lib/intprops.h

   1 /* intprops.h -- properties of integer types
   2
   3    Copyright (C) 2001-2005, 2009-2011 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 a integer value, converted to the same type as the integer
  26    expression E after integer type promotion.  V is the unconverted value.
  27    E should not have side effects.  */
  28 #define _GL_INT_CONVERT(e, v) ((e) - (e) + (v))
  29
  30 /* The extra casts in the following macros work around compiler bugs,
  31    e.g., in Cray C 5.0.3.0.  */
  32
  33 /* True if the arithmetic type T is an integer type.  bool counts as
  34    an integer.  */
  35 #define TYPE_IS_INTEGER(t) ((t) 1.5 == 1)
  36
  37 /* True if negative values of the signed integer type T use two's
  38    complement, ones' complement, or signed magnitude representation,
  39    respectively.  Much GNU code assumes two's complement, but some
  40    people like to be portable to all possible C hosts.  */
  41 #define TYPE_TWOS_COMPLEMENT(t) ((t) ~ (t) 0 == (t) -1)
  42 #define TYPE_ONES_COMPLEMENT(t) ((t) ~ (t) 0 == 0)
  43 #define TYPE_SIGNED_MAGNITUDE(t) ((t) ~ (t) 0 < (t) -1)
  44
  45 /* True if the signed integer expression E uses two's complement.  */
  46 #define _GL_INT_TWOS_COMPLEMENT(e) (~ _GL_INT_CONVERT (e, 0) == -1)
  47
  48 /* True if the arithmetic type T is signed.  */
  49 #define TYPE_SIGNED(t) (! ((t) 0 < (t) -1))
  50
  51 /* Return 1 if the integer expression E, after integer promotion, has
  52    a signed type.  E should not have side effects.  */
  53 #define _GL_INT_SIGNED(e) (_GL_INT_CONVERT (e, -1) < 0)
  54
  55
  56 /* Minimum and maximum values for integer types and expressions.  These
  57    macros have undefined behavior if T is signed and has padding bits.
  58    If this is a problem for you, please let us know how to fix it for
  59    your host.  */
  60
  61 /* The maximum and minimum values for the integer type T.  */
  62 #define TYPE_MINIMUM(t)                                                 \
  63   ((t) (! TYPE_SIGNED (t)                                               \
  64         ? (t) 0                                                         \
  65         : TYPE_SIGNED_MAGNITUDE (t)                                     \
  66         ? ~ (t) 0                                                       \
  67         : ~ TYPE_MAXIMUM (t)))
  68 #define TYPE_MAXIMUM(t)                                                 \
  69   ((t) (! TYPE_SIGNED (t)                                               \
  70         ? (t) -1                                                        \
  71         : ((((t) 1 << (sizeof (t) * CHAR_BIT - 2)) - 1) * 2 + 1)))
  72
  73 /* The maximum and minimum values for the type of the expression E,
  74    after integer promotion.  E should not have side effects.  */
  75 #define _GL_INT_MINIMUM(e)                                              \
  76   (_GL_INT_SIGNED (e)                                                   \
  77    ? - _GL_INT_TWOS_COMPLEMENT (e) - _GL_SIGNED_INT_MAXIMUM (e)         \
  78    : _GL_INT_CONVERT (e, 0))
  79 #define _GL_INT_MAXIMUM(e)                                              \
  80   (_GL_INT_SIGNED (e)                                                   \
  81    ? _GL_SIGNED_INT_MAXIMUM (e)                                         \
  82    : _GL_INT_CONVERT (e, -1))
  83 #define _GL_SIGNED_INT_MAXIMUM(e)                                       \
  84   (((_GL_INT_CONVERT (e, 1) << (sizeof ((e) + 0) * CHAR_BIT - 2)) - 1) * 2 + 1)
  85
  86
  87 /* Return 1 if the __typeof__ keyword works.  This could be done by
  88    'configure', but for now it's easier to do it by hand.  */
  89 #if 2 <= __GNUC__ || 0x5110 <= __SUNPRO_C
  90 # define _GL_HAVE___TYPEOF__ 1
  91 #else
  92 # define _GL_HAVE___TYPEOF__ 0
  93 #endif
  94
  95 /* Return 1 if the integer type or expression T might be signed.  Return 0
  96    if it is definitely unsigned.  This macro does not evaluate its argument,
  97    and expands to an integer constant expression.  */
  98 #if _GL_HAVE___TYPEOF__
  99 # define _GL_SIGNED_TYPE_OR_EXPR(t) TYPE_SIGNED (__typeof__ (t))
 100 #else
 101 # define _GL_SIGNED_TYPE_OR_EXPR(t) 1
 102 #endif
 103
 104 /* Bound on length of the string representing an unsigned integer
 105    value representable in B bits.  log10 (2.0) < 146/485.  The
 106    smallest value of B where this bound is not tight is 2621.  */
 107 #define INT_BITS_STRLEN_BOUND(b) (((b) * 146 + 484) / 485)
 108
 109 /* Bound on length of the string representing an integer type or expression T.
