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-/* intprops.h -- properties of integer types
-
- Copyright (C) 2001-2018 Free Software Foundation, Inc.
-
- This program is free software: you can redistribute it and/or modify it
- under the terms of the GNU General Public License as published
- by the Free Software Foundation; either version 3 of the License, or
- (at your option) any later version.
-
- This program is distributed in the hope that it will be useful,
- but WITHOUT ANY WARRANTY; without even the implied warranty of
- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- GNU General Public License for more details.
-
- You should have received a copy of the GNU General Public License
- along with this program. If not, see <https://www.gnu.org/licenses/>. */
-
-/* Written by Paul Eggert. */
-
-#ifndef _GL_INTPROPS_H
-#define _GL_INTPROPS_H
-
-#include <limits.h>
-
-/* Return a value with the common real type of E and V and the value of V. */
-#define _GL_INT_CONVERT(e, v) (0 * (e) + (v))
-
-/* Act like _GL_INT_CONVERT (E, -V) but work around a bug in IRIX 6.5 cc; see
- <https://lists.gnu.org/r/bug-gnulib/2011-05/msg00406.html>. */
-#define _GL_INT_NEGATE_CONVERT(e, v) (0 * (e) - (v))
-
-/* The extra casts in the following macros work around compiler bugs,
- e.g., in Cray C 5.0.3.0. */
-
-/* True if the arithmetic type T is an integer type. bool counts as
- an integer. */
-#define TYPE_IS_INTEGER(t) ((t) 1.5 == 1)
-
-/* True if the real type T is signed. */
-#define TYPE_SIGNED(t) (! ((t) 0 < (t) -1))
-
-/* Return 1 if the real expression E, after promotion, has a
- signed or floating type. */
-#define EXPR_SIGNED(e) (_GL_INT_NEGATE_CONVERT (e, 1) < 0)
-
-
-/* Minimum and maximum values for integer types and expressions. */
-
-/* The width in bits of the integer type or expression T.
- Padding bits are not supported; this is checked at compile-time below. */
-#define TYPE_WIDTH(t) (sizeof (t) * CHAR_BIT)
-
-/* The maximum and minimum values for the integer type T. */
-#define TYPE_MINIMUM(t) ((t) ~ TYPE_MAXIMUM (t))
-#define TYPE_MAXIMUM(t) \
- ((t) (! TYPE_SIGNED (t) \
- ? (t) -1 \
- : ((((t) 1 << (TYPE_WIDTH (t) - 2)) - 1) * 2 + 1)))
-
-/* The maximum and minimum values for the type of the expression E,
- after integer promotion. E should not have side effects. */
-#define _GL_INT_MINIMUM(e) \
- (EXPR_SIGNED (e) \
- ? ~ _GL_SIGNED_INT_MAXIMUM (e) \
- : _GL_INT_CONVERT (e, 0))
-#define _GL_INT_MAXIMUM(e) \
- (EXPR_SIGNED (e) \
- ? _GL_SIGNED_INT_MAXIMUM (e) \
- : _GL_INT_NEGATE_CONVERT (e, 1))
-#define _GL_SIGNED_INT_MAXIMUM(e) \
- (((_GL_INT_CONVERT (e, 1) << (TYPE_WIDTH ((e) + 0) - 2)) - 1) * 2 + 1)
-
-/* Work around OpenVMS incompatibility with C99. */
-#if !defined LLONG_MAX && defined __INT64_MAX
-# define LLONG_MAX __INT64_MAX
-# define LLONG_MIN __INT64_MIN
-#endif
-
-/* This include file assumes that signed types are two's complement without
- padding bits; the above macros have undefined behavior otherwise.
- If this is a problem for you, please let us know how to fix it for your host.
- This assumption is tested by the intprops-tests module. */
-
-/* Does the __typeof__ keyword work? This could be done by
- 'configure', but for now it's easier to do it by hand. */
-#if (2 <= __GNUC__ \
- || (1210 <= __IBMC__ && defined __IBM__TYPEOF__) \
- || (0x5110 <= __SUNPRO_C && !__STDC__))
-# define _GL_HAVE___TYPEOF__ 1
-#else
-# define _GL_HAVE___TYPEOF__ 0
-#endif
-
-/* Return 1 if the integer type or expression T might be signed. Return 0
- if it is definitely unsigned. This macro does not evaluate its argument,
- and expands to an integer constant expression. */
-#if _GL_HAVE___TYPEOF__
-# define _GL_SIGNED_TYPE_OR_EXPR(t) TYPE_SIGNED (__typeof__ (t))
-#else
-# define _GL_SIGNED_TYPE_OR_EXPR(t) 1
-#endif
-
-/* Bound on length of the string representing an unsigned integer
- value representable in B bits. log10 (2.0) < 146/485. The
- smallest value of B where this bound is not tight is 2621. */
-#define INT_BITS_STRLEN_BOUND(b) (((b) * 146 + 484) / 485)
-
-/* Bound on length of the string representing an integer type or expression T.
