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|
(** * SimplifyArith: Remove things like (_ * 1), (_ + 0), etc *)
Require Import Coq.ZArith.ZArith.
Require Import Crypto.Compilers.Syntax.
Require Import Crypto.Compilers.ExprInversion.
Require Import Crypto.Compilers.Rewriter.
Require Import Crypto.Compilers.Z.Syntax.
Require Import Crypto.Compilers.Z.Syntax.Equality.
Require Import Crypto.Util.ZUtil.Definitions.
Section language.
Context (convert_adc_to_sbb : bool).
Local Notation exprf := (@exprf base_type op).
Section with_var.
Context {var : base_type -> Type}.
Inductive inverted_expr t :=
| const_of (v : Z)
| gen_expr (e : exprf (var:=var) (Tbase t))
| neg_expr (e : exprf (var:=var) (Tbase t)).
Fixpoint interp_as_expr_or_const {t} (x : exprf (var:=var) t)
: option (interp_flat_type inverted_expr t)
:= match x in Syntax.exprf _ _ t return option (interp_flat_type _ t) with
| Op t1 (Tbase _) opc args
=> Some (match opc in op src dst
return exprf dst
-> exprf src
-> match dst with
| Tbase t => inverted_expr t
| Prod _ _ => True
| _ => inverted_expr TZ
end
with
| OpConst _ z => fun _ _ => const_of _ z
| Opp TZ TZ => fun _ args => neg_expr _ args
| MulSplit _ _ _ _ _ => fun _ _ => I
| AddWithGetCarry _ _ _ _ _ _ => fun _ _ => I
| SubWithGetBorrow _ _ _ _ _ _ => fun _ _ => I
| _ => fun e _ => gen_expr _ e
end (Op opc args) args)
| TT => Some tt
| Var t v => Some (gen_expr _ (Var v))
| Op _ _ _ _
| LetIn _ _ _ _
=> None
| Pair tx ex ty ey
=> match @interp_as_expr_or_const tx ex, @interp_as_expr_or_const ty ey with
| Some vx, Some vy => Some (vx, vy)
| _, None | None, _ => None
end
end.
Fixpoint uninterp_expr_or_const {t} : interp_flat_type inverted_expr t -> exprf (var:=var) t
:= match t with
| Tbase T => fun e => match e with
| const_of v => Op (OpConst v) TT
| gen_expr e => e
| neg_expr e => Op (Opp _ _) e
end
| Unit => fun _ => TT
| Prod A B => fun (ab : interp_flat_type _ A * interp_flat_type _ B)
=> Pair (@uninterp_expr_or_const A (fst ab))
(@uninterp_expr_or_const B (snd ab))
end.
Definition simplify_op_expr {src dst} (opc : op src dst)
: exprf (var:=var) src -> exprf (var:=var) dst
:= match opc in op src dst return exprf src -> exprf dst with
| Add TZ TZ TZ as opc
=> fun args
=> match interp_as_expr_or_const args with
| Some (const_of l, const_of r)
=> Op (OpConst (interp_op _ _ opc (l, r))) TT
| Some (const_of v, gen_expr e)
| Some (gen_expr e, const_of v)
=> if (v =? 0)%Z
then e
else Op opc args
| Some (const_of v, neg_expr e)
| Some (neg_expr e, const_of v)
=> if (v =? 0)%Z
then Op (Opp _ _) e
else Op opc args
| Some (gen_expr ep, neg_expr en)
| Some (neg_expr en, gen_expr ep)
=> Op (Sub _ _ _) (Pair ep en)
| _ => Op opc args
end
| Add T1 T2 Tout as opc
=> fun args
=> match interp_as_expr_or_const args with
| Some (const_of v, gen_expr e)
