From a680811dcbd532f3bdc55bc1ac3437e761359469 Mon Sep 17 00:00:00 2001 From: Jason Gross Date: Sat, 13 May 2017 13:09:48 -0400 Subject: Split off pull_Zmod, push_Zmod from ZUtil --- src/Util/ZUtil.v | 206 +------------------------------------------------------ 1 file changed, 1 insertion(+), 205 deletions(-) (limited to 'src/Util/ZUtil.v') diff --git a/src/Util/ZUtil.v b/src/Util/ZUtil.v index 91e42598e..936b4ce76 100644 --- a/src/Util/ZUtil.v +++ b/src/Util/ZUtil.v @@ -17,6 +17,7 @@ Require Export Crypto.Util.ZUtil.EquivModulo. Require Export Crypto.Util.ZUtil.Hints. Require Export Crypto.Util.ZUtil.Land. Require Export Crypto.Util.ZUtil.Modulo. +Require Export Crypto.Util.ZUtil.Modulo.PullPush. Require Export Crypto.Util.ZUtil.Morphisms. Require Export Crypto.Util.ZUtil.Notations. Require Export Crypto.Util.ZUtil.Pow2Mod. @@ -924,16 +925,6 @@ Module Z. Hint Rewrite div_l_distr_if : push_Zdiv. Hint Rewrite <- div_l_distr_if : pull_Zdiv. - Lemma mod_r_distr_if (b : bool) x y z : z mod (if b then x else y) = if b then z mod x else z mod y. - Proof. destruct b; reflexivity. Qed. - Hint Rewrite mod_r_distr_if : push_Zmod. - Hint Rewrite <- mod_r_distr_if : pull_Zmod. - - Lemma mod_l_distr_if (b : bool) x y z : (if b then x else y) mod z = if b then x mod z else y mod z. - Proof. destruct b; reflexivity. Qed. - Hint Rewrite mod_l_distr_if : push_Zmod. - Hint Rewrite <- mod_l_distr_if : pull_Zmod. - Lemma div_add_exact x y d : d <> 0 -> x mod d = 0 -> (x + y) / d = x / d + y / d. Proof. intros; rewrite (Z_div_exact_full_2 x d) at 1 by assumption. @@ -941,121 +932,6 @@ Module Z. Qed. Hint Rewrite div_add_exact using zutil_arith : zsimplify. - (** Version without the [n <> 0] assumption *) - Lemma mul_mod_full a b n : (a * b) mod n = ((a mod n) * (b mod n)) mod n. - Proof. auto using Zmult_mod. Qed. - Hint Rewrite <- mul_mod_full : pull_Zmod. - Hint Resolve mul_mod_full : zarith. - - Lemma mul_mod_l a b n : (a * b) mod n = ((a mod n) * b) mod n. - Proof. - intros; rewrite (mul_mod_full a b), (mul_mod_full (a mod n) b). - autorewrite with zsimplify; reflexivity. - Qed. - Hint Rewrite <- mul_mod_l : pull_Zmod. - Hint Resolve mul_mod_l : zarith. - - Lemma mul_mod_r a b n : (a * b) mod n = (a * (b mod n)) mod n. - Proof. - intros; rewrite (mul_mod_full a b), (mul_mod_full a (b mod n)). - autorewrite with zsimplify; reflexivity. - Qed. - Hint Rewrite <- mul_mod_r : pull_Zmod. - Hint Resolve mul_mod_r : zarith. - - Lemma add_mod_full a b n : (a + b) mod n = ((a mod n) + (b mod n)) mod n. - Proof. auto using Zplus_mod. Qed. - Hint Rewrite <- add_mod_full : pull_Zmod. - Hint Resolve add_mod_full : zarith. - - Lemma add_mod_l a b n : (a + b) mod n = ((a mod n) + b) mod n. - Proof. - intros; rewrite (add_mod_full a b), (add_mod_full (a mod n) b). - autorewrite with zsimplify; reflexivity. - Qed. - Hint Rewrite <- add_mod_l : pull_Zmod. - Hint Resolve add_mod_l : zarith. - - Lemma add_mod_r a b n : (a + b) mod n = (a + (b mod n)) mod n. - Proof. - intros; rewrite (add_mod_full a b), (add_mod_full a (b mod n)). - autorewrite with zsimplify; reflexivity. - Qed. - Hint Rewrite <- add_mod_r : pull_Zmod. - Hint Resolve add_mod_r : zarith. - - Lemma opp_mod_mod a n : (-a) mod n = (-(a mod n)) mod