dhcpd-pools  2.28
ISC dhcpd lease usage analyser
intprops.h
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1 /* intprops.h -- properties of integer types
2 
3  Copyright (C) 2001-2005, 2009-2015 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 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  <http://lists.gnu.org/archive/html/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 negative values of the signed integer type T use two's
40  complement, ones' complement, or signed magnitude representation,
41  respectively. Much GNU code assumes two's complement, but some
42  people like to be portable to all possible C hosts. */
43 #define TYPE_TWOS_COMPLEMENT(t) ((t) ~ (t) 0 == (t) -1)
44 #define TYPE_ONES_COMPLEMENT(t) ((t) ~ (t) 0 == 0)
45 #define TYPE_SIGNED_MAGNITUDE(t) ((t) ~ (t) 0 < (t) -1)
46 
47 /* True if the signed integer expression E uses two's complement. */
48 #define _GL_INT_TWOS_COMPLEMENT(e) (~ _GL_INT_CONVERT (e, 0) == -1)
49 
50 /* True if the real type T is signed. */
51 #define TYPE_SIGNED(t) (! ((t) 0 < (t) -1))
52 
53 /* Return 1 if the real expression E, after promotion, has a
54  signed or floating type. */
55 #define EXPR_SIGNED(e) (_GL_INT_NEGATE_CONVERT (e, 1) < 0)
56 
57 
58 /* Minimum and maximum values for integer types and expressions. These
59  macros have undefined behavior if T is signed and has padding bits.
60  If this is a problem for you, please let us know how to fix it for
61  your host. */
62 
63 /* The maximum and minimum values for the integer type T. */
64 #define TYPE_MINIMUM(t) \
65  ((t) (! TYPE_SIGNED (t) \
66  ? (t) 0 \
67  : TYPE_SIGNED_MAGNITUDE (t) \
68  ? ~ (t) 0 \
69  : ~ TYPE_MAXIMUM (t)))
70 #define TYPE_MAXIMUM(t) \
71  ((t) (! TYPE_SIGNED (t) \
72  ? (t) -1 \
73  : ((((t) 1 << (sizeof (t) * CHAR_BIT - 2)) - 1) * 2 + 1)))
74 
75 /* The maximum and minimum values for the type of the expression E,
76  after integer promotion. E should not have side effects. */
77 #define _GL_INT_MINIMUM(e) \
78  (EXPR_SIGNED (e) \
79  ? - _GL_INT_TWOS_COMPLEMENT (e) - _GL_SIGNED_INT_MAXIMUM (e) \
80  : _GL_INT_CONVERT (e, 0))
81 #define _GL_INT_MAXIMUM(e) \
82  (EXPR_SIGNED (e) \
83  ? _GL_SIGNED_INT_MAXIMUM (e) \
84  : _GL_INT_NEGATE_CONVERT (e, 1))
85 #define _GL_SIGNED_INT_MAXIMUM(e) \
86  (((_GL_INT_CONVERT (e, 1) << (sizeof ((e) + 0) * CHAR_BIT - 2)) - 1) * 2 + 1)
87 
88 
89 /* Return 1 if the __typeof__ keyword works. This could be done by
90  'configure', but for now it's easier to do it by hand. */
91 #if (2 <= __GNUC__ || defined __IBM__TYPEOF__ \
92  || (0x5110 <= __SUNPRO_C && !__STDC__))
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 /* Check for integer overflow, and report low order bits of answer.
266 
267  The INT_<op>_OVERFLOW macros return 1 if the corresponding C operators
268  might not yield numerically correct answers due to arithmetic overflow.
269  The INT_<op>_WRAPV macros also store the low-order bits of the answer.
270  These macros work correctly on all known practical hosts, and do not rely
271  on undefined behavior due to signed arithmetic overflow.