- Subtract 1 for the sign bit if T is signed, and then add 1 more for
- a minus sign if needed.
-
- Because _GL_SIGNED_TYPE_OR_EXPR sometimes returns 0 when its argument is
- signed, this macro may overestimate the true bound by one byte when
- applied to unsigned types of size 2, 4, 16, ... bytes. */
-#define INT_STRLEN_BOUND(t) \
- (INT_BITS_STRLEN_BOUND (TYPE_WIDTH (t) - _GL_SIGNED_TYPE_OR_EXPR (t)) \
- + _GL_SIGNED_TYPE_OR_EXPR (t))
-
-/* Bound on buffer size needed to represent an integer type or expression T,
- including the terminating null. */
-#define INT_BUFSIZE_BOUND(t) (INT_STRLEN_BOUND (t) + 1)
-
-
-/* Range overflow checks.
-
- The INT_<op>_RANGE_OVERFLOW macros return 1 if the corresponding C
- operators might not yield numerically correct answers due to
- arithmetic overflow. They do not rely on undefined or
- implementation-defined behavior. Their implementations are simple
- and straightforward, but they are a bit harder to use than the
- INT_<op>_OVERFLOW macros described below.
-
- Example usage:
-
- long int i = ...;
- long int j = ...;
- if (INT_MULTIPLY_RANGE_OVERFLOW (i, j, LONG_MIN, LONG_MAX))
- printf ("multiply would overflow");
- else
- printf ("product is %ld", i * j);
-
- Restrictions on *_RANGE_OVERFLOW macros:
-
- These macros do not check for all possible numerical problems or
- undefined or unspecified behavior: they do not check for division
- by zero, for bad shift counts, or for shifting negative numbers.
-
- These macros may evaluate their arguments zero or multiple times,
- so the arguments should not have side effects. The arithmetic
- arguments (including the MIN and MAX arguments) must be of the same
- integer type after the usual arithmetic conversions, and the type
- must have minimum value MIN and maximum MAX. Unsigned types should
- use a zero MIN of the proper type.
-
- These macros are tuned for constant MIN and MAX. For commutative
- operations such as A + B, they are also tuned for constant B. */
-
-/* Return 1 if A + B would overflow in [MIN,MAX] arithmetic.
- See above for restrictions. */
-#define INT_ADD_RANGE_OVERFLOW(a, b, min, max) \
- ((b) < 0 \
- ? (a) < (min) - (b) \
- : (max) - (b) < (a))
-
-/* Return 1 if A - B would overflow in [MIN,MAX] arithmetic.
- See above for restrictions. */
-#define INT_SUBTRACT_RANGE_OVERFLOW(a, b, min, max) \
- ((b) < 0 \
- ? (max) + (b) < (a) \
- : (a) < (min) + (b))
-
-/* Return 1 if - A would overflow in [MIN,MAX] arithmetic.
- See above for restrictions. */
-#define INT_NEGATE_RANGE_OVERFLOW(a, min, max) \
- ((min) < 0 \
- ? (a) < - (max) \
- : 0 < (a))
-
-/* Return 1 if A * B would overflow in [MIN,MAX] arithmetic.
- See above for restrictions. Avoid && and || as they tickle
- bugs in Sun C 5.11 2010/08/13 and other compilers; see
- <https://lists.gnu.org/r/bug-gnulib/2011-05/msg00401.html>. */
-#define INT_MULTIPLY_RANGE_OVERFLOW(a, b, min, max) \
- ((b) < 0 \
- ? ((a) < 0 \
- ? (a) < (max) / (b) \
- : (b) == -1 \
- ? 0 \
- : (min) / (b) < (a)) \
- : (b) == 0 \
- ? 0 \
- : ((a) < 0 \
- ? (a) < (min) / (b) \
- : (max) / (b) < (a)))
-
-/* Return 1 if A / B would overflow in [MIN,MAX] arithmetic.
