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