1/* intprops.h -- properties of integer types 2 3 Copyright (C) 2001-2022 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 19#ifndef _GL_INTPROPS_H 20#define _GL_INTPROPS_H 21 22#include <limits.h> 23 24/* Return a value with the common real type of E and V and the value of V. 25 Do not evaluate E. */ 26#define _GL_INT_CONVERT(e, v) ((1 ? 0 : (e)) + (v)) 27 28/* Act like _GL_INT_CONVERT (E, -V) but work around a bug in IRIX 6.5 cc; see 29 <https://lists.gnu.org/r/bug-gnulib/2011-05/msg00406.html>. */ 30#define _GL_INT_NEGATE_CONVERT(e, v) ((1 ? 0 : (e)) - (v)) 31 32/* The extra casts in the following macros work around compiler bugs, 33 e.g., in Cray C 5.0.3.0. */ 34 35/* True if the arithmetic type T is an integer type. bool counts as 36 an integer. */ 37#define TYPE_IS_INTEGER(t) ((t) 1.5 == 1) 38 39/* True if the real type T is signed. */ 40#define TYPE_SIGNED(t) (! ((t) 0 < (t) -1)) 41 42/* Return 1 if the real expression E, after promotion, has a 43 signed or floating type. Do not evaluate E. */ 44#define EXPR_SIGNED(e) (_GL_INT_NEGATE_CONVERT (e, 1) < 0) 45 46 47/* Minimum and maximum values for integer types and expressions. */ 48 49/* The width in bits of the integer type or expression T. 50 Do not evaluate T. T must not be a bit-field expression. 51 Padding bits are not supported; this is checked at compile-time below. */ 52#define TYPE_WIDTH(t) (sizeof (t) * CHAR_BIT) 53 54/* The maximum and minimum values for the integer type T. */ 55#define TYPE_MINIMUM(t) ((t) ~ TYPE_MAXIMUM (t)) 56#define TYPE_MAXIMUM(t) \ 57 ((t) (! TYPE_SIGNED (t) \ 58 ? (t) -1 \ 59 : ((((t) 1 << (TYPE_WIDTH (t) - 2)) - 1) * 2 + 1))) 60 61/* The maximum and minimum values for the type of the expression E, 62 after integer promotion. E is not evaluated. */ 63#define _GL_INT_MINIMUM(e) \ 64 (EXPR_SIGNED (e) \ 65 ? ~ _GL_SIGNED_INT_MAXIMUM (e) \ 66 : _GL_INT_CONVERT (e, 0)) 67#define _GL_INT_MAXIMUM(e) \ 68 (EXPR_SIGNED (e) \ 69 ? _GL_SIGNED_INT_MAXIMUM (e) \ 70 : _GL_INT_NEGATE_CONVERT (e, 1)) 71#define _GL_SIGNED_INT_MAXIMUM(e) \ 72 (((_GL_INT_CONVERT (e, 1) << (TYPE_WIDTH (+ (e)) - 2)) - 1) * 2 + 1) 73 74/* Work around OpenVMS incompatibility with C99. */ 75#if !defined LLONG_MAX && defined __INT64_MAX 76# define LLONG_MAX __INT64_MAX 77# define LLONG_MIN __INT64_MIN 78#endif 79 80/* This include file assumes that signed types are two's complement without 81 padding bits; the above macros have undefined behavior otherwise. 82 If this is a problem for you, please let us know how to fix it for your host. 83 This assumption is tested by the intprops-tests module. */ 84 85/* Does the __typeof__ keyword work? This could be done by 86 'configure', but for now it's easier to do it by hand. */ 87#if (2 <= __GNUC__ \ 88 || (4 <= __clang_major__) \ 89 || (1210 <= __IBMC__ && defined __IBM__TYPEOF__) \ 90 || (0x5110 <= __SUNPRO_C && !__STDC__)) 91# define _GL_HAVE___TYPEOF__ 1 92#else 93# define _GL_HAVE___TYPEOF__ 0 94#endif 95 96/* Return 1 if the integer type or expression T might be signed. Return 0 97 if it is definitely unsigned. T must not be a bit-field expression. 