Why Are Denormalized Floating-Point Numbers So Slow?

Impact of Denormalized Floating-Point on Performance

The performance disparity observed in the provided code arises from the presence of denormalized floating-point values. Denormalized values represent numbers extremely close to zero and are typically stored in a compressed format. While this compression improves memory efficiency, it drastically slows down operations involving denormalized numbers.

Code Analysis

In the first code snippet, the use of 0.1f introduces denormalized values into the calculations. This is because 0.1f is represented internally as a normalized value of 0x3f800000, but as the operations progress, it eventually becomes denormalized due to successive additions and subtractions.

Effect on Performance

Denormalized floating-point operations can be significantly slower than normalized operations. This is because many processors do not have dedicated circuitry to handle denormalized values and must resort to software emulation, which incurs substantial overhead.

Comparison of Code Versions

The second code snippet, which uses 0 instead of 0.1f, avoids the creation of denormalized values. As a result, the code executes much faster.

Conclusion

Performance-sensitive applications should generally avoid using denormalized floating-point values. The introduction of denormalization can significantly impact performance, especially in loops that perform multiple operations on floating-point variables.

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