(****************************************************************************  IEEE754  :  Fcomp  Laurent Thery  ******************************************************************************)
Require Export Float.
Section comparisons.
Variable radix : Z.
Hypothesis radixMoreThanOne : (1 < radix)%Z.
Let radixMoreThanZERO := Zlt_1_O _ (Zlt_le_weak _ _ radixMoreThanOne).
Hint Resolve radixMoreThanZERO: zarith.
Definition Fdiff (x y : float) :=
(Fnum x * Zpower_nat radix (Zabs_nat (Fexp x - Zmin (Fexp x) (Fexp y))) -
Fnum y * Zpower_nat radix (Zabs_nat (Fexp y - Zmin (Fexp x) (Fexp y))))%Z.
Let FtoRradix := FtoR radix.
Local Coercion FtoRradix : float >-> R.

Theorem Fdiff_correct :
forall x y : float,
(Fdiff x y * powerRZ radix (Zmin (Fexp x) (Fexp y)))%R = (x - y)%R.