1/* intprops.h -- properties of integer types 2 3 Copyright (C) 2001-2020 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 General Public License as published 7 by 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 <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. 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) + 0) - 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 || (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. This macro does not evaluate its argument, 98 and expands to an integer constant expression. */ 99#if _GL_HAVE___TYPEOF__ 100# define _GL_SIGNED_TYPE_OR_EXPR(t) TYPE_SIGNED (__typeof__ (t)) 101#else 102# define _GL_SIGNED_TYPE_OR_EXPR(t) 1 103#endif 104 105/* Bound on length of the string representing an unsigned integer 106 value representable in B bits. log10 (2.0) < 146/485. The 107 smallest value of B where this bound is not tight is 2621. */ 108#define INT_BITS_STRLEN_BOUND(b) (((b) * 146 + 484) / 485) 109 110/* Bound on length of the string representing an integer type or expression T. 111 Subtract 1 for the sign bit if T is signed, and then add 1 more for 112 a minus sign if needed. 113 114 Because _GL_SIGNED_TYPE_OR_EXPR sometimes returns 1 when its argument is 115 unsigned, this macro may overestimate the true bound by one byte when 116 applied to unsigned types of size 2, 4, 16, ... bytes. */ 117#define INT_STRLEN_BOUND(t) \ 118 (INT_BITS_STRLEN_BOUND (TYPE_WIDTH (t) - _GL_SIGNED_TYPE_OR_EXPR (t)) \ 119 + _GL_SIGNED_TYPE_OR_EXPR (t)) 120 121/* Bound on buffer size needed to represent an integer type or expression T, 122 including the terminating null. */ 123#define INT_BUFSIZE_BOUND(t) (INT_STRLEN_BOUND (t) + 1) 124 125 126/* Range overflow checks. 127 128 The INT_<op>_RANGE_OVERFLOW macros return 1 if the corresponding C 129 operators might not yield numerically correct answers due to 130 arithmetic overflow. They do not rely on undefined or 131 implementation-defined behavior. Their implementations are simple 132 and straightforward, but they are a bit harder to use than the 133 INT_<op>_OVERFLOW macros described below. 134 135 Example usage: 136 137 long int i = ...; 138 long int j = ...; 139 if (INT_MULTIPLY_RANGE_OVERFLOW (i, j, LONG_MIN, LONG_MAX)) 140 printf ("multiply would overflow"); 141 else 142 printf ("product is %ld", i * j); 143 144 Restrictions on *_RANGE_OVERFLOW macros: 145 146 These macros do not check for all possible numerical problems or 147 undefined or unspecified behavior: they do not check for division 148 by zero, for bad shift counts, or for shifting negative numbers. 149 150 These macros may evaluate their arguments zero or multiple times, 151 so the arguments should not have side effects. The arithmetic 152 arguments (including the MIN and MAX arguments) must be of the same 153 integer type after the usual arithmetic conversions, and the type 154 must have minimum value MIN and maximum MAX. Unsigned types should 155 use a zero MIN of the proper type. 156 157 These macros are tuned for constant MIN and MAX. For commutative 158 operations such as A + B, they are also tuned for constant B. */ 159 160/* Return 1 if A + B would overflow in [MIN,MAX] arithmetic. 161 See above for restrictions. */ 162#define INT_ADD_RANGE_OVERFLOW(a, b, min, max) \ 163 ((b) < 0 \ 164 ? (a) < (min) - (b) \ 165 : (max) - (b) < (a)) 166 167/* Return 1 if A - B would overflow in [MIN,MAX] arithmetic. 168 See above for restrictions. */ 169#define INT_SUBTRACT_RANGE_OVERFLOW(a, b, min, max) \ 170 ((b) < 0 \ 171 ? (max) + (b) < (a) \ 172 : (a) < (min) + (b)) 173 174/* Return 1 if - A would overflow in [MIN,MAX] arithmetic. 