lib/intprops.h

   1 /* intprops.h -- properties of integer types
   2
   3    Copyright (C) 2001-2005, 2009-2013 Free Software Foundation, Inc.
   4
   5    This program is free software: you can redistribute it and/or modify
   6    it under the terms of the GNU General Public License as published by
   7    the Free Software Foundation; either version 3 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 General Public License for more details.
  14
  15    You should have received a copy of the GNU General Public License
  16    along with this program.  If not, see <http://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 an integer value, converted to the same type as the integer
  26    expression E after integer type promotion.  V is the unconverted value.  */
  27 #define _GL_INT_CONVERT(e, v) (0 * (e) + (v))
  28
  29 /* Act like _GL_INT_CONVERT (E, -V) but work around a bug in IRIX 6.5 cc; see
  30    <http://lists.gnu.org/archive/html/bug-gnulib/2011-05/msg00406.html>.  */
  31 #define _GL_INT_NEGATE_CONVERT(e, v) (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 negative values of the signed integer type T use two's
  41    complement, ones' complement, or signed magnitude representation,
  42    respectively.  Much GNU code assumes two's complement, but some
  43    people like to be portable to all possible C hosts.  */
  44 #define TYPE_TWOS_COMPLEMENT(t) ((t) ~ (t) 0 == (t) -1)
  45 #define TYPE_ONES_COMPLEMENT(t) ((t) ~ (t) 0 == 0)
  46 #define TYPE_SIGNED_MAGNITUDE(t) ((t) ~ (t) 0 < (t) -1)
  47
  48 /* True if the signed integer expression E uses two's complement.  */
  49 #define _GL_INT_TWOS_COMPLEMENT(e) (~ _GL_INT_CONVERT (e, 0) == -1)
  50
  51 /* True if the arithmetic type T is signed.  */
  52 #define TYPE_SIGNED(t) (! ((t) 0 < (t) -1))
  53
  54 /* Return 1 if the integer expression E, after integer promotion, has
  55    a signed type.  */
  56 #define _GL_INT_SIGNED(e) (_GL_INT_NEGATE_CONVERT (e, 1) < 0)
  57
  58
  59 /* Minimum and maximum values for integer types and expressions.  These
  60    macros have undefined behavior if T is signed and has padding bits.
  61    If this is a problem for you, please let us know how to fix it for
  62    your host.  */
  63
  64 /* The maximum and minimum values for the integer type T.  */
  65 #define TYPE_MINIMUM(t)                                                 \
  66   ((t) (! TYPE_SIGNED (t)                                               \
  67         ? (t) 0                                                         \
  68         : TYPE_SIGNED_MAGNITUDE (t)                                     \
  69         ? ~ (t) 0                                                       \
  70         : ~ TYPE_MAXIMUM (t)))
  71 #define TYPE_MAXIMUM(t)                                                 \
  72   ((t) (! TYPE_SIGNED (t)                                               \
  73         ? (t) -1                                                        \
  74         : ((((t) 1 << (sizeof (t) * CHAR_BIT - 2)) - 1) * 2 + 1)))
  75
  76 /* The maximum and minimum values for the type of the expression E,
  77    after integer promotion.  E should not have side effects.  */
  78 #define _GL_INT_MINIMUM(e)                                              \
  79   (_GL_INT_SIGNED (e)                                                   \
  80    ? - _GL_INT_TWOS_COMPLEMENT (e) - _GL_SIGNED_INT_MAXIMUM (e)         \
  81    : _GL_INT_CONVERT (e, 0))
  82 #define _GL_INT_MAXIMUM(e)                                              \
  83   (_GL_INT_SIGNED (e)                                                   \
  84    ? _GL_SIGNED_INT_MAXIMUM (e)                                         \
  85    : _GL_INT_NEGATE_CONVERT (e, 1))
  86 #define _GL_SIGNED_INT_MAXIMUM(e)                                       \
  87   (((_GL_INT_CONVERT (e, 1) << (sizeof ((e) + 0) * CHAR_BIT - 2)) - 1) * 2 + 1)
  88
  89
  90 /* Return 1 if the __typeof__ keyword works.  This could be done by
  91    'configure', but for now it's easier to do it by hand.  */
  92 #if 2 <= __GNUC__ || 0x5110 <= __SUNPRO_C
  93 # define _GL_HAVE___TYPEOF__ 1
  94 #else
  95 # define _GL_HAVE___TYPEOF__ 0
  96 #endif
  97
  98 /* Return 1 if the integer type or expression T might be signed.  Return 0
  99    if it is definitely unsigned.  This macro does not evaluate its argument,
 100    and expands to an integer constant expression.  */
 101 #if _GL_HAVE___TYPEOF__
 102 # define _GL_SIGNED_TYPE_OR_EXPR(t) TYPE_SIGNED (__typeof__ (t))
 103 #else
 104 # define _GL_SIGNED_TYPE_OR_EXPR(t) 1
 105 #endif
 106
 107 /* Bound on length of the string representing an unsigned integer
 108    value representable in B bits.  log10 (2.0) < 146/485.  The
 109    smallest value of B where this bound is not tight is 2621.  */
 110 #define INT_BITS_STRLEN_BOUND(b) (((b) * 146 + 484) / 485)
 111
 112 /* Bound on length of the string representing an integer type or expression T.
