1/* $NetBSD: intprops.h,v 1.6 2024/08/18 20:47:24 christos Exp $ */ 2 3/* intprops.h -- properties of integer types 4 5 Copyright (C) 2001-2018 Free Software Foundation, Inc. 6 7 This program is free software: you can redistribute it and/or modify it 8 under the terms of the GNU Lesser General Public License as published 9 by the Free Software Foundation; either version 2.1 of the License, or 10 (at your option) any later version. 11 12 This program is distributed in the hope that it will be useful, 13 but WITHOUT ANY WARRANTY; without even the implied warranty of 14 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 15 GNU Lesser General Public License for more details. 16 17 You should have received a copy of the GNU Lesser General Public License 18 along with this program. If not, see <https://www.gnu.org/licenses/>. */ 19 20/* Written by Paul Eggert. */ 21 22#ifndef _GL_INTPROPS_H 23#define _GL_INTPROPS_H 24 25#include <limits.h> 26 27/* Return a value with the common real type of E and V and the value of V. */ 28#define _GL_INT_CONVERT(e, v) (0 * (e) + (v)) 29 30/* Act like _GL_INT_CONVERT (E, -V) but work around a bug in IRIX 6.5 cc; see 31 <https://lists.gnu.org/r/bug-gnulib/2011-05/msg00406.html>. */ 32#define _GL_INT_NEGATE_CONVERT(e, v) (0 * (e) - (v)) 33 34/* The extra casts in the following macros work around compiler bugs, 35 e.g., in Cray C 5.0.3.0. */ 36 37/* True if the arithmetic type T is an integer type. bool counts as 38 an integer. */ 39#define TYPE_IS_INTEGER(t) ((t) 1.5 == 1) 40 41/* True if the real type T is signed. */ 42#define TYPE_SIGNED(t) (! ((t) 0 < (t) -1)) 43 44/* Return 1 if the real expression E, after promotion, has a 45 signed or floating type. */ 46#define EXPR_SIGNED(e) (_GL_INT_NEGATE_CONVERT (e, 1) < 0) 47 48 49/* Minimum and maximum values for integer types and expressions. */ 50 51/* The width in bits of the integer type or expression 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 should not have side effects. */ 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 0 when its argument is 115 signed, 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) works when P is non-null. */ 224#if 5 <= __GNUC__ && !defined __ICC 225# define _GL_HAS_BUILTIN_OVERFLOW 1 226#else 227# define _GL_HAS_BUILTIN_OVERFLOW 0 228#endif 229 230/* True if __builtin_add_overflow_p (A, B, C) works. */ 231#define _GL_HAS_BUILTIN_OVERFLOW_P (7 <= __GNUC__) 232 233/* The _GL*_OVERFLOW macros have the same restrictions as the 234 *_RANGE_OVERFLOW macros, except that they do not assume that operands 235 (e.g., A and B) have the same type as MIN and MAX. Instead, they assume 236 that the result (e.g., A + B) has that type. */ 237#if _GL_HAS_BUILTIN_OVERFLOW_P 238# define _GL_ADD_OVERFLOW(a, b, min, max) \ 239 __builtin_add_overflow_p (a, b, (__typeof__ ((a) + (b))) 0) 240# define _GL_SUBTRACT_OVERFLOW(a, b, min, max) \ 241 __builtin_sub_overflow_p (a, b, (__typeof__ ((a) - (b))) 0) 242# define _GL_MULTIPLY_OVERFLOW(a, b, min, max) \ 243 __builtin_mul_overflow_p (a, b, (__typeof__ ((a) * (b))) 0) 244#else 245# define _GL_ADD_OVERFLOW(a, b, min, max) \ 246 ((min) < 0 ? INT_ADD_RANGE_OVERFLOW (a, b, min, max) \ 247 : (a) < 0 ? (b) <= (a) + (b) \ 248 : (b) < 0 ? (a) <= (a) + (b) \ 249 : (a) + (b) < (b)) 250# define _GL_SUBTRACT_OVERFLOW(a, b, min, max) \ 251 ((min) < 0 ? INT_SUBTRACT_RANGE_OVERFLOW (a, b, min, max) \ 252 : (a) < 0 ? 1 \ 253 : (b) < 0 ? (a) - (b) <= (a) \ 254 : (a) < (b)) 255# define _GL_MULTIPLY_OVERFLOW(a, b, min, max) \ 256 (((min) == 0 && (((a) < 0 && 0 < (b)) || ((b) < 0 && 0 < (a)))) \ 257 || INT_MULTIPLY_RANGE_OVERFLOW (a, b, min, max)) 258#endif 259#define _GL_DIVIDE_OVERFLOW(a, b, min, max) \ 260 ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max) \ 261 : (a) < 0 ? (b) <= (a) + (b) - 1 \ 262 : (b) < 0 && (a) + (b) <= (a)) 263#define _GL_REMAINDER_OVERFLOW(a, b, min, max) \ 264 ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max) \ 265 : (a) < 0 ? (a) % (b) != ((max) - (b) + 1) % (b) \ 266 : (b) < 0 && ! _GL_UNSIGNED_NEG_MULTIPLE (a, b, max)) 267 268/* Return a nonzero value if A is a mathematical multiple of B, where 269 A is unsigned, B is negative, and MAX is the maximum value of A's 270 type. A's type must be the same as (A % B)'s type. Normally (A % 271 -B == 0) suffices, but things get tricky if -B would overflow. */ 272#define _GL_UNSIGNED_NEG_MULTIPLE(a, b, max) \ 273 (((b) < -_GL_SIGNED_INT_MAXIMUM (b) \ 274 ? (_GL_SIGNED_INT_MAXIMUM (b) == (max) \ 275 ? (a) \ 276 : (a) % (_GL_INT_CONVERT (a, _GL_SIGNED_INT_MAXIMUM (b)) + 1)) \ 277 : (a) % - (b)) \ 278 == 0) 279 280/* Check for integer overflow, and report low order bits of answer. 