Why Is Double Multiplication in .NET Imprecise?

Understanding Inaccuracies in .NET Double Precision Multiplication

The term "double precision" in .NET might be misleading. Double-precision floating-point arithmetic isn't always perfectly accurate. Let's examine a common example:

<code>double i = 10 * 0.69;</code>

Instead of the expected 6.9, the result is often 6.8999999999999995. This imprecision arises from how floating-point numbers are represented and stored.

Doubles, like other floating-point types, approximate real numbers using a specific binary format. Many decimal values, such as 0.69 and 1/3, cannot be precisely represented in this binary format due to its inherent limitations.

The compiler typically optimizes multiplication at compile time, storing the result as a constant. However, since 6.9 lacks an exact binary representation, the stored constant is an approximation.

To mitigate this, consider using the decimal type, which offers higher precision at the cost of reduced performance. For applications requiring extremely high accuracy, libraries providing rational number support, such as BigRational, offer an alternative approach.

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