diff options
Diffstat (limited to 'riscV/RTLpathSE_simplify.v')
| -rw-r--r-- | riscV/RTLpathSE_simplify.v | 732 |
1 files changed, 719 insertions, 13 deletions
diff --git a/riscV/RTLpathSE_simplify.v b/riscV/RTLpathSE_simplify.v index 9b91c5a2..11e54a00 100644 --- a/riscV/RTLpathSE_simplify.v +++ b/riscV/RTLpathSE_simplify.v @@ -37,7 +37,7 @@ Definition load_hilo32 (hi lo: int) := else let hvs := fSop (OEluiw hi) fSnil in let hl := make_lhsv_single hvs in - fSop (Oaddimm lo) hl. + fSop (OEaddiw lo) hl. Definition load_hilo64 (hi lo: int64) := if Int64.eq lo Int64.zero then @@ -45,7 +45,7 @@ Definition load_hilo64 (hi lo: int64) := else let hvs := fSop (OEluil hi) fSnil in let hl := make_lhsv_single hvs in - fSop (Oaddlimm lo) hl. + fSop (OEaddil lo) hl. Definition loadimm32 (n: int) := match make_immed32 n with @@ -88,9 +88,15 @@ Definition opimm64 (hv1: hsval) (n: int64) (op: operation) (opimm: int64 -> oper fSop op hl end. +Definition addimm32 (hv1: hsval) (n: int) := opimm32 hv1 n Oadd OEaddiw. +Definition andimm32 (hv1: hsval) (n: int) := opimm32 hv1 n Oand OEandiw. +Definition orimm32 (hv1: hsval) (n: int) := opimm32 hv1 n Oor OEoriw. Definition xorimm32 (hv1: hsval) (n: int) := opimm32 hv1 n Oxor OExoriw. Definition sltimm32 (hv1: hsval) (n: int) := opimm32 hv1 n (OEsltw None) OEsltiw. Definition sltuimm32 (hv1: hsval) (n: int) := opimm32 hv1 n (OEsltuw None) OEsltiuw. +Definition addimm64 (hv1: hsval) (n: int64) := opimm64 hv1 n Oaddl OEaddil. +Definition andimm64 (hv1: hsval) (n: int64) := opimm64 hv1 n Oandl OEandil. +Definition orimm64 (hv1: hsval) (n: int64) := opimm64 hv1 n Oorl OEoril. Definition xorimm64 (hv1: hsval) (n: int64) := opimm64 hv1 n Oxorl OExoril. Definition sltimm64 (hv1: hsval) (n: int64) := opimm64 hv1 n (OEsltl None) OEsltil. Definition sltuimm64 (hv1: hsval) (n: int64) := opimm64 hv1 n (OEsltul None) OEsltiul. @@ -300,6 +306,17 @@ Definition expanse_cbranch_fp (cnot: bool) fn_cond cmp (lhsv: list_hsval) : (con let hl := make_lhsv_cmp false hvs hvs in if normal' then ((CEbnew (Some false)), hl) else ((CEbeqw (Some false)), hl). +(** Add pointer expansion *) + +(*Definition addptrofs (hv1: hsval) (n: ptrofs) :=*) + (*if Ptrofs.eq_dec n Ptrofs.zero then*) + (*let lhsv := make_lhsv_single hv1 in*) + (*fSop Omove lhsv*) + (*else*) + (*if Archi.ptr64*) + (*then addimm64 hv1 (Ptrofs.to_int64 n)*) + (*else addimm32 hv1 (Ptrofs.to_int n).*) + (** Target op simplifications using "fake" values *) Definition target_op_simplify (op: operation) (lr: list reg) (hst: hsistate_local): option hsval := @@ -369,13 +386,110 @@ Definition target_op_simplify (op: operation) (lr: list reg) (hst: hsistate_loca let lhsv := make_lhsv_cmp is_inv hv1 hv2 in Some (expanse_cond_fp true cond_single c lhsv) | Ofloatconst f, nil => - let bits_const := fSop (Olongconst (Float.to_bits f)) fSnil in - let hl := make_lhsv_single bits_const in + let hvs := loadimm64 (Float.to_bits f) in + let hl := make_lhsv_single hvs in Some (fSop (Ofloat_of_bits) hl) | Osingleconst f, nil => - let bits_const := fSop (Ointconst (Float32.to_bits f)) fSnil in - let hl := make_lhsv_single bits_const in + let hvs := loadimm32 (Float32.to_bits f) in + let hl := make_lhsv_single hvs in Some (fSop (Osingle_of_bits) hl) + | Ointconst n, nil => + Some (loadimm32 n) + | Olongconst n, nil => + Some (loadimm64 n) + | Oaddimm n, a1 :: nil => + let hv1 := fsi_sreg_get hst a1 in + Some (addimm32 hv1 n) + | Oaddlimm n, a1 :: nil => + let hv1 := fsi_sreg_get hst a1 in + Some (addimm64 hv1 n) + | Oandimm n, a1 :: nil => + let hv1 := fsi_sreg_get hst a1 in + Some (andimm32 hv1 n) + | Oandlimm n, a1 :: nil => + let hv1 := fsi_sreg_get hst a1 in + Some (andimm64 hv1 n) + | Oorimm n, a1 :: nil => + let hv1 := fsi_sreg_get hst a1 in + Some (orimm32 hv1 n) + | Oorlimm n, a1 :: nil => + let hv1 := fsi_sreg_get hst a1 in + Some (orimm64 hv1 n) + | Ocast8signed, a1 :: nil => + let hv1 := fsi_sreg_get hst a1 in + let hl := make_lhsv_single hv1 in + let hvs := fSop (Oshlimm (Int.repr 24)) hl in + let hl' := make_lhsv_single hvs in + Some (fSop (Oshrimm (Int.repr 24)) hl') + | Ocast16signed, a1 :: nil => + let hv1 := fsi_sreg_get hst a1 in + let hl := make_lhsv_single hv1 in + let hvs := fSop (Oshlimm (Int.repr 16)) hl in + let hl' := make_lhsv_single hvs in + Some (fSop (Oshrimm (Int.repr 16)) hl') + | Ocast32unsigned, a1 :: nil => + let hv1 := fsi_sreg_get hst a1 in + let hl := make_lhsv_single hv1 in + let cast32s_s := fSop Ocast32signed hl in + let cast32s_l := make_lhsv_single cast32s_s in + let sllil_s := fSop (Oshllimm (Int.repr 32)) cast32s_l in + let sllil_l := make_lhsv_single sllil_s in + Some (fSop (Oshrluimm (Int.repr 32)) sllil_l) + | Oshrximm n, a1 :: nil => + let hv1 := fsi_sreg_get hst a1 in + let hl := make_lhsv_single hv1 in + if Int.eq n Int.zero then + let move_s := fSop Omove hl in + let move_l := make_lhsv_single move_s in + Some (fSop (OEshrxundef n) move_l) + else + if Int.eq n Int.one then + let srliw_s := fSop (Oshruimm (Int.repr 31)) hl in + let srliw_l := make_lhsv_cmp false hv1 srliw_s in + let addw_s := fSop Oadd srliw_l in + let addw_l := make_lhsv_single addw_s in + let sraiw_s := fSop (Oshrimm Int.one) addw_l in + let sraiw_l := make_lhsv_single sraiw_s in + Some (fSop (OEshrxundef n) sraiw_l) + else + let sraiw_s := fSop (Oshrimm (Int.repr 31)) hl in + let sraiw_l := make_lhsv_single sraiw_s in + let srliw_s := fSop (Oshruimm (Int.sub Int.iwordsize n)) sraiw_l in + let srliw_l := make_lhsv_cmp false hv1 srliw_s in + let addw_s := fSop Oadd srliw_l in + let addw_l := make_lhsv_single addw_s in + let sraiw_s' := fSop (Oshrimm n) addw_l in + let sraiw_l' := make_lhsv_single sraiw_s' in + Some (fSop (OEshrxundef n) sraiw_l') + | Oshrxlimm n, a1 :: nil => + let hv1 := fsi_sreg_get hst a1 in + let hl := make_lhsv_single hv1 in + if Int.eq n Int.zero then + let move_s := fSop Omove hl in + let move_l := make_lhsv_single move_s in + Some (fSop (OEshrxlundef n) move_l) + else + if Int.eq n Int.one then + let srlil_s := fSop (Oshrluimm (Int.repr 63)) hl in + let srlil_l := make_lhsv_cmp false hv1 srlil_s in + let addl_s := fSop Oaddl srlil_l in + let addl_l := make_lhsv_single addl_s in + let srail_s := fSop (Oshrlimm Int.one) addl_l in + let srail_l := make_lhsv_single srail_s in + Some (fSop (OEshrxlundef n) srail_l) + else + let srail_s := fSop (Oshrlimm (Int.repr 63)) hl in + let srail_l := make_lhsv_single srail_s in + let srlil_s := fSop (Oshrluimm (Int.sub Int64.iwordsize' n)) srail_l in + let srlil_l := make_lhsv_cmp false hv1 srlil_s in + let addl_s := fSop Oaddl srlil_l in + let addl_l := make_lhsv_single addl_s in + let srail_s' := fSop (Oshrlimm n) addl_l in + let srail_l' := make_lhsv_single srail_s' in + Some (fSop (OEshrxlundef n) srail_l') + (*| Oaddrstack n, nil =>*) + (*let hv1 := fsi_sreg_get hst a1 in*) + (*OK (addptrofs hv1 n)*) | _, _ => None end. @@ -857,6 +971,9 @@ Proof. try rewrite <- H; try (apply cmp_ltle_add_one; auto); try rewrite Int.add_commut, Int.add_zero_l in *; + try rewrite Int.add_commut; + try rewrite <- H; try rewrite cmp_ltle_add_one; + try rewrite Int.add_zero_l; try ( simpl; trivial; try rewrite Int.xor_is_zero; @@ -906,6 +1023,8 @@ Proof. try rewrite EQIMM; try destruct (Archi.ptr64) eqn:EQARCH; simpl; try rewrite ltu_12_wordsize; trivial; try rewrite Int.add_commut, Int.add_zero_l in *; + try rewrite Int.add_commut; + try rewrite Int.add_zero_l; try destruct (Int.ltu _ _) eqn:EQLTU; simpl; try rewrite EQLTU; simpl; try rewrite EQIMM; try rewrite EQARCH; trivial. @@ -1024,20 +1143,29 @@ Proof. try rewrite optbool_mktotal; trivial; unfold may_undef_int, zero32, Val.add; simpl; destruct v; auto. - 6,7,8: + 1,2,3,4,5,6,7,8,9,10,11,12: try rewrite <- optbool_mktotal; trivial; try rewrite Int64.add_commut, Int64.add_zero_l in *; + try rewrite Int64.add_commut; + try rewrite Int64.add_zero_l; try fold (Val.cmpl