Equality between two float values

When checking if two values are the same, mathematically speacking we go with a simple equality condition: if a = b: .... This can be a valid solution in general math, where $2.01$ needs to be equal to some expression like $1 + 1 + 0.01$.

When writing code, things become a little more complex.

Don’t want to go deep into float arithmetic in programming - this is just a personal note, but to keep this simple, sometimes when writing floating point numbers in code, you don’t really get the number you thought to get. For example, doing something like float x = 2.01; can be evaluated as x = 2.01000001 or x = 2.00999999. This may not look like a big deal, but when processing those numbers over and over again, we can accumulate this error and have a resulting calculation that is completely off compared to the pure mathematical result.

To approach this problem when checking if two floating numbers are the same, instead of using the == operator, can be wise to calculate the error resulting from the absolute difference between the two numbers.

float error = abs(a - b);
if (error <= 0.000001)
{
    # magic...
}

This way we use a more rigorous mathematical approach into veryfying if two real numbers are “so close to each other that their difference is smaller than any small number” (in this case any small number is represented by an error threshold value like $0.000001$).