- See above for restrictions. Do not check for division by zero. */
-#define INT_DIVIDE_RANGE_OVERFLOW(a, b, min, max) \
- ((min) < 0 && (b) == -1 && (a) < - (max))
-
-/* Return 1 if A % B would overflow in [MIN,MAX] arithmetic.
- See above for restrictions. Do not check for division by zero.
- Mathematically, % should never overflow, but on x86-like hosts
- INT_MIN % -1 traps, and the C standard permits this, so treat this
- as an overflow too. */
-#define INT_REMAINDER_RANGE_OVERFLOW(a, b, min, max) \
- INT_DIVIDE_RANGE_OVERFLOW (a, b, min, max)
-
-/* Return 1 if A << B would overflow in [MIN,MAX] arithmetic.
- See above for restrictions. Here, MIN and MAX are for A only, and B need
- not be of the same type as the other arguments. The C standard says that
- behavior is undefined for shifts unless 0 <= B < wordwidth, and that when
- A is negative then A << B has undefined behavior and A >> B has
- implementation-defined behavior, but do not check these other
- restrictions. */
-#define INT_LEFT_SHIFT_RANGE_OVERFLOW(a, b, min, max) \
- ((a) < 0 \
- ? (a) < (min) >> (b) \
- : (max) >> (b) < (a))
-
-/* True if __builtin_add_overflow (A, B, P) works when P is non-null. */
-#if 5 <= __GNUC__ && !defined __ICC
-# define _GL_HAS_BUILTIN_OVERFLOW 1
-#else
-# define _GL_HAS_BUILTIN_OVERFLOW 0
-#endif
-
-/* True if __builtin_add_overflow_p (A, B, C) works. */
-#define _GL_HAS_BUILTIN_OVERFLOW_P (7 <= __GNUC__)
-
-/* The _GL*_OVERFLOW macros have the same restrictions as the
- *_RANGE_OVERFLOW macros, except that they do not assume that operands
- (e.g., A and B) have the same type as MIN and MAX. Instead, they assume
- that the result (e.g., A + B) has that type. */
-#if _GL_HAS_BUILTIN_OVERFLOW_P
-# define _GL_ADD_OVERFLOW(a, b, min, max) \
- __builtin_add_overflow_p (a, b, (__typeof__ ((a) + (b))) 0)
-# define _GL_SUBTRACT_OVERFLOW(a, b, min, max) \
- __builtin_sub_overflow_p (a, b, (__typeof__ ((a) - (b))) 0)
-# define _GL_MULTIPLY_OVERFLOW(a, b, min, max) \
- __builtin_mul_overflow_p (a, b, (__typeof__ ((a) * (b))) 0)
-#else
-# define _GL_ADD_OVERFLOW(a, b, min, max) \
- ((min) < 0 ? INT_ADD_RANGE_OVERFLOW (a, b, min, max) \
- : (a) < 0 ? (b) <= (a) + (b) \
- : (b) < 0 ? (a) <= (a) + (b) \
- : (a) + (b) < (b))
-# define _GL_SUBTRACT_OVERFLOW(a, b, min, max) \
- ((min) < 0 ? INT_SUBTRACT_RANGE_OVERFLOW (a, b, min, max) \
- : (a) < 0 ? 1 \
- : (b) < 0 ? (a) - (b) <= (a) \
- : (a) < (b))
-# define _GL_MULTIPLY_OVERFLOW(a, b, min, max) \
- (((min) == 0 && (((a) < 0 && 0 < (b)) || ((b) < 0 && 0 < (a)))) \
- || INT_MULTIPLY_RANGE_OVERFLOW (a, b, min, max))
-#endif
-#define _GL_DIVIDE_OVERFLOW(a, b, min, max) \
- ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max) \
- : (a) < 0 ? (b) <= (a) + (b) - 1 \
- : (b) < 0 && (a) + (b) <= (a))
-#define _GL_REMAINDER_OVERFLOW(a, b, min, max) \
- ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max) \
- : (a) < 0 ? (a) % (b) != ((max) - (b) + 1) % (b) \
- : (b) < 0 && ! _GL_UNSIGNED_NEG_MULTIPLE (a, b, max))
-
-/* Return a nonzero value if A is a mathematical multiple of B, where
- A is unsigned, B is negative, and MAX is the maximum value of A's
- type. A's type must be the same as (A % B)'s type. Normally (A %
- -B == 0) suffices, but things get tricky if -B would overflow. */
-#define _GL_UNSIGNED_NEG_MULTIPLE(a, b, max) \
- (((b) < -_GL_SIGNED_INT_MAXIMUM (b) \
- ? (_GL_SIGNED_INT_MAXIMUM (b) == (max) \
- ? (a) \
- : (a) % (_GL_INT_CONVERT (a, _GL_SIGNED_INT_MAXIMUM (b)) + 1)) \
- : (a) % - (b)) \
- == 0)
-
-/* Check for integer overflow, and report low order bits of answer.
