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| author | Xavier Leroy <xavier.leroy@inria.fr> | 2016-10-04 15:52:16 +0200 |
|---|---|---|
| committer | Xavier Leroy <xavier.leroy@inria.fr> | 2016-10-04 15:52:16 +0200 |
| commit | d2af79a77ed2936ff0ed90cadf8e48637d774d4c (patch) | |
| tree | 09300943e12a98ae80598c79d455b31725271ead /backend/SplitLongproof.v | |
| parent | a44893028eb1dd434c68001234ad56d030205a8e (diff) | |
| download | compcert-kvx-d2af79a77ed2936ff0ed90cadf8e48637d774d4c.tar.gz compcert-kvx-d2af79a77ed2936ff0ed90cadf8e48637d774d4c.zip | |
Turn 64-bit integer division and modulus by constants into multiply-high
This trick was already implemented for 32-bit integer division and modulus. Here we extend it to the 64-bit case.
For 32-bit target processors, the runtime library must implement 64-bit multiply-high (signed and unsigned). Tentative implementations are provided for IA32 and PowerPC, but need testing.
Diffstat (limited to 'backend/SplitLongproof.v')
| -rw-r--r-- | backend/SplitLongproof.v | 22 |
1 files changed, 20 insertions, 2 deletions
diff --git a/backend/SplitLongproof.v b/backend/SplitLongproof.v index a10ee3f7..31f5db67 100644 --- a/backend/SplitLongproof.v +++ b/backend/SplitLongproof.v @@ -48,7 +48,9 @@ Axiom i64_helpers_correct : /\ (forall x y z, Val.modlu x y = Some z -> external_implements "__i64_umod" sig_ll_l (x::y::nil) z) /\ (forall x y, external_implements "__i64_shl" sig_li_l (x::y::nil) (Val.shll x y)) /\ (forall x y, external_implements "__i64_shr" sig_li_l (x::y::nil) (Val.shrlu x y)) - /\ (forall x y, external_implements "__i64_sar" sig_li_l (x::y::nil) (Val.shrl x y)). + /\ (forall x y, external_implements "__i64_sar" sig_li_l (x::y::nil) (Val.shrl x y)) + /\ (forall x y, external_implements "__i64_umulh" sig_ll_l (x::y::nil) (Val.mullhu x y)) + /\ (forall x y, external_implements "__i64_smulh" sig_ll_l (x::y::nil) (Val.mullhs x y)). Definition helper_declared {F V: Type} (p: AST.program (AST.fundef F) V) (id: ident) (name: string) (sg: signature) : Prop := (prog_defmap p)!id = Some (Gfun (External (EF_runtime name sg))). @@ -66,7 +68,9 @@ Definition helper_functions_declared {F V: Type} (p: AST.program (AST.fundef F) /\ helper_declared p i64_umod "__i64_umod" sig_ll_l /\ helper_declared p i64_shl "__i64_shl" sig_li_l /\ helper_declared p i64_shr "__i64_shr" sig_li_l - /\ helper_declared p i64_sar "__i64_sar" sig_li_l. + /\ helper_declared p i64_sar "__i64_sar" sig_li_l + /\ helper_declared p i64_umulh "__i64_umulh" sig_ll_l + /\ helper_declared p i64_smulh "__i64_smulh" sig_ll_l. (** * Correctness of the instruction selection functions for 64-bit operators *) @@ -823,6 +827,20 @@ Proof. - apply eval_mull_base; auto. Qed. +Theorem eval_mullhu: + forall n, unary_constructor_sound (fun a => mullhu a n) (fun v => Val.mullhu v (Vlong n)). +Proof. + unfold mullhu; intros; red; intros. econstructor; split; eauto. + eapply eval_helper_2; eauto. apply eval_longconst. DeclHelper; eauto. UseHelper. +Qed. + +Theorem eval_mullhs: + forall n, unary_constructor_sound (fun a => mullhs a n) (fun v => Val.mullhs v (Vlong n)). +Proof. + unfold mullhs; intros; red; intros. econstructor; split; eauto. + eapply eval_helper_2; eauto. apply eval_longconst. DeclHelper; eauto. UseHelper. +Qed. + Theorem eval_shrxlimm: forall le a n x z, Archi.ptr64 = false -> |