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author | Cyril SIX <cyril.six@kalray.eu> | 2019-03-08 11:30:46 +0100 |
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committer | Cyril SIX <cyril.six@kalray.eu> | 2019-03-08 11:30:46 +0100 |
commit | f88eb3311e606c1d8de616c3c231f95144ff4825 (patch) | |
tree | 6d601e032bd5dd9189bfb01acf6e946228280607 /mppa_k1c/Asmblockgenproof1.v | |
parent | 405f173c02e73a929ce9e9debb3f2bfa704702c7 (diff) | |
parent | 8e68be1345bef8e2f8ee428c51d4290e4464ebd6 (diff) | |
download | compcert-kvx-f88eb3311e606c1d8de616c3c231f95144ff4825.tar.gz compcert-kvx-f88eb3311e606c1d8de616c3c231f95144ff4825.zip |
Merge remote-tracking branch 'origin/mppa_postpass' into mppa_memory_model_patch
Diffstat (limited to 'mppa_k1c/Asmblockgenproof1.v')
-rw-r--r-- | mppa_k1c/Asmblockgenproof1.v | 312 |
1 files changed, 310 insertions, 2 deletions
diff --git a/mppa_k1c/Asmblockgenproof1.v b/mppa_k1c/Asmblockgenproof1.v index d9ce95ab..1a55f58e 100644 --- a/mppa_k1c/Asmblockgenproof1.v +++ b/mppa_k1c/Asmblockgenproof1.v @@ -222,8 +222,6 @@ Qed. *) *) -Definition yolo := 4. - Lemma opimm64_correct: forall (op: arith_name_rrr) (opi: arith_name_rri64) @@ -428,6 +426,288 @@ Proof. rewrite H0. simpl; auto. Qed. +Lemma swap_comparison_cmpf_eq: + forall v1 v2 cmp, + (Val.cmpf cmp v1 v2) = (Val.cmpf (swap_comparison cmp) v2 v1). +Proof. + intros. unfold Val.cmpf. unfold Val.cmpf_bool. destruct v1; destruct v2; auto. + rewrite Float.cmp_swap. auto. +Qed. + +Lemma swap_comparison_cmpf_bool: + forall cmp ft v1 v2, + ftest_for_cmp cmp = Reversed ft -> + Val.cmpf_bool cmp v1 v2 = Val.cmpf_bool (swap_comparison cmp) v2 v1. +Proof. + intros. unfold Val.cmpf_bool. destruct v1; destruct v2; auto. rewrite Float.cmp_swap. reflexivity. +Qed. + +Lemma transl_compf_correct: + forall cmp r1 r2 lbl k rs m tbb b, + exists rs', + exec_straight ge (transl_comp_float64 cmp r1 r2 lbl k) rs m (Pcb BTwnez RTMP lbl ::g k) rs' m + /\ (forall r : preg, r <> PC -> r <> RTMP -> rs' r = rs r) + /\ ( Val.cmpf_bool cmp rs#r1 rs#r2 = Some b -> + exec_control ge fn (Some (PCtlFlow (Pcb BTwnez RTMP lbl))) (nextblock tbb rs') m + = eval_branch fn lbl (nextblock tbb rs') m (Some b)) + . +Proof. + intros. unfold transl_comp_float64. destruct (ftest_for_cmp cmp) eqn:FT. + * esplit. split. + - apply exec_straight_one; simpl; eauto. + - split. + + intros; Simpl. + + intros. remember (rs # RTMP <- (compare_float _ _ _)) as rs'. + simpl. assert (Val.cmp_bool Cne (nextblock tbb rs') # RTMP (Vint (Int.repr 0)) = Some b). + { + assert ((nextblock tbb rs') # RTMP = (compare_float ft (rs r1) (rs r2))). + { rewrite Heqrs'. auto. } + rewrite H0. rewrite <- H. + remember (Val.cmpf_bool cmp rs#r1 rs#r2) as cmpbool. + destruct cmp; simpl; + unfold compare_float; + unfold