175 See above for restrictions. */ 176#define INT_NEGATE_RANGE_OVERFLOW(a, min, max) \ 177 ((min) < 0 \ 178 ? (a) < - (max) \ 179 : 0 < (a)) 180 181/* Return 1 if A * B would overflow in [MIN,MAX] arithmetic. 182 See above for restrictions. Avoid && and || as they tickle 183 bugs in Sun C 5.11 2010/08/13 and other compilers; see 184 <https://lists.gnu.org/r/bug-gnulib/2011-05/msg00401.html>. */ 185#define INT_MULTIPLY_RANGE_OVERFLOW(a, b, min, max) \ 186 ((b) < 0 \ 187 ? ((a) < 0 \ 188 ? (a) < (max) / (b) \ 189 : (b) == -1 \ 190 ? 0 \ 191 : (min) / (b) < (a)) \ 192 : (b) == 0 \ 193 ? 0 \ 194 : ((a) < 0 \ 195 ? (a) < (min) / (b) \ 196 : (max) / (b) < (a))) 197 198/* Return 1 if A / B would overflow in [MIN,MAX] arithmetic. 199 See above for restrictions. Do not check for division by zero. */ 200#define INT_DIVIDE_RANGE_OVERFLOW(a, b, min, max) \ 201 ((min) < 0 && (b) == -1 && (a) < - (max)) 202 203/* Return 1 if A % B would overflow in [MIN,MAX] arithmetic. 204 See above for restrictions. Do not check for division by zero. 205 Mathematically, % should never overflow, but on x86-like hosts 206 INT_MIN % -1 traps, and the C standard permits this, so treat this 207 as an overflow too. */ 208#define INT_REMAINDER_RANGE_OVERFLOW(a, b, min, max) \ 209 INT_DIVIDE_RANGE_OVERFLOW (a, b, min, max) 210 211/* Return 1 if A << B would overflow in [MIN,MAX] arithmetic. 212 See above for restrictions. Here, MIN and MAX are for A only, and B need 213 not be of the same type as the other arguments. The C standard says that 214 behavior is undefined for shifts unless 0 <= B < wordwidth, and that when 215 A is negative then A << B has undefined behavior and A >> B has 216 implementation-defined behavior, but do not check these other 217 restrictions. */ 218#define INT_LEFT_SHIFT_RANGE_OVERFLOW(a, b, min, max) \ 219 ((a) < 0 \ 220 ? (a) < (min) >> (b) \ 221 : (max) >> (b) < (a)) 222 223/* True if __builtin_add_overflow (A, B, P) and __builtin_sub_overflow 224 (A, B, P) work when P is non-null. */ 225#if 5 <= __GNUC__ && !defined __ICC 226# define _GL_HAS_BUILTIN_ADD_OVERFLOW 1 227#elif defined __has_builtin 228# define _GL_HAS_BUILTIN_ADD_OVERFLOW __has_builtin (__builtin_add_overflow) 229#else 230# define _GL_HAS_BUILTIN_ADD_OVERFLOW 0 231#endif 232 233/* True if __builtin_mul_overflow (A, B, P) works when P is non-null. */ 234#ifdef __clang__ 235/* Work around Clang bug <https://bugs.llvm.org/show_bug.cgi?id=16404>. */ 236# define _GL_HAS_BUILTIN_MUL_OVERFLOW 0 237#else 238# define _GL_HAS_BUILTIN_MUL_OVERFLOW _GL_HAS_BUILTIN_ADD_OVERFLOW 239#endif 240 241/* True if __builtin_add_overflow_p (A, B, C) works, and similarly for 242 __builtin_mul_overflow_p and __builtin_mul_overflow_p. */ 243#define _GL_HAS_BUILTIN_OVERFLOW_P (7 <= __GNUC__) 244 245/* The _GL*_OVERFLOW macros have the same restrictions as the 246 *_RANGE_OVERFLOW macros, except that they do not assume that operands 247 (e.g., A and B) have the same type as MIN and MAX. Instead, they assume 248 that the result (e.g., A + B) has that type. */ 249#if _GL_HAS_BUILTIN_OVERFLOW_P 250# define _GL_ADD_OVERFLOW(a, b, min, max) \ 251 __builtin_add_overflow_p (a, b, (__typeof__ ((a) + (b))) 0) 252# define _GL_SUBTRACT_OVERFLOW(a, b, min, max) \ 253 __builtin_sub_overflow_p (a, b, (__typeof__ ((a) - (b))) 0) 254# define _GL_MULTIPLY_OVERFLOW(a, b, min, max) \ 255 __builtin_mul_overflow_p (a, b, (__typeof__ ((a) * (b))) 0) 256#else 257# define _GL_ADD_OVERFLOW(a, b, min, max) \ 258 ((min) < 0 ? INT_ADD_RANGE_OVERFLOW (a, b, min, max) \ 259 : (a) < 0 ? (b) <= (a) + (b) \ 260 : (b) < 0 ? (a) <= (a) + (b) \ 261 : (a) + (b) < (b)) 262# define _GL_SUBTRACT_OVERFLOW(a, b, min, max) \ 263 ((min) < 0 ? INT_SUBTRACT_RANGE_OVERFLOW (a, b, min, max) \ 264 : (a) < 0 ? 