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 /* tnum: tracked (or tristate) numbers * * A tnum tracks knowledge about the bits of a value. Each bit can be either * known (0 or 1), or unknown (x). Arithmetic operations on tnums will * propagate the unknown bits such that the tnum result represents all the * possible results for possible values of the operands. */ #include #include #define TNUM(_v, _m) (struct tnum){.value = _v, .mask = _m} /* A completely unknown value */ const struct tnum tnum_unknown = { .value = 0, .mask = -1 }; struct tnum tnum_const(u64 value) { return TNUM(value, 0); } struct tnum tnum_range(u64 min, u64 max) { u64 chi = min ^ max, delta; u8 bits = fls64(chi); /* special case, needed because 1ULL << 64 is undefined */ if (bits > 63) return tnum_unknown; /* e.g. if chi = 4, bits = 3, delta = (1<<3) - 1 = 7. * if chi = 0, bits = 0, delta = (1<<0) - 1 = 0, so we return * constant min (since min == max). */ delta = (1ULL << bits) - 1; return TNUM(min & ~delta, delta); } struct tnum tnum_lshift(struct tnum a, u8 shift) { return TNUM(a.value << shift, a.mask << shift); } struct tnum tnum_rshift(struct tnum a, u8 shift) { return TNUM(a.value >> shift, a.mask >> shift); } struct tnum tnum_add(struct tnum a, struct tnum b) { u64 sm, sv, sigma, chi, mu; sm = a.mask + b.mask; sv = a.value + b.value; sigma = sm + sv; chi = sigma ^ sv; mu = chi | a.mask | b.mask; return TNUM(sv & ~mu, mu); } struct tnum tnum_sub(struct tnum a, struct tnum b) { u64 dv, alpha, beta, chi, mu; dv = a.value - b.value; alpha = dv + a.mask; beta = dv - b.mask; chi = alpha ^ beta; mu = chi | a.mask | b.mask; return TNUM(dv & ~mu, mu); } struct tnum tnum_and(struct tnum a, struct tnum b) { u64 alpha, beta, v; alpha = a.value | a.mask; beta = b.value | b.mask; v = a.value & b.value; return TNUM(v, alpha & beta & ~v); } struct tnum tnum_or(struct tnum a, struct tnum b) { u64 v, mu; v = a.value | b.value; mu = a.mask | b.mask; return TNUM(v, mu & ~v); } struct tnum tnum_xor(struct tnum a, struct tnum b) { u64 v, mu; v = a.value ^ b.value; mu = a.mask | b.mask; return TNUM(v & ~mu, mu); } /* half-multiply add: acc += (unknown * mask * value). * An intermediate step in the multiply algorithm. */ static struct tnum hma(struct tnum acc, u64 value, u64 mask) { while (mask) { if (mask & 1) acc = tnum_add(acc, TNUM(0, value)); mask >>= 1; value <<= 1; } return acc; } struct tnum tnum_mul(struct tnum a, struct tnum b) { struct tnum acc; u64 pi; pi = a.value * b.value; acc = hma(TNUM(pi, 0), a.mask, b.mask | b.value); return hma(acc, b.mask, a.value); } /* Note that if a and b disagree - i.e. one has a 'known 1' where the other has * a 'known 0' - this will return a 'known 1' for that bit. */ struct tnum tnum_intersect(struct tnum a, struct tnum b) { u64 v, mu; v = a.value | b.value; mu = a.mask & b.mask; return TNUM(v & ~mu, mu); } struct tnum tnum_cast(struct tnum a, u8 size) { a.value &= (1ULL << (size * 8)) - 1; a.mask &= (1ULL << (size * 8)) - 1; return a; } bool tnum_is_aligned(struct tnum a, u64 size) { if (!size) return true; return !((a.value | a.mask) & (size - 1)); } bool tnum_in(struct tnum a, struct tnum b) { if (b.mask & ~a.mask) return false; b.value &= ~a.mask; return a.value == b.value; } int tnum_strn(char *str, size_t size, struct tnum a) { return snprintf(str, size, "(%#llx; %#llx)", a.value, a.mask); } EXPORT_SYMBOL_GPL(tnum_strn); int tnum_sbin(char *str, size_t size, struct tnum a) { size_t n; for (n = 64; n; n--) { if (n < size) { if (a.mask & 1) str[n - 1] = 'x'; else if (a.value & 1) str[n - 1] = '1'; else str[n - 1] = '0'; } a.mask >>= 1; a.value >>= 1; } str[min(size - 1, (size_t)64)] = 0; return 64; }