// 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));}