(**************************************
 ** NUMBER_THEORY.sml
 ** sml
 **
 ** Aleksandar Nanevski
 **
 ** Various useful functions over
 ** infinite integers
 **************************************)

signature NUMBER_THEORY =
sig
    type int

    val zero : int
    val one : int

    (* should not depend on the current rounding mode *)
    val intervalApprox : int -> {lo : real, hi : real}

    (* returns positive value no matter the *)
    (* signs of the operands *)
    val gcd : int * int -> int
   
    (* return {odd=0,exp=0} on 0 *)
    val toOddExp : int -> {odd : int, exp : Int.int}

    (* raise Overflow on posInf and negInf *)
    (* raise Domain on NaN *)
    (* returns {odd=0, exp=0} on 0.0 *)
    val fromReal : real -> {odd : int, exp : Int.int} 
    val approx : IEEEReal.rounding_mode -> int -> real
end