1 // SPDX-License-Identifier: GPL-2.0-only
2 /* tnum: tracked (or tristate) numbers
3 *
4 * A tnum tracks knowledge about the bits of a value. Each bit can be either
5 * known (0 or 1), or unknown (x). Arithmetic operations on tnums will
6 * propagate the unknown bits such that the tnum result represents all the
7 * possible results for possible values of the operands.
8 */
9 #include <linux/kernel.h>
10 #include <linux/tnum.h>
11
12 #define TNUM(_v, _m) (struct tnum){.value = _v, .mask = _m}
13 /* A completely unknown value */
14 const struct tnum tnum_unknown = { .value = 0, .mask = -1 };
15
16 struct tnum tnum_const(u64 value)
17 {
18 return TNUM(value, 0);
19 }
20
21 struct tnum tnum_range(u64 min, u64 max)
22 {
23 u64 chi = min ^ max, delta;
24 u8 bits = fls64(chi);
25
26 /* special case, needed because 1ULL << 64 is undefined */
27 if (bits > 63)
28 return tnum_unknown;
29 /* e.g. if chi = 4, bits = 3, delta = (1<<3) - 1 = 7.
30 * if chi = 0, bits = 0, delta = (1<<0) - 1 = 0, so we return
31 * constant min (since min == max).
32 */
33 delta = (1ULL << bits) - 1;
34 return TNUM(min & ~delta, delta);
35 }
36
37 struct tnum tnum_lshift(struct tnum a, u8 shift)
38 {
39 return TNUM(a.value << shift, a.mask << shift);
40 }
41
42 struct tnum tnum_rshift(struct tnum a, u8 shift)
43 {
44 return TNUM(a.value >> shift, a.mask >> shift);
45 }
46
47 struct tnum tnum_arshift(struct tnum a, u8 min_shift, u8 insn_bitness)
48 {
49 /* if a.value is negative, arithmetic shifting by minimum shift
50 * will have larger negative offset compared to more shifting.
51 * If a.value is nonnegative, arithmetic shifting by minimum shift
52 * will have larger positive offset compare to more shifting.
53 */
54 if (insn_bitness == 32)
55 return TNUM((u32)(((s32)a.value) >> min_shift),
56 (u32)(((s32)a.mask) >> min_shift));
57 else
58 return TNUM((s64)a.value >> min_shift,
59 (s64)a.mask >> min_shift);
60 }
61
62 struct tnum tnum_add(struct tnum a, struct tnum b)
63 {
64 u64 sm, sv, sigma, chi, mu;
65
66 sm = a.mask + b.mask;
67 sv = a.value + b.value;
68 sigma = sm + sv;
69 chi = sigma ^ sv;
70 mu = chi | a.mask | b.mask;
71 return TNUM(sv & ~mu, mu);
72 }
73
74 struct tnum tnum_sub(struct tnum a, struct tnum b)
75 {
76 u64 dv, alpha, beta, chi, mu;
77
78 dv = a.value - b.value;
79 alpha = dv + a.mask;
80 beta = dv - b.mask;
81 chi = alpha ^ beta;
82 mu = chi | a.mask | b.mask;
83 return TNUM(dv & ~mu, mu);
84 }
85
86 struct tnum tnum_and(struct tnum a, struct tnum b)
87 {
88 u64 alpha, beta, v;
89
90 alpha = a.value | a.mask;
91 beta = b.value | b.mask;
92 v = a.value & b.value;
93 return TNUM(v, alpha & beta & ~v);
94 }
95
96 struct tnum tnum_or(struct tnum a, struct tnum b)
97 {
98 u64 v, mu;
99
100 v = a.value | b.value;
101 mu = a.mask | b.mask;
102 return TNUM(v, mu & ~v);
103 }
104
105 struct tnum tnum_xor(struct tnum a, struct tnum b)
106 {
107 u64 v, mu;
108
109 v = a.value ^ b.value;
110 mu = a.mask | b.mask;
111 return TNUM(v & ~mu, mu);
112 }
113
114 /* Generate partial products by multiplying each bit in the multiplier (tnum a)
115 * with the multiplicand (tnum b), and add the partial products after
116 * appropriately bit-shifting them. Instead of directly performing tnum addition
117 * on the generated partial products, equivalenty, decompose each partial
118 * product into two tnums, consisting of the value-sum (acc_v) and the
119 * mask-sum (acc_m) and then perform tnum addition on them. The following paper
120 * explains the algorithm in more detail: https://arxiv.org/abs/2105.05398.
121 */
122 struct tnum tnum_mul(struct tnum a, struct tnum b)
123 {
124 u64 acc_v = a.value * b.value;
125 struct tnum acc_m = TNUM(0, 0);
126
127 while (a.value || a.mask) {
128 /* LSB of tnum a is a certain 1 */
129 if (a.value & 1)
130 acc_m = tnum_add(acc_m, TNUM(0, b.mask));
131 /* LSB of tnum a is uncertain */
132 else if (a.mask & 1)
133 acc_m = tnum_add(acc_m, TNUM(0, b.value | b.mask));
134 /* Note: no case for LSB is certain 0 */
135 a = tnum_rshift(a, 1);
136 b = tnum_lshift(b, 1);
137 }
138 return tnum_add(TNUM(acc_v, 0), acc_m);
139 }
140
141 /* Note that if a and b disagree - i.e. one has a 'known 1' where the other has
142 * a 'known 0' - this will return a 'known 1' for that bit.
143 */
144 struct tnum tnum_intersect(struct tnum a, struct tnum b)
145 {
146 u64 v, mu;
147
148 v = a.value | b.value;
149 mu = a.mask & b.mask;
150 return TNUM(v & ~mu, mu);
151 }
152
153 struct tnum tnum_cast(struct tnum a, u8 size)
154 {
155 a.value &= (1ULL << (size * 8)) - 1;
156 a.mask &= (1ULL << (size * 8)) - 1;
157 return a;
158 }
159
160 bool tnum_is_aligned(struct tnum a, u64 size)
161 {
162 if (!size)
163 return true;
164 return !((a.value | a.mask) & (size - 1));
165 }
166
167 bool tnum_in(struct tnum a, struct tnum b)
168 {
169 if (b.mask & ~a.mask)
170 return false;
171 b.value &= ~a.mask;
172 return a.value == b.value;
173 }
174
175 int tnum_sbin(char *str, size_t size, struct tnum a)
176 {
177 size_t n;
178
179 for (n = 64; n; n--) {
180 if (n < size) {
181 if (a.mask & 1)
182 str[n - 1] = 'x';
183 else if (a.value & 1)
184 str[n - 1] = '1';
185 else
186 str[n - 1] = '';
187 }
188 a.mask >>= 1;
189 a.value >>= 1;
190 }
191 str[min(size - 1, (size_t)64)] = 0;
192 return 64;
193 }
194
195 struct tnum tnum_subreg(struct tnum a)
196 {
197 return tnum_cast(a, 4);
198 }
199
200 struct tnum tnum_clear_subreg(struct tnum a)
201 {
202 return tnum_lshift(tnum_rshift(a, 32), 32);
203 }
204
205 struct tnum tnum_with_subreg(struct tnum reg, struct tnum subreg)
206 {
207 return tnum_or(tnum_clear_subreg(reg), tnum_subreg(subreg));
208 }
209
210 struct tnum tnum_const_subreg(struct tnum a, u32 value)
211 {
212 return tnum_with_subreg(a, tnum_const(value));
213 }
214
Linux® is a registered trademark of Linus Torvalds in the United States and other countries.
TOMOYO® is a registered trademark of NTT DATA CORPORATION.