1 files changed, 214 insertions, 0 deletions
diff --git a/kernel/bpf/tnum.c b/kernel/bpf/tnum.c
new file mode 100644
index 000000000..3d7127f43
--- /dev/null
+++ b/kernel/bpf/tnum.c
@@ -0,0 +1,214 @@
+// 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));
+}