Why does it seem like my floating point value is not equal to itself?

Question

#include<iostream.h>
using namespace std;
int main()
{
      float x=1.1;
      if(x==1.1)
         cout<<"yes";
      else
         cout<<"no";
      return 0;
}

I assign value 1.1 to x and checked value of x is 1.1 or not?

Answer 1

You've wandered into an interesting area of almost all programming languages. Floating point values are tricky things, and testing them for equality is very rarely recommended. The basic problem is that floating point values on modern computers are represented as binary decimals with a finite number of digits of precision.

To make this simpler to understand, lets work with base 10 decimals and use a number that can't be accurately represented using them. Take 1/3. If you are representing it as a base 10 decimal you get this:

0.̅3 (there is a bar over the three if it isn't showing up properly). Basically, it goes on forever, there is no finite number of digits that can represent 1/3 as a base ten decimal with perfect accuracy. So, if you only have so many digits, you chop it off and approximate:

0.333333

That's actually 333333/1000000, which is really close to 1/3, but not quite.

C++ has a few different floating point types. And these types usually (it depends on the platform the program is being compiled for) have different numbers of significant digits. By default, a floating point constant is of type double which usually has more digits than a float (and it never has less). Again, using base 10 as an example, since you were storing your value in a float you were doing something like this:

0.333333 == 0.3333333333333333333

which of course is false.

If you wrote your code this way:

#include <iostream>
using namespace std;
int main()
{
      float x = 1.1f;
      if(x == 1.1f)
         cout<<"yes";
      else
         cout<<"no";
      return 0;
}

you would likely get the expected result. Putting an f at the end of a bare floating point value (aka, a floating point literal) tells C++ that it's of type float.

This is all very fascinating of course, and there's a lot to get into. If you would like to learn a lot more about how floating point numbers are really represented, there is a nice Wikipedia page on IEEE 754 floating point representation, which is how most modern processors represent floating point numbers nowadays.

From a practical standpoint, you should rarely (if ever) compare floating point numbers for equality. Usually, a desire to do so indicates some sort of design flaw in your program. And if you really must than use an 'epsilon' comparison. Basically, test to see if your number is 'close enough', though determining what that means in any given situation isn't necessarily a trivial task, which is why it usually represents a design flaw if you need to compare them for equality at all. But, in your case, it could look like this:

#include <iostream>
#include <cmath>
using namespace std;
int main()
{
      float x=1.1;
      if (fabs(x - 1.1) < 0.000001)
         cout<<"yes";
      else
         cout<<"no";
      return 0;
}

Answer 2

The reason the compare fails is that you're comparing a double value to a float variable.

Some compilers will issue a warning when you assign a double value to a float variable.

To get the desired output, you could try this:

double x = 1.1;
if (x == 1.1)

or this:

float x = 1.1f;
if (x == 1.1f)