Why Does Comparing Double Values in C# Sometimes Return False?

Understanding Double Precision Comparisons in C#

Problem:

Direct comparison of double variables in C# can yield unexpected results. For example, if (x == 0.1) might evaluate to false even when x is assigned the value 0.1.

Root Cause:

The issue stems from how floating-point numbers (like float and double) are represented in computer memory. They use a binary fractional representation, unlike the decimal fractional representation we're accustomed to. This means that many decimal values, such as 0.1, cannot be precisely represented in binary. The resulting approximation introduces subtle rounding errors.

Resolution:

The most effective solution is to use the decimal data type when precision is paramount. decimal employs a decimal fractional representation, capable of accurately storing values like 0.1.

Further Details:

Binary fractions, similar to decimal fractions, use powers of 2 instead of powers of 10. Just as 1/3 (0.3333...) cannot be exactly represented in decimal, 1/10 (0.1) lacks an exact binary representation. This inherent limitation leads to the rounding errors that cause comparison discrepancies. The computer stores a close approximation of 0.1, but this approximation is not exactly equal to the literal 0.1 used in the comparison.

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