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authorGuillaume Melquiond <guillaume.melquiond@inria.fr>2019-02-13 18:53:17 +0100
committerXavier Leroy <xavierleroy@users.noreply.github.com>2019-03-27 11:38:25 +0100
commit0f919eb26c68d3882e612a1b3a9df45bee6d3624 (patch)
treeb8bcf57e06d761be09b8d2cf2f80741acb1e4949 /flocq/Core/Fcore_FIX.v
parentd5c0b4054c8490bda3b3d191724c58d5d4002e58 (diff)
downloadcompcert-0f919eb26c68d3882e612a1b3a9df45bee6d3624.tar.gz
compcert-0f919eb26c68d3882e612a1b3a9df45bee6d3624.zip
Upgrade embedded version of Flocq to 3.1.
Main changes to CompCert outside of Flocq are as follows: - Minimal supported version of Coq is now 8.7, due to Flocq requirements. - Most modifications are due to Z2R being dropped in favor of IZR and to the way Flocq now handles NaNs. - CompCert now correctly handles NaNs for the Risc-V architecture (hopefully).
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-(**
-This file is part of the Flocq formalization of floating-point
-arithmetic in Coq: http://flocq.gforge.inria.fr/
-
-Copyright (C) 2010-2013 Sylvie Boldo
-#<br />#
-Copyright (C) 2010-2013 Guillaume Melquiond
-
-This library is free software; you can redistribute it and/or
-modify it under the terms of the GNU Lesser General Public
-License as published by the Free Software Foundation; either
-version 3 of the License, or (at your option) any later version.
-
-This library is distributed in the hope that it will be useful,
-but WITHOUT ANY WARRANTY; without even the implied warranty of
-MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-COPYING file for more details.
-*)
-
-(** * Fixed-point format *)
-Require Import Fcore_Raux.
-Require Import Fcore_defs.
-Require Import Fcore_rnd.
-Require Import Fcore_generic_fmt.
-Require Import Fcore_ulp.
-Require Import Fcore_rnd_ne.
-
-Section RND_FIX.
-
-Variable beta : radix.
-
-Notation bpow := (bpow beta).
-
-Variable emin : Z.
-
-(* fixed-point format with exponent emin *)
-Definition FIX_format (x : R) :=
- exists f : float beta,
- x = F2R f /\ (Fexp f = emin)%Z.
-
-Definition FIX_exp (e : Z) := emin.
-
-(** Properties of the FIX format *)
-
-Global Instance FIX_exp_valid : Valid_exp FIX_exp.
-Proof.
-intros k.
-unfold FIX_exp.
-split ; intros H.
-now apply Zlt_le_weak.
-split.
-apply Zle_refl.
-now intros _ _.
-Qed.
-
-Theorem generic_format_FIX :
- forall x, FIX_format x -> generic_format beta FIX_exp x.
-Proof.
-intros x ((xm, xe), (Hx1, Hx2)).
-rewrite Hx1.
-now apply generic_format_canonic.
-Qed.
-
-Theorem FIX_format_generic :
- forall x, generic_format beta FIX_exp x -> FIX_format x.
-Proof.
-intros x H.
-rewrite H.
-eexists ; repeat split.
-Qed.
-
-Theorem FIX_format_satisfies_any :
- satisfies_any FIX_format.
-Proof.
-refine (satisfies_any_eq _ _ _ (generic_format_satisfies_any beta FIX_exp)).
-intros x.
-split.
-apply FIX_format_generic.
-apply generic_format_FIX.
-Qed.
-
-Global Instance FIX_exp_monotone : Monotone_exp FIX_exp.
-Proof.
-intros ex ey H.
-apply Zle_refl.
-Qed.
-
-Theorem ulp_FIX: forall x, ulp beta FIX_exp x = bpow emin.
-Proof.
-intros x; unfold ulp.
-case Req_bool_spec; intros Zx.
-case (negligible_exp_spec FIX_exp).
-intros T; specialize (T (emin-1)%Z); contradict T.
-unfold FIX_exp; omega.
-intros n _; reflexivity.
-reflexivity.
-Qed.
-
-
-End RND_FIX.