dhcpd-pools  3.0
ISC dhcpd lease usage analyser
intprops.h
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1 /* intprops.h -- properties of integer types
2 
3  Copyright (C) 2001-2017 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 General Public License as published
7  by 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 <https://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 value with the common real type of E and V and the value of V. */
26 #define _GL_INT_CONVERT(e, v) (0 * (e) + (v))
27 
28 /* Act like _GL_INT_CONVERT (E, -V) but work around a bug in IRIX 6.5 cc; see
29  <https://lists.gnu.org/r/bug-gnulib/2011-05/msg00406.html>. */
30 #define _GL_INT_NEGATE_CONVERT(e, v) (0 * (e) - (v))
31 
32 /* The extra casts in the following macros work around compiler bugs,
33  e.g., in Cray C 5.0.3.0. */
34 
35 /* True if the arithmetic type T is an integer type. bool counts as
36  an integer. */
37 #define TYPE_IS_INTEGER(t) ((t) 1.5 == 1)
38 
39 /* True if the real type T is signed. */
40 #define TYPE_SIGNED(t) (! ((t) 0 < (t) -1))
41 
42 /* Return 1 if the real expression E, after promotion, has a
43  signed or floating type. */
44 #define EXPR_SIGNED(e) (_GL_INT_NEGATE_CONVERT (e, 1) < 0)
45 
46 
47 /* Minimum and maximum values for integer types and expressions. */
48 
49 /* The width in bits of the integer type or expression T.
50  Padding bits are not supported; this is checked at compile-time below. */
51 #define TYPE_WIDTH(t) (sizeof (t) * CHAR_BIT)
52 
53 /* The maximum and minimum values for the integer type T. */
54 #define TYPE_MINIMUM(t) ((t) ~ TYPE_MAXIMUM (t))
55 #define TYPE_MAXIMUM(t) \
56  ((t) (! TYPE_SIGNED (t) \
57  ? (t) -1 \
58  : ((((t) 1 << (TYPE_WIDTH (t) - 2)) - 1) * 2 + 1)))
59 
60 /* The maximum and minimum values for the type of the expression E,
61  after integer promotion. E should not have side effects. */
62 #define _GL_INT_MINIMUM(e) \
63  (EXPR_SIGNED (e) \
64  ? ~ _GL_SIGNED_INT_MAXIMUM (e) \
65  : _GL_INT_CONVERT (e, 0))
66 #define _GL_INT_MAXIMUM(e) \
67  (EXPR_SIGNED (e) \
68  ? _GL_SIGNED_INT_MAXIMUM (e) \
69  : _GL_INT_NEGATE_CONVERT (e, 1))
70 #define _GL_SIGNED_INT_MAXIMUM(e) \
71  (((_GL_INT_CONVERT (e, 1) << (TYPE_WIDTH ((e) + 0) - 2)) - 1) * 2 + 1)
72 
73 /* Work around OpenVMS incompatibility with C99. */
74 #if !defined LLONG_MAX && defined __INT64_MAX
75 # define LLONG_MAX __INT64_MAX
76 # define LLONG_MIN __INT64_MIN
77 #endif
78 
79 /* This include file assumes that signed types are two's complement without
80  padding bits; the above macros have undefined behavior otherwise.
81  If this is a problem for you, please let us know how to fix it for your host.
82  This assumption is tested by the intprops-tests module. */
83 
84 /* Does the __typeof__ keyword work? This could be done by
85  'configure', but for now it's easier to do it by hand. */
86 #if (2 <= __GNUC__ \
87  || (1210 <= __IBMC__ && defined __IBM__TYPEOF__) \
88  || (0x5110 <= __SUNPRO_C && !__STDC__))
89 # define _GL_HAVE___TYPEOF__ 1
90 #else
91 # define _GL_HAVE___TYPEOF__ 0
92 #endif
93 
94 /* Return 1 if the integer type or expression T might be signed. Return 0
95  if it is definitely unsigned. This macro does not evaluate its argument,
96  and expands to an integer constant expression. */
97 #if _GL_HAVE___TYPEOF__
98 # define _GL_SIGNED_TYPE_OR_EXPR(t) TYPE_SIGNED (__typeof__ (t))
99 #else
100 # define _GL_SIGNED_TYPE_OR_EXPR(t) 1
101 #endif
102 
103 /* Bound on length of the string representing an unsigned integer
104  value representable in B bits. log10 (2.0) < 146/485. The
105  smallest value of B where this bound is not tight is 2621. */
106 #define INT_BITS_STRLEN_BOUND(b) (((b) * 146 + 484) / 485)
107 
108 /* Bound on length of the string representing an integer type or expression T.