 113    Subtract 1 for the sign bit if T is signed, and then add 1 more for
 114    a minus sign if needed.
 115
 116    Because _GL_SIGNED_TYPE_OR_EXPR sometimes returns 0 when its argument is
 117    signed, this macro may overestimate the true bound by one byte when
 118    applied to unsigned types of size 2, 4, 16, ... bytes.  */
 119 #define INT_STRLEN_BOUND(t)                                     \
 120   (INT_BITS_STRLEN_BOUND (sizeof (t) * CHAR_BIT                 \
 121                           - _GL_SIGNED_TYPE_OR_EXPR (t))        \
 122    + _GL_SIGNED_TYPE_OR_EXPR (t))
 123
 124 /* Bound on buffer size needed to represent an integer type or expression T,
 125    including the terminating null.  */
 126 #define INT_BUFSIZE_BOUND(t) (INT_STRLEN_BOUND (t) + 1)
 127
 128
 129 /* Range overflow checks.
 130
 131    The INT_<op>_RANGE_OVERFLOW macros return 1 if the corresponding C
 132    operators might not yield numerically correct answers due to
 133    arithmetic overflow.  They do not rely on undefined or
 134    implementation-defined behavior.  Their implementations are simple
 135    and straightforward, but they are a bit harder to use than the
 136    INT_<op>_OVERFLOW macros described below.
 137
 138    Example usage:
 139
 140      long int i = ...;
 141      long int j = ...;
 142      if (INT_MULTIPLY_RANGE_OVERFLOW (i, j, LONG_MIN, LONG_MAX))
 143        printf ("multiply would overflow");
 144      else
 145        printf ("product is %ld", i * j);
 146
 147    Restrictions on *_RANGE_OVERFLOW macros:
 148
 149    These macros do not check for all possible numerical problems or
 150    undefined or unspecified behavior: they do not check for division
 151    by zero, for bad shift counts, or for shifting negative numbers.
 152
 153    These macros may evaluate their arguments zero or multiple times,
 154    so the arguments should not have side effects.  The arithmetic
 155    arguments (including the MIN and MAX arguments) must be of the same
 156    integer type after the usual arithmetic conversions, and the type
 157    must have minimum value MIN and maximum MAX.  Unsigned types should
 158    use a zero MIN of the proper type.
 159
 160    These macros are tuned for constant MIN and MAX.  For commutative
 161    operations such as A + B, they are also tuned for constant B.  */
 162
 163 /* Return 1 if A + B would overflow in [MIN,MAX] arithmetic.
 164    See above for restrictions.  */
 165 #define INT_ADD_RANGE_OVERFLOW(a, b, min, max)          \
 166   ((b) < 0                                              \
 167    ? (a) < (min) - (b)                                  \
 168    : (max) - (b) < (a))
 169
 170 /* Return 1 if A - B would overflow in [MIN,MAX] arithmetic.
 171    See above for restrictions.  */
 172 #define INT_SUBTRACT_RANGE_OVERFLOW(a, b, min, max)     \
 173   ((b) < 0                                              \
 174    ? (max) + (b) < (a)                                  \
 175    : (a) < (min) + (b))
 176
 177 /* Return 1 if - A would overflow in [MIN,MAX] arithmetic.
