How Can I Accurately Compare Floating-Point Numbers for Equality in Go?

Go: A Smarter Way to Compare Floats

As you delve into the complexities of IEEE 754 and binary float representations, you may encounter a lingering question: how to accurately compare two floats for equality in Go. One potential approach is to examine the bit-level differences, using a solution like this:

func Equal(a, b float64) bool {
    ba := math.Float64bits(a)
    bb := math.Float64bits(b)
    diff := ba - bb
    if diff < 0 {
        diff = -diff
    }
    return diff < 2
}

This method aims to allow for a single bit difference, considering this as "almost equal." However, this approach has limitations.

A More Effective Approach

Instead of relying on bit manipulation, a more reliable solution is to directly subtract the two numbers and check the absolute difference against a predefined threshold. This approach is more intuitive and accurate:

const float64EqualityThreshold = 1e-9

func almostEqual(a, b float64) bool {
    return math.Abs(a - b) <= float64EqualityThreshold
}

Why It's Superior

This method avoids the pitfalls of bit representation, which can lead to imprecise comparisons in certain situations. By directly comparing the numerical difference, you gain increased precision and accuracy. Additionally, it eliminates the need to manually inspect bit differences, making the code more concise and maintainable.

In summary, for comparing floats in Go, the recommended approach is to subtract the two numbers and compare the absolute difference against a predefined threshold. This method provides a more accurate and efficient way to determine "almost equalness" compared to bit manipulations.

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