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-rw-r--r--mppa_k1c/ValueAOp.v134
1 files changed, 133 insertions, 1 deletions
diff --git a/mppa_k1c/ValueAOp.v b/mppa_k1c/ValueAOp.v
index 439138da..2c9bdf3e 100644
--- a/mppa_k1c/ValueAOp.v
+++ b/mppa_k1c/ValueAOp.v
@@ -12,7 +12,37 @@
Require Import Coqlib Compopts.
Require Import AST Integers Floats Values Memory Globalenvs.
-Require Import Op ExtValues RTL ValueDomain.
+Require Import Op ExtValues ExtFloats RTL ValueDomain.
+
+Definition minf := binop_float ExtFloat.min.
+Definition maxf := binop_float ExtFloat.max.
+Definition minfs := binop_single ExtFloat32.min.
+Definition maxfs := binop_single ExtFloat32.max.
+
+Definition ntop3 (x y z: aval) : aval := Ifptr (plub (provenance x) (plub (provenance y) (provenance z))).
+
+Definition triple_op_float (sem: float -> float -> float -> float) (x y z: aval) :=
+ match x, y, z with
+ | F a, F b, F c => F (sem a b c)
+ | _, _, _ => ntop3 x y z
+ end.
+
+Definition triple_op_single (sem: float32 -> float32 -> float32 -> float32) (x y z: aval) :=
+ match x, y, z with
+ | FS a, FS b, FS c => FS (sem a b c)
+ | _, _, _ => ntop3 x y z
+ end.
+
+Definition fmaddf := triple_op_float (fun x y z => Float.fma y z x).
+Definition fmsubf := triple_op_float (fun x y z => Float.fma (Float.neg y) z x).
+Definition fmaddfs := triple_op_single (fun x y z => Float32.fma y z x).
+Definition fmsubfs := triple_op_single (fun x y z => Float32.fma (Float32.neg y) z x).
+
+Definition invfs (y : aval) :=
+ match y with
+ | FS f => FS (ExtFloat32.inv f)
+ | _ => ntop1 y
+ end.
(** Value analysis for RISC V operators *)
@@ -235,12 +265,21 @@ Definition eval_static_operation (op: operation) (vl: list aval): aval :=
| Osubf, v1::v2::nil => subf v1 v2
| Omulf, v1::v2::nil => mulf v1 v2
| Odivf, v1::v2::nil => divf v1 v2
+ | Ominf, v1::v2::nil => minf v1 v2
+ | Omaxf, v1::v2::nil => maxf v1 v2
+ | Ofmaddf, v1::v2::v3::nil => fmaddf v1 v2 v3
+ | Ofmsubf, v1::v2::v3::nil => fmsubf v1 v2 v3
| Onegfs, v1::nil => negfs v1
| Oabsfs, v1::nil => absfs v1
| Oaddfs, v1::v2::nil => addfs v1 v2
| Osubfs, v1::v2::nil => subfs v1 v2
| Omulfs, v1::v2::nil => mulfs v1 v2
| Odivfs, v1::v2::nil => divfs v1 v2
+ | Ominfs, v1::v2::nil => minfs v1 v2
+ | Omaxfs, v1::v2::nil => maxfs v1 v2
+ | Oinvfs, v1::nil => invfs v1
+ | Ofmaddfs, v1::v2::v3::nil => fmaddfs v1 v2 v3
+ | Ofmsubfs, v1::v2::v3::nil => fmsubfs v1 v2 v3
| Osingleoffloat, v1::nil => singleoffloat v1
| Ofloatofsingle, v1::nil => floatofsingle v1
| Ointoffloat, v1::nil => intoffloat v1
@@ -278,6 +317,99 @@ Hypothesis GENV: genv_match bc ge.
Variable sp: block.
Hypothesis STACK: bc sp = BCstack.
+Lemma minf_sound:
+ forall v x w y, vmatch bc v x -> vmatch bc w y -> vmatch bc (ExtValues.minf v w) (minf x y).
+Proof.
+ apply (binop_float_sound bc ExtFloat.min); assumption.
