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Diffstat (limited to 'kvx/FPExtra.v')
| -rw-r--r-- | kvx/FPExtra.v | 117 |
1 files changed, 117 insertions, 0 deletions
diff --git a/kvx/FPExtra.v b/kvx/FPExtra.v new file mode 100644 index 00000000..9e3b55b6 --- /dev/null +++ b/kvx/FPExtra.v @@ -0,0 +1,117 @@ +Require Import Coqlib. +Require Import Compopts. +Require Import AST Integers Floats. +Require Import Op CminorSel. +Require Import OpHelpers. +Require Import SelectOp SplitLong. +Require Import Values ExtValues. +Require Import DecBoolOps. + +Local Open Scope cminorsel_scope. +Local Open Scope string_scope. + +Definition e_andl a b := Eop Oandl (a ::: b ::: Enil). +Definition e_addl a b := Eop Oaddl (a ::: b ::: Enil). +Definition e_orl a b := Eop Oorl (a ::: b ::: Enil). +Definition e_constl n := Eop (Olongconst (Int64.repr n)) Enil. +Definition e_float_of_longu a := Eop Ofloatoflongu (a ::: Enil). +Definition e_float_of_long a := Eop Ofloatoflong (a ::: Enil). +Definition e_single_of_float a := Eop Osingleoffloat (a ::: Enil). +Definition e_ite ty c vc v1 v2 := Eop (Osel c ty) (v1 ::: v2 ::: vc ::: Enil). +Definition e_cmpluimm c v n := Eop (Ocmp (Ccompluimm c n)) (v ::: Enil). +Definition e_absl a := Eop (Oabsdifflimm Int64.zero) (a ::: Enil). + +Definition a_var := Eletvar 0%nat. + +Definition e_single_of_longu a := + Elet a (e_single_of_float (e_float_of_longu + (e_ite Tlong (Ccompu0 Cne) (e_cmpluimm Cle a_var (Int64.repr (2^53))) a_var + (e_andl (e_orl a_var (e_addl (e_andl a_var (e_constl 2047)) + (e_constl 2047))) + (e_constl (-2048))))))%Z. + +Theorem e_single_of_longu_correct : + forall (ge : genv) (sp: val) cmenv memenv + (le : letenv) (expr_a : expr) (va : val) + (EVAL_a : eval_expr ge sp cmenv memenv le expr_a va), + eval_expr ge sp cmenv memenv le (e_single_of_longu expr_a) + (Val.maketotal (Val.singleoflongu va)). +Proof. + intros. + unfold e_single_of_longu. + repeat econstructor. eassumption. + cbn. + destruct va; cbn. + all: try reflexivity. + f_equal. + unfold Int64.ltu. + change (Int64.unsigned (Int64.repr 9007199254740992))%Z with 9007199254740992%Z. + destruct zlt as [LT | GE]; cbn. + { change (Int.eq Int.zero Int.zero) with true. cbn. + f_equal. + symmetry. + apply Float32.of_longu_double_2. + lia. + } + change (Int.eq Int.one Int.zero) with false. cbn. + f_equal. + symmetry. + apply Float32.of_longu_double_1. + lia. +Qed. + +Definition e_single_of_long a := + Elet a (e_single_of_float (e_float_of_long + (e_ite Tlong (Ccompu0 Cne) (e_cmpluimm Cle (e_absl a_var) (Int64.repr (2^53))) a_var + (e_andl (e_orl a_var (e_addl (e_andl a_var (e_constl 2047)) + (e_constl 2047))) + (e_constl (-2048))))))%Z. + +Theorem e_single_of_long_correct : + forall (ge : genv) (sp: val) cmenv memenv + (le : letenv) (expr_a : expr) (va : val) + (EVAL_a : eval_expr ge sp cmenv memenv le expr_a va), + eval_expr ge sp cmenv memenv le (e_single_of_long expr_a) + (Val.maketotal (Val.singleoflong va)). +Proof. + intros. + unfold e_single_of_long. + repeat econstructor. eassumption. + cbn. + destruct va; cbn. + all: try reflexivity. + f_equal. + unfold Int64.ltu. + change (Int64.unsigned (Int64.repr 9007199254740992))%Z with 9007199254740992%Z. + destruct zlt as [LT | GE]; cbn. + { change (Int.eq Int.zero Int.zero) with true. cbn. + f_equal. + symmetry. + apply Float32.of_long_double_2. + unfold long_absdiff, Z_abs_diff in LT. + change (Int64.signed Int64.zero) with 0%Z in LT. + rewrite Z.sub_0_r in LT. + rewrite Int64.unsigned_repr in LT. + lia. + pose proof (Int64.signed_range i). + change Int64.min_signed with (-9223372036854775808)%Z in *. + change Int64.max_signed with (9223372036854775807)%Z in *. + change Int64.max_unsigned with (18446744073709551615)%Z. + lia. + } + change (Int.eq Int.one Int.zero) with false. cbn. + f_equal. + symmetry. + apply Float32.of_long_double_1. + unfold long_absdiff, Z_abs_diff in GE. + change (Int64.signed Int64.zero) with 0%Z in GE. + rewrite Z.sub_0_r in GE. + rewrite Int64.unsigned_repr in GE. + lia. + pose proof (Int64.signed_range i). + change Int64.min_signed with (-9223372036854775808)%Z in *. + change Int64.max_signed with (9223372036854775807)%Z in *. + change Int64.max_unsigned with (18446744073709551615)%Z. + lia. +Qed. + |