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 Lesser General Public License as published by 7 the Free Software Foundation; either version 2.1 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 Lesser General Public License for more details. 14 15 You should have received a copy of the GNU Lesser 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__ || defined __IBM__TYPEOF__ \ 93 || (0x5110 <= __SUNPRO_C && !__STDC__)) 94 # define _GL_HAVE___TYPEOF__ 1 95 #else 96 # define _GL_HAVE___TYPEOF__ 0 97 #endif 98 99 /* Return 1 if the integer type or expression T might be signed. Return 0 100 if it is definitely unsigned. This macro does not evaluate its argument, 101 and expands to an integer constant expression. */ 102 #if _GL_HAVE___TYPEOF__ 103 # define _GL_SIGNED_TYPE_OR_EXPR(t) TYPE_SIGNED (__typeof__ (t)) 104 #else 105 # define _GL_SIGNED_TYPE_OR_EXPR(t) 1 106 #endif 107 108 /* Bound on length of the string representing an unsigned integer 109 value representable in B bits. log10 (2.0) < 146/485. The 110 smallest value of B where this bound is not tight is 2621. */ 111 #define INT_BITS_STRLEN_BOUND(b) (((b) * 146 + 484) / 485) 112 113 /* Bound on length of the string representing an integer type or expression T. 114 Subtract 1 for the sign bit if T is signed, and then add 1 more for 115 a minus sign if needed. 116 117 Because _GL_SIGNED_TYPE_OR_EXPR sometimes returns 0 when its argument is 118 signed, this macro may overestimate the true bound by one byte when 119 applied to unsigned types of size 2, 4, 16, ... bytes. */ 120 #define INT_STRLEN_BOUND(t) \ 121 (INT_BITS_STRLEN_BOUND (sizeof (t) * CHAR_BIT \ 122 - _GL_SIGNED_TYPE_OR_EXPR (t)) \ 123 + _GL_SIGNED_TYPE_OR_EXPR (t)) 124 125 /* Bound on buffer size needed to represent an integer type or expression T, 126 including the terminating null. */ 127 #define INT_BUFSIZE_BOUND(t) (INT_STRLEN_BOUND (t) + 1) 128 129 130 /* Range overflow checks. 131 132 The INT_<op>_RANGE_OVERFLOW macros return 1 if the corresponding C 133 operators might not yield numerically correct answers due to 134 arithmetic overflow. They do not rely on undefined or 135 implementation-defined behavior. Their implementations are simple 136 and straightforward, but they are a bit harder to use than the 137 INT_<op>_OVERFLOW macros described below. 138 139 Example usage: 140 141 long int i = ...; 142 long int j = ...; 143 if (INT_MULTIPLY_RANGE_OVERFLOW (i, j, LONG_MIN, LONG_MAX)) 144 printf ("multiply would overflow"); 145 else 146 printf ("product is %ld", i * j); 147 148 Restrictions on *_RANGE_OVERFLOW macros: 149 150 These macros do not check for all possible numerical problems or 151 undefined or unspecified behavior: they do not check for division 152 by zero, for bad shift counts, or for shifting negative numbers. 153 154 These macros may evaluate their arguments zero or multiple times, 155 so the arguments should not have side effects. The arithmetic 156 arguments (including the MIN and MAX arguments) must be of the same 157 integer type after the usual arithmetic conversions, and the type 158 must have minimum value MIN and maximum MAX. Unsigned types should 159 use a zero MIN of the proper type. 160 161 These macros are tuned for constant MIN and MAX. For commutative 162 operations such as A + B, they are also tuned for constant B. */ 163 164 /* Return 1 if A + B would overflow in [MIN,MAX] arithmetic. 