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author | Guillaume Melquiond <guillaume.melquiond@inria.fr> | 2019-02-13 18:53:17 +0100 |
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committer | Xavier Leroy <xavierleroy@users.noreply.github.com> | 2019-03-27 11:38:25 +0100 |
commit | 0f919eb26c68d3882e612a1b3a9df45bee6d3624 (patch) | |
tree | b8bcf57e06d761be09b8d2cf2f80741acb1e4949 /flocq/Core/FIX.v | |
parent | d5c0b4054c8490bda3b3d191724c58d5d4002e58 (diff) | |
download | compcert-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).
Diffstat (limited to 'flocq/Core/FIX.v')
-rw-r--r-- | flocq/Core/FIX.v | 94 |
1 files changed, 94 insertions, 0 deletions
diff --git a/flocq/Core/FIX.v b/flocq/Core/FIX.v new file mode 100644 index 00000000..4e0a25e6 --- /dev/null +++ b/flocq/Core/FIX.v @@ -0,0 +1,94 @@ +(** +This file is part of the Flocq formalization of floating-point +arithmetic in Coq: http://flocq.gforge.inria.fr/ + +Copyright (C) 2009-2018 Sylvie Boldo +#<br /># +Copyright (C) 2009-2018 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 Raux Defs Round_pred Generic_fmt Ulp Round_NE. + +Section RND_FIX. + +Variable beta : radix. + +Notation bpow := (bpow beta). + +Variable emin : Z. + +Inductive FIX_format (x : R) : Prop := + FIX_spec (f : float beta) : + x = F2R f -> (Fexp f = emin)%Z -> FIX_format x. + +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 Z.le_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_canonical. +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 Z.le_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. |