// ----------------------------
//  nzefplay.cpp
// ----------------------------
#include "w.h"

  double g(double x) { return (cos(x) - x); } // test fun

  // Newton-Raphson with a step counter
  double nzef(fptype1 f,
				 double x,
				 int &count,
				 double h = 0.01,
				 double ytol = 1e-6)

	 { double y = f(x), x1(1);
		count = 0;

		do { x1 = x - y*h/(f(x+h) - y);
			  x = x1; y = f(x); count++; }
		while (fabs(y) > ytol);

		return x; }

 // --------------------------------------------------
	 void main()
	  {
       nl(0);
		 banner("nzefplay.cpp");
		 pl("g(x) = cos(x) - x");
		 nl();
		 precision(14);
		 int count;

		 double z = nzef(g, 0.5,count,0.001,1e-10);

		 pl("The zero of g is  z = ",z);
		 pl("Check:         g(z) = ",g(z));
		 pl("Number of steps     = ",count);
		}
  /* output
   ---------
    Zefplay
   ---------
   f(x) = cos(x) - x

   The zero of g is  z = 0.73908513321823
   Check:         g(z) = -5.1350483652561e-12
   Number of steps     = 4


  */