Скачать или смотреть How to Vectorize Math Functions in C+ + Without Falling into Intel's Math Library Pitfalls

Discover effective techniques for vectorizing C+ + code with math functions, avoiding the limitations imposed by traditional libraries like Intel's.
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This video is based on the question https://stackoverflow.com/q/63933350/ asked by the user 'Arnab Majumdar' ( https://stackoverflow.com/u/10457569/ ) and on the answer https://stackoverflow.com/a/63933683/ provided by the user 'Roy2511' ( https://stackoverflow.com/u/3089908/ ) at 'Stack Overflow' website. Thanks to these great users and Stackexchange community for their contributions.

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Understanding the Problem: Vectorization and Math Functions in C+ +

Vectorization is a powerful optimization technique that allows programs to process multiple data elements simultaneously, significantly boosting performance, especially in numerical computing. However, when certain mathematical functions, such as sine (sin) and cosine (cos), are involved, vectorization can often become challenging.

In this guide, we’ll explore why your C+ + code that uses math functions might prevent vectorization and how you can effectively modify it to leverage the benefits of this optimization technique without relying on external libraries like Intel’s short vector math library.

The Initial Code Structure

Let’s examine the code snippet that leads to the vectorization issue:

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In this loop:

Ar and Ai accumulate values based on the cosine and sine of a computed variable p.

The issue arises because Ar and Ai depend on the results from prior iterations of the loop, making it impossible for the processor to execute independent iterations simultaneously.

The Solution: Using Arrays to Enable Vectorization

To enable vectorization, we need to change the way Ar and Ai are accumulated. Instead of directly summing values into these variables within the loop, we can store results in arrays and perform the accumulation after the loop has finished executing. This disassociates the result of one iteration from another, making them independent.

Step-by-Step Modifications

Initialize Temporary Arrays:
Start by declaring two arrays to hold the intermediate results.

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Modify the Loop to Populate Arrays:
Update the loop to store the results of calculations in the arrays instead of accumulating them directly into Ar and Ai.

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Sum the Arrays After the Loop:
Use a function like std::accumulate to sum all elements in each array to get the final values for Ar and Ai.

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Summary of Changes

Here’s a complete, updated version of the code:

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Conclusion

With these modifications, the code can now be vectorized effectively. By using temporary arrays to store intermediate results, we ensure that each iteration of the loop operates independently, thus enabling the compiler and processor to apply vectorization techniques. This approach allows for optimized performance without the overhead of external libraries, making your C+ + programming more efficient and streamlined.

Implementing vectorization effectively can lead to significant performance gains, especially in computation-heavy applications. Hopefully, this breakdown assists you in transforming your code into a more efficient and modern form!