(*************************************
 ** RATIONAL.sml
 ** sml
 **
 ** Aleksandar Nanevski
 **
 ** Signature for rational numbers
 *************************************)


signature RATIONAL =
sig
    type rat
    type t = rat

    (* arithmetic *)

    val zero : rat
    val one : rat
	
    val + : rat * rat -> rat
    val - : rat * rat -> rat
    val * : rat * rat -> rat
    val / : rat * rat -> rat
    val ~ : rat -> rat
    val inv : rat -> rat


    (* total ordering *)

    val == : rat * rat -> bool
    val < : rat * rat -> bool
    val > : rat * rat -> bool
    val >= : rat * rat -> bool
    val <= : rat * rat -> bool
    val != : rat * rat -> bool
    val sign : rat -> int
    val min : rat * rat -> rat
    val max : rat * rat -> rat
    val compare : rat * rat -> order
	
    val abs : rat -> rat

    (* we may want to add sup and inf here    *)
    (* to match signatures for partial orders *)
    (* but then do we want to add scale to    *)
    (* match signatures for vector spaces?    *)

	

    (* coercions *)

    val fromInt : int -> rat	
    val fromIntInf : IntInf.int -> rat
    val fromIntFrac : {num: int, denom: int} -> rat	
    val fromFrac : {num: IntInf.int, denom: IntInf.int} -> rat
    val fromManExp : {man:IntInf.int, exp:Int.int} -> rat
    val toFrac : rat -> {num : IntInf.int, denom : IntInf.int}
    val toString : rat -> string

    (* raise Domain on NaN                 *)
    (* raise Overflow on posInf and negInf *)
    val fromReal : real -> rat


    (* signature-specific functions *)

    val approx : IEEEReal.rounding_mode -> rat -> real
    val intervalApprox : rat -> {lo: real, hi:real}
end