diff options
-rw-r--r-- | src/Util/WordUtil.v | 31 | ||||
-rw-r--r-- | src/Util/ZUtil.v | 5 |
2 files changed, 36 insertions, 0 deletions
diff --git a/src/Util/WordUtil.v b/src/Util/WordUtil.v index de5cd0847..3c52146dc 100644 --- a/src/Util/WordUtil.v +++ b/src/Util/WordUtil.v @@ -15,6 +15,8 @@ Create HintDb push_wordToN discriminated. Hint Extern 1 => autorewrite with pull_wordToN in * : pull_wordToN. Hint Extern 1 => autorewrite with push_wordToN in * : push_wordToN. +Ltac word_util_arith := omega. + Lemma pow2_id : forall n, pow2 n = 2 ^ n. Proof. induction n; intros; simpl; auto. @@ -268,3 +270,32 @@ Proof. | [ H : weqb _ _ = true |- _ ] => apply weqb_true_iff in H; subst end. Qed. + +Local Notation bounds_2statement wop Zop + := (forall {sz} (x y : word sz), + (Z.log2 (Z.of_N (wordToN x)) < Z.of_nat sz + -> Z.log2 (Z.of_N (wordToN y)) < Z.of_nat sz + -> 0 <= Zop (Z.of_N (wordToN x)) (Z.of_N (wordToN y)) + -> Z.log2 (Zop (Z.of_N (wordToN x)) (Z.of_N (wordToN y))) < Z.of_nat sz + -> Z.of_N (wordToN (wop x y)) = (Zop (Z.of_N (wordToN x)) (Z.of_N (wordToN y))))%Z). + +Lemma wordToN_wplus : bounds_2statement (@wplus _) Z.add. +Proof. + admit. +Admitted. +Hint Rewrite @wordToN_wplus using word_util_arith : push_wordToN. +Hint Rewrite <- @wordToN_wplus using word_util_arith : pull_wordToN. + +Lemma wordToN_wminus : bounds_2statement (@wminus _) Z.sub. +Proof. + admit. +Admitted. +Hint Rewrite @wordToN_wminus using word_util_arith : push_wordToN. +Hint Rewrite <- @wordToN_wminus using word_util_arith : pull_wordToN. + +Lemma wordToN_wmult : bounds_2statement (@wmult _) Z.mul. +Proof. + admit. +Admitted. +Hint Rewrite @wordToN_wmult using word_util_arith : push_wordToN. +Hint Rewrite <- @wordToN_wmult using word_util_arith : pull_wordToN. diff --git a/src/Util/ZUtil.v b/src/Util/ZUtil.v index 852803638..c5a2ae99d 100644 --- a/src/Util/ZUtil.v +++ b/src/Util/ZUtil.v @@ -77,6 +77,8 @@ Create HintDb pull_Zshift discriminated. Create HintDb push_Zshift discriminated. Create HintDb pull_Zof_N discriminated. Create HintDb push_Zof_N discriminated. +Create HintDb pull_Zto_N discriminated. +Create HintDb push_Zto_N discriminated. Create HintDb Zshift_to_pow discriminated. Create HintDb Zpow_to_shift discriminated. Hint Extern 1 => autorewrite with push_Zopp in * : push_Zopp. @@ -101,6 +103,8 @@ Hint Extern 1 => autorewrite with Zshift_to_pow in * : Zshift_to_pow. Hint Extern 1 => autorewrite with Zpow_to_shift in * : Zpow_to_shift. Hint Extern 1 => autorewrite with pull_Zof_N in * : pull_Zof_N. Hint Extern 1 => autorewrite with push_Zof_N in * : push_Zof_N. +Hint Extern 1 => autorewrite with pull_Zto_N in * : pull_Zto_N. +Hint Extern 1 => autorewrite with push_Zto_N in * : push_Zto_N. Hint Rewrite Z.div_opp_l_nz Z.div_opp_l_z using zutil_arith : pull_Zopp. Hint Rewrite Z.mul_opp_l : pull_Zopp. Hint Rewrite <- Z.opp_add_distr : pull_Zopp. @@ -119,6 +123,7 @@ Hint Rewrite Z_mod_nz_opp_full using zutil_arith : push_Zmod. Hint Rewrite Z_mod_same_full : push_Zmod. Hint Rewrite Nat2Z.id N2Z.id : zsimplify. Hint Rewrite Nat2Z.id : push_Zof_nat. +Hint Rewrite N2Z.id : push_Zto_N. Hint Rewrite N2Z.id : pull_Zof_N. Hint Rewrite N2Z.inj_pos N2Z.inj_abs_N N2Z.inj_add N2Z.inj_mul N2Z.inj_sub_max N2Z.inj_succ N2Z.inj_pred_max N2Z.inj_min N2Z.inj_max N2Z.inj_div N2Z.inj_quot N2Z.inj_rem N2Z.inj_div2 N2Z.inj_pow N2Z.inj_0 : push_Zof_N. Hint Rewrite N2Z.inj_compare N2Z.inj_testbit : pull_Zof_N. |