 178    See above for restrictions.  */
 179 #define INT_NEGATE_RANGE_OVERFLOW(a, min, max)          \
 180   ((min) < 0                                            \
 181    ? (a) < - (max)                                      \
 182    : 0 < (a))
 183
 184 /* Return 1 if A * B would overflow in [MIN,MAX] arithmetic.
 185    See above for restrictions.  Avoid && and || as they tickle
 186    bugs in Sun C 5.11 2010/08/13 and other compilers; see
 187    <http://lists.gnu.org/archive/html/bug-gnulib/2011-05/msg00401.html>.  */
 188 #define INT_MULTIPLY_RANGE_OVERFLOW(a, b, min, max)     \
 189   ((b) < 0                                              \
 190    ? ((a) < 0                                           \
 191       ? (a) < (max) / (b)                               \
 192       : (b) == -1                                       \
 193       ? 0                                               \
 194       : (min) / (b) < (a))                              \
 195    : (b) == 0                                           \
 196    ? 0                                                  \
 197    : ((a) < 0                                           \
 198       ? (a) < (min) / (b)                               \
 199       : (max) / (b) < (a)))
 200
 201 /* Return 1 if A / B would overflow in [MIN,MAX] arithmetic.
 202    See above for restrictions.  Do not check for division by zero.  */
 203 #define INT_DIVIDE_RANGE_OVERFLOW(a, b, min, max)       \
 204   ((min) < 0 && (b) == -1 && (a) < - (max))
 205
 206 /* Return 1 if A % B would overflow in [MIN,MAX] arithmetic.
 207    See above for restrictions.  Do not check for division by zero.
 208    Mathematically, % should never overflow, but on x86-like hosts
 209    INT_MIN % -1 traps, and the C standard permits this, so treat this
 210    as an overflow too.  */
 211 #define INT_REMAINDER_RANGE_OVERFLOW(a, b, min, max)    \
 212   INT_DIVIDE_RANGE_OVERFLOW (a, b, min, max)
 213
 214 /* Return 1 if A << B would overflow in [MIN,MAX] arithmetic.
 215    See above for restrictions.  Here, MIN and MAX are for A only, and B need
 216    not be of the same type as the other arguments.  The C standard says that
 217    behavior is undefined for shifts unless 0 <= B < wordwidth, and that when
 218    A is negative then A << B has undefined behavior and A >> B has
 219    implementation-defined behavior, but do not check these other
 220    restrictions.  */
 221 #define INT_LEFT_SHIFT_RANGE_OVERFLOW(a, b, min, max)   \
 222   ((a) < 0                                              \
 223    ? (a) < (min) >> (b)                                 \
 224    : (max) >> (b) < (a))
 225
 226
 227 /* The _GL*_OVERFLOW macros have the same restrictions as the
 228    *_RANGE_OVERFLOW macros, except that they do not assume that operands
 229    (e.g., A and B) have the same type as MIN and MAX.  Instead, they assume
 230    that the result (e.g., A + B) has that type.  */
 231 #define _GL_ADD_OVERFLOW(a, b, min, max)                                \
 232   ((min) < 0 ? INT_ADD_RANGE_OVERFLOW (a, b, min, max)                  \
 233    : (a) < 0 ? (b) <= (a) + (b)                                         \
 234    : (b) < 0 ? (a) <= (a) + (b)                                         \
 235    : (a) + (b) < (b))
 236 #define _GL_SUBTRACT_OVERFLOW(a, b, min, max)                           \
 237   ((min) < 0 ? INT_SUBTRACT_RANGE_OVERFLOW (a, b, min, max)             \
 238    : (a) < 0 ? 1                                                        \
 239    : (b) < 0 ? (a) - (b) <= (a)                                         \
 240    : (a) < (b))
 241 #define _GL_MULTIPLY_OVERFLOW(a, b, min, max)                           \
 242   (((min) == 0 && (((a) < 0 && 0 < (b)) || ((b) < 0 && 0 < (a))))       \
 243    || INT_MULTIPLY_RANGE_OVERFLOW (a, b, min, max))
 244 #define _GL_DIVIDE_OVERFLOW(a, b, min, max)                             \
 245   ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max)  \
 246    : (a) < 0 ? (b) <= (a) + (b) - 1                                     \
 247    : (b) < 0 && (a) + (b) <= (a))
 248 #define _GL_REMAINDER_OVERFLOW(a, b, min, max)                          \
 249   ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max)  \
 250    : (a) < 0 ? (a) % (b) != ((max) - (b) + 1) % (b)                     \
 251    : (b) < 0 && ! _GL_UNSIGNED_NEG_MULTIPLE (a, b, max))
 252
 253 /* Return a nonzero value if A is a mathematical multiple of B, where
 254    A is unsigned, B is negative, and MAX is the maximum value of A's
 255    type.  A's type must be the same as (A % B)'s type.  Normally (A %
 256    -B == 0) suffices, but things get tricky if -B would overflow.  */
 257 #define _GL_UNSIGNED_NEG_MULTIPLE(a, b, max)                            \
 258   (((b) < -_GL_SIGNED_INT_MAXIMUM (b)                                   \
 259     ? (_GL_SIGNED_INT_MAXIMUM (b) == (max)                              \
 260        ? (a)                                                            \
 261        : (a) % (_GL_INT_CONVERT (a, _GL_SIGNED_INT_MAXIMUM (b)) + 1))   \
 262     : (a) % - (b))                                                      \
 263    == 0)
 264
 265
 266 /* Integer overflow checks.
