) + (b) < (a)                                  \
   : (a) < (min) + (b))

/* Return 1 if - A would overflow in [MIN,MAX] arithmetic.
   See above for restrictions.  */
#define INT_NEGATE_RANGE_OVERFLOW(a, min, max)          \
  ((min) < 0                                            \
   ? (a) < - (max)                                      \
   : 0 < (a))

/* Return 1 if A * B would overflow in [MIN,MAX] arithmetic.
   See above for restrictions.  */
#define INT_MULTIPLY_RANGE_OVERFLOW(a, b, min, max)     \
  ((b) < 0                                              \
   ? ((a) < 0                                           \
      ? (a) < (max) / (b)                               \
      : (b) < -1 && (min) / (b) < (a))                  \
   : (0 < (b)                                           \
      && ((a) < 0                                       \
          ? (a) < (min) / (b)                           \
          : (max) / (b) < (a))))

/* Return 1 if A / B would overflow in [MIN,MAX] arithmetic.
   See above for restrictions.  Do not check for division by zero.  */
#define INT_DIVIDE_RANGE_OVERFLOW(a, b, min, max)       \
  ((min) < 0 && (b) == -1 && (a) < - (max))

/* Return 1 if A % B would overflow in [MIN,MAX] arithmetic.
   See above for restrictions.  Do not check for division by zero.
   Mathematically, % should never overflow, but on x86-like hosts
   INT_MIN % -1 traps, and the C standard permits this, so treat this
   as an overflow too.  */
#define INT_REMAINDER_RANGE_OVERFLOW(a, b, min, max)    \
  INT_DIVIDE_RANGE_OVERFLOW (a, b, min, max)

/* Return 1 if A << B would overflow in [MIN,MAX] arithmetic.
   See above for restrictions.  Here, MIN and MAX are for A only, and B need
   not be of the same type as the other arguments.  The C standard says that
   behavior is undefined for shifts unless 0 <= B < wordwidth, and that when
   A is negative then A << B has undefined behavior and A >> B has
   implementation-defined behavior, but do not check these other
   restrictions.  */
#define INT_LEFT_SHIFT_RANGE_OVERFLOW(a, b, min, max)   \
  ((a) < 0                                              \
   ? (a) < (min) >> (b)                                 \
   : (max) >> (b) < (a))


/* The _GL*_OVERFLOW macros have the same restrictions as the
   *_RANGE_OVERFLOW macros, except that they do not assume that operands
   (e.g., A and B) have the same type as MIN and MAX.  Instead, they assume
   that the result (e.g., A + B) has that type.  */
#define _GL_ADD_OVERFLOW(a, b, min, max)                                \
  ((min) < 0 ? INT_ADD_RANGE_OVERFLOW (a, b, min, max)                  \
   : (a) < 0 ? (b) <= (a) + (b)                                         \
   : (b) < 0 ? (a) <= (a) + (b)                                         \
   : (a) + (b) < (b))
#define _GL_SUBTRACT_OVERFLOW(a, b, min, max)                           \
  ((min) < 0 ? INT_SUBTRACT_RANGE_OVERFLOW (a, b, min, max)             \
   : (a) < 0 ? 1                                                        \
   : (b) < 0 ? (a) - (b) <= (a)                                         \
   : (a) < (b))
#define _GL_MULTIPLY_OVERFLOW(a, b, min, max)                           \
  (((min) == 0 && (((a) < 0 && 0 < (b)) || ((b) < 0 && 0 < (a))))       \
   || INT_MULTIPLY_RANGE_OVERFLOW (a, b, min, max))
#define _GL_DIVIDE_OVERFLOW(a, b, min, max)                             \
  ((min) < 0 ? (b) == _GL_INT_CONVERT (min, -1) && (a) < - (max)        \
   : (a) < 0 ? (b) <= (a) + (b) - 1                                     \
   : (b) < 0 && (a) + (b) <= (a))
#define _GL_REMAINDER_OVERFLOW(a, b, min, max)                          \
  ((min) < 0 ? (b) == _GL_INT_CONVERT (min, -1) && (a) < - (max)        \
   : (a) < 0 ? (a) % (b) != ((max) - (b) + 1) % (b)                     \
   : (b) < 0 && ! _GL_UNSIGNED_NEG_MULTIPLE (a, b, max))

