335 lines
15 KiB
C
335 lines
15 KiB
C
/* intprops.h -- properties of integer types
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Copyright (C) 2001-2023 Free Software Foundation, Inc.
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This program is free software: you can redistribute it and/or modify it
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under the terms of the GNU Lesser General Public License as published
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by the Free Software Foundation; either version 2.1 of the License, or
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(at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public License
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along with this program. If not, see <https://www.gnu.org/licenses/>. */
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#ifndef _GL_INTPROPS_H
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#define _GL_INTPROPS_H
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#include "intprops-internal.h"
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/* The extra casts in the following macros work around compiler bugs,
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e.g., in Cray C 5.0.3.0. */
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/* True if the arithmetic type T is an integer type. bool counts as
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an integer. */
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#define TYPE_IS_INTEGER(t) ((t) 1.5 == 1)
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/* True if the real type T is signed. */
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#define TYPE_SIGNED(t) _GL_TYPE_SIGNED (t)
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/* Return 1 if the real expression E, after promotion, has a
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signed or floating type. Do not evaluate E. */
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#define EXPR_SIGNED(e) _GL_EXPR_SIGNED (e)
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/* Minimum and maximum values for integer types and expressions. */
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/* The width in bits of the integer type or expression T.
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Do not evaluate T. T must not be a bit-field expression.
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Padding bits are not supported; this is checked at compile-time below. */
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#define TYPE_WIDTH(t) _GL_TYPE_WIDTH (t)
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/* The maximum and minimum values for the integer type T. */
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#define TYPE_MINIMUM(t) ((t) ~ TYPE_MAXIMUM (t))
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#define TYPE_MAXIMUM(t) \
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((t) (! TYPE_SIGNED (t) \
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? (t) -1 \
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: ((((t) 1 << (TYPE_WIDTH (t) - 2)) - 1) * 2 + 1)))
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/* Bound on length of the string representing an unsigned integer
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value representable in B bits. log10 (2.0) < 146/485. The
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smallest value of B where this bound is not tight is 2621. */
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#define INT_BITS_STRLEN_BOUND(b) (((b) * 146 + 484) / 485)
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/* Bound on length of the string representing an integer type or expression T.
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T must not be a bit-field expression.
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Subtract 1 for the sign bit if T is signed, and then add 1 more for
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a minus sign if needed.
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Because _GL_SIGNED_TYPE_OR_EXPR sometimes returns 1 when its argument is
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unsigned, this macro may overestimate the true bound by one byte when
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applied to unsigned types of size 2, 4, 16, ... bytes. */
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#define INT_STRLEN_BOUND(t) \
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(INT_BITS_STRLEN_BOUND (TYPE_WIDTH (t) - _GL_SIGNED_TYPE_OR_EXPR (t)) \
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+ _GL_SIGNED_TYPE_OR_EXPR (t))
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/* Bound on buffer size needed to represent an integer type or expression T,
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including the terminating null. T must not be a bit-field expression. */
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#define INT_BUFSIZE_BOUND(t) (INT_STRLEN_BOUND (t) + 1)
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/* Range overflow checks.
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The INT_<op>_RANGE_OVERFLOW macros return 1 if the corresponding C
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operators overflow arithmetically when given the same arguments.
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These macros do not rely on undefined or implementation-defined behavior.
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Although their implementations are simple and straightforward,
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they are harder to use and may be less efficient than the
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INT_<op>_WRAPV, INT_<op>_OK, and INT_<op>_OVERFLOW macros described below.
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Example usage:
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long int i = ...;
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long int j = ...;
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if (INT_MULTIPLY_RANGE_OVERFLOW (i, j, LONG_MIN, LONG_MAX))
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printf ("multiply would overflow");
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else
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printf ("product is %ld", i * j);
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Restrictions on *_RANGE_OVERFLOW macros:
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These macros do not check for all possible numerical problems or
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undefined or unspecified behavior: they do not check for division
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by zero, for bad shift counts, or for shifting negative numbers.
