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diff --git a/lib/intprops.h b/lib/intprops.h new file mode 100644 index 0000000..44b5e60 --- /dev/null +++ b/lib/intprops.h @@ -0,0 +1,335 @@ +/* intprops.h -- properties of integer types + + Copyright (C) 2001-2023 Free Software Foundation, Inc. + + This program is free software: you can redistribute it and/or modify it + under the terms of the GNU Lesser General Public License as published + by the Free Software Foundation; either version 2.1 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 Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public License + along with this program. If not, see <https://www.gnu.org/licenses/>. */ + +#ifndef _GL_INTPROPS_H +#define _GL_INTPROPS_H + +#include "intprops-internal.h" + +/* 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) _GL_TYPE_SIGNED (t) + +/* Return 1 if the real expression E, after promotion, has a + signed or floating type. Do not evaluate E. */ +#define EXPR_SIGNED(e) _GL_EXPR_SIGNED (e) + + +/* Minimum and maximum values for integer types and expressions. */ + +/* The width in bits of the integer type or expression T. + Do not evaluate T. T must not be a bit-field expression. + Padding bits are not supported; this is checked at compile-time below. */ +#define TYPE_WIDTH(t) _GL_TYPE_WIDTH (t) + +/* 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))) + +/* 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. + T must not be a bit-field expression. + + 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 1 when its argument is + unsigned, 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. T must not be a bit-field expression. */ +#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 overflow arithmetically when given the same arguments. + These macros do not rely on undefined or implementation-defined behavior. + Although their implementations are simple and straightforward, + they are harder to use and may be less efficient than the + INT_<op>_WRAPV, INT_<op>_OK, and 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. + + Because all arguments are subject to integer promotions, these + macros typically do not work on types narrower than 'int'. + + 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) \ + _GL_INT_NEGATE_RANGE_OVERFLOW (a, min, max) + +/* 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)) + +/* 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 compute the low-order bits of the sum, + difference, and product of two C integers, and return 1 if these + low-order bits are not numerically correct. + 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 *. + + Because the WRAPV macros convert the result, they report overflow + in different circumstances than the OVERFLOW macros do. For + example, in the typical case with 16-bit 'short' and 32-bit 'int', + if A, B and *R are all of type 'short' then INT_ADD_OVERFLOW (A, B) + returns false because the addition cannot overflow after A and B + are converted to 'int', whereas INT_ADD_WRAPV (A, B, R) returns + true or false depending on whether the sum fits into 'short'. + + These macros are tuned for their last input argument being a constant. + + A, B, and *R should be integers; they need not be the same type, + and they need not be all signed or all unsigned. + However, none of the integer types should be bit-precise, + and *R's type should not be char, bool, or an enumeration type. + + 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) _GL_INT_NEGATE_OVERFLOW (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 (_GL_INT_CONVERT (a, b)), \ + _GL_INT_MAXIMUM (_GL_INT_CONVERT (a, b))) + +/* 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_ADD_WRAPV (a, b, r) +#define INT_SUBTRACT_WRAPV(a, b, r) _GL_INT_SUBTRACT_WRAPV (a, b, r) +#define INT_MULTIPLY_WRAPV(a, b, r) _GL_INT_MULTIPLY_WRAPV (a, b, r) + +/* The following macros compute A + B, A - B, and A * B, respectively. + If no overflow occurs, they set *R to the result and return 1; + otherwise, they return 0 and may modify *R. + + Example usage: + + long int result; + if (INT_ADD_OK (a, b, &result)) + printf ("result is %ld\n", result); + else + printf ("overflow\n"); + + A, B, and *R should be integers; they need not be the same type, + and they need not be all signed or all unsigned. + However, none of the integer types should be bit-precise, + and *R's type should not be char, bool, or an enumeration type. + + These macros work correctly on all known practical hosts, and do not rely + on undefined behavior due to signed arithmetic overflow. + + These macros are not constant expressions. + + These macros may evaluate their arguments zero or multiple times, so the + arguments should not have side effects. + + These macros are tuned for B being a constant. */ + +#define INT_ADD_OK(a, b, r) (! INT_ADD_WRAPV (a, b, r)) +#define INT_SUBTRACT_OK(a, b, r) (! INT_SUBTRACT_WRAPV (a, b, r)) +#define INT_MULTIPLY_OK(a, b, r) (! INT_MULTIPLY_WRAPV (a, b, r)) + +#endif /* _GL_INTPROPS_H */ |