possible problem with long double

[Vivaldo <vlcampo at iccmp dot org>]

Dear Sir,

I have found a difficult do work with long double. I have written a 
simple test code and compiled it with gcc 4.0.0. The code was the following

#include <cmath>
#include <iostream>

using namespace std;

main(){

long double x,y,a;
x = 1.000000000000001;  //(1 at 15th decimal place)
y = 1.000000000000002; //(idem)
a = y - x;
cout.precision(30);
cout << a << endl;
}

Surprinsingly, the output written in the screen was not

1.0000....e-15

with 19 correct decimal places. Instead the result was

8.88178419700125232338905334473e-16

with error at the 16-th place!

How should I proceed to have the precision of 19 significative digits?

Thanks.

Vivaldo L. Campo.
Physicist - ICCMP - Brasilia - Brazil.