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These macros may evaluate their arguments zero or multiple times,
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so the arguments should not have side effects. The arithmetic
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arguments (including the MIN and MAX arguments) must be of the same
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integer type after the usual arithmetic conversions, and the type
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must have minimum value MIN and maximum MAX. Unsigned types should
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use a zero MIN of the proper type.
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Because all arguments are subject to integer promotions, these
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macros typically do not work on types narrower than 'int'.
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These macros are tuned for constant MIN and MAX. For commutative
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operations such as A + B, they are also tuned for constant B. */
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/* Return 1 if A + B would overflow in [MIN,MAX] arithmetic.
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See above for restrictions. */
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#define INT_ADD_RANGE_OVERFLOW(a, b, min, max) \
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((b) < 0 \
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? (a) < (min) - (b) \
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: (max) - (b) < (a))
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/* Return 1 if A - B would overflow in [MIN,MAX] arithmetic.
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See above for restrictions. */
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#define INT_SUBTRACT_RANGE_OVERFLOW(a, b, min, max) \
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((b) < 0 \
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? (max) + (b) < (a) \
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: (a) < (min) + (b))
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/* Return 1 if - A would overflow in [MIN,MAX] arithmetic.
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See above for restrictions. */
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#define INT_NEGATE_RANGE_OVERFLOW(a, min, max) \
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_GL_INT_NEGATE_RANGE_OVERFLOW (a, min, max)
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/* Return 1 if A * B would overflow in [MIN,MAX] arithmetic.
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See above for restrictions. Avoid && and || as they tickle
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bugs in Sun C 5.11 2010/08/13 and other compilers; see
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<https://lists.gnu.org/r/bug-gnulib/2011-05/msg00401.html>. */
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#define INT_MULTIPLY_RANGE_OVERFLOW(a, b, min, max) \
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((b) < 0 \
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? ((a) < 0 \
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? (a) < (max) / (b) \
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: (b) == -1 \
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? 0 \
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: (min) / (b) < (a)) \
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: (b) == 0 \
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? 0 \
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: ((a) < 0 \
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? (a) < (min) / (b) \
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: (max) / (b) < (a)))
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/* Return 1 if A / B would overflow in [MIN,MAX] arithmetic.
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See above for restrictions. Do not check for division by zero. */
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#define INT_DIVIDE_RANGE_OVERFLOW(a, b, min, max) \
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((min) < 0 && (b) == -1 && (a) < - (max))
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/* Return 1 if A % B would overflow in [MIN,MAX] arithmetic.
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See above for restrictions. Do not check for division by zero.
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Mathematically, % should never overflow, but on x86-like hosts
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INT_MIN % -1 traps, and the C standard permits this, so treat this
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as an overflow too. */
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#define INT_REMAINDER_RANGE_OVERFLOW(a, b, min, max) \
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INT_DIVIDE_RANGE_OVERFLOW (a, b, min, max)
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/* Return 1 if A << B would overflow in [MIN,MAX] arithmetic.