272 
273  Example usage, assuming A and B are long int:
274 
275  long int result = INT_MULTIPLY_WRAPV (a, b);
276  printf ("result is %ld (%s)\n", result,
277  INT_MULTIPLY_OVERFLOW (a, b) ? "after overflow" : "no overflow");
278 
279  Example usage with WRAPV flavor:
280 
281  long int result;
282  bool overflow = INT_MULTIPLY_WRAPV (a, b, &result);
283  printf ("result is %ld (%s)\n", result,
284  overflow ? "after overflow" : "no overflow");
285 
286  Restrictions on these macros:
287 
288  These macros do not check for all possible numerical problems or
289  undefined or unspecified behavior: they do not check for division
290  by zero, for bad shift counts, or for shifting negative numbers.
291 
292  These macros may evaluate their arguments zero or multiple times, so the
293  arguments should not have side effects.
294 
295  The WRAPV macros are not constant expressions. They support only
296  +, binary -, and *. The result type must be signed.
297 
298  These macros are tuned for their last argument being a constant.
299 
300  Return 1 if the integer expressions A * B, A - B, -A, A * B, A / B,
301  A % B, and A << B would overflow, respectively. */
302 
303 #define INT_ADD_OVERFLOW(a, b) \
304  _GL_BINARY_OP_OVERFLOW (a, b, _GL_ADD_OVERFLOW)
305 #define INT_SUBTRACT_OVERFLOW(a, b) \
306  _GL_BINARY_OP_OVERFLOW (a, b, _GL_SUBTRACT_OVERFLOW)
307 #define INT_NEGATE_OVERFLOW(a) \
308  INT_NEGATE_RANGE_OVERFLOW (a, _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
309 #define INT_MULTIPLY_OVERFLOW(a, b) \
310  _GL_BINARY_OP_OVERFLOW (a, b, _GL_MULTIPLY_OVERFLOW)
311 #define INT_DIVIDE_OVERFLOW(a, b) \
312  _GL_BINARY_OP_OVERFLOW (a, b, _GL_DIVIDE_OVERFLOW)
313 #define INT_REMAINDER_OVERFLOW(a, b) \
314  _GL_BINARY_OP_OVERFLOW (a, b, _GL_REMAINDER_OVERFLOW)
315 #define INT_LEFT_SHIFT_OVERFLOW(a, b) \
316  INT_LEFT_SHIFT_RANGE_OVERFLOW (a, b, \
317  _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
318 
319 /* Return 1 if the expression A <op> B would overflow,
320  where OP_RESULT_OVERFLOW (A, B, MIN, MAX) does the actual test,
321  assuming MIN and MAX are the minimum and maximum for the result type.
322  Arguments should be free of side effects. */
323 #define _GL_BINARY_OP_OVERFLOW(a, b, op_result_overflow) \
324  op_result_overflow (a, b, \
325  _GL_INT_MINIMUM (0 * (b) + (a)), \
326  _GL_INT_MAXIMUM (0 * (b) + (a)))
327 
328 /* Compute A + B, A - B, A * B, respectively, storing the result into *R.
329  Return 1 if the result overflows. See above for restrictions. */
330 #define INT_ADD_WRAPV(a, b, r) \
331  _GL_INT_OP_WRAPV (a, b, r, +, __builtin_add_overflow, INT_ADD_OVERFLOW)
332 #define INT_SUBTRACT_WRAPV(a, b, r) \
333  _GL_INT_OP_WRAPV (a, b, r, -, __builtin_sub_overflow, INT_SUBTRACT_OVERFLOW)
334 #define INT_MULTIPLY_WRAPV(a, b, r) \
335  _GL_INT_OP_WRAPV (a, b, r, *, __builtin_mul_overflow, INT_MULTIPLY_OVERFLOW)
336 
337 #ifndef __has_builtin
338 # define __has_builtin(x) 0
339 #endif
340 
341 /* Nonzero if this compiler has GCC bug 68193 or Clang bug 25390. See:
342  https://gcc.gnu.org/bugzilla/show_bug.cgi?id=68193
343  https://llvm.org/bugs/show_bug.cgi?id=25390
344  For now, assume all versions of GCC-like compilers generate bogus
345  warnings for _Generic. This matters only for older compilers that
346  lack __builtin_add_overflow. */
347 #if __GNUC__
348 # define _GL__GENERIC_BOGUS 1
349 #else
350 # define _GL__GENERIC_BOGUS 0
351 #endif
352 
353 /* Store A <op> B into *R, where OP specifies the operation.