98 This macro does not evaluate its argument, and expands to an 99 integer constant expression. */ 100#if _GL_HAVE___TYPEOF__ 101# define _GL_SIGNED_TYPE_OR_EXPR(t) TYPE_SIGNED (__typeof__ (t)) 102#else 103# define _GL_SIGNED_TYPE_OR_EXPR(t) 1 104#endif 105 106/* Bound on length of the string representing an unsigned integer 107 value representable in B bits. log10 (2.0) < 146/485. The 108 smallest value of B where this bound is not tight is 2621. */ 109#define INT_BITS_STRLEN_BOUND(b) (((b) * 146 + 484) / 485) 110 111/* Bound on length of the string representing an integer type or expression T. 112 T must not be a bit-field expression. 113 114 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 1 when its argument is 118 unsigned, 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 (TYPE_WIDTH (t) - _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. T must not be a bit-field expression. */ 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 harder to use and may be less 136 efficient than the INT_<op>_WRAPV, INT_<op>_OK, and 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 Because all arguments are subject to integer promotions, these 162 macros typically do not work on types narrower than 'int'. 163 164 These macros are tuned for constant MIN and MAX. For commutative 165 operations such as A + B, they are also tuned for constant B. */ 166 167/* Return 1 if A + B would overflow in [MIN,MAX] arithmetic. 168 See above for restrictions. */ 169#define INT_ADD_RANGE_OVERFLOW(a, b, min, max) \ 170 ((b) < 0 \ 171 ? (a) < (min) - (b) \ 172 : (max) - (b) < (a)) 173 174/* Return 1 if A - B would overflow in [MIN,MAX] arithmetic. 175 See above for restrictions. */ 176#define INT_SUBTRACT_RANGE_OVERFLOW(a, b, min, max) \ 177 ((b) < 0 \ 178 ? (max) + (b) < (a) \ 179 : (a) < (min) + (b)) 180 181/* Return 1 if - A would overflow in [MIN,MAX] arithmetic. 182 See above for restrictions. */ 183#define INT_NEGATE_RANGE_OVERFLOW(a, min, max) \ 184 ((min) < 0 \ 185 ? (a) < - (max) \ 186 : 0 < (a)) 187 188/* Return 1 if A * B would overflow in [MIN,MAX] arithmetic. 189 See above for restrictions. Avoid && and || as they tickle 190 bugs in Sun C 5.11 2010/08/13 and other compilers; see 191 <https://lists.gnu.org/r/bug-gnulib/2011-05/msg00401.html>. */ 192#define INT_MULTIPLY_RANGE_OVERFLOW(a, b, min, max) \ 193 ((b) < 0 \ 194 ? ((a) < 0 \ 195 ? (a) < (max) / (b) \ 196 : (b) == -1 \ 197 ? 0 \ 198 : (min) / (b) < (a)) \ 199 : (b) == 0 \ 200 ? 0 \ 201 : ((a) < 0 \ 202 ? (a) < (min) / (b) \ 203 : (max) / (b) < (a))) 204 205/* Return 1 if A / B would overflow in [MIN,MAX] arithmetic. 206 See above for restrictions. Do not check for division by zero. */ 207#define INT_DIVIDE_RANGE_OVERFLOW(a, b, min, max) \ 208 ((min) < 0 && (b) == -1 && (a) < - (max)) 209 210/* Return 1 if A % B would overflow in [MIN,MAX] arithmetic. 211 See above for restrictions. Do not check for division by zero. 212 Mathematically, % should never overflow, but on x86-like hosts 213 INT_MIN % -1 traps, and the C standard permits this, so treat this 214 as an overflow too. */ 215#define INT_REMAINDER_RANGE_OVERFLOW(a, b, min, max) \ 216 INT_DIVIDE_RANGE_OVERFLOW (a, b, min, max) 217 218/* Return 1 if A << B would overflow in [MIN,MAX] arithmetic. 