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 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))
28:
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))
32:
33: /* The extra casts in the following macros work around compiler bugs,
34: e.g., in Cray C 5.0.3.0. */
35:
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)
39:
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)
47:
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)
50:
51: /* True if the arithmetic type T is signed. */
52: #define TYPE_SIGNED(t) (! ((t) 0 < (t) -1))
53:
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)
57:
58:
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. */
63:
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)))
75:
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)
88:
89:
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
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:
266: /* Integer overflow checks.
267:
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.
272:
273: Example usage:
274:
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);
281:
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.
285:
286: These macros may evaluate their arguments zero or multiple times, so the
287: arguments should not have side effects.
288:
289: These macros are tuned for their last argument being a constant.
290:
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. */
293:
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))
309:
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)))
318:
319: #endif /* _GL_INTPROPS_H */
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