281 282 The INT_<op>_OVERFLOW macros return 1 if the corresponding C operators 283 might not yield numerically correct answers due to arithmetic overflow. 284 The INT_<op>_WRAPV macros also store the low-order bits of the answer. 285 These macros work correctly on all known practical hosts, and do not rely 286 on undefined behavior due to signed arithmetic overflow. 287 288 Example usage, assuming A and B are long int: 289 290 if (INT_MULTIPLY_OVERFLOW (a, b)) 291 printf ("result would overflow\n"); 292 else 293 printf ("result is %ld (no overflow)\n", a * b); 294 295 Example usage with WRAPV flavor: 296 297 long int result; 298 bool overflow = INT_MULTIPLY_WRAPV (a, b, &result); 299 printf ("result is %ld (%s)\n", result, 300 overflow ? "after overflow" : "no overflow"); 301 302 Restrictions on these macros: 303 304 These macros do not check for all possible numerical problems or 305 undefined or unspecified behavior: they do not check for division 306 by zero, for bad shift counts, or for shifting negative numbers. 307 308 These macros may evaluate their arguments zero or multiple times, so the 309 arguments should not have side effects. 310 311 The WRAPV macros are not constant expressions. They support only 312 +, binary -, and *. The result type must be signed. 313 314 These macros are tuned for their last argument being a constant. 315 316 Return 1 if the integer expressions A * B, A - B, -A, A * B, A / B, 317 A % B, and A << B would overflow, respectively. */ 318 319#define INT_ADD_OVERFLOW(a, b) \ 320 _GL_BINARY_OP_OVERFLOW (a, b, _GL_ADD_OVERFLOW) 321#define INT_SUBTRACT_OVERFLOW(a, b) \ 322 _GL_BINARY_OP_OVERFLOW (a, b, _GL_SUBTRACT_OVERFLOW) 323#if _GL_HAS_BUILTIN_OVERFLOW_P 324# define INT_NEGATE_OVERFLOW(a) INT_SUBTRACT_OVERFLOW (0, a) 325#else 326# define INT_NEGATE_OVERFLOW(a) \ 327 INT_NEGATE_RANGE_OVERFLOW (a, _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a)) 328#endif 329#define INT_MULTIPLY_OVERFLOW(a, b) \ 330 _GL_BINARY_OP_OVERFLOW (a, b, _GL_MULTIPLY_OVERFLOW) 331#define INT_DIVIDE_OVERFLOW(a, b) \ 332 _GL_BINARY_OP_OVERFLOW (a, b, _GL_DIVIDE_OVERFLOW) 333#define INT_REMAINDER_OVERFLOW(a, b) \ 334 _GL_BINARY_OP_OVERFLOW (a, b, _GL_REMAINDER_OVERFLOW) 335#define INT_LEFT_SHIFT_OVERFLOW(a, b) \ 336 INT_LEFT_SHIFT_RANGE_OVERFLOW (a, b, \ 337 _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a)) 338 339/* Return 1 if the expression A <op> B would overflow, 340 where OP_RESULT_OVERFLOW (A, B, MIN, MAX) does the actual test, 341 assuming MIN and MAX are the minimum and maximum for the result type. 342 Arguments should be free of side effects. */ 343#define _GL_BINARY_OP_OVERFLOW(a, b, op_result_overflow) \ 344 op_result_overflow (a, b, \ 345 _GL_INT_MINIMUM (0 * (b) + (a)), \ 346 _GL_INT_MAXIMUM (0 * (b) + (a))) 347 348/* Store the low-order bits of A + B, A - B, A * B, respectively, into *R. 349 Return 1 if the result overflows. See above for restrictions. */ 350#define INT_ADD_WRAPV(a, b, r) \ 351 _GL_INT_OP_WRAPV (a, b, r, +, __builtin_add_overflow, INT_ADD_OVERFLOW) 352#define INT_SUBTRACT_WRAPV(a, b, r) \ 353 _GL_INT_OP_WRAPV (a, b, r, -, __builtin_sub_overflow, INT_SUBTRACT_OVERFLOW) 354#define INT_MULTIPLY_WRAPV(a, b, r) \ 355 _GL_INT_OP_WRAPV (a, b, r, *, __builtin_mul_overflow, INT_MULTIPLY_OVERFLOW) 356 357/* Nonzero if this compiler has GCC bug 68193 or Clang bug 25390. See: 358 https://gcc.gnu.org/bugzilla/show_bug.cgi?id=68193 359 https://llvm.org/bugs/show_bug.cgi?id=25390 360 For now, assume all versions of GCC-like compilers generate bogus 361 warnings for _Generic. This matters only for older compilers that 362 lack __builtin_add_overflow. */ 363#if __GNUC__ 364# define _GL__GENERIC_BOGUS 1 365#else 366# define _GL__GENERIC_BOGUS 0 367#endif 368 369/* Store the low-order bits of A <op> B into *R, where OP specifies 370 the operation. BUILTIN is the builtin operation, and OVERFLOW the 371 overflow predicate. Return 1 if the result overflows. See above 372 for restrictions. */ 373#if _GL_HAS_BUILTIN_OVERFLOW 374# define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) builtin (a, b, r) 375#elif 201112 <= __STDC_VERSION__ && !