1;; Rewrites for `band`, `bnot`, `bor`, `bxor`
2
3;; x | 0 == x | x == x.
4(rule (simplify (bor ty
5                     x
6                     (iconst_u ty 0)))
7      (subsume x))
8(rule (simplify (bor ty x x))
9      (subsume x))
10
11;; x ^ 0 == x.
12(rule (simplify (bxor ty
13                     x
14                     (iconst_u ty 0)))
15      (subsume x))
16
17;; x ^ x == 0.
18(rule (simplify (bxor (ty_int ty) x x))
19      (subsume (iconst_u ty 0)))
20
21;; x ^ not(x) == not(x) ^ x == x | not(x) == not(x) | x == -1.
22;; This identity also holds for non-integer types, vectors, and wider types.
23(rule (simplify (bxor (ty_int ty) x (bnot ty x))) (subsume (iconst_s ty -1)))
24(rule (simplify (bxor (ty_int ty) (bnot ty x) x)) (subsume (iconst_s ty -1)))
25(rule (simplify (bor (ty_int ty) x (bnot ty x))) (subsume (iconst_s ty -1)))
26(rule (simplify (bor (ty_int ty) (bnot ty x) x)) (subsume (iconst_s ty -1)))
27
28;; x & x == x & -1 == x.
29(rule (simplify (band ty x x)) (subsume x))
30(rule (simplify (band ty x (iconst_s ty -1)))
31      (subsume x))
32
33;; x & 0 == x & not(x) == not(x) & x == 0.
34(rule (simplify (band ty _ zero @ (iconst_u ty 0))) (subsume zero))
35(rule (simplify (band (ty_int ty) x (bnot ty x))) (subsume (iconst_u ty 0)))
36(rule (simplify (band (ty_int ty) (bnot ty x) x)) (subsume (iconst_u ty 0)))
37
38;; not(not(x)) == x.
39(rule (simplify (bnot ty (bnot ty x))) (subsume x))
40
41;; DeMorgan's rule (two versions):
42;; bnot(bor(x, y)) == band(bnot(x), bnot(y))
43(rule (simplify (bnot ty (bor ty x y)))
44      (band ty (bnot ty x) (bnot ty y)))
45;; bnot(band(x, y)) == bor(bnot(x), bnot(y))
46(rule (simplify (bnot ty (band t x y)))
47      (bor ty (bnot ty x) (bnot ty y)))
48
49;; `or(and(x, y), not(y)) == or(x, not(y))`
50(rule (simplify (bor ty
51                     (band ty x y)
52                     z @ (bnot ty y)))
53      (bor ty x z))
54;; Duplicate the rule but swap the `bor` operands because `bor` is
55;; commutative. We could, of course, add a `simplify` rule to do the commutative
56;; swap for all `bor`s but this will bloat the e-graph with many e-nodes. It is
57;; cheaper to have additional rules, rather than additional e-nodes, because we
58;; amortize their cost via ISLE's smart codegen.
59(rule (simplify (bor ty
60                     z @ (bnot ty y)
61                     (band ty x y)))
62      (bor ty x z))
63
64;; `or(and(x, y), not(y)) == or(x, not(y))` specialized for constants, since
65;; otherwise we may not know that `z == not(y)` since we don't generally expand
66;; constants in the e-graph.
67;;
68;; (No need to duplicate for commutative `bor` for this constant version because
69;; we move constants to the right.)
70(rule (simplify (bor ty
71                     (band ty x (iconst_u ty y))
72                     z @ (iconst_u ty zk)))
73      (if-let true (u64_eq (u64_and (ty_mask ty) zk)
74                            (u64_and (ty_mask ty) (u64_not y))))
75      (bor ty x z))
76
77;; (x ^ -1) can be replaced with the `bnot` instruction
78(rule (simplify (bxor ty x (iconst_s ty -1)))
79  (bnot ty x))
80
81;; sshr((x | -x), N) == bmask(x) where N = ty_bits(ty) - 1.
82;;
83;; (x | -x) sets the sign bit to 1 if x is nonzero, and 0 if x is zero. sshr propagates
84;; the sign bit to the rest of the value.
85(rule (simplify (sshr ty (bor ty x (ineg ty x)) (iconst_u ty shift_amt)))
86      (if-let true (u64_eq shift_amt (ty_shift_mask ty)))
87      (bmask ty x))
88
89(rule (simplify (sshr ty (bor ty (ineg ty x) x) (iconst_u ty shift_amt)))
90      (if-let true (u64_eq shift_amt (ty_shift_mask ty)))
91      (bmask ty x))
92
93;; Since icmp is always 0 or 1, bmask is just a negation.
