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 (fits_in_64 (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;; But `iconst` is only valid for integers up to 64 bits wide.
24(rule (simplify (bxor (fits_in_64 (ty_int ty)) x (bnot ty x))) (subsume (iconst ty (imm64 (ty_mask ty)))))
25(rule (simplify (bxor (fits_in_64 (ty_int ty)) (bnot ty x) x)) (subsume (iconst ty (imm64 (ty_mask ty)))))
26(rule (simplify (bor (fits_in_64 (ty_int ty)) x (bnot ty x))) (subsume (iconst ty (imm64 (ty_mask ty)))))
27(rule (simplify (bor (fits_in_64 (ty_int ty)) (bnot ty x) x)) (subsume (iconst ty (imm64 (ty_mask ty)))))
28
29;; x & x == x & -1 == x.
30(rule (simplify (band ty x x)) (subsume x))
31(rule (simplify (band ty x (iconst_s ty -1)))
32      (subsume x))
33
34;; x & 0 == x & not(x) == not(x) & x == 0.
35(rule (simplify (band ty _ zero @ (iconst_u ty 0))) (subsume zero))
36(rule (simplify (band (fits_in_64 (ty_int ty)) x (bnot ty x))) (subsume (iconst_u ty 0)))
37(rule (simplify (band (fits_in_64 (ty_int ty)) (bnot ty x) x)) (subsume (iconst_u ty 0)))
38
39;; not(not(x)) == x.
40(rule (simplify (bnot ty (bnot ty x))) (subsume x))
41
42;; DeMorgan's rule (two versions):
43;; bnot(bor(x, y)) == band(bnot(x), bnot(y))
44(rule (simplify (bnot ty (bor ty x y)))
45      (band ty (bnot ty x) (bnot ty y)))
46;; bnot(band(x, y)) == bor(bnot(x), bnot(y))
47(rule (simplify (bnot ty (band t x y)))
48      (bor ty (bnot ty x) (bnot ty y)))
49
50;; `or(and(x, y), not(y)) == or(x, not(y))`
51(rule (simplify (bor ty
52                     (band ty x y)
53                     z @ (bnot ty y)))
54      (bor ty x z))
55;; Duplicate the rule but swap the `bor` operands because `bor` is
56;; commutative. We could, of course, add a `simplify` rule to do the commutative
57;; swap for all `bor`s but this will bloat the e-graph with many e-nodes. It is
58;; cheaper to have additional rules, rather than additional e-nodes, because we
59;; amortize their cost via ISLE's smart codegen.
60(rule (simplify (bor ty
61                     z @ (bnot ty y)
62                     (band ty x y)))
63      (bor ty x z))
64
65;; `or(and(x, y), not(y)) == or(x, not(y))` specialized for constants, since
66;; otherwise we may not know that `z == not(y)` since we don't generally expand
67;; constants in the e-graph.
68;;
69;; (No need to duplicate for commutative `bor` for this constant version because
70;; we move constants to the right.)
71(rule (simplify (bor ty
72                     (band ty x (iconst ty (u64_from_imm64 y)))
73                     z @ (iconst ty (u64_from_imm64 zk))))
74      (if-let $true (u64_eq (u64_and (ty_mask ty) zk)
75                            (u64_and (ty_mask ty) (u64_not y))))
76      (bor ty x z))
77
78;; (x ^ -1) can be replaced with the `bnot` instruction
79(rule (simplify (bxor ty x (iconst_s ty -1)))
80  (bnot ty x))
81
82;; sshr((x | -x), N) == bmask(x) where N = ty_bits(ty) - 1.
83;;
84;; (x | -x) sets the sign bit to 1 if x is nonzero, and 0 if x is zero. sshr propagates
85;; the sign bit to the rest of the value.
86(rule (simplify (sshr ty (bor ty x (ineg ty x)) (iconst ty (u64_from_imm64 shift_amt))))
87      (if-let $true (u64_eq shift_amt (ty_shift_mask ty)))
88      (bmask ty x))
89
90(rule (simplify (sshr ty (bor ty (ineg ty x) x) (iconst ty (u64_from_imm64 shift_amt))))
91      (if-let $true (u64_eq shift_amt (ty_shift_mask ty)))
92      (bmask ty x))
93
94;; Matches any expressions that preserve "truthiness".