_GL__GENERIC_BOGUS 376# define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) \ 377 (_Generic \ 378 (*(r), \ 379 signed char: \ 380 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \ 381 signed char, SCHAR_MIN, SCHAR_MAX), \ 382 short int: \ 383 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \ 384 short int, SHRT_MIN, SHRT_MAX), \ 385 int: \ 386 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \ 387 int, INT_MIN, INT_MAX), \ 388 long int: \ 389 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \ 390 long int, LONG_MIN, LONG_MAX), \ 391 long long int: \ 392 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \ 393 long long int, LLONG_MIN, LLONG_MAX))) 394#else 395# define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) \ 396 (sizeof *(r) == sizeof (signed char) \ 397 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \ 398 signed char, SCHAR_MIN, SCHAR_MAX) \ 399 : sizeof *(r) == sizeof (short int) \ 400 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \ 401 short int, SHRT_MIN, SHRT_MAX) \ 402 : sizeof *(r) == sizeof (int) \ 403 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \ 404 int, INT_MIN, INT_MAX) \ 405 : _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow)) 406# ifdef LLONG_MAX 407# define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \ 408 (sizeof *(r) == sizeof (long int) \ 409 ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \ 410 long int, LONG_MIN, LONG_MAX) \ 411 : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \ 412 long long int, LLONG_MIN, LLONG_MAX)) 413# else 414# define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \ 415 _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \ 416 long int, LONG_MIN, LONG_MAX) 417# endif 418#endif 419 420/* Store the low-order bits of A <op> B into *R, where the operation 421 is given by OP. Use the unsigned type UT for calculation to avoid 422 overflow problems. *R's type is T, with extrema TMIN and TMAX. 423 T must be a signed integer type. Return 1 if the result overflows. */ 424#define _GL_INT_OP_CALC(a, b, r, op, overflow, ut, t, tmin, tmax) \ 425 (sizeof ((a) op (b)) < sizeof (t) \ 426 ? _GL_INT_OP_CALC1 ((t) (a), (t) (b), r, op, overflow, ut, t, tmin, tmax) \ 427 : _GL_INT_OP_CALC1 (a, b, r, op, overflow, ut, t, tmin, tmax)) 428#define _GL_INT_OP_CALC1(a, b, r, op, overflow, ut, t, tmin, tmax) \ 429 ((overflow (a, b) \ 430 || (EXPR_SIGNED ((a) op (b)) && ((a) op (b)) < (tmin)) \ 431 || (tmax) < ((a) op (b))) \ 432 ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 1) \ 433 : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 0)) 434 435/* Return the low-order bits of A <op> B, where the operation is given 436 by OP. Use the unsigned type UT for calculation to avoid undefined 437 behavior on signed integer overflow, and convert the result to type T. 438 UT is at least as wide as T and is no narrower than unsigned int, 439 T is two's complement, and there is no padding or trap representations. 440 Assume that converting UT to T yields the low-order bits, as is 441 done in all known two's-complement C compilers. E.g., see: 442 https://gcc.gnu.org/onlinedocs/gcc/Integers-implementation.html 443 444 According to the C standard, converting UT to T yields an 445 implementation-defined result or signal for values outside T's 446 range. However, code that works around this theoretical problem 447 runs afoul of a compiler bug in Oracle Studio 12.3 x86. See: 448 https://lists.gnu.org/r/bug-gnulib/2017-04/msg00049.html 449 As the compiler bug is real, don't try to work around the 450 theoretical problem. */ 451 452#define _GL_INT_OP_WRAPV_VIA_UNSIGNED(a, b, op, ut, t) \ 453 ((t) ((ut) (a) op (ut) (b))) 454 455#endif /* _GL_INTPROPS_H */ 456