xref: /linux/kernel/bpf/tnum.c (revision 32e940f2bd3b16551f23ea44be47f6f5d1746d64) !

// 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;
}