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See above for restrictions. Here, MIN and MAX are for A only, and B need
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not be of the same type as the other arguments. The C standard says that
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behavior is undefined for shifts unless 0 <= B < wordwidth, and that when
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A is negative then A << B has undefined behavior and A >> B has
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implementation-defined behavior, but do not check these other
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restrictions. */
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#define INT_LEFT_SHIFT_RANGE_OVERFLOW(a, b, min, max) \
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((a) < 0 \
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? (a) < (min) >> (b) \
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: (max) >> (b) < (a))
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/* The _GL*_OVERFLOW macros have the same restrictions as the
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*_RANGE_OVERFLOW macros, except that they do not assume that operands
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(e.g., A and B) have the same type as MIN and MAX. Instead, they assume
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that the result (e.g., A + B) has that type. */
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#if _GL_HAS_BUILTIN_OVERFLOW_P
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# define _GL_ADD_OVERFLOW(a, b, min, max) \
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__builtin_add_overflow_p (a, b, (__typeof__ ((a) + (b))) 0)
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# define _GL_SUBTRACT_OVERFLOW(a, b, min, max) \
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__builtin_sub_overflow_p (a, b, (__typeof__ ((a) - (b))) 0)
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# define _GL_MULTIPLY_OVERFLOW(a, b, min, max) \
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__builtin_mul_overflow_p (a, b, (__typeof__ ((a) * (b))) 0)
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#else
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# define _GL_ADD_OVERFLOW(a, b, min, max) \
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((min) < 0 ? INT_ADD_RANGE_OVERFLOW (a, b, min, max) \
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: (a) < 0 ? (b) <= (a) + (b) \
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: (b) < 0 ? (a) <= (a) + (b) \
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: (a) + (b) < (b))
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# define _GL_SUBTRACT_OVERFLOW(a, b, min, max) \
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((min) < 0 ? INT_SUBTRACT_RANGE_OVERFLOW (a, b, min, max) \
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: (a) < 0 ? 1 \
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: (b) < 0 ? (a) - (b) <= (a) \
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: (a) < (b))
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# define _GL_MULTIPLY_OVERFLOW(a, b, min, max) \
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(((min) == 0 && (((a) < 0 && 0 < (b)) || ((b) < 0 && 0 < (a)))) \
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|| INT_MULTIPLY_RANGE_OVERFLOW (a, b, min, max))
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#endif
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#define _GL_DIVIDE_OVERFLOW(a, b, min, max) \
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((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max) \
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: (a) < 0 ? (b) <= (a) + (b) - 1 \
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: (b) < 0 && (a) + (b) <= (a))
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#define _GL_REMAINDER_OVERFLOW(a, b, min, max) \
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((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max) \
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: (a) < 0 ? (a) % (b) != ((max) - (b) + 1) % (b) \
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: (b) < 0 && ! _GL_UNSIGNED_NEG_MULTIPLE (a, b, max))
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/* Return a nonzero value if A is a mathematical multiple of B, where
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A is unsigned, B is negative, and MAX is the maximum value of A's
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type. A's type must be the same as (A % B)'s type. Normally (A %
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-B == 0) suffices, but things get tricky if -B would overflow. */
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#define _GL_UNSIGNED_NEG_MULTIPLE(a, b, max) \
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(((b) < -_GL_SIGNED_INT_MAXIMUM (b) \
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? (_GL_SIGNED_INT_MAXIMUM (b) == (max) \
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? (a) \
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: (a) % (_GL_INT_CONVERT (a, _GL_SIGNED_INT_MAXIMUM (b)) + 1)) \
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: (a) % - (b)) \
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== 0)
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/* Check for integer overflow, and report low order bits of answer.
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The INT_<op>_OVERFLOW macros return 1 if the corresponding C operators
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might not yield numerically correct answers due to arithmetic overflow.
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The INT_<op>_WRAPV macros compute the low-order bits of the sum,
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difference, and product of two C integers, and return 1 if these
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low-order bits are not numerically correct.
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These macros work correctly on all known practical hosts, and do not rely
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on undefined behavior due to signed arithmetic overflow.
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Example usage, assuming A and B are long int:
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if (INT_MULTIPLY_OVERFLOW (a, b))
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printf ("result would overflow\n");
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else
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printf ("result is %ld (no overflow)\n", a * b);
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Example usage with WRAPV flavor:
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long int result;
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bool overflow = INT_MULTIPLY_WRAPV (a, b, &result);
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printf ("result is %ld (%s)\n", result,
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overflow ? "after overflow" : "no overflow");
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Restrictions on these macros:
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These macros do not check for all possible numerical problems or
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undefined or unspecified behavior: they do not check for division
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by zero, for bad shift counts, or for shifting negative numbers.
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These macros may evaluate their arguments zero or multiple times, so the
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arguments should not have side effects.
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The WRAPV macros are not constant expressions. They support only
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+, binary -, and *.
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Because the WRAPV macros convert the result, they report overflow
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in different circumstances than the OVERFLOW macros do. For
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example, in the typical case with 16-bit 'short' and 32-bit 'int',
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if A, B and *R are all of type 'short' then INT_ADD_OVERFLOW (A, B)
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returns false because the addition cannot overflow after A and B
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are converted to 'int', whereas INT_ADD_WRAPV (A, B, R) returns
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true or false depending on whether the sum fits into 'short'.
