Q:

float numerical error. How does c++ know 0.99999982 is 1?

I normalized a vector and length of it should be 1. But the result of length method is 0.99999982
I don't know it's right or wrong. But if I print it out, the result is 1. Not 0.99999982( printed by cout )
But how std::cout knows it's 1? [This is my first question]
And another question is why the result of comparing function is false.
I have a comparing method like below. And lhs is the length of a vector and the rhs is just 1.

  return (fabsf(rhs-lhs) <= FLT_EPSILON) ? true : false;

Result of this method is false. 
Is length of the normalized vector is already wrong to be considered normalized? or epsilon is too small?
What did I wrong? 

A:

The epsilon is too small. That's because epsilon is the smallest as it can be. (by definition)
So you will need a larger tolerance.

A:

The IEEE standard requires that the result of addition, subtraction, multiplication and division be exactly rounded. The result must then be rounded to the nearest floating-point number. Floating point error is accumulated in the many operators it takes to normalize a vector.
Like the other poster said FLT_EPSILON is too small.

