From 76ea1108be6f8b4ba9dc0118a13f685bcb62bc2b Mon Sep 17 00:00:00 2001 From: xleroy 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 --- arm/ConstpropOp.vp | 7 +++++++ arm/ConstpropOpproof.v | 32 ++++++++++++++++++++++++++++++++ arm/Nan.v | 47 +++++++++++++++++++++-------------------------- 3 files changed, 60 insertions(+), 26 deletions(-) (limited to 'arm') 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. -- cgit v1.2.3