1 /* intprops.h -- properties of integer types 2 3 Copyright (C) 2001-2021 Free Software Foundation, Inc. 4 5 This program is free software: you can redistribute it and/or modify it 6 under the terms of the GNU Lesser General Public License as published 7 by 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 <https://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 Do not evaluate E. */ 27 #define _GL_INT_CONVERT(e, v) ((1 ? 0 : (e)) + (v)) 28 29 /* Act like _GL_INT_CONVERT (E, -V) but work around a bug in IRIX 6.5 cc; see 30 <https://lists.gnu.org/r/bug-gnulib/2011-05/msg00406.html>. */ 31 #define _GL_INT_NEGATE_CONVERT(e, v) ((1 ? 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 the real type T is signed. */ 41 #define TYPE_SIGNED(t) (! ((t) 0 < (t) -1)) 42 43 /* Return 1 if the real expression E, after promotion, has a 44 signed or floating type. Do not evaluate E. */ 45 #define EXPR_SIGNED(e) (_GL_INT_NEGATE_CONVERT (e, 1) < 0) 46 47 48 /* Minimum and maximum values for integer types and expressions. */ 49 50 /* The width in bits of the integer type or expression T. 51 Do not evaluate T. T must not be a bit-field expression. 52 Padding bits are not supported; this is checked at compile-time below. */ 53 #define TYPE_WIDTH(t) (sizeof (t) * CHAR_BIT) 54 55 /* The maximum and minimum values for the integer type T. */ 56 #define TYPE_MINIMUM(t) ((t) ~ TYPE_MAXIMUM (t)) 57 #define TYPE_MAXIMUM(t) \ 58 ((t) (! TYPE_SIGNED (t) \ 59 ? (t) -1 \ 60 : ((((t) 1 << (TYPE_WIDTH (t) - 2)) - 1) * 2 + 1))) 61 62 /* The maximum and minimum values for the type of the expression E, 63 after integer promotion. E is not evaluated. */ 64 #define _GL_INT_MINIMUM(e) \ 65 (EXPR_SIGNED (e) \ 66 ? ~ _GL_SIGNED_INT_MAXIMUM (e) \ 67 : _GL_INT_CONVERT (e, 0)) 68 #define _GL_INT_MAXIMUM(e) \ 69 (EXPR_SIGNED (e) \ 70 ? _GL_SIGNED_INT_MAXIMUM (e) \ 71 : _GL_INT_NEGATE_CONVERT (e, 1)) 72 #define _GL_SIGNED_INT_MAXIMUM(e) \ 73 (((_GL_INT_CONVERT (e, 1) << (TYPE_WIDTH (+ (e)) - 2)) - 1) * 2 + 1) 74 75 /* Work around OpenVMS incompatibility with C99. */ 76 #if !defined LLONG_MAX && defined __INT64_MAX 77 # define LLONG_MAX __INT64_MAX 78 # define LLONG_MIN __INT64_MIN 79 #endif 80 81 /* This include file assumes that signed types are two's complement without 82 padding bits; the above macros have undefined behavior otherwise. 83 If this is a problem for you, please let us know how to fix it for your host. 84 This assumption is tested by the intprops-tests module. */ 85 86 /* Does the __typeof__ keyword work? This could be done by 87 'configure', but for now it's easier to do it by hand. */ 88 #if (2 <= __GNUC__ \ 89 || (4 <= __clang_major__) \ 90 || (1210 <= __IBMC__ && defined __IBM__TYPEOF__) \ 91 || (0x5110 <= __SUNPRO_C && !__STDC__)) 92 # define _GL_HAVE___TYPEOF__ 1 93 #else 94 # define _GL_HAVE___TYPEOF__ 0 95 #endif 96 97 /* Return 1 if the integer type or expression T might be signed. Return 0 98 if it is definitely unsigned. T must not be a bit-field expression. 