Why Does Adding 0.04 Repeatedly in Java Lead to Unexpected Results?

Floating-Point Discrepancies in Java: Precision Limitations

In a Java program, it's possible to encounter peculiar behaviors when summing floating-point values. As observed in the query, a simple loop adding 0.04 to an array of 25 double values produces results with unexpected behavior.

Floating-point values, such as IEEE singles and doubles, are commonly used in programming languages. However, these formats do not represent most decimal fractions exactly. This is due to their binary floating-point representation, which is fundamentally different from decimal floating-point.

Specifically, the only fractional values that can be represented exactly in binary floating-point are sums of negative powers of two, such as 0.5 (2^-1), 0.125 (2^-3), or 0.625 (2^-1 2^-3). When decimal fractions cannot be represented exactly as such sums, the result is a slight approximation.

In the example provided, the value 0.96 cannot be expressed precisely as a sum of negative powers of two. Therefore, when it is added to 0.04 and printed with full decimal precision, the result slightly deviates from its original value.

This precision limitation is inherent in binary floating-point representation and should be taken into account when working with floating-point computations. In cases where exact precision is crucial, using alternative representations or algorithms may be necessary.

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