(** 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. *)
(** Basic operations on floats: alignment, addition, multiplication *)
Section Float_ops.
Variable beta : radix.
Notation bpow e := (bpow beta e).
Arguments Float {beta} Fnum Fexp.
Definition Falign (f1 f2 : float beta) :=
let '(Float m1 e1) := f1 in
let '(Float m2 e2) := f2 in
if Zle_bool e1 e2
then (m1, (m2 * Zpower beta (e2 - e1))%Z, e1)
else ((m1 * Zpower beta (e1 - e2))%Z, m2, e2).

(* Specifications: *)
Theorem Falign_spec :
forall f1 f2 : float beta,
let '(m1, m2, e) := Falign f1 f2 in
F2R f1 = @F2R beta (Float m1 e) /\ F2R f2 = @F2R beta (Float m2 e).
Theorem Falign_spec_exp:
forall f1 f2 : float beta,
snd (Falign f1 f2) = Zmin (Fexp f1) (Fexp f2).