99 This macro does not evaluate its argument, and expands to an 100 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 T must not be a bit-field expression. 114 115 Subtract 1 for the sign bit if T is signed, and then add 1 more for 116 a minus sign if needed. 117 118 Because _GL_SIGNED_TYPE_OR_EXPR sometimes returns 1 when its argument is 119 unsigned, this macro may overestimate the true bound by one byte when 120 applied to unsigned types of size 2, 4, 16, ... bytes. */ 121 #define INT_STRLEN_BOUND(t) \ 122 (INT_BITS_STRLEN_BOUND (TYPE_WIDTH (t) - _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. T must not be a bit-field expression. */ 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 <https://lists.gnu.org/r/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 /* True if __builtin_add_overflow (A, B, P) and __builtin_sub_overflow 228 (A, B, P) work when P is non-null. */ 229 /* __builtin_{add,sub}_overflow exists but is not reliable in GCC 5.x and 6.x, 230 see <https://gcc.gnu.org/bugzilla/show_bug.cgi?id=98269>. */ 231 #if 7 <= __GNUC__ && !defined __ICC 232 # define _GL_HAS_BUILTIN_ADD_OVERFLOW 1 233 #elif defined __has_builtin 234 # define _GL_HAS_BUILTIN_ADD_OVERFLOW __has_builtin (__builtin_add_overflow) 235 #else 236 # define _GL_HAS_BUILTIN_ADD_OVERFLOW 0 237 #endif 238 239 /* True if __builtin_mul_overflow (A, B, P) works when P is non-null. */ 240 #ifdef __clang__ 241 /* Work around Clang bug <https://bugs.llvm.org/show_bug.cgi?id=16404>. */ 242 # define _GL_HAS_BUILTIN_MUL_OVERFLOW 0 243 #else 244 # define _GL_HAS_BUILTIN_MUL_OVERFLOW _GL_HAS_BUILTIN_ADD_OVERFLOW 245 #endif 246 247 /* True if __builtin_add_overflow_p (A, B, C) works, and similarly for 248 __builtin_sub_overflow_p and __builtin_mul_overflow_p. */ 249 #if defined __clang__ || defined __ICC 250 /* Clang 11 lacks __builtin_mul_overflow_p, and even if it did it 251 would presumably run afoul of Clang bug 16404. ICC 2021.1's 252 __builtin_add_overflow_p etc. are not treated as integral constant 253 expressions even when all arguments are. */ 254 # define _GL_HAS_BUILTIN_OVERFLOW_P 0 255 #elif defined __has_builtin 256 # define _GL_HAS_BUILTIN_OVERFLOW_P __has_builtin (__builtin_mul_overflow_p) 257 #else 258 # define _GL_HAS_BUILTIN_OVERFLOW_P (7 <= __GNUC__) 259 #endif 260 261 /* The _GL*_OVERFLOW macros have the same restrictions as the 262 *_RANGE_OVERFLOW macros, except that they do not assume that operands 263 (e.g., A and B) have the same type as MIN and MAX. Instead, they assume 264 that the result (e.g., A + B) has that type. */ 265 #if _GL_HAS_BUILTIN_OVERFLOW_P 266 # define _GL_ADD_OVERFLOW(a, b, min, max) \ 267 __builtin_add_overflow_p (a, b, (__typeof__ ((a) + (b))) 0) 268 # define _GL_SUBTRACT_OVERFLOW(a, b, min, max) \ 269 __builtin_sub_overflow_p (a, b, (__typeof__ ((a) - (b))) 0) 270 # define _GL_MULTIPLY_OVERFLOW(a, b, min, max) \ 271 __builtin_mul_overflow_p (a, b, (__typeof__ ((a) * (b))) 0) 272 #else 273 # define _GL_ADD_OVERFLOW(a, b, min, max) \ 274 ((min) < 0 ? INT_ADD_RANGE_OVERFLOW (a, b, min, max) \ 275 : (a) < 0 ? (b) <= (a) + (b) \ 276 : (b) < 0 ? (a) <= (a) + (b) \ 277 : (a) + (b) < (b)) 278 # define _GL_SUBTRACT_OVERFLOW(a, b, min, max) \ 279 ((min) < 0 ? INT_SUBTRACT_RANGE_OVERFLOW (a, b, min, max) \ 280 : (a) < 0 ? 