(** ** Conversion from a FP number to an integer *)

(** Always rounds toward zero. *)

Definition ZofB (f: binary_float): option Z :=
  match f with
    | B754_finite _ _ s m (Zpos e) _ => Some (cond_Zopp s (Zpos m) * Z.pow_pos radix2 e)%Z
    | B754_finite _ _ s m 0 _ => Some (cond_Zopp s (Zpos m))
    | B754_finite _ _ s m (Zneg e) _ => Some (cond_Zopp s (Zpos m / Z.pow_pos radix2 e))%Z
    | B754_zero _ _ _ => Some 0%Z
    | _ => None
  end.

Theorem ZofB_correct: forall f, ZofB f = if is_finite _ _ f then Some (Ztrunc (B2R _ _ f)) else None.