1/* intprops.h -- properties of integer types 2 3 Copyright (C) 2001-2005, 2009-2012 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 */ 320