Safe Floating-Point Comparisons
How do I handle floating-point comparisons when the numbers might not be exactly equal?
When working with floating-point numbers, direct comparisons using == can be problematic because of how computers represent decimal numbers. Let's look at why this happens and how to handle it properly.
The Problem
Here's an example that demonstrates why floating-point comparisons can be tricky:
#include <iostream>
using namespace std;
int main() {
float x{0.1f + 0.2f};
float y{0.3f};
// This might print "false" even though
// mathematically they're equal!
cout << "Direct comparison (x == y): "
<< (x == y) << "\n";
cout << "Value of x: " << x << "\n";
cout << "Value of y: " << y;
}Direct comparison (x == y): false
Value of x: 0.3
Value of y: 0.3Even though both numbers print as 0.3, they might not be exactly equal internally due to how floating-point numbers are stored in memory.
The Solution: Compare with Tolerance
Instead of checking for exact equality, we should check if the numbers are "close enough" by defining an acceptable difference (often called epsilon or tolerance):
#include <iostream>
using namespace std;
int main() {
float Health{100.0f};
float MaxHealth{100.0f};
float Damage{33.33f};
// Apply damage
Health = Health - Damage;
// This is safer than using ==
float Tolerance{0.0001f};
bool areEqual{
(Health - MaxHealth) < Tolerance &&
(MaxHealth - Health) < Tolerance
};
cout << "Health: " << Health << "\n";
cout << "Are equal?: " << areEqual << "\n";
// For less/greater comparisons
// we can still use < and >
bool isHealthy{Health > 50.0f};
cout << "Is healthy?: " << isHealthy;
}Health: 66.67
Are equal?: false
Is healthy?: trueNote that < and > comparisons are generally safe with floating-point numbers. It's primarily the equality comparison that needs special handling.
The actual value you use for Tolerance depends on your specific needs - smaller values mean more precise comparisons but are more likely to fail due to floating-point imprecision.
Booleans - true and false values
An overview of the fundamental true or false data type, how we can create them, and how we can combine them.