include/linux/overflow.h

/* SPDX-License-Identifier: GPL-2.0 OR MIT */
#ifndef __LINUX_OVERFLOW_H
#define __LINUX_OVERFLOW_H

#include <linux/compiler.h>

/*
 * In the fallback code below, we need to compute the minimum and
 * maximum values representable in a given type. These macros may also
 * be useful elsewhere, so we provide them outside the
 * COMPILER_HAS_GENERIC_BUILTIN_OVERFLOW block.
 *
 * It would seem more obvious to do something like
 *
 * #define type_min(T) (T)(is_signed_type(T) ? (T)1 << (8*sizeof(T)-1) : 0)
 * #define type_max(T) (T)(is_signed_type(T) ? ((T)1 << (8*sizeof(T)-1)) - 1 : ~(T)0)
 *
 * Unfortunately, the middle expressions, strictly speaking, have
 * undefined behaviour, and at least some versions of gcc warn about
 * the type_max expression (but not if -fsanitize=undefined is in
 * effect; in that case, the warning is deferred to runtime...).
 *
 * The slightly excessive casting in type_min is to make sure the
 * macros also produce sensible values for the exotic type _Bool. [The
 * overflow checkers only almost work for _Bool, but that's
 * a-feature-not-a-bug, since people shouldn't be doing arithmetic on
 * _Bools. Besides, the gcc builtins don't allow _Bool* as third
 * argument.]
 *
 * Idea stolen from
 * https://mail-index.netbsd.org/tech-misc/2007/02/05/0000.html -
 * credit to Christian Biere.
 */
#define is_signed_type(type)       (((type)(-1)) < (type)1)
#define __type_half_max(type) ((type)1 << (8*sizeof(type) - 1 - is_signed_type(type)))
#define type_max(T) ((T)((__type_half_max(T) - 1) + __type_half_max(T)))
#define type_min(T) ((T)((T)-type_max(T)-(T)1))


#ifdef COMPILER_HAS_GENERIC_BUILTIN_OVERFLOW
/*
 * For simplicity and code hygiene, the fallback code below insists on
 * a, b and *d having the same type (similar to the min() and max()
 * macros), whereas gcc's type-generic overflow checkers accept
 * different types. Hence we don't just make check_add_overflow an
 * alias for __builtin_add_overflow, but add type checks similar to
 * below.
 */
#define check_add_overflow(a, b, d) ({		\
	typeof(a) __a = (a);			\
	typeof(b) __b = (b);			\
	typeof(d) __d = (d);			\
	(void) (&__a == &__b);			\
	(void) (&__a == __d);			\
	__builtin_add_overflow(__a, __b, __d);	\
})

#define check_sub_overflow(a, b, d) ({		\
	typeof(a) __a = (a);			\
	typeof(b) __b = (b);			\
	typeof(d) __d = (d);			\
	(void) (&__a == &__b);			\
	(void) (&__a == __d);			\
	__builtin_sub_overflow(__a, __b, __d);	\
})

#define check_mul_overflow(a, b, d) ({		\
	typeof(a) __a = (a);			\
	typeof(b) __b = (b);			\
	typeof(d) __d = (d);			\
	(void) (&__a == &__b);			\
	(void) (&__a == __d);			\
	__builtin_mul_overflow(__a, __b, __d);	\
})

#else


/* Checking for unsigned overflow is relatively easy without causing UB. */
#define __unsigned_add_overflow(a, b, d) ({	\
	typeof(a) __a = (a);			\
	typeof(b) __b = (b);			\
	typeof(d) __d = (d);			\
	(void) (&__a == &__b);			\
	(void) (&__a == __d);			\
	*__d = __a + __b;			\
	*__d < __a;				\
})
#define __unsigned_sub_overflow(a, b, d) ({	\
	typeof(a) __a = (a);			\
	typeof(b) __b = (b);			\
	typeof(d) __d = (d);			\
	(void) (&__a == &__b);			\
	(void) (&__a == __d);			\
	*__d = __a - __b;			\
	__a < __b;				\
})
/*
 * If one of a or b is a compile-time constant, this avoids a division.
 */
#define __unsigned_mul_overflow(a, b, d) ({		\
	typeof(a) __a = (a);				\
	typeof(b) __b = (b);				\
	typeof(d) __d = (d);				\
	(void) (&__a == &__b);				\
	(void) (&__a == __d);				\
	*__d = __a * __b;				\
	__builtin_constant_p(__b) ?			\
	  __b > 0 && __a > type_max(typeof(__a)) / __b : \
	  __a > 0 && __b > type_max(typeof(__b)) / __a;	 \
})

