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author | Xavier Leroy <xavier.leroy@college-de-france.fr> | 2019-04-23 15:00:41 +0200 |
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committer | Xavier Leroy <xavier.leroy@college-de-france.fr> | 2019-04-23 15:00:41 +0200 |
commit | 51c497b2e5a2b09788f2cf05f414634b037f52bf (patch) | |
tree | d1cfcc98a74cb78a042d90f91f6092078b3f3a0f /backend | |
parent | b66ddea9b0304d390b56afadda80fa4d2f2184d6 (diff) | |
download | compcert-51c497b2e5a2b09788f2cf05f414634b037f52bf.tar.gz compcert-51c497b2e5a2b09788f2cf05f414634b037f52bf.zip |
lib/Coqlib.v: remove defns about multiplication, division, modulus
Instead, use definitions and lemmas from the Coq standard library
(ZArith, Znumtheory).
Diffstat (limited to 'backend')
-rw-r--r-- | backend/Inliningproof.v | 6 | ||||
-rw-r--r-- | backend/Lineartyping.v | 2 | ||||
-rw-r--r-- | backend/SelectDivproof.v | 28 | ||||
-rw-r--r-- | backend/Selectionproof.v | 2 | ||||
-rw-r--r-- | backend/ValueDomain.v | 4 |
5 files changed, 22 insertions, 20 deletions
diff --git a/backend/Inliningproof.v b/backend/Inliningproof.v index 2dcb8956..45051bcf 100644 --- a/backend/Inliningproof.v +++ b/backend/Inliningproof.v @@ -755,13 +755,13 @@ Proof. assert (2 <= sz -> (2 | n)). intros. destruct (zle sz 1). omegaContradiction. destruct (zle sz 2). auto. - destruct (zle sz 4). apply Zdivides_trans with 4; auto. exists 2; auto. - apply Zdivides_trans with 8; auto. exists 4; auto. + destruct (zle sz 4). apply Z.divide_trans with 4; auto. exists 2; auto. + apply Z.divide_trans with 8; auto. exists 4; auto. assert (4 <= sz -> (4 | n)). intros. destruct (zle sz 1). omegaContradiction. destruct (zle sz 2). omegaContradiction. destruct (zle sz 4). auto. - apply Zdivides_trans with 8; auto. exists 2; auto. + apply Z.divide_trans with 8; auto. exists 2; auto. assert (8 <= sz -> (8 | n)). intros. destruct (zle sz 1). omegaContradiction. destruct (zle sz 2). omegaContradiction. diff --git a/backend/Lineartyping.v b/backend/Lineartyping.v index fc163719..55fa7a67 100644 --- a/backend/Lineartyping.v +++ b/backend/Lineartyping.v @@ -39,7 +39,7 @@ Definition slot_valid (sl: slot) (ofs: Z) (ty: typ): bool := | Outgoing => zle 0 ofs | Incoming => In_dec Loc.eq (S Incoming ofs ty) (regs_of_rpairs (loc_parameters funct.(fn_sig))) end - && Zdivide_dec (typealign ty) ofs (typealign_pos ty). + && Zdivide_dec (typealign ty) ofs. Definition slot_writable (sl: slot) : bool := match sl with diff --git a/backend/SelectDivproof.v b/backend/SelectDivproof.v index 9e24857a..e660677a 100644 --- a/backend/SelectDivproof.v +++ b/backend/SelectDivproof.v @@ -57,13 +57,13 @@ Proof. apply Z.mul_nonneg_nonneg; omega. assert (k * n <= two_p (N + l) - two_p l). apply Z.le_trans with (two_p l * n). - apply Zmult_le_compat_r. omega. omega. + apply Z.mul_le_mono_nonneg_r; omega. replace (N + l) with (l + N) by omega. rewrite two_p_is_exp. replace (two_p l * two_p N - two_p l) with (two_p l * (two_p N - 1)) by ring. - apply Zmult_le_compat_l. omega. exploit (two_p_gt_ZERO l). omega. omega. + apply Z.mul_le_mono_nonneg_l. omega. exploit (two_p_gt_ZERO l). omega. omega. omega. omega. assert (0 <= two_p (N + l) * r). apply Z.mul_nonneg_nonneg. @@ -72,7 +72,7 @@ Proof. assert (two_p (N + l) * r <= two_p (N + l) * d - two_p (N + l)). replace (two_p (N + l) * d - two_p (N + l)) with (two_p (N + l) * (d - 1)) by ring. - apply Zmult_le_compat_l. + apply Z.mul_le_mono_nonneg_l. omega. exploit (two_p_gt_ZERO (N + l)). omega. omega. assert (0 <= m * n - two_p (N + l) * q). @@ -138,13 +138,13 @@ Proof. rewrite H2. assert (k * n <= two_p (N + l)). rewrite Z.add_comm. rewrite two_p_is_exp; try omega. - apply Z.le_trans with (two_p l * n). apply Zmult_le_compat_r. omega. omega. - apply Zmult_le_compat_l. omega. exploit (two_p_gt_ZERO l). omega. omega. + apply Z.le_trans with (two_p l * n). apply Z.mul_le_mono_nonneg_r; omega. + apply Z.mul_le_mono_nonneg_l. omega. exploit (two_p_gt_ZERO l). omega. omega. assert (two_p (N + l) * r <= two_p (N + l) * d - two_p (N + l)). replace (two_p (N + l) * d - two_p (N + l)) with (two_p (N + l) * (d - 1)) by