DEFINITION MODULE Newton;

   (* EXPORT QUALIFIED RtNewt, RtSafe; *)

   TYPE
      DerivFunction   = PROCEDURE(REAL, VAR REAL, VAR REAL);

   PROCEDURE RtNewt(funcd: DerivFunction; x1, x2, xacc: REAL): REAL; 
   (*
     Using the Newton-Raphson method, find the root of a function
     known to lie in the interval (x1, x2). The root RtNewt will be 
     refined until its accuracy is known within (+-)xacc. funcd is a
     user-supplied routine that provides both the function value and
     the first derivative of the function at the point x.
   *)

   PROCEDURE RtSafe(funcd: DerivFunction; x1, x2, xacc: REAL): REAL; 
   (*
     Using a combination of Newton-Raphson and bisection, find the root 
     of a function bracketed between x1 and x2. The root, returned
     as the function value RtSafe, will be refined until its accuracy 
     is known within (+-)xacc. funcd is a user-supplied routine that 
     provides both the function value and the first derivative of the 
     function.
   *)

END Newton.