| 1 | /* intprops.h -- properties of integer types
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| 2 |
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| 3 | Copyright (C) 2001-2005, 2009-2012 Free Software Foundation, Inc.
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| 4 |
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| 5 | This program is free software: you can redistribute it and/or modify
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| 6 | it under the terms of the GNU General Public License as published by
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| 7 | the Free Software Foundation; either version 3 of the License, or
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| 8 | (at your option) any later version.
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| 9 |
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| 10 | This program is distributed in the hope that it will be useful,
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| 11 | but WITHOUT ANY WARRANTY; without even the implied warranty of
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| 12 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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| 13 | GNU General Public License for more details.
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| 14 |
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| 15 | You should have received a copy of the GNU General Public License
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| 16 | along with this program. If not, see <http://www.gnu.org/licenses/>. */
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| 17 |
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| 18 | /* Written by Paul Eggert. */
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| 19 |
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| 20 | #ifndef _GL_INTPROPS_H
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| 21 | #define _GL_INTPROPS_H
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| 22 |
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| 23 | #include <limits.h>
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| 24 |
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| 25 | /* Return an integer value, converted to the same type as the integer
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| 26 | expression E after integer type promotion. V is the unconverted value. */
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| 27 | #define _GL_INT_CONVERT(e, v) (0 * (e) + (v))
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| 28 |
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| 29 | /* Act like _GL_INT_CONVERT (E, -V) but work around a bug in IRIX 6.5 cc; see
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| 30 | <http://lists.gnu.org/archive/html/bug-gnulib/2011-05/msg00406.html>. */
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| 31 | #define _GL_INT_NEGATE_CONVERT(e, v) (0 * (e) - (v))
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| 32 |
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| 33 | /* The extra casts in the following macros work around compiler bugs,
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| 34 | e.g., in Cray C 5.0.3.0. */
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| 35 |
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| 36 | /* True if the arithmetic type T is an integer type. bool counts as
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| 37 | an integer. */
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| 38 | #define TYPE_IS_INTEGER(t) ((t) 1.5 == 1)
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| 39 |
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| 40 | /* True if negative values of the signed integer type T use two's
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| 41 | complement, ones' complement, or signed magnitude representation,
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| 42 | respectively. Much GNU code assumes two's complement, but some
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| 43 | people like to be portable to all possible C hosts. */
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| 44 | #define TYPE_TWOS_COMPLEMENT(t) ((t) ~ (t) 0 == (t) -1)
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| 45 | #define TYPE_ONES_COMPLEMENT(t) ((t) ~ (t) 0 == 0)
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| 46 | #define TYPE_SIGNED_MAGNITUDE(t) ((t) ~ (t) 0 < (t) -1)
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| 47 |
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| 48 | /* True if the signed integer expression E uses two's complement. */
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| 49 | #define _GL_INT_TWOS_COMPLEMENT(e) (~ _GL_INT_CONVERT (e, 0) == -1)
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| 50 |
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| 51 | /* True if the arithmetic type T is signed. */
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| 52 | #define TYPE_SIGNED(t) (! ((t) 0 < (t) -1))
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| 53 |
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| 54 | /* Return 1 if the integer expression E, after integer promotion, has
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| 55 | a signed type. */
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| 56 | #define _GL_INT_SIGNED(e) (_GL_INT_NEGATE_CONVERT (e, 1) < 0)
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| 57 |
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| 58 |
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| 59 | /* Minimum and maximum values for integer types and expressions. These
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| 60 | macros have undefined behavior if T is signed and has padding bits.