219 See above for restrictions. Here, MIN and MAX are for A only, and B need 220 not be of the same type as the other arguments. The C standard says that 221 behavior is undefined for shifts unless 0 <= B < wordwidth, and that when 222 A is negative then A << B has undefined behavior and A >> B has 223 implementation-defined behavior, but do not check these other 224 restrictions. */ 225#define INT_LEFT_SHIFT_RANGE_OVERFLOW(a, b, min, max) \ 226 ((a) < 0 \ 227 ? (a) < (min) >> (b) \ 228 : (max) >> (b) < (a)) 229 230/* True if __builtin_add_overflow (A, B, P) and __builtin_sub_overflow 231 (A, B, P) work when P is non-null. */ 232#ifdef __EDG__ 233/* EDG-based compilers like nvc 22.1 cannot add 64-bit signed to unsigned 234 <https://bugs.gnu.org/53256>. */ 235# define _GL_HAS_BUILTIN_ADD_OVERFLOW 0 236#elif defined __has_builtin 237# define _GL_HAS_BUILTIN_ADD_OVERFLOW __has_builtin (__builtin_add_overflow) 238/* __builtin_{add,sub}_overflow exists but is not reliable in GCC 5.x and 6.x, 239 see <https://gcc.gnu.org/bugzilla/show_bug.cgi?id=98269>. */ 240#elif 7 <= __GNUC__ 241# define _GL_HAS_BUILTIN_ADD_OVERFLOW 1 242#else 243# define _GL_HAS_BUILTIN_ADD_OVERFLOW 0 244#endif 245 246/* True if __builtin_mul_overflow (A, B, P) works when P is non-null. */ 247#if defined __clang_major__ && __clang_major__ < 14 248/* Work around Clang bug <https://bugs.llvm.org/show_bug.cgi?id=16404>. */ 249# define _GL_HAS_BUILTIN_MUL_OVERFLOW 0 250#else 251# define _GL_HAS_BUILTIN_MUL_OVERFLOW _GL_HAS_BUILTIN_ADD_OVERFLOW 252#endif 253 254/* True if __builtin_add_overflow_p (A, B, C) works, and similarly for 255 __builtin_sub_overflow_p and __builtin_mul_overflow_p. */ 256#ifdef __EDG__ 257/* In EDG-based compilers like ICC 2021.3 and earlier, 258 __builtin_add_overflow_p etc. are not treated as integral constant 259 expressions even when all arguments are. */ 260# define _GL_HAS_BUILTIN_OVERFLOW_P 0 261#elif defined __has_builtin 262# define _GL_HAS_BUILTIN_OVERFLOW_P __has_builtin (__builtin_mul_overflow_p) 263#else 264# define _GL_HAS_BUILTIN_OVERFLOW_P (7 <= __GNUC__) 265#endif 266 267/* The _GL*_OVERFLOW macros have the same restrictions as the 268 *_RANGE_OVERFLOW macros, except that they do not assume that operands 269 (e.g., A and B) have the same type as MIN and MAX. Instead, they assume 270 that the result (e.g., A + B) has that type. */ 271#if _GL_HAS_BUILTIN_OVERFLOW_P 272# define _GL_ADD_OVERFLOW(a, b, min, max) \ 273 __builtin_add_overflow_p (a, b, (__typeof__ ((a) + (b))) 0) 274# define _GL_SUBTRACT_OVERFLOW(a, b, min, max) \ 275 __builtin_sub_overflow_p (a, b, (__typeof__ ((a) - (b))) 0) 276# define _GL_MULTIPLY_OVERFLOW(a, b, min, max) \ 277 __builtin_mul_overflow_p (a, b, (__typeof__ ((a) * (b))) 0) 278#else 279# define _GL_ADD_OVERFLOW(a, b, min, max) \ 280 ((min) < 0 ? INT_ADD_RANGE_OVERFLOW (a, b, min, max) \ 281 : (a) < 0 ? (b) <= (a) + (b) \ 282 : (b) < 0 ? (a) <= (a) + (b) \ 283 : (a) + (b) < (b)) 284# define _GL_SUBTRACT_OVERFLOW(a, b, min, max) \ 285 ((min) < 0 ? INT_SUBTRACT_RANGE_OVERFLOW (a, b, min, max) \ 286 : (a) < 0 ? 