kernel/bpf/tnum.c

   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_arshift(struct tnum a, u8 min_shift)
  47 {
  48         /* if a.value is negative, arithmetic shifting by minimum shift
  49          * will have larger negative offset compared to more shifting.
  50          * If a.value is nonnegative, arithmetic shifting by minimum shift
  51          * will have larger positive offset compare to more shifting.
  52          */
  53         return TNUM((s64)a.value >> min_shift, (s64)a.mask >> min_shift);
  54 }
  55
  56 struct tnum tnum_add(struct tnum a, struct tnum b)
  57 {
  58         u64 sm, sv, sigma, chi, mu;
  59
  60         sm = a.mask + b.mask;
  61         sv = a.value + b.value;
  62         sigma = sm + sv;
  63         chi = sigma ^ sv;
  64         mu = chi | a.mask | b.mask;
  65         return TNUM(sv & ~mu, mu);
  66 }
  67
  68 struct tnum tnum_sub(struct tnum a, struct tnum b)
  69 {
  70         u64 dv, alpha, beta, chi, mu;
  71
  72         dv = a.value - b.value;
  73         alpha = dv + a.mask;
  74         beta = dv - b.mask;
  75         chi = alpha ^ beta;
  76         mu = chi | a.mask | b.mask;
  77         return TNUM(dv & ~mu, mu);
  78 }
  79
  80 struct tnum tnum_and(struct tnum a, struct tnum b)
  81 {
  82         u64 alpha, beta, v;
  83
  84         alpha = a.value | a.mask;
  85         beta = b.value | b.mask;
  86         v = a.value & b.value;
  87         return TNUM(v, alpha & beta & ~v);
  88 }
  89
  90 struct tnum tnum_or(struct tnum a, struct tnum b)
  91 {
  92         u64 v, mu;
  93
  94         v = a.value | b.value;
  95         mu = a.mask | b.mask;
  96         return TNUM(v, mu & ~v);
  97 }
  98
  99 struct tnum tnum_xor(struct tnum a, struct tnum b)
 100 {
 101         u64 v, mu;
 102
 103         v = a.value ^ b.value;
 104         mu = a.mask | b.mask;
 105         return TNUM(v & ~mu, mu);
 106 }
 107
 108 /* half-multiply add: acc += (unknown * mask * value).
 109  * An intermediate step in the multiply algorithm.
 110  */
 111 static struct tnum hma(struct tnum acc, u64 value, u64 mask)
 112 {
 113         while (mask) {
 114                 if (mask & 1)
 115                         acc = tnum_add(acc, TNUM(0, value));
 116                 mask >>= 1;
 117                 value <<= 1;
 118         }
 119         return acc;
 120 }
 121
 122 struct tnum tnum_mul(struct tnum a, struct tnum b)
 123 {
 124         struct tnum acc;
 125         u64 pi;
 126
 127         pi = a.value * b.value;
 128         acc = hma(TNUM(pi, 0), a.mask, b.mask | b.value);
 129         return hma(acc, b.mask, a.value);
 130 }
 131
 132 /* Note that if a and b disagree - i.e. one has a 'known 1' where the other has
 133  * a 'known 0' - this will return a 'known 1' for that bit.
 134  */
 135 struct tnum tnum_intersect(struct tnum a, struct tnum b)
 136 {
 137         u64 v, mu;
 138
 139         v = a.value | b.value;
 140         mu = a.mask & b.mask;
 141         return TNUM(v & ~mu, mu);
 142 }
 143
 144 struct tnum tnum_cast(struct tnum a, u8 size)
 145 {
 146         a.value &= (1ULL << (size * 8)) - 1;
 147         a.mask &= (1ULL << (size * 8)) - 1;
 148         return a;
 149 }
 150
 151 bool tnum_is_aligned(struct tnum a, u64 size)
 152 {
 153         if (!size)
 154                 return true;
 155         return !((a.value | a.mask) & (size - 1));
 156 }
 157
 158 bool tnum_in(struct tnum a, struct tnum b)
 159 {
 160         if (b.mask & ~a.mask)
 161                 return false;
 162         b.value &= ~a.mask;
 163         return a.value == b.value;
 164 }
 165
 166 int tnum_strn(char *str, size_t size, struct tnum a)
 167 {
 168         return snprintf(str, size, "(%#llx; %#llx)", a.value, a.mask);
 169 }
 170 EXPORT_SYMBOL_GPL(tnum_strn);
 171
 172 int tnum_sbin(char *str, size_t size, struct tnum a)
 173 {
 174         size_t n;
 175
 176         for (n = 64; n; n--) {
 177                 if (n < size) {
 178                         if (a.mask & 1)
 179                                 str[n - 1] = 'x';
 180                         else if (a.value & 1)
 181                                 str[n - 1] = '1';
 182                         else
 183                                 str[n - 1] = '0';
 184                 }
 185                 a.mask >>= 1;
 186                 a.value >>= 1;
 187         }
 188         str[min(size - 1, (size_t)64)] = 0;
 189         return 64;
 190 }