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_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 }