blob: 8314b991e611004c9a2954efe40d409c3e9020b8 (
plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
|
Require Import Coq.micromega.Psatz.
Require Import Coq.ZArith.ZArith.
Require Import Crypto.Compilers.Syntax.
Require Import Crypto.Compilers.SmartMap.
Require Import Crypto.Compilers.TypeInversion.
Require Import Crypto.Compilers.ExprInversion.
Require Import Crypto.Compilers.RewriterInterp.
Require Import Crypto.Compilers.Z.Syntax.
Require Import Crypto.Compilers.Z.OpInversion.
Require Import Crypto.Compilers.Z.ArithmeticSimplifier.
Require Import Crypto.Compilers.Z.ArithmeticSimplifierUtil.
Require Import Crypto.Compilers.Z.Syntax.Equality.
Require Import Crypto.Util.ZUtil.
Require Import Crypto.Util.ZUtil.AddGetCarry.
Require Import Crypto.Util.Option.
Require Import Crypto.Util.Prod.
Require Import Crypto.Util.Sum.
Require Import Crypto.Util.HProp.
Require Import Crypto.Util.Tactics.BreakMatch.
Require Import Crypto.Util.Tactics.DestructHead.
Local Notation exprf := (@exprf base_type op interp_base_type).
Local Notation expr := (@expr base_type op interp_base_type).
Local Notation Expr := (@Expr base_type op).
Local Ltac fin_t :=
first [ exact I
| reflexivity
| congruence
| assumption
| lia
| exfalso; assumption ].
Local Ltac break_t_step :=
first [ progress subst
| progress inversion_option
| progress inversion_sum
| progress inversion_expr
| progress inversion_prod
| progress inversion_inverted_expr
| progress inversion_flat_type
| progress subst_prod
| progress destruct_head'_and
| progress destruct_head'_prod
| progress eliminate_hprop_eq
| progress break_innermost_match_step
| progress break_match_hyps ].
Definition interpf_as_expr_or_const {t}
: interp_flat_type (@inverted_expr interp_base_type) t -> interp_flat_type interp_base_type t
:= SmartVarfMap
(fun t z => match z with
| const_of z => cast_const (t1:=TZ) z
| gen_expr e => interpf interp_op e
| neg_expr e => interpf interp_op (Op (Opp _ _) e)
end).
Lemma interp_as_expr_or_const_correct {t} e z
: @interp_as_expr_or_const interp_base_type t e = Some z
-> interpf interp_op e = interpf_as_expr_or_const z.
Proof.
induction e;
repeat first [ progress subst
| progress inversion_option
| progress simpl in *
| progress cbn [interpf_as_expr_or_const SmartVarfMap smart_interp_flat_map]
| reflexivity
| break_innermost_match_hyps_step
| intro
| match goal with
| [ H : forall z, Some _ = Some z -> _ |- _ ] => specialize (H _ eq_refl)
| [ H : interpf _ ?e = interpf_as_expr_or_const _ |- _ ]
=> rewrite H
| [ |- context[match ?e with _ => _ end] ]
=> is_var e; invert_one_op e
end
| break_innermost_match_step ].
Qed.
Local Ltac rewrite_interp_as_expr_or_const_correct _ :=
match goal with
| [ |- context[interpf _ ?e] ]
=> erewrite !(@interp_as_expr_or_const_correct _ e) by eassumption; cbv beta iota;
cbn [interpf_as_expr_or_const SmartVarfMap smart_interp_flat_map]
end.
Local Arguments Z.mul !_ !_.
Local Arguments Z.add !_ !_.
Local Arguments Z.sub !_ !_.
Local Arguments Z.opp !_.
Local Arguments interp_op _ _ !_ _ / .
Local Arguments lift_op / .
Lemma InterpSimplifyArith {convert_adc_to_sbb} {t} (e : Expr t)
: forall x, Interp interp_op (SimplifyArith convert_adc_to_sbb e) x = Interp interp_op e x.
Proof.
apply InterpRewriteOp; intros; unfold simplify_op_expr.
Time break_innermost_match;
repeat first [ reflexivity
| progress subst
| progress simpl in *
| progress inversion_prod
| progress invert_expr_subst
| inversion_base_type_constr_step
| match goal with
| [ |- context[match ?e with _ => _ end] ]
=> is_var e; invert_one_op e;
repeat match goal with
| [ |- match ?T with _ => _ end _ ]
=> break_innermost_match_step; try exact I
end
end
| break_innermost_match_step
| rewrite_interp_as_expr_or_const_correct ()
| intro ].
all:repeat first [ reflexivity
| omega
| discriminate
| progress cbv [LetIn.Let_In Z.zselect IdfunWithAlt.id_with_alt]
| progress subst
| progress simpl in *
| progress Z.ltb_to_lt
| break_innermost_match_step
| rewrite FixedWordSizesEquality.ZToWord_wordToZ
| rewrite FixedWordSizesEquality.ZToWord_wordToZ_ZToWord by reflexivity
| rewrite FixedWordSizesEquality.wordToZ_ZToWord_0
| progress rewrite ?Z.land_0_l, ?Z.land_0_r, ?Z.lor_0_l, ?Z.lor_0_r
| rewrite !Z.sub_with_borrow_to_add_get_carry
| progress autorewrite with zsimplify_fast
| progress cbv [cast_const ZToInterp interpToZ]
| nia ].
Qed.
Hint Rewrite @InterpSimplifyArith : reflective_interp.
|