1 \ 287 : (b) < 0 ? (a) - (b) <= (a) \ 288 : (a) < (b)) 289# define _GL_MULTIPLY_OVERFLOW(a, b, min, max) \ 290 (((min) == 0 && (((a) < 0 && 0 < (b)) || ((b) < 0 && 0 < (a)))) \ 291 || INT_MULTIPLY_RANGE_OVERFLOW (a, b, min, max)) 292#endif 293#define _GL_DIVIDE_OVERFLOW(a, b, min, max) \ 294 ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max) \ 295 : (a) < 0 ? (b) <= (a) + (b) - 1 \ 296 : (b) < 0 && (a) + (b) <= (a)) 297#define _GL_REMAINDER_OVERFLOW(a, b, min, max) \ 298 ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max) \ 299 : (a) < 0 ? (a) % (b) != ((max) - (b) + 1) % (b) \ 300 : (b) < 0 && ! _GL_UNSIGNED_NEG_MULTIPLE (a, b, max)) 301 302/* Return a nonzero value if A is a mathematical multiple of B, where 303 A is unsigned, B is negative, and MAX is the maximum value of A's 304 type. A's type must be the same as (A % B)'s type. Normally (A % 305 -B == 0) suffices, but things get tricky if -B would overflow. */ 306#define _GL_UNSIGNED_NEG_MULTIPLE(a, b, max) \ 307 (((b) < -_GL_SIGNED_INT_MAXIMUM (b) \ 308 ? (_GL_SIGNED_INT_MAXIMUM (b) == (max) \ 309 ? (a) \ 310 : (a) % (_GL_INT_CONVERT (a, _GL_SIGNED_INT_MAXIMUM (b)) + 1)) \ 311 : (a) % - (b)) \ 312 == 0) 313 314/* Check for integer overflow, and report low order bits of answer. 315 316 The INT_<op>_OVERFLOW macros return 1 if the corresponding C operators 317 might not yield numerically correct answers due to arithmetic overflow. 318 The INT_<op>_WRAPV macros compute the low-order bits of the sum, 319 difference, and product of two C integers, and return 1 if these 320 low-order bits are not numerically correct. 321 These macros work correctly on all known practical hosts, and do not rely 322 on undefined behavior due to signed arithmetic overflow. 323 324 Example usage, assuming A and B are long int: 325 326 if (INT_MULTIPLY_OVERFLOW (a, b)) 327 printf ("result would overflow\n"); 328 else 329 printf ("result is %ld (no overflow)\n", a * b); 330 331 Example usage with WRAPV flavor: 332 333 long int result; 334 bool overflow = INT_MULTIPLY_WRAPV (a, b, &result); 335 printf ("result is %ld (%s)\n", result, 336 overflow ? "after overflow" : "no overflow"); 337 338 Restrictions on these macros: 339 340 These macros do not check for all possible numerical problems or 341 undefined or unspecified behavior: they do not check for division 342 by zero, for bad shift counts, or for shifting negative numbers. 343 344 These macros may evaluate their arguments zero or multiple times, so the 345 arguments should not have side effects. 346 347 The WRAPV macros are not constant expressions. They support only 348 +, binary -, and *. 349 350 Because the WRAPV macros convert the result, they report overflow 351 in different circumstances than the OVERFLOW macros do. For 352 example, in the typical case with 16-bit 'short' and 32-bit 'int', 353 if A, B and R are all of type 'short' then INT_ADD_OVERFLOW (A, B) 354 returns false because the addition cannot overflow after A and B 355 are converted to 'int', whereas INT_ADD_WRAPV (A, B, &R) returns 356 true or false depending on whether the sum fits into 'short'. 