=> if (v =? 0)%Z
then match base_type_eq_semidec_transparent T2 Tout with
| Some pf => eq_rect _ (fun t => exprf (Tbase t)) e _ pf
| None => Op opc args
end
else Op opc args
| Some (gen_expr e, const_of v)
=> if (v =? 0)%Z
then match base_type_eq_semidec_transparent T1 Tout with
| Some pf => eq_rect _ (fun t => exprf (Tbase t)) e _ pf
| None => Op opc args
end
else Op opc args
| _ => Op opc args
end
| Sub TZ TZ TZ as opc
=> fun args
=> match interp_as_expr_or_const args with
| Some (const_of l, const_of r)
=> Op (OpConst (interp_op _ _ opc (l, r))) TT
| Some (gen_expr e, const_of v)
=> if (v =? 0)%Z
then e
else Op opc args
| Some (neg_expr e, const_of v)
=> if (v =? 0)%Z
then Op (Opp _ _) e
else Op opc args
| Some (gen_expr e1, neg_expr e2)
=> Op (Add _ _ _) (Pair e1 e2)
| Some (neg_expr e1, neg_expr e2)
=> Op (Sub _ _ _) (Pair e2 e1)
| _ => Op opc args
end
| Mul TZ TZ TZ as opc
=> fun args
=> match interp_as_expr_or_const args with
| Some (const_of l, const_of r)
=> Op (OpConst (interp_op _ _ opc (l, r))) TT
| Some (const_of v, gen_expr e)
| Some (gen_expr e, const_of v)
=> if (v =? 0)%Z
then Op (OpConst 0%Z) TT
else if (v =? 1)%Z
then e
else if (v =? -1)%Z
then Op (Opp _ _) e
else Op opc args
| Some (const_of v, neg_expr e)
| Some (neg_expr e, const_of v)
=> if (v =? 0)%Z
then Op (OpConst 0%Z) TT
else if (v =? 1)%Z
then Op (Opp _ _) e
else if (v =? -1)%Z
then e
else if (v >? 0)%Z
then Op (Opp _ _) (Op opc (Pair (Op (OpConst v) TT) e))
else Op opc args
| Some (gen_expr e1, neg_expr e2)
| Some (neg_expr e1, gen_expr e2)
=> Op (Opp _ _) (Op (Mul _ _ TZ) (Pair e1 e2))
| Some (neg_expr e1, neg_expr e2)
=> Op (Mul _ _ _) (Pair e1 e2)
| _ => Op opc args
end
| Mul (TWord bw1 as T1) (TWord bw2 as T2) (TWord bwout as Tout) as opc
=> fun args
=> let sz1 := (2^Z.of_nat (2^bw1))%Z in
let sz2 := (2^Z.of_nat (2^bw2))%Z in
let szout := (2^Z.of_nat (2^bwout))%Z in
match interp_as_expr_or_const args with
| Some (const_of l, const_of r)
=> Op (OpConst (((Z.max 0 l mod sz1) * (Z.max 0 r mod sz2)) mod szout)%Z) TT
| Some (const_of v, gen_expr e)
=> if ((Z.max 0 v mod sz1) mod szout =? 0)%Z
then Op (OpConst 0%Z) TT
else if ((Z.max 0 v mod sz1) mod szout =? 1)%Z
then match base_type_eq_semidec_transparent T2 Tout with
| Some pf => eq_rect _ (fun t => exprf (Tbase t)) e _ pf
| None => Op opc args
end
else Op opc args
| Some (gen_expr e, const_of v)
=> if ((Z.max 0 v mod sz2) mod szout =? 0)%Z
then Op (OpConst 0%Z) TT
else if ((Z.max 0 v mod sz2) mod szout =? 1)%Z
then match base_type_eq_semidec_transparent T1 Tout with
| Some pf => eq_rect _ (fun t => exprf (Tbase t)) e _ pf
| None => Op opc args
end
else Op opc args
| _ => Op opc args
end
| Shl TZ TZ TZ as opc
| Shr TZ TZ TZ as opc
=> fun args
=> match interp_as_expr_or_const args with
| Some (const_of l, const_of r)
