1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
|
// SPDX-License-Identifier: GPL-2.0-only
/* tnum: tracked (or tristate) numbers
*
* A tnum tracks knowledge about the bits of a value. Each bit can be either
* known (0 or 1), or unknown (x). Arithmetic operations on tnums will
* propagate the unknown bits such that the tnum result represents all the
* possible results for possible values of the operands.
*/
#include <linux/kernel.h>
#include <linux/tnum.h>
#define TNUM(_v, _m) (struct tnum){.value = _v, .mask = _m}
/* A completely unknown value */
const struct tnum tnum_unknown = { .value = 0, .mask = -1 };
struct tnum tnum_const(u64 value)
{
return TNUM(value, 0);
}
struct tnum tnum_range(u64 min, u64 max)
{
u64 chi = min ^ max, delta;
u8 bits = fls64(chi);
/* special case, needed because 1ULL << 64 is undefined */
if (bits > 63)
return tnum_unknown;
/* e.g. if chi = 4, bits = 3, delta = (1<<3) - 1 = 7.
* if chi = 0, bits = 0, delta = (1<<0) - 1 = 0, so we return
* constant min (since min == max).
*/
delta = (1ULL << bits) - 1;
return TNUM(min & ~delta, delta);
}
struct tnum tnum_lshift(struct tnum a, u8 shift)
{
return TNUM(a.value << shift, a.mask << shift);
}
struct tnum tnum_rshift(struct tnum a, u8 shift)
{
return TNUM(a.value >> shift, a.mask >> shift);
}
struct tnum tnum_arshift(struct tnum a, u8 min_shift, u8 insn_bitness)
{
/* if a.value is negative, arithmetic shifting by minimum shift
* will have larger negative offset compared to more shifting.
* If a.value is nonnegative, arithmetic shifting by minimum shift
* will have larger positive offset compare to more shifting.
*/
if (insn_bitness == 32)
return TNUM((u32)(((s32)a.value) >> min_shift),
(u32)(((s32)a.mask) >> min_shift));
else
return TNUM((s64)a.value >> min_shift,
(s64)a.mask >> min_shift);
}
struct tnum tnum_add(struct tnum a, struct tnum b)
{
u64 sm, sv, sigma, chi, mu;
sm = a.mask + b.mask;
sv = a.value + b.value;
sigma = sm + sv;
chi = sigma ^ sv;
mu = chi | a.mask | b.mask;
return TNUM(sv & ~mu, mu);
}
struct tnum tnum_sub(struct tnum a, struct tnum b)
{
u64 dv, alpha, beta, chi, mu;
dv = a.value - b.value;
alpha = dv + a.mask;
beta = dv - b.mask;
chi = alpha ^ beta;
mu = chi | a.mask | b.mask;
return TNUM(dv & ~mu, mu);
}
struct tnum tnum_and(struct tnum a, struct tnum b)
{
u64 alpha, beta, v;
alpha = a.value | a.mask;
beta = b.value | b.mask;
v = a.value & b.value;
return TNUM(v, alpha & beta & ~v);
}
struct tnum tnum_or(struct tnum a, struct tnum b)
{
u64 v, mu;
v = a.value | b.value;
mu = a.mask | b.mask;
return TNUM(v, mu & ~v);
}
struct tnum tnum_xor(struct tnum a, struct tnum b)
{
u64 v, mu;
v = a.value ^ b.value;
mu = a.mask | b.mask;
return TNUM(v & ~mu, mu);
}
/* half-multiply add: acc += (unknown * mask * value).
* An intermediate step in the multiply algorithm.
*/
static struct tnum hma(struct tnum acc, u64 value, u64 mask)
{
while (mask) {
if (mask & 1)
acc = tnum_add(acc, TNUM(0, value));
mask >>= 1;
value <<= 1;
}
return acc;
}
struct tnum tnum_mul(struct tnum a, struct tnum b)
{
struct tnum acc;
u64 pi;
pi = a.value * b.value;
acc = hma(TNUM(pi, 0), a.mask, b.mask | b.value);
return hma(acc, b.mask, a.value);
}
/* Note that if a and b disagree - i.e. one has a 'known 1' where the other has
* a 'known 0' - this will return a 'known 1' for that bit.
*/
struct tnum tnum_intersect(struct tnum a, struct tnum b)
{
u64 v, mu;
v = a.value | b.value;
mu = a.mask & b.mask;
return TNUM(v & ~mu, mu);
}
struct tnum tnum_cast(struct tnum a, u8 size)
{
a.value &= (1ULL << (size * 8)) - 1;
a.mask &= (1ULL << (size * 8)) - 1;
return a;
}
bool tnum_is_aligned(struct tnum a, u64 size)
{
if (!size)
return true;
return !((a.value | a.mask) & (size - 1));
}
bool tnum_in(struct tnum a, struct tnum b)
{
if (b.mask & ~a.mask)
return false;
b.value &= ~a.mask;
return a.value == b.value;
}
int tnum_strn(char *str, size_t size, struct tnum a)
{
return snprintf(str, size, "(%#llx; %#llx)", a.value, a.mask);
}
EXPORT_SYMBOL_GPL(tnum_strn);
int tnum_sbin(char *str, size_t size, struct tnum a)
{
size_t n;
for (n = 64; n; n--) {
if (n < size) {
if (a.mask & 1)
str[n - 1] = 'x';
else if (a.value & 1)
str[n - 1] = '1';
else
str[n - 1] = '0';
}
a.mask >>= 1;
a.value >>= 1;
}
str[min(size - 1, (size_t)64)] = 0;
return 64;
}
|