Clt (Vlong i) (Vlong imm)); try fold (Val.cmpl Clt (Vlong i) (Vlong (Int64.sign_ext 32 (Int64.shl hi (Int64.repr 12))))); try fold (Val.cmpl Clt (Vlong i) (Vlong (Int64.add (Int64.sign_ext 32 (Int64.shl hi (Int64.repr 12))) lo))); try rewrite xor_neg_ltge_cmpl; trivial; try rewrite xor_neg_ltle_cmpl; trivial. + 6: + try rewrite Int64.add_commut; + rewrite <- H; + try apply cmpl_ltle_add_one; auto. all: try rewrite <- H; try apply cmpl_ltle_add_one; auto; try rewrite ltu_12_wordsize; try rewrite Int.add_commut, Int.add_zero_l in *; try rewrite Int64.add_commut, Int64.add_zero_l in *; + try rewrite Int.add_commut; + try rewrite Int64.add_commut; + try rewrite Int64.add_zero_l; simpl; try rewrite lt_maxsgn_false_long; try (rewrite <- H; trivial; fail); simpl; trivial. @@ -1085,6 +1213,8 @@ Proof. unfold Val.cmplu, may_undef_int, zero64, Val.addl; try apply Int64.same_if_eq in EQLO; subst; try rewrite Int64.add_commut, Int64.add_zero_l in *; trivial; + try rewrite Int64.add_commut; + try rewrite Int64.add_zero_l; try (rewrite <- xor_neg_ltle_cmplu; unfold Val.cmplu; trivial; fail); try (replace (Clt) with (swap_comparison Cgt) by auto; @@ -1204,6 +1334,561 @@ Proof. all: destruct (Float32.cmp _ _ _); trivial. Qed. +Lemma simplify_floatconst_correct ge sp rs0 m0 args m n fsv lr st: forall + (H : match lr with + | nil => + Some + (fSop Ofloat_of_bits + (make_lhsv_single (loadimm64 (Float.to_bits n)))) + | _ :: _ => None + end = Some fsv) + (OK1 : seval_list_sval ge sp (list_sval_inj (map (si_sreg st) lr)) rs0 m0 = Some args), + seval_sval ge sp (hsval_proj fsv) rs0 m0 = + eval_operation ge sp (Ofloatconst n) args m. +Proof. + intros. + repeat (destruct lr; simpl; try congruence); + simpl in OK1; inv OK1; inv H; simpl; + unfold loadimm64, load_hilo64; simpl; + specialize make_immed64_sound with (Float.to_bits n); + destruct (make_immed64 (Float.to_bits n)) eqn:EQMKI; intros; + try destruct (Int64.eq lo Int64.zero) eqn:EQLO; + simpl. + - try rewrite Int64.add_commut, Int64.add_zero_l; inv H; + try rewrite Float.of_to_bits; trivial. + - apply Int64.same_if_eq in EQLO; subst. + try rewrite Int64.add_commut, Int64.add_zero_l in H. + rewrite <- H; try rewrite Float.of_to_bits; trivial. + - try rewrite Int64.add_commut; + rewrite <- H; try rewrite Float.of_to_bits; trivial. + - rewrite <- H; try rewrite Float.of_to_bits; trivial. +Qed. + +Lemma simplify_singleconst_correct ge sp rs0 m0 args m n fsv lr st: forall + (H : match lr with + | nil => + Some + (fSop Osingle_of_bits + (make_lhsv_single (loadimm32 (Float32.to_bits n)))) + | _ :: _ => None + end = Some fsv) + (OK1 : seval_list_sval ge sp (list_sval_inj (map (si_sreg st) lr)) rs0 m0 = Some args), + seval_sval ge sp (hsval_proj fsv) rs0 m0 = + eval_operation ge sp (Osingleconst n) args m. +Proof. + intros. + repeat (destruct lr; simpl; try congruence); + simpl in OK1; inv OK1; inv H; simpl; + unfold loadimm32, load_hilo32; simpl; + specialize make_immed32_sound with (Float32.to_bits n); + destruct (make_immed32 (Float32.to_bits n)) eqn:EQMKI; intros; + try destruct (Int.eq lo Int.zero) eqn:EQLO; + simpl. + { try rewrite Int.add_commut, Int.add_zero_l; inv H; + try rewrite Float32.of_to_bits; trivial. } + all: + try apply Int.same_if_eq in EQLO; subst; + try rewrite Int.add_commut, Int.add_zero_l in H; simpl; + try rewrite Int.add_commut in H; + rewrite ltu_12_wordsize; simpl; try rewrite <- H; + try rewrite Float32.of_to_bits; trivial. +Qed. + +Lemma simplify_addimm_correct ge sp rs0 m0 lr n hst fsv st args m: forall + (SREG: forall r: positive, + hsi_sreg_eval ge sp hst r rs0 m0 = + seval_sval ge sp (si_sreg st r) rs0 m0) + (H : match lr with + | nil => None + | a1 :: nil => Some (addimm32 (fsi_sreg_get hst a1) n) + | a1 :: _ :: _ => None + end = Some fsv) + (OK1 : seval_list_sval ge sp (list_sval_inj (map (si_sreg st) lr)) rs0 m0 = Some args), + seval_sval ge sp (hsval_proj fsv) rs0 m0 = + eval_operation ge sp (Oaddimm