version 1.1, 2012/02/21 22:57:48
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version 1.1.1.2, 2012/05/29 09:29:43
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/* intprops.h -- properties of integer types |
/* intprops.h -- properties of integer types |
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Copyright (C) 2001, 2002, 2003, 2004, 2005 Free Software Foundation, Inc. | Copyright (C) 2001-2005, 2009-2011 Free Software Foundation, Inc. |
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This program is free software: you can redistribute it and/or modify |
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 |
it under the terms of the GNU General Public License as published by |
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/* Written by Paul Eggert. */ |
/* Written by Paul Eggert. */ |
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#ifndef _GL_INTPROPS_H |
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#define _GL_INTPROPS_H |
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#include <limits.h> |
#include <limits.h> |
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/* Return an integer value, converted to the same type as the integer |
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expression E after integer type promotion. V is the unconverted value. */ |
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#define _GL_INT_CONVERT(e, v) (0 * (e) + (v)) |
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/* Act like _GL_INT_CONVERT (E, -V) but work around a bug in IRIX 6.5 cc; see |
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<http://lists.gnu.org/archive/html/bug-gnulib/2011-05/msg00406.html>. */ |
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#define _GL_INT_NEGATE_CONVERT(e, v) (0 * (e) - (v)) |
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/* The extra casts in the following macros work around compiler bugs, |
/* The extra casts in the following macros work around compiler bugs, |
e.g., in Cray C 5.0.3.0. */ |
e.g., in Cray C 5.0.3.0. */ |
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#define TYPE_ONES_COMPLEMENT(t) ((t) ~ (t) 0 == 0) |
#define TYPE_ONES_COMPLEMENT(t) ((t) ~ (t) 0 == 0) |
#define TYPE_SIGNED_MAGNITUDE(t) ((t) ~ (t) 0 < (t) -1) |
#define TYPE_SIGNED_MAGNITUDE(t) ((t) ~ (t) 0 < (t) -1) |
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/* True if the signed integer expression E uses two's complement. */ |
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#define _GL_INT_TWOS_COMPLEMENT(e) (~ _GL_INT_CONVERT (e, 0) == -1) |
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/* True if the arithmetic type T is signed. */ |
/* True if the arithmetic type T is signed. */ |
#define TYPE_SIGNED(t) (! ((t) 0 < (t) -1)) |
#define TYPE_SIGNED(t) (! ((t) 0 < (t) -1)) |
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/* The maximum and minimum values for the integer type T. These | /* 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) |
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| /* Minimum and maximum values for integer types and expressions. These |
macros have undefined behavior if T is signed and has padding bits. |
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 |
If this is a problem for you, please let us know how to fix it for |
your host. */ |
your host. */ |
#define TYPE_MINIMUM(t) \ |
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((t) (! TYPE_SIGNED (t) \ |
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? (t) 0 \ |
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: TYPE_SIGNED_MAGNITUDE (t) \ |
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? ~ (t) 0 \ |
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: ~ (t) 0 << (sizeof (t) * CHAR_BIT - 1))) |
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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) 0 << (sizeof (t) * CHAR_BIT - 1)))) |
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/* Return zero if T can be determined to be an unsigned type. | /* The maximum and minimum values for the integer type T. */ |
Otherwise, return 1. | #define TYPE_MINIMUM(t) \ |
When compiling with GCC, INT_STRLEN_BOUND uses this macro to obtain a | ((t) (! TYPE_SIGNED (t) \ |
tighter bound. Otherwise, it overestimates the true bound by one byte | ? (t) 0 \ |
when applied to unsigned types of size 2, 4, 16, ... bytes. | : TYPE_SIGNED_MAGNITUDE (t) \ |
The symbol signed_type_or_expr__ is private to this header file. */ | ? ~ (t) 0 \ |
#if __GNUC__ >= 2 | : ~ TYPE_MAXIMUM (t))) |
# define signed_type_or_expr__(t) TYPE_SIGNED (__typeof__ (t)) | #define TYPE_MAXIMUM(t) \ |
| ((t) (! TYPE_SIGNED (t) \ |
| ? (t) -1 \ |
| : ((((t) 1 << (sizeof (t) * CHAR_BIT - 2)) - 1) * 2 + 1))) |
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| /* 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) |
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| /* 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 |
#else |
# define signed_type_or_expr__(t) 1 | # define _GL_HAVE___TYPEOF__ 0 |
#endif |
#endif |
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/* Return 1 if the integer type or expression T might be signed. Return 0 |
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if it is definitely unsigned. This macro does not evaluate its argument, |
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and expands to an integer constant expression. */ |
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#if _GL_HAVE___TYPEOF__ |
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# define _GL_SIGNED_TYPE_OR_EXPR(t) TYPE_SIGNED (__typeof__ (t)) |
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#else |
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# define _GL_SIGNED_TYPE_OR_EXPR(t) 1 |
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#endif |
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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. |
/* Bound on length of the string representing an integer type or expression T. |
Subtract 1 for the sign bit if T is signed; log10 (2.0) < 146/485; | Subtract 1 for the sign bit if T is signed, and then add 1 more for |
add 1 for integer division truncation; add 1 more for a minus sign | a minus sign if needed. |
if needed. */ | |
#define INT_STRLEN_BOUND(t) \ | |
((sizeof (t) * CHAR_BIT - signed_type_or_expr__ (t)) * 146 / 485 \ | |
+ signed_type_or_expr__ (t) + 1) | |
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Because _GL_SIGNED_TYPE_OR_EXPR sometimes returns 0 when its argument is |
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signed, 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 (sizeof (t) * CHAR_BIT \ |
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- _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, |
/* Bound on buffer size needed to represent an integer type or expression T, |
including the terminating null. */ |
including the terminating null. */ |
#define INT_BUFSIZE_BOUND(t) (INT_STRLEN_BOUND (t) + 1) |
#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 might not yield numerically correct answers due to |
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arithmetic overflow. They do not rely on undefined or |
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implementation-defined behavior. Their implementations are simple |
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and straightforward, but they are a bit harder to use than the |
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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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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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((min) < 0 \ |
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? (a) < - (max) \ |
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: 0 < (a)) |
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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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<http://lists.gnu.org/archive/html/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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#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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#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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/* Integer overflow checks. |
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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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They 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: |
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long int i = ...; |
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long int j = ...; |
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if (INT_MULTIPLY_OVERFLOW (i, j)) |
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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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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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These macros are tuned for their last argument being a constant. |
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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) \ |
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INT_NEGATE_RANGE_OVERFLOW (a, _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (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 (0 * (b) + (a)), \ |
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_GL_INT_MAXIMUM (0 * (b) + (a))) |
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#endif /* _GL_INTPROPS_H */ |