Why is Adding 0.1f Significantly Slower Than Adding 0 in Floating-Point Computations?

Performance Impact of Handling Denormalized Numbers

In the provided code, the significant performance difference between adding 0.1f and 0 in the inner loop stems from the handling of denormalized floating-point numbers.

Denormalized Numbers

Denormalized numbers represent values extremely close to zero and are used to extend the precision of the floating-point representation. However, their handling can be considerably slower than normalized floating-point operations.

Performance Impact

The inner loop involves several operations on floating-point numbers, and adding 0.1f introduces the introduction of denormalized numbers into the calculation. Since the vast majority of the numbers in the loop are relatively large, the addition of a small value like 0.1f results in the result being rounded down to the nearest denormalized value, which can significantly impact performance.

Floating-to-Integer Conversion

While the question refers to the addition of an integer (0), the actual code uses a floating-point constant (0.0f). In the loop, both values are converted to floating-point numbers and subsequently handled as such. Hence, this aspect doesn't directly contribute to the performance difference.

Avoiding Denormalization

To mitigate the performance hit caused by denormalized numbers, one can utilize the _MM_SET_FLUSH_ZERO_MODE(_MM_FLUSH_ZERO_ON) function to instruct the processor to treat denormalized numbers as zero. By doing so, the code executes significantly faster and becomes comparable to the version that adds 0.

Conclusion

The performance difference between adding 0.1f and 0 in this specific code scenario is primarily attributable to the utilization of denormalized numbers, which can dramatically slow down floating-point operations on certain processors. Avoiding denormalization through appropriate techniques can alleviate this performance impact.

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