1 \ 265 : (b) < 0 ? (a) - (b) <= (a) \ 266 : (a) < (b)) 267# define _GL_MULTIPLY_OVERFLOW(a, b, min, max) \ 268 (((min) == 0 && (((a) < 0 && 0 < (b)) || ((b) < 0 && 0 < (a)))) \ 269 || INT_MULTIPLY_RANGE_OVERFLOW (a, b, min, max)) 270#endif 271#define _GL_DIVIDE_OVERFLOW(a, b, min, max) \ 272 ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max) \ 273 : (a) < 0 ? (b) <= (a) + (b) - 1 \ 274 : (b) < 0 && (a) + (b) <= (a)) 275#define _GL_REMAINDER_OVERFLOW(a, b, min, max) \ 276 ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max) \ 277 : (a) < 0 ? (a) % (b) != ((max) - (b) + 1) % (b) \ 278 : (b) < 0 && ! _GL_UNSIGNED_NEG_MULTIPLE (a, b, max)) 279 280/* Return a nonzero value if A is a mathematical multiple of B, where 281 A is unsigned, B is negative, and MAX is the maximum value of A's 282 type. A's type must be the same as (A % B)'s type. Normally (A % 283 -B == 0) suffices, but things get tricky if -B would overflow. */ 284#define _GL_UNSIGNED_NEG_MULTIPLE(a, b, max) \ 285 (((b) < -_GL_SIGNED_INT_MAXIMUM (b) \ 286 ? (_GL_SIGNED_INT_MAXIMUM (b) == (max) \ 287 ? (a) \ 288 : (a) % (_GL_INT_CONVERT (a, _GL_SIGNED_INT_MAXIMUM (b)) + 1)) \ 289 : (a) % - (b)) \ 290 == 0) 291 292/* Check for integer overflow, and report low order bits of answer. 293 294 The INT_<op>_OVERFLOW macros return 1 if the corresponding C operators 295 might not yield numerically correct answers due to arithmetic overflow. 296 The INT_<op>_WRAPV macros compute the low-order bits of the sum, 297 difference, and product of two C integers, and return 1 if these 298 low-order bits are not numerically correct. 299 These macros work correctly on all known practical hosts, and do not rely 300 on undefined behavior due to signed arithmetic overflow. 301 302 Example usage, assuming A and B are long int: 303 304 if (INT_MULTIPLY_OVERFLOW (a, b)) 305 printf ("result would overflow\n"); 306 else 307 printf ("result is %ld (no overflow)\n", a * b); 308 309 Example usage with WRAPV flavor: 310 311 long int result; 312 bool overflow = INT_MULTIPLY_WRAPV (a, b, &result); 313 printf ("result is %ld (%s)\n", result, 314 overflow ? "after overflow" : "no overflow"); 315 316 Restrictions on these macros: 317 318 These macros do not check for all possible numerical problems or 319 undefined or unspecified behavior: they do not check for division 320 by zero, for bad shift counts, or for shifting negative numbers. 321 322 These macros may evaluate their arguments zero or multiple times, so the 323 arguments should not have side effects. 324 325 The WRAPV macros are not constant expressions. They support only 326 +, binary -, and *. Because the WRAPV macros convert the result, 327 they report overflow in different circumstances than the OVERFLOW 328 macros do. 329 330 These macros are tuned for their last input argument being a constant. 