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] = '0'; 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