ring. - apply Zmult_le_compat_l. omega. exploit (two_p_gt_ZERO (N + l)). omega. omega. + apply Z.mul_le_mono_nonneg_l. exploit (two_p_gt_ZERO (N + l)). omega. omega. omega. omega. Qed. @@ -246,10 +246,11 @@ Proof. unfold Int.max_signed; omega. apply Zdiv_interval_1. generalize Int.min_signed_neg; omega. apply Int.half_modulus_pos. apply Int.modulus_pos. - split. apply Z.le_trans with (Int.min_signed * m). apply Zmult_le_compat_l_neg. omega. generalize Int.min_signed_neg; omega. - apply Zmult_le_compat_r. unfold n; generalize (Int.signed_range x); tauto. tauto. + split. apply Z.le_trans with (Int.min_signed * m). + apply Z.mul_le_mono_nonpos_l. generalize Int.min_signed_neg; omega. omega. + apply Z.mul_le_mono_nonneg_r. omega. unfold n; generalize (Int.signed_range x); tauto. apply Z.le_lt_trans with (Int.half_modulus * m). - apply Zmult_le_compat_r. generalize (Int.signed_range x); unfold n, Int.max_signed; omega. tauto. + apply Z.mul_le_mono_nonneg_r. tauto. generalize (Int.signed_range x); unfold n, Int.max_signed; omega. apply Zmult_lt_compat_l. generalize Int.half_modulus_pos; omega. tauto. assert (32 < Int.max_unsigned) by (compute; auto). omega. unfold Int.lt; fold n. rewrite Int.signed_zero. destruct (zlt n 0); apply Int.eqm_unsigned_repr. @@ -290,7 +291,7 @@ Proof. apply Int.eqm_sym. eapply Int.eqm_trans. apply Int.eqm_signed_unsigned. apply Int.eqm_unsigned_repr_l. apply Int.eqm_refl2. apply (f_equal (fun x => n * x / Int.modulus)). - rewrite Int.signed_repr_eq. rewrite Zmod_small by assumption. + rewrite Int.signed_repr_eq. rewrite Z.mod_small by assumption. apply zlt_false. assumption. Qed. @@ -400,8 +401,9 @@ Proof. unfold Int64.max_signed; omega. apply Zdiv_interval_1. generalize Int64.min_signed_neg; omega. apply Int64.half_modulus_pos. apply Int64.modulus_pos. - split. apply Z.le_trans with (Int64.min_signed * m). apply Zmult_le_compat_l_neg. omega. generalize Int64.min_signed_neg; omega. - apply Zmult_le_compat_r. unfold n; generalize (Int64.signed_range x); tauto. tauto. + split. apply Z.le_trans with (Int64.min_signed * m). + apply Z.mul_le_mono_nonpos_l. generalize Int64.min_signed_neg; omega. omega. + apply Z.mul_le_mono_nonneg_r. tauto. unfold n; generalize (Int64.signed_range x); tauto. apply Z.le_lt_trans with (Int64.half_modulus * m). apply Zmult_le_compat_r. generalize (Int64.signed_range x); unfold n, Int64.max_signed; omega. tauto. apply Zmult_lt_compat_l. generalize Int64.half_modulus_pos; omega. tauto. @@ -444,7 +446,7 @@ Proof. apply Int64.eqm_sym. eapply Int64.eqm_trans. apply Int64.eqm_signed_unsigned. apply Int64.eqm_unsigned_repr_l. apply Int64.eqm_refl2. apply (f_equal (fun x => n * x / Int64.modulus)). - rewrite Int64.signed_repr_eq. rewrite Zmod_small by assumption. + rewrite Int64.signed_repr_eq. rewrite Z.mod_small by assumption. apply zlt_false. assumption. Qed. diff --git a/backend/Selectionproof.v b/backend/Selectionproof.v index afc470b3..621459d0 100644 --- a/backend/Selectionproof.v +++ b/backend/Selectionproof.v @@ -506,7 +506,7 @@ Proof. unfold Int.sub. rewrite Int.unsigned_repr_eq. f_equal. f_equal. apply Int.unsigned_repr. unfold Int.max_unsigned; omega. - intros until i0; intros EVAL R. exists v; split; auto. - inv R. rewrite Zmod_small by (apply Int.unsigned_range). constructor. + inv R. rewrite Z.mod_small by (apply Int.unsigned_range). constructor. - constructor. - apply Int.unsigned_range. Qed. diff --git a/backend/ValueDomain.v b/backend/ValueDomain.v index 37a9ecf2..47b87bfb 100644 --- a/backend/ValueDomain.v +++ b/backend/ValueDomain.v @@ -1492,12 +1492,12 @@ Proof. inv H; auto with va. - apply vmatch_uns. red; intros. rewrite Int.bits_rol by auto. generalize (Int.unsigned_range n); intros. - rewrite Zmod_small by omega. + rewrite Z.mod_small by omega. apply H1. omega. omega. - destruct (zlt n0 Int.zwordsize); auto with va. apply vmatch_sgn. red; intros. rewrite ! Int.bits_rol by omega. generalize (Int.unsigned_range n); intros. - rewrite ! Zmod_small by omega. + rewrite ! Z.mod_small by omega. rewrite H1 by omega. symmetry. rewrite H1 by omega. auto. - destruct (zlt n0 Int.zwordsize); auto with va. Qed. |