How to Compare Float and Double While Accounting for Precision Loss?

Directly comparing floats and doubles in C++ using == and != is not an easy task. Due to precision loss, the small rounding errors might make direct comparisons unreliable, thus gaining odd and unexpected results. The ways to overcome this are epsilon comparisons, relative tolerance methods, and so on. In this article, we’ll explore the precision loss, problems with direct comparison, methods to compare, and best practices for comparing float and double in C++ while accounting for precision loss.

Table of Contents:

What is Precision Loss in C++

C++ floating-point numbers follow the IEEE 754 standard, where values are stored as combinations of a sign, exponent, and mantissa. Due to the limited number of bits in the mantissa, some decimal points (like 0.1) cannot be represented exactly, therefore leading to small rounding errors. These accumulated errors over arithmetic operations will make direct comparisons (==) fail.

Problems With Direct Comparison in C++

Floating-point number comparisons using == or != may give you unexpected results due to incomparable precision losses. Due to these inaccuracies of the finite nature of floating-point arithmetic, where, in some cases, two values that are mathematically equal differ at most by a small margin, direct comparisons may fail. 

Methods to Compare float and double in C++

Due to floating-point precision loss, direct comparison (==) is unreliable. Below are the methods that you can use to compare float and double in C++:

1. Epsilon-Based Comparison (Absolute Tolerance)

You already know that the floating point numbers have small rounding errors, therefore, a direct comparison a==b is unreliable. Instead, the absolute difference is used with a small tolerance.

Example:

Output:

The above code checks if the sum of 0.1f and 0.2f is approximately equal to 0.3f using an epsilon-based comparison to compare floats and doubles.

2. Relative Tolerance Comparison

Absolute tolerance is supposed to work quite well in the region of smaller numbers, yet this is not for very large or very small values, as they can have scaling issues. Relative tolerance scales the comparison threshold relative to the size of the numbers, making it more reliable across different ranges.

Example:

Output:

The code shows how a template function is defined to compare two values using relative tolerance based on their magnitude for both float and double values.

3. Using std::numeric_limits<T>::epsilon()

Machine epsilon std::numeric_limits::epsilon() is defined as the smallest possible difference between two distinct floating point numbers. It thus provides a safe way for comparing floating point values in C++ based on precision.

Example:

Output:

The above code shows how the two double values are compared using std::numeric_limits::epsilon() based on their magnitudes.

4. Using std::isnan() and std::isinf()

Some floating-point operations can lead to NaN (Not-a-Number) or Infinity and produce comparison behavior that can be unexpected. std::isnan() and std::isinf() help point out these exceptions before comparison and give better results.

Example:

Output:

The code shows how a given double value is checked, that it is a NaN (Not a Number), infinite (positive or negative), or a valid finite number, and then prints the appropriate message for each case.

Best Practices to Compare Float and Double in C++ 

1. Prefer double over float for enhanced precision unless memory or performance concerns are important.
2. For very small values, you should always use epsilon-based comparison (fabs(a-b) <= epsilon).
3. When dealing with large or varying magnitude values, use relative tolerance (epsilon * (max(|a|, |b|)).
4. For precision-safe comparisons, use std::numeric_limits<T>::epsilon().
5. Check for NaN and Infinity using std::isnan() and std::isinf() before comparison.
6. If possible, avoid equality checking using subtraction, as it can cause precision errors.
7. Be careful about compiler optimizations and floating point settings, as these can affect precision.

Conclusion

Comparing float and double in C++ requires careful handling due to precision loss. Direct equality checks (==) are unreliable, so you should use epsilon-based or relative tolerance comparisons. For better accuracy, prefer double over float and use std::numeric_limits<T>:: epsilon(), and handle special cases like NaN and Infinity. By following these best practices, you can easily ensure accurate, stable, and portable floating-point comparisons.

How to Compare Float and Double While Accounting for Precision Loss – FAQs