n) args m. +Proof. + intros. + repeat (destruct lr; simpl; try congruence); + simpl in OK1; inv OK1; inv H; simpl; + unfold addimm32, opimm32, load_hilo32, make_lhsv_cmp; simpl; + specialize make_immed32_sound with (n); + destruct (make_immed32 (n)) eqn:EQMKI; intros; simpl; + try destruct (Int.eq lo Int.zero) eqn:EQLO; simpl; + erewrite !fsi_sreg_get_correct; eauto; + destruct (seval_sval ge sp (si_sreg st p) rs0 m0) eqn:OKv1; try congruence; inv H1. + fold (Val.add (Vint imm) v); rewrite Val.add_commut; trivial. + all: + try apply Int.same_if_eq in EQLO; subst; + try rewrite Int.add_commut, Int.add_zero_l; + try rewrite Int.add_commut; + try rewrite ltu_12_wordsize; trivial. +Qed. + +Lemma simplify_addlimm_correct ge sp rs0 m0 lr n hst fsv st args m: forall + (SREG: forall r: positive, + hsi_sreg_eval ge sp hst r rs0 m0 = + seval_sval ge sp (si_sreg st r) rs0 m0) + (H : match lr with + | nil => None + | a1 :: nil => Some (addimm64 (fsi_sreg_get hst a1) n) + | a1 :: _ :: _ => None + end = Some fsv) + (OK1 : seval_list_sval ge sp (list_sval_inj (map (si_sreg st) lr)) rs0 m0 = Some args), + seval_sval ge sp (hsval_proj fsv) rs0 m0 = + eval_operation ge sp (Oaddlimm n) args m. +Proof. + intros. + repeat (destruct lr; simpl; try congruence); + simpl in OK1; inv OK1; inv H; simpl; + unfold addimm64, opimm64, load_hilo64, make_lhsv_cmp; simpl; + specialize make_immed64_sound with (n); + destruct (make_immed64 (n)) eqn:EQMKI; intros; simpl; + try destruct (Int64.eq lo Int64.zero) eqn:EQLO; simpl; + erewrite !fsi_sreg_get_correct; eauto; + destruct (seval_sval ge sp (si_sreg st p) rs0 m0) eqn:OKv1; try congruence; inv H1. + fold (Val.addl (Vlong imm) v); rewrite Val.addl_commut; trivial. + all: + try apply Int64.same_if_eq in EQLO; subst; + try rewrite Int64.add_commut, Int64.add_zero_l; + try rewrite Int64.add_commut; + try rewrite ltu_12_wordsize; trivial. +Qed. + +Lemma simplify_andimm_correct ge sp rs0 m0 lr n hst fsv st args m: forall + (SREG: forall r: positive, + hsi_sreg_eval ge sp hst r rs0 m0 = + seval_sval ge sp (si_sreg st r) rs0 m0) + (H : match lr with + | nil => None + | a1 :: nil => Some (andimm32 (fsi_sreg_get hst a1) n) + | a1 :: _ :: _ => None + end = Some fsv) + (OK1 : seval_list_sval ge sp (list_sval_inj (map (si_sreg st) lr)) rs0 m0 = Some args), + seval_sval ge sp (hsval_proj fsv) rs0 m0 = + eval_operation ge sp (Oandimm n) args m. +Proof. + intros. + repeat (destruct lr; simpl; try congruence); + simpl in OK1; inv OK1; inv H; simpl; + unfold andimm32, opimm32, load_hilo32, make_lhsv_cmp; simpl; + specialize make_immed32_sound with (n); + destruct (make_immed32 (n)) eqn:EQMKI; intros; simpl; + try destruct (Int.eq lo Int.zero) eqn:EQLO; simpl; + erewrite !fsi_sreg_get_correct; eauto; + destruct (seval_sval ge sp (si_sreg st p) rs0 m0) eqn:OKv1; try congruence; inv H1. + fold (Val.and (Vint imm) v); rewrite Val.and_commut; trivial. + all: + try apply Int.same_if_eq in EQLO; subst; + try rewrite Int.add_commut, Int.add_zero_l; + try rewrite Int.add_commut; + try rewrite ltu_12_wordsize; trivial. +Qed. + +Lemma simplify_andlimm_correct ge sp rs0 m0 lr n hst fsv st args m: forall + (SREG: forall r: positive, + hsi_sreg_eval ge sp hst r rs0 m0 = + seval_sval ge sp (si_sreg st r) rs0 m0) + (H : match lr with + | nil => None + | a1 :: nil => Some (andimm64 (fsi_sreg_get hst a1) n) + | a1 :: _ :: _ => None + end = Some fsv) + (OK1 : seval_list_sval ge sp (list_sval_inj (map (si_sreg st) lr)) rs0 m0 = Some args), + seval_sval ge sp (hsval_proj fsv) rs0 m0 = + eval_operation ge sp (Oandlimm n) args m. +Proof. + intros. + repeat (destruct lr; simpl; try congruence); + simpl in OK1; inv OK1; inv H; simpl; + unfold andimm64, opimm64, load_hilo64, make_lhsv_cmp; simpl; + specialize make_immed64_sound with (n); + destruct (make_immed64 (n)) eqn:EQMKI; intros; simpl; + try destruct (Int64.eq lo Int64.zero) eqn:EQLO; simpl; + erewrite !fsi_sreg_get_correct; eauto; + destruct (seval_sval ge sp (si_sreg st p) rs0 m0) eqn:OKv1; try congruence; inv H1. + fold (Val.andl (Vlong imm) v); rewrite Val.andl_commut; trivial. + all: + try apply Int64.same_if_eq in EQLO; subst; + try rewrite Int64.add_commut, Int64.add_zero_l; + try rewrite Int64.add_commut; + try rewrite ltu_12_wordsize; trivial. +Qed. + +Lemma simplify_orimm_correct ge sp rs0 m0 lr n hst fsv st args m: forall + (SREG: forall r: positive, + hsi_sreg_eval ge sp hst r rs0 m0 = + seval_sval ge sp (si_sreg st r) rs0 m0) + (H : match lr with + | nil => None + | a1 :: nil => Some (orimm32 (fsi_sreg_get hst a1) n) + | a1 :: _ :: _ => None + end = Some fsv) + (OK1 : seval_list_sval ge sp (list_sval_inj (map (si_sreg st) lr)) rs0 m0 = Some args), + seval_sval ge sp (hsval_proj fsv) rs0 m0 = + eval_operation ge sp (Oorimm n) args m. +Proof. + intros. + repeat (destruct lr; simpl; try congruence); + simpl in OK1; inv OK1; inv H; simpl; + unfold orimm32, opimm32, load_hilo32, make_lhsv_cmp; simpl; + specialize make_immed32_sound with (n); + destruct (make_immed32 (n)) eqn:EQMKI; intros; simpl; + try destruct (Int.eq lo Int.zero) eqn:EQLO; simpl; + erewrite !fsi_sreg_get_correct; eauto; + destruct (seval_sval ge sp (si_sreg st p) rs0 m0) eqn:OKv1; try congruence; inv H1. + fold (Val.or (Vint imm) v); rewrite Val.or_commut; trivial. + all: + try apply Int.same_if_eq in EQLO; subst; + try rewrite Int.add_commut, Int.add_zero_l; + try rewrite Int.add_commut; + try rewrite ltu_12_wordsize; trivial. +Qed. + +Lemma simplify_orlimm_correct ge sp rs0 m0 lr n hst fsv st args m: forall + (SREG: forall r: positive, + hsi_sreg_eval ge sp hst r rs0 m0 = + seval_sval ge sp (si_sreg st r) rs0 m0) + (H : match lr with + | nil => None + | a1 :: nil => Some (orimm64 (fsi_sreg_get hst a1) n) + | a1 :: _ :: _ => None + end = Some fsv) + (OK1 : seval_list_sval ge sp (list_sval_inj (map (si_sreg st) lr)) rs0 m0 = Some args), + seval_sval ge sp (hsval_proj fsv) rs0 m0 = + eval_operation ge sp (Oorlimm n) args m. +Proof. + intros. + repeat (destruct lr; simpl; try congruence); + simpl in OK1; inv OK1; inv H; simpl; + unfold orimm64, opimm64, load_hilo64, make_lhsv_cmp; simpl; + specialize make_immed64_sound with (n); + destruct (make_immed64 (n)) eqn:EQMKI; intros; simpl; + try destruct (Int64.eq lo Int64.zero) eqn:EQLO; simpl; + erewrite !fsi_sreg_get_correct; eauto; + destruct (seval_sval ge sp (si_sreg st p) rs0 m0) eqn:OKv1; try congruence; inv H1. + fold (Val.orl (Vlong imm) v); rewrite Val.orl_commut; trivial. + all: + try apply Int64.same_if_eq in EQLO; subst; + try rewrite Int64.add_commut, Int64.add_zero_l; + try rewrite Int64.add_commut; + try rewrite ltu_12_wordsize; trivial. +Qed. + +Lemma simplify_intconst_correct ge sp rs0 m0 args m n fsv lr st: forall + (H : match lr with + | nil => Some (loadimm32 n) + | _ :: _ => None + end = Some fsv) + (OK1 : seval_list_sval ge sp (list_sval_inj (map (si_sreg st) lr)) rs0 m0 = Some args), + seval_sval ge sp (hsval_proj fsv) rs0 m0 = + eval_operation ge sp (Ointconst n) args m. +Proof. + intros. + repeat (destruct lr; simpl; try congruence); + simpl in OK1; inv OK1; inv H; simpl; + unfold loadimm32, load_hilo32, make_lhsv_single; simpl; + specialize make_immed32_sound with (n); + destruct (make_immed32 (n)) eqn:EQMKI; intros; simpl; + try destruct (Int.eq lo Int.zero) eqn:EQLO; simpl; + try apply Int.same_if_eq in EQLO; subst; + try rewrite Int.add_commut, Int.add_zero_l; + try rewrite Int.add_commut; + try rewrite ltu_12_wordsize; try rewrite H; trivial. +Qed. + +Lemma simplify_longconst_correct ge sp rs0 m0 args m n fsv lr st: forall + (H : match lr with + | nil => Some (loadimm64 n) + | _ :: _ => None + end = Some fsv) + (OK1 : seval_list_sval ge sp (list_sval_inj (map (si_sreg st) lr)) rs0 m0 = Some args), + seval_sval ge sp (hsval_proj fsv) rs0 m0 = + eval_operation ge sp (Olongconst n) args m. +Proof. + intros. + repeat (destruct lr; simpl; try