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Diffstat (limited to 'lib/intprops.h')
| -rw-r--r-- | lib/intprops.h | 428 |
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diff --git a/lib/intprops.h b/lib/intprops.h new file mode 100644 index 0000000..3152139 --- /dev/null +++ b/lib/intprops.h @@ -0,0 +1,428 @@ +/* intprops.h -- properties of integer types + + Copyright (C) 2001-2016 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 <http://www.gnu.org/licenses/>. */ + +/* Written by Paul Eggert. */ + +#ifndef _GL_INTPROPS_H +#define _GL_INTPROPS_H + +#include <limits.h> +#include <verify.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 + <http://lists.gnu.org/archive/html/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 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 << (sizeof (t) * CHAR_BIT - 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) << (sizeof ((e) + 0) * CHAR_BIT - 2)) - 1) * 2 + 1) + +/* 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. + As a sanity check, test the assumption for some signed types that + <limits.h> bounds. */ +verify (TYPE_MINIMUM (signed char) == SCHAR_MIN); +verify (TYPE_MAXIMUM (signed char) == SCHAR_MAX); +verify (TYPE_MINIMUM (short int) == SHRT_MIN); +verify (TYPE_MAXIMUM (short int) == SHRT_MAX); +verify (TYPE_MINIMUM (int) == INT_MIN); +verify (TYPE_MAXIMUM (int) == INT_MAX); +verify (TYPE_MINIMUM (long int) == LONG_MIN); +verify (TYPE_MAXIMUM (long int) == LONG_MAX); +#ifdef LLONG_MAX +verify (TYPE_MINIMUM (long long int) == LLONG_MIN); +verify (TYPE_MAXIMUM (long long int) == LLONG_MAX); +#endif + +/* 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__ || 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 (sizeof (t) * CHAR_BIT \ + - _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 + <http://lists.gnu.org/archive/html/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)) + + +/* 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. */ +#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)) +#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) +#define INT_NEGATE_OVERFLOW(a) \ + INT_NEGATE_RANGE_OVERFLOW (a, _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a)) +#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))) + +/* Compute A + B, A - B, A * B, respectively, storing the result 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) + +#ifndef __has_builtin +# define __has_builtin(x) 0 +#endif + +/* 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 A <op> B into *R, where OP specifies the operation. + BUILTIN is the builtin operation, and OVERFLOW the overflow predicate. + See above for restrictions. */ +#if 5 <= __GNUC__ || __has_builtin (__builtin_add_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 char, \ + signed char, SCHAR_MIN, SCHAR_MAX), \ + short int: \ + _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned short 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 char, \ + signed char, SCHAR_MIN, SCHAR_MAX) \ + : sizeof *(r) == sizeof (short int) \ + ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned short 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 extremal values TMIN and + TMAX. T must be a signed integer type. */ +#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, tmin, tmax), 1) \ + : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t, tmin, tmax), 0)) + +/* Return A <op> B, where the operation is given by OP. Use the + unsigned type UT for calculation to avoid overflow problems. + Convert the result to type T without overflow by subtracting TMIN + from large values before converting, and adding it afterwards. + Compilers can optimize all the operations except OP. */ +#define _GL_INT_OP_WRAPV_VIA_UNSIGNED(a, b, op, ut, t, tmin, tmax) \ + (((ut) (a) op (ut) (b)) <= (tmax) \ + ? (t) ((ut) (a) op (ut) (b)) \ + : ((t) (((ut) (a) op (ut) (b)) - (tmin)) + (tmin))) + +#endif /* _GL_INTPROPS_H */ |