Require Import Coq.ZArith.ZArith.
Require Import Coq.Lists.List.
Local Open Scope Z_scope.

Require Import Crypto.Arithmetic.Core.
Require Import Crypto.Util.FixedWordSizes.
Require Import Crypto.Arithmetic.MontgomeryReduction.WordByWord.Definition.
Require Import Crypto.Arithmetic.Core. Import B.
Require Crypto.Arithmetic.Saturated.MontgomeryAPI.
Require Import Crypto.Arithmetic.Saturated.UniformWeight.
Require Import Crypto.Specific.MontgomeryP256_128.
Require Import Crypto.Arithmetic.PrimeFieldTheorems.
Require Import Crypto.Util.Tuple Crypto.Util.Sigma Crypto.Util.Sigma.MapProjections Crypto.Util.Sigma.Lift Crypto.Util.Notations Crypto.Util.ZRange Crypto.Util.BoundedWord.
Require Import Crypto.Util.Tactics.Head.
Require Import Crypto.Util.Tactics.MoveLetIn.
Require Import Crypto.Util.Tactics.DestructHead.
Require Import Crypto.Util.ZUtil.Tactics.LtbToLt.
Import ListNotations.

Require Import Crypto.Specific.Framework.IntegrationTestTemporaryMiscCommon.

Require Import Crypto.Compilers.Z.Bounds.Pipeline.

Section BoundedField25p5.
  Local Coercion Z.of_nat : nat >-> Z.

  Let bound1 : zrange
    := Eval compute in
        {| lower := 0 ; upper := r-1 |}.
  Let bounds : Tuple.tuple zrange sz
    := Eval compute in
        Tuple.repeat bound1 sz.

  Let lgbitwidth := Eval compute in (Z.to_nat (Z.log2_up (Z.log2_up r))).
  Let bitwidth := Eval compute in (2^lgbitwidth)%nat.
  Let feZ : Type := tuple Z sz.
  Let feW : Type := tuple (wordT lgbitwidth) sz.
  Let feBW : Type := BoundedWord sz bitwidth bounds.
  Let eval : feBW -> Z :=
    fun x => MontgomeryAPI.eval (Z.pos r) (BoundedWordToZ _ _ _ x).
  Let feBW_small : Type := { v : feBW | eval v < MontgomeryAPI.eval (n:=sz) (Z.pos r) p256 }.
  Let feBW_of_feBW_small : feBW_small -> feBW := @proj1_sig _ _.
  Local Coercion feBW_of_feBW_small : feBW_small >-> feBW.
  Let phi : feBW -> F m :=
    fun x => montgomery_to_F (eval x).

  Local Ltac op_sig_side_conditions_t _ :=
    try (hnf; rewrite <- (is_bounded_by_None_repeat_In_iff_lt _ _ _)); destruct_head_hnf' sig; try assumption.

  (* TODO : change this to field once field isomorphism happens *)
  Definition nonzero
    : { nonzero : feBW_small -> BoundedWord  1 bitwidth bound1
      | forall A, (BoundedWordToZ _ _ _ (nonzero A) =? 0) = (if Decidable.dec (phi A = F.of_Z m 0) then true else false) }.
  Proof.
    apply_lift_sig; intros; eexists_sig_etransitivity.
    all:cbv [feBW_of_feBW_small phi eval].
    refine (_ : (if Decidable.dec (_ = 0) then true else false) = _).
    lazymatch goal with
    | [ |- (if Decidable.dec ?x then _ else _) = (if Decidable.dec ?y then _ else _) ]
      => cut (x <-> y);
           [ destruct (Decidable.dec x), (Decidable.dec y); try reflexivity; intros [? ?];
             generalize dependent x; generalize dependent y; solve [ intuition congruence ]
           | ]
    end.
    etransitivity; [ | eapply (proj2_sig nonzero) ];
      [ | solve [ op_sig_side_conditions_t () ].. ].
    reflexivity.
    let decP := lazymatch goal with |- { c | _ = if Decidable.dec (?decP = 0) then _ else _ } => decP end in
    apply (@proj2_sig_map _ (fun c => BoundedWordToZ 1 _ _ c = decP) _).
    { intros a' H'; rewrite H'.
      let H := fresh in
      lazymatch goal with |- context[Decidable.dec ?x] => destruct (Decidable.dec x) as [H|H]; try rewrite H end.
      { reflexivity. }
      { let H := fresh in
        lazymatch goal with |- context[?x =? 0] => destruct (x =? 0) eqn:? end;
          try reflexivity.
        Z.ltb_to_lt; congruence. } }
    eexists_sig_etransitivity.
    do_set_sig nonzero.
    cbv_runtime.
    reflexivity.
    sig_dlet_in_rhs_to_context.
    cbv [proj1_sig].
    match goal with
    | [ H : feBW_small |- _ ] => destruct H as [? _]
    end.
    (* jgross start here! *)
    Set Ltac Profiling.
    (*     Set Ltac Profiling.
    Print Ltac ReflectiveTactics.solve_side_conditions.
    Ltac ReflectiveTactics.solve_side_conditions ::= idtac.
    Time refine_reflectively128_with_uint8_with anf. (* Finished transaction in 212.693 secs (212.576u,0.184s) (successful) *)
    { Time ReflectiveTactics.do_reify. }
    { Time UnifyAbstractReflexivity.unify_abstract_vm_compute_rhs_reflexivity. }
    { Time UnifyAbstractReflexivity.unify_abstract_vm_compute_rhs_reflexivity. }
    { Time UnifyAbstractReflexivity.unify_abstract_vm_compute_rhs_reflexivity. }
    { Require Import CNotations.
      Time UnifyAbstractReflexivity.unify_abstract_vm_compute_rhs_reflexivity. }
    { Time UnifyAbstractReflexivity.unify_abstract_vm_compute_rhs_reflexivity. }
    { Time UnifyAbstractReflexivity.unify_abstract_rhs_reflexivity. }
  { Time ReflectiveTactics.unify_abstract_renamify_rhs_reflexivity. }
  { Time SubstLet.subst_let; clear; abstract vm_cast_no_check eq_refl. }
  { Time SubstLet.subst_let; clear; vm_compute; reflexivity. }
  { Time UnifyAbstractReflexivity.unify_abstract_compute_rhs_reflexivity. }
  { Time ReflectiveTactics.unify_abstract_cbv_interp_rhs_reflexivity. }
  { Time abstract ReflectiveTactics.handle_bounds_from_hyps. }
  { Time ReflectiveTactics.handle_boundedness_side_condition. } *)
    Time refine_reflectively128_with_uint8_with anf. (* Finished transaction in 212.693 secs (212.576u,0.184s) (successful) *)
    Show Ltac Profile.
  Time Defined. (* Finished transaction in 21.291 secs (21.231u,0.032s) (successful) *)

Time End BoundedField25p5. (* Finished transaction in 14.666 secs (14.556u,0.111s) (successful) *)

Print Assumptions nonzero.