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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.Specific.ArithmeticSynthesisTest.
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.
Import ListNotations.
Require Import Crypto.Specific.IntegrationTestTemporaryMiscCommon.
Require Import Crypto.Compilers.Z.Bounds.Pipeline.
Section BoundedField25p5.
Local Coercion Z.of_nat : nat >-> Z.
Let limb_widths := Eval vm_compute in (List.map (fun i => Z.log2 (wt (S i) / wt i)) (seq 0 sz)).
Let length_lw := Eval compute in List.length limb_widths.
Local Notation b_of exp := {| lower := 0 ; upper := 2^exp + 2^(exp-3) |}%Z (only parsing). (* max is [(0, 2^(exp+2) + 2^exp + 2^(exp-1) + 2^(exp-3) + 2^(exp-4) + 2^(exp-5) + 2^(exp-6) + 2^(exp-10) + 2^(exp-12) + 2^(exp-13) + 2^(exp-14) + 2^(exp-15) + 2^(exp-17) + 2^(exp-23) + 2^(exp-24))%Z] *)
(* The definition [bounds_exp] is a tuple-version of the
limb-widths, which are the [exp] argument in [b_of] above, i.e.,
the approximate base-2 exponent of the bounds on the limb in that
position. *)
Let bounds_exp : Tuple.tuple Z length_lw
:= Eval compute in
Tuple.from_list length_lw limb_widths eq_refl.
Let bounds : Tuple.tuple zrange length_lw
:= Eval compute in
Tuple.map (fun e => b_of e) bounds_exp.
Let lgbitwidth := Eval compute in (Z.to_nat (Z.log2_up (List.fold_right Z.max 0 limb_widths))).
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 phi : feBW -> F m :=
fun x => B.Positional.Fdecode wt (BoundedWordToZ _ _ _ x).
(* TODO : change this to field once field isomorphism happens *)
Definition mul :
{ mul : feBW -> feBW -> feBW
| forall a b, phi (mul a b) = F.mul (phi a) (phi b) }.
Proof.
lazymatch goal with
| [ |- { f | forall a b, ?phi (f a b) = @?rhs a b } ]
=> apply lift2_sig with (P:=fun a b f => phi f = rhs a b)
end.
intros.
eexists_sig_etransitivity. all:cbv [phi].
rewrite <- (proj2_sig mul_sig).
symmetry; rewrite <- (proj2_sig carry_sig); symmetry.
set (carry_mulZ := fun a b => proj1_sig carry_sig (proj1_sig mul_sig a b)).
change (proj1_sig carry_sig (proj1_sig mul_sig ?a ?b)) with (carry_mulZ a b).
context_to_dlet_in_rhs carry_mulZ.
cbv beta iota delta [carry_mulZ proj1_sig mul_sig carry_sig fst snd runtime_add runtime_and runtime_mul runtime_opp runtime_shr sz].
reflexivity.
sig_dlet_in_rhs_to_context.
apply (fun f => proj2_sig_map (fun THIS_NAME_MUST_NOT_BE_UNDERSCORE_TO_WORK_AROUND_CONSTR_MATCHING_ANAOMLIES___BUT_NOTE_THAT_IF_THIS_NAME_IS_LOWERCASE_A___THEN_REIFICATION_STACK_OVERFLOWS___AND_I_HAVE_NO_IDEA_WHATS_GOING_ON p => f_equal f p)).
(* jgross start here! *)
(*Set Ltac Profiling.*)
Time refine_reflectively. (* Finished transaction in 19.348 secs (19.284u,0.036s) (successful) *)
(*Show Ltac Profile.*)
(* total time: 19.632s
tactic local total calls max
────────────────────────────────────────┴──────┴──────┴───────┴─────────┘
─refine_reflectively ------------------- 0.0% 98.4% 1 19.320s
─ReflectiveTactics.do_reflective_pipelin -0.0% 96.2% 1 18.884s
─ReflectiveTactics.solve_side_conditions 1.2% 96.1% 1 18.860s
─ReflectiveTactics.do_reify ------------ 27.7% 44.0% 1 8.640s
─ReflectiveTactics.abstract_vm_compute_r 12.3% 13.9% 2 2.024s
─ReflectiveTactics.abstract_vm_compute_r 8.9% 12.2% 2 1.576s
─Reify_rhs_gen ------------------------- 0.8% 11.7% 1 2.300s
─ReflectiveTactics.renamify_rhs -------- 10.4% 11.5% 1 2.260s
─ReflectiveTactics.abstract_rhs -------- 4.6% 5.8% 1 1.148s
─clear (var_list) ---------------------- 5.2% 5.2% 57 0.184s
─eexact -------------------------------- 4.1% 4.1% 68 0.028s
─prove_interp_compile_correct ---------- 0.0% 3.4% 1 0.664s
─ReflectiveTactics.abstract_cbv_interp_r 2.7% 3.3% 1 0.648s
─unify (constr) (constr) --------------- 3.2% 3.2% 6 0.248s
─rewrite ?EtaInterp.InterpExprEta ------ 3.1% 3.1% 1 0.612s
─ReflectiveTactics.abstract_cbv_rhs ---- 2.0% 2.7% 1 0.532s
─Glue.refine_to_reflective_glue -------- 0.0% 2.2% 1 0.436s
─rewrite H ----------------------------- 2.1% 2.1% 1 0.420s
tactic local total calls max
────────────────────────────────────────┴──────┴──────┴───────┴─────────┘
─refine_reflectively ------------------- 0.0% 98.4% 1 19.320s
├─ReflectiveTactics.do_reflective_pipel -0.0% 96.2% 1 18.884s
│└ReflectiveTactics.solve_side_conditio 1.2% 96.1% 1 18.860s
│ ├─ReflectiveTactics.do_reify -------- 27.7% 44.0% 1 8.640s
│ │ ├─Reify_rhs_gen ------------------- 0.8% 11.7% 1 2.300s
│ │ │ ├─prove_interp_compile_correct -- 0.0% 3.4% 1 0.664s
│ │ │ │└rewrite ?EtaInterp.InterpExprEt 3.1% 3.1% 1 0.612s
│ │ │ └─rewrite H --------------------- 2.1% 2.1% 1 0.420s
│ │ └─eexact -------------------------- 4.1% 4.1% 68 0.028s
│ ├─ReflectiveTactics.abstract_vm_compu 12.3% 13.9% 2 2.024s
│ ├─ReflectiveTactics.abstract_vm_compu 8.9% 12.2% 2 1.576s
│ ├─ReflectiveTactics.renamify_rhs ---- 10.4% 11.5% 1 2.260s
│ ├─ReflectiveTactics.abstract_rhs ---- 4.6% 5.8% 1 1.148s
│ ├─ReflectiveTactics.abstract_cbv_inte 2.7% 3.3% 1 0.648s
│ └─ReflectiveTactics.abstract_cbv_rhs 2.0% 2.7% 1 0.532s
└─Glue.refine_to_reflective_glue ------ 0.0% 2.2% 1 0.436s
*)
Time Defined. (* Finished transaction in 10.167 secs (10.123u,0.023s) (successful) *)
End BoundedField25p5.
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