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| 61 | If this is a problem for you, please let us know how to fix it for
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| 62 | your host. */
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| 63 |
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| 64 | /* The maximum and minimum values for the integer type T. */
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| 65 | #define TYPE_MINIMUM(t) \
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| 66 | ((t) (! TYPE_SIGNED (t) \
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| 67 | ? (t) 0 \
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| 68 | : TYPE_SIGNED_MAGNITUDE (t) \
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| 69 | ? ~ (t) 0 \
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| 70 | : ~ TYPE_MAXIMUM (t)))
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| 71 | #define TYPE_MAXIMUM(t) \
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| 72 | ((t) (! TYPE_SIGNED (t) \
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| 73 | ? (t) -1 \
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| 74 | : ((((t) 1 << (sizeof (t) * CHAR_BIT - 2)) - 1) * 2 + 1)))
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| 75 |
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| 76 | /* The maximum and minimum values for the type of the expression E,
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| 77 | after integer promotion. E should not have side effects. */
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| 78 | #define _GL_INT_MINIMUM(e) \
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| 79 | (_GL_INT_SIGNED (e) \
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| 80 | ? - _GL_INT_TWOS_COMPLEMENT (e) - _GL_SIGNED_INT_MAXIMUM (e) \
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| 81 | : _GL_INT_CONVERT (e, 0))
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| 82 | #define _GL_INT_MAXIMUM(e) \
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| 83 | (_GL_INT_SIGNED (e) \
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| 84 | ? _GL_SIGNED_INT_MAXIMUM (e) \
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| 85 | : _GL_INT_NEGATE_CONVERT (e, 1))
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| 86 | #define _GL_SIGNED_INT_MAXIMUM(e) \
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| 87 | (((_GL_INT_CONVERT (e, 1) << (sizeof ((e) + 0) * CHAR_BIT - 2)) - 1) * 2 + 1)
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| 88 |
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| 89 |
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| 90 | /* Return 1 if the __typeof__ keyword works. This could be done by
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| 91 | 'configure', but for now it's easier to do it by hand. */
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| 92 | #if 2 <= __GNUC__ || 0x5110 <= __SUNPRO_C
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| 93 | # define _GL_HAVE___TYPEOF__ 1
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| 94 | #else
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| 95 | # define _GL_HAVE___TYPEOF__ 0
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| 96 | #endif
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| 97 |
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| 98 | /* Return 1 if the integer type or expression T might be signed. Return 0
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| 99 | if it is definitely unsigned. This macro does not evaluate its argument,
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| 100 | and expands to an integer constant expression. */
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| 101 | #if _GL_HAVE___TYPEOF__
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| 102 | # define _GL_SIGNED_TYPE_OR_EXPR(t) TYPE_SIGNED (__typeof__ (t))
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| 103 | #else
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| 104 | # define _GL_SIGNED_TYPE_OR_EXPR(t) 1
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| 105 | #endif
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| 106 |
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| 107 | /* Bound on length of the string representing an unsigned integer
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| 108 | value representable in B bits. log10 (2.0) < 146/485. The
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| 109 | smallest value of B where this bound is not tight is 2621. */
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| 110 | #define INT_BITS_STRLEN_BOUND(b) (((b) * 146 + 484) / 485)
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| 111 |
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| 112 | /* Bound on length of the string representing an integer type or expression T.
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| 113 | Subtract 1 for the sign bit if T is signed, and then add 1 more for
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| 114 | a minus sign if needed.
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| 115 |
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| 116 | Because _GL_SIGNED_TYPE_OR_EXPR sometimes returns 0 when its argument is
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| 117 | signed, this macro may overestimate the true bound by one byte when
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| 118 | applied to unsigned types of size 2, 4, 16, ... bytes. */
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| 119 | #define INT_STRLEN_BOUND(t) \
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| 120 | (INT_BITS_STRLEN_BOUND (sizeof (t) * CHAR_BIT \
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| 121 | - _GL_SIGNED_TYPE_OR_EXPR (t)) \
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| 122 | + _GL_SIGNED_TYPE_OR_EXPR (t))
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| 123 |
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| 124 | /* Bound on buffer size needed to represent an integer type or expression T,
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| 125 | including the terminating null. */
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| 126 | #define INT_BUFSIZE_BOUND(t) (INT_STRLEN_BOUND (t) + 1)
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| 127 |
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| 128 |
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| 129 | /* Range overflow checks.
