(** 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 *)
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.

(* Specifications: *)
Theorem generic_format_FIX :
forall x, FIX_format x -> generic_format beta FIX_exp x.
Theorem FIX_format_generic :
forall x, generic_format beta FIX_exp x -> FIX_format x.
Theorem FIX_format_satisfies_any :
satisfies_any FIX_format.
Theorem generic_format_FIX :
forall x, FIX_format x -> generic_format beta FIX_exp x.
Theorem FIX_format_generic :
forall x, generic_format beta FIX_exp x -> FIX_format x.
Theorem FIX_format_satisfies_any :
satisfies_any FIX_format.