Val.cmpf; simpl in FT; inversion FT; rewrite <- Heqcmpbool; destruct cmpbool; simpl; auto; + destruct b0; simpl; auto. + } + rewrite H0. simpl; auto. + * esplit. split. + - apply exec_straight_one; simpl; eauto. + - split. + + intros; Simpl. + + intros. remember (rs # RTMP <- (compare_float _ _ _)) as rs'. + simpl. assert (Val.cmp_bool Cne (nextblock tbb rs') # RTMP (Vint (Int.repr 0)) = Some b). + { + assert ((nextblock tbb rs') # RTMP = (compare_float ft (rs r2) (rs r1))). + { rewrite Heqrs'. auto. } + rewrite H0. rewrite <- H. + remember (Val.cmpf_bool cmp rs#r1 rs#r2) as cmpbool. + erewrite swap_comparison_cmpf_bool in Heqcmpbool; eauto. + destruct cmp; simpl; + unfold compare_float; + unfold Val.cmpf; simpl in FT; inversion FT; simpl in Heqcmpbool; rewrite <- Heqcmpbool; destruct cmpbool; simpl; auto; + destruct b0; simpl; auto. + } + rewrite H0. simpl; auto. +Qed. + +Lemma cmpf_bool_ne_eq: + forall v1 v2, + Val.cmpf_bool Cne v1 v2 = option_map negb (Val.cmpf_bool Ceq v1 v2). +Proof. + intros. unfold Val.cmpf_bool. destruct v1; destruct v2; auto. rewrite Float.cmp_ne_eq. simpl. reflexivity. +Qed. + +Lemma cmpf_bool_ne_eq_rev: + forall v1 v2, + Val.cmpf_bool Ceq v1 v2 = option_map negb (Val.cmpf_bool Cne v1 v2). +Proof. + intros. unfold Val.cmpf_bool. destruct v1; destruct v2; auto. rewrite Float.cmp_ne_eq. simpl. rewrite negb_involutive. reflexivity. +Qed. + +Lemma option_map_negb_negb: + forall v, + option_map negb (option_map negb v) = v. +Proof. + destruct v; simpl; auto. rewrite negb_involutive. reflexivity. +Qed. + +Lemma notbool_option_map_negb: + forall v, Val.notbool (Val.of_optbool v) = Val.of_optbool (option_map negb v). +Proof. + unfold Val.notbool. unfold Val.of_optbool. + destruct v; auto. destruct b; auto. +Qed. + +Lemma swap_comparison_cmpf_bool_notftest: + forall cmp ft v1 v2, + notftest_for_cmp cmp = Reversed ft -> + Val.cmpf_bool cmp v1 v2 = Val.cmpf_bool (swap_comparison cmp) v2 v1. +Proof. + intros. unfold Val.cmpf_bool. destruct v1; destruct v2; auto. rewrite Float.cmp_swap. reflexivity. +Qed. + +Lemma transl_compnotf_correct: + forall cmp r1 r2 lbl k rs m tbb b, + exists rs', + exec_straight ge (transl_comp_notfloat64 cmp r1 r2 lbl k) rs m (Pcb BTwnez RTMP lbl ::g k) rs' m + /\ (forall r : preg, r <> PC -> r <> RTMP -> rs' r = rs r) + /\ (option_map negb (Val.cmpf_bool cmp rs#r1 rs#r2) = Some b -> + exec_control ge fn (Some (PCtlFlow (Pcb BTwnez RTMP lbl))) (nextblock tbb rs') m + = eval_branch fn lbl (nextblock tbb rs') m (Some b)) + . +Proof. + intros. unfold transl_comp_notfloat64. destruct (notftest_for_cmp cmp) eqn:FT. + * esplit. split. + - apply exec_straight_one; simpl; eauto. + - split. + + intros; Simpl. + + intros. remember (rs # RTMP <- (compare_float _ _ _)) as rs'. + simpl. assert (Val.cmp_bool Cne (nextblock tbb rs') # RTMP (Vint (Int.repr 0)) = Some b). + { + assert ((nextblock tbb rs') # RTMP = (compare_float ft (rs r1) (rs r2))). + { rewrite Heqrs'. auto. } + rewrite H0. rewrite <- H. + remember (option_map negb (Val.cmpf_bool cmp rs#r1 rs#r2)) as cmpbool. + destruct cmp; simpl; + unfold compare_float; + unfold Val.cmpf; simpl in FT; inversion FT. + * rewrite cmpf_bool_ne_eq; rewrite <- Heqcmpbool; destruct cmpbool; simpl; auto; destruct b0; simpl; auto. + * rewrite cmpf_bool_ne_eq_rev. rewrite <- Heqcmpbool; destruct cmpbool; simpl; auto; destruct b0; simpl; auto. + * rewrite notbool_option_map_negb. rewrite <- Heqcmpbool; destruct cmpbool; simpl; auto; destruct b0; simpl; auto. + * rewrite notbool_option_map_negb. rewrite <- Heqcmpbool; destruct cmpbool; simpl; auto; destruct b0; simpl; auto. + } + rewrite H0. simpl; auto. + * esplit. split. + - apply exec_straight_one; simpl; eauto. + - split. + + intros; Simpl. + + intros. remember (rs # RTMP <- (compare_float _ _ _)) as rs'. + simpl. assert (Val.cmp_bool Cne (nextblock tbb rs') # RTMP (Vint (Int.repr 0)) = Some b). + { + assert ((nextblock tbb rs') # RTMP = (compare_float ft (rs r2) (rs r1))). + { rewrite Heqrs'. auto. } + rewrite H0. rewrite <- H. + remember (Val.cmpf_bool cmp rs#r1 rs#r2) as cmpbool. + erewrite swap_comparison_cmpf_bool_notftest in Heqcmpbool; eauto. + destruct cmp; simpl; + unfold compare_float; + unfold Val.cmpf; simpl in FT; inversion FT; simpl in Heqcmpbool. + * rewrite notbool_option_map_negb. rewrite <- Heqcmpbool; destruct cmpbool; simpl; auto; destruct b0; simpl; auto. + * rewrite notbool_option_map_negb. rewrite <- Heqcmpbool; destruct cmpbool; simpl; auto; destruct b0; simpl; auto. + } + rewrite H0. simpl; auto. +Qed. + +Lemma swap_comparison_cmpfs_bool: + forall cmp ft v1 v2, + ftest_for_cmp cmp = Reversed ft -> + Val.cmpfs_bool cmp v1 v2 = Val.cmpfs_bool (swap_comparison cmp) v2 v1. +Proof. + intros. unfold Val.cmpfs_bool. destruct v1; destruct v2; auto. rewrite Float32.cmp_swap. reflexivity. +Qed. + +Lemma transl_compfs_correct: + forall cmp r1 r2 lbl k rs m tbb b, + exists rs', + exec_straight ge (transl_comp_float32 cmp r1 r2 lbl k) rs m (Pcb BTwnez RTMP lbl ::g k) rs' m + /\ (forall r : preg, r <> PC -> r <> RTMP -> rs' r = rs r) + /\ ( Val.cmpfs_bool cmp rs#r1 rs#r2 = Some b -> + exec_control ge fn (Some (PCtlFlow (Pcb BTwnez RTMP lbl))) (nextblock tbb rs') m + = eval_branch fn lbl (nextblock tbb rs') m (Some b)) + . +Proof. + intros. unfold transl_comp_float32. destruct (ftest_for_cmp cmp) eqn:FT. + * esplit. split. + - apply exec_straight_one; simpl; eauto. + - split. + + intros; Simpl. + + intros. remember (rs # RTMP <- (compare_single _ _ _)) as rs'. + simpl. assert (Val.cmp_bool Cne (nextblock tbb rs') # RTMP (Vint (Int.repr 0)) = Some b). + { + assert ((nextblock tbb rs') # RTMP = (compare_single ft (rs r1) (rs r2))). + { rewrite Heqrs'. auto. } + rewrite H0. rewrite <- H. + remember (Val.cmpfs_bool cmp rs#r1 rs#r2) as cmpbool. + destruct cmp; simpl; + unfold compare_single; + unfold Val.cmpfs; simpl in FT; inversion FT; rewrite <- Heqcmpbool; destruct cmpbool; simpl; auto; + destruct b0; simpl; auto. + } + rewrite H0. simpl; auto. + * esplit. split. + - apply exec_straight_one; simpl; eauto. + - split. + + intros; Simpl. + + intros. remember (rs # RTMP <- (compare_single _ _ _)) as rs'. + simpl. assert (Val.cmp_bool Cne (nextblock tbb rs') # RTMP (Vint (Int.repr 0)) = Some b). + { + assert ((nextblock tbb rs') # RTMP = (compare_single ft (rs r2) (rs r1))). + { rewrite Heqrs'. auto. } + rewrite H0. rewrite <- H. + remember (Val.cmpfs_bool cmp rs#r1 rs#r2) as cmpbool. + erewrite swap_comparison_cmpfs_bool in Heqcmpbool; eauto. + destruct cmp; simpl; + unfold compare_single; + unfold Val.cmpfs; simpl in FT; inversion FT; simpl in Heqcmpbool; rewrite <- Heqcmpbool; destruct cmpbool; simpl; auto; + destruct b0; simpl; auto. + } + rewrite H0. simpl; auto. +Qed. + +Lemma swap_comparison_cmpfs_bool_notftest: + forall cmp ft v1 v2, + notftest_for_cmp cmp = Reversed ft -> + Val.cmpfs_bool cmp v1 v2 = Val.cmpfs_bool (swap_comparison cmp) v2 v1. +Proof. + intros. unfold Val.cmpfs_bool. destruct v1; destruct v2; auto. rewrite Float32.cmp_swap. reflexivity. +Qed. + +Lemma cmpfs_bool_ne_eq: + forall v1 v2, + Val.cmpfs_bool Cne v1 v2 = option_map negb (Val.cmpfs_bool Ceq v1 v2). +Proof. + intros. unfold Val.cmpfs_bool. destruct v1; destruct v2; auto. rewrite Float32.cmp_ne_eq. simpl. reflexivity. +Qed. + +Lemma cmpfs_bool_ne_eq_rev: + forall v1 v2, + Val.cmpfs_bool Ceq v1 v2 = option_map negb (Val.cmpfs_bool Cne v1 v2). +Proof. + intros. unfold Val.cmpfs_bool. destruct v1; destruct v2; auto. rewrite Float32.cmp_ne_eq. simpl. rewrite negb_involutive. reflexivity. +Qed. + +Lemma transl_compnotfs_correct: + forall cmp r1 r2 lbl k rs m tbb b, + exists rs', + exec_straight ge (transl_comp_notfloat32 cmp r1 r2 lbl k) rs m (Pcb BTwnez RTMP lbl ::g k) rs' m + /\ (forall r : preg, r <> PC -> r <> RTMP -> rs' r = rs r) + /\ (option_map negb (Val.cmpfs_bool cmp rs#r1 rs#r2) = Some b -> + exec_control ge fn (Some (PCtlFlow (Pcb BTwnez RTMP lbl))) (nextblock tbb rs') m + = eval_branch fn lbl (nextblock tbb rs') m (Some b)) + . +Proof. + intros. unfold transl_comp_notfloat32. destruct (notftest_for_cmp cmp) eqn:FT. + * esplit. split. + - apply exec_straight_one; simpl; eauto. + - split. + + intros; Simpl. + + intros. remember (rs # RTMP <- (compare_single _ _ _)) as rs'. + simpl. assert (Val.cmp_bool Cne (nextblock tbb rs') # RTMP (Vint (Int.repr 0)) = Some