95;; i.e. If the input is zero it remains zero, and if it is nonzero it can have
96;; a different value as long as it is still nonzero.
97(decl pure multi truthy (Value) Value)
98(rule (truthy (sextend _ x)) x)
99(rule (truthy (uextend _ x)) x)
100(rule (truthy (bmask _ x)) x)
101(rule (truthy (ineg _ x)) x)
102(rule (truthy (bswap _ x)) x)
103(rule (truthy (bitrev _ x)) x)
104(rule (truthy (popcnt _ x)) x)
105(rule (truthy (rotl _ x _)) x)
106(rule (truthy (rotr _ x _)) x)
107(rule (truthy (select _ x (iconst _ (u64_from_imm64 (u64_nonzero _))) (iconst _ (u64_from_imm64 0)))) x)
108;; (ne ty (iconst 0) v) is also canonicalized into this form via another rule
109(rule (truthy (ne _ x (iconst_u _ 0))) x)
110
111;; All of these expressions don't care about their input as long as it is truthy.
112;; so we can remove expressions that preserve that property from the input.
113(rule (simplify (bmask ty v)) (if-let x (truthy v)) (bmask ty x))
114(rule (simplify (select ty v t f)) (if-let c (truthy v)) (select ty c t f))
115;; (ne ty (iconst 0) v) is also canonicalized into this form via another rule
116(rule (simplify (ne cty v (iconst_u _ 0)))
117      (if-let c (truthy v))
118      (if-let (value_type (ty_int_ref_scalar_64 ty)) c)
119      (ne cty c (iconst_u ty 0)))
120
121
122
123;; (sextend (bmask x)) can be replaced with (bmask x) since bmask
124;; supports any size of output type, regardless of input.
125;; Same with `ireduce`
126(rule (simplify (sextend ty (bmask _ x))) (bmask ty x))
127(rule (simplify (ireduce ty (bmask _ x))) (bmask ty x))
128
129;; (bswap (bswap x)) == x
130(rule (simplify (bswap ty (bswap ty x))) (subsume x))
131
132;; (bitrev (bitrev x)) == x
133(rule (simplify (bitrev ty (bitrev ty x))) (subsume x))
134
135;; WebAssembly doesn't have a native byte-swapping instruction at this time so
136;; languages which have a byte-swapping operation will compile it down to bit
137;; shifting and twiddling. This attempts to pattern match what LLVM currently
138;; generates today for the Rust code `a.swap_bytes()`. This might be a bit
139;; brittle over time and/or with other possible LLVM backend optimizations, but
140;; it's at least one way to generate a byte swap.
141;;
142;; Technically this could be permuted quite a few ways and currently there's no
143;; easy way to match all of them, so only one is matched here.
144(rule (simplify (bor ty @ $I32
145    (bor ty
146      (ishl ty x (iconst_u ty 24))
147      (ishl ty
148        (band ty x (iconst_u ty 0xff00))
149        (iconst_u ty 8)))
150    (bor ty
151      (band ty
152        (ushr ty x (iconst_u ty 8))
153        (iconst_u ty 0xff00))
154      (ushr ty x (iconst_u ty 24)))))
155  (bswap ty x))
156
157(rule (simplify (bor ty @ $I64
158    (bor ty
159      (bor ty
160        (ishl ty x (iconst_u ty 56))
161        (ishl ty
162          (band ty x (iconst_u ty 0xff00))
163          (iconst_u ty 40)))
164      (bor ty
165        (ishl ty
166          (band ty x (iconst_u ty 0xff_0000))
167          (iconst_u ty 24))
168        (ishl ty
169          (band ty x (iconst_u ty 0xff00_0000))
170          (iconst_u ty 8))))
171    (bor ty
172      (bor ty
173        (band ty
174          (ushr ty x (iconst_u ty 8))
175          (iconst_u ty 0xff00_0000))
176        (band ty
177          (ushr ty x (iconst_u ty 24))
178          (iconst_u ty 0xff_0000)))
179      (bor ty
180        (band ty
181          (ushr ty x (iconst_u ty 40))
182          (iconst_u ty 0xff00))
183        (ushr ty x (iconst_u ty 56))))))
184  (bswap ty x))
185