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
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
|
Require Import Crypto.Assembly.QhasmCommon Crypto.Assembly.QhasmUtil Crypto.Assembly.State.
Require Import Crypto.Assembly.Language Crypto.Assembly.QhasmEvalCommon.
Require Import Coq.Lists.List Coq.Arith.Compare_dec Coq.omega.Omega.
Require Import Crypto.Util.Notations.
Require Export Crypto.Util.FixCoqMistakes.
Module Pseudo <: Language.
Import EvalUtil ListState.
Inductive Pseudo {w: nat} {s: Width w}: nat -> nat -> Type :=
| PVar: forall n, option bool -> Index n -> Pseudo n 1
| PMem: forall n m , Index n -> Index m -> Pseudo n 1
| PConst: forall n, word w -> Pseudo n 1
| PBin: forall n, IntOp -> Pseudo n 2 -> Pseudo n 1
| PDual: forall n, DualOp -> Pseudo n 2 -> Pseudo n 2
| PCarry: forall n, CarryOp -> Pseudo n 2 -> Pseudo n 1
| PShift: forall n, RotOp -> Index w -> Pseudo n 1 -> Pseudo n 1
| PFunExp: forall n, Pseudo n n -> nat -> Pseudo n n
| PLet: forall n k m, Pseudo n k -> Pseudo (n + k) m -> Pseudo n m
| PComb: forall n a b, Pseudo n a -> Pseudo n b -> Pseudo n (a + b)
| PCall: forall n m, Label -> Pseudo n m -> Pseudo n m
| PIf: forall n m, TestOp -> Index n -> Index n ->
Pseudo n m -> Pseudo n m -> Pseudo n m.
Hint Constructors Pseudo.
Record Params': Type := mkParams {
width: nat;
spec: Width width;
inputs: nat;
outputs: nat
}.
Definition Params := Params'.
Definition State (p: Params) : Type := ListState (width p).
Definition Program (p: Params) : Type :=
@Pseudo (width p) (spec p) (inputs p) (outputs p).
Definition Unary32: Params := mkParams 32 W32 1 1.
Definition Unary64: Params := mkParams 64 W64 1 1.
(* Evaluation *)
Fixpoint pseudoEval {n m w s} (prog: @Pseudo w s n m) (st: ListState w) : option (ListState w) :=
match prog with
| PVar n _ i => omap (getVar i st) (fun x => Some (setList [x] st))
| PMem n m v i => omap (getMem v i st) (fun x => Some (setList [x] st))
| PConst n c => Some (setList [c] st)
| PBin n o p =>
omap (pseudoEval p st) (fun sp =>
match (getList sp) with
| [wa; wb] =>
let (v, c) := evalIntOp o wa wb in
Some (setList [v] (setCarryOpt c sp))
| _ => None
end)
| PCarry n o p =>
omap (pseudoEval p st) (fun sp =>
match (getList sp, getCarry sp) with
| ([wa; wb], Some c) =>
let (v, c') := evalCarryOp o wa wb c in
Some (setList [v] (setCarry c' sp))
| _ => None
end)
| PDual n o p =>
omap (pseudoEval p st) (fun sp =>
match (getList sp) with
| [wa; wb] =>
let (low, high) := evalDualOp o wa wb in
Some (setList [low; high] sp)
| _ => None
end)
| PShift n o a x =>
omap (pseudoEval x st) (fun sx =>
match (getList sx) with
| [wx] => Some (setList [evalRotOp o wx a] sx)
| _ => None
end)
| PLet n k m f g =>
omap (pseudoEval f st) (fun sf =>
omap (pseudoEval g (setList ((getList st) ++ (getList sf)) sf))
(fun sg => Some sg))
| PComb n a b f g =>
omap (pseudoEval f st) (fun sf =>
omap (pseudoEval g (setList (getList st) sf)) (fun sg =>
Some (setList ((getList sf) ++ (getList sg)) sg)))
| PIf n m t i0 i1 l r =>
omap (getVar i0 st) (fun v0 =>
omap (getVar i1 st) (fun v1 =>
if (evalTest t v0 v1)
then pseudoEval l st
else pseudoEval r st ))
| PFunExp n p e =>
(fix funexpseudo (e': nat) (st': ListState w) :=
match e' with
| O => Some st'
| S e'' =>
omap (pseudoEval p st') (fun st'' =>
funexpseudo e'' st'')
end) e st
| PCall n m _ p => pseudoEval p st
end.
Definition evaluatesTo (p: Params) (prog: Program p) (st st': State p) :=
pseudoEval prog st = Some st'.
Delimit Scope pseudo_notations with p.
Local Open Scope pseudo_notations.
Definition indexize {n: nat} (x: nat) : Index n.
intros; destruct (le_dec n 0).
- exists 0; abstract intuition auto with zarith.
- exists (x mod n)%nat; abstract (
pose proof (Nat.mod_bound_pos x n); omega).
Defined.
Notation "% A" := (PVar _ (Some false) (indexize A))
: pseudo_notations.
Notation "$ A" := (PVar _ (Some true) (indexize A))
: pseudo_notations.
Notation "A :[ B ]:" := (PMem _ _ (indexize A) (indexize B))
: pseudo_notations.
Notation "# A" := (PConst _ (natToWord _ A))
: pseudo_notations.
Notation "A :+: B" := (PBin _ IAdd (PComb _ _ _ A B))
: pseudo_notations.
Notation "A :+c: B" := (PCarry _ AddWithCarry (PComb _ _ _ A B))
: pseudo_notations.
Notation "A :-: B" := (PBin _ ISub (PComb _ _ _ A B))
: pseudo_notations.
Notation "A :&: B" := (PBin _ IAnd (PComb _ _ _ A B))
: pseudo_notations.
Notation "A :^: B" := (PBin _ IXor (PComb _ _ _ A B))
: pseudo_notations.
Notation "A :>>: B" := (PShift _ Shr (indexize B) A)
: pseudo_notations.
Notation "A :<<: B" := (PShift _ Shl (indexize B) A)
: pseudo_notations.
Notation "A :*: B" := (PDual _ Mult (PComb _ _ _ A B))
: pseudo_notations.
(* TODO(rsloan, from jgross): This notation is not okay. It breaks
[constr:(nat)] and [((1):nat)]. Please remove all frowny faces
from notations, and then move [Reserved Notation] line to
Fiat.Crypto.Util.Notations. *)
Reserved Notation "O :( A , B ): :?: L ::: R" (at level 70, right associativity).
Notation "O :( A , B ): :?: L ::: R" :=
(PIf _ _ O (indexize A) (indexize B) L R)
: pseudo_notations.
Notation "F :**: e" :=
(PFunExp _ F e)
: pseudo_notations.
Notation "E :->: F" :=
(PLet _ _ _ E F)
: pseudo_notations.
Notation "A :|: B" :=
(PComb _ _ _ A B)
: pseudo_notations.
Notation "n ::: A :():" :=
(PCall _ _ n A)
: pseudo_notations.
Close Scope pseudo_notations.
End Pseudo.
|