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These macros are tuned for their last input argument being a constant.
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A, B, and *R should be integers; they need not be the same type,
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and they need not be all signed or all unsigned.
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However, none of the integer types should be bit-precise,
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and *R's type should not be char, bool, or an enumeration type.
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Return 1 if the integer expressions A * B, A - B, -A, A * B, A / B,
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A % B, and A << B would overflow, respectively. */
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#define INT_ADD_OVERFLOW(a, b) \
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_GL_BINARY_OP_OVERFLOW (a, b, _GL_ADD_OVERFLOW)
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#define INT_SUBTRACT_OVERFLOW(a, b) \
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_GL_BINARY_OP_OVERFLOW (a, b, _GL_SUBTRACT_OVERFLOW)
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#define INT_NEGATE_OVERFLOW(a) _GL_INT_NEGATE_OVERFLOW (a)
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#define INT_MULTIPLY_OVERFLOW(a, b) \
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_GL_BINARY_OP_OVERFLOW (a, b, _GL_MULTIPLY_OVERFLOW)
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#define INT_DIVIDE_OVERFLOW(a, b) \
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_GL_BINARY_OP_OVERFLOW (a, b, _GL_DIVIDE_OVERFLOW)
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#define INT_REMAINDER_OVERFLOW(a, b) \
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_GL_BINARY_OP_OVERFLOW (a, b, _GL_REMAINDER_OVERFLOW)
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#define INT_LEFT_SHIFT_OVERFLOW(a, b) \
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INT_LEFT_SHIFT_RANGE_OVERFLOW (a, b, \
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_GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
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/* Return 1 if the expression A <op> B would overflow,
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where OP_RESULT_OVERFLOW (A, B, MIN, MAX) does the actual test,
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assuming MIN and MAX are the minimum and maximum for the result type.
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Arguments should be free of side effects. */
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#define _GL_BINARY_OP_OVERFLOW(a, b, op_result_overflow) \
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op_result_overflow (a, b, \
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_GL_INT_MINIMUM (_GL_INT_CONVERT (a, b)), \
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_GL_INT_MAXIMUM (_GL_INT_CONVERT (a, b)))
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/* Store the low-order bits of A + B, A - B, A * B, respectively, into *R.
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Return 1 if the result overflows. See above for restrictions. */
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#define INT_ADD_WRAPV(a, b, r) _GL_INT_ADD_WRAPV (a, b, r)
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#define INT_SUBTRACT_WRAPV(a, b, r) _GL_INT_SUBTRACT_WRAPV (a, b, r)
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#define INT_MULTIPLY_WRAPV(a, b, r) _GL_INT_MULTIPLY_WRAPV (a, b, r)
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/* The following macros compute A + B, A - B, and A * B, respectively.
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If no overflow occurs, they set *R to the result and return 1;
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otherwise, they return 0 and may modify *R.
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Example usage:
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long int result;
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if (INT_ADD_OK (a, b, &result))
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printf ("result is %ld\n", result);
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else
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printf ("overflow\n");
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A, B, and *R should be integers; they need not be the same type,
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and they need not be all signed or all unsigned.
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However, none of the integer types should be bit-precise,
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and *R's type should not be char, bool, or an enumeration type.
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These macros work correctly on all known practical hosts, and do not rely
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on undefined behavior due to signed arithmetic overflow.
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These macros are not constant expressions.
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These macros may evaluate their arguments zero or multiple times, so the
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arguments should not have side effects.
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These macros are tuned for B being a constant. */
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#define INT_ADD_OK(a, b, r) (! INT_ADD_WRAPV (a, b, r))
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#define INT_SUBTRACT_OK(a, b, r) (! INT_SUBTRACT_WRAPV (a, b, r))
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#define INT_MULTIPLY_OK(a, b, r) (! INT_MULTIPLY_WRAPV (a, b, r))
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#endif /* _GL_INTPROPS_H */
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