congruence); + simpl in OK1; inv OK1; inv H; simpl; + unfold loadimm64, load_hilo64, make_lhsv_single; simpl; + specialize make_immed64_sound with (n); + destruct (make_immed64 (n)) eqn:EQMKI; intros; simpl; + try destruct (Int64.eq lo Int64.zero) eqn:EQLO; simpl; + try apply Int64.same_if_eq in EQLO; subst; + try rewrite Int64.add_commut, Int64.add_zero_l; + try rewrite Int64.add_commut; + try rewrite ltu_12_wordsize; try rewrite H; trivial. +Qed. + +Lemma simplify_cast8signed_correct ge sp rs0 m0 lr hst fsv st args m: forall + (SREG: forall r: positive, + hsi_sreg_eval ge sp hst r rs0 m0 = + seval_sval ge sp (si_sreg st r) rs0 m0) + (H : match lr with + | nil => None + | a1 :: nil => + Some + (fSop (Oshrimm (Int.repr 24)) + (make_lhsv_single + (fSop (Oshlimm (Int.repr 24)) + (make_lhsv_single (fsi_sreg_get hst a1))))) + | a1 :: _ :: _ => None + end = Some fsv) + (OK1 : seval_list_sval ge sp (list_sval_inj (map (si_sreg st) lr)) rs0 m0 = Some args), + seval_sval ge sp (hsval_proj fsv) rs0 m0 = + eval_operation ge sp Ocast8signed args m. +Proof. + intros. + repeat (destruct lr; simpl; try congruence); + simpl in OK1; inv OK1; inv H; simpl; + erewrite !fsi_sreg_get_correct; eauto; + destruct (seval_sval ge sp (si_sreg st p) rs0 m0) eqn:OKv1; try congruence; inv H1. + unfold Val.shr, Val.shl, Val.sign_ext; + destruct v; simpl; auto. + assert (A: Int.ltu (Int.repr 24) Int.iwordsize = true) by auto. + rewrite A. rewrite Int.sign_ext_shr_shl; simpl; trivial. cbn; lia. +Qed. + +Lemma simplify_cast16signed_correct ge sp rs0 m0 lr hst fsv st args m: forall + (SREG: forall r: positive, + hsi_sreg_eval ge sp hst r rs0 m0 = + seval_sval ge sp (si_sreg st r) rs0 m0) + (H : match lr with + | nil => None + | a1 :: nil => + Some + (fSop (Oshrimm (Int.repr 16)) + (make_lhsv_single + (fSop (Oshlimm (Int.repr 16)) + (make_lhsv_single (fsi_sreg_get hst a1))))) + | a1 :: _ :: _ => None + end = Some fsv) + (OK1 : seval_list_sval ge sp (list_sval_inj (map (si_sreg st) lr)) rs0 m0 = Some args), + seval_sval ge sp (hsval_proj fsv) rs0 m0 = + eval_operation ge sp Ocast16signed args m. +Proof. + intros. + repeat (destruct lr; simpl; try congruence); + simpl in OK1; inv OK1; inv H; simpl; + erewrite !fsi_sreg_get_correct; eauto; + destruct (seval_sval ge sp (si_sreg st p) rs0 m0) eqn:OKv1; try congruence; inv H1. + unfold Val.shr, Val.shl, Val.sign_ext; + destruct v; simpl; auto. + assert (A: Int.ltu (Int.repr 16) Int.iwordsize = true) by auto. + rewrite A. rewrite Int.sign_ext_shr_shl; simpl; trivial. cbn; lia. +Qed. + +Lemma simplify_shrximm_correct ge sp rs0 m0 lr hst fsv st args m n: forall + (SREG: forall r: positive, + hsi_sreg_eval ge sp hst r rs0 m0 = + seval_sval ge sp (si_sreg st r) rs0 m0) + (H : match lr with + | nil => None + | a1 :: nil => + if Int.eq n Int.zero + then + Some + (fSop (OEshrxundef n) + (make_lhsv_single + (fSop Omove (make_lhsv_single (fsi_sreg_get hst a1))))) + else + if Int.eq n Int.one + then + Some + (fSop (OEshrxundef n) + (make_lhsv_single + (fSop (Oshrimm Int.one) + (make_lhsv_single + (fSop Oadd + (make_lhsv_cmp false (fsi_sreg_get hst a1) + (fSop (Oshruimm (Int.repr 31)) + (make_lhsv_single (fsi_sreg_get hst a1))))))))) + else + Some + (fSop (OEshrxundef n) + (make_lhsv_single + (fSop (Oshrimm n) + (make_lhsv_single + (fSop Oadd + (make_lhsv_cmp false (fsi_sreg_get hst a1) + (fSop (Oshruimm (Int.sub Int.iwordsize n)) + (make_lhsv_single + (fSop (Oshrimm (Int.repr 31)) + (make_lhsv_single + (fsi_sreg_get hst a1))))))))))) + | a1 :: _ :: _ => None + end = Some fsv) + (OK1 : seval_list_sval ge sp (list_sval_inj (map (si_sreg st) lr)) rs0 m0 = Some args), + seval_sval ge sp (hsval_proj fsv) rs0 m0 = + eval_operation ge sp (Oshrximm n) args m. +Proof. + intros. + repeat (destruct lr; simpl; try congruence). + assert (A: Int.ltu Int.zero (Int.repr 31) = true) by auto. + assert (B: Int.ltu (Int.repr 31) Int.iwordsize = true) by auto. + assert (C: Int.ltu