Significantly faster wordToN, I hope

After    | File Name                                           | Before   || Change
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3m22.43s | Total                                               | 3m22.13s || +0m00.30s
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0m34.51s | Spec/Ed25519                                        | 0m34.56s || -0m00.05s
0m28.83s | Experiments/Ed25519                                 | 0m28.60s || +0m00.22s
0m17.28s | EdDSARepChange                                      | 0m17.25s || +0m00.03s
0m08.66s | [require-in-module,deprecated]
src/Assembly/GF25519 | 0m08.66s || +0m00.00s
0m08.46s | Encoding/PointEncoding                              | 0m08.47s || -0m00.00s
0m08.35s | Specific/GF25519BoundedCommonWord                   | 0m08.44s || -0m00.08s
0m07.74s | Specific/GF25519Reflective                          | 0m07.69s || +0m00.04s
0m07.59s | Specific/GF25519Reflective/Reified/Mul              | 0m07.65s || -0m00.06s
0m07.35s | Specific/GF25519BoundedCommon                       | 0m07.39s || -0m00.04s
0m06.88s | Specific/GF25519Reflective/Reified/Freeze           | 0m06.86s || +0m00.01s
0m05.80s | Bedrock/Word                                        | 0m05.74s || +0m00.05s
0m05.43s | Specific/SC25519                                    | 0m05.32s || +0m00.10s
0m04.76s | Reflection/Z/Interpretations                        | 0m04.65s || +0m00.10s
0m04.27s | Encoding/PointEncodingPre                           | 0m04.31s || -0m00.04s
0m03.72s | Assembly/GF25519BoundedInstantiation                | 0m03.68s || +0m00.04s
0m03.21s | Specific/GF25519Reflective/Reified/CarrySub         | 0m03.34s || -0m00.12s
0m02.91s | Specific/GF25519Reflective/Reified/CarryOpp         | 0m02.86s || +0m00.05s
0m02.84s | Specific/GF25519Reflective/Reified/CarryAdd         | 0m02.87s || -0m00.03s
0m02.70s | Assembly/State                                      | 0m02.67s || +0m00.03s
0m02.00s | Specific/GF25519Reflective/Reified/Unpack           | 0m01.96s || +0m00.04s
0m01.97s | Specific/GF25519Reflective/Reified/Sub              | 0m01.95s || +0m00.02s
0m01.95s | Specific/GF25519Reflective/Reified/Pack             | 0m02.03s || -0m00.07s
0m01.81s | Assembly/Evaluables                                 | 0m01.88s || -0m00.06s
0m01.78s | Specific/GF25519Bounded                             | 0m01.77s || +0m00.01s
0m01.71s | Specific/GF25519Reflective/Reified/Opp              | 0m01.68s || +0m00.03s
0m01.66s | Specific/GF25519Reflective/Reified/Add              | 0m01.66s || +0m00.00s
0m01.52s | Assembly/Compile                                    | 0m01.48s || +0m00.04s
0m01.49s | Specific/GF25519Reflective/Reified/GeModulus        | 0m01.48s || +0m00.01s
0m01.44s | Assembly/WordizeUtil                                | 0m01.51s || -0m00.07s
0m01.33s | Assembly/Bounds                                     | 0m01.34s || -0m00.01s
0m01.22s | Assembly/Conversions                                | 0m01.23s || -0m00.01s
0m01.05s | Util/WordUtil                                       | 0m01.03s || +0m00.02s
0m00.94s | Assembly/LL                                         | 0m00.94s || +0m00.00s
0m00.94s | Assembly/Pipeline                                   | 0m00.90s || +0m00.03s
0m00.87s | Assembly/HL                                         | 0m00.89s || -0m00.02s
0m00.81s | Assembly/PhoasCommon                                | 0m00.77s || +0m00.04s
0m00.79s | Assembly/QhasmEvalCommon                            | 0m00.83s || -0m00.03s
0m00.75s | Specific/GF25519Reflective/Reified                  | 0m00.80s || -0m00.05s
0m00.72s | Specific/GF25519Reflective/Common                   | 0m00.71s || +0m00.01s
0m00.70s | Encoding/ModularWordEncodingTheorems                | 0m00.65s || +0m00.04s
0m00.66s | Spec/EdDSA                                          | 0m00.66s || +0m00.00s
0m00.61s | Spec/ModularWordEncoding                            | 0m00.58s || +0m00.03s
0m00.61s | Encoding/ModularWordEncodingPre                     | 0m00.67s || -0m00.06s
0m00.51s | Assembly/Qhasm                                      | 0m00.51s || +0m00.00s
0m00.48s | Assembly/StringConversion                           | 0m00.50s || -0m00.02s
0m00.47s | Assembly/QhasmUtil                                  | 0m00.40s || +0m00.06s
0m00.36s | Assembly/QhasmCommon                                | 0m00.31s || +0m00.04s

1 files changed, 6 insertions, 4 deletions

diff --git a/Bedrock/Word.v b/Bedrock/Word.v
index 036b3198a..2c518807d 100644
--- a/Bedrock/Word.v
+++ b/Bedrock/Word.v
@@ -48,8 +48,8 @@ Fixpoint natToWord (sz n : nat) : word sz :=
 Fixpoint wordToN sz (w : word sz) : N :=
   match w with
     | WO => 0
-    | WS false _ w' => 2 * wordToN w'
-    | WS true _ w' => Nsucc (2 * wordToN w')
+    | WS false _ w' => N.double (wordToN w')
+    | WS true _ w' => N.succ_double (wordToN w')
   end%N.
 
 Definition Nmod2 (n : N) : bool :=
@@ -506,6 +506,8 @@ Theorem wordToN_nat : forall sz (w : word sz), wordToN w = N_of_nat (wordToNat w
   rewrite N_of_mult.
   rewrite <- IHw.
   rewrite Nmult_comm.
+  rewrite N.succ_double_spec.
+  rewrite N.add_1_r.
   reflexivity.
 
   rewrite N_of_mult.
@@ -1038,12 +1040,12 @@ Proof.
   induction a; intro b0; rewrite (shatter_word b0); intuition.
   simpl in H.
   destruct b; destruct (whd b0); intros.
-  f_equal. eapply IHa. eapply Nsucc_inj in H.
+  f_equal. eapply IHa. eapply N.succ_double_inj in H.
   destruct (wordToN a); destruct (wordToN (wtl b0)); try congruence.
   destruct (wordToN (wtl b0)); destruct (wordToN a); inversion H.
   destruct (wordToN (wtl b0)); destruct (wordToN a); inversion H.
   f_equal. eapply IHa.
-  destruct (wordToN a); destruct (wordToN (wtl b0)); try congruence.
+  destruct (wordToN a); destruct (wordToN (wtl b0)); simpl in *; try congruence.
 Qed.
 Lemma unique_inverse : forall sz (a b1 b2 : word sz),
   a ^+ b1 = wzero _ ->