b). + { + assert ((nextblock tbb rs') # RTMP = (compare_single ft (rs r1) (rs r2))). + { rewrite Heqrs'. auto. } + rewrite H0. rewrite <- H. + remember (option_map negb (Val.cmpfs_bool cmp rs#r1 rs#r2)) as cmpbool. + destruct cmp; simpl; + unfold compare_single; + unfold Val.cmpfs; simpl in FT; inversion FT. + * rewrite cmpfs_bool_ne_eq; rewrite <- Heqcmpbool; destruct cmpbool; simpl; auto; destruct b0; simpl; auto. + * rewrite cmpfs_bool_ne_eq_rev. rewrite <- Heqcmpbool; destruct cmpbool; simpl; auto; destruct b0; simpl; auto. + * rewrite notbool_option_map_negb. rewrite <- Heqcmpbool; destruct cmpbool; simpl; auto; destruct b0; simpl; auto. + * rewrite notbool_option_map_negb. rewrite <- Heqcmpbool; destruct cmpbool; simpl; auto; destruct b0; simpl; auto. + } + rewrite H0. simpl; auto. + * esplit. split. + - apply exec_straight_one; simpl; eauto. + - split. + + intros; Simpl. + + intros. remember (rs # RTMP <- (compare_single _ _ _)) as rs'. + simpl. assert (Val.cmp_bool Cne (nextblock tbb rs') # RTMP (Vint (Int.repr 0)) = Some b). + { + assert ((nextblock tbb rs') # RTMP = (compare_single ft (rs r2) (rs r1))). + { rewrite Heqrs'. auto. } + rewrite H0. rewrite <- H. + remember (Val.cmpfs_bool cmp rs#r1 rs#r2) as cmpbool. + erewrite swap_comparison_cmpfs_bool_notftest in Heqcmpbool; eauto. + destruct cmp; simpl; + unfold compare_single; + unfold Val.cmpfs; simpl in FT; inversion FT; simpl in Heqcmpbool. + * rewrite notbool_option_map_negb. rewrite <- Heqcmpbool; destruct cmpbool; simpl; auto; destruct b0; simpl; auto. + * rewrite notbool_option_map_negb. rewrite <- Heqcmpbool; destruct cmpbool; simpl; auto; destruct b0; simpl; auto. + } + rewrite H0. simpl; auto. +Qed. + Lemma transl_complu_correct: forall cmp r1 r2 lbl k rs m tbb b, exists rs', @@ -753,6 +1033,34 @@ Proof. * split; auto. { apply C'; auto. rewrite B, C; eauto with asmgen. } { intros. rewrite B'; eauto with asmgen. } + +(* Ccompf *) +- exploit (transl_compf_correct c0 x x0 lbl); eauto. intros (rs' & A & B & C). + exists rs', (Pcb BTwnez RTMP lbl). + split. + + constructor. eexact A. + + split; auto. apply C; auto. + +(* Cnotcompf *) +- exploit (transl_compnotf_correct c0 x x0 lbl); eauto. intros (rs' & A & B & C). + exists rs', (Pcb BTwnez RTMP lbl). + split. + + constructor. eexact A. + + split; auto. apply C; auto. + +(* Ccompfs *) +- exploit (transl_compfs_correct c0 x x0 lbl); eauto. intros (rs' & A & B & C). + exists rs', (Pcb BTwnez RTMP lbl). + split. + + constructor. eexact A. + + split; auto. apply C; auto. + +(* Cnotcompfs *) +- exploit (transl_compnotfs_correct c0 x x0 lbl); eauto. intros (rs' & A & B & C). + exists rs', (Pcb BTwnez RTMP lbl). + split. + + constructor. eexact A. + + split; auto. apply C; auto. Qed. Lemma transl_cbranch_correct_true: |