diff options
Diffstat (limited to 'lib/intprops.h')
| -rw-r--r-- | lib/intprops.h | 298 |
1 files changed, 263 insertions, 35 deletions
diff --git a/lib/intprops.h b/lib/intprops.h index 58b1b3fbf4..a84bd6af53 100644 --- a/lib/intprops.h +++ b/lib/intprops.h @@ -17,70 +17,298 @@ /* Written by Paul Eggert. */ -#ifndef GL_INTPROPS_H -# define GL_INTPROPS_H +#ifndef _GL_INTPROPS_H +#define _GL_INTPROPS_H -# include <limits.h> +#include <limits.h> + +/* Return a integer value, converted to the same type as the integer + expression E after integer type promotion. V is the unconverted value. + E should not have side effects. */ +#define _GL_INT_CONVERT(e, v) ((e) - (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) +#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) +#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)) +#define TYPE_SIGNED(t) (! ((t) 0 < (t) -1)) + +/* Return 1 if the integer expression E, after integer promotion, has + a signed type. E should not have side effects. */ +#define _GL_INT_SIGNED(e) (_GL_INT_CONVERT (e, -1) < 0) -/* The maximum and minimum values for the integer type T. These + +/* 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. */ -# define TYPE_MINIMUM(t) \ - ((t) (! TYPE_SIGNED (t) \ - ? (t) 0 \ - : TYPE_SIGNED_MAGNITUDE (t) \ - ? ~ (t) 0 \ + +/* 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 \ +#define TYPE_MAXIMUM(t) \ + ((t) (! TYPE_SIGNED (t) \ + ? (t) -1 \ : ((((t) 1 << (sizeof (t) * CHAR_BIT - 2)) - 1) * 2 + 1))) -/* Return zero if T can be determined to be an unsigned type. - Otherwise, return 1. - When compiling with GCC, INT_STRLEN_BOUND uses this macro to obtain a - tighter bound. Otherwise, it overestimates the true bound by one byte - when applied to unsigned types of size 2, 4, 16, ... bytes. - The symbol signed_type_or_expr__ is private to this header file. */ -# if __GNUC__ >= 2 -# define signed_type_or_expr__(t) TYPE_SIGNED (__typeof__ (t)) -# else -# define signed_type_or_expr__(t) 1 -# endif +/* 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_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) +#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. */ -# define INT_STRLEN_BOUND(t) \ - (INT_BITS_STRLEN_BOUND (sizeof (t) * CHAR_BIT - signed_type_or_expr__ (t)) \ - + signed_type_or_expr__ (t)) + 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) +#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. */ +#define INT_MULTIPLY_RANGE_OVERFLOW(a, b, min, max) \ + ((b) < 0 \ + ? ((a) < 0 \ + ? (a) < (max) / (b) \ + : (b) < -1 && (min) / (b) < (a)) \ + : (0 < (b) \ + && ((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_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_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. + + This macro assumes that A | B is a valid integer if both A and B are, + which is true of all known practical hosts. If this is a problem + for you, please let us know how to fix it for your host. */ +#define _GL_BINARY_OP_OVERFLOW(a, b, op_result_overflow) \ + op_result_overflow (a, b, \ + _GL_INT_MINIMUM ((a) | (b)), \ + _GL_INT_MAXIMUM ((a) | (b))) -#endif /* GL_INTPROPS_H */ +#endif /* _GL_INTPROPS_H */ |