354  BUILTIN is the builtin operation, and OVERFLOW the overflow predicate.
355  See above for restrictions. */
356 #if 5 <= __GNUC__ || __has_builtin (__builtin_add_overflow)
357 # define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) builtin (a, b, r)
358 #elif 201112 <= __STDC_VERSION__ && !_GL__GENERIC_BOGUS
359 # define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) \
360  (_Generic \
361  (*(r), \
362  signed char: \
363  _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned char, \
364  signed char, SCHAR_MIN, SCHAR_MAX), \
365  short int: \
366  _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned short int, \
367  short int, SHRT_MIN, SHRT_MAX), \
368  int: \
369  _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
370  int, INT_MIN, INT_MAX), \
371  long int: \
372  _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
373  long int, LONG_MIN, LONG_MAX), \
374  long long int: \
375  _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
376  long long int, LLONG_MIN, LLONG_MAX)))
377 #else
378 # define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) \
379  (sizeof *(r) == sizeof (signed char) \
380  ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned char, \
381  signed char, SCHAR_MIN, SCHAR_MAX) \
382  : sizeof *(r) == sizeof (short int) \
383  ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned short int, \
384  short int, SHRT_MIN, SHRT_MAX) \
385  : sizeof *(r) == sizeof (int) \
386  ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
387  int, INT_MIN, INT_MAX) \
388  : _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow))
389 # ifdef LLONG_MAX
390 # define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
391  (sizeof *(r) == sizeof (long int) \
392  ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
393  long int, LONG_MIN, LONG_MAX) \
394  : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
395  long long int, LLONG_MIN, LLONG_MAX))
396 # else
397 # define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
398  _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
399  long int, LONG_MIN, LONG_MAX))
400 # endif
401 #endif
402 
403 /* Store the low-order bits of A <op> B into *R, where the operation
404  is given by OP. Use the unsigned type UT for calculation to avoid
405  overflow problems. *R's type is T, with extremal values TMIN and
406  TMAX. T must be a signed integer type. */
407 #define _GL_INT_OP_CALC(a, b, r, op, overflow, ut, t, tmin, tmax) \
408  (sizeof ((a) op (b)) < sizeof (t) \
409  ? _GL_INT_OP_CALC1 ((t) (a), (t) (b), r, op, overflow, ut, t, tmin, tmax) \
410  : _GL_INT_OP_CALC1 (a, b, r, op, overflow, ut, t, tmin, tmax))
411 #define _GL_INT_OP_CALC1(a, b, r, op, overflow, ut, t, tmin, tmax) \
412  ((overflow (a, b) \
413  || (EXPR_SIGNED ((a) op (b)) && ((a) op (b)) < (tmin)) \
414  || (tmax) < ((a) op (b))) \
415  ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t, tmin, tmax), 1) \
416  : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t, tmin, tmax), 0))
417 
418 /* Return A <op> B, where the operation is given by OP. Use the
419  unsigned type UT for calculation to avoid overflow problems.
420  Convert the result to type T without overflow by subtracting TMIN
421  from large values before converting, and adding it afterwards.
422  Compilers can optimize all the operations except OP. */
423 #define _GL_INT_OP_WRAPV_VIA_UNSIGNED(a, b, op, ut, t, tmin, tmax) \
424  (((ut) (a) op (ut) (b)) <= (tmax) \
425  ? (t) ((ut) (a) op (ut) (b)) \
426  : ((t) (((ut) (a) op (ut) (b)) - (tmin)) + (tmin)))
427 
428 #endif /* _GL_INTPROPS_H */