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| 130 |
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| 131 | The INT_<op>_RANGE_OVERFLOW macros return 1 if the corresponding C
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| 132 | operators might not yield numerically correct answers due to
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| 133 | arithmetic overflow. They do not rely on undefined or
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| 134 | implementation-defined behavior. Their implementations are simple
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| 135 | and straightforward, but they are a bit harder to use than the
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| 136 | INT_<op>_OVERFLOW macros described below.
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| 137 |
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| 138 | Example usage:
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| 139 |
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| 140 | long int i = ...;
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| 141 | long int j = ...;
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| 142 | if (INT_MULTIPLY_RANGE_OVERFLOW (i, j, LONG_MIN, LONG_MAX))
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| 143 | printf ("multiply would overflow");
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| 144 | else
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| 145 | printf ("product is %ld", i * j);
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| 146 |
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| 147 | Restrictions on *_RANGE_OVERFLOW macros:
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| 148 |
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| 149 | These macros do not check for all possible numerical problems or
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| 150 | undefined or unspecified behavior: they do not check for division
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| 151 | by zero, for bad shift counts, or for shifting negative numbers.
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| 152 |
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| 153 | These macros may evaluate their arguments zero or multiple times,
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| 154 | so the arguments should not have side effects. The arithmetic
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| 155 | arguments (including the MIN and MAX arguments) must be of the same
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| 156 | integer type after the usual arithmetic conversions, and the type
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| 157 | must have minimum value MIN and maximum MAX. Unsigned types should
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| 158 | use a zero MIN of the proper type.
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| 159 |
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| 160 | These macros are tuned for constant MIN and MAX. For commutative
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| 161 | operations such as A + B, they are also tuned for constant B. */
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| 162 |
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| 163 | /* Return 1 if A + B would overflow in [MIN,MAX] arithmetic.
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| 164 | See above for restrictions. */
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| 165 | #define INT_ADD_RANGE_OVERFLOW(a, b, min, max) \
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| 166 | ((b) < 0 \
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| 167 | ? (a) < (min) - (b) \
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| 168 | : (max) - (b) < (a))
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| 169 |
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| 170 | /* Return 1 if A - B would overflow in [MIN,MAX] arithmetic.
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| 171 | See above for restrictions. */
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| 172 | #define INT_SUBTRACT_RANGE_OVERFLOW(a, b, min, max) \
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| 173 | ((b) < 0 \
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| 174 | ? (max) + (b) < (a) \
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| 175 | : (a) < (min) + (b))
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| 176 |
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| 177 | /* Return 1 if - A would overflow in [MIN,MAX] arithmetic.
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| 178 | See above for restrictions. */
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| 179 | #define INT_NEGATE_RANGE_OVERFLOW(a, min, max) \
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| 180 | ((min) < 0 \
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| 181 | ? (a) < - (max) \
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| 182 | : 0 < (a))
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| 183 |
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| 184 | /* Return 1 if A * B would overflow in [MIN,MAX] arithmetic.
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| 185 | See above for restrictions. Avoid && and || as they tickle
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| 186 | bugs in Sun C 5.11 2010/08/13 and other compilers; see
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| 187 | <http://lists.gnu.org/archive/html/bug-gnulib/2011-05/msg00401.html>. */
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| 188 | #define INT_MULTIPLY_RANGE_OVERFLOW(a, b, min, max) \
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| 189 | ((b) < 0 \
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| 190 | ? ((a) < 0 \
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| 191 | ? (a) < (max) / (b) \
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| 192 | : (b) == -1 \
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| 193 | ? 0 \
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| 194 | : (min) / (b) < (a)) \
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| 195 | : (b) == 0 \
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| 196 | ? 0 \
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| 197 | : ((a) < 0 \
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| 198 | ? (a) < (min) / (b) \
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| 199 | : (max) / (b) < (a)))
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| 200 |
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| 201 | /* Return 1 if A / B would overflow in [MIN,MAX] arithmetic.
