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// SPDX-License-Identifier: GPL-2.0-only
/* 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 <linux/kernel.h>
#include <linux/tnum.h>
#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_arshift(struct tnum a, u8 min_shift, u8 insn_bitness)
{
/* if a.value is negative, arithmetic shifting by minimum shift
* will have larger negative offset compared to more shifting.
* If a.value is nonnegative, arithmetic shifting by minimum shift
* will have larger positive offset compare to more shifting.
*/
if (insn_bitness == 32)
return TNUM((u32)(((s32)a.value) >> min_shift),
(u32)(((s32)a.mask) >> min_shift));
else
return TNUM((s64)a.value >> min_shift,
(s64)a.mask >> min_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);
}
/* Generate partial products by multiplying each bit in the multiplier (tnum a)
* with the multiplicand (tnum b), and add the partial products after
* appropriately bit-shifting them. Instead of directly performing tnum addition
* on the generated partial products, equivalenty, decompose each partial
* product into two tnums, consisting of the value-sum (acc_v) and the
* mask-sum (acc_m) and then perform tnum addition on them. The following paper
* explains the algorithm in more detail: https://arxiv.org/abs/2105.05398.
*/
struct tnum tnum_mul(struct tnum a, struct tnum b)
{
u64 acc_v = a.value * b.value;
struct tnum acc_m = TNUM(0, 0);
while (a.value || a.mask) {
/* LSB of tnum a is a certain 1 */
if (a.value & 1)
acc_m = tnum_add(acc_m, TNUM(0, b.mask));
/* LSB of tnum a is uncertain */
else if (a.mask & 1)
acc_m = tnum_add(acc_m, TNUM(0, b.value | b.mask));
/* Note: no case for LSB is certain 0 */
a = tnum_rshift(a, 1);
b = tnum_lshift(b, 1);
}
return tnum_add(TNUM(acc_v, 0), acc_m);
}
/* 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_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;
}
struct tnum tnum_subreg(struct tnum a)
{
return tnum_cast(a, 4);
}
struct tnum tnum_clear_subreg(struct tnum a)
{
return tnum_lshift(tnum_rshift(a, 32), 32);
}
struct tnum tnum_with_subreg(struct tnum reg, struct tnum subreg)
{
return tnum_or(tnum_clear_subreg(reg), tnum_subreg(subreg));
}
struct tnum tnum_const_subreg(struct tnum a, u32 value)
{
return tnum_with_subreg(a, tnum_const(value));
}
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