1 \ 281 : (b) < 0 ? (a) - (b) <= (a) \ 282 : (a) < (b)) 283 # define _GL_MULTIPLY_OVERFLOW(a, b, min, max) \ 284 (((min) == 0 && (((a) < 0 && 0 < (b)) || ((b) < 0 && 0 < (a)))) \ 285 || INT_MULTIPLY_RANGE_OVERFLOW (a, b, min, max)) 286 #endif 287 #define _GL_DIVIDE_OVERFLOW(a, b, min, max) \ 288 ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max) \ 289 : (a) < 0 ? (b) <= (a) + (b) - 1 \ 290 : (b) < 0 && (a) + (b) <= (a)) 291 #define _GL_REMAINDER_OVERFLOW(a, b, min, max) \ 292 ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max) \ 293 : (a) < 0 ? (a) % (b) != ((max) - (b) + 1) % (b) \ 294 : (b) < 0 && ! _GL_UNSIGNED_NEG_MULTIPLE (a, b, max)) 295 296 /* Return a nonzero value if A is a mathematical multiple of B, where 297 A is unsigned, B is negative, and MAX is the maximum value of A's 298 type. A's type must be the same as (A % B)'s type. Normally (A % 299 -B == 0) suffices, but things get tricky if -B would overflow. */ 300 #define _GL_UNSIGNED_NEG_MULTIPLE(a, b, max) \ 301 (((b) < -_GL_SIGNED_INT_MAXIMUM (b) \ 302 ? (_GL_SIGNED_INT_MAXIMUM (b) == (max) \ 303 ? (a) \ 304 : (a) % (_GL_INT_CONVERT (a, _GL_SIGNED_INT_MAXIMUM (b)) + 1)) \ 305 : (a) % - (b)) \ 306 == 0) 307 308 /* Check for integer overflow, and report low order bits of answer. 309 310 The INT_<op>_OVERFLOW macros return 1 if the corresponding C operators 311 might not yield numerically correct answers due to arithmetic overflow. 312 The INT_<op>_WRAPV macros compute the low-order bits of the sum, 313 difference, and product of two C integers, and return 1 if these 314 low-order bits are not numerically correct. 315 These macros work correctly on all known practical hosts, and do not rely 316 on undefined behavior due to signed arithmetic overflow. 317 318 Example usage, assuming A and B are long int: 319 320 if (INT_MULTIPLY_OVERFLOW (a, b)) 321 printf ("result would overflow\n"); 322 else 323 printf ("result is %ld (no overflow)\n", a * b); 324 325 Example usage with WRAPV flavor: 326 327 long int result; 328 bool overflow = INT_MULTIPLY_WRAPV (a, b, &result); 329 printf ("result is %ld (%s)\n", result, 330 overflow ? "after overflow" : "no overflow"); 331 332 Restrictions on these macros: 333 334 These macros do not check for all possible numerical problems or 335 undefined or unspecified behavior: they do not check for division 336 by zero, for bad shift counts, or for shifting negative numbers. 337 338 These macros may evaluate their arguments zero or multiple times, so the 339 arguments should not have side effects. 340 341 The WRAPV macros are not constant expressions. They support only 342 +, binary -, and *. Because the WRAPV macros convert the result, 343 they report overflow in different circumstances than the OVERFLOW 344 macros do. 345 346 These macros are tuned for their last input argument being a constant. 