How Can Floating-Point Values Be Compared Accurately While Accounting for Precision Loss?

Comparing Floating-Point Values with Precision Conservation

Floating-point comparison poses a challenge due to precision loss. Simply comparing doubles or floats using == is unreliable.

Epsilon-based Comparison

One approach involves using an epsilon (ε) threshold to account for precision loss:

bool CompareDoubles2(double A, double B) {
  double diff = A - B;
  return (diff < EPSILON) && (-diff < EPSILON);
}

However, this approach can be inefficient.

Context-Dependent Considerations

The choice of comparison method depends on the context and expected values. Consider the following potential pitfalls:

• Presuming a == b and b == c implies a == c.
• Using the same epsilon for different units of measurement.
• Using epsilon for both angles and line lengths.
• Sorting using such a comparison function.

Standard Epsilon

std::numeric_limits::epsilon() represents the difference between 1.0 and the next value representable by a double. It can be used in comparison functions, but only if expected values are less than 1.

Consequences of Integer Arithmetic

Using doubles to hold integer values can lead to correct arithmetic, as long as fractions or values outside the range of an integer are avoided. For example, 4.0/2.0 will equal 1.0 1.0.

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