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Require Import Crypto.Assembly.Pipeline.
Require Import Crypto.Spec.ModularArithmetic.
Require Import Crypto.ModularArithmetic.ModularBaseSystem.
Require Import Crypto.Specific.GF25519.
Require Import Crypto.Util.Tuple.
Module GF25519.
Definition bits: nat := 64.
Definition width: Width bits := W64.
Existing Instance ZEvaluable.
Fixpoint makeBoundList {n} k (b: @BoundedWord n) :=
match k with
| O => nil
| S k' => cons b (makeBoundList k' b)
end.
Section DefaultBounds.
Import ListNotations.
Local Notation rr exp := (2^exp + 2^exp/10)%Z.
Definition feBound: list Z :=
[rr 26; rr 27; rr 26; rr 27; rr 26;
rr 27; rr 26; rr 27; rr 26; rr 27].
End DefaultBounds.
Definition FE: type.
Proof.
let T := eval vm_compute in fe25519 in
let t := HL.reify_type T in
exact t.
Defined.
Section Expressions.
Definition flatten {T}: (@interp_type Z FE -> T) -> NAry 10 Z T.
intro F; refine (fun (a b c d e f g h i j: Z) =>
F (a, b, c, d, e, f, g, h, i, j)).
Defined.
Definition unflatten {T}:
(forall a b c d e f g h i j, T (a, b, c, d, e, f, g, h, i, j))
-> (forall x: @interp_type Z FE, T x).
Proof.
intro F; refine (fun (x: @interp_type Z FE) =>
let '(a, b, c, d, e, f, g, h, i, j) := x in
F a b c d e f g h i j).
Defined.
Ltac intro_vars_for R := revert R;
match goal with
| [ |- forall x, @?T x ] => apply (@unflatten T); intros
end.
Definition ge25519_add_expr :=
Eval cbv beta delta [fe25519 carry_add mul carry_sub opp Let_In] in carry_add.
Definition ge25519_sub_expr :=
Eval cbv beta delta [fe25519 carry_add mul carry_sub opp Let_In] in carry_sub.
Definition ge25519_mul_expr :=
Eval cbv beta delta [fe25519 carry_add mul carry_sub opp Let_In] in mul.
Definition ge25519_opp_expr :=
Eval cbv beta delta [fe25519 carry_add mul carry_sub opp Let_In] in opp.
Definition ge25519_add' (P Q: @interp_type Z FE):
{ r: @HL.Expr Z FE | HL.Interp r = ge25519_add_expr P Q }.
Proof.
intro_vars_for P.
intro_vars_for Q.
eexists.
cbv beta delta [ge25519_add_expr].
etransitivity; [reflexivity|].
let R := HL.rhs_of_goal in
let X := HL.Reify R in
transitivity (HL.Interp (X bits)); [reflexivity|].
cbv iota beta delta [ HL.Interp
interp_type interp_binop HL.interp
Z.land ZEvaluable eadd esub emul eshiftr eand].
reflexivity.
Defined.
Definition ge25519_sub' (P Q: @interp_type Z FE):
{ r: @HL.Expr Z FE | HL.Interp r = ge25519_sub_expr P Q }.
Proof.
intro_vars_for P.
intro_vars_for Q.
eexists.
cbv beta delta [ge25519_sub_expr].
etransitivity; [reflexivity|].
let R := HL.rhs_of_goal in
let X := HL.Reify R in
transitivity (HL.Interp (X bits)); [reflexivity|].
cbv iota beta delta [ HL.Interp
interp_type interp_binop HL.interp
Z.land ZEvaluable eadd esub emul eshiftr eand].
reflexivity.
Defined.
Definition ge25519_mul' (P Q: @interp_type Z FE):
{ r: @HL.Expr Z FE | HL.Interp r = ge25519_mul_expr P Q }.
Proof.
intro_vars_for P.
intro_vars_for Q.
eexists.
cbv beta delta [ge25519_mul_expr].
etransitivity; [reflexivity|].
let R := HL.rhs_of_goal in
let X := HL.Reify R in
transitivity (HL.Interp (X bits)); [reflexivity|].
cbv iota beta delta [ HL.Interp
interp_type interp_binop HL.interp
Z.land ZEvaluable eadd esub emul eshiftr eand].
reflexivity.
Defined.
Definition ge25519_opp' (P: @interp_type Z FE):
{ r: @HL.Expr Z FE | HL.Interp r = ge25519_opp_expr P }.
Proof.
intro_vars_for P.
eexists.
cbv beta delta [ge25519_opp_expr zero_].
etransitivity; [reflexivity|].
let R := HL.rhs_of_goal in
let X := HL.Reify R in
transitivity (HL.Interp (X bits)); [reflexivity|].
cbv iota beta delta [ HL.Interp
interp_type interp_binop HL.interp
Z.land ZEvaluable eadd esub emul eshiftr eand].
reflexivity.
Defined.
Definition ge25519_add (P Q: @interp_type Z FE) :=
proj1_sig (ge25519_add' P Q).
Definition ge25519_sub (P Q: @interp_type Z FE) :=
proj1_sig (ge25519_sub' P Q).
Definition ge25519_mul (P Q: @interp_type Z FE) :=
proj1_sig (ge25519_mul' P Q).
Definition ge25519_opp (P: @interp_type Z FE) :=
proj1_sig (ge25519_opp' P).
End Expressions.
Module AddExpr <: Expression.
Definition bits: nat := bits.
Definition inputs: nat := 20.
Definition width: Width bits := width.
Definition ResultType := FE.
Definition inputBounds := feBound ++ feBound.
Definition prog: NAry 20 Z (@HL.Expr Z ResultType) :=
Eval cbv in (flatten (fun p => (flatten (fun q => ge25519_add p q)))).
End AddExpr.
Module SubExpr <: Expression.
Definition bits: nat := bits.
Definition inputs: nat := 20.
Definition width: Width bits := width.
Definition ResultType := FE.
Definition inputBounds := feBound ++ feBound.
Definition ge25519_sub_expr :=
Eval cbv beta delta [fe25519 carry_add mul carry_sub opp Let_In] in
carry_sub.
Definition prog: NAry 20 Z (@HL.Expr Z ResultType) :=
Eval cbv in (flatten (fun p => (flatten (fun q => ge25519_sub p q)))).
End SubExpr.
Module MulExpr <: Expression.
Definition bits: nat := bits.
Definition inputs: nat := 20.
Definition width: Width bits := width.
Definition ResultType := FE.
Definition inputBounds := feBound ++ feBound.
Definition prog: NAry 20 Z (@HL.Expr Z ResultType) :=
Eval cbv in (flatten (fun p => (flatten (fun q => ge25519_mul p q)))).
End MulExpr.
Module OppExpr <: Expression.
Definition bits: nat := bits.
Definition inputs: nat := 10.
Definition width: Width bits := width.
Definition ResultType := FE.
Definition inputBounds := feBound.
Definition prog: NAry 10 Z (@HL.Expr Z ResultType) :=
Eval cbv in (flatten ge25519_opp).
End OppExpr.
Module Add := Pipeline AddExpr.
Module Sub := Pipeline SubExpr.
Module Mul := Pipeline MulExpr.
Module Opp := Pipeline OppExpr.
End GF25519.
Extraction "GF25519Add" GF25519.Add.
Extraction "GF25519Sub" GF25519.Sub.
Extraction "GF25519Mul" GF25519.Mul.
Extraction "GF25519Opp" GF25519.Opp.
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