Factor out specific code underlying ReificationTypes

After    | File Name                                   | Before   || Change
------------------------------------------------------------------------------
4m29.48s | Total                                       | 4m30.12s || -0m00.63s
------------------------------------------------------------------------------
0m27.97s | Specific/X25519/C32/fesquare                | 0m26.68s || +0m01.28s
0m00.73s | Specific/X25519/C32/ReificationTypes        | 0m02.43s || -0m01.70s
1m54.60s | Specific/X25519/C64/ladderstep              | 1m55.11s || -0m00.51s
0m52.88s | Specific/X25519/C32/femul                   | 0m53.07s || -0m00.18s
0m29.56s | Specific/X25519/C32/ArithmeticSynthesisTest | 0m29.57s || -0m00.01s
0m10.01s | Specific/X25519/C64/femul                   | 0m10.08s || -0m00.07s
0m08.84s | Specific/IntegrationTestSub                 | 0m08.39s || +0m00.44s
0m08.42s | Specific/X25519/C64/ArithmeticSynthesisTest | 0m08.17s || +0m00.25s
0m07.64s | Specific/IntegrationTestFreeze              | 0m08.01s || -0m00.37s
0m07.23s | Specific/X25519/C64/fesquare                | 0m07.31s || -0m00.07s
0m00.86s | Specific/ReificationTypes                   |   N/A    || +0m00.86s
0m00.74s | Specific/X25519/C64/ReificationTypes        | 0m01.30s || -0m00.56s

5 files changed, 22 insertions, 110 deletions

diff --git a/src/Specific/X25519/C32/ArithmeticSynthesisTest.v b/src/Specific/X25519/C32/ArithmeticSynthesisTest.v
index 6b1d5ee11..c961afd69 100644
--- a/src/Specific/X25519/C32/ArithmeticSynthesisTest.v
+++ b/src/Specific/X25519/C32/ArithmeticSynthesisTest.v
@@ -52,6 +52,8 @@ Section Ops.
   Lemma sz_nonzero : sz <> 0%nat. Proof. vm_decide. Qed.
   Lemma wt_nonzero i : wt i <> 0.
   Proof. eapply pow_ceil_mul_nat_nonzero; vm_decide. Qed.
+  Lemma wt_nonneg i : 0 <= wt i.
+  Proof. apply pow_ceil_mul_nat_nonneg; vm_decide. Qed.
   Lemma wt_divides i : wt (S i) / wt i > 0.
   Proof. apply pow_ceil_mul_nat_divide; vm_decide. Qed.
   Lemma wt_divides' i : wt (S i) / wt i <> 0.
diff --git a/src/Specific/X25519/C32/ReificationTypes.v b/src/Specific/X25519/C32/ReificationTypes.v
index 6b2a47070..c5a9e0fd3 100644
--- a/src/Specific/X25519/C32/ReificationTypes.v
+++ b/src/Specific/X25519/C32/ReificationTypes.v
@@ -1,58 +1,12 @@
-Require Import Coq.ZArith.ZArith.
-Require Import Coq.romega.ROmega.
-Require Import Coq.Lists.List.
-Local Open Scope Z_scope.
-
-Require Import Crypto.Arithmetic.Core.
-Require Import Crypto.Arithmetic.PrimeFieldTheorems.
-Require Import Crypto.Util.FixedWordSizes.
-Require Import Crypto.Util.Tuple.
-Require Import Crypto.Util.ZRange Crypto.Util.BoundedWord.
-Require Import Crypto.Util.Tactics.DestructHead.
+Require Import Crypto.Specific.ReificationTypes.
 Require Import Crypto.Specific.X25519.C32.ArithmeticSynthesisTest.
 
