From 76ea1108be6f8b4ba9dc0118a13f685bcb62bc2b Mon Sep 17 00:00:00 2001
From: xleroy <xleroy@fca1b0fc-160b-0410-b1d3-a4f43f01ea2e>
Date: Sat, 14 Sep 2013 16:24:30 +0000
Subject: Floats.v, Nan.v: hard-wire the general shape of binop_pl, so that no
 axioms are necessary, only two parameters (default_pl and choose_binop_pl).
 SelectDiv: optimize FP division by a power of 2. ConstpropOp: optimize 2.0 *
 x and x * 2.0 into x + x.

git-svn-id: https://yquem.inria.fr/compcert/svn/compcert/trunk@2326 fca1b0fc-160b-0410-b1d3-a4f43f01ea2e
---
 backend/Constprop.v      |  4 +++-
 backend/Constpropproof.v | 12 ++++++++----
 backend/SelectDiv.vp     | 18 +++++++++++++++++-
 backend/SelectDivproof.v | 18 ++++++++++++++++++
 4 files changed, 46 insertions(+), 6 deletions(-)

(limited to 'backend')

diff --git a/backend/Constprop.v b/backend/Constprop.v
index 24573a5..e5ea64d 100644
--- a/backend/Constprop.v
+++ b/backend/Constprop.v
@@ -322,7 +322,9 @@ Function annot_strength_reduction
       let (targs'', args'') := annot_strength_reduction app targs' args' in
       match ty, approx_reg app arg with
       | Tint, I n => (AA_int n :: targs'', args'')
-      | Tfloat, F n => (AA_float n :: targs'', args'')
+      | Tfloat, F n => if generate_float_constants tt
+                       then (AA_float n :: targs'', args'')
+                       else (AA_arg ty :: targs'', arg :: args'')
       | _, _ => (AA_arg ty :: targs'', arg :: args'')
       end
   | targ :: targs', _ =>
diff --git a/backend/Constpropproof.v b/backend/Constpropproof.v
index 328f724..898c4df 100644
--- a/backend/Constpropproof.v
+++ b/backend/Constpropproof.v
@@ -517,10 +517,14 @@ Proof.
       exists (ev1 :: eargs''); split.
       simpl; constructor; auto. simpl. congruence.
     }
-    destruct ty; destruct (approx_reg app arg) as [] eqn:E2; inv H; auto;
-    exists eargs''; split; auto; simpl; f_equal; auto;
-    generalize (MATCH arg); rewrite E2; simpl; intros E3;
-    rewrite E3 in H5; inv H5; auto.
+    destruct ty; destruct (approx_reg app arg) as [] eqn:E2; inv H; auto.
+    * exists eargs''; split; auto; simpl; f_equal; auto.
+      generalize (MATCH arg); rewrite E2; simpl; intros E3;
+      rewrite E3 in H5; inv H5; auto.
+    * destruct (generate_float_constants tt); inv H1; auto. 
+      exists eargs''; split; auto; simpl; f_equal; auto.
+      generalize (MATCH arg); rewrite E2; simpl; intros E3;
+      rewrite E3 in H5; inv H5; auto.
   + destruct (annot_strength_reduction app targs args) as [targs'' args''] eqn:E.
     inv H.
     exploit IHtargs; eauto. intros [eargs'' [A B]].
diff --git a/backend/SelectDiv.vp b/backend/SelectDiv.vp
index e60a97d..1d9168c 100644
--- a/backend/SelectDiv.vp
+++ b/backend/SelectDiv.vp
@@ -10,7 +10,7 @@
 (*                                                                     *)
 (* *********************************************************************)
 
-(** Instruction selection for integer division and modulus *)
+(** Instruction selection for division and modulus *)
 
 Require Import Coqlib.
 Require Import AST.
@@ -154,3 +154,19 @@ Nondetfunction mods (e1: expr) (e2: expr) :=
   | _ => mods_base e1 e2
   end.
 
+(** Floating-point division by a constant can also be turned into a FP
+    multiplication by the inverse constant, but only for powers of 2. *)
+
+Definition divfimm (e: expr) (n: float) :=
+  match Float.exact_inverse n with
+  | Some n' => Eop Omulf (e ::: Eop (Ofloatconst n') Enil ::: Enil)
+  | None    => Eop Odivf (e ::: Eop (Ofloatconst n) Enil ::: Enil)
+  end.
+
+Nondetfunction divf (e1: expr) (e2: expr) :=
+  match e2 with
+  | Eop (Ofloatconst n2) Enil => divfimm e1 n2
+  | _ => Eop Odivf (e1 ::: e2 ::: Enil)
+  end.
+
+
diff --git a/backend/SelectDivproof.v b/backend/SelectDivproof.v
index 4d8f96a..0719a5e 100644
--- a/backend/SelectDivproof.v
+++ b/backend/SelectDivproof.v
@@ -544,4 +544,22 @@ Proof.
 - eapply eval_mods_base; eauto. 
 Qed.
 
+(** * Floating-point division *)
+
+Theorem eval_divf:
+  forall le a b x y,
+  eval_expr ge sp e m le a x ->
+  eval_expr ge sp e m le b y ->
+  exists v, eval_expr ge sp e m le (divf a b) v /\ Val.lessdef (Val.divf x y) v.
+Proof.
+  intros until y. unfold divf. destruct (divf_match b); intros.
+- unfold divfimm. destruct (Float.exact_inverse n2) as [n2' | ] eqn:EINV.
+  + inv H0. inv H4. simpl in H6. inv H6. econstructor; split.
+    EvalOp. constructor. eauto. constructor. EvalOp. simpl; eauto. constructor. 
+    simpl; eauto. 
+    destruct x; simpl; auto. erewrite Float.div_mul_inverse; eauto. 
+  + TrivialExists. 
+- TrivialExists.
+Qed.
+
 End CMCONSTRS.
-- 
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