+Qed.
+
+Lemma maxf_sound:
+ forall v x w y, vmatch bc v x -> vmatch bc w y -> vmatch bc (ExtValues.maxf v w) (maxf x y).
+Proof.
+ apply (binop_float_sound bc ExtFloat.max); assumption.
+Qed.
+
+Lemma minfs_sound:
+ forall v x w y, vmatch bc v x -> vmatch bc w y -> vmatch bc (ExtValues.minfs v w) (minfs x y).
+Proof.
+ apply (binop_single_sound bc ExtFloat32.min); assumption.
+Qed.
+
+Lemma maxfs_sound:
+ forall v x w y, vmatch bc v x -> vmatch bc w y -> vmatch bc (ExtValues.maxfs v w) (maxfs x y).
+Proof.
+ apply (binop_single_sound bc ExtFloat32.max); assumption.
+Qed.
+
+Lemma invfs_sound:
+ forall v x, vmatch bc v x -> vmatch bc (ExtValues.invfs v) (invfs x).
+Proof.
+ intros v x;
+ intro MATCH;
+ inversion MATCH;
+ simpl;
+ constructor.
+Qed.
+
+Lemma triple_op_float_sound:
+ forall f a x b y c z,
+ vmatch bc a x -> vmatch bc b y -> vmatch bc c z ->
+ vmatch bc (ExtValues.triple_op_float f a b c)
+ (triple_op_float f x y z).
+Proof.
+ intros until z.
+ intros Hax Hby Hcz.
+ inv Hax; simpl; try constructor;
+ inv Hby; simpl; try constructor;
+ inv Hcz; simpl; try constructor.
+Qed.
+
+Lemma triple_op_single_sound:
+ forall f a x b y c z,
+ vmatch bc a x -> vmatch bc b y -> vmatch bc c z ->
+ vmatch bc (ExtValues.triple_op_single f a b c)
+ (triple_op_single f x y z).
+Proof.
+ intros until z.
+ intros Hax Hby Hcz.
+ inv Hax; simpl; try constructor;
+ inv Hby; simpl; try constructor;
+ inv Hcz; simpl; try constructor.
+Qed.
+
+Lemma fmaddf_sound :
+ forall a x b y c z, vmatch bc a x -> vmatch bc b y -> vmatch bc c z ->
+ vmatch bc (ExtValues.fmaddf a b c) (fmaddf x y z).
+Proof.
+ intros. unfold ExtValues.fmaddf, fmaddf.
+ apply triple_op_float_sound; assumption.
+Qed.
+
+Lemma fmaddfs_sound :
+ forall a x b y c z, vmatch bc a x -> vmatch bc b y -> vmatch bc c z ->
+ vmatch bc (ExtValues.fmaddfs a b c) (fmaddfs x y z).
+Proof.
+ intros. unfold ExtValues.fmaddfs, fmaddfs.
+ apply triple_op_single_sound; assumption.
+Qed.
+
+Lemma fmsubf_sound :
+ forall a x b y c z, vmatch bc a x -> vmatch bc b y -> vmatch bc c z ->
+ vmatch bc (ExtValues.fmsubf a b c) (fmsubf x y z).
+Proof.
+ intros. unfold ExtValues.fmsubf, fmsubf.
+ apply triple_op_float_sound; assumption.
+Qed.
+
+Lemma fmsubfs_sound :
+ forall a x b y c z, vmatch bc a x -> vmatch bc b y -> vmatch bc c z ->
+ vmatch bc (ExtValues.fmsubfs a b c) (fmsubfs x y z).
+Proof.
+ intros. unfold ExtValues.fmsubfs, fmsubfs.
+ apply triple_op_single_sound; assumption.
+Qed.
+Hint Resolve minf_sound maxf_sound minfs_sound maxfs_sound invfs_sound fmaddf_sound fmaddfs_sound fmsubf_sound fmsubfs_sound : va.
+
Theorem eval_static_condition_sound:
forall cond vargs m aargs,
list_forall2 (vmatch bc) vargs aargs ->