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[emacs.git] / lib / intprops.h
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1 /* intprops.h -- properties of integer types
3 Copyright (C) 2001-2005, 2009-2012 Free Software Foundation, Inc.
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.
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.
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/>. */
18 /* Written by Paul Eggert. */
20 #ifndef _GL_INTPROPS_H
21 #define _GL_INTPROPS_H
23 #include <limits.h>
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))
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))
33 /* The extra casts in the following macros work around compiler bugs,
34 e.g., in Cray C 5.0.3.0. */
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)
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)
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)
51 /* True if the arithmetic type T is signed. */
52 #define TYPE_SIGNED(t) (! ((t) 0 < (t) -1))
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)
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. */
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)))
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)
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
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
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)
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.
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))
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)
129 /* Range overflow checks.
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.
138 Example usage:
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);
147 Restrictions on *_RANGE_OVERFLOW macros:
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.
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.
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. */
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))
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))
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))
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)))
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))
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)
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))
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))
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)
266 /* Integer overflow checks.
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.
273 Example usage:
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);
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.
286 These macros may evaluate their arguments zero or multiple times, so the
287 arguments should not have side effects.
289 These macros are tuned for their last argument being a constant.
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. */
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))
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)))
319 #endif /* _GL_INTPROPS_H */