347 348 Return 1 if the integer expressions A * B, A - B, -A, A * B, A / B, 349 A % B, and A << B would overflow, respectively. */ 350 351 #define INT_ADD_OVERFLOW(a, b) \ 352 _GL_BINARY_OP_OVERFLOW (a, b, _GL_ADD_OVERFLOW) 353 #define INT_SUBTRACT_OVERFLOW(a, b) \ 354 _GL_BINARY_OP_OVERFLOW (a, b, _GL_SUBTRACT_OVERFLOW) 355 #if _GL_HAS_BUILTIN_OVERFLOW_P 356 # define INT_NEGATE_OVERFLOW(a) INT_SUBTRACT_OVERFLOW (0, a) 357 #else 358 # define INT_NEGATE_OVERFLOW(a) \ 359 INT_NEGATE_RANGE_OVERFLOW (a, _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a)) 360 #endif 361 #define INT_MULTIPLY_OVERFLOW(a, b) \ 362 _GL_BINARY_OP_OVERFLOW (a, b, _GL_MULTIPLY_OVERFLOW) 363 #define INT_DIVIDE_OVERFLOW(a, b) \ 364 _GL_BINARY_OP_OVERFLOW (a, b, _GL_DIVIDE_OVERFLOW) 365 #define INT_REMAINDER_OVERFLOW(a, b) \ 366 _GL_BINARY_OP_OVERFLOW (a, b, _GL_REMAINDER_OVERFLOW) 367 #define INT_LEFT_SHIFT_OVERFLOW(a, b) \ 368 INT_LEFT_SHIFT_RANGE_OVERFLOW (a, b, \ 369 _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a)) 370 371 /* Return 1 if the expression A <op> B would overflow, 372 where OP_RESULT_OVERFLOW (A, B, MIN, MAX) does the actual test, 373 assuming MIN and MAX are the minimum and maximum for the result type. 374 Arguments should be free of side effects. */ 375 #define _GL_BINARY_OP_OVERFLOW(a, b, op_result_overflow) \ 376 op_result_overflow (a, b, \ 377 _GL_INT_MINIMUM (_GL_INT_CONVERT (a, b)), \ 378 _GL_INT_MAXIMUM (_GL_INT_CONVERT (a, b))) 379 380 /* Store the low-order bits of A + B, A - B, A * B, respectively, into *R. 381 Return 1 if the result overflows. See above for restrictions. */ 382 #if _GL_HAS_BUILTIN_ADD_OVERFLOW 383 # define INT_ADD_WRAPV(a, b, r) __builtin_add_overflow (a, b, r) 384 # define INT_SUBTRACT_WRAPV(a, b, r) __builtin_sub_overflow (a, b, r) 385 #else 386 # define INT_ADD_WRAPV(a, b, r) \ 387 _GL_INT_OP_WRAPV (a, b, r, +, _GL_INT_ADD_RANGE_OVERFLOW) 388 # define INT_SUBTRACT_WRAPV(a, b, r) \ 389 _GL_INT_OP_WRAPV (a, b, r, -, _GL_INT_SUBTRACT_RANGE_OVERFLOW) 390 #endif 391 #if _GL_HAS_BUILTIN_MUL_OVERFLOW 392 # if ((9 < __GNUC__ + (3 <= __GNUC_MINOR__) \ 393 || (__GNUC__ == 8 && 4 <= __GNUC_MINOR__)) \ 394 && !defined __ICC) 395 # define INT_MULTIPLY_WRAPV(a, b, r) __builtin_mul_overflow (a, b, r) 396 # else 397 /* Work around GCC bug 91450. */ 398 # define INT_MULTIPLY_WRAPV(a, b, r) \ 399 ((!_GL_SIGNED_TYPE_OR_EXPR (*(r)) && EXPR_SIGNED (a) && EXPR_SIGNED (b) \ 400 && _GL_INT_MULTIPLY_RANGE_OVERFLOW (a, b, 0, (__typeof__ (*(r))) -1)) \ 401 ? ((void) __builtin_mul_overflow (a, b, r), 1) \ 402 : __builtin_mul_overflow (a, b, r)) 403 # endif 404 #else 405 # define INT_MULTIPLY_WRAPV(a, b, r) \ 406 _GL_INT_OP_WRAPV (a, b, r, *, _GL_INT_MULTIPLY_RANGE_OVERFLOW) 407 #endif 408 409 /* Nonzero if this compiler has GCC bug 68193 or Clang bug 25390. See: 410 https://gcc.gnu.org/bugzilla/show_bug.cgi?id=68193 411 https://llvm.org/bugs/show_bug.cgi?id=25390 412 For now, assume all versions of GCC-like compilers generate bogus 413 warnings for _Generic. This matters only for compilers that 414 lack relevant builtins. */ 415 #if __GNUC__ || defined __clang__ 416 # define _GL__GENERIC_BOGUS 1 417 #else 418 # define _GL__GENERIC_BOGUS 0 419 #endif 420 421 /* Store the low-order bits of A <op> B into *R, where OP specifies 422 the operation and OVERFLOW the overflow predicate. Return 1 if the 423 result overflows. See above for restrictions. */ 424 #if 201112 <= __STDC_VERSION__ && !