// 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>
#include <linux/swab.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_neg(struct tnum a)
{
        return tnum_sub(TNUM(0, 0), a);
}

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);
}

/* Perform long multiplication, iterating through the bits in a using rshift:
 * - if LSB(a) is a known 0, keep current accumulator
 * - if LSB(a) is a known 1, add b to current accumulator
 * - if LSB(a) is unknown, take a union of the above cases.
 *
 * For example:
 *
 *               acc_0:        acc_1:
 *
 *     11 *  ->      11 *  ->      11 *  -> union(0011, 1001) == x0x1
 *     x1            01            11
 * ------        ------        ------
 *     11            11            11
 *    xx            00            11
 * ------        ------        ------
 *   ????          0011          1001
 */
struct tnum tnum_mul(struct tnum a, struct tnum b)
{
        struct tnum acc = TNUM(0, 0);

        while (a.value || a.mask) {
                /* LSB of tnum a is a certain 1 */
                if (a.value & 1)
                        acc = tnum_add(acc, b);
                /* LSB of tnum a is uncertain */
                else if (a.mask & 1) {
                        /* acc = tnum_union(acc_0, acc_1), where acc_0 and
                         * acc_1 are partial accumulators for cases
                         * LSB(a) = certain 0 and LSB(a) = certain 1.
                         * acc_0 = acc + 0 * b = acc.
                         * acc_1 = acc + 1 * b = tnum_add(acc, b).
                         */

                        acc = tnum_union(acc, tnum_add(acc, b));
                }
                /* Note: no case for LSB is certain 0 */
                a = tnum_rshift(a, 1);
                b = tnum_lshift(b, 1);
        }
        return acc;
}

bool tnum_overlap(struct tnum a, struct tnum b)
{
        u64 mu;

        mu = ~a.mask & ~b.mask;
        return (a.value & mu) == (b.value & mu);
}

/* 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);
}

/* Returns a tnum with the uncertainty from both a and b, and in addition, new
 * uncertainty at any position that a and b disagree. This represents a
 * superset of the union of the concrete sets of both a and b. Despite the
 * overapproximation, it is optimal.
 */
struct tnum tnum_union(struct tnum a, struct tnum b)
{
        u64 v = a.value & b.value;
        u64 mu = (a.value ^ b.value) | 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));
}

struct tnum tnum_bswap16(struct tnum a)
{
        return TNUM(swab16(a.value & 0xFFFF), swab16(a.mask & 0xFFFF));
}

struct tnum tnum_bswap32(struct tnum a)
{
        return TNUM(swab32(a.value & 0xFFFFFFFF), swab32(a.mask & 0xFFFFFFFF));
}

struct tnum tnum_bswap64(struct tnum a)
{
        return TNUM(swab64(a.value), swab64(a.mask));
}

/* Given tnum t, and a number z such that tmin <= z < tmax, where tmin
 * is the smallest member of the t (= t.value) and tmax is the largest
 * member of t (= t.value | t.mask), returns the smallest member of t
 * larger than z.
 *
 * For example,
 * t      = x11100x0
 * z      = 11110001 (241)
 * result = 11110010 (242)
 *
 * Note: if this function is called with z >= tmax, it just returns
 * early with tmax; if this function is called with z < tmin, the
 * algorithm already returns tmin.
 */
u64 tnum_step(struct tnum t, u64 z)
{
        u64 tmax, d, carry_mask, filled, inc;

        tmax = t.value | t.mask;

        /* if z >= largest member of t, return largest member of t */
        if (z >= tmax)
                return tmax;

        /* if z < smallest member of t, return smallest member of t */
        if (z < t.value)
                return t.value;

        /*
         * Let r be the result tnum member, z = t.value + d.
         * Every tnum member is t.value | s for some submask s of t.mask,
         * and since t.value & t.mask == 0, t.value | s == t.value + s.
         * So r > z becomes s > d where d = z - t.value.
         *
         * Find the smallest submask s of t.mask greater than d by
         * "incrementing d within the mask": fill every non-mask
         * position with 1 (`filled`) so +1 ripples through the gaps,
         * then keep only mask bits. `carry_mask` additionally fills
         * positions below the highest non-mask 1 in d, preventing
         * it from trapping the carry.
         */
        d = z - t.value;
        carry_mask = (1ULL << fls64(d & ~t.mask)) - 1;
        filled = d | carry_mask | ~t.mask;
        inc = (filled + 1) & t.mask;
        return t.value | inc;
}