357 358 These macros are tuned for their last input argument being a constant. 359 360 Return 1 if the integer expressions A * B, A - B, -A, A * B, A / B, 361 A % B, and A << B would overflow, respectively. */ 362 363#define INT_ADD_OVERFLOW(a, b) \ 364 _GL_BINARY_OP_OVERFLOW (a, b, _GL_ADD_OVERFLOW) 365#define INT_SUBTRACT_OVERFLOW(a, b) \ 366 _GL_BINARY_OP_OVERFLOW (a, b, _GL_SUBTRACT_OVERFLOW) 367#if _GL_HAS_BUILTIN_OVERFLOW_P 368# define INT_NEGATE_OVERFLOW(a) INT_SUBTRACT_OVERFLOW (0, a) 369#else 370# define INT_NEGATE_OVERFLOW(a) \ 371 INT_NEGATE_RANGE_OVERFLOW (a, _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a)) 372#endif 373#define INT_MULTIPLY_OVERFLOW(a, b) \ 374 _GL_BINARY_OP_OVERFLOW (a, b, _GL_MULTIPLY_OVERFLOW) 375#define INT_DIVIDE_OVERFLOW(a, b) \ 376 _GL_BINARY_OP_OVERFLOW (a, b, _GL_DIVIDE_OVERFLOW) 377#define INT_REMAINDER_OVERFLOW(a, b) \ 378 _GL_BINARY_OP_OVERFLOW (a, b, _GL_REMAINDER_OVERFLOW) 379#define INT_LEFT_SHIFT_OVERFLOW(a, b) \ 380 INT_LEFT_SHIFT_RANGE_OVERFLOW (a, b, \ 381 _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a)) 382 383/* Return 1 if the expression A <op> B would overflow, 384 where OP_RESULT_OVERFLOW (A, B, MIN, MAX) does the actual test, 385 assuming MIN and MAX are the minimum and maximum for the result type. 386 Arguments should be free of side effects. */ 387#define _GL_BINARY_OP_OVERFLOW(a, b, op_result_overflow) \ 388 op_result_overflow (a, b, \ 389 _GL_INT_MINIMUM (_GL_INT_CONVERT (a, b)), \ 390 _GL_INT_MAXIMUM (_GL_INT_CONVERT (a, b))) 391 392/* Store the low-order bits of A + B, A - B, A * B, respectively, into *R. 393 Return 1 if the result overflows. See above for restrictions. */ 394#if _GL_HAS_BUILTIN_ADD_OVERFLOW 395# define INT_ADD_WRAPV(a, b, r) __builtin_add_overflow (a, b, r) 396# define INT_SUBTRACT_WRAPV(a, b, r) __builtin_sub_overflow (a, b, r) 397#else 398# define INT_ADD_WRAPV(a, b, r) \ 399 _GL_INT_OP_WRAPV (a, b, r, +, _GL_INT_ADD_RANGE_OVERFLOW) 400# define INT_SUBTRACT_WRAPV(a, b, r) \ 401 _GL_INT_OP_WRAPV (a, b, r, -, _GL_INT_SUBTRACT_RANGE_OVERFLOW) 402#endif 403#if _GL_HAS_BUILTIN_MUL_OVERFLOW 404# if ((9 < __GNUC__ + (3 <= __GNUC_MINOR__) \ 405 || (__GNUC__ == 8 && 4 <= __GNUC_MINOR__)) \ 406 && !defined __EDG__) 407# define INT_MULTIPLY_WRAPV(a, b, r) __builtin_mul_overflow (a, b, r) 408# else 409 /* Work around GCC bug 91450. */ 410# define INT_MULTIPLY_WRAPV(a, b, r) \ 411 ((!