 267
 268    The INT_<op>_OVERFLOW macros return 1 if the corresponding C operators
 269    might not yield numerically correct answers due to arithmetic overflow.
 270    They work correctly on all known practical hosts, and do not rely
 271    on undefined behavior due to signed arithmetic overflow.
 272
 273    Example usage:
 274
 275      long int i = ...;
 276      long int j = ...;
 277      if (INT_MULTIPLY_OVERFLOW (i, j))
 278        printf ("multiply would overflow");
 279      else
 280        printf ("product is %ld", i * j);
 281
 282    These macros do not check for all possible numerical problems or
 283    undefined or unspecified behavior: they do not check for division
 284    by zero, for bad shift counts, or for shifting negative numbers.
 285
 286    These macros may evaluate their arguments zero or multiple times, so the
 287    arguments should not have side effects.
 288
 289    These macros are tuned for their last argument being a constant.
 290
 291    Return 1 if the integer expressions A * B, A - B, -A, A * B, A / B,
 292    A % B, and A << B would overflow, respectively.  */
 293
 294 #define INT_ADD_OVERFLOW(a, b) \
 295   _GL_BINARY_OP_OVERFLOW (a, b, _GL_ADD_OVERFLOW)
 296 #define INT_SUBTRACT_OVERFLOW(a, b) \
 297   _GL_BINARY_OP_OVERFLOW (a, b, _GL_SUBTRACT_OVERFLOW)
 298 #define INT_NEGATE_OVERFLOW(a) \
 299   INT_NEGATE_RANGE_OVERFLOW (a, _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
 300 #define INT_MULTIPLY_OVERFLOW(a, b) \
 301   _GL_BINARY_OP_OVERFLOW (a, b, _GL_MULTIPLY_OVERFLOW)
 302 #define INT_DIVIDE_OVERFLOW(a, b) \
 303   _GL_BINARY_OP_OVERFLOW (a, b, _GL_DIVIDE_OVERFLOW)
 304 #define INT_REMAINDER_OVERFLOW(a, b) \
 305   _GL_BINARY_OP_OVERFLOW (a, b, _GL_REMAINDER_OVERFLOW)
 306 #define INT_LEFT_SHIFT_OVERFLOW(a, b) \
 307   INT_LEFT_SHIFT_RANGE_OVERFLOW (a, b, \
 308                                  _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
 309
 310 /* Return 1 if the expression A <op> B would overflow,
 311    where OP_RESULT_OVERFLOW (A, B, MIN, MAX) does the actual test,
 312    assuming MIN and MAX are the minimum and maximum for the result type.
 313    Arguments should be free of side effects.  */
 314 #define _GL_BINARY_OP_OVERFLOW(a, b, op_result_overflow)        \
 315   op_result_overflow (a, b,                                     \
 316                       _GL_INT_MINIMUM (0 * (b) + (a)),          \
 317                       _GL_INT_MAXIMUM (0 * (b) + (a)))
 318
 319 #endif /* _GL_INTPROPS_H */