94;; TODO: Explore whether this makes sense for things needing extension too.
95(rule (simplify (bmask $I8 cmp@(icmp $I8 _ _ _)))
96      (ineg $I8 cmp))
97
98;; Matches any expressions that preserve "truthiness".
99;; i.e. If the input is zero it remains zero, and if it is nonzero it can have
100;; a different value as long as it is still nonzero.
101(decl pure multi truthy (Value) Value)
102(rule (truthy (sextend _ x)) x)
103(rule (truthy (uextend _ x)) x)
104(rule (truthy (bmask _ x)) x)
105(rule (truthy (ineg _ x)) x)
106(rule (truthy (bswap _ x)) x)
107(rule (truthy (bitrev _ x)) x)
108(rule (truthy (popcnt _ x)) x)
109(rule (truthy (rotl _ x _)) x)
110(rule (truthy (rotr _ x _)) x)
111(rule (truthy (select _ x (iconst_u _ (u64_nonzero _)) (iconst_u _ 0))) x)
112;; (ne ty (iconst 0) v) is also canonicalized into this form via another rule
113(rule (truthy (ne _ x (iconst_u _ 0))) x)
114
115;; All of these expressions don't care about their input as long as it is truthy.
116;; so we can remove expressions that preserve that property from the input.
117(rule (simplify (bmask ty v)) (if-let x (truthy v)) (bmask ty x))
118(rule (simplify (select ty v t f)) (if-let c (truthy v)) (select ty c t f))
119;; (ne ty (iconst 0) v) is also canonicalized into this form via another rule
120(rule (simplify (ne cty v (iconst_u _ 0)))
121      (if-let c (truthy v))
122      (if-let (value_type (ty_int_ref_scalar_64 ty)) c)
123      (ne cty c (iconst_u ty 0)))
124
125
126
127;; (sextend (bmask x)) can be replaced with (bmask x) since bmask
128;; supports any size of output type, regardless of input.
129;; Same with `ireduce`
130(rule (simplify (sextend ty (bmask _ x))) (bmask ty x))
131(rule (simplify (ireduce ty (bmask _ x))) (bmask ty x))
132
133;; (bswap (bswap x)) == x
134(rule (simplify (bswap ty (bswap ty x))) (subsume x))
135
136;; (bitrev (bitrev x)) == x
137(rule (simplify (bitrev ty (bitrev ty x))) (subsume x))
138
139;; WebAssembly doesn't have a native byte-swapping instruction at this time so
140;; languages which have a byte-swapping operation will compile it down to bit
141;; shifting and twiddling. This attempts to pattern match what LLVM currently
142;; generates today for the Rust code `a.swap_bytes()`. This might be a bit
143;; brittle over time and/or with other possible LLVM backend optimizations, but
144;; it's at least one way to generate a byte swap.
145;;
146;; Technically this could be permuted quite a few ways and currently there's no
147;; easy way to match all of them, so only one is matched here.
148(rule (simplify (bor ty @ $I32
149    (bor ty
150      (ishl ty x (iconst_u ty 24))
151      (ishl ty
152        (band ty x (iconst_u ty 0xff00))
153        (iconst_u ty 8)))
154    (bor ty
155      (band ty
156        (ushr ty x (iconst_u ty 8))
157        (iconst_u ty 0xff00))
158      (ushr ty x (iconst_u ty 24)))))
159  (bswap ty x))
160
161(rule (simplify (bor ty @ $I64
162    (bor ty
163      (bor ty
164        (ishl ty x (iconst_u ty 56))
165        (ishl ty
166          (band ty x (iconst_u ty 0xff00))
167          (iconst_u ty 40)))
168      (bor ty
169        (ishl ty
170          (band ty x (iconst_u ty 0xff_0000))
171          (iconst_u ty 24))
172        (ishl ty
173          (band ty x (iconst_u ty 0xff00_0000))
174          (iconst_u ty 8))))
175    (bor ty
176      (bor ty
177        (band ty
178          (ushr ty x (iconst_u ty 8))
179          (iconst_u ty 0xff00_0000))
180        (band ty
181          (ushr ty x (iconst_u ty 24))
182          (iconst_u ty 0xff_0000)))
183      (bor ty
184        (band ty
185          (ushr ty x (iconst_u ty 40))
186          (iconst_u ty 0xff00))
187        (ushr ty x (iconst_u ty 56))))))
188  (bswap ty x))
189