109  Subtract 1 for the sign bit if T is signed, and then add 1 more for
110  a minus sign if needed.
111 
112  Because _GL_SIGNED_TYPE_OR_EXPR sometimes returns 0 when its argument is
113  signed, this macro may overestimate the true bound by one byte when
114  applied to unsigned types of size 2, 4, 16, ... bytes. */
115 #define INT_STRLEN_BOUND(t) \
116  (INT_BITS_STRLEN_BOUND (TYPE_WIDTH (t) - _GL_SIGNED_TYPE_OR_EXPR (t)) \
117  + _GL_SIGNED_TYPE_OR_EXPR (t))
118 
119 /* Bound on buffer size needed to represent an integer type or expression T,
120  including the terminating null. */
121 #define INT_BUFSIZE_BOUND(t) (INT_STRLEN_BOUND (t) + 1)
122 
123 
124 /* Range overflow checks.
125 
126  The INT_<op>_RANGE_OVERFLOW macros return 1 if the corresponding C
127  operators might not yield numerically correct answers due to
128  arithmetic overflow. They do not rely on undefined or
129  implementation-defined behavior. Their implementations are simple
130  and straightforward, but they are a bit harder to use than the
131  INT_<op>_OVERFLOW macros described below.
132 
133  Example usage:
134 
135  long int i = ...;
136  long int j = ...;
137  if (INT_MULTIPLY_RANGE_OVERFLOW (i, j, LONG_MIN, LONG_MAX))
138  printf ("multiply would overflow");
139  else
140  printf ("product is %ld", i * j);
141 
142  Restrictions on *_RANGE_OVERFLOW macros:
143 
144  These macros do not check for all possible numerical problems or
145  undefined or unspecified behavior: they do not check for division
146  by zero, for bad shift counts, or for shifting negative numbers.
147 
148  These macros may evaluate their arguments zero or multiple times,
149  so the arguments should not have side effects. The arithmetic
150  arguments (including the MIN and MAX arguments) must be of the same
151  integer type after the usual arithmetic conversions, and the type
152  must have minimum value MIN and maximum MAX. Unsigned types should
153  use a zero MIN of the proper type.
154 
155  These macros are tuned for constant MIN and MAX. For commutative
156  operations such as A + B, they are also tuned for constant B. */
157 
158 /* Return 1 if A + B would overflow in [MIN,MAX] arithmetic.
159  See above for restrictions. */
160 #define INT_ADD_RANGE_OVERFLOW(a, b, min, max) \
161  ((b) < 0 \
162  ? (a) < (min) - (b) \
163  : (max) - (b) < (a))
164 
165 /* Return 1 if A - B would overflow in [MIN,MAX] arithmetic.
166  See above for restrictions. */
167 #define INT_SUBTRACT_RANGE_OVERFLOW(a, b, min, max) \
168  ((b) < 0 \
169  ? (max) + (b) < (a) \
170  : (a) < (min) + (b))
171 
172 /* Return 1 if - A would overflow in [MIN,MAX] arithmetic.
173  See above for restrictions. */
174 #define INT_NEGATE_RANGE_OVERFLOW(a, min, max) \
175  ((min) < 0 \
176  ? (a) < - (max) \
177  : 0 < (a))
178 
179 /* Return 1 if A * B would overflow in [MIN,MAX] arithmetic.
180  See above for restrictions. Avoid && and || as they tickle
181  bugs in Sun C 5.11 2010/08/13 and other compilers; see
182  <https://lists.gnu.org/r/bug-gnulib/2011-05/msg00401.html>. */
183 #define INT_MULTIPLY_RANGE_OVERFLOW(a, b, min, max) \
184  ((b) < 0 \
185  ? ((a) < 0 \
186  ? (a) < (max) / (b) \
187  : (b) == -1 \
188  ? 0 \
189  : (min) / (b) < (a)) \
190  : (b) == 0 \
191  ? 0 \
192  : ((a) < 0 \
193  ? (a) < (min) / (b) \
194  : (max) / (b) < (a)))
195 
196 /* Return 1 if A / B would overflow in [MIN,MAX] arithmetic.
