Go Float Equality: Bitwise vs. Epsilon-Based Comparison – Which is Better?

Go Float Comparison: Bit-Level vs. Epsilon-Based Equality

Question:

Within the realm of Go's floating-point arithmetic, what approach offers superior accuracy and efficiency for determining equality between two floats (float64) with an approximate tolerance?

Approach 1: Bit-Level Comparison

This approach leverages the mathematical representation of IEEE 754 floating-point numbers to check for equality at the bit level:

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
}

Approach 2: Absolute Difference with Epsilon

The traditional approach involves subtracting the two floats and comparing the absolute value with an arbitrary tolerance (epsilon, usually 1e-9):

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

Analysis:

Despite its appeal for hardware efficiency, the bit-level comparison approach can lead to incorrect results in certain scenarios.

For instance, comparing two denormalized floats (floats with subnormal exponents) may mistakenly indicate equality despite a non-zero difference due to the presence of implicit leading zeros. Additionally, this approach becomes less reliable as the magnitude of the floats increases.

In contrast, the epsilon-based approach handles denormalized floats correctly. By considering only the absolute difference, it eliminates the potential for bit-level false positives and provides consistent equality checks across a wide range of float values.

Conclusion:

While bit-level comparison may seem like an intuitive approach to float equality, the epsilon-based approach proves to be more generic, precise, and efficient for general-purpose applications. It ensures accurate equality testing without the pitfalls of bit-level representations.

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