/*
 * For signed types, detecting overflow is much harder, especially if
 * we want to avoid UB. But the interface of these macros is such that
 * we must provide a result in *d, and in fact we must produce the
 * result promised by gcc's builtins, which is simply the possibly
 * wrapped-around value. Fortunately, we can just formally do the
 * operations in the widest relevant unsigned type (u64) and then
 * truncate the result - gcc is smart enough to generate the same code
 * with and without the (u64) casts.
 */

/*
 * Adding two signed integers can overflow only if they have the same
 * sign, and overflow has happened iff the result has the opposite
 * sign.
 */
#define __signed_add_overflow(a, b, d) ({	\
	typeof(a) __a = (a);			\
	typeof(b) __b = (b);			\
	typeof(d) __d = (d);			\
	(void) (&__a == &__b);			\
	(void) (&__a == __d);			\
	*__d = (u64)__a + (u64)__b;		\
	(((~(__a ^ __b)) & (*__d ^ __a))	\
		& type_min(typeof(__a))) != 0;	\
})

/*
 * Subtraction is similar, except that overflow can now happen only
 * when the signs are opposite. In this case, overflow has happened if
 * the result has the opposite sign of a.
 */
#define __signed_sub_overflow(a, b, d) ({	\
	typeof(a) __a = (a);			\
	typeof(b) __b = (b);			\
	typeof(d) __d = (d);			\
	(void) (&__a == &__b);			\
	(void) (&__a == __d);			\
	*__d = (u64)__a - (u64)__b;		\
	((((__a ^ __b)) & (*__d ^ __a))		\
		& type_min(typeof(__a))) != 0;	\
})

/*
 * Signed multiplication is rather hard. gcc always follows C99, so
 * division is truncated towards 0. This means that we can write the
 * overflow check like this:
 *
 * (a > 0 && (b > MAX/a || b < MIN/a)) ||
 * (a < -1 && (b > MIN/a || b < MAX/a) ||
 * (a == -1 && b == MIN)
 *
 * The redundant casts of -1 are to silence an annoying -Wtype-limits
 * (included in -Wextra) warning: When the type is u8 or u16, the
 * __b_c_e in check_mul_overflow obviously selects
 * __unsigned_mul_overflow, but unfortunately gcc still parses this
 * code and warns about the limited range of __b.
 */

#define __signed_mul_overflow(a, b, d) ({				\
	typeof(a) __a = (a);						\
	typeof(b) __b = (b);						\
	typeof(d) __d = (d);						\
	typeof(a) __tmax = type_max(typeof(a));				\
	typeof(a) __tmin = type_min(typeof(a));				\
	(void) (&__a == &__b);						\
	(void) (&__a == __d);						\
	*__d = (u64)__a * (u64)__b;					\
	(__b > 0   && (__a > __tmax/__b || __a < __tmin/__b)) ||	\
	(__b < (typeof(__b))-1  && (__a > __tmin/__b || __a < __tmax/__b)) || \
	(__b == (typeof(__b))-1 && __a == __tmin);			\
})


#define check_add_overflow(a, b, d)					\
	__builtin_choose_expr(is_signed_type(typeof(a)),		\
			__signed_add_overflow(a, b, d),			\
			__unsigned_add_overflow(a, b, d))

#define check_sub_overflow(a, b, d)					\
	__builtin_choose_expr(is_signed_type(typeof(a)),		\
			__signed_sub_overflow(a, b, d),			\
			__unsigned_sub_overflow(a, b, d))

#define check_mul_overflow(a, b, d)					\
	__builtin_choose_expr(is_signed_type(typeof(a)),		\
			__signed_mul_overflow(a, b, d),			\
			__unsigned_mul_overflow(a, b, d))


#endif /* COMPILER_HAS_GENERIC_BUILTIN_OVERFLOW */

#endif /* __LINUX_OVERFLOW_H */