C++ rounding behavior

Question

#include <iostream>
#include <iomanip>

int main()
{
    float f = 0.115;

    std::cout << f << std::endl;
    std::cout << std::fixed << std::setprecision(2) << f << std::endl;

    return 0;
}

The output of the above code is:

0.115
0.12

It makes sense that 0.115 is rounded to 0.12. However, when we change f to 0.225 the output is:

0.225
0.22

Why isn't this rounded to 0.23?

Try and see what happens when you use `std::setprecision(20)` instead. — Frxstrem, Jun 07 '15 at 18:44
[See](http://en.wikipedia.org/wiki/Rounding#Round_half_to_even). — n. m. could be an AI, Jun 07 '15 at 18:47
@n.m. Not relevant here; `0.245`, for instance, will round *up* to `0.25`. — Frxstrem, Jun 07 '15 at 18:50
possible duplicate of [How to specify setprecision rounding](http://stackoverflow.com/questions/20264681/how-to-specify-setprecision-rounding) — Christophe, Jun 07 '15 at 19:03
@Frxstrem setprecision(20) shows 0.22499999403953552246. If I change from float to double: 0.22500000000000000555. I guess that explains it. Maybe I should be using doubles instead. — user974967, Jun 07 '15 at 19:04
@user974967 Using `double` instead of `float` will not solve the problem itself, you'll just get the same effect for different numbers. — Frxstrem, Jun 07 '15 at 19:06

score 3 · Accepted Answer · answered Jun 07 '15 at 19:04

Your computer can't represent most decimal fractions numbers exactly, since it works with binary numbers. Instead, it tries to find the closest number it can represent, and use that instead.

For instance, my computer represents the following numbers as:

decimal      actual representation
0.115        0.115000002
0.225        0.224999994
0.245        0.245000005
0.335        0.335000008
0.445        0.444999993

By default, C++ will use normal rounding to closest, i.e., digits 5-9 are rounded up and 0-4 are rounded down. Therefore, of the numbers above, 0.115, 0.245 and 0.335 will be rounded up to 0.12, 0.24 and 0.34, while 0.225 and 0.445 will be rounded down to 0.22 and 0.44.

C++ rounding behavior

1 Answers1