n. - Proof. - intros; destruct (Z_zerop (a mod n)) as [H'|H']; [ rewrite H' | ]; - [ | rewrite !Z_mod_nz_opp_full ]; - autorewrite with zsimplify; lia. - Qed. - Hint Rewrite <- opp_mod_mod : pull_Zmod. - Hint Resolve opp_mod_mod : zarith. - - (** Give alternate names for the next three lemmas, for consistency *) - Lemma sub_mod_full a b n : (a - b) mod n = ((a mod n) - (b mod n)) mod n. - Proof. auto using Zminus_mod. Qed. - Hint Rewrite <- sub_mod_full : pull_Zmod. - Hint Resolve sub_mod_full : zarith. - - Lemma sub_mod_l a b n : (a - b) mod n = ((a mod n) - b) mod n. - Proof. auto using Zminus_mod_idemp_l. Qed. - Hint Rewrite <- sub_mod_l : pull_Zmod. - Hint Resolve sub_mod_l : zarith. - - Lemma sub_mod_r a b n : (a - b) mod n = (a - (b mod n)) mod n. - Proof. auto using Zminus_mod_idemp_r. Qed. - Hint Rewrite <- sub_mod_r : pull_Zmod. - Hint Resolve sub_mod_r : zarith. - - Definition NoZMod (x : Z) := True. - Ltac NoZMod := - lazymatch goal with - | [ |- NoZMod (?x mod ?y) ] => fail 0 "Goal has" x "mod" y - | [ |- NoZMod _ ] => constructor - end. - - Lemma mul_mod_push a b n : NoZMod a -> NoZMod b -> (a * b) mod n = ((a mod n) * (b mod n)) mod n. - Proof. intros; apply mul_mod_full; assumption. Qed. - Hint Rewrite mul_mod_push using solve [ NoZMod ] : push_Zmod. - - Lemma add_mod_push a b n : NoZMod a -> NoZMod b -> (a + b) mod n = ((a mod n) + (b mod n)) mod n. - Proof. intros; apply add_mod_full; assumption. Qed. - Hint Rewrite add_mod_push using solve [ NoZMod ] : push_Zmod. - - Lemma mul_mod_l_push a b n : NoZMod a -> (a * b) mod n = ((a mod n) * b) mod n. - Proof. intros; apply mul_mod_l; assumption. Qed. - Hint Rewrite mul_mod_l_push using solve [ NoZMod ] : push_Zmod. - - Lemma mul_mod_r_push a b n : NoZMod b -> (a * b) mod n = (a * (b mod n)) mod n. - Proof. intros; apply mul_mod_r; assumption. Qed. - Hint Rewrite mul_mod_r_push using solve [ NoZMod ] : push_Zmod. - - Lemma add_mod_l_push a b n : NoZMod a -> (a + b) mod n = ((a mod n) + b) mod n. - Proof. intros; apply add_mod_l; assumption. Qed. - Hint Rewrite add_mod_l_push using solve [ NoZMod ] : push_Zmod. - - Lemma add_mod_r_push a b n : NoZMod b -> (a + b) mod n = (a + (b mod n)) mod n. - Proof. intros; apply add_mod_r; assumption. Qed. - Hint Rewrite add_mod_r_push using solve [ NoZMod ] : push_Zmod. - - Lemma sub_mod_push a b n : NoZMod a -> NoZMod b -> (a - b) mod n = ((a mod n) - (b mod n)) mod n. - Proof. intros; apply Zminus_mod; assumption. Qed. - Hint Rewrite sub_mod_push using solve [ NoZMod ] : push_Zmod. - - Lemma sub_mod_l_push a b n : NoZMod a -> (a - b) mod n = ((a mod n) - b) mod n. - Proof. intros; symmetry; apply Zminus_mod_idemp_l; assumption. Qed. - Hint Rewrite sub_mod_l_push using solve [ NoZMod ] : push_Zmod. - - Lemma sub_mod_r_push a b n : NoZMod b -> (a - b) mod n = (a - (b mod n)) mod n. - Proof. intros; symmetry; apply Zminus_mod_idemp_r; assumption. Qed. - Hint Rewrite sub_mod_r_push using solve [ NoZMod ] : push_Zmod. - - Lemma opp_mod_mod_push a n : NoZMod a -> (-a) mod n = (-(a mod n)) mod n. - Proof. intros; apply opp_mod_mod; assumption. Qed. - Hint Rewrite opp_mod_mod using solve [ NoZMod ] : push_Zmod. - Lemma sub_mod_mod_0 x d : (x - x mod d) mod d = 0. Proof. destruct (Z_zerop d); subst; autorewrite