331 332 Return 1 if the integer expressions A * B, A - B, -A, A * B, A / B, 333 A % B, and A << B would overflow, respectively. */ 334 335#define INT_ADD_OVERFLOW(a, b) \ 336 _GL_BINARY_OP_OVERFLOW (a, b, _GL_ADD_OVERFLOW) 337#define INT_SUBTRACT_OVERFLOW(a, b) \ 338 _GL_BINARY_OP_OVERFLOW (a, b, _GL_SUBTRACT_OVERFLOW) 339#if _GL_HAS_BUILTIN_OVERFLOW_P 340# define INT_NEGATE_OVERFLOW(a) INT_SUBTRACT_OVERFLOW (0, a) 341#else 342# define INT_NEGATE_OVERFLOW(a) \ 343 INT_NEGATE_RANGE_OVERFLOW (a, _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a)) 344#endif 345#define INT_MULTIPLY_OVERFLOW(a, b) \ 346 _GL_BINARY_OP_OVERFLOW (a, b, _GL_MULTIPLY_OVERFLOW) 347#define INT_DIVIDE_OVERFLOW(a, b) \ 348 _GL_BINARY_OP_OVERFLOW (a, b, _GL_DIVIDE_OVERFLOW) 349#define INT_REMAINDER_OVERFLOW(a, b) \ 350 _GL_BINARY_OP_OVERFLOW (a, b, _GL_REMAINDER_OVERFLOW) 351#define INT_LEFT_SHIFT_OVERFLOW(a, b) \ 352 INT_LEFT_SHIFT_RANGE_OVERFLOW (a, b, \ 353 _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a)) 354 355/* Return 1 if the expression A <op> B would overflow, 356 where OP_RESULT_OVERFLOW (A, B, MIN, MAX) does the actual test, 357 assuming MIN and MAX are the minimum and maximum for the result type. 358 Arguments should be free of side effects. */ 359#define _GL_BINARY_OP_OVERFLOW(a, b, op_result_overflow) \ 360 op_result_overflow (a, b, \ 361 _GL_INT_MINIMUM (_GL_INT_CONVERT (a, b)), \ 362 _GL_INT_MAXIMUM (_GL_INT_CONVERT (a, b))) 363 364/* Store the low-order bits of A + B, A - B, A * B, respectively, into *R. 365 Return 1 if the result overflows. See above for restrictions. */ 366#if _GL_HAS_BUILTIN_ADD_OVERFLOW 367# define INT_ADD_WRAPV(a, b, r) __builtin_add_overflow (a, b, r) 368# define INT_SUBTRACT_WRAPV(a, b, r) __builtin_sub_overflow (a, b, r) 369#else 370# define INT_ADD_WRAPV(a, b, r) \ 371 _GL_INT_OP_WRAPV (a, b, r, +, _GL_INT_ADD_RANGE_OVERFLOW) 372# define INT_SUBTRACT_WRAPV(a, b, r) \ 373 _GL_INT_OP_WRAPV (a, b, r, -, _GL_INT_SUBTRACT_RANGE_OVERFLOW) 374#endif 375#if _GL_HAS_BUILTIN_MUL_OVERFLOW 376# if (9 < __GNUC__ + (3 <= __GNUC_MINOR__) \ 377 || (__GNUC__ == 8 && 4 <= __GNUC_MINOR__)) 378# define INT_MULTIPLY_WRAPV(a, b, r) __builtin_mul_overflow (a, b, r) 379# else 380 /* Work around GCC bug 91450. */ 381# define INT_MULTIPLY_WRAPV(a, b, r) \ 382 ((!_GL_SIGNED_TYPE_OR_EXPR (*(r)) && EXPR_SIGNED (a) && EXPR_SIGNED (b) \ 383 && _GL_INT_MULTIPLY_RANGE_OVERFLOW (a, b, 0, (__typeof__ (*(r))) -1)) \ 384 ? ((void) __builtin_mul_overflow (a, b, r), 1) \ 385 : __builtin_mul_overflow (a, b, r)) 386# endif 387#else 388# define INT_MULTIPLY_WRAPV(a, b, r) \ 389 _GL_INT_OP_WRAPV (a, b, r, *, _GL_INT_MULTIPLY_RANGE_OVERFLOW) 390#endif 391 392/* Nonzero if this compiler has GCC bug 68193 or Clang bug 25390. See: 393 https://gcc.gnu.org/bugzilla/show_bug.cgi?id=68193 394 https://llvm.org/bugs/show_bug.cgi?id=25390 395 For now, assume all versions of GCC-like compilers generate bogus 396 warnings for _Generic. This matters only for compilers that 397 lack relevant builtins. */ 398#if __GNUC__ 399# define _GL__GENERIC_BOGUS 1 400#else 401# define _GL__GENERIC_BOGUS 0 402#endif 403 404/* Store the low-order bits of A <op> B into *R, where OP specifies 405 the operation and OVERFLOW the overflow predicate. Return 1 if the 406 result overflows. See above for restrictions. */ 407#if 201112 <= __STDC_VERSION__ && !_GL__GENERIC_BOGUS 408# define _GL_INT_OP_WRAPV(a, b, r, op, overflow) \ 409 (_Generic \ 410 (*(r), \ 411 signed char: \ 412 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \ 413 signed char, SCHAR_MIN, SCHAR_MAX), \ 414 unsigned char: \ 415 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \ 416 unsigned char, 0, UCHAR_MAX), \ 417 short int: \ 418 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \ 419 short int, SHRT_MIN, SHRT_MAX), \ 420 unsigned short int: \ 421 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \ 422 unsigned short int, 0, USHRT_MAX), \ 423 int: \ 424 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \ 425 int, INT_MIN, INT_MAX), \ 426 unsigned int: \ 427 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \ 428 unsigned int, 0, UINT_MAX), \ 429 long int: \ 430 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \ 431 long int, LONG_MIN, LONG_MAX), \ 432 unsigned long int: \ 433 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \ 434 unsigned long int, 0, ULONG_MAX), \ 435 long long int: \ 436 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \ 437 long long int, LLONG_MIN, LLONG_MAX), \ 438 unsigned long long int: \ 439 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \ 440 unsigned long long int, 0, ULLONG_MAX))) 441#else 442/* Store the low-order bits of A <op> B into *R, where OP specifies 443 the operation and OVERFLOW the overflow predicate. If *R is 444 signed, its type is ST with bounds SMIN..SMAX; otherwise its type 445 is UT with bounds U..UMAX. ST and UT are narrower than int. 446 Return 1 if the result overflows. See above for restrictions. */ 447# if _GL_HAVE___TYPEOF__ 448# define _GL_INT_OP_WRAPV_SMALLISH(a,b,r,op,overflow,st,smin,smax,ut,umax) \ 449 (TYPE_SIGNED (__typeof__ (*(r))) \ 450 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, st, smin, smax) \ 451 : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, ut, 0, umax)) 452# else 453# define _GL_INT_OP_WRAPV_SMALLISH(a,b,r,op,overflow,st,smin,smax,ut,umax) \ 454 (overflow (a, b, smin, smax) \ 455 ? (overflow (a, b, 0, umax) \ 456 ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st), 1) \ 457 : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st)) < 0) \ 458 : (overflow (a, b, 0, umax) \ 459 ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st)) >= 0 \ 460 : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a,b,op,unsigned,st), 0))) 461# endif 462 463# define _GL_INT_OP_WRAPV(a, b, r, op, overflow) \ 464 (sizeof *(r) == sizeof (signed char) \ 465 ? _GL_INT_OP_WRAPV_SMALLISH (a, b, r, op, overflow, \ 466 signed char, SCHAR_MIN, SCHAR_MAX, \ 467 unsigned char, UCHAR_MAX) \ 468 : sizeof *(r) == sizeof (short int) \ 469 ? _GL_INT_OP_WRAPV_SMALLISH (a, b, r, op, overflow, \ 470 short int, SHRT_MIN, SHRT_MAX, \ 471 unsigned short int, USHRT_MAX) \ 472 : sizeof *(r) == sizeof (int) \ 473 ? (EXPR_SIGNED (*(r)) \ 474 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \ 475 int, INT_MIN, INT_MAX) \ 476 : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \ 477 unsigned int, 0, UINT_MAX)) \ 478 : _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow)) 479# ifdef LLONG_MAX 480# define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \ 481 (sizeof *(r) == sizeof (long int) \ 482 ? (EXPR_SIGNED (*(r)) \ 483 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \ 484 long int, LONG_MIN, LONG_MAX) \ 485 : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \ 486 unsigned long int, 0, ULONG_MAX)) \ 487 : (EXPR_SIGNED (*(r)) \ 488 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \ 489 long long int, LLONG_MIN, LLONG_MAX) \ 490 : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \ 491 unsigned long long int, 0, ULLONG_MAX))) 492# else 493# define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \ 494 (EXPR_SIGNED (*(r)) \ 495 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \ 496 long int, LONG_MIN, LONG_MAX) \ 497 : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \ 498 unsigned long int, 0, ULONG_MAX)) 499# endif 500#endif 501 502/* Store the low-order bits of A <op> B into *R, where the operation 503 is given by OP. Use the unsigned type UT for calculation to avoid 504 overflow problems. *R's