1 /* tnum: tracked (or tristate) numbers
2 *
3 * A tnum tracks knowledge about the bits of a value. Each bit can be either
4 * known (0 or 1), or unknown (x). Arithmetic operations on tnums will
5 * propagate the unknown bits such that the tnum result represents all the
6 * possible results for possible values of the operands.
7 */
8
9 #ifndef _LINUX_TNUM_H
10 #define _LINUX_TNUM_H
11
12 #include <linux/types.h>
13
14 struct tnum {
15 u64 value;
16 u64 mask;
17 };
18
19 /* Constructors */
20 /* Represent a known constant as a tnum. */
21 struct tnum tnum_const(u64 value);
22 /* A completely unknown value */
23 extern const struct tnum tnum_unknown;
24 /* An unknown value that is a superset of @min <= value <= @max.
25 *
26 * Could include values outside the range of [@min, @max].
27 * For example tnum_range(0, 2) is represented by {0, 1, 2, *3*},
28 * rather than the intended set of {0, 1, 2}.
29 */
30 struct tnum tnum_range(u64 min, u64 max);
31
32 /* Arithmetic and logical ops */
33 /* Shift a tnum left (by a fixed shift) */
34 struct tnum tnum_lshift(struct tnum a, u8 shift);
35 /* Shift (rsh) a tnum right (by a fixed shift) */
36 struct tnum tnum_rshift(struct tnum a, u8 shift);
37 /* Shift (arsh) a tnum right (by a fixed min_shift) */
38 struct tnum tnum_arshift(struct tnum a, u8 min_shift, u8 insn_bitness);
39 /* Add two tnums, return @a + @b */
40 struct tnum tnum_add(struct tnum a, struct tnum b);
41 /* Subtract two tnums, return @a - @b */
42 struct tnum tnum_sub(struct tnum a, struct tnum b);
43 /* Neg of a tnum, return 0 - @a */
44 struct tnum tnum_neg(struct tnum a);
45 /* Bitwise-AND, return @a & @b */
46 struct tnum tnum_and(struct tnum a, struct tnum b);
47 /* Bitwise-OR, return @a | @b */
48 struct tnum tnum_or(struct tnum a, struct tnum b);
49 /* Bitwise-XOR, return @a ^ @b */
50 struct tnum tnum_xor(struct tnum a, struct tnum b);
51 /* Multiply two tnums, return @a * @b */
52 struct tnum tnum_mul(struct tnum a, struct tnum b);
53
54 /* Return true if the known bits of both tnums have the same value */
55 bool tnum_overlap(struct tnum a, struct tnum b);
56
57 /* Return a tnum representing numbers satisfying both @a and @b */
58 struct tnum tnum_intersect(struct tnum a, struct tnum b);
59
60 /* Returns a tnum representing numbers satisfying either @a or @b */
61 struct tnum tnum_union(struct tnum t1, struct tnum t2);
62
63 /* Return @a with all but the lowest @size bytes cleared */
64 struct tnum tnum_cast(struct tnum a, u8 size);
65
66 /* Swap the bytes of a tnum */
67 struct tnum tnum_bswap16(struct tnum a);
68 struct tnum tnum_bswap32(struct tnum a);
69 struct tnum tnum_bswap64(struct tnum a);
70
71 /* Returns true if @a is a known constant */
tnum_is_const(struct tnum a)72 static inline bool tnum_is_const(struct tnum a)
73 {
74 return !a.mask;
75 }
76
77 /* Returns true if @a == tnum_const(@b) */
tnum_equals_const(struct tnum a,u64 b)78 static inline bool tnum_equals_const(struct tnum a, u64 b)
79 {
80 return tnum_is_const(a) && a.value == b;
81 }
82
83 /* Returns true if @a is completely unknown */
tnum_is_unknown(struct tnum a)84 static inline bool tnum_is_unknown(struct tnum a)
85 {
86 return !~a.mask;
87 }
88
89 /* Returns true if @a is known to be a multiple of @size.
90 * @size must be a power of two.
91 */
92 bool tnum_is_aligned(struct tnum a, u64 size);
93
94 /* Returns true if @b represents a subset of @a.
95 *
96 * Note that using tnum_range() as @a requires extra cautions as tnum_in() may
97 * return true unexpectedly due to tnum limited ability to represent tight
98 * range, e.g.
99 *
100 * tnum_in(tnum_range(0, 2), tnum_const(3)) == true
101 *
102 * As a rule of thumb, if @a is explicitly coded rather than coming from
103 * reg->var_off, it should be in form of tnum_const(), tnum_range(0, 2**n - 1),
104 * or tnum_range(2**n, 2**(n+1) - 1).
105 */
106 bool tnum_in(struct tnum a, struct tnum b);
107
108 /* Formatting functions. These have snprintf-like semantics: they will write
109 * up to @size bytes (including the terminating NUL byte), and return the number
110 * of bytes (excluding the terminating NUL) which would have been written had
111 * sufficient space been available. (Thus tnum_sbin always returns 64.)
112 */
113 /* Format a tnum as a pair of hex numbers (value; mask) */
114 int tnum_strn(char *str, size_t size, struct tnum a);
115 /* Format a tnum as tristate binary expansion */
116 int tnum_sbin(char *str, size_t size, struct tnum a);
117
118 /* Returns the 32-bit subreg */
119 struct tnum tnum_subreg(struct tnum a);
120 /* Returns the tnum with the lower 32-bit subreg cleared */
121 struct tnum tnum_clear_subreg(struct tnum a);
122 /* Returns the tnum with the lower 32-bit subreg in *reg* set to the lower
123 * 32-bit subreg in *subreg*
124 */
125 struct tnum tnum_with_subreg(struct tnum reg, struct tnum subreg);
126 /* Returns the tnum with the lower 32-bit subreg set to value */
127 struct tnum tnum_const_subreg(struct tnum a, u32 value);
128 /* Returns true if 32-bit subreg @a is a known constant*/
tnum_subreg_is_const(struct tnum a)129 static inline bool tnum_subreg_is_const(struct tnum a)
130 {
131 return !(tnum_subreg(a)).mask;
132 }
133
134 /* Returns the smallest member of t larger than z */
135 u64 tnum_step(struct tnum t, u64 z);
136
137 #endif /* _LINUX_TNUM_H */
138