165 See above for restrictions. */ 166 #define INT_ADD_RANGE_OVERFLOW(a, b, min, max) \ 167 ((b) < 0 \ 168 ? (a) < (min) - (b) \ 169 : (max) - (b) < (a)) 170 171 /* Return 1 if A - B would overflow in [MIN,MAX] arithmetic. 172 See above for restrictions. */ 173 #define INT_SUBTRACT_RANGE_OVERFLOW(a, b, min, max) \ 174 ((b) < 0 \ 175 ? (max) + (b) < (a) \ 176 : (a) < (min) + (b)) 177 178 /* Return 1 if - A would overflow in [MIN,MAX] arithmetic. 179 See above for restrictions. */ 180 #define INT_NEGATE_RANGE_OVERFLOW(a, min, max) \ 181 ((min) < 0 \ 182 ? (a) < - (max) \ 183 : 0 < (a)) 184 185 /* Return 1 if A * B would overflow in [MIN,MAX] arithmetic. 186 See above for restrictions. Avoid && and || as they tickle 187 bugs in Sun C 5.11 2010/08/13 and other compilers; see 188 <http://lists.gnu.org/archive/html/bug-gnulib/2011-05/msg00401.html>. */ 189 #define INT_MULTIPLY_RANGE_OVERFLOW(a, b, min, max) \ 190 ((b) < 0 \ 191 ? ((a) < 0 \ 192 ? (a) < (max) / (b) \ 193 : (b) == -1 \ 194 ? 0 \ 195 : (min) / (b) < (a)) \ 196 : (b) == 0 \ 197 ? 0 \ 198 : ((a) < 0 \ 199 ? (a) < (min) / (b) \ 200 : (max) / (b) < (a))) 201 202 /* Return 1 if A / B would overflow in [MIN,MAX] arithmetic. 203 See above for restrictions. Do not check for division by zero. */ 204 #define INT_DIVIDE_RANGE_OVERFLOW(a, b, min, max) \ 205 ((min) < 0 && (b) == -1 && (a) < - (max)) 206 207 /* Return 1 if A % B would overflow in [MIN,MAX] arithmetic. 208 See above for restrictions. Do not check for division by zero. 209 Mathematically, % should never overflow, but on x86-like hosts 210 INT_MIN % -1 traps, and the C standard permits this, so treat this 211 as an overflow too. */ 212 #define INT_REMAINDER_RANGE_OVERFLOW(a, b, min, max) \ 213 INT_DIVIDE_RANGE_OVERFLOW (a, b, min, max) 214 215 /* Return 1 if A << B would overflow in [MIN,MAX] arithmetic. 216 See above for restrictions. Here, MIN and MAX are for A only, and B need 217 not be of the same type as the other arguments. The C standard says that 218 behavior is undefined for shifts unless 0 <= B < wordwidth, and that when 219 A is negative then A << B has undefined behavior and A >> B has 220 implementation-defined behavior, but do not check these other 221 restrictions. */ 222 #define INT_LEFT_SHIFT_RANGE_OVERFLOW(a, b, min, max) \ 223 ((a) < 0 \ 224 ? (a) < (min) >> (b) \ 225 : (max) >> (b) < (a)) 226 227 228 /* The _GL*_OVERFLOW macros have the same restrictions as the 229 *_RANGE_OVERFLOW macros, except that they do not assume that operands 230 (e.g., A and B) have the same type as MIN and MAX. Instead, they assume 231 that the result (e.g., A + B) has that type. */ 232 #define _GL_ADD_OVERFLOW(a, b, min, max) \ 233 ((min) < 0 ? INT_ADD_RANGE_OVERFLOW (a, b, min, max) \ 234 : (a) < 0 ? (b) <= (a) + (b) \ 235 : (b) < 0 ? (a) <= (a) + (b) \ 236 : (a) + (b) < (b)) 237 #define _GL_SUBTRACT_OVERFLOW(a, b, min, max) \ 238 ((min) < 0 ? INT_SUBTRACT_RANGE_OVERFLOW (a, b, min, max) \ 239 : (a) < 0 ? 