/* intprops.h -- properties of integer types | |

Copyright (C) 2001-2005, 2009-2012 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> | |

/* Return an integer value, converted to the same type as the integer | |

expression E after integer type promotion. V is the unconverted value. */ | |

#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 negative values of the signed integer type T use two's | |

complement, ones' complement, or signed magnitude representation, | |

respectively. Much GNU code assumes two's complement, but some | |

people like to be portable to all possible C hosts. */ | |

#define TYPE_TWOS_COMPLEMENT(t) ((t) ~ (t) 0 == (t) -1) | |

#define TYPE_ONES_COMPLEMENT(t) ((t) ~ (t) 0 == 0) | |

#define TYPE_SIGNED_MAGNITUDE(t) ((t) ~ (t) 0 < (t) -1) | |

/* True if the signed integer expression E uses two's complement. */ | |

#define _GL_INT_TWOS_COMPLEMENT(e) (~ _GL_INT_CONVERT (e, 0) == -1) | |

/* True if the arithmetic type T is signed. */ | |

#define TYPE_SIGNED(t) (! ((t) 0 < (t) -1)) | |

/* Return 1 if the integer expression E, after integer promotion, has | |

a signed type. */ | |

#define _GL_INT_SIGNED(e) (_GL_INT_NEGATE_CONVERT (e, 1) < 0) | |

/* Minimum and maximum values for integer types and expressions. These | |

macros have undefined behavior if T is signed and has padding bits. | |

If this is a problem for you, please let us know how to fix it for | |

your host. */ | |

/* The maximum and minimum values for the integer type T. */ | |

#define TYPE_MINIMUM(t) \ | |

((t) (! TYPE_SIGNED (t) \ | |

? (t) 0 \ | |

: TYPE_SIGNED_MAGNITUDE (t) \ | |

? ~ (t) 0 \ | |

: ~ 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) \ | |

(_GL_INT_SIGNED (e) \ | |

? - _GL_INT_TWOS_COMPLEMENT (e) - _GL_SIGNED_INT_MAXIMUM (e) \ | |

: _GL_INT_CONVERT (e, 0)) | |

#define _GL_INT_MAXIMUM(e) \ | |

(_GL_INT_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) | |

/* Return 1 if the __typeof__ keyword works. This could be done by | |

'configure', but for now it's easier to do it by hand. */ | |

#if 2 <= __GNUC__ || 0x5110 <= __SUNPRO_C | |

# 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) | |

/* Integer overflow checks. | |

The INT_<op>_OVERFLOW macros return 1 if the corresponding C operators | |

might not yield numerically correct answers due to arithmetic overflow. | |

They work correctly on all known practical hosts, and do not rely | |

on undefined behavior due to signed arithmetic overflow. | |

Example usage: | |

long int i = ...; | |

long int j = ...; | |

if (INT_MULTIPLY_OVERFLOW (i, j)) | |

printf ("multiply would overflow"); | |

else | |

printf ("product is %ld", i * j); | |

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. | |

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))) | |

#endif /* _GL_INTPROPS_H */ |