=> Op (OpConst (interp_op _ _ opc (l, r))) TT
| Some (gen_expr e, const_of v)
=> if (v =? 0)%Z
then e
else Op opc args
| Some (neg_expr e, const_of v)
=> if (v =? 0)%Z
then Op (Opp _ _) e
else Op opc args
| _ => Op opc args
end
| Land TZ TZ TZ as opc
=> fun args
=> match interp_as_expr_or_const args with
| Some (const_of l, const_of r)
=> Op (OpConst (interp_op _ _ opc (l, r))) TT
| Some (const_of v, gen_expr _)
| Some (gen_expr _, const_of v)
| Some (const_of v, neg_expr _)
| Some (neg_expr _, const_of v)
=> if (v =? 0)%Z
then Op (OpConst 0%Z) TT
else Op opc args
| _ => Op opc args
end
| Lor TZ TZ TZ as opc
=> fun args
=> match interp_as_expr_or_const args with
| Some (const_of l, const_of r)
=> Op (OpConst (interp_op _ _ opc (l, r))) TT
| Some (const_of v, gen_expr e)
| Some (gen_expr e, const_of v)
=> if (v =? 0)%Z
then e
else Op opc args
| Some (const_of v, neg_expr e)
| Some (neg_expr e, const_of v)
=> if (v =? 0)%Z
then Op (Opp _ _) e
else Op opc args
| _ => Op opc args
end
| Opp TZ TZ as opc
=> fun args
=> match interp_as_expr_or_const args with
| Some (const_of v)
=> Op (OpConst (interp_op _ _ opc v)) TT
| Some (neg_expr e)
=> e
| _
=> Op opc args
end
| MulSplit bitwidth (TWord bw1 as T1) (TWord bw2 as T2) (TWord bwout1 as Tout1) (TWord bwout2 as Tout2) as opc
=> fun args
=> let sz1 := (2^Z.of_nat (2^bw1))%Z in
let sz2 := (2^Z.of_nat (2^bw2))%Z in
let szout1 := (2^Z.of_nat (2^bwout1))%Z in
let szout2 := (2^Z.of_nat (2^bwout2))%Z in
match interp_as_expr_or_const args with
| Some (const_of l, const_of r)
=> let '(a, b) := Z.mul_split_at_bitwidth bitwidth (Z.max 0 l mod sz1) (Z.max 0 r mod sz2) in
Pair (Op (OpConst (a mod szout1)%Z) TT)
(Op (OpConst (b mod szout2)%Z) TT)
| Some (const_of v, gen_expr e)
=> let v' := (Z.max 0 v mod sz1)%Z in
if (v' =? 0)%Z
then Pair (Op (OpConst 0%Z) TT) (Op (OpConst 0%Z) TT)
else if ((v' =? 1) && (2^Z.of_nat (2^bw2) <=? 2^bitwidth))%Z%bool
then match base_type_eq_semidec_transparent T2 Tout1 with
| Some pf => Pair (eq_rect _ (fun t => exprf (Tbase t)) e _ pf)
(Op (OpConst 0%Z) TT)
| None => Op opc args
end
else Op opc args
| Some (gen_expr e, const_of v)
=> let v' := (Z.max 0 v mod sz2)%Z in
if (v' =? 0)%Z
then Pair (Op (OpConst 0%Z) TT) (Op (OpConst 0%Z) TT)
else if ((v' =? 1) && (2^Z.of_nat (2^bw1) <=? 2^bitwidth))%Z%bool
then match base_type_eq_semidec_transparent T1 Tout1 with
| Some pf => Pair (eq_rect _ (fun t => exprf (Tbase t)) e _ pf)
(Op (OpConst 0%Z) TT)
| None => Op opc args
end
else Op opc args
| _ => Op opc args
end
| IdWithAlt (TWord _ as T1) _ (TWord _ as Tout) as opc
=> fun args
=> match base_type_eq_semidec_transparent T1 Tout with
| Some pf
=> match interp_as_expr_or_const args with
| Some (const_of c, _)
=> Op (OpConst c) TT
| Some (neg_expr e, _)
=> Op (Opp _ _) e
| Some (gen_expr e, _)
=> eq_rect _ (fun t => exprf (Tbase t)) e _ pf
