Setprecision is Confusing

Question

I just want to ask about setprecision because I'm a bit confused.

here's the code:

#include <iostream>
#include <iomanip>
using namespace std;

int main()

{
  double rate = x;
  cout << fixed << setprecision(2) << rate;
}

where x = to following:

the left side of equation are the values of x.

1.105 = 1.10 should be 1.11

1.115 = 1.11 should be 1.12

1.125 = 1.12 should be 1.13

1.135 = 1.14 which is correct

1.145 = 1.15 also correct

but if x is:

2.115 = 2.12 which is correct

2.125 = 2.12 should be 2.13

so why in a certain value it's correct but sometimes it's wrong?

please enlighten me. thanks

Answer 1

There is no reason to expect that any of the constants in your post can be represented exactly using the floating-point system. As a consequence, the exact halves that you have may no longer be exact halves once you store them in a double variable (regardless of how the iostreams are meant to round such numbers.)

The following code illustrates my point:

#include <iostream>
#include <iomanip>

using namespace std;

int main()

{
  double rate = 1.115;
  cout << fixed << setprecision(20) << rate;
}

Output:

1.11499999999999999112

I would recommend taking a look at the FAQ.

Answer 2

Some of the numbers you're printing may not be representable as a floating point number and may actually be lower or higher than you think, directly affecting the rounding.

Since you're trying to format a floating point number to fixed point, have you considered actually USING a fixed point number (int/long scaled by say 1000 depending on your needs) that has its own insert operator defined? Then you'll always get accurate display and rounding without needing to rely on setprecision having any particular behavior (I couldn't find the relevant conversion section in the standard in a quick look).