_GL__GENERIC_BOGUS 425 # define _GL_INT_OP_WRAPV(a, b, r, op, overflow) \ 426 (_Generic \ 427 (*(r), \ 428 signed char: \ 429 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \ 430 signed char, SCHAR_MIN, SCHAR_MAX), \ 431 unsigned char: \ 432 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \ 433 unsigned char, 0, UCHAR_MAX), \ 434 short int: \ 435 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \ 436 short int, SHRT_MIN, SHRT_MAX), \ 437 unsigned short int: \ 438 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \ 439 unsigned short int, 0, USHRT_MAX), \ 440 int: \ 441 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \ 442 int, INT_MIN, INT_MAX), \ 443 unsigned int: \ 444 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \ 445 unsigned int, 0, UINT_MAX), \ 446 long int: \ 447 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \ 448 long int, LONG_MIN, LONG_MAX), \ 449 unsigned long int: \ 450 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \ 451 unsigned long int, 0, ULONG_MAX), \ 452 long long int: \ 453 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \ 454 long long int, LLONG_MIN, LLONG_MAX), \ 455 unsigned long long int: \ 456 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \ 457 unsigned long long int, 0, ULLONG_MAX))) 458 #else 459 /* Store the low-order bits of A <op> B into *R, where OP specifies 460 the operation and OVERFLOW the overflow predicate. If *R is 461 signed, its type is ST with bounds SMIN..SMAX; otherwise its type 462 is UT with bounds U..UMAX. ST and UT are narrower than int. 463 Return 1 if the result overflows. See above for restrictions. */ 464 # if _GL_HAVE___TYPEOF__ 465 # define _GL_INT_OP_WRAPV_SMALLISH(a,b,r,op,overflow,st,smin,smax,ut,umax) \ 466 (TYPE_SIGNED (__typeof__ (*(r))) \ 467 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, st, smin, smax) \ 468 : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, ut, 0, umax)) 469 # else 470 # define _GL_INT_OP_WRAPV_SMALLISH(a,b,r,op,overflow,st,smin,smax,ut,umax) \ 471 (overflow (a, b, smin, smax) \ 472 ? (overflow (a, b, 0, umax) \ 473 ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st), 1) \ 474 : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st)) < 0) \ 475 : (overflow (a, b, 0, umax) \ 476 ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st)) >= 0 \ 477 : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st), 0))) 478 # endif 479 480 # define _GL_INT_OP_WRAPV(a, b, r, op, overflow) \ 481 (sizeof *(r) == sizeof (signed char) \ 482 ? _GL_INT_OP_WRAPV_SMALLISH (a, b, r, op, overflow, \ 483 signed char, SCHAR_MIN, SCHAR_MAX, \ 484 unsigned char, UCHAR_MAX) \ 485 : sizeof *(r) == sizeof (short int) \ 486 ? _GL_INT_OP_WRAPV_SMALLISH (a, b, r, op, overflow, \ 487 short int, SHRT_MIN, SHRT_MAX, \ 488 unsigned short int, USHRT_MAX) \ 489 : sizeof *(r) == sizeof (int) \ 490 ? (EXPR_SIGNED (*(r)) \ 491 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \ 492 int, INT_MIN, INT_MAX) \ 493 : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \ 494 unsigned int, 0, UINT_MAX)) \ 495 : _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow)) 496 # ifdef LLONG_MAX 497 # define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \ 498 (sizeof *(r) == sizeof (long int) \ 499 ? (EXPR_SIGNED (*(r)) \ 500 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \ 501 long int, LONG_MIN, LONG_MAX) \ 502 : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \ 503 unsigned long int, 0, ULONG_MAX)) \ 504 : (EXPR_SIGNED (*(r)) \ 505 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \ 506 long long int, LLONG_MIN, LLONG_MAX) \ 507 : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \ 508 unsigned long long int, 0, ULLONG_MAX))) 509 # else 510 # define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \ 511 (EXPR_SIGNED (*(r)) \ 512 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \ 513 long int, LONG_MIN, LONG_MAX) \ 514 : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \ 515 unsigned long int, 0, ULONG_MAX)) 516 # endif 517 #endif 518 519 /* Store the low-order bits of A <op> B into *R, where the operation 520 is given by OP. Use the unsigned type UT for calculation to avoid 521 overflow problems. *R's type is T, with extrema TMIN and TMAX. 522 T must be a signed integer type. Return 1 if the result overflows. */ 523 #define _GL_INT_OP_CALC(a, b, r, op, overflow, ut, t, tmin, tmax) \ 524 (overflow (a, b, tmin, tmax) \ 525 ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 1) \ 526 : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 0)) 527 528 /* Return the low-order bits of A <op> B, where the operation is given 529 by OP. Use the unsigned type UT for calculation to avoid undefined 530 behavior on signed integer overflow, and convert the result to type T. 531 UT is at least as wide as T and is no narrower than unsigned int, 532 T is two's complement, and there is no padding or trap representations. 533 Assume that converting UT to T yields the low-order bits, as is 534 done in all known two's-complement C compilers. E.g., see: 535 https://gcc.gnu.org/onlinedocs/gcc/Integers-implementation.html 536 537 According to the C standard, converting UT to T yields an 538 implementation-defined result or signal for values outside T's 539 range. However, code that works around this theoretical problem 540 runs afoul of a compiler bug in Oracle Studio 12.3 x86. See: 541 https://lists.gnu.org/r/bug-gnulib/2017-04/msg00049.html 542 As the compiler bug is real, don't try to work around the 543 theoretical problem. */ 544 545 #define _GL_INT_OP_WRAPV_VIA_UNSIGNED(a, b, op, ut, t) \ 546 ((t) ((ut) (a) op (ut) (b))) 547 548 /* Return true if the numeric values A + B, A - B, A * B fall outside 549 the range TMIN..TMAX. Arguments should be integer expressions 550 without side effects. TMIN should be signed and nonpositive. 