| None
=> Op opc args
end
| None
=> Op opc args
end
| IdWithAlt TZ TZ TZ as opc
=> fun args
=> match interp_as_expr_or_const args with
| Some (gen_expr e1, gen_expr e2)
=> match invert_Op e1, invert_Op e2 with
| Some (existT _ (Add TZ TZ TZ as opc1, args1)),
Some (existT _ (Add TZ TZ TZ as opc2, args2))
| Some (existT _ (Sub TZ TZ TZ as opc1, args1)),
Some (existT _ (Sub TZ TZ TZ as opc2, args2))
| Some (existT _ (Mul TZ TZ TZ as opc1, args1)),
Some (existT _ (Mul TZ TZ TZ as opc2, args2))
=> match interp_as_expr_or_const args1, interp_as_expr_or_const args2 with
| Some (gen_expr e1, const_of c1),
Some (gen_expr e2, const_of c2)
=> if Z.eqb c1 c2
then Op opc1 (Op opc (e1, e2), Op (OpConst c1) TT)%expr
else Op opc args
| _, _
=> Op opc args
end
| _, _
=> Op opc args
end
| Some (neg_expr e1, neg_expr e2)
=> Op (Opp _ _) (Op opc (e1, e2)%expr)
| Some (const_of c1, const_of c2)
=> Op (OpConst c1) TT
| _
=> Op opc args
end
| IdWithAlt _ _ (TWord _ as Tout) as opc
=> fun args
=> match interp_as_expr_or_const args with
| Some (gen_expr e1, _)
=> match invert_Op e1 with
| Some (existT _ (Add (TWord _) (TWord _) TZ as opc1, args1))
=> Op (Add _ _ Tout) args1
| Some (existT _ (Sub (TWord _) (TWord _) TZ as opc1, args1))
=> Op (Sub _ _ Tout) args1
| Some (existT _ (Mul (TWord _) (TWord _) TZ as opc1, args1))
=> Op (Mul _ _ Tout) args1
| _
=> Op opc args
end
| _
=> Op opc args
end
| Zselect TZ TZ TZ TZ as opc
=> fun args
=> match interp_as_expr_or_const args with
| Some (const_of c, x, y)
=> match (c =? 0)%Z, x, y with
| true, const_of c, _
| false, _, const_of c
=> Op (OpConst c) TT
| true, gen_expr e, _
| false, _, gen_expr e
=> e
| true, neg_expr e, _
| false, _, neg_expr e
=> Op (Opp TZ TZ) e
end
| Some (neg_expr e, x, y)
=> let x := uninterp_expr_or_const (t:=Tbase _) x in
let y := uninterp_expr_or_const (t:=Tbase _) y in
Op (Zselect TZ TZ TZ TZ) (e, x, y)%expr
| _ => Op opc args
end
| AddWithCarry TZ TZ TZ TZ as opc
=> fun args
=> let first_pass
:= match interp_as_expr_or_const args with
| Some (const_of c, const_of x, const_of y)
=> Some (Op (OpConst (interp_op _ _ opc (c, x, y))) TT)
| Some (gen_expr e, const_of c1, const_of c2)
| Some (const_of c1, gen_expr e, const_of c2)
| Some (const_of c1, const_of c2, gen_expr e)
=> if (c1 + c2 =? 0)%Z
then Some e
else None
| _ => None
end in
match first_pass with
| Some e => e
| None
=> if convert_adc_to_sbb
then match interp_as_expr_or_const args with
| Some (const_of c, const_of x, const_of y)
=> Op (OpConst (interp_op _ _ opc (c, x, y))) TT
| Some (c, gen_expr x, y)
=> let y' := match y with
| const_of y => if (y <? 0)%Z
then Some (Op (OpConst (-y)) TT)
else None
| neg_expr y => Some y
| gen_expr _ => None
end in
match y' with
| Some y => Op (SubWithBorrow TZ TZ TZ TZ)
(match c with
| const_of c => Op (OpConst (-c)) TT