197  See above for restrictions. Do not check for division by zero. */
198 #define INT_DIVIDE_RANGE_OVERFLOW(a, b, min, max) \
199  ((min) < 0 && (b) == -1 && (a) < - (max))
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  Mathematically, % should never overflow, but on x86-like hosts
204  INT_MIN % -1 traps, and the C standard permits this, so treat this
205  as an overflow too. */
206 #define INT_REMAINDER_RANGE_OVERFLOW(a, b, min, max) \
207  INT_DIVIDE_RANGE_OVERFLOW (a, b, min, max)
208 
209 /* Return 1 if A << B would overflow in [MIN,MAX] arithmetic.
210  See above for restrictions. Here, MIN and MAX are for A only, and B need
211  not be of the same type as the other arguments. The C standard says that
212  behavior is undefined for shifts unless 0 <= B < wordwidth, and that when
213  A is negative then A << B has undefined behavior and A >> B has
214  implementation-defined behavior, but do not check these other
215  restrictions. */
216 #define INT_LEFT_SHIFT_RANGE_OVERFLOW(a, b, min, max) \
217  ((a) < 0 \
218  ? (a) < (min) >> (b) \
219  : (max) >> (b) < (a))
220 
221 /* True if __builtin_add_overflow (A, B, P) works when P is non-null. */
222 #if 5 <= __GNUC__ && !defined __ICC
223 # define _GL_HAS_BUILTIN_OVERFLOW 1
224 #else
225 # define _GL_HAS_BUILTIN_OVERFLOW 0
226 #endif
227 
228 /* True if __builtin_add_overflow_p (A, B, C) works. */
229 #define _GL_HAS_BUILTIN_OVERFLOW_P (7 <= __GNUC__)
230 
231 /* The _GL*_OVERFLOW macros have the same restrictions as the
232  *_RANGE_OVERFLOW macros, except that they do not assume that operands
233  (e.g., A and B) have the same type as MIN and MAX. Instead, they assume
234  that the result (e.g., A + B) has that type. */
235 #if _GL_HAS_BUILTIN_OVERFLOW_P
236 # define _GL_ADD_OVERFLOW(a, b, min, max) \
237  __builtin_add_overflow_p (a, b, (__typeof__ ((a) + (b))) 0)
238 # define _GL_SUBTRACT_OVERFLOW(a, b, min, max) \
239  __builtin_sub_overflow_p (a, b, (__typeof__ ((a) - (b))) 0)
240 # define _GL_MULTIPLY_OVERFLOW(a, b, min, max) \
241  __builtin_mul_overflow_p (a, b, (__typeof__ ((a) * (b))) 0)
242 #else
243 # define _GL_ADD_OVERFLOW(a, b, min, max) \
244  ((min) < 0 ? INT_ADD_RANGE_OVERFLOW (a, b, min, max) \
245  : (a) < 0 ? (b) <= (a) + (b) \
246  : (b) < 0 ? (a) <= (a) + (b) \
247  : (a) + (b) < (b))
248 # define _GL_SUBTRACT_OVERFLOW(a, b, min, max) \
249  ((min) < 0 ? INT_SUBTRACT_RANGE_OVERFLOW (a, b, min, max) \
250  : (a) < 0 ? 1 \
251  : (b) < 0 ? (a) - (b) <= (a) \
252  : (a) < (b))
253 # define _GL_MULTIPLY_OVERFLOW(a, b, min, max) \
254  (((min) == 0 && (((a) < 0 && 0 < (b)) || ((b) < 0 && 0 < (a)))) \
255  || INT_MULTIPLY_RANGE_OVERFLOW (a, b, min, max))
256 #endif
257 #define _GL_DIVIDE_OVERFLOW(a, b, min, max) \
258  ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max) \
259  : (a) < 0 ? (b) <= (a) + (b) - 1 \
260  : (b) < 0 && (a) + (b) <= (a))
261 #define _GL_REMAINDER_OVERFLOW(a, b, min, max) \
262  ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max) \
263  : (a) < 0 ? (a) % (b) != ((max) - (b) + 1) % (b) \
264  : (b) < 0 && ! _GL_UNSIGNED_NEG_MULTIPLE (a, b, max))
265 
266 /* Return a nonzero value if A is a mathematical multiple of B, where
267  A is unsigned, B is negative, and MAX is the maximum value of A's
268  type. A's type must be the same as (A % B)'s type. Normally (A %
269  -B == 0) suffices, but things get tricky if -B would overflow. */
270 #define _GL_UNSIGNED_NEG_MULTIPLE(a, b, max) \
271  (((b) < -_GL_SIGNED_INT_MAXIMUM (b) \
272  ? (_GL_SIGNED_INT_MAXIMUM (b) == (max) \
273  ? (a) \
274  : (a) % (_GL_INT_CONVERT (a, _GL_SIGNED_INT_MAXIMUM (b)) + 1)) \
275  : (a) % - (b)) \
276  == 0)
277 
278 /* Check for integer overflow, and report low order bits of answer.