with push_Zmod zsimplify; reflexivity. @@ -1703,83 +1579,3 @@ Module Export BoundsTactics. Ltac prime_bound := Z.prime_bound. Ltac zero_bounds := Z.zero_bounds. End BoundsTactics. - -Ltac push_Zmod := - repeat match goal with - | _ => progress autorewrite with push_Zmod - | [ |- context[(?x * ?y) mod ?z] ] - => first [ rewrite (Z.mul_mod_push x y z) by Z.NoZMod - | rewrite (Z.mul_mod_l_push x y z) by Z.NoZMod - | rewrite (Z.mul_mod_r_push x y z) by Z.NoZMod ] - | [ |- context[(?x + ?y) mod ?z] ] - => first [ rewrite (Z.add_mod_push x y z) by Z.NoZMod - | rewrite (Z.add_mod_l_push x y z) by Z.NoZMod - | rewrite (Z.add_mod_r_push x y z) by Z.NoZMod ] - | [ |- context[(?x - ?y) mod ?z] ] - => first [ rewrite (Z.sub_mod_push x y z) by Z.NoZMod - | rewrite (Z.sub_mod_l_push x y z) by Z.NoZMod - | rewrite (Z.sub_mod_r_push x y z) by Z.NoZMod ] - | [ |- context[(-?y) mod ?z] ] - => rewrite (Z.opp_mod_mod_push y z) by Z.NoZMod - end. - -Ltac push_Zmod_hyps := - repeat match goal with - | _ => progress autorewrite with push_Zmod in * |- - | [ H : context[(?x * ?y) mod ?z] |- _ ] - => first [ rewrite (Z.mul_mod_push x y z) in H by Z.NoZMod - | rewrite (Z.mul_mod_l_push x y z) in H by Z.NoZMod - | rewrite (Z.mul_mod_r_push x y z) in H by Z.NoZMod ] - | [ H : context[(?x + ?y) mod ?z] |- _ ] - => first [ rewrite (Z.add_mod_push x y z) in H by Z.NoZMod - | rewrite (Z.add_mod_l_push x y z) in H by Z.NoZMod - | rewrite (Z.add_mod_r_push x y z) in H by Z.NoZMod ] - | [ H : context[(?x - ?y) mod ?z] |- _ ] - => first [ rewrite (Z.sub_mod_push x y z) in H by Z.NoZMod - | rewrite (Z.sub_mod_l_push x y z) in H by Z.NoZMod - | rewrite (Z.sub_mod_r_push x y z) in H by Z.NoZMod ] - | [ H : context[(-?y) mod ?z] |- _ ] - => rewrite (Z.opp_mod_mod_push y z) in H by Z.NoZMod - end. - -Ltac has_no_mod x z := - lazymatch x with - | context[_ mod z] => fail - | _ => idtac - end. -Ltac pull_Zmod := - repeat match goal with - | [ |- context[((?x mod ?z) * (?y mod ?z)) mod ?z] ] - => has_no_mod x z; has_no_mod y z; - rewrite <- (Z.mul_mod_full x y z) - | [ |- context[((?x mod ?z) * ?y) mod ?z] ] - => has_no_mod x z; has_no_mod y z; - rewrite <- (Z.mul_mod_l x y z) - | [ |- context[(?x * (?y mod ?z)) mod ?z] ] - => has_no_mod x z; has_no_mod y z; - rewrite <- (Z.mul_mod_r x y z) - | [ |- context[((?x mod ?z) + (?y mod ?z)) mod ?z] ] - => has_no_mod x z; has_no_mod y z; - rewrite <- (Z.add_mod_full x y z) - | [ |- context[((?x mod ?z) + ?y) mod ?z] ] - => has_no_mod x z; has_no_mod y z; - rewrite <- (Z.add_mod_l x y z) - | [ |- context[(?x + (?y mod ?z)) mod ?z] ] - => has_no_mod x z; has_no_mod y z; - rewrite <- (Z.add_mod_r x y z) - | [ |- context[((?x mod ?z) - (?y mod ?z)) mod ?z] ] - => has_no_mod x z; has_no_mod y z; - rewrite <- (Z.sub_mod_full x y z) - | [ |- context[((?x mod ?z) - ?y) mod ?z] ] - => has_no_mod x z; has_no_mod y z; - rewrite <- (Z.sub_mod_l x y z) - | [ |- context[(?x - (?y mod ?z)) mod ?z] ] - => has_no_mod x z; has_no_mod y z; - rewrite <- (Z.sub_mod_r x y z) - | [ |- context[(((-?y) mod ?z)) mod ?z] ] - => has_no_mod y z; - rewrite <- (Z.opp_mod_mod y z) - | [ |- context[(?x mod ?z) mod ?z] ] - => rewrite (Zmod_mod x z) - | _ => progress autorewrite with pull_Zmod - end. -- cgit v1.2.3