| neg_expr c => c
| gen_expr c => Op (Opp TZ TZ) c
end,
x, y)%expr
| None => Op opc args
end
| _ => Op opc args
end
else Op opc args
end
| AddWithGetCarry bw TZ TZ TZ TZ TZ as opc
=> fun args
=> if convert_adc_to_sbb
then match interp_as_expr_or_const args with
| Some (const_of c, const_of x, const_of y)
=> let '(v, c) := interp_op _ _ opc (c, x, y) in
(Op (OpConst v) TT, Op (OpConst c) TT)%expr
| Some (c, gen_expr x, y)
=> let y' := match y with
| const_of y => if (y <? 0)%Z
then Some (Op (OpConst (-y)) TT)
else None
| neg_expr y => Some y
| gen_expr _ => None
end in
let c' := match c with
| const_of c => if (c <? 0)%Z
then Some (Op (OpConst (-c)) TT)
else None
| neg_expr c => Some c
| gen_expr _ => None
end in
match c', y' with
| _, Some y => LetIn (Op (SubWithGetBorrow bw TZ TZ TZ TZ TZ)
(match c with
| const_of c => Op (OpConst (-c)) TT
| neg_expr c => c
| gen_expr c => Op (Opp TZ TZ) c
end,
x, y)%expr)
(fun '(v, c) => (Var v, Op (Opp TZ TZ) (Var c))%expr)
| Some c, _ => LetIn (Op (SubWithGetBorrow bw TZ TZ TZ TZ TZ)
(c,
x,
match y with
| const_of y => Op (OpConst (-y)) TT
| neg_expr y => y
| gen_expr y => Op (Opp TZ TZ) y
end)%expr)
(fun '(v, c) => (Var v, Op (Opp TZ TZ) (Var c))%expr)
| None, None => Op opc args
end
| Some (c, const_of x, y)
=> let y' := match y with
| const_of y => if (y <? 0)%Z
then Some (Op (OpConst (-y)) TT)
else None
| neg_expr y => Some y
| gen_expr _ => None
end in
let c' := match c with
| const_of c => if (c <? 0)%Z
then Some (Op (OpConst (-c)) TT)
else None
| neg_expr c => Some c
| gen_expr _ => None
end in
match c', y' with
| _, Some y => LetIn (Op (SubWithGetBorrow bw TZ TZ TZ TZ TZ)
(match c with
| const_of c => Op (OpConst (-c)) TT
| neg_expr c => c
| gen_expr c => Op (Opp TZ TZ) c
end,
Op (OpConst x) TT, y)%expr)
(fun '(v, c) => (Var v, Op (Opp TZ TZ) (Var c))%expr)
| Some c, _ => LetIn (Op (SubWithGetBorrow bw TZ TZ TZ TZ TZ)
(c,
Op (OpConst x) TT,
match y with
| const_of y => Op (OpConst (-y)) TT
| neg_expr y => y
| gen_expr y => Op (Opp TZ TZ) y
end)%expr)
(fun '(v, c) => (Var v, Op (Opp TZ TZ) (Var c))%expr)
| None, None => Op opc args
end
| _ => Op opc args
end
else Op opc args
| AddWithGetCarry bw (TWord bw1 as T1) (TWord bw2 as T2) (TWord bw3 as T3) (TWord bwout as Tout) Tout2 as opc
=> fun args
=> let pass0
:= if ((0 <=? bw)%Z && (2^Z.of_nat (2^bw1) + 2^Z.of_nat (2^bw2) + 2^Z.of_nat (2^bw3) - 3 <=? 2^bw - 1)%Z)%nat%bool
then Some (Pair (LetIn args (fun '(a, b, c) => Op (Add _ _ _) (Pair (Op (Add _ _ Tout) (Pair (Var a) (Var b))) (Var c))))
(Op (OpConst 0) TT))
else None
in
match pass0 with
| Some e => e
| None
=> match interp_as_expr_or_const args with
| Some (const_of c, const_of x, const_of y)
=> if ((c =? 0) && (x =? 0) && (y =? 0))%Z%bool
then Pair (Op (OpConst 0) TT) (Op (OpConst 0) TT)
else Op opc args