_GL_SIGNED_TYPE_OR_EXPR (*(r)) && EXPR_SIGNED (a) && EXPR_SIGNED (b) \ 412 && _GL_INT_MULTIPLY_RANGE_OVERFLOW (a, b, 0, (__typeof__ (*(r))) -1)) \ 413 ? ((void) __builtin_mul_overflow (a, b, r), 1) \ 414 : __builtin_mul_overflow (a, b, r)) 415# endif 416#else 417# define INT_MULTIPLY_WRAPV(a, b, r) \ 418 _GL_INT_OP_WRAPV (a, b, r, *, _GL_INT_MULTIPLY_RANGE_OVERFLOW) 419#endif 420 421/* Nonzero if this compiler has GCC bug 68193 or Clang bug 25390. See: 422 https://gcc.gnu.org/bugzilla/show_bug.cgi?id=68193 423 https://llvm.org/bugs/show_bug.cgi?id=25390 424 For now, assume all versions of GCC-like compilers generate bogus 425 warnings for _Generic. This matters only for compilers that 426 lack relevant builtins. */ 427#if __GNUC__ || defined __clang__ 428# define _GL__GENERIC_BOGUS 1 429#else 430# define _GL__GENERIC_BOGUS 0 431#endif 432 433/* Store the low-order bits of A <op> B into *R, where OP specifies 434 the operation and OVERFLOW the overflow predicate. Return 1 if the 435 result overflows. See above for restrictions. */ 436#if 201112 <= __STDC_VERSION__ && !_GL__GENERIC_BOGUS 437# define _GL_INT_OP_WRAPV(a, b, r, op, overflow) \ 438 (_Generic \ 439 (*(r), \ 440 signed char: \ 441 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \ 442 signed char, SCHAR_MIN, SCHAR_MAX), \ 443 unsigned char: \ 444 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \ 445 unsigned char, 0, UCHAR_MAX), \ 446 short int: \ 447 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \ 448 short int, SHRT_MIN, SHRT_MAX), \ 449 unsigned short int: \ 450 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \ 451 unsigned short int, 0, USHRT_MAX), \ 452 int: \ 453 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \ 454 int, INT_MIN, INT_MAX), \ 455 unsigned int: \ 456 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \ 457 unsigned int, 0, UINT_MAX), \ 458 long int: \ 459 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \ 460 long int, LONG_MIN, LONG_MAX), \ 461 unsigned long int: \ 462 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \ 463 unsigned long int, 0, ULONG_MAX), \ 464 long long int: \ 465 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \ 466 long long int, LLONG_MIN, LLONG_MAX), \ 467 unsigned long long int: \ 468 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \ 469 unsigned long long int, 0, ULLONG_MAX))) 470#else 471/* Store the low-order bits of A <op> B into *R, where OP specifies 472 the operation and OVERFLOW the overflow predicate. If *R is 473 signed, its type is ST with bounds SMIN..SMAX; otherwise its type 474 is UT with bounds U..UMAX. ST and UT are narrower than int. 475 Return 1 if the result overflows. See above for restrictions. */ 476# if _GL_HAVE___TYPEOF__ 477# define _GL_INT_OP_WRAPV_SMALLISH(a,b,r,op,overflow,st,smin,smax,ut,umax) \ 478 (TYPE_SIGNED (__typeof__ (*(r))) \ 479 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, st, smin, smax) \ 480 : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, ut, 0, umax)) 481# else 482# define _GL_INT_OP_WRAPV_SMALLISH(a,b,r,op,overflow,st,smin,smax,ut,umax) \ 483 (overflow (a, b, smin, smax) \ 484 ? (overflow (a, b, 0, umax) \ 485 ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st), 1) \ 486 : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st)) < 0) \ 487 : (overflow (a, b, 0, umax) \ 488 ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st)) >= 0 \ 489 : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st), 0))) 490# endif 491 492# define _GL_INT_OP_WRAPV(a, b, r, op, overflow) \ 