 110    Subtract 1 for the sign bit if T is signed, and then add 1 more for
 111    a minus sign if needed.
 112
 113    Because _GL_SIGNED_TYPE_OR_EXPR sometimes returns 0 when its argument is
 114    signed, this macro may overestimate the true bound by one byte when
 115    applied to unsigned types of size 2, 4, 16, ... bytes.  */
 116 #define INT_STRLEN_BOUND(t)                                     \
 117   (INT_BITS_STRLEN_BOUND (sizeof (t) * CHAR_BIT                 \
 118                           - _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.  */
 183 #define INT_MULTIPLY_RANGE_OVERFLOW(a, b, min, max)     \
 184   ((b) < 0                                              \
 185    ? ((a) < 0                                           \
 186       ? (a) < (max) / (b)                               \
 187       : (b) < -1 && (min) / (b) < (a))                  \
 188    : (0 < (b)                                           \
 189       && ((a) < 0                                       \
 190           ? (a) < (min) / (b)                           \
 191           : (max) / (b) < (a))))
 192
 193 /* Return 1 if A / B would overflow in [MIN,MAX] arithmetic.
 194    See above for restrictions.  Do not check for division by zero.  */
 195 #define INT_DIVIDE_RANGE_OVERFLOW(a, b, min, max)       \
 196   ((min) < 0 && (b) == -1 && (a) < - (max))
 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    Mathematically, % should never overflow, but on x86-like hosts
 201    INT_MIN % -1 traps, and the C standard permits this, so treat this
 202    as an overflow too.  */
 203 #define INT_REMAINDER_RANGE_OVERFLOW(a, b, min, max)    \
 204   INT_DIVIDE_RANGE_OVERFLOW (a, b, min, max)
 205
 206 /* Return 1 if A << B would overflow in [MIN,MAX] arithmetic.
 207    See above for restrictions.  Here, MIN and MAX are for A only, and B need
 208    not be of the same type as the other arguments.  The C standard says that
 209    behavior is undefined for shifts unless 0 <= B < wordwidth, and that when
 210    A is negative then A << B has undefined behavior and A >> B has
 211    implementation-defined behavior, but do not check these other
 212    restrictions.  */
 213 #define INT_LEFT_SHIFT_RANGE_OVERFLOW(a, b, min, max)   \
 214   ((a) < 0                                              \
 215    ? (a) < (min) >> (b)                                 \
 216    : (max) >> (b) < (a))
 217
 218
 219 /* The _GL*_OVERFLOW macros have the same restrictions as the
 220    *_RANGE_OVERFLOW macros, except that they do not assume that operands
 221    (e.g., A and B) have the same type as MIN and MAX.  Instead, they assume
 222    that the result (e.g., A + B) has that type.  */
 223 #define _GL_ADD_OVERFLOW(a, b, min, max)                                \
 224   ((min) < 0 ? INT_ADD_RANGE_OVERFLOW (a, b, min, max)                  \
 225    : (a) < 0 ? (b) <= (a) + (b)                                         \
 226    : (b) < 0 ? (a) <= (a) + (b)                                         \
 227    : (a) + (b) < (b))
 228 #define _GL_SUBTRACT_OVERFLOW(a, b, min, max)                           \
 229   ((min) < 0 ? INT_SUBTRACT_RANGE_OVERFLOW (a, b, min, max)             \
 230    : (a) < 0 ? 1                                                        \
 231    : (b) < 0 ? (a) - (b) <= (a)                                         \
 232    : (a) < (b))
 233 #define _GL_MULTIPLY_OVERFLOW(a, b, min, max)                           \
 234   (((min) == 0 && (((a) < 0 && 0 < (b)) || ((b) < 0 && 0 < (a))))       \
 235    || INT_MULTIPLY_RANGE_OVERFLOW (a, b, min, max))
 236 #define _GL_DIVIDE_OVERFLOW(a, b, min, max)                             \
 237   ((min) < 0 ? (b) == _GL_INT_CONVERT (min, -1) && (a) < - (max)        \
 238    : (a) < 0 ? (b) <= (a) + (b) - 1                                     \