| Some (gen_expr e, const_of c1, const_of c2)
=> match base_type_eq_semidec_transparent T1 Tout with
| Some pf
=> if ((c1 =? 0) && (c2 =? 0) && (2^Z.of_nat bw1 <=? bw))%Z%bool
then Pair (eq_rect _ (fun t => exprf (Tbase t)) e _ pf) (Op (OpConst 0) TT)
else Op opc args
| None
=> Op opc args
end
| Some (const_of c1, gen_expr e, const_of c2)
=> match base_type_eq_semidec_transparent T2 Tout with
| Some pf
=> if ((c1 =? 0) && (c2 =? 0) && (2^Z.of_nat bw2 <=? bw))%Z%bool
then Pair (eq_rect _ (fun t => exprf (Tbase t)) e _ pf) (Op (OpConst 0) TT)
else Op opc args
| None
=> Op opc args
end
| Some (const_of c1, const_of c2, gen_expr e)
=> match base_type_eq_semidec_transparent T3 Tout with
| Some pf
=> if ((c1 =? 0) && (c2 =? 0) && (2^Z.of_nat bw3 <=? bw))%Z%bool
then Pair (eq_rect _ (fun t => exprf (Tbase t)) e _ pf) (Op (OpConst 0) TT)
else Op opc args
| None
=> Op opc args
end
| _ => Op opc args
end
end
| SubWithBorrow TZ TZ TZ TZ as opc
=> fun args
=> if convert_adc_to_sbb
then match interp_as_expr_or_const args with
| Some (const_of c, const_of x, const_of y)
=> Op (OpConst (interp_op _ _ opc (c, x, y))) TT
| Some (c, gen_expr x, y)
=> let y' := match y with
| const_of y => if (y <? 0)%Z
then Some (Op (OpConst (-y)) TT)
else None
| neg_expr y => Some y
| gen_expr _ => None
end in
match y' with
| Some y => Op (AddWithCarry TZ TZ TZ TZ)
(match c with
| const_of c => Op (OpConst (-c)) TT
| neg_expr c => c
| gen_expr c => Op (Opp TZ TZ) c
end,
x, y)%expr
| None => Op opc args
end
| _ => Op opc args
end
else Op opc args
| SubWithGetBorrow bw TZ TZ TZ TZ TZ as opc
=> fun args
=> if convert_adc_to_sbb
then match interp_as_expr_or_const args with
| Some (const_of c, const_of x, const_of y)
=> let '(v, c) := interp_op _ _ opc (c, x, y) in
(Op (OpConst v) TT, Op (OpConst c) TT)%expr
| Some (c, gen_expr x, y)
=> let y' := match y with
| const_of y => if (y <? 0)%Z
then Some (Op (OpConst (-y)) TT)
else None
| neg_expr y => Some y
| gen_expr _ => None
end in
match y' with
| Some y => LetIn (Op (AddWithGetCarry bw TZ TZ TZ TZ TZ)
(match c with
| const_of c => Op (OpConst (-c)) TT
| neg_expr c => c
| gen_expr c => Op (Opp TZ TZ) c
end,
x, y)%expr)
(fun '(v, c) => (Var v, Op (Opp TZ TZ) (Var c))%expr)
| None => Op opc args
end
| _ => Op opc args
end
else Op opc args
| Sub _ _ _ as opc
| Mul _ _ _ as opc
| Shl _ _ _ as opc
| Shr _ _ _ as opc
| Land _ _ _ as opc
| Lor _ _ _ as opc
| OpConst _ _ as opc
| Opp _ _ as opc
| IdWithAlt _ _ _ as opc
| Zselect _ _ _ _ as opc
| MulSplit _ _ _ _ _ as opc
| AddWithCarry _ _ _ _ as opc
| AddWithGetCarry _ _ _ _ _ _ as opc
| SubWithBorrow _ _ _ _ as opc
| SubWithGetBorrow _ _ _ _ _ _ as opc
=> Op opc
end.
End with_var.
Definition SimplifyArith {t} (e : Expr t) : Expr t
:= @RewriteOp base_type op (@simplify_op_expr) t e.
End language.
|
