(****************************************************************************  IEEE754  :  Float  Laurent Thery  ***************************************************************************** ****************************************************** Module Float.v Inspired by the Diadic of Patrick Loiseleur *******************************************************)
Require Export Omega.
Require Export Compare.
Require Export Rpow.
Section definitions.
Variable radix : Z.
Hypothesis radixMoreThanOne : (1 < radix)%Z.
Let radixMoreThanZERO := Zlt_1_O _ (Zlt_le_weak _ _ radixMoreThanOne).
Hint Resolve radixMoreThanZERO: zarith.
(* The type float represents the set of numbers who can be written: x = n*b^p with  n and p in Z. (pdic numbers) n = Fnum and p = Fexp 						*)
Record float : Set := Float {Fnum : Z; Fexp : Z}.

Theorem floatEq :
forall p q : float, Fnum p = Fnum q -> Fexp p = Fexp q -> p = q.