 239    : (b) < 0 && (a) + (b) <= (a))
 240 #define _GL_REMAINDER_OVERFLOW(a, b, min, max)                          \
 241   ((min) < 0 ? (b) == _GL_INT_CONVERT (min, -1) && (a) < - (max)        \
 242    : (a) < 0 ? (a) % (b) != ((max) - (b) + 1) % (b)                     \
 243    : (b) < 0 && ! _GL_UNSIGNED_NEG_MULTIPLE (a, b, max))
 244
 245 /* Return a nonzero value if A is a mathematical multiple of B, where
 246    A is unsigned, B is negative, and MAX is the maximum value of A's
 247    type.  A's type must be the same as (A % B)'s type.  Normally (A %
 248    -B == 0) suffices, but things get tricky if -B would overflow.  */
 249 #define _GL_UNSIGNED_NEG_MULTIPLE(a, b, max)                            \
 250   (((b) < -_GL_SIGNED_INT_MAXIMUM (b)                                   \
 251     ? (_GL_SIGNED_INT_MAXIMUM (b) == (max)                              \
 252        ? (a)                                                            \
 253        : (a) % (_GL_INT_CONVERT (a, _GL_SIGNED_INT_MAXIMUM (b)) + 1))   \
 254     : (a) % - (b))                                                      \
 255    == 0)
 256
 257
 258 /* Integer overflow checks.
 259
 260    The INT_<op>_OVERFLOW macros return 1 if the corresponding C operators
 261    might not yield numerically correct answers due to arithmetic overflow.
 262    They work correctly on all known practical hosts, and do not rely
 263    on undefined behavior due to signed arithmetic overflow.
 264
 265    Example usage:
 266
 267      long int i = ...;
 268      long int j = ...;
 269      if (INT_MULTIPLY_OVERFLOW (i, j))
 270        printf ("multiply would overflow");
 271      else
 272        printf ("product is %ld", i * j);
 273
 274    These macros do not check for all possible numerical problems or
 275    undefined or unspecified behavior: they do not check for division
 276    by zero, for bad shift counts, or for shifting negative numbers.
 277
 278    These macros may evaluate their arguments zero or multiple times, so the
 279    arguments should not have side effects.
 280
 281    These macros are tuned for their last argument being a constant.
 282
 283    Return 1 if the integer expressions A * B, A - B, -A, A * B, A / B,
 284    A % B, and A << B would overflow, respectively.  */
 285
 286 #define INT_ADD_OVERFLOW(a, b) \
 287   _GL_BINARY_OP_OVERFLOW (a, b, _GL_ADD_OVERFLOW)
 288 #define INT_SUBTRACT_OVERFLOW(a, b) \
 289   _GL_BINARY_OP_OVERFLOW (a, b, _GL_SUBTRACT_OVERFLOW)
 290 #define INT_NEGATE_OVERFLOW(a) \
 291   INT_NEGATE_RANGE_OVERFLOW (a, _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
 292 #define INT_MULTIPLY_OVERFLOW(a, b) \
 293   _GL_BINARY_OP_OVERFLOW (a, b, _GL_MULTIPLY_OVERFLOW)
 294 #define INT_DIVIDE_OVERFLOW(a, b) \
 295   _GL_BINARY_OP_OVERFLOW (a, b, _GL_DIVIDE_OVERFLOW)
 296 #define INT_REMAINDER_OVERFLOW(a, b) \
 297   _GL_BINARY_OP_OVERFLOW (a, b, _GL_REMAINDER_OVERFLOW)
 298 #define INT_LEFT_SHIFT_OVERFLOW(a, b) \
 299   INT_LEFT_SHIFT_RANGE_OVERFLOW (a, b, \
 300                                  _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
 301
 302 /* Return 1 if the expression A <op> B would overflow,
 303    where OP_RESULT_OVERFLOW (A, B, MIN, MAX) does the actual test,
 304    assuming MIN and MAX are the minimum and maximum for the result type.
 305
 306    This macro assumes that A | B is a valid integer if both A and B are,
 307    which is true of all known practical hosts.  If this is a problem
 308    for you, please let us know how to fix it for your host.  */
 309 #define _GL_BINARY_OP_OVERFLOW(a, b, op_result_overflow)        \
 310   op_result_overflow (a, b,                                     \
 311                       _GL_INT_MINIMUM ((a) | (b)),              \
 312                       _GL_INT_MAXIMUM ((a) | (b)))
 313
 314 #endif /* _GL_INTPROPS_H */