4  * A tnum tracks knowledge about the bits of a value.  Each bit can be either
5  * known (0 or 1), or unknown (x).  Arithmetic operations on tnums will
13 /* A completely unknown value */
14 const struct tnum tnum_unknown = { .value = 0, .mask = -1 };
26 	/* special case, needed because 1ULL << 64 is undefined */  in tnum_range()
29 	/* e.g. if chi = 4, bits = 3, delta = (1<<3) - 1 = 7.  in tnum_range()
30 	 * if chi = 0, bits = 0, delta = (1<<0) - 1 = 0, so we return  in tnum_range()
33 	delta = (1ULL << bits) - 1;  in tnum_range()
37 struct tnum tnum_lshift(struct tnum a, u8 shift)  in tnum_lshift()  argument
39 	return TNUM(a.value << shift, a.mask << shift);  in tnum_lshift()
42 struct tnum tnum_rshift(struct tnum a, u8 shift)  in tnum_rshift()  argument
44 	return TNUM(a.value >> shift, a.mask >> shift);  in tnum_rshift()
47 struct tnum tnum_arshift(struct tnum a, u8 min_shift, u8 insn_bitness)  in tnum_arshift()  argument
49 	/* if a.value is negative, arithmetic shifting by minimum shift  in tnum_arshift()
51 	 * If a.value is nonnegative, arithmetic shifting by minimum shift  in tnum_arshift()
55 		return TNUM((u32)(((s32)a.value) >> min_shift),  in tnum_arshift()
56 			    (u32)(((s32)a.mask)  >> min_shift));  in tnum_arshift()
58 		return TNUM((s64)a.value >> min_shift,  in tnum_arshift()
59 			    (s64)a.mask  >> min_shift);  in tnum_arshift()
62 struct tnum tnum_add(struct tnum a, struct tnum b)  in tnum_add()  argument
66 	sm = a.mask + b.mask;  in tnum_add()
67 	sv = a.value + b.value;  in tnum_add()
70 	mu = chi | a.mask | b.mask;  in tnum_add()
74 struct tnum tnum_sub(struct tnum a, struct tnum b)  in tnum_sub()  argument
78 	dv = a.value - b.value;  in tnum_sub()
79 	alpha = dv + a.mask;  in tnum_sub()
82 	mu = chi | a.mask | b.mask;  in tnum_sub()
86 struct tnum tnum_and(struct tnum a, struct tnum b)  in tnum_and()  argument
90 	alpha = a.value | a.mask;  in tnum_and()
92 	v = a.value & b.value;  in tnum_and()
96 struct tnum tnum_or(struct tnum a, struct tnum b)  in tnum_or()  argument
100 	v = a.value | b.value;  in tnum_or()
101 	mu = a.mask | b.mask;  in tnum_or()
105 struct tnum tnum_xor(struct tnum a, struct tnum b)  in tnum_xor()  argument
109 	v = a.value ^ b.value;  in tnum_xor()
110 	mu = a.mask | b.mask;  in tnum_xor()
114 /* Generate partial products by multiplying each bit in the multiplier (tnum a)
122 struct tnum tnum_mul(struct tnum a, struct tnum b)  in tnum_mul()  argument
124 	u64 acc_v = a.value * b.value;  in tnum_mul()
127 	while (a.value || a.mask) {  in tnum_mul()
128 		/* LSB of tnum a is a certain 1 */  in tnum_mul()
129 		if (a.value & 1)  in tnum_mul()
131 		/* LSB of tnum a is uncertain */  in tnum_mul()
132 		else if (a.mask & 1)  in tnum_mul()
135 		a = tnum_rshift(a, 1);  in tnum_mul()
136 		b = tnum_lshift(b, 1);  in tnum_mul()
141 /* Note that if a and b disagree - i.e. one has a 'known 1' where the other has
142  * a 'known 0' - this will return a 'known 1' for that bit.
144 struct tnum tnum_intersect(struct tnum a, struct tnum b)  in tnum_intersect()  argument
148 	v = a.value | b.value;  in tnum_intersect()
149 	mu = a.mask & b.mask;  in tnum_intersect()
153 struct tnum tnum_cast(struct tnum a, u8 size)  in tnum_cast()  argument
155 	a.value &= (1ULL << (size * 8)) - 1;  in tnum_cast()
156 	a.mask &= (1ULL << (size * 8)) - 1;  in tnum_cast()
157 	return a;  in tnum_cast()
160 bool tnum_is_aligned(struct tnum a, u64 size)  in tnum_is_aligned()  argument
164 	return !((a.value | a.mask) & (size - 1));  in tnum_is_aligned()
167 bool tnum_in(struct tnum a, struct tnum b)  in tnum_in()  argument
169 	if (b.mask & ~a.mask)  in tnum_in()
171 	b.value &= ~a.mask;  in tnum_in()
172 	return a.value == b.value;  in tnum_in()
175 int tnum_sbin(char *str, size_t size, struct tnum a)  in tnum_sbin()  argument
181 			if (a.mask & 1)  in tnum_sbin()
182 				str[n - 1] = 'x';  in tnum_sbin()
183 			else if (a.value & 1)  in tnum_sbin()
184 				str[n - 1] = '1';  in tnum_sbin()
186 				str[n - 1] = '0';  in tnum_sbin()
188 		a.mask >>= 1;  in tnum_sbin()
189 		a.value >>= 1;  in tnum_sbin()
191 	str[min(size - 1, (size_t)64)] = 0;  in tnum_sbin()
195 struct tnum tnum_subreg(struct tnum a)  in tnum_subreg()  argument
197 	return tnum_cast(a, 4);  in tnum_subreg()
200 struct tnum tnum_clear_subreg(struct tnum a)  in tnum_clear_subreg()  argument
202 	return tnum_lshift(tnum_rshift(a, 32), 32);  in tnum_clear_subreg()
210 struct tnum tnum_const_subreg(struct tnum a, u32 value)  in tnum_const_subreg()  argument
212 	return tnum_with_subreg(a, tnum_const(value));  in tnum_const_subreg()