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

3 files changed, 60 insertions, 26 deletions

diff --git a/arm/ConstpropOp.vp b/arm/ConstpropOp.vp
index caf0da6..47d2086 100644
--- a/arm/ConstpropOp.vp
+++ b/arm/ConstpropOp.vp
@@ -287,6 +287,11 @@ Definition make_xorimm (n: int) (r: reg) :=
   else if Int.eq n Int.mone then (Onot, r :: nil)
   else (Oxorimm n, r :: nil).
 
+Definition make_mulfimm (n: float) (r r1 r2: reg) :=
+  if Float.eq_dec n (Float.floatofint (Int.repr 2))
+  then (Oaddf, r :: r :: nil)
+  else (Omulf, r1 :: r2 :: nil).
+
 Nondetfunction op_strength_reduction 
               (op: operation) (args: list reg) (vl: list approx) :=
   match op, args, vl with
@@ -317,6 +322,8 @@ Nondetfunction op_strength_reduction
   | Oshru, r1 :: r2 :: nil, v1 :: I n2 :: nil => make_shruimm n2 r1 r2
   | Ocmp c, args, vl =>
       let (c', args') := cond_strength_reduction c args vl in (Ocmp c', args')
+  | Omulf, r1 :: r2 :: nil, v1 :: F n2 :: nil => make_mulfimm n2 r1 r1 r2
+  | Omulf, r1 :: r2 :: nil, F n1 :: v2 :: nil => make_mulfimm n1 r2 r1 r2
   | _, _, _ => (op, args)
   end.
 
diff --git a/arm/ConstpropOpproof.v b/arm/ConstpropOpproof.v
index 687e08f..f0d6b7f 100644
--- a/arm/ConstpropOpproof.v
+++ b/arm/ConstpropOpproof.v
@@ -372,6 +372,33 @@ Proof.
   econstructor; split; eauto. auto. 
 Qed.
 
+Lemma make_mulfimm_correct:
+  forall n r1 r2,
+  rs#r2 = Vfloat n ->
+  let (op, args) := make_mulfimm n r1 r1 r2 in
+  exists v, eval_operation ge sp op rs##args m = Some v /\ Val.lessdef (Val.mulf rs#r1 rs#r2) v.
+Proof.
+  intros; unfold make_mulfimm. 
+  destruct (Float.eq_dec n (Float.floatofint (Int.repr 2))); intros. 
+  simpl. econstructor; split. eauto. rewrite H; subst n.
+  destruct (rs#r1); simpl; auto. rewrite Float.mul2_add; auto. 
+  simpl. econstructor; split; eauto. 
+Qed.
+
+Lemma make_mulfimm_correct_2:
+  forall n r1 r2,
+  rs#r1 = Vfloat n ->
+  let (op, args) := make_mulfimm n r2 r1 r2 in
+  exists v, eval_operation ge sp op rs##args m = Some v /\ Val.lessdef (Val.mulf rs#r1 rs#r2) v.
+Proof.
+  intros; unfold make_mulfimm. 
+  destruct (Float.eq_dec n (Float.floatofint (Int.repr 2))); intros. 
+  simpl. econstructor; split. eauto. rewrite H; subst n.
+  destruct (rs#r2); simpl; auto. rewrite Float.mul2_add; auto. 
+  rewrite Float.mul_commut; auto. 
+  simpl. econstructor; split; eauto. 
+Qed.
+
 Lemma op_strength_reduction_correct:
   forall op args vl v,
   vl = approx_regs app args ->
@@ -431,6 +458,11 @@ Proof.
   generalize (cond_strength_reduction_correct c args0 vl0). 
   destruct (cond_strength_reduction c args0 vl0) as [c' args']; intros.
   rewrite <- H1 in H0; auto. econstructor; split; eauto.
+(* mulf *)
+  inv H0. assert (rs#r2 = Vfloat n2). InvApproxRegs; SimplVMA; auto.
+  apply make_mulfimm_correct; auto.
+  inv H0. assert (rs#r1 = Vfloat n1). InvApproxRegs; SimplVMA; auto.
+  apply make_mulfimm_correct_2; auto.
 (* default *)
   exists v; auto.
 Qed.
diff --git a/arm/Nan.v b/arm/Nan.v
index d66d6ec..e2bddf6 100644
--- a/arm/Nan.v
+++ b/arm/Nan.v
@@ -1,34 +1,29 @@
+(* *********************************************************************)
+(*                                                                     *)
+(*              The Compcert verified compiler                         *)
+(*                                                                     *)
+(*          Xavier Leroy, INRIA Paris-Rocquencourt                     *)
+(*          Jacques-Henri Jourdan, 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 GNU General Public License as published by  *)
+(*  the Free Software Foundation, either version 2 of the License, or  *)
+(*  (at your option) any later version.  This file is also distributed *)
+(*  under the terms of the INRIA Non-Commercial License Agreement.     *)
+(*                                                                     *)
+(* *********************************************************************)
+
 Require Import Fappli_IEEE.
 Require Import Fappli_IEEE_bits.
 Require Import Floats.
 Require Import ZArith.
 Require Import Integers.
 
-(* Needed to break a circular reference after extraction *)
-Definition transform_quiet_pl :=
-  Eval unfold Float.transform_quiet_pl in Float.transform_quiet_pl.
-
 Program Definition default_pl : bool * nan_pl 53 := (false, nat_iter 51 xO xH).
 
-Definition binop_pl (pl1 pl2:binary64) : bool*nan_pl 53 :=
-  match pl1, pl2 with
-    | B754_nan s1 pl1, B754_nan s2 pl2 =>
-      if (Pos.testbit (proj1_sig pl1) 51 && (* pl2 is sNan but pl1 is qNan *)
-         negb (Pos.testbit (proj1_sig pl2) 51))%bool
-      then (s2, transform_quiet_pl pl2)
-      else (s1, transform_quiet_pl pl1)
-    | B754_nan s1 pl1, _ => (s1, transform_quiet_pl pl1)
-    | _, B754_nan s2 pl2 => (s2, transform_quiet_pl pl2)
-    | _, _ => default_pl
-  end.
-
-Theorem binop_propagate1: Float.binop_propagate1_prop binop_pl.
-Proof.
-  repeat intro. destruct f1, f2; try discriminate; simpl;
-  destruct Pos.testbit; reflexivity.
-Qed.
-
-Theorem binop_propagate2: Float.binop_propagate2_prop binop_pl.
-Proof.
-  repeat intro. destruct f1, f2, f3; try discriminate; simpl; reflexivity.
-Qed.
+Definition choose_binop_pl (s1: bool) (pl1: nan_pl 53) (s2: bool) (pl2: nan_pl 53) :=
+  (** Choose second NaN if pl2 is sNaN but pl1 is qNan.
+      In all other cases, choose first NaN *)
+  (Pos.testbit (proj1_sig pl1) 51 &&
+   negb (Pos.testbit (proj1_sig pl2) 51))%bool.