551 TMAX should be positive, and should be signed unless TMIN is zero. */ 552 #define _GL_INT_ADD_RANGE_OVERFLOW(a, b, tmin, tmax) \ 553 ((b) < 0 \ 554 ? (((tmin) \ 555 ? ((EXPR_SIGNED (_GL_INT_CONVERT (a, (tmin) - (b))) || (b) < (tmin)) \ 556 && (a) < (tmin) - (b)) \ 557 : (a) <= -1 - (b)) \ 558 || ((EXPR_SIGNED (a) ? 0 <= (a) : (tmax) < (a)) && (tmax) < (a) + (b))) \ 559 : (a) < 0 \ 560 ? (((tmin) \ 561 ? ((EXPR_SIGNED (_GL_INT_CONVERT (b, (tmin) - (a))) || (a) < (tmin)) \ 562 && (b) < (tmin) - (a)) \ 563 : (b) <= -1 - (a)) \ 564 || ((EXPR_SIGNED (_GL_INT_CONVERT (a, b)) || (tmax) < (b)) \ 565 && (tmax) < (a) + (b))) \ 566 : (tmax) < (b) || (tmax) - (b) < (a)) 567 #define _GL_INT_SUBTRACT_RANGE_OVERFLOW(a, b, tmin, tmax) \ 568 (((a) < 0) == ((b) < 0) \ 569 ? ((a) < (b) \ 570 ? !(tmin) || -1 - (tmin) < (b) - (a) - 1 \ 571 : (tmax) < (a) - (b)) \ 572 : (a) < 0 \ 573 ? ((!EXPR_SIGNED (_GL_INT_CONVERT ((a) - (tmin), b)) && (a) - (tmin) < 0) \ 574 || (a) - (tmin) < (b)) \ 575 : ((! (EXPR_SIGNED (_GL_INT_CONVERT (tmax, b)) \ 576 && EXPR_SIGNED (_GL_INT_CONVERT ((tmax) + (b), a))) \ 577 && (tmax) <= -1 - (b)) \ 578 || (tmax) + (b) < (a))) 579 #define _GL_INT_MULTIPLY_RANGE_OVERFLOW(a, b, tmin, tmax) \ 580 ((b) < 0 \ 581 ? ((a) < 0 \ 582 ? (EXPR_SIGNED (_GL_INT_CONVERT (tmax, b)) \ 583 ? (a) < (tmax) / (b) \ 584 : ((INT_NEGATE_OVERFLOW (b) \ 585 ? _GL_INT_CONVERT (b, tmax) >> (TYPE_WIDTH (+ (b)) - 1) \ 586 : (tmax) / -(b)) \ 587 <= -1 - (a))) \ 588 : INT_NEGATE_OVERFLOW (_GL_INT_CONVERT (b, tmin)) && (b) == -1 \ 589 ? (EXPR_SIGNED (a) \ 590 ? 0 < (a) + (tmin) \ 591 : 0 < (a) && -1 - (tmin) < (a) - 1) \ 592 : (tmin) / (b) < (a)) \ 593 : (b) == 0 \ 594 ? 0 \ 595 : ((a) < 0 \ 596 ? (INT_NEGATE_OVERFLOW (_GL_INT_CONVERT (a, tmin)) && (a) == -1 \ 597 ? (EXPR_SIGNED (b) ? 0 < (b) + (tmin) : -1 - (tmin) < (b) - 1) \ 598 : (tmin) / (a) < (b)) \ 599 : (tmax) / (b) < (a))) 600 601 /* The following macros compute A + B, A - B, and A * B, respectively. 602 If no overflow occurs, they set *R to the result and return 1; 603 otherwise, they return 0 and may modify *R. 604 605 Example usage: 606 607 long int result; 608 if (INT_ADD_OK (a, b, &result)) 609 printf ("result is %ld\n", result); 610 else 611 printf ("overflow\n"); 612 613 A, B, and *R should be integers; they need not be the same type, 614 and they need not be all signed or all unsigned. 615 616 These macros work correctly on all known practical hosts, and do not rely 617 on undefined behavior due to signed arithmetic overflow. 618 619 These macros are not constant expressions. 620 621 These macros may evaluate their arguments zero or multiple times, so the 622 arguments should not have side effects. 623 624 These macros are tuned for B being a constant. */ 625 626 #define INT_ADD_OK(a, b, r) ! INT_ADD_WRAPV (a, b, r) 627 #define INT_SUBTRACT_OK(a, b, r) ! INT_SUBTRACT_WRAPV (a, b, r) 628 #define INT_MULTIPLY_OK(a, b, r) ! INT_MULTIPLY_WRAPV (a, b, r) 629 630 #endif /* _GL_INTPROPS_H */ 631