type is T, with extrema TMIN and TMAX. 505 T must be a signed integer type. Return 1 if the result overflows. */ 506#define _GL_INT_OP_CALC(a, b, r, op, overflow, ut, t, tmin, tmax) \ 507 (overflow (a, b, tmin, tmax) \ 508 ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 1) \ 509 : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 0)) 510 511/* Return the low-order bits of A <op> B, where the operation is given 512 by OP. Use the unsigned type UT for calculation to avoid undefined 513 behavior on signed integer overflow, and convert the result to type T. 514 UT is at least as wide as T and is no narrower than unsigned int, 515 T is two's complement, and there is no padding or trap representations. 516 Assume that converting UT to T yields the low-order bits, as is 517 done in all known two's-complement C compilers. E.g., see: 518 https://gcc.gnu.org/onlinedocs/gcc/Integers-implementation.html 519 520 According to the C standard, converting UT to T yields an 521 implementation-defined result or signal for values outside T's 522 range. However, code that works around this theoretical problem 523 runs afoul of a compiler bug in Oracle Studio 12.3 x86. See: 524 https://lists.gnu.org/r/bug-gnulib/2017-04/msg00049.html 525 As the compiler bug is real, don't try to work around the 526 theoretical problem. */ 527 528#define _GL_INT_OP_WRAPV_VIA_UNSIGNED(a, b, op, ut, t) \ 529 ((t) ((ut) (a) op (ut) (b))) 530 531/* Return true if the numeric values A + B, A - B, A * B fall outside 532 the range TMIN..TMAX. Arguments should be integer expressions 533 without side effects. TMIN should be signed and nonpositive. 534 TMAX should be positive, and should be signed unless TMIN is zero. */ 535#define _GL_INT_ADD_RANGE_OVERFLOW(a, b, tmin, tmax) \ 536 ((b) < 0 \ 537 ? (((tmin) \ 538 ? ((EXPR_SIGNED (_GL_INT_CONVERT (a, (tmin) - (b))) || (b) < (tmin)) \ 539 && (a) < (tmin) - (b)) \ 540 : (a) <= -1 - (b)) \ 541 || ((EXPR_SIGNED (a) ? 0 <= (a) : (tmax) < (a)) && (tmax) < (a) + (b))) \ 542 : (a) < 0 \ 543 ? (((tmin) \ 544 ? ((EXPR_SIGNED (_GL_INT_CONVERT (b, (tmin) - (a))) || (a) < (tmin)) \ 545 && (b) < (tmin) - (a)) \ 546 : (b) <= -1 - (a)) \ 547 || ((EXPR_SIGNED (_GL_INT_CONVERT (a, b)) || (tmax) < (b)) \ 548 && (tmax) < (a) + (b))) \ 549 : (tmax) < (b) || (tmax) - (b) < (a)) 550#define _GL_INT_SUBTRACT_RANGE_OVERFLOW(a, b, tmin, tmax) \ 551 (((a) < 0) == ((b) < 0) \ 552 ? ((a) < (b) \ 553 ? !(tmin) || -1 - (tmin) < (b) - (a) - 1 \ 554 : (tmax) < (a) - (b)) \ 555 : (a) < 0 \ 556 ? ((!EXPR_SIGNED (_GL_INT_CONVERT ((a) - (tmin), b)) && (a) - (tmin) < 0) \ 557 || (a) - (tmin) < (b)) \ 558 : ((! (EXPR_SIGNED (_GL_INT_CONVERT (tmax, b)) \ 559 && EXPR_SIGNED (_GL_INT_CONVERT ((tmax) + (b), a))) \ 560 && (tmax) <= -1 - (b)) \ 561 || (tmax) + (b) < (a))) 562#define _GL_INT_MULTIPLY_RANGE_OVERFLOW(a, b, tmin, tmax) \ 563 ((b) < 0 \ 564 ? ((a) < 0 \ 565 ? (EXPR_SIGNED (_GL_INT_CONVERT (tmax, b)) \ 566 ? (a) < (tmax) / (b) \ 567 : ((INT_NEGATE_OVERFLOW (b) \ 568 ? _GL_INT_CONVERT (b, tmax) >> (TYPE_WIDTH (b) - 1) \ 569 : (tmax) / -(b)) \ 570 <= -1 - (a))) \ 571 : INT_NEGATE_OVERFLOW (_GL_INT_CONVERT (b, tmin)) && (b) == -1 \ 572 ? (EXPR_SIGNED (a) \ 573 ? 0 < (a) + (tmin) \ 574 : 0 < (a) && -1 - (tmin) < (a) - 1) \ 575 : (tmin) / (b) < (a)) \ 576 : (b) == 0 \ 577 ? 0 \ 578 : ((a) < 0 \ 579 ? (INT_NEGATE_OVERFLOW (_GL_INT_CONVERT (a, tmin)) && (a) == -1 \ 580 ? (EXPR_SIGNED (b) ? 0 < (b) + (tmin) : -1 - (tmin) < (b) - 1) \ 581 : (tmin) / (a) < (b)) \ 582 : (tmax) / (b) < (a))) 583 584#endif /* _GL_INTPROPS_H */ 585