source: coreutils/trunk/lib/intprops.h@ 1652

Last change on this file since 1652 was 1648, checked in by Silvan Scherrer, 9 years ago

coreutils: update trunk to version 8.25
File size: 19.5 KB
Line 
1/* intprops.h -- properties of integer types
2
3 Copyright (C) 2001-2005, 2009-2016 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 if (INT_MULTIPLY_OVERFLOW (a, b))
276 printf ("result would overflow\n");
277 else
278 printf ("result is %ld (no overflow)\n", a * b);
279
280 Example usage with WRAPV flavor:
281
282 long int result;
283 bool overflow = INT_MULTIPLY_WRAPV (a, b, &result);
284 printf ("result is %ld (%s)\n", result,
285 overflow ? "after overflow" : "no overflow");
286
287 Restrictions on these macros:
288
289 These macros do not check for all possible numerical problems or
290 undefined or unspecified behavior: they do not check for division
291 by zero, for bad shift counts, or for shifting negative numbers.
292
293 These macros may evaluate their arguments zero or multiple times, so the
294 arguments should not have side effects.
295
296 The WRAPV macros are not constant expressions. They support only
297 +, binary -, and *. The result type must be signed.
298
299 These macros are tuned for their last argument being a constant.
300
301 Return 1 if the integer expressions A * B, A - B, -A, A * B, A / B,
302 A % B, and A << B would overflow, respectively. */
303
304#define INT_ADD_OVERFLOW(a, b) \
305 _GL_BINARY_OP_OVERFLOW (a, b, _GL_ADD_OVERFLOW)
306#define INT_SUBTRACT_OVERFLOW(a, b) \
307 _GL_BINARY_OP_OVERFLOW (a, b, _GL_SUBTRACT_OVERFLOW)
308#define INT_NEGATE_OVERFLOW(a) \
309 INT_NEGATE_RANGE_OVERFLOW (a, _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
310#define INT_MULTIPLY_OVERFLOW(a, b) \
311 _GL_BINARY_OP_OVERFLOW (a, b, _GL_MULTIPLY_OVERFLOW)
312#define INT_DIVIDE_OVERFLOW(a, b) \
313 _GL_BINARY_OP_OVERFLOW (a, b, _GL_DIVIDE_OVERFLOW)
314#define INT_REMAINDER_OVERFLOW(a, b) \
315 _GL_BINARY_OP_OVERFLOW (a, b, _GL_REMAINDER_OVERFLOW)
316#define INT_LEFT_SHIFT_OVERFLOW(a, b) \
317 INT_LEFT_SHIFT_RANGE_OVERFLOW (a, b, \
318 _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
319
320/* Return 1 if the expression A <op> B would overflow,
321 where OP_RESULT_OVERFLOW (A, B, MIN, MAX) does the actual test,
322 assuming MIN and MAX are the minimum and maximum for the result type.
323 Arguments should be free of side effects. */
324#define _GL_BINARY_OP_OVERFLOW(a, b, op_result_overflow) \
325 op_result_overflow (a, b, \
326 _GL_INT_MINIMUM (0 * (b) + (a)), \
327 _GL_INT_MAXIMUM (0 * (b) + (a)))
328
329/* Compute A + B, A - B, A * B, respectively, storing the result into *R.
330 Return 1 if the result overflows. See above for restrictions. */
331#define INT_ADD_WRAPV(a, b, r) \
332 _GL_INT_OP_WRAPV (a, b, r, +, __builtin_add_overflow, INT_ADD_OVERFLOW)
333#define INT_SUBTRACT_WRAPV(a, b, r) \
334 _GL_INT_OP_WRAPV (a, b, r, -, __builtin_sub_overflow, INT_SUBTRACT_OVERFLOW)
335#define INT_MULTIPLY_WRAPV(a, b, r) \
336 _GL_INT_OP_WRAPV (a, b, r, *, __builtin_mul_overflow, INT_MULTIPLY_OVERFLOW)
337
338#ifndef __has_builtin
339# define __has_builtin(x) 0
340#endif
341
342/* Nonzero if this compiler has GCC bug 68193 or Clang bug 25390. See:
343 https://gcc.gnu.org/bugzilla/show_bug.cgi?id=68193
344 https://llvm.org/bugs/show_bug.cgi?id=25390
345 For now, assume all versions of GCC-like compilers generate bogus
346 warnings for _Generic. This matters only for older compilers that
347 lack __builtin_add_overflow. */
348#if __GNUC__
349# define _GL__GENERIC_BOGUS 1
350#else
351# define _GL__GENERIC_BOGUS 0
352#endif
353
354/* Store A <op> B into *R, where OP specifies the operation.