493 (sizeof *(r) == sizeof (signed char) \ 494 ? _GL_INT_OP_WRAPV_SMALLISH (a, b, r, op, overflow, \ 495 signed char, SCHAR_MIN, SCHAR_MAX, \ 496 unsigned char, UCHAR_MAX) \ 497 : sizeof *(r) == sizeof (short int) \ 498 ? _GL_INT_OP_WRAPV_SMALLISH (a, b, r, op, overflow, \ 499 short int, SHRT_MIN, SHRT_MAX, \ 500 unsigned short int, USHRT_MAX) \ 501 : sizeof *(r) == sizeof (int) \ 502 ? (EXPR_SIGNED (*(r)) \ 503 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \ 504 int, INT_MIN, INT_MAX) \ 505 : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \ 506 unsigned int, 0, UINT_MAX)) \ 507 : _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow)) 508# ifdef LLONG_MAX 509# define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \ 510 (sizeof *(r) == sizeof (long int) \ 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 : (EXPR_SIGNED (*(r)) \ 517 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \ 518 long long int, LLONG_MIN, LLONG_MAX) \ 519 : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \ 520 unsigned long long int, 0, ULLONG_MAX))) 521# else 522# define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \ 523 (EXPR_SIGNED (*(r)) \ 524 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \ 525 long int, LONG_MIN, LONG_MAX) \ 526 : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \ 527 unsigned long int, 0, ULONG_MAX)) 528# endif 529#endif 530 531/* Store the low-order bits of A <op> B into *R, where the operation 532 is given by OP. Use the unsigned type UT for calculation to avoid 533 overflow problems. *R's type is T, with extrema TMIN and TMAX. 534 T must be a signed integer type. Return 1 if the result overflows. */ 535#define _GL_INT_OP_CALC(a, b, r, op, overflow, ut, t, tmin, tmax) \ 536 (overflow (a, b, tmin, tmax) \ 537 ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 1) \ 538 : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 0)) 539 540/* Return the low-order bits of A <op> B, where the operation is given 541 by OP. Use the unsigned type UT for calculation to avoid undefined 542 behavior on signed integer overflow, and convert the result to type T. 543 UT is at least as wide as T and is no narrower than unsigned int, 544 T is two's complement, and there is no padding or trap representations. 545 Assume that converting UT to T yields the low-order bits, as is 546 done in all known two's-complement C compilers. E.g., see: 547 https://gcc.gnu.org/onlinedocs/gcc/Integers-implementation.html 548 549 According to the C standard, converting UT to T yields an 550 implementation-defined result or signal for values outside T's 551 range. However, code that works around this theoretical problem 552 runs afoul of a compiler bug in Oracle Studio 12.3 x86. See: 553 https://lists.gnu.org/r/bug-gnulib/2017-04/msg00049.html 554 As the compiler bug is real, don't try to work around the 555 theoretical problem. */ 556 557#define _GL_INT_OP_WRAPV_VIA_UNSIGNED(a, b, op, ut, t) \ 558 ((t) ((ut) (a) op (ut) (b))) 559 560/* Return true if the numeric values A + B, A - B, A * B fall outside 561 the range TMIN..TMAX. Arguments should be integer expressions 562 without side effects. TMIN should be signed and nonpositive. 