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| 202 | See above for restrictions. Do not check for division by zero. */
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| 203 | #define INT_DIVIDE_RANGE_OVERFLOW(a, b, min, max) \
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| 204 | ((min) < 0 && (b) == -1 && (a) < - (max))
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| 205 |
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| 206 | /* Return 1 if A % B would overflow in [MIN,MAX] arithmetic.
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| 207 | See above for restrictions. Do not check for division by zero.
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| 208 | Mathematically, % should never overflow, but on x86-like hosts
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| 209 | INT_MIN % -1 traps, and the C standard permits this, so treat this
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| 210 | as an overflow too. */
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| 211 | #define INT_REMAINDER_RANGE_OVERFLOW(a, b, min, max) \
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| 212 | INT_DIVIDE_RANGE_OVERFLOW (a, b, min, max)
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| 213 |
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| 214 | /* Return 1 if A << B would overflow in [MIN,MAX] arithmetic.
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| 215 | See above for restrictions. Here, MIN and MAX are for A only, and B need
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| 216 | not be of the same type as the other arguments. The C standard says that
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| 217 | behavior is undefined for shifts unless 0 <= B < wordwidth, and that when
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| 218 | A is negative then A << B has undefined behavior and A >> B has
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| 219 | implementation-defined behavior, but do not check these other
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| 220 | restrictions. */
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| 221 | #define INT_LEFT_SHIFT_RANGE_OVERFLOW(a, b, min, max) \
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| 222 | ((a) < 0 \
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| 223 | ? (a) < (min) >> (b) \
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| 224 | : (max) >> (b) < (a))
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| 225 |
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| 226 |
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| 227 | /* The _GL*_OVERFLOW macros have the same restrictions as the
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| 228 | *_RANGE_OVERFLOW macros, except that they do not assume that operands
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| 229 | (e.g., A and B) have the same type as MIN and MAX. Instead, they assume
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| 230 | that the result (e.g., A + B) has that type. */
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| 231 | #define _GL_ADD_OVERFLOW(a, b, min, max) \
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| 232 | ((min) < 0 ? INT_ADD_RANGE_OVERFLOW (a, b, min, max) \
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| 233 | : (a) < 0 ? (b) <= (a) + (b) \
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| 234 | : (b) < 0 ? (a) <= (a) + (b) \
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| 235 | : (a) + (b) < (b))
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| 236 | #define _GL_SUBTRACT_OVERFLOW(a, b, min, max) \
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| 237 | ((min) < 0 ? INT_SUBTRACT_RANGE_OVERFLOW (a, b, min, max) \
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| 238 | : (a) < 0 ? 1 \
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| 239 | : (b) < 0 ? (a) - (b) <= (a) \
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| 240 | : (a) < (b))
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| 241 | #define _GL_MULTIPLY_OVERFLOW(a, b, min, max) \
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| 242 | (((min) == 0 && (((a) < 0 && 0 < (b)) || ((b) < 0 && 0 < (a)))) \
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| 243 | || INT_MULTIPLY_RANGE_OVERFLOW (a, b, min, max))
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| 244 | #define _GL_DIVIDE_OVERFLOW(a, b, min, max) \
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| 245 | ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max) \
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| 246 | : (a) < 0 ? (b) <= (a) + (b) - 1 \
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| 247 | : (b) < 0 && (a) + (b) <= (a))
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| 248 | #define _GL_REMAINDER_OVERFLOW(a, b, min, max) \
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| 249 | ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max) \
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| 250 | : (a) < 0 ? (a) % (b) != ((max) - (b) + 1) % (b) \
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| 251 | : (b) < 0 && ! _GL_UNSIGNED_NEG_MULTIPLE (a, b, max))
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| 252 |
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| 253 | /* Return a nonzero value if A is a mathematical multiple of B, where
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| 254 | A is unsigned, B is negative, and MAX is the maximum value of A's
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| 255 | type. A's type must be the same as (A % B)'s type. Normally (A %
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| 256 | -B == 0) suffices, but things get tricky if -B would overflow. */
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| 257 | #define _GL_UNSIGNED_NEG_MULTIPLE(a, b, max) \
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| 258 | (((b) < -_GL_SIGNED_INT_MAXIMUM (b) \
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| 259 | ? (_GL_SIGNED_INT_MAXIMUM (b) == (max) \
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| 260 | ? (a) \
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| 261 | : (a) % (_GL_INT_CONVERT (a, _GL_SIGNED_INT_MAXIMUM (b)) + 1)) \
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| 262 | : (a) % - (b)) \
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| 263 | == 0)
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| 264 |
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| 265 |
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| 266 | /* Integer overflow checks.