-
- The INT_<op>_OVERFLOW macros return 1 if the corresponding C operators
- might not yield numerically correct answers due to arithmetic overflow.
- The INT_<op>_WRAPV macros also store the low-order bits of the answer.
- These macros work correctly on all known practical hosts, and do not rely
- on undefined behavior due to signed arithmetic overflow.
-
- Example usage, assuming A and B are long int:
-
- if (INT_MULTIPLY_OVERFLOW (a, b))
- printf ("result would overflow\n");
- else
- printf ("result is %ld (no overflow)\n", a * b);
-
- Example usage with WRAPV flavor:
-
- long int result;
- bool overflow = INT_MULTIPLY_WRAPV (a, b, &result);
- printf ("result is %ld (%s)\n", result,
- overflow ? "after overflow" : "no overflow");
-
- Restrictions on these macros:
-
- These macros do not check for all possible numerical problems or
- undefined or unspecified behavior: they do not check for division
- by zero, for bad shift counts, or for shifting negative numbers.
-
- These macros may evaluate their arguments zero or multiple times, so the
- arguments should not have side effects.
-
- The WRAPV macros are not constant expressions. They support only
- +, binary -, and *. The result type must be signed.
-
- These macros are tuned for their last argument being a constant.
-
- Return 1 if the integer expressions A * B, A - B, -A, A * B, A / B,
- A % B, and A << B would overflow, respectively. */
-
-#define INT_ADD_OVERFLOW(a, b) \
- _GL_BINARY_OP_OVERFLOW (a, b, _GL_ADD_OVERFLOW)
-#define INT_SUBTRACT_OVERFLOW(a, b) \
- _GL_BINARY_OP_OVERFLOW (a, b, _GL_SUBTRACT_OVERFLOW)
-#if _GL_HAS_BUILTIN_OVERFLOW_P
-# define INT_NEGATE_OVERFLOW(a) INT_SUBTRACT_OVERFLOW (0, a)
-#else
-# define INT_NEGATE_OVERFLOW(a) \
- INT_NEGATE_RANGE_OVERFLOW (a, _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
-#endif
-#define INT_MULTIPLY_OVERFLOW(a, b) \
- _GL_BINARY_OP_OVERFLOW (a, b, _GL_MULTIPLY_OVERFLOW)
-#define INT_DIVIDE_OVERFLOW(a, b) \
- _GL_BINARY_OP_OVERFLOW (a, b, _GL_DIVIDE_OVERFLOW)
-#define INT_REMAINDER_OVERFLOW(a, b) \
- _GL_BINARY_OP_OVERFLOW (a, b, _GL_REMAINDER_OVERFLOW)
-#define INT_LEFT_SHIFT_OVERFLOW(a, b) \
- INT_LEFT_SHIFT_RANGE_OVERFLOW (a, b, \
- _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
-
-/* Return 1 if the expression A <op> B would overflow,
- where OP_RESULT_OVERFLOW (A, B, MIN, MAX) does the actual test,
- assuming MIN and MAX are the minimum and maximum for the result type.
- Arguments should be free of side effects. */
-#define _GL_BINARY_OP_OVERFLOW(a, b, op_result_overflow) \
- op_result_overflow (a, b, \
- _GL_INT_MINIMUM (0 * (b) + (a)), \
- _GL_INT_MAXIMUM (0 * (b) + (a)))
-
-/* Store the low-order bits of A + B, A - B, A * B, respectively, into *R.
