Question

sorry if dumb but could not find an answer.

#include <iostream>

using namespace std;

int main()
{
double a(0);
double b(0.001);
cout << a - 0.0 << endl;
for (;a<1.0;a+=b);
cout << a - 1.0 << endl;
for (;a<10.0;a+=b);
cout << a - 10.0 << endl;
cout << a - 10.0-b << endl;
return 0;
}

Output:
0
6.66134e-16
0.001
-1.03583e-13

Tried compiling it with MSVC9, MSVC10, Borland C++ 2010. All of them arrive in the end to the error of about 1e-13.
Is it normal to have such a significant error accumulation over only a 1000, 10000 increments?

Answer 1

Yes, this is normal numeric representation floating point error. It has to do with the fact that the hardware must approximate most floating point numbers, rather than storing them exactly. Thus, the compiler you use should not matter.

What Every Computer Scientist Should Know About Floating-Point Arithmetic