Draw a ellipse

[Gunnar <gunix@comhem.se>]

Hello.
I'm trying to draw the following figure with epix:  
|x|^n + |y|^n = 1   for n=2,3,4,5...

Here is the c++ code.

#include "epix.h"
#include <cmath>
using namespace ePiX;

// the function to be plotted
double f(double x){return exp(log(1.0-abs(x*x))/2.0);}
double g(double x){return -exp(log(1.0-abs(x*x))/2.0);}

double h1(double x){return sqrt(1-x*x);}
double h2(double x){return -sqrt(1-x*x);}
main(){
	bounding_box(P(-1,-1),P(1,1));
	unitlength("1in"); 	picture(P(1,1));
	begin();
	plot(f, x_min,x_max,80);
        plot(g, x_min,x_max,80);
	plot(h1, x_min,x_max,40);
	plot(h2, x_min,x_max,40);
	end();
}


What I would like to do is to plot f and g, and they should be the same as h1 
and h2, but they are not!! Why? It's the same bad result with n=3,4,5...

It's more like a square for n=2 (which should be a circle!)
Is the problem related to accuracy, rounding, resolution? 

It works fine with a parametric solution and trig. functions. But what's the 
matter with the exp and log version?
I have to use exp and log if I would like to use n=2.5 (something between 2 
and 3).

Gunnar.