- Return 1 if the result overflows. See above for restrictions. */
-#define INT_ADD_WRAPV(a, b, r) \
- _GL_INT_OP_WRAPV (a, b, r, +, __builtin_add_overflow, INT_ADD_OVERFLOW)
-#define INT_SUBTRACT_WRAPV(a, b, r) \
- _GL_INT_OP_WRAPV (a, b, r, -, __builtin_sub_overflow, INT_SUBTRACT_OVERFLOW)
-#define INT_MULTIPLY_WRAPV(a, b, r) \
- _GL_INT_OP_WRAPV (a, b, r, *, __builtin_mul_overflow, INT_MULTIPLY_OVERFLOW)
-
-/* Nonzero if this compiler has GCC bug 68193 or Clang bug 25390. See:
- https://gcc.gnu.org/bugzilla/show_bug.cgi?id=68193
- https://llvm.org/bugs/show_bug.cgi?id=25390
- For now, assume all versions of GCC-like compilers generate bogus
- warnings for _Generic. This matters only for older compilers that
- lack __builtin_add_overflow. */
-#if __GNUC__
-# define _GL__GENERIC_BOGUS 1
-#else
-# define _GL__GENERIC_BOGUS 0
-#endif
-
-/* Store the low-order bits of A <op> B into *R, where OP specifies
- the operation. BUILTIN is the builtin operation, and OVERFLOW the
- overflow predicate. Return 1 if the result overflows. See above
- for restrictions. */
-#if _GL_HAS_BUILTIN_OVERFLOW
-# define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) builtin (a, b, r)
-#elif 201112 <= __STDC_VERSION__ && !_GL__GENERIC_BOGUS
-# define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) \
- (_Generic \
- (*(r), \
- signed char: \
- _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
- signed char, SCHAR_MIN, SCHAR_MAX), \
- short int: \
- _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
- short int, SHRT_MIN, SHRT_MAX), \
- int: \
- _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
- int, INT_MIN, INT_MAX), \
- long int: \
- _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
- long int, LONG_MIN, LONG_MAX), \
- long long int: \
- _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
- long long int, LLONG_MIN, LLONG_MAX)))
-#else
-# define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) \
- (sizeof *(r) == sizeof (signed char) \
- ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
- signed char, SCHAR_MIN, SCHAR_MAX) \
- : sizeof *(r) == sizeof (short int) \
- ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
- short int, SHRT_MIN, SHRT_MAX) \
- : sizeof *(r) == sizeof (int) \
- ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
- int, INT_MIN, INT_MAX) \
- : _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow))
-# ifdef LLONG_MAX
-# define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
- (sizeof *(r) == sizeof (long int) \
- ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
- long int, LONG_MIN, LONG_MAX) \
- : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
- long long int, LLONG_MIN, LLONG_MAX))
-# else
-# define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
- _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
- long int, LONG_MIN, LONG_MAX)
-# endif
-#endif
-
-/* Store the low-order bits of A <op> B into *R, where the operation
- is given by OP. Use the unsigned type UT for calculation to avoid
- overflow problems. *R's type is T, with extrema TMIN and TMAX.
- T must be a signed integer type. Return 1 if the result overflows. */
-#define _GL_INT_OP_CALC(a, b, r, op, overflow, ut, t, tmin, tmax) \
- (sizeof ((a) op (b)) < sizeof (t) \
- ? _GL_INT_OP_CALC1 ((t) (a), (t) (b), r, op, overflow, ut, t, tmin, tmax) \
- : _GL_INT_OP_CALC1 (a, b, r, op, overflow, ut, t, tmin, tmax))
-#define _GL_INT_OP_CALC1(a, b, r, op, overflow, ut, t, tmin, tmax) \
- ((overflow (a, b) \
- || (EXPR_SIGNED ((a) op (b)) && ((a) op (b)) < (tmin)) \
- || (tmax) < ((a) op (b))) \
- ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 1) \
- : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 0))
-
-/* Return the low-order bits of A <op> B, where the operation is given
- by OP. Use the unsigned type UT for calculation to avoid undefined
- behavior on signed integer overflow, and convert the result to type T.
- UT is at least as wide as T and is no narrower than unsigned int,
- T is two's complement, and there is no padding or trap representations.
- Assume that converting UT to T yields the low-order bits, as is
- done in all known two's-complement C compilers. E.g., see:
- https://gcc.gnu.org/onlinedocs/gcc/Integers-implementation.html
-
- According to the C standard, converting UT to T yields an
- implementation-defined result or signal for values outside T's
- range. However, code that works around this theoretical problem
- runs afoul of a compiler bug in Oracle Studio 12.3 x86. See:
- https://lists.gnu.org/r/bug-gnulib/2017-04/msg00049.html
- As the compiler bug is real, don't try to work around the
- theoretical problem. */
-
-#define _GL_INT_OP_WRAPV_VIA_UNSIGNED(a, b, op, ut, t) \
- ((t) ((ut) (a) op (ut) (b)))
-
-#endif /* _GL_INTPROPS_H */