// 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_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;
}

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_const_subreg(struct tnum a, u32 value)
{
        return tnum_or(tnum_clear_subreg(a), tnum_const(value));
}