355 BUILTIN is the builtin operation, and OVERFLOW the overflow predicate.
356 See above for restrictions. */
357#if 5 <= __GNUC__ || __has_builtin (__builtin_add_overflow)
358# define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) builtin (a, b, r)
359#elif 201112 <= __STDC_VERSION__ && !_GL__GENERIC_BOGUS
360# define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) \
361 (_Generic \
362 (*(r), \
363 signed char: \
364 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned char, \
365 signed char, SCHAR_MIN, SCHAR_MAX), \
366 short int: \
367 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned short int, \
368 short int, SHRT_MIN, SHRT_MAX), \
369 int: \
370 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
371 int, INT_MIN, INT_MAX), \
372 long int: \
373 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
374 long int, LONG_MIN, LONG_MAX), \
375 long long int: \
376 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
377 long long int, LLONG_MIN, LLONG_MAX)))
378#else
379# define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) \
380 (sizeof *(r) == sizeof (signed char) \
381 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned char, \
382 signed char, SCHAR_MIN, SCHAR_MAX) \
383 : sizeof *(r) == sizeof (short int) \
384 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned short int, \
385 short int, SHRT_MIN, SHRT_MAX) \
386 : sizeof *(r) == sizeof (int) \
387 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
388 int, INT_MIN, INT_MAX) \
389 : _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow))
390# ifdef LLONG_MAX
391# define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
392 (sizeof *(r) == sizeof (long int) \
393 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
394 long int, LONG_MIN, LONG_MAX) \
395 : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
396 long long int, LLONG_MIN, LLONG_MAX))
397# else
398# define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
399 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
400 long int, LONG_MIN, LONG_MAX))
401# endif
402#endif
403
404/* Store the low-order bits of A <op> B into *R, where the operation
405 is given by OP. Use the unsigned type UT for calculation to avoid
406 overflow problems. *R's type is T, with extremal values TMIN and
407 TMAX. T must be a signed integer type. */
408#define _GL_INT_OP_CALC(a, b, r, op, overflow, ut, t, tmin, tmax) \
409 (sizeof ((a) op (b)) < sizeof (t) \
410 ? _GL_INT_OP_CALC1 ((t) (a), (t) (b), r, op, overflow, ut, t, tmin, tmax) \
411 : _GL_INT_OP_CALC1 (a, b, r, op, overflow, ut, t, tmin, tmax))
412#define _GL_INT_OP_CALC1(a, b, r, op, overflow, ut, t, tmin, tmax) \
413 ((overflow (a, b) \
414 || (EXPR_SIGNED ((a) op (b)) && ((a) op (b)) < (tmin)) \
415 || (tmax) < ((a) op (b))) \
416 ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t, tmin, tmax), 1) \
417 : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t, tmin, tmax), 0))
418
419/* Return A <op> B, where the operation is given by OP. Use the
420 unsigned type UT for calculation to avoid overflow problems.
421 Convert the result to type T without overflow by subtracting TMIN
422 from large values before converting, and adding it afterwards.
423 Compilers can optimize all the operations except OP. */
424#define _GL_INT_OP_WRAPV_VIA_UNSIGNED(a, b, op, ut, t, tmin, tmax) \
425 (((ut) (a) op (ut) (b)) <= (tmax) \
426 ? (t) ((ut) (a) op (ut) (b)) \
427 : ((t) (((ut) (a) op (ut) (b)) - (tmin)) + (tmin)))
428
429#endif /* _GL_INTPROPS_H */
Note: See TracBrowser for help on using the repository browser.