-Section BoundedField.
-  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)).
-
-  Local Notation b_of exp := {| lower := 0 ; upper := P.upper_bound_of_exponent exp |}%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 sz
-    := Eval compute in
-        Tuple.from_list sz limb_widths eq_refl.
-  Let bounds : Tuple.tuple zrange sz
-    := 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.
-  Definition feW : Type := Eval cbv [lgbitwidth] in tuple (wordT lgbitwidth) sz.
-  Definition feW_bounded : feW -> Prop
-    := Eval cbv [bounds] in fun w => is_bounded_by None bounds (map wordToZ w).
-  Definition feBW : Type := Eval cbv [bitwidth bounds] in BoundedWord sz bitwidth bounds.
+Module RP <: ReificationTypesPrePackage.
+  Definition ReificationTypes_package' : { T : _ & T }.
+  Proof. make_ReificationTypes_package wt sz bounds m wt_nonneg P.upper_bound_of_exponent. Defined.
 
-  Lemma feBW_bounded (a : feBW)
-    : 0 <= B.Positional.eval wt (BoundedWordToZ sz bitwidth bounds a) < 2 * Z.pos m.
-  Proof.
-    destruct a as [a H]; unfold BoundedWordToZ, proj1_sig.
-    destruct_head_hnf' and.
-    cbv -[Z.le Z.add Z.mul Z.lt fst snd wordToZ wt] in *; cbn [fst snd] in *.
-    repeat match goal with
-           | [ |- context[@wordToZ ?n ?x] ]
-             => generalize dependent (@wordToZ n x); intros
-           | [ |- context[wt ?n] ]
-             => let v := (eval compute in (wt n)) in change (wt n) with v
-           end.
-    romega.
-  Qed.
+  Definition ReificationTypes_package
+    := Eval cbv [ReificationTypes_package' projT2] in projT2 ReificationTypes_package'.
+End RP.
 
-  Definition phiW : feW -> F m :=
-    fun x => B.Positional.Fdecode wt (Tuple.map wordToZ x).
-  Definition phiBW : feBW -> F m :=
-    fun x => B.Positional.Fdecode wt (BoundedWordToZ _ _ _ x).
-End BoundedField.
+Module Export ReificationTypes := MakeReificationTypes RP.
diff --git a/src/Specific/X25519/C64/ArithmeticSynthesisTest.v b/src/Specific/X25519/C64/ArithmeticSynthesisTest.v
index f4ef43f20..6994e13be 100644
--- a/src/Specific/X25519/C64/ArithmeticSynthesisTest.v
+++ b/src/Specific/X25519/C64/ArithmeticSynthesisTest.v
@@ -52,6 +52,8 @@ Section Ops.
   Lemma sz_nonzero : sz <> 0%nat. Proof. vm_decide. Qed.
   Lemma wt_nonzero i : wt i <> 0.
   Proof. eapply pow_ceil_mul_nat_nonzero; vm_decide. Qed.
+  Lemma wt_nonneg i : 0 <= wt i.
+  Proof. apply pow_ceil_mul_nat_nonneg; vm_decide. Qed.
   Lemma wt_divides i : wt (S i) / wt i > 0.
   Proof. apply pow_ceil_mul_nat_divide; vm_decide. Qed.
   Lemma wt_divides' i : wt (S i) / wt i <> 0.
diff --git a/src/Specific/X25519/C64/ReificationTypes.v b/src/Specific/X25519/C64/ReificationTypes.v
index 009145467..0e999b2fc 100644
--- a/src/Specific/X25519/C64/ReificationTypes.v
+++ b/src/Specific/X25519/C64/ReificationTypes.v
@@ -1,58 +1,12 @@
-Require Import Coq.ZArith.ZArith.
-Require Import Coq.romega.ROmega.
-Require Import Coq.Lists.List.
-Local Open Scope Z_scope.
-
-Require Import Crypto.Arithmetic.Core.
-Require Import Crypto.Arithmetic.PrimeFieldTheorems.
-Require Import Crypto.Util.FixedWordSizes.
-Require Import Crypto.Util.Tuple.
-Require Import Crypto.Util.ZRange Crypto.Util.BoundedWord.
-Require Import Crypto.Util.Tactics.DestructHead.
+Require Import Crypto.Specific.ReificationTypes.
 Require Import Crypto.Specific.X25519.C64.ArithmeticSynthesisTest.
 