563 TMAX should be positive, and should be signed unless TMIN is zero. */ 564#define _GL_INT_ADD_RANGE_OVERFLOW(a, b, tmin, tmax) \ 565 ((b) < 0 \ 566 ? (((tmin) \ 567 ? ((EXPR_SIGNED (_GL_INT_CONVERT (a, (tmin) - (b))) || (b) < (tmin)) \ 568 && (a) < (tmin) - (b)) \ 569 : (a) <= -1 - (b)) \ 570 || ((EXPR_SIGNED (a) ? 0 <= (a) : (tmax) < (a)) && (tmax) < (a) + (b))) \ 571 : (a) < 0 \ 572 ? (((tmin) \ 573 ? ((EXPR_SIGNED (_GL_INT_CONVERT (b, (tmin) - (a))) || (a) < (tmin)) \ 574 && (b) < (tmin) - (a)) \ 575 : (b) <= -1 - (a)) \ 576 || ((EXPR_SIGNED (_GL_INT_CONVERT (a, b)) || (tmax) < (b)) \ 577 && (tmax) < (a) + (b))) \ 578 : (tmax) < (b) || (tmax) - (b) < (a)) 579#define _GL_INT_SUBTRACT_RANGE_OVERFLOW(a, b, tmin, tmax) \ 580 (((a) < 0) == ((b) < 0) \ 581 ? ((a) < (b) \ 582 ? !(tmin) || -1 - (tmin) < (b) - (a) - 1 \ 583 : (tmax) < (a) - (b)) \ 584 : (a) < 0 \ 585 ? ((!EXPR_SIGNED (_GL_INT_CONVERT ((a) - (tmin), b)) && (a) - (tmin) < 0) \ 586 || (a) - (tmin) < (b)) \ 587 : ((! (EXPR_SIGNED (_GL_INT_CONVERT (tmax, b)) \ 588 && EXPR_SIGNED (_GL_INT_CONVERT ((tmax) + (b), a))) \ 589 && (tmax) <= -1 - (b)) \ 590 || (tmax) + (b) < (a))) 591#define _GL_INT_MULTIPLY_RANGE_OVERFLOW(a, b, tmin, tmax) \ 592 ((b) < 0 \ 593 ? ((a) < 0 \ 594 ? (EXPR_SIGNED (_GL_INT_CONVERT (tmax, b)) \ 595 ? (a) < (tmax) / (b) \ 596 : ((INT_NEGATE_OVERFLOW (b) \ 597 ? _GL_INT_CONVERT (b, tmax) >> (TYPE_WIDTH (+ (b)) - 1) \ 598 : (tmax) / -(b)) \ 599 <= -1 - (a))) \ 600 : INT_NEGATE_OVERFLOW (_GL_INT_CONVERT (b, tmin)) && (b) == -1 \ 601 ? (EXPR_SIGNED (a) \ 602 ? 0 < (a) + (tmin) \ 603 : 0 < (a) && -1 - (tmin) < (a) - 1) \ 604 : (tmin) / (b) < (a)) \ 605 : (b) == 0 \ 606 ? 0 \ 607 : ((a) < 0 \ 608 ? (INT_NEGATE_OVERFLOW (_GL_INT_CONVERT (a, tmin)) && (a) == -1 \ 609 ? (EXPR_SIGNED (b) ? 0 < (b) + (tmin) : -1 - (tmin) < (b) - 1) \ 610 : (tmin) / (a) < (b)) \ 611 : (tmax) / (b) < (a))) 612 613/* The following macros compute A + B, A - B, and A * B, respectively. 614 If no overflow occurs, they set *R to the result and return 1; 615 otherwise, they return 0 and may modify *R. 616 617 Example usage: 618 619 long int result; 620 if (INT_ADD_OK (a, b, &result)) 621 printf ("result is %ld\n", result); 622 else 623 printf ("overflow\n"); 624 625 A, B, and *R should be integers; they need not be the same type, 626 and they need not be all signed or all unsigned. 627 628 These macros work correctly on all known practical hosts, and do not rely 629 on undefined behavior due to signed arithmetic overflow. 630 631 These macros are not constant expressions. 632 633 These macros may evaluate their arguments zero or multiple times, so the 634 arguments should not have side effects. 635 636 These macros are tuned for B being a constant. */ 637 638#define INT_ADD_OK(a, b, r) ! INT_ADD_WRAPV (a, b, r) 639#define INT_SUBTRACT_OK(a, b, r) ! INT_SUBTRACT_WRAPV (a, b, r) 640#define INT_MULTIPLY_OK(a, b, r) ! INT_MULTIPLY_WRAPV (a, b, r) 641 642#endif /* _GL_INTPROPS_H */ 643