1 \ 240 : (b) < 0 ? (a) - (b) <= (a) \ 241 : (a) < (b)) 242 #define _GL_MULTIPLY_OVERFLOW(a, b, min, max) \ 243 (((min) == 0 && (((a) < 0 && 0 < (b)) || ((b) < 0 && 0 < (a)))) \ 244 || INT_MULTIPLY_RANGE_OVERFLOW (a, b, min, max)) 245 #define _GL_DIVIDE_OVERFLOW(a, b, min, max) \ 246 ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max) \ 247 : (a) < 0 ? (b) <= (a) + (b) - 1 \ 248 : (b) < 0 && (a) + (b) <= (a)) 249 #define _GL_REMAINDER_OVERFLOW(a, b, min, max) \ 250 ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max) \ 251 : (a) < 0 ? (a) % (b) != ((max) - (b) + 1) % (b) \ 252 : (b) < 0 && ! _GL_UNSIGNED_NEG_MULTIPLE (a, b, max)) 253 254 /* Return a nonzero value if A is a mathematical multiple of B, where 255 A is unsigned, B is negative, and MAX is the maximum value of A's 256 type. A's type must be the same as (A % B)'s type. Normally (A % 257 -B == 0) suffices, but things get tricky if -B would overflow. */ 258 #define _GL_UNSIGNED_NEG_MULTIPLE(a, b, max) \ 259 (((b) < -_GL_SIGNED_INT_MAXIMUM (b) \ 260 ? (_GL_SIGNED_INT_MAXIMUM (b) == (max) \ 261 ? (a) \ 262 : (a) % (_GL_INT_CONVERT (a, _GL_SIGNED_INT_MAXIMUM (b)) + 1)) \ 263 : (a) % - (b)) \ 264 == 0) 265 266 267 /* Integer overflow checks. 268 269 The INT_<op>_OVERFLOW macros return 1 if the corresponding C operators 270 might not yield numerically correct answers due to arithmetic overflow. 271 They work correctly on all known practical hosts, and do not rely 272 on undefined behavior due to signed arithmetic overflow. 273 274 Example usage: 275 276 long int i = ...; 277 long int j = ...; 278 if (INT_MULTIPLY_OVERFLOW (i, j)) 279 printf ("multiply would overflow"); 280 else 281 printf ("product is %ld", i * j); 282 283 These macros do not check for all possible numerical problems or 284 undefined or unspecified behavior: they do not check for division 285 by zero, for bad shift counts, or for shifting negative numbers. 286 287 These macros may evaluate their arguments zero or multiple times, so the 288 arguments should not have side effects. 289 290 These macros are tuned for their last argument being a constant. 291 292 Return 1 if the integer expressions A * B, A - B, -A, A * B, A / B, 293 A % B, and A << B would overflow, respectively. */ 294 295 #define INT_ADD_OVERFLOW(a, b) \ 296 _GL_BINARY_OP_OVERFLOW (a, b, _GL_ADD_OVERFLOW) 297 #define INT_SUBTRACT_OVERFLOW(a, b) \ 298 _GL_BINARY_OP_OVERFLOW (a, b, _GL_SUBTRACT_OVERFLOW) 299 #define INT_NEGATE_OVERFLOW(a) \ 300 INT_NEGATE_RANGE_OVERFLOW (a, _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a)) 301 #define INT_MULTIPLY_OVERFLOW(a, b) \ 302 _GL_BINARY_OP_OVERFLOW (a, b, _GL_MULTIPLY_OVERFLOW) 303 #define INT_DIVIDE_OVERFLOW(a, b) \ 304 _GL_BINARY_OP_OVERFLOW (a, b, _GL_DIVIDE_OVERFLOW) 305 #define INT_REMAINDER_OVERFLOW(a, b) \ 306 _GL_BINARY_OP_OVERFLOW (a, b, _GL_REMAINDER_OVERFLOW) 307 #define INT_LEFT_SHIFT_OVERFLOW(a, b) \ 308 INT_LEFT_SHIFT_RANGE_OVERFLOW (a, b, \ 309 _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a)) 310 311 /* Return 1 if the expression A <op> B would overflow, 312 where OP_RESULT_OVERFLOW (A, B, MIN, MAX) does the actual test, 313 assuming MIN and MAX are the minimum and maximum for the result type. 314 Arguments should be free of side effects. */ 315 #define _GL_BINARY_OP_OVERFLOW(a, b, op_result_overflow) \ 316 op_result_overflow (a, b, \ 317 _GL_INT_MINIMUM (0 * (b) + (a)), \ 318 _GL_INT_MAXIMUM (0 * (b) + (a))) 319 320 #endif /* _GL_INTPROPS_H */ 321