279 
280  The INT_<op>_OVERFLOW macros return 1 if the corresponding C operators
281  might not yield numerically correct answers due to arithmetic overflow.
282  The INT_<op>_WRAPV macros also store the low-order bits of the answer.
283  These macros work correctly on all known practical hosts, and do not rely
284  on undefined behavior due to signed arithmetic overflow.
285 
286  Example usage, assuming A and B are long int:
287 
288  if (INT_MULTIPLY_OVERFLOW (a, b))
289  printf ("result would overflow\n");
290  else
291  printf ("result is %ld (no overflow)\n", a * b);
292 
293  Example usage with WRAPV flavor:
294 
295  long int result;
296  bool overflow = INT_MULTIPLY_WRAPV (a, b, &result);
297  printf ("result is %ld (%s)\n", result,
298  overflow ? "after overflow" : "no overflow");
299 
300  Restrictions on these macros:
301 
302  These macros do not check for all possible numerical problems or
303  undefined or unspecified behavior: they do not check for division
304  by zero, for bad shift counts, or for shifting negative numbers.
305 
306  These macros may evaluate their arguments zero or multiple times, so the
307  arguments should not have side effects.
308 
309  The WRAPV macros are not constant expressions. They support only
310  +, binary -, and *. The result type must be signed.
311 
312  These macros are tuned for their last argument being a constant.
313 
314  Return 1 if the integer expressions A * B, A - B, -A, A * B, A / B,
315  A % B, and A << B would overflow, respectively. */
316 
317 #define INT_ADD_OVERFLOW(a, b) \
318  _GL_BINARY_OP_OVERFLOW (a, b, _GL_ADD_OVERFLOW)
319 #define INT_SUBTRACT_OVERFLOW(a, b) \
320  _GL_BINARY_OP_OVERFLOW (a, b, _GL_SUBTRACT_OVERFLOW)
321 #if _GL_HAS_BUILTIN_OVERFLOW_P
322 # define INT_NEGATE_OVERFLOW(a) INT_SUBTRACT_OVERFLOW (0, a)
323 #else
324 # define INT_NEGATE_OVERFLOW(a) \
325  INT_NEGATE_RANGE_OVERFLOW (a, _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
326 #endif
327 #define INT_MULTIPLY_OVERFLOW(a, b) \
328  _GL_BINARY_OP_OVERFLOW (a, b, _GL_MULTIPLY_OVERFLOW)
329 #define INT_DIVIDE_OVERFLOW(a, b) \
330  _GL_BINARY_OP_OVERFLOW (a, b, _GL_DIVIDE_OVERFLOW)
331 #define INT_REMAINDER_OVERFLOW(a, b) \
332  _GL_BINARY_OP_OVERFLOW (a, b, _GL_REMAINDER_OVERFLOW)
333 #define INT_LEFT_SHIFT_OVERFLOW(a, b) \
334  INT_LEFT_SHIFT_RANGE_OVERFLOW (a, b, \
335  _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
336 
337 /* Return 1 if the expression A <op> B would overflow,
338  where OP_RESULT_OVERFLOW (A, B, MIN, MAX) does the actual test,
339  assuming MIN and MAX are the minimum and maximum for the result type.
340  Arguments should be free of side effects. */
341 #define _GL_BINARY_OP_OVERFLOW(a, b, op_result_overflow) \
342  op_result_overflow (a, b, \
343  _GL_INT_MINIMUM (0 * (b) + (a)), \
344  _GL_INT_MAXIMUM (0 * (b) + (a)))
345 
346 /* Store the low-order bits of A + B, A - B, A * B, respectively, into *R.