/* Return a nonzero value if A is a mathematical multiple of B, where
   A is unsigned, B is negative, and MAX is the maximum value of A's
   type.  A's type must be the same as (A % B)'s type.  Normally (A %
   -B == 0) suffices, but things get tricky if -B would overflow.  */
#define _GL_UNSIGNED_NEG_MULTIPLE(a, b, max)                            \
  (((b) < -_GL_SIGNED_INT_MAXIMUM (b)                                   \
    ? (_GL_SIGNED_INT_MAXIMUM (b) == (max)                              \
       ? (a)                                                            \
       : (a) % (_GL_INT_CONVERT (a, _GL_SIGNED_INT_MAXIMUM (b)) + 1))   \
    : (a) % - (b))                                                      \
   == 0)


/* Integer overflow checks.

   The INT_<op>_OVERFLOW macros return 1 if the corresponding C operators
   might not yield numerically correct answers due to arithmetic overflow.
   They work correctly on all known practical hosts, and do not rely
   on undefined behavior due to signed arithmetic overflow.

   Example usage:

     long int i = ...;
     long int j = ...;
     if (INT_MULTIPLY_OVERFLOW (i, j))
       printf ("multiply would overflow");
     else
       printf ("product is %ld", i * j);

   These macros do not check for all possible numerical problems or
   undefined or unspecified behavior: they do not check for division
   by zero, for bad shift counts, or for shifting negative numbers.

   These macros may evaluate their arguments zero or multiple times, so the
   arguments should not have side effects.

   These macros are tuned for their last argument being a constant.

   Return 1 if the integer expressions A * B, A - B, -A, A * B, A / B,
   A % B, and A << B would overflow, respectively.  */

#define INT_ADD_OVERFLOW(a, b) \
  _GL_BINARY_OP_OVERFLOW (a, b, _GL_ADD_OVERFLOW)
#define INT_SUBTRACT_OVERFLOW(a, b) \
  _GL_BINARY_OP_OVERFLOW (a, b, _GL_SUBTRACT_OVERFLOW)
#define INT_NEGATE_OVERFLOW(a) \
  INT_NEGATE_RANGE_OVERFLOW (a, _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
#define INT_MULTIPLY_OVERFLOW(a, b) \
  _GL_BINARY_OP_OVERFLOW (a, b, _GL_MULTIPLY_OVERFLOW)
#define INT_DIVIDE_OVERFLOW(a, b) \
  _GL_BINARY_OP_OVERFLOW (a, b, _GL_DIVIDE_OVERFLOW)
#define INT_REMAINDER_OVERFLOW(a, b) \
  _GL_BINARY_OP_OVERFLOW (a, b, _GL_REMAINDER_OVERFLOW)
#define INT_LEFT_SHIFT_OVERFLOW(a, b) \
  INT_LEFT_SHIFT_RANGE_OVERFLOW (a, b, \
                                 _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))

/* Return 1 if the expression A <op> B would overflow,
   where OP_RESULT_OVERFLOW (A, B, MIN, MAX) does the actual test,
   assuming MIN and MAX are the minimum and maximum for the result type.

   This macro assumes that A | B is a valid integer if both A and B are,
   which is true of all known practical hosts.  If this is a problem
   for you, please let us know how to fix it for your host.  */
#define _GL_BINARY_OP_OVERFLOW(a, b, op_result_overflow)        \
  op_result_overflow (a, b,                                     \
                      _GL_INT_MINIMUM ((a) | (b)),              \
                      _GL_INT_MAXIMUM ((a) | (b)))
Paul Eggert's avatar
Paul Eggert committed
313

Paul Eggert's avatar
Paul Eggert committed
314
#endif /* _GL_INTPROPS_H */