Why Does Replacing 0.1f with 0 Result in a 10x Performance Increase in My Code?

Influence of Subnormal Floating-Point Numerals on Performance

In the provided code snippet, a minor alteration that seemed insignificant significantly impacted performance: changing 0.1f to 0 resulted in a 10x slowdown. This performance difference arises from the handling of subnormal (denormalized) floating-point numbers.

Subnormal numbers are an approximation of zero, being smaller than the smallest normal floating-point number that can be represented. They often result from operations that produce very small values. Operations on subnormal numbers are notoriously slow compared to operations on normalized floating-point numbers. This is because many processors lack the ability to handle subnormal numbers directly and instead must resort to slower microcode routines.

Numerical Examination

The two code snippets, one using 0.1f and the other using 0, produce different outputs after repeated iterations. When using 0.1f, the values converge to non-zero values close to zero. However, when using 0, the values converge to zero itself. This difference in numerical behavior explains the performance gap.

Denormal Flushing

To verify that subnormal numbers are responsible for the performance disparity, we can flush them to zero by adding the following line to the beginning of the code:

_MM_SET_FLUSH_ZERO_MODE(_MM_FLUSH_ZERO_ON);

This instructs the processor to treat all subnormal numbers as zero. With this modification, the performance difference between using 0.1f and 0 becomes negligible. This confirms that subnormal numbers are indeed the source of the slowdown.

Conclusion

In this scenario, avoiding the creation of subnormal numbers by replacing 0.1f with 0 dramatically improves performance by preventing the processor from engaging in slow subnormal number handling routines. This optimization serves as a reminder of the sometimes detrimental impact of denormalized floating-point numbers on performance and the importance of considering their potential presence in numerical computations.

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