(*****************************************************************
 ** XFLOAT.sml
 ** sml
 **
 ** Aleksandar Nanevski
 **
 ** An extension of floating point numbers. Operations are
 ** performed exactly except if overflow or underflow 
 ** occured.
 **
 ** WARNING: 
 ** - The implementation assumes rounding-to-even. 
 ** - Pentium's 80bit arithmetic has to be turned off.
 ** - If overflow or underflow happen, the results
 **   can be completely meaningless.
 **
 ** TODO: 
 ** - need to install handlers for overflow and underflow.
 **   SML doesn't let us do that yet.
 ** - rename the structure since Extended is used for 80 bit
 **   arithmetic in IEEE.
 ****************************************************************)  

signature XFLOAT =
sig
    type xfloat 
    type t = xfloat

    val zero : xfloat
    val one : xfloat

    (* arithmetic *)

    val + : xfloat * xfloat -> xfloat
    val * : xfloat * xfloat -> xfloat
    val - : xfloat * xfloat -> xfloat
    val ~ : xfloat -> xfloat
    val scale : real * xfloat -> xfloat
    val double : xfloat -> xfloat

    (* ordering *)

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

    val abs : xfloat -> xfloat 


    (* coercions *)

    val fromReal : real -> xfloat
    val toRational : xfloat -> NormalizedRational.rat
    val toString : xfloat -> string
    val toList : xfloat -> real list


    (* signature-specific functions *)

    val approx: xfloat -> real
    val add : xfloat * real -> xfloat
    val sub : xfloat * real -> xfloat
    val isub : real * xfloat -> xfloat
    val compress : xfloat -> xfloat
    val distill : real list -> xfloat

end