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| 267 |
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| 268 | The INT_<op>_OVERFLOW macros return 1 if the corresponding C operators
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| 269 | might not yield numerically correct answers due to arithmetic overflow.
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| 270 | They work correctly on all known practical hosts, and do not rely
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| 271 | on undefined behavior due to signed arithmetic overflow.
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| 272 |
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| 273 | Example usage:
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| 274 |
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| 275 | long int i = ...;
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| 276 | long int j = ...;
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| 277 | if (INT_MULTIPLY_OVERFLOW (i, j))
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| 278 | printf ("multiply would overflow");
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| 279 | else
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| 280 | printf ("product is %ld", i * j);
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| 281 |
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| 282 | These macros do not check for all possible numerical problems or
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| 283 | undefined or unspecified behavior: they do not check for division
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| 284 | by zero, for bad shift counts, or for shifting negative numbers.
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| 285 |
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| 286 | These macros may evaluate their arguments zero or multiple times, so the
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| 287 | arguments should not have side effects.
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| 288 |
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| 289 | These macros are tuned for their last argument being a constant.
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| 290 |
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| 291 | Return 1 if the integer expressions A * B, A - B, -A, A * B, A / B,
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| 292 | A % B, and A << B would overflow, respectively. */
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| 293 |
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| 294 | #define INT_ADD_OVERFLOW(a, b) \
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| 295 | _GL_BINARY_OP_OVERFLOW (a, b, _GL_ADD_OVERFLOW)
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| 296 | #define INT_SUBTRACT_OVERFLOW(a, b) \
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| 297 | _GL_BINARY_OP_OVERFLOW (a, b, _GL_SUBTRACT_OVERFLOW)
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| 298 | #define INT_NEGATE_OVERFLOW(a) \
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| 299 | INT_NEGATE_RANGE_OVERFLOW (a, _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
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| 300 | #define INT_MULTIPLY_OVERFLOW(a, b) \
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| 301 | _GL_BINARY_OP_OVERFLOW (a, b, _GL_MULTIPLY_OVERFLOW)
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| 302 | #define INT_DIVIDE_OVERFLOW(a, b) \
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| 303 | _GL_BINARY_OP_OVERFLOW (a, b, _GL_DIVIDE_OVERFLOW)
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| 304 | #define INT_REMAINDER_OVERFLOW(a, b) \
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| 305 | _GL_BINARY_OP_OVERFLOW (a, b, _GL_REMAINDER_OVERFLOW)
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| 306 | #define INT_LEFT_SHIFT_OVERFLOW(a, b) \
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| 307 | INT_LEFT_SHIFT_RANGE_OVERFLOW (a, b, \
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| 308 | _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
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| 309 |
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| 310 | /* Return 1 if the expression A <op> B would overflow,
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| 311 | where OP_RESULT_OVERFLOW (A, B, MIN, MAX) does the actual test,
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| 312 | assuming MIN and MAX are the minimum and maximum for the result type.
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| 313 | Arguments should be free of side effects. */
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| 314 | #define _GL_BINARY_OP_OVERFLOW(a, b, op_result_overflow) \
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| 315 | op_result_overflow (a, b, \
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| 316 | _GL_INT_MINIMUM (0 * (b) + (a)), \
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| 317 | _GL_INT_MAXIMUM (0 * (b) + (a)))
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| 318 |
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| 319 | #endif /* _GL_INTPROPS_H */
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