347  Return 1 if the result overflows. See above for restrictions. */
348 #define INT_ADD_WRAPV(a, b, r) \
349  _GL_INT_OP_WRAPV (a, b, r, +, __builtin_add_overflow, INT_ADD_OVERFLOW)
350 #define INT_SUBTRACT_WRAPV(a, b, r) \
351  _GL_INT_OP_WRAPV (a, b, r, -, __builtin_sub_overflow, INT_SUBTRACT_OVERFLOW)
352 #define INT_MULTIPLY_WRAPV(a, b, r) \
353  _GL_INT_OP_WRAPV (a, b, r, *, __builtin_mul_overflow, INT_MULTIPLY_OVERFLOW)
354 
355 /* Nonzero if this compiler has GCC bug 68193 or Clang bug 25390. See:
356  https://gcc.gnu.org/bugzilla/show_bug.cgi?id=68193
357  https://llvm.org/bugs/show_bug.cgi?id=25390
358  For now, assume all versions of GCC-like compilers generate bogus
359  warnings for _Generic. This matters only for older compilers that
360  lack __builtin_add_overflow. */
361 #if __GNUC__
362 # define _GL__GENERIC_BOGUS 1
363 #else
364 # define _GL__GENERIC_BOGUS 0
365 #endif
366 
367 /* Store the low-order bits of A <op> B into *R, where OP specifies
368  the operation. BUILTIN is the builtin operation, and OVERFLOW the
369  overflow predicate. Return 1 if the result overflows. See above
370  for restrictions. */
371 #if _GL_HAS_BUILTIN_OVERFLOW
372 # define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) builtin (a, b, r)
373 #elif 201112 <= __STDC_VERSION__ && !_GL__GENERIC_BOGUS
374 # define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) \
375  (_Generic \
376  (*(r), \
377  signed char: \
378  _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
379  signed char, SCHAR_MIN, SCHAR_MAX), \
380  short int: \
381  _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
382  short int, SHRT_MIN, SHRT_MAX), \
383  int: \
384  _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
385  int, INT_MIN, INT_MAX), \
386  long int: \
387  _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
388  long int, LONG_MIN, LONG_MAX), \
389  long long int: \
390  _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
391  long long int, LLONG_MIN, LLONG_MAX)))
392 #else
393 # define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) \
394  (sizeof *(r) == sizeof (signed char) \
395  ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
396  signed char, SCHAR_MIN, SCHAR_MAX) \
397  : sizeof *(r) == sizeof (short int) \
398  ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
399  short int, SHRT_MIN, SHRT_MAX) \
400  : sizeof *(r) == sizeof (int) \
401  ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
402  int, INT_MIN, INT_MAX) \
403  : _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow))
404 # ifdef LLONG_MAX
405 # define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
406  (sizeof *(r) == sizeof (long int) \
407  ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
408  long int, LONG_MIN, LONG_MAX) \
409  : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
410  long long int, LLONG_MIN, LLONG_MAX))
411 # else
412 # define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
413  _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
414  long int, LONG_MIN, LONG_MAX)
415 # endif
416 #endif
417 
418 /* Store the low-order bits of A <op> B into *R, where the operation
419  is given by OP. Use the unsigned type UT for calculation to avoid
420  overflow problems. *R's type is T, with extrema TMIN and TMAX.
421  T must be a signed integer type. Return 1 if the result overflows. */
422 #define _GL_INT_OP_CALC(a, b, r, op, overflow, ut, t, tmin, tmax) \
423  (sizeof ((a) op (b)) < sizeof (t) \
424  ? _GL_INT_OP_CALC1 ((t) (a), (t) (b), r, op, overflow, ut, t, tmin, tmax) \
425  : _GL_INT_OP_CALC1 (a, b, r, op, overflow, ut, t, tmin, tmax))
426 #define _GL_INT_OP_CALC1(a, b, r, op, overflow, ut, t, tmin, tmax) \
427  ((overflow (a, b) \
428  || (EXPR_SIGNED ((a) op (b)) && ((a) op (b)) < (tmin)) \
429  || (tmax) < ((a) op (b))) \
430  ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 1) \
431  : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 0))
432 
433 /* Return the low-order bits of A <op> B, where the operation is given
434  by OP. Use the unsigned type UT for calculation to avoid undefined
435  behavior on signed integer overflow, and convert the result to type T.
436  UT is at least as wide as T and is no narrower than unsigned int,
437  T is two's complement, and there is no padding or trap representations.
438  Assume that converting UT to T yields the low-order bits, as is
439  done in all known two's-complement C compilers. E.g., see:
440  https://gcc.gnu.org/onlinedocs/gcc/Integers-implementation.html
441 
442  According to the C standard, converting UT to T yields an
443  implementation-defined result or signal for values outside T's
444  range. However, code that works around this theoretical problem
445  runs afoul of a compiler bug in Oracle Studio 12.3 x86. See:
446  https://lists.gnu.org/r/bug-gnulib/2017-04/msg00049.html
447  As the compiler bug is real, don't try to work around the
448  theoretical problem. */
449 
450 #define _GL_INT_OP_WRAPV_VIA_UNSIGNED(a, b, op, ut, t) \
451  ((t) ((ut) (a) op (ut) (b)))
452 
453 #endif /* _GL_INTPROPS_H */