(* *********************************************************************)
(*                                                                     *)
(*              The Compcert verified compiler                         *)
(*                                                                     *)
(*          Xavier Leroy, INRIA Paris-Rocquencourt                     *)
(*                                                                     *)
(*  Copyright Institut National de Recherche en Informatique et en     *)
(*  Automatique.  All rights reserved.  This file is distributed       *)
(*  under the terms of the INRIA Non-Commercial License Agreement.     *)
(*                                                                     *)
(* *********************************************************************)
(** Correctness of instruction selection for integer division *)
Local Open Scope cminorsel_scope.
Local Open Scope string_scope.
(** * Axiomatization of the helper functions *)
Definition external_implements (name: string) (sg: signature) (vargs: list val) (vres: val) : Prop :=
forall F V (ge: Genv.t F V) m,
external_call (EF_runtime name sg) ge vargs m E0 vres m.
Definition builtin_implements (name: string) (sg: signature) (vargs: list val) (vres: val) : Prop :=
forall F V (ge: Genv.t F V) m,
external_call (EF_builtin name sg) ge vargs m E0 vres m.

Axiom i64_helpers_correct :
(forall x z, Val.longoffloat x = Some z -> external_implements "__compcert_i64_dtos" sig_f_l (x::nil) z)
/\ (forall x z, Val.longuoffloat x = Some z -> external_implements "__compcert_i64_dtou" sig_f_l (x::nil) z)
/\ (forall x z, Val.floatoflong x = Some z -> external_implements "__compcert_i64_stod" sig_l_f (x::nil) z)
/\ (forall x z, Val.floatoflongu x = Some z -> external_implements "__compcert_i64_utod" sig_l_f (x::nil) z)
/\ (forall x z, Val.singleoflong x = Some z -> external_implements "__compcert_i64_stof" sig_l_s (x::nil) z)
/\ (forall x z, Val.singleoflongu x = Some z -> external_implements "__compcert_i64_utof" sig_l_s (x::nil) z)
/\ (forall x, builtin_implements "__builtin_negl" sig_l_l (x::nil) (Val.negl x))
/\ (forall x y, builtin_implements "__builtin_addl" sig_ll_l (x::y::nil) (Val.addl x y))
/\ (forall x y, builtin_implements "__builtin_subl" sig_ll_l (x::y::nil) (Val.subl x y))
/\ (forall x y, builtin_implements "__builtin_mull" sig_ii_l (x::y::nil) (Val.mull' x y))
/\ (forall x y z, Val.divls x y = Some z -> external_implements "__compcert_i64_sdiv" sig_ll_l (x::y::nil) z)
/\ (forall x y z, Val.divlu x y = Some z -> external_implements "__compcert_i64_udiv" sig_ll_l (x::y::nil) z)
/\ (forall x y z, Val.modls x y = Some z -> external_implements "__compcert_i64_smod" sig_ll_l (x::y::nil) z)
/\ (forall x y z, Val.modlu x y = Some z -> external_implements "__compcert_i64_umod" sig_ll_l (x::y::nil) z)
/\ (forall x y, external_implements "__compcert_i64_shl" sig_li_l (x::y::nil) (Val.shll x y))
/\ (forall x y, external_implements "__compcert_i64_shr" sig_li_l (x::y::nil) (Val.shrlu x y))
/\ (forall x y, external_implements "__compcert_i64_sar" sig_li_l (x::y::nil) (Val.shrl x y))
/\ (forall x y, external_implements "__compcert_i64_umulh" sig_ll_l (x::y::nil) (Val.mullhu x y))
/\ (forall x y, external_implements "__compcert_i64_smulh" sig_ll_l (x::y::nil) (Val.mullhs x y)).