-Section BoundedField.
-  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)).
-
-  Local Notation b_of exp := {| lower := 0 ; upper := P.upper_bound_of_exponent exp |}%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 sz
-    := Eval compute in
-        Tuple.from_list sz limb_widths eq_refl.
-  Let bounds : Tuple.tuple zrange sz
-    := 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.
-  Definition feW : Type := Eval cbv [lgbitwidth] in tuple (wordT lgbitwidth) sz.
-  Definition feW_bounded : feW -> Prop
-    := Eval cbv [bounds] in fun w => is_bounded_by None bounds (map wordToZ w).
-  Definition feBW : Type := Eval cbv [bitwidth bounds] in BoundedWord sz bitwidth bounds.
+Module RP <: ReificationTypesPrePackage.
+  Definition ReificationTypes_package' : { T : _ & T }.
+  Proof. make_ReificationTypes_package wt sz bounds m wt_nonneg P.upper_bound_of_exponent. Defined.
 
-  Lemma feBW_bounded (a : feBW)
-    : 0 <= B.Positional.eval wt (BoundedWordToZ sz bitwidth bounds a) < 2 * Z.pos m.
-  Proof.
-    destruct a as [a H]; unfold BoundedWordToZ, proj1_sig.
-    destruct_head_hnf' and.
-    cbv -[Z.le Z.add Z.mul Z.lt fst snd wordToZ wt] in *; cbn [fst snd] in *.
-    repeat match goal with
-           | [ |- context[@wordToZ ?n ?x] ]
-             => generalize dependent (@wordToZ n x); intros
-           | [ |- context[wt ?n] ]
-             => let v := (eval compute in (wt n)) in change (wt n) with v
-           end.
-    romega.
-  Qed.
+  Definition ReificationTypes_package
+    := Eval cbv [ReificationTypes_package' projT2] in projT2 ReificationTypes_package'.
+End RP.
 
-  Definition phiW : feW -> F m :=
-    fun x => B.Positional.Fdecode wt (Tuple.map wordToZ x).
-  Definition phiBW : feBW -> F m :=
-    fun x => B.Positional.Fdecode wt (BoundedWordToZ _ _ _ x).
-End BoundedField.
+Module Export ReificationTypes := MakeReificationTypes RP.
diff --git a/src/Specific/X25519/C64/ladderstepDisplay.log b/src/Specific/X25519/C64/ladderstepDisplay.log
index ca8ba4396..4e22b729f 100644
--- a/src/Specific/X25519/C64/ladderstepDisplay.log
+++ b/src/Specific/X25519/C64/ladderstepDisplay.log
@@ -1,4 +1,4 @@
-λ x x0 x1 x2 x3 : ReificationTypes.feW,
+λ x x0 x1 x2 x3 : ReificationTypes.RP.feW,
 let (a, b) := Interp-η
 (λ var : Syntax.base_type → Type,
  λ '(x15, x16, x14, x12, x10, (x25, x26, x24, x22, x20, (x33, x34, x32, x30, x28)), (x43, x44, x42, x40, x38, (x51, x52, x50, x48, x46)))%core,
@@ -367,4 +367,4 @@ let (a, b) := Interp-η
 (let (a0, b0) := a in
 (a0, b0), let (a0, b0) := b in
 (a0, b0))%core
-     : ReificationTypes.feW → ReificationTypes.feW → ReificationTypes.feW → ReificationTypes.feW → ReificationTypes.feW → ReificationTypes.feW * ReificationTypes.feW * (ReificationTypes.feW * ReificationTypes.feW)
+     : ReificationTypes.RP.feW → ReificationTypes.RP.feW → ReificationTypes.RP.feW → ReificationTypes.RP.feW → ReificationTypes.RP.feW → ReificationTypes.RP.feW * ReificationTypes.RP.feW * (ReificationTypes.RP.feW * ReificationTypes.RP.feW)