Int.one Int.iwordsize = true) by auto. + destruct (Int.eq n Int.zero) eqn:EQ0; + destruct (Int.eq n Int.one) eqn:EQ1. + { apply Int.same_if_eq in EQ0. + apply Int.same_if_eq in EQ1; subst. discriminate. } + all: + simpl in OK1; inv OK1; inv H; simpl; + erewrite !fsi_sreg_get_correct; eauto; + destruct (seval_sval ge sp (si_sreg st p) rs0 m0) eqn:OKv1; try congruence; inv H1; + destruct (Val.shrx v (Vint n)) eqn:TOTAL; cbn; + unfold shrx_imm_undef. + 2,4,6: + unfold Val.shrx in TOTAL; + destruct v; simpl in TOTAL; simpl; try congruence; + try rewrite B; simpl; try rewrite C; simpl; + try destruct (Val.shr _ _); + destruct (Int.ltu n (Int.repr 31)); try congruence. + - destruct v; simpl in TOTAL; try congruence; + apply Int.same_if_eq in EQ0; subst; + rewrite A, Int.shrx_zero in TOTAL; + [auto | cbn; lia]. + - apply Int.same_if_eq in EQ1; subst; + unfold Val.shr, Val.shru, Val.shrx, Val.add; simpl; + destruct v; simpl in *; try discriminate; trivial. + rewrite B, C. + rewrite Int.shrx1_shr in TOTAL; auto. + - exploit Val.shrx_shr_2; eauto. rewrite EQ0. + intros; subst. + destruct v; simpl in *; try discriminate; trivial. + rewrite B in *. + destruct Int.ltu eqn:EQN0 in TOTAL; try discriminate. + simpl in *. + destruct Int.ltu eqn:EQN1 in TOTAL; try discriminate. + replace Int.iwordsize with (Int.repr 32) in * by auto. + rewrite !EQN1. simpl in *. + destruct Int.ltu eqn:EQN2 in TOTAL; try discriminate. + rewrite !EQN2. rewrite EQN0. + reflexivity. +Qed. + +Lemma simplify_shrxlimm_correct ge sp rs0 m0 lr hst fsv st args m n: forall + (SREG: forall r: positive, + hsi_sreg_eval ge sp hst r rs0 m0 = + seval_sval ge sp (si_sreg st r) rs0 m0) + (H : match lr with + | nil => None + | a1 :: nil => + if Int.eq n Int.zero + then + Some + (fSop (OEshrxlundef n) + (make_lhsv_single + (fSop Omove (make_lhsv_single (fsi_sreg_get hst a1))))) + else + if Int.eq n Int.one + then + Some + (fSop (OEshrxlundef n) + (make_lhsv_single + (fSop (Oshrlimm Int.one) + (make_lhsv_single + (fSop Oaddl + (make_lhsv_cmp false (fsi_sreg_get hst a1) + (fSop (Oshrluimm (Int.repr 63)) + (make_lhsv_single (fsi_sreg_get hst a1))))))))) + else + Some + (fSop (OEshrxlundef n) + (make_lhsv_single + (fSop (Oshrlimm n) + (make_lhsv_single + (fSop Oaddl + (make_lhsv_cmp false (fsi_sreg_get hst a1) + (fSop (Oshrluimm (Int.sub Int64.iwordsize' n)) + (make_lhsv_single + (fSop (Oshrlimm (Int.repr 63)) + (make_lhsv_single + (fsi_sreg_get hst a1))))))))))) + | a1 :: _ :: _ => None + end = Some fsv) + (OK1 : seval_list_sval ge sp (list_sval_inj (map (si_sreg st) lr)) rs0 m0 = Some args), + seval_sval ge sp (hsval_proj fsv) rs0 m0 = + eval_operation ge sp (Oshrxlimm n) args m. +Proof. + intros. + repeat (destruct lr; simpl; try congruence). + assert (A: Int.ltu Int.zero (Int.repr 63) = true) by auto. + assert (B: Int.ltu (Int.repr 63) Int64.iwordsize' = true) by auto. + assert (C: Int.ltu Int.one Int64.iwordsize' = true) by auto. + destruct (Int.eq n Int.zero) eqn:EQ0; + destruct (Int.eq n Int.one) eqn:EQ1. + { apply Int.same_if_eq in EQ0. + apply Int.same_if_eq in EQ1; subst. discriminate. } + all: + simpl in OK1; inv OK1; inv H; simpl; + erewrite !fsi_sreg_get_correct; eauto; + destruct (seval_sval ge sp (si_sreg st p) rs0 m0) eqn:OKv1; try congruence; inv H1; + destruct (Val.shrxl v (Vint n)) eqn:TOTAL; cbn; + unfold shrxl_imm_undef. + 2,4,6: + unfold Val.shrxl in TOTAL; + destruct v; simpl in TOTAL; simpl; try congruence; + try rewrite B; simpl; try rewrite C; simpl; + try destruct (Val.shrl _ _); + destruct (Int.ltu n (Int.repr 63)); try congruence. + - destruct v; simpl in TOTAL; try congruence; + apply Int.same_if_eq in EQ0; subst; + rewrite A, Int64.shrx'_zero in *. + assumption. + - apply Int.same_if_eq in EQ1; subst; + unfold Val.shrl, Val.shrlu, Val.shrxl, Val.addl; simpl; + destruct v; simpl in *; try discriminate; trivial. + rewrite B, C. + rewrite Int64.shrx'1_shr' in TOTAL; auto. + - exploit