// SPDX-License-Identifier: GPL-2.0-only
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/* tnum: tracked (or tristate) numbers
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*
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* A tnum tracks knowledge about the bits of a value. Each bit can be either
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* known (0 or 1), or unknown (x). Arithmetic operations on tnums will
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* propagate the unknown bits such that the tnum result represents all the
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* possible results for possible values of the operands.
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*/
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#include <linux/kernel.h>
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#include <linux/tnum.h>
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#define TNUM(_v, _m) (struct tnum){.value = _v, .mask = _m}
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/* A completely unknown value */
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const struct tnum tnum_unknown = { .value = 0, .mask = -1 };
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struct tnum tnum_const(u64 value)
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{
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return TNUM(value, 0);
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}
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struct tnum tnum_range(u64 min, u64 max)
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{
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u64 chi = min ^ max, delta;
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u8 bits = fls64(chi);
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/* special case, needed because 1ULL << 64 is undefined */
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if (bits > 63)
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return tnum_unknown;
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/* e.g. if chi = 4, bits = 3, delta = (1<<3) - 1 = 7.
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* if chi = 0, bits = 0, delta = (1<<0) - 1 = 0, so we return
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* constant min (since min == max).
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*/
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delta = (1ULL << bits) - 1;
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return TNUM(min & ~delta, delta);
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}
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struct tnum tnum_lshift(struct tnum a, u8 shift)
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{
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return TNUM(a.value << shift, a.mask << shift);
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}
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struct tnum tnum_rshift(struct tnum a, u8 shift)
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{
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return TNUM(a.value >> shift, a.mask >> shift);
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}
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struct tnum tnum_arshift(struct tnum a, u8 min_shift, u8 insn_bitness)
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{
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/* if a.value is negative, arithmetic shifting by minimum shift
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* will have larger negative offset compared to more shifting.
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* If a.value is nonnegative, arithmetic shifting by minimum shift
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* will have larger positive offset compare to more shifting.
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*/
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if (insn_bitness == 32)
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return TNUM((u32)(((s32)a.value) >> min_shift),
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(u32)(((s32)a.mask) >> min_shift));
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else
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return TNUM((s64)a.value >> min_shift,
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(s64)a.mask >> min_shift);
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}
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struct tnum tnum_add(struct tnum a, struct tnum b)
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{
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u64 sm, sv, sigma, chi, mu;
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sm = a.mask + b.mask;
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sv = a.value + b.value;
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sigma = sm + sv;
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chi = sigma ^ sv;
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mu = chi | a.mask | b.mask;
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return TNUM(sv & ~mu, mu);
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}
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struct tnum tnum_sub(struct tnum a, struct tnum b)
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{
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u64 dv, alpha, beta, chi, mu;
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dv = a.value - b.value;
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alpha = dv + a.mask;
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beta = dv - b.mask;
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chi = alpha ^ beta;
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mu = chi | a.mask | b.mask;
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return TNUM(dv & ~mu, mu);
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}
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struct tnum tnum_and(struct tnum a, struct tnum b)
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{
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u64 alpha, beta, v;
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alpha = a.value | a.mask;
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beta = b.value | b.mask;
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v = a.value & b.value;
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return TNUM(v, alpha & beta & ~v);
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}
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struct tnum tnum_or(struct tnum a, struct tnum b)
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{
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u64 v, mu;
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v = a.value | b.value;
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mu = a.mask | b.mask;
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return TNUM(v, mu & ~v);
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}
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struct tnum tnum_xor(struct tnum a, struct tnum b)
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{
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u64 v, mu;
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v = a.value ^ b.value;
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mu = a.mask | b.mask;
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return TNUM(v & ~mu, mu);
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}
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/* half-multiply add: acc += (unknown * mask * value).
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* An intermediate step in the multiply algorithm.
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*/
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static struct tnum hma(struct tnum acc, u64 value, u64 mask)
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{
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while (mask) {
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if (mask & 1)
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acc = tnum_add(acc, TNUM(0, value));
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mask >>= 1;
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value <<= 1;
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}
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return acc;
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}
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struct tnum tnum_mul(struct tnum a, struct tnum b)
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{
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struct tnum acc;
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u64 pi;
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pi = a.value * b.value;
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acc = hma(TNUM(pi, 0), a.mask, b.mask | b.value);
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return hma(acc, b.mask, a.value);
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}
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/* Note that if a and b disagree - i.e. one has a 'known 1' where the other has
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* a 'known 0' - this will return a 'known 1' for that bit.
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*/
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struct tnum tnum_intersect(struct tnum a, struct tnum b)
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{
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u64 v, mu;
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v = a.value | b.value;
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mu = a.mask & b.mask;
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return TNUM(v & ~mu, mu);
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}
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struct tnum tnum_cast(struct tnum a, u8 size)
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{
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a.value &= (1ULL << (size * 8)) - 1;
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a.mask &= (1ULL << (size * 8)) - 1;
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return a;
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}
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bool tnum_is_aligned(struct tnum a, u64 size)
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{
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if (!size)
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return true;
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return !((a.value | a.mask) & (size - 1));
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}
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bool tnum_in(struct tnum a, struct tnum b)
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{
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if (b.mask & ~a.mask)
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return false;
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b.value &= ~a.mask;
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return a.value == b.value;
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}
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int tnum_strn(char *str, size_t size, struct tnum a)
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{
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return snprintf(str, size, "(%#llx; %#llx)", a.value, a.mask);
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}
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EXPORT_SYMBOL_GPL(tnum_strn);
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int tnum_sbin(char *str, size_t size, struct tnum a)
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{
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size_t n;
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for (n = 64; n; n--) {
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if (n < size) {
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if (a.mask & 1)
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str[n - 1] = 'x';
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else if (a.value & 1)
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str[n - 1] = '1';
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else
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str[n - 1] = '0';
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}
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a.mask >>= 1;
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a.value >>= 1;
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}
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str[min(size - 1, (size_t)64)] = 0;
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return 64;
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}
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struct tnum tnum_subreg(struct tnum a)
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{
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return tnum_cast(a, 4);
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}
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struct tnum tnum_clear_subreg(struct tnum a)
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{
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return tnum_lshift(tnum_rshift(a, 32), 32);
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}
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struct tnum tnum_const_subreg(struct tnum a, u32 value)
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{
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return tnum_or(tnum_clear_subreg(a), tnum_const(value));
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}
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