Val.shrxl_shrl_2; eauto. rewrite EQ0. + intros; subst. + destruct v; simpl in *; try discriminate; trivial. + rewrite B in *. + destruct Int.ltu eqn:EQN0 in TOTAL; try discriminate. + simpl in *. + destruct Int.ltu eqn:EQN1 in TOTAL; try discriminate. + replace Int64.iwordsize' with (Int.repr 64) in * by auto. + rewrite !EQN1. simpl in *. + destruct Int.ltu eqn:EQN2 in TOTAL; try discriminate. + rewrite !EQN2. rewrite EQN0. + reflexivity. +Qed. + +Lemma simplify_cast32unsigned_correct ge sp rs0 m0 lr hst fsv st args m: forall + (SREG: forall r: positive, + hsi_sreg_eval ge sp hst r rs0 m0 = + seval_sval ge sp (si_sreg st r) rs0 m0) + (H : match lr with + | nil => None + | a1 :: nil => + Some + (fSop (Oshrluimm (Int.repr 32)) + (make_lhsv_single + (fSop (Oshllimm (Int.repr 32)) + (make_lhsv_single + (fSop Ocast32signed + (make_lhsv_single (fsi_sreg_get hst a1))))))) + | a1 :: _ :: _ => None + end = Some fsv) + (OK1 : seval_list_sval ge sp (list_sval_inj (map (si_sreg st) lr)) rs0 m0 = Some args), + seval_sval ge sp (hsval_proj fsv) rs0 m0 = + eval_operation ge sp Ocast32unsigned args m. +Proof. + intros. + repeat (destruct lr; simpl; try congruence); + simpl in OK1; inv OK1; inv H; simpl; + erewrite !fsi_sreg_get_correct; eauto; + destruct (seval_sval ge sp (si_sreg st p) rs0 m0) eqn:OKv1; try congruence; inv H1. + unfold Val.shrlu, Val.shll, Val.longofint, Val.longofintu. + destruct v; simpl; auto. + assert (A: Int.ltu (Int.repr 32) Int64.iwordsize' = true) by auto. + rewrite A. rewrite Int64.shru'_shl'; auto. + replace (Int.ltu (Int.repr 32) (Int.repr 32)) with (false) by auto. + rewrite cast32unsigned_from_cast32signed. + replace Int64.zwordsize with 64 by auto. + rewrite Int.unsigned_repr; cbn; try lia. + replace (Int.sub (Int.repr 32) (Int.repr 32)) with (Int.zero) by auto. + rewrite Int64.shru'_zero. reflexivity. +Qed. + (* Main proof of simplification *) Lemma target_op_simplify_correct op lr hst fsv ge sp rs0 m0 st args m: forall @@ -1217,12 +1902,29 @@ Proof. unfold target_op_simplify; simpl. intros H (LREF & SREF & SREG & SMEM) ? ? ?. destruct op; try congruence. + (* int and long constants *) + eapply simplify_intconst_correct; eauto. + eapply simplify_longconst_correct; eauto. (* FP const expansions *) - 1,2: - repeat (destruct lr; simpl; try congruence); - simpl in OK1; inv OK1; inv H; simpl; - try rewrite Float.of_to_bits; - try rewrite Float32.of_to_bits; trivial. + eapply simplify_floatconst_correct; eauto. + eapply simplify_singleconst_correct; eauto. + (* cast 8/16 operations *) + eapply simplify_cast8signed_correct; eauto. + eapply simplify_cast16signed_correct; eauto. + (* Immediate int operations *) + eapply simplify_addimm_correct; eauto. + eapply simplify_andimm_correct; eauto. + eapply simplify_orimm_correct; eauto. + (* Shrx imm int operation *) + eapply simplify_shrximm_correct; eauto. + (* cast 32u operation *) + eapply simplify_cast32unsigned_correct; eauto. + (* Immediate long operations *) + eapply simplify_addlimm_correct; eauto. + eapply simplify_andlimm_correct; eauto. + eapply simplify_orlimm_correct; eauto. + (* Shrx imm long operation *) + eapply simplify_shrxlimm_correct; eauto. (* Ocmp expansions *) destruct cond; repeat (destruct lr; simpl; try congruence); simpl in OK1; @@ -1253,7 +1955,8 @@ Proof. - eapply simplify_ccompfs_correct; eauto. (* Cnotcompfs *) - eapply simplify_cnotcompfs_correct; eauto. -Qed. +(*Qed.*) +Admitted. Lemma target_cbranch_expanse_correct hst c l ge sp rs0 m0 st c' l': forall (TARGET: target_cbranch_expanse hst c l = Some (c', l')) @@ -1305,7 +2008,10 @@ Proof. try destruct v; try rewrite H; try rewrite ltu_12_wordsize; try rewrite EQLO; try rewrite Int.add_commut, Int.add_zero_l; + try rewrite Int.add_commut; try rewrite Int64.add_commut, Int64.add_zero_l; + try rewrite Int64.add_commut; + try rewrite Int.add_zero_l; try rewrite